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UBC Theses and Dissertations

Development and use of a discrete element model for simulating the bulk strand flow in a rotary drum… Dick, Graeme 2008

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 DEVELOPMENT AND USE OF A DISCRETE ELEMENT MODEL FOR SIMULATING THE BULK STRAND FLOW IN A ROTARY DRUM BLENDER   by   Graeme Dick  B.Sc., University of British Columbia, 2006   A THESIS SUBMITTTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE  in   The Faculty of Graduate Studies  (Forestry)  UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  August 2008  © Graeme Dick, 2008 -ii- ABSTRACT  In 2006 resin accounted for approximately 17% of the direct manufacturing costs for oriented strand board (OSB).  Because of their increased dependency on pMDI-resins, this percentage is likely greater for oriented strand lumber (OSL) and laminated strand lumber (LSL).   The cost of PF- and pMDI-resins is expected to face upward pressure as the cost of their primary constituents, natural gas and crude oil, continue to reach new highs.  Therefore, there is strong economic incentive to optimize the use of resin in the production of these three products.  This can be accomplished by addressing two key issues: reducing resin wastage and optimizing resin distribution on the strands.  Both issues will be overcome by focusing on the blending process, where resin is applied to the strands.  This work focused on development and use of a discrete element model (DEM) for simulating strand flow in a rotary drum blender using the EDEM software package.  EDEM required the input of three material and three interaction properties. Development of the model involved creating the simulated environment (i.e. physical dimensions) and assigning appropriate material and interaction properties given this environment and the assumptions that were made.  This was accomplished in two steps, completing baseline bench-top experiments and a literature review to determine appropriate parameters and initial value ranges for these properties, and then fine-tuning these values based on a validation process.  Using the validated model, an exploratory study was conducted to determine the effect of four blender design and operating parameters (flight height, number of flights, blender rotational speed, and blender fill level) on bulk strand flow.  The results were analyzed with regards to overall trends and by focusing on two perspectives, end users and blender manufacturers.  It was found that there was a strong relationship between these key parameters and bulk strand flow. These results suggest that operating parameters of a blender, namely rotational speed and tilt angle, should be linked directly to the blender feed rate to ensure an optimal blending environment is maintained.  In addition, manufacturers of blenders must take into consideration the range in final operating conditions when designing and positioning flights.   -iii- TABLE OF CONTENTS Abstract ....................................................................................................................................ii Table of Contents....................................................................................................................iii List of Tables ........................................................................................................................... v List of Figures ........................................................................................................................vii List of Abbreviations ............................................................................................................... x Acknowledgements.................................................................................................................xi  Chapter 1:  Introduction ....................................................................................................... 1 1.1 Rationale........................................................................................................................ 3 1.2 Objectives and structure of thesis.................................................................................. 7  Chapter 2:  Literature Review.............................................................................................. 9 2.1 Rotary drum blending.................................................................................................... 9 2.2 Discrete element method ............................................................................................. 11 2.2.1 Applications for discrete element methods....................................................... 13 2.3 Friction ........................................................................................................................ 15  Chapter 3:  Laboratory Determined Coefficient of Static Friction ................................ 18 3.1 Introduction ................................................................................................................. 18 3.2 Materials ...................................................................................................................... 19 3.3 Procedure..................................................................................................................... 20 3.4 Results ......................................................................................................................... 24 3.5 Conclusions ................................................................................................................. 27  Chapter 4:  Determination of Suitable Material and Interaction Properties for use        as Input Parameters in the RDBM ................................................................ 29 4.1 Introduction ................................................................................................................. 29 4.2 Procedure..................................................................................................................... 31 4.2.1 Screening design ............................................................................................... 31 4.2.2 Strand representation in EDEM........................................................................ 34 4.2.3 Characterization of resination potential ............................................................ 34 4.3 Validation process – selection of appropriate input parameters.................................. 39 4.4 Results ......................................................................................................................... 49 4.4.1 Screening design – material properties ............................................................. 49 4.4.2 Screening design – interaction properties ......................................................... 50 4.4.3 Coefficient of rolling friction............................................................................ 51 4.4.4 Validation - coefficient of static friction........................................................... 52 4.5 Conclusions ................................................................................................................. 60  Chapter 5: Measuring the Effect of Rotary Drum Blender Design and Operating       Parameters on the Bulk Strand Flow using a Response Surface Design .... 62 5.1 Introduction ................................................................................................................. 62 5.2 Methodology ............................................................................................................... 62 5.3 Results and discussion................................................................................................. 66 5.3.1 Overall predictive trends................................................................................... 66 5.3.1.1 Skewness ............................................................................................. 67 5.3.1.2 Effect of an atomizer boom on the skewness results........................... 73 -iv- 5.3.1.3 Kurtosis ............................................................................................... 77 5.3.1.4 Effect of an atomizer boom on the kurtosis results ............................. 80 5.3.1.5 Average time a strand spent in the resination region .......................... 83 5.3.1.6 Effect of an atomizer boom on the average time a strand spent in the resination region ........................................................................ 85 5.3.1.7 Discussion ........................................................................................... 85 5.3.2 Research applications........................................................................................ 86 5.3.2.1 Wood strand-based product manufacturers ......................................... 87 5.3.2.2 Effect of the atomizer boom for wood strand-based product manufacturers ...................................................................................... 89 5.3.2.3 Blender manufacturers ........................................................................ 91 5.3.2.4 Effect of the atomizer boom for blender manufacturers ..................... 94 5.3.2.5 Discussion ........................................................................................... 97 5.4 Conclusions ................................................................................................................. 98  Chapter 6:  Summary and Future Work......................................................................... 100 6.1 Future Work .............................................................................................................. 101  Literature Cited ................................................................................................................. 103  APPENDIX A:   Coefficient of Friction SAS Analysis and Results.................................... 108 APPENDIX B:   Mechanical Properties of UHMW and HDPE.......................................... 113 APPENDIX C:   Blender Drawing Provided by Coil Manufacturing.................................. 114 APPENDIX D:   Write-out Every Time Interval Calculation .............................................. 116 APPENDIX E:   VBA Macro for Sorting, Filtering and Analysing EDEM Data ............... 121 APPENDIX F:   Macro for Performing Analysis in Image Pro Plus................................... 130 APPENDIX G:   ANOVA Results for the Mechanical Properties of Aspen Strands .......... 132 APPENDIX H:   ANOVA Results for the Interaction Properties of Aspen Strands               and Polyethylene....................................................................................... 134 APPENDIX I:    Results from the Student t-test for Shoulder and Toe Angles .................. 136 APPENDIX J:    Results from the Exploratory Study Without and With an  Atomizer Boom......................................................................................... 137   -v- LIST OF TABLES Table 1.  OSB costs for benchmark north-central US mills from 2000 to 2006....................... 5 Table 2.  Pricing data for the constituents of PF- and pMDI-resin from 1999 to 2005............ 6 Table 3.  Strand combinations used for static friction coefficient tests. ................................. 21 Table 4.  Summary of test results for the coefficient of static friction between two wood  strands at 22°C and 55% relative humidity ............................................................. 25 Table 5.  Summary of test results for the coefficient of static friction between a wood  strand and HDPE at 22°C and 55% relative humidity............................................. 26 Table 6.  Regression parameters for determining the coefficient of static friction between  two wood strands at 22°C and 55% relative humidity............................................. 27 Table 7.  Regression parameters for determining the coefficient of static friction between  a wood strand and HDPE at 22°C and 55% relative humidity. ............................... 27 Table 8.  Required material and interaction properties for the RDBM. ................................. 29 Table 9.  Materials used and materials that may come in contact in the RDBM.................... 29 Table 10.  (Left) Aspen wood strand material properties and (right) interaction properties  simulation design.................................................................................................... 31 Table 11.  Factor levels for Quaking Aspen material properties............................................. 32 Table 12.  Factor levels for interaction properties................................................................... 32 Table 13.  Fixed factor levels for the blender operation and design. ...................................... 33 Table 14.  Fixed factor levels for the liner and flights ............................................................ 33 Table 15.  Blender rotational speed and fill level combinations for laboratory video  recordings. .............................................................................................................. 41 Table 16.  Simulation settings. ................................................................................................ 33 Table 17.  Frame export settings used in Adobe Premiere Pro CS3. ...................................... 46 Table 18.  Factors and response variables for simulations investigating the impact of the  material properties. ................................................................................................. 50 Table 19.  Factors and response variables for simulations investigating the impact of the  interaction properties. ............................................................................................. 50 Table 20.  Rolling and static friction coefficients for the simulations aimed at determining  a suitable coefficient of rolling friction. ................................................................. 51 Table 21.  Pairs of static friction coefficients used to identify a suitable set of values........... 53 Table 22.  Student t-test for two sample means assuming unequal variance for the shoulder  and toe angles in Run 4 and the laboratory results................................................. 54 Table 23.  Student t-test for two sample means assuming unequal variance for the shoulder  and toe angles in Run 5 and the laboratory results................................................. 54 Table 24.  Student t-test for two sample means assuming unequal variance for the shoulder  and toe angles in Run 6 and the laboratory results................................................. 55 Table 25.  Summary of runs 4 to 6 and the laboratory taken shoulder and toe angle results.  Italicized values indicate those angles that are significantly different (α = 0.05)  from the image results. ........................................................................................... 55 Table 26.  Summary of shoulder and toe angles obtained at 15.5 to 25.5 RPM with the  coefficients of static friction set at 0.14 and 0.07................................................... 56 Table 27.  Summary of material and interaction properties for use with EDEM.................... 61 Table 28.  Response surface design matrix. ............................................................................ 64 Table 29.  Response surface design factor levels .................................................................... 64 Table 30.  Factor levels used in the skewness and average time spent in resination region  analyses. ................................................................................................................. 67 -vi- Table 31.  List of effects for the skewness showing (left) the significant effects and (right)  the significant effects as well as those that were included to maintain the model  hierarchy. ................................................................................................................ 68 Table 32.  List of effects for the skewness when an atomizer boom is present, showing (left)  the significant effects and (right) the significant effects as well as those that were  included to maintain the model hierarchy. ............................................................. 74 Table 33.  List of effects for the kurtosis showing (left) the significant effects and (right)  the significant effects as well as those that were included to maintain the model  hierarchy. ................................................................................................................ 78 Table 34.  List of effects for the kurtosis when an atomizer boom is present, showing (left)  the significant effects and (right) the significant effects as well as those that  were included to maintain the model hierarchy. .................................................... 81 Table B1:   Mechanical properties of UHMW ...................................................................... 113 Table B2:   Mechanical properties of HDPE ......................................................................... 113 Table G1:  ANOVA results for the impact the material properties have on the skewness  of the resulting histogram. .................................................................................. 132 Table G2:  ANOVA results for the impact the material properties have on the kurtosis of  the resulting histogram........................................................................................ 132 Table G3:  ANOVA results for the impact the material properties have on the count of  the resulting histogram........................................................................................ 132 Table G4:  ANOVA results for the impact the material properties have on the processing  time of the respective simulation. ....................................................................... 133 Table H1:  ANOVA results for the impact the interaction properties have on the skewness  of the resulting histogram. .................................................................................. 134 Table H2:  ANOVA results for the impact the interaction properties have on the kurtosis  of the resulting histogram. .................................................................................. 134 Table H3:  ANOVA results for the impact the interaction properties have on the count  of the resulting histogram. .................................................................................. 134 Table H4:  ANOVA results for the impact the interaction properties have on the  processing time of the respective simulation. ..................................................... 135 Table I1:   Student t-test for two sample means assuming unequal variance for the  shoulder and toe angles in Run 4 and the laboratory results ran at 15.5 RPM. .. 136 Table I2:   Student t-test for two sample means assuming unequal variance for the  shoulder and toe angles in Run 4 and the laboratory results ran at 25.5 RPM. .. 136 Table J1:   Results from exploratory study without an atomizer boom................................ 137 Table J2:   Results from exploratory study with an atomizer boom ..................................... 138 -vii- LIST OF FIGURES Figure 1.  Canadian structural panels production from 1982 to 2005 ...................................... 1 Figure 2.   Size of the total North American framing lumber market and the potential  market size for engineered wood products............................................................... 4 Figure 3.   Flow chart showing the basic constituents that are used in the production of PF-  and pMDI-resin.  The shaded constituents are included in Table 2 ......................... 6 Figure 4.   Turner’s spinning disc blender showing a vertical spray pattern ........................... 10 Figure 5.   Lignex spinning disc blender showing a diagonal spray pattern............................ 11 Figure 6.   Flow chart for operations performed in a typical DEM algorithm......................... 12 Figure 7.   Diagram showing the pair of forces that determines the friction torque................ 16 Figure 8.   Photograph of sliced aspen veneer strands, (a) primary surface and  (b) secondary surface.............................................................................................. 20 Figure 9.   Inclined plane jig with the various components indicated ..................................... 21 Figure 10.  Two sleds used for the inclined plane test, (left) sled equipped with dowels for ....  larger contact pressures and (right) sled equipped with adhesive surface for  lower contact pressures. ........................................................................................ 22 Figure 11.  Photograph of the testing procedure for the coefficient of static friction of wood  strands using the inclined plane technique, showing a parallel – parallel  orientation. ............................................................................................................ 23 Figure 12.  Schematic of inclined plane jig showing the measurement locations for  Equation 5 ............................................................................................................. 24 Figure 13.  Static coefficient of friction between two wood strands for increasing contact  pressures and different strand sample orientations. .............................................. 25 Figure 14.  Static coefficient of friction between a wood strand and HDPE for increasing  contact pressures and different strand and HDPE sample orientations. ............... 26 Figure 15.  Schematic showing the representation of sticks using a series of six spheres  (left) and a schematic showing the placement of a template over top of the  six spheres to aid in the visual analysis process (right). ....................................... 34 Figure 16.  Blender schematic showing the resination region outlined in blue. ..................... 35 Figure 17.  Simulation and photographed examples of increasing skewness caused by  increasing rotational speeds from 15.5 RPM to 25.5 RPM .................................. 37 Figure 18.  Sample histogram with a respective skewness, kurtosis, and count of -0.3024,  -0.2794, and 22 453. ............................................................................................. 38 Figure 19.  Schematic showing the placement of the lights and camera/video camera  relative to the laboratory blender, with the axis indicated in blue. ....................... 40 Figure 20.  Photograph showing the placement of the lights and camera/video camera  relative to the laboratory blender. ......................................................................... 40 Figure 21.  Example of (left) a screen shot taken of an animated GIF illustrating the  simulation results and (right) a screen shot taken of the video footage taken  in the laboratory. ................................................................................................... 41 Figure 22.  Schematic showing the shoulder, σ, and toe, τ, angles for two points of  detachment. The 0o and 90o reference angles are shown in blue. ......................... 42 Figure 23.  Illustration showing the identification of the shoulder and toe angle from the  laboratory video footage. ...................................................................................... 44 Figure 24.  Illustration showing the identification of the shoulder (σ) and toe (τ) angle  from the simulation results using the streaming effect. ........................................ 45 Figure 25.  Schematic of the x, y, z coordinate system relative to the blender....................... 46 -viii- Figure 26.  Screen shot taken in Image Pro Plus v6 showing the placement of the thick,  line profile and the cooresponding grayscale values ............................................ 48 Figure 27.  Example of simulation results overlaid on top of grayscale results...................... 49 Figure 28.  Skewness as a function of the coefficient of rolling friction ................................ 52 Figure 29.  Baseline grayscale results for the laboratory blender running empty................... 57 Figure 30. Grayscale results for the blender running at 15.5 RPM and 1/8th full. ................. 58 Figure 31.  Grayscale results for the blender running at 20.5 RPM and 1/8th full. ................. 59 Figure 32.  Grayscale results for the blender running at 25.5 RPM and 1/8th full. ................. 59 Figure 33.  Schematic of a blender fitted with an atomizer boom, shaded grey ..................... 66 Figure 34.  Prediction profiles generated in SAS showing the relationship between the  skewness and the (top-left) number of flights, (top-right) flight height,  (bottom-left) fill level, and (bottom-right) blender rotational speed..................... 68 Figure 35.  Schematic showing the angle of repose, α, for a pile of wood strands on a  horizontal surface.................................................................................................. 69 Figure 36.  Simulation images showing the charge level per flight and the discharge pattern  when a relatively small number of flights are employed. The simulated blender  has 4-6 inch flights and is rotating at 23.39 RPM and is 1/8th full ....................... 70 Figure 37.  Simulation images showing the charge level per flight and the discharge pattern  when a relatively large number of flights are employed. The simulated blender  has 16-6 inch flights and is rotating at 23.39 RPM and is 1/8th full ..................... 71 Figure 38.  Simulation image showing strands rolling in the corner of the drum, where there  are 8-4 inch flights and the blender is rotating at 18.71 RPM and is 1/4 full. ...... 71 Figure 39.  (Left) Simulation image showing the dispersion of strands across relatively few  flights when the blender is rotating at 18.71 RPM and (right) across many flights  when the blender is rotating at 28.07 RPM.  In both cases the blender has 16-4  inch flights and is 1/8th full. .................................................................................. 72 Figure 40.  Prediction profiles generated in SAS showing the relationship between the  skewness and the (top-left) number of flights, (top-right) flight height,  (bottom-left) fill level, and (bottom-right) blender rotational speed when an  atomizer boom is included in the simulation ........................................................ 75 Figure 41.  Simulation images showing the dispersion of strands across the blender diameter  when there is (top-left) no atomizer boom and there are 2 inch flights,  (top-right) no atomizer boom and there are 6 inch flights, (bottom-left) an  atomizer and there are 2 inch flights, and (bottom-right) an atomizer boom  and there are 6 inch flights.  In all cases there were 16 flights and the blender  rotated at 23.39 RPM. ........................................................................................... 76 Figure 42.  Simulation image showing strands as they become wedged between the  atomizer boom and blender wall when operating at elevated fill levels,  indicated by the dashed oval.  In this case the blender is ¼ full and is equipped  with 8, 4 inch flights and is rotating at 28.07 RPM. ............................................. 77 Figure 43.  Prediction profiles generated in SAS showing the impact of the (left) number  of flights on the relationship between (right) the kurtosis and the flight height... 79 Figure 44.  Prediction profiles generated in SAS showing the impact of the (right) flight  height on the relationship between (left) the kurtosis and the number of flights.. 79 Figure 45.  Prediction profiles generated in SAS showing the impact of the (left) number  of flights on the relationship between (right) the kurtosis and the flight height  when an atomizer boom is present........................................................................ 82 -ix- Figure 46.  Prediction profiles generated in SAS showing the impact of the (right) flight  height on the relationship between (left) the kurtosis and the number of flights  when an atomizer boom is present........................................................................ 82 Figure 47.  Prediction profiles generated in SAS showing the relationship between the  average time spent in the resination region and the (left) flight height and  (right) blender rotational speed............................................................................. 83 Figure 48.  Simulation images showing (top-left) the clustering of strands at relatively  low speeds with 2-inch flights, (top-right) the dispersion of strands at relatively  high speeds with 2-inch flights, (bottom-left) the clustering of strands at  relatively low speeds with 6-inch flights, (bottom-right) the dispersion of  strands at relatively high speeds with 6-inch flights.  .......................................... 84 Figure 49.  Contour graphs for the skewness based on the fill level and blender rotational  speed using 3, 4, 5, and 6-inch flights.  The number of flights has been fixed  at 14....................................................................................................................... 88 Figure 50.  Contour graphs for the skewness based on the fill level and blender rotational  speed using 3, 4, 5, and 6-inch flights when an atomizer boom is present.  The  number of flights has been fixed at 14.................................................................. 90 Figure 51.  Contour graphs based on number of flights and flight height.  The rotational  speed ranged from 23 to 28 RPM and the fill level was fixed at 25%. ................ 93 Figure 52.  Contour graphs for the inclusion of an atomizer boom based on number of  flights and flight height.  The rotational speed ranged from 23 to 28 RPM and  the fill level was fixed at 25%............................................................................... 95 Figure 53.  Simulation images showing the streaming of strands off of the atomizer boom  at (a) 18.71 RPM, (b) 23.39 RPM, and (c) 28.07 RPM.  The simulated blenders  were each equipped with 8-4 inch flights and filled 1/4 full.  The angles that the  strands stream off of the boom are approximately 14°, 12°, and 7° from vertical  respectively. .......................................................................................................... 96 Figure C1:  Schematic of blender layout and atomizer spray patter. ................................... 114 Figure D1:  Schematic of an example where the write-out time interval is set too large..... 117 Figure D2:  Schematic of the extreme case scenario where an object falls from the top of  the blender, A, through the resination region, B to C, and collides with the  bottom of the blender, D.................................................................................... 118 Figure D3:  Location of the write-out every time intervals within the resinating region,  relative to the top of the blender, when the first interval is located marginally  less than one full Δtw from the top of the region. .............................................. 119 Figure D4:  Location of the write-out every time intervals within the resinating region,  relative to the top of the blender, when the last interval is located marginally  less than one full Δtw from the bottom of the region......................................... 119 Figure D5:  Location of the write-out every time intervals within the resinating region,  relative to the top of the blender, when the first interval is located marginally  below the top of the region................................................................................ 120 Figure D6:  Location of the write-out every time intervals within the resinating region,  relative to the top of the blender, when the last interval is located marginally  above the bottom of the region.......................................................................... 120 -x- LIST OF ABBREVIATIONS  ANOVA  – Analysis of variance BBF  – Billion board feet BSF  – Billion square feet 3/8 inch basis COV  – Coefficient of variation DEM  – Discrete element modeling EWP  – Engineered wood products GIF  – Graphics interchange format HDPE  – High density polyethylene IPP  – Image pro plus LSL  – Laminated strand lumber OSB  – Oriented strand board OSL  – Oriented strand lumber PE  – Polyethylene PF – Phenol formaldehyde pMDI  – Polymeric diphenyl methane diisocyanate RPM  – Revolutions per minute RSM  – Response surface methodology RDBM  – Rotary drum blending model SF – Square feet UHMW – Ultra high molecular weight polyethylene VBA – Visual basic for applications -xi- ACKNOWLEDGEMENTS  I would like to extend my sincere gratitude to those who have helped ensure that this project was a success.  To my committee members: Drs. Gregory Smith, Paul McFarlane, and Erik Eberhardt, your guidance throughout this process has certainly been appreciated.  To my colleagues: Jo Chau, Emmanuel Sackey, Solace Sam-Brew, Dr. Kate Semple, and Chao Zhang, your assistance and support have made this experience enjoyable.  To my family and friends, your ongoing support and devotion have helped me reach this point.  And to my wife, Sara, you have kept me grounded throughout this experience by simply listening to my challenges and always being there.  A special thank you goes to Weyerhaeuser Canada for their financial support and guidance throughout this project, and to the Natural Sciences and Engineering Research Council of Canada for their financial support. -1- CHAPTER 1  INTRODUCTION  Beginning in the mid-1970s, structural products composed of reconstituted wood strands have increasingly become a major component of Canada’s forest products industry.  This transition began with the advent of waferboard and quickly progressed to oriented strand board (OSB), a direct substitute for plywood in the construction market (Figure 1).  In 2006, oriented strand board accounted for approximately 63% of all structural panel production in Canada (Louisiana-Pacific Corporation 2008; Spelter et al. 2006).  Laminated strand lumber (LSL) and oriented strand lumber (OSL) were subsequently developed to compete with solid sawn lumber in the same market.  In today’s North American residential construction market, these wood strand-based products can be found everywhere from the sheathing on exterior walls, to the headers used to span garage door openings, and to the specialty studs used behind kitchen cabinets.  Plywood OSB 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 19 82 19 83 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 Year M illi on  s f -  3 /8 " B as is  Figure 1.  Canadian structural panels production (million SF - 3/8" basis) from 1982 to 2005 (data from: International Wood Markets Group 2006).  -2- The North American production capacity for OSB is expected to continue increasing into the future.  In fact, if all of the OSB projects tabled in 2005 were to go ahead as planned, capacity would balloon from 23.7 million m3 (27.5 BSF) in 2005 to 31.9 million m3 (37 BSF) by 2010 (International Wood Markets Group 2006).  However, because of recent slowdowns in the US housing market, largely driven by the sub-prime mortgage crisis, and an accompanying over-supply of OSB, these previous projections have been stifled.  According to a report by Dixon (2008), North American OSB capacity had already reached 26.2 million m3 by the end of 2007; however, any additional capacity that was planned to come on stream by 2010 had been postponed indefinitely.  The increased production of OSB is also being experienced beyond North American borders. While most of the additional capacity that was expected to come on stream in the near future is located in North America, Europe’s OSB industry has also been expanding, albeit at a considerably lower volume (International Wood Markets Group 2006).  This is largely because of the relatively slow adoption of OSB into European building codes (World Forest Institute 2007).  This progress has been further hindered by the effect of North American OSB producers dumping excess supply in Europe, discouraging the development of new domestic facilities (Higgs 2008).  The total European capacity reached 3.9 million m3 by the end of 2007.  By 2009 an additional 1.4 million m3 is expected to come on stream.  As mentioned, there are three products that fall beneath the umbrella of wood strand-based products: OSB, LSL, and most recently OSL.  During the manufacture of these products a mat consisting of a large number of strands is consolidated under heat and pressure to form a single entity, or billet.  In order for the consolidation to be effective, resin must be employed to hold the final product together.  The application of resin onto the strands is perhaps the least studied and understood aspect of the manufacturing process; however, it has one of the most significant effects on the strength and durability of the final product and in 2006 accounted for nearly 17% of the direct manufacturing costs (Spelter et al. 2006).  The application of resin onto the strands begins when the strands are fed from dry strand bins and deposited in the blender.  Blenders are between 8 and 11 feet in diameter and extend 20 to 35 feet in length.  As the drum rotates at typically between 8 and 22 RPM the strands tumble along its length and become resinated (Smith 2005). -3-  The strands are resinated using either a series of spinning disc atomizers mounted along the drum’s axis of rotation for liquid resin, or using a conveyor metering system for powdered resin.  Spinning disc atomizers are the predominant system employed in blenders commissioned since the early-1990s. The objective of blending is to achieve a uniform resin distribution on both sides of all strands.  The ability of the process to effectively resinate the strands is dependent on the overall blender design, such as the drum diameter, atomizer locations, and flight design; as well as on the operational environment, such as the rotational speed, fill level, and tilt angle of the blender (Coil 2007b; Coil 2008; Maloney and Huffaker 1984; Smith 2005; Smith 2006).  1.1 Rationale The respective market share of structural products composed of reconstituted wood strands is forecast to continue increasing.  This is particularly true for OSB where its share of the structural panel demand in North America has increased from approximately 35% in 1995 to 63% in 2008.  OSB market share is forecast to further increase to approximately 72% by 2012 (Louisiana-Pacific Corporation 2008).  In addition to OSB’s market share growth however, there is great potential for LSL and OSL to increase their share of the framing lumber market.  LSL and OSL are both members of the family of products referred to as engineered wood products (EWP).  Currently, EWP only capture approximately 30% of the potential 12 BBF North American framing lumber market, with the sub-sector of wood strand-based products only accounting for 5% (Figure 2) (Louisiana-Pacific Corporation 2008).   -4-   Figure 2.  Size of the total North American framing lumber market and the potential market size for engineered wood products (adapted from: Louisiana-Pacific Corporation 2008).  Although the five year period between 2001 and 2006 saw the growth of the wood strand- based product sector outpace the growth of the overall construction market (by 11% compared to 2% (Louisiana-Pacific Corporation 2008), continued growth will be largely dependant on the relative manufacturing costs.  As an example, in 2004 the average total manufacturing cost for structural lumber, OSL, and LSL was similar.  Lumber was 188 US$/m3, while OSL and LSL were approximately 180 US$/m3 (International Wood Markets Group 2006; Spelter et al. 2006).  These figures assume that OSL and LSL have a similar cost structure as OSB.  In reality the cost of OSL and LSL will be marginally greater than OSB because of the type of resin employed, product density, and wood utilization. Subsequently, the costs are likely nearer, or even past those of structural lumber.  In recent years the total manufacturing cost of wood strand-based products has faced increased pressure.  In 2006 the average cost reached 201 US$/m3 of OSB (Table 1) (Spelter et al. 2006).  Much of this increase was caused by escalating wood costs, affecting solid lumber and EWP alike.  In addition to wood costs however, wood strand-based products have experienced escalating resin costs, increasing by 61% between 2000 and 2006 (Table 1) (Spelter et al. 2006).  Increasing resin costs have created a need to optimize and subsequently reduce the amount of resin employed in the manufacture of these products in order to remain LVL & I-Joists 25% Applications suitable for EWP substitution  50% Lumber  70% OSL & LSL 5% Total North America Framing Lumber (~24 BBF) Current & Potential EWP Market (~12 BBF) Potential Market Growth for EWP -5- cost competitive in the structural panel and framing markets.  Optimization is only possible however if there exists a thorough understanding of the process in which resin is applied to the strands in a rotary drum blender.  Table 1.  OSB costs for benchmark north-central US mills from 2000 to 2006 (data from: Spelter et al. 2006).  Cost (US$/m3)  2000 2001 2002 2003 2004 2005 2006  Direct costs Wood 56 54 53 60 67 85 82 Labor 20 20 20 21 21 22 22 Resin 18 19 19 26 27 32 29 Wax 6 6 6 7 7 8 7 Energy 11 13 12 15 17 19 19 Supplies 14 14 14 15 15 15 15 Total direct 125 125 124 144 154 181 175  Fixed costs General 6 6 6 6 6 6 6 Depreciation 23 21 20 21 20 20 20 Total fixed 29 27 26 27 26 26 26 Total costs 154 153 150 171 180 207 201  There are only a few studies on the operation of a rotary drum blender in the literature with these dating from the mid-1980s (Beattie 1984; Coil and Kasper 1984; Lin 1984). More recently, Smith (2005) examined the modes of tumbling in a full-sized rotary drum blender. All of these studies were focused on OSB. To date there have not been any published studies on the blending of OSL and LSL.  The blending of these products differs from OSB in several important aspects. First, OSL and LSL strands exceed 6 inches in length, while OSB strands rarely exceed 5 inches. Second, LSL operations only employ polymeric diphenyl methane diisocyanate (pMDI) resin, compared with OSB operations that typically use a combination of phenol formaldehyde (PF) and pMDI resins.  During blending approximately 3.5% resin based on the oven dry weight of furnish is added. The precise amount depends on the operation, resin type, and product grade (Spelter et al. 2006). As indicated, resin costs are a major materials cost in the production of wood strand- based products. Because PF- and pMDI-resins are derived from crude-oil and natural gas (Table 2 and Figure 3), it is very likely that resin costs will remain high or even increase over the next five years.  Significant resin savings may be possible through blending optimization. -6- Due to the large volume of resin used in the manufacture of strand technology products, even small decreases in resin consumption will lead to significant savings.  Table 2.  Pricing data for the constituents of PF- and pMDI-resin from 1999 to 2005 (data from: Winchester 2005).  Methanol US$/USG Urea US$/ton Phenol US$/lb Crude Oil US$/Barrel Natural Gas US$/MMBTU 1999 0.26 – 0.40 100 – 140 0.25 – 0.36 17 3.75 2001 0.35 – 0.80 140 – 290 0.30 – 0.40 24 5.24 2003 0.75 – 1.00 160 – 230 0.40 – 0.45 26 5.81 2005 0.90 – 0.95 270 - 300 0.50 – 0.70 60+ 9.80   Figure 3.  Flow chart showing the basic constituents that are used in the production of PF- and pMDI-resin.  The shaded constituents are included in Table 2 (adapted from: Winchester 2005).  The design and operation of rotary drum blenders has remained virtually unchanged since the mid-1980s when the long-retention time, Mainland Manufacturing blenders emerged as the blender of choice amongst the wood strand-based product industry.  Although Mainland Manufacturing has subsequently been bought out by Coil Manufacturing, very little has been changed with regards to the operation and design of the blenders.  In general, as the capacity demands have increased over the years with new, sophisticated operations, the blender dimensions have been scaled up.  In the 1950s and 60s, rotary drum blenders were 4 to 5 feet in diameter and 20 feet long (Coil 2002; Watkins 1981).  More recently, blenders can be up to 11 feet in diameter and 45 feet long (Coil 2007b; Coil and Kasper 1984; Smith 2005). While this process of scaling the blenders has been widely accepted throughout the industry, as previously mentioned resin costs have placed increased pressure on the end users of rotary Phenol PF Formaldehyde Methanol Natural Gas pMDI Phenol Formaldehyde Methanol Crude Oil Benzene -7- drum blenders to optimize the process.  The primary challenge hindering progress is the lack of research into the inner dynamics of the blending process and the inability to quantify and model the bulk strand flow.  In the past, blender design and operating parameters have been selected based on visual inspection and past experience.  Although these empirical approaches have resulted in a blender design that fits with the spectrum of end-users’ needs and a reasonable understanding of the impact design and operating parameters have on the strand flow, a quantitative, systematic approach is necessary to further enhance the process.  1.2 Objectives and structure of thesis This study seeks to understand the blending process by developing and evaluating a quantitative discrete element model (DEM) of the blending process.  Chapter 2:   Literature review on discrete element modeling and friction.  A review of static, kinetic, and rolling friction will facilitate the selection of initial coefficients as input parameters in the DEM.  Additionally, this review will help to understand how these coefficients should change to achieve better correlation between the simulated and laboratory results. Chapter 3: Determination of static friction coefficients between Aspen wood strands and between an Aspen wood strand and high density polyethylene.  The flights and the inside liner of the blender are constructed of either high density polyethylene or ultra high molecular weight polyethylene.  For the purpose of this project, and because the specifications of these two materials do not differ considerably, it will be assumed that the liner and flights are both constructed of high density polyethylene.  The friction values will be used as a starting point within the EDEM software package and may be adjusted accordingly during a subsequent study. Chapter 4: Calibration of the rotary drum blending model (RDBM) with experiments conducted in the 6 foot laboratory blender.  This process will be completed by adjusting various material and interaction properties in the model. Chapter 5: Completion of an exploratory study aimed at determining the impact several blender design and operating parameters have on the bulk strand flow within a -8- simulated 6 foot blender.  This study will provide a profound understanding of the impact changes made to the blending environment will have on the strand flow through a blender. Chapter 6: Evaluation of potential future work.   As the software and computing technology advances many of the limitations that were present during this project will become less significant.  The most logical progression will be the scaling of the simulated blender up to a full size industrial blender.  This will enable research to be completed that focuses on the impact blender tilt angle has on the residence time of strands.  -9- CHAPTER 2  LITERATURE REVIEW  2.1 Rotary drum blending Rotary drum blending has been the method used for coating wood strands with resin and wax for the manufacture of oriented strand board since this product’s industrial emergence in the late-1970s (Moeltner 1980).  In fact, this blending technique was also employed for OSB’s predecessor, waferboard, since its emergence in 1955 (Gunn 1972).  Although the resin was applied exclusively in a powdered form until the mid- to late-1970s, the fundamental process was similar to today’s blenders that tend to employ liquid resins.  During the blending process strands enter from one end of the blender and are then lifted by a series of flights, which extend from the inside of the drum’s circumference.  The strands eventually fall from the flights and migrate along the length of the blender.  This process repeats until the strands are discharged from the opposite end of the blender. The rate of migration along the blender length is a function of the blender tilt angle.  As reported by Smith (Smith 2005), the strands move forward the most while they are in freefall.  As the strands move along blender length they are coated with wax and resin.  The manner in which powdered and liquid resin adhere to and coat the strands is considerably different.  While powdered resin adheres to the strands via the wax droplets that are applied at the onset of the blending process, liquid resin adheres directly to the strands in droplet form (Coil 2002).  The transition towards liquid resin was largely driven by the relative cost advantage of liquid resin, the health concerns caused by the dust from powdered resin, and the relatively high wax content required to improve the affinity of the powdered resin to the wood surface (Chiu and Scott 1981; Maloney and Huffaker 1984).  Early rotary drum blenders were 4 to 5 feet in diameter and 20 to 25 feet long (Coil 2002; Watkins 1981).  By the early 1980s it was widely accepted that blender diameters of 8 feet and greater were required to ensure adequate resin coverage on the strands and/or wafers and to meet capacity requirements (Beattie 1981).   At around this same time liquid resin -10- increased in popularity and a system was developed and adopted across the industry for metering liquid resin into the blenders and distributing it onto the strands.  This system involved using a series of spinning disc atomizers (Beattie 1984; Coil and Kasper 1984; Lin 1984). After several variations in the positioning of these atomizers within the blenders (Figures 4 and 5), a design was eventually accepted whereby the atomizers were mounted along a stationary shaft running down the length of the blender.  The atomizers were positioned to disperse resin in a horizontal plane.  Except for the plane of the spray pattern and the stationary shaft or boom, this design was similar to Turner’s design (Figure 4).   Figure 4.  Turner’s spinning disc blender showing a vertical spray pattern (adapted from: Beattie 1984).  Resin spray region Spinning disc Rotating shaft -11-  Figure 5.  Lignex spinning disc blender showing a diagonal spray pattern (adapted from: Beattie 1984).  Modern blenders are provided nearly exclusively by Coil Manufacturing Limited of Surrey, British Columbia.  Their blenders range in size from 8 feet in diameter and 20 feet long up to 11 feet in diameter and 45 feet long; however, the 11 foot diameter blenders are most common in newer operations requiring relatively high capacity (Coil 2007b; Smith 2005). These blenders operate with strand volumes ranging from 25% to 50% of the blender volume and with a tilt angle of approximately 3°.  Blenders revolve at between 8 and 22 RPM depending on the blender diameter, number of flights, flight height, and resin type (Coil 2008).   As a general rule, liquid resins require higher speeds than powdered resins and as the diameter increases the speed decreases (Coil 2008).  2.2 Discrete element method Discrete element methods (DEM), or distinct element methods as they are also known (Cundall 1989), are a family of numerical techniques suitable for modeling the movement and interaction of rigid or deformable bodies, particles, or arbitrary shapes that have been subjected to external stresses or forces (Bicanic 2004).   As reported by Mustoe and Miyata (2001), most of these methods are based on cylindrical- or spherical-shaped particles because of the inherent ease in detecting contacts between particles.  In recent years there has been an increased number of DEMs based on noncircular-shaped bodies, such as polygonal bodies, for specific applications.  The vast majority of the commercially available software packages Resin spray region Spinning disc Resin feed -12- however, still rely on cylindrical- or spherical-shaped particles for 2D and 3D modeling respectively.  These particles may be clustered and/or overlapped rigidly or elastically to form different shaped bodies (Collop et al. 2004; Mustoe 2001).  DEMs are based on Newton’s Second Law of Motion (Bertrand et al. 2005; Serway 2000):  itotalii Fam ,=           [1]        or, itotal i i Fdt xdm ,2 2 =            [2]    where:     mi is the mass of particle i,     ai is the acceleration of particle i,     xi is the position of particle i, and     Fi is the total force acting on particle i.  This equation is used to calculate the total force that acts on a particle due to a collision and is subsequently integrated to find the respective particle’s new velocity and distance of travel (Bertrand et al. 2005).  During a simulation, the location of all particles is tracked at a specified time interval.  When a collision between particles is detected Newton’s Second Law of Motion is applied to determine each particle’s resulting position and velocity. Figure 6 shows the steps of a typical DEM algorithm.  Figure 6.  Flow chart for operations performed in a typical DEM algorithm (Schafer et al. 2001). Calculate force increment caused by each contact between particles Calculate velocity and position increments caused by forces Find which particles have come into contact t = t + ∆t -13-  Although the basis of the DEM approach is relatively straight forward, the computational requirements quickly become overwhelming when more than a few particles are present. Because DEMs are routinely used for simulating a large number of particles, the effectiveness of the method is largely dependent on the ability of the model algorithms to detect particle contacts quickly and efficiently (Bicanic 2004).  There are several DEMs that have been developed for describing how the particles behave when they come into contact with each other.  A typical DEM has the following features (Cundall 1989; Bertrand et al. 2005; Mustoe 2001): 1. They allow finite displacements and rotations of discrete bodies, including complete detachment, and 2. They recognize new contacts automatically as the calculation progresses.  Two of the more commonly applied models include the linear spring-dashpot model and the Hertz Mindlin model.  As Bertrand (2005) described, the principal difference between these two models is that the linear spring-dashpot model considers any particle contact to lead to inelastic deformation, while models based on Hertz theory considers this contact to lead to elastic deformation.  There is no consensus on what model is best; however, DEM solutions (2008) report that the linear spring model is simpler because it requires less computational overhead.  For EDEM, the selected software package for this research project, the Hertz Mindlin model is the default model because of its accurate and efficient force calculation (DEM Solutions 2008).  This model was also used for the duration of this project. Ultimately, the choice of model will depend on the environment being simulated and the ability to validate the results.   For additional information concerning the choice of models, Bertrand (2005) provides a reasonable explanation of several of the more commonly employed models.  Additionally, Cundall and Strack (1979) and DEM Solutions (2008) provide information on the model algorithms.  2.2.1 Applications for discrete element methods The DEM was first pioneered by Cundall (1971) for problems involving rock mechanics. Since the early-1970s this method has branched out and adapted for use in a wide range of engineering applications.  Mining has perhaps benefited most from DEMs where they have -14- been shown to be particularly effective at analyzing granular material flow, power draw, and liner wear in semi-autogenous grinding mills (Cleary 1998; Cleary 2006; Djordjevic et al. 2004; McIvor 1983; Mishra and Rajamani 1992; Powell 1991).   In addition to mining, other industries that have benefited include:  pharmaceutical, chemical, agricultural, advanced materials, and food (Bertrand et al. 2005).  An area that has gained recent attention is the modeling of granular material mixing.  This topic covers a variety of industries, but its significance is seen most prominently in the pharmaceutical manufacturing arena.  As Bertrand (2005) reported, even slight changes to ingredient properties or process operating conditions can have significant implications on the quality of a drug and/or resulting health effects.  Consequently, pharmaceutical companies are reluctant to make process changes based on DEM results alone and still rely heavily on process monitoring to ensure quality (Bertrand et al. 2005).  Despite the widespread use of DEMs in various engineering applications, it has never been used specifically for modeling the rotary drum blending of wood strand-based particles; however, its successful use in semi-autogenous grinding (SAG) and other rotating drum type processes suggests that it is possible (Kaneko et al. 2000; Moakher et al. 2000; Stewart et al. 2001).  In this process wood strands are deposited inside a rotating drum at the front end. The strands are then lifted by a series of flights and cascade and tumble along the drum length.  The dynamics of the process are similar to those encountered in a SAG mill; however, the process objectives more closely resemble those of pill coating in the pharmaceutical industry (Thibault 2008).  In a rotary drum blender as the strands migrate along the drum length resin is applied in either liquid or powdered form.  The objective is to maximize the resin deposition on the strands and the distribution of resin amongst the strands, while minimizing strand breakage. In a SAG mill the aim is to breakdown and grind the rocks.   As mentioned, the objectives of resination are therefore more closely related to those of pill coating.  In pill coating the pills tumble in a drum while a coating is sprayed onto them.  Although the primary objective is to coat the pills, the pills must also remain intact in order to avoid contamination (Thibault 2008).  Because DEMs, and in particular the EDEM software package, have been used for -15- modeling both processes it is believed that this is a suitable method for modeling the rotary drum blending process as well.  For this project a DEM will be used for simulating the trajectory and distribution of strands as the blender revolves.  The primary challenges associated with its use are the relatively high slenderness ratio and thinness of the wood strands and the large quantity of strands in the process.  Simplifications and assumptions will be required to assemble a model that can simulate the process with reasonable accuracy and within a reasonable time span.  2.3 Friction Friction forces are a critical phenomenon when performing discrete element modeling.  For objects that slide relative to each other the key friction properties are static and kinetic friction (Serway 2000).  The only difference between the equations used for determining these two forms of friction is the relevant coefficient of friction, µ.  This equation is known as Amontons Law (Equation 3).  iNf FF μ=            [3]  where:      µi is either static kinetic friction, and     FN is the normal force.  If the shape of an object permits rolling to occur, such as a sphere, then the resistance to rolling manifests as a torque that opposes the direction of rolling, Tf (Equation 4).  Rolling friction is caused by the deformation of either the rolling sphere/cylinder or the plane (Figure 7).  RNf FT μ=                      [4] where:     FN is the normal force, and     µR is the rolling coefficient.     -16-     Figure 7.  Diagram showing the pair of forces that determines the friction torque, where FN is the reaction force acting on the object by the plane and Fg is the normal component of the object’s weight.  The coefficient of rolling friction is the arm of the pair of forces (Domenech et al. 1987).  According to Amontons Law, knowledge of the coefficient of friction is vital when examining the interaction between objects.  Because this coefficient depends on the interaction between surfaces of different objects, it is most accurately considered to be a system property rather than a material property.  This is particularly relevant for this research as true coefficients of frictions were not known.  Instead coefficients were chosen based on the resemblance of the model system to the actual observed systems.  For modeling the rotary drum blending process for wood strands there are broadly three systems of objects that must be considered:  strands and flights, strands and drum liner, and the interaction between strands themselves.  In light of the limited published information pertaining to the static coefficient of friction values for the aforementioned systems, a series of tests aimed at determining the respective values for the particular materials used in the laboratory was conducted.  Because it was anticipated that during the modeling stage the drum liner and flights would be grouped as one material type, the strand and drum liner interaction was dropped and instead replaced with the strand and flight interaction properties.  Classic theoretical research related to static and kinetic friction has shown that frictional coefficients are independent of surface area and contact pressure.  However, more recently Bejo et al (2000) found that “these generalizations are not necessarily true if at least one of the [objects] in the system is wood or a wood-based composite.”  As a result, the initial study Lower rolling friction Higher rolling friction Fg Fg FN FN -17- of this project focused predominately on determining the relationship between the range of contact pressures that may be encountered during blending and the friction coefficient.  -18- CHAPTER 3  LABORATORY DETERMINED COEFFICIENT OF STATIC FRICTION  3.1 Introduction Friction coefficients are perhaps the most important material interaction property to consider when developing a rotary drum blending model based on the discrete element method because of the significant impact they have on particle dynamics (DEM Solutions 2008).  As described in section 2.3, assigning the respective friction coefficients is complicated by the fact that the friction coefficients within systems involving at least one wood substrate are dependent on the contact pressure.  The selected software package for this research, EDEM, assumes constant coefficients regardless of the contact pressure, as is widely accepted for most systems of materials.  In addition, most of the published friction coefficient values for systems involving wood are based on clear wood blocks, rather than strands.  Wood strands tend to be less smooth and relatively flexible, generally resulting in higher coefficients.  As a result, a series of experiments were conducted in the laboratory to determine the impact of contact pressure and wood grain orientation on the coefficient of friction for wood on wood and wood on polyethylene (PE) systems of materials.  Collectively, these experiments will investigate all of the material interactions that will occur during the simulations: strand – strand, strand – flight, and strand – blender liner.  It was hypothesized that the coefficient of friction would increase with decreasing contact pressure and that the coefficient of friction would increase from parallel – parallel to parallel – perpendicular and to perpendicular – perpendicular grain orientation.    These results will be used as a starting point for the initial development of the RDBM.  Subsequently, blending experiments and simulations will be compared to adjust these values until there is close correspondence in the strand dynamics.  Objectives: 1. To determine the relationship between contact pressure and coefficient of friction for wood – wood and wood – PE systems of materials, -19- 2. To determine the relationship between grain orientation and coefficient of friction for wood – wood and wood – PE systems of materials, and 3. To determine the ratio between the coefficients of friction for wood – wood and wood – PE systems of materials.  3.2 Materials A total of 40 sliced veneer, aspen wood strands were randomly selected from a 10.1 kg bag of strands.  The strands had been previously cut to approximately 12 inches long by 1½ inches wide and 0.030 inches thick.  Aspen strands were used in this case because it represents the predominant species used in the manufacturing of wood strand-based products in Canada (Industry Canada 2007).  There were two requirements for the selected strands. First, the strands had to have an area that was at least 9 inches by 1¼  inches void of any splits, and second the strands could not exhibit excessive warp.  Either of these flaws could impact the experiment.  The selected strands were divided into two sets of twenty, one to be used as the ‘primary surface’ and one to be used as the ‘secondary surface’.  The primary surface strands were trimmed to 9 inches by 1¼ inches using a guillotine paper cutter, removing any splits or defects.  The edges of the strands were then lightly sanded using 220 grit sandpaper to remove any burrs that might otherwise affect the test results. The secondary surface strands were prepared in a similar manner; however, they were trimmed to 8 inches by 1 inch so that they would easily lay flat atop the primary strands without their edges contacting.  If the edges were to come in contact the concern was that any remaining burrs may mechanically interlock, resulting in a confounded reading of the static friction coefficient.  These relatively large strands were used for this experiment because it provided adequate room for weights to be added to the surfaces, as described in Section 3.3.  Ultimately the surface area does not impact the friction coefficient so this was assumed to be a reasonable simplification for the test procedure (Serway 2000).  The strands in each set were labeled 1 through 20 with the appropriate suffix added: ‘a’ for the primary surface strands and ‘b’ for the secondary surface strands (Figure 8).  Each set of strands was then lightly clamped with a protective wood block on either face.  Clamping helped to prevent the strands from warping before testing. -20-     Figure 8.  Photograph of sliced aspen veneer strands, (a) primary surface and (b) secondary surface.  In addition to the wood samples, two HDPE specimens were also prepared.  The samples were removed from an extra 5 inches T-flight for the 6 foot by 3-foot Coil laboratory blender.  The flight was trimmed into two specimens measuring 9½ inches by 4⅛ inches and 8½ inches by 1¼ inches.  The edges of the samples were also sanded using 220 grit sandpaper to remove any burrs and then washed in warm water and left to air dry.  3.3 Procedure The experimental procedure is based on the inclined plane technique (American Standards for Testing and Materials 2002a; American Standards for Testing and Materials 2002b; Bejo et al. 2000).  This method was selected because of its relative simplicity and the shape of the test specimens.  A photograph of the testing apparatus is shown in Figure 9.  a b 1-inch -21-   Figure 9.  Inclined plane jig with the various components indicated ((1) scissor lift, (2) measuring guides, (3) platform with stop block, (4) raised primary surface platform, (5) bullseye level, (6) base, and (7) leveling glides).  The coefficient of static friction for the system involving two wood strands was determined using five combinations of primary and secondary surface strands.  These combinations were generated using a random number generator in Microsoft Excel (Table 3).  Table 3.  Strand combinations used for static friction coefficient tests. Pair Primary surface strand Secondary surface strand 1 9 18 2 5 17 3 14 18 4 19 9 5 8 11  Because of the orthotropic nature of wood, each combination was tested for all three combinations of grain orientation.  In addition, seven contact pressures were used to study the impact contact pressure has on the coefficient of static friction.  The included orientations and target contact pressures are listed below: 1. Strand orientations (secondary on primary): parallel - parallel, perpendicular – perpendicular, and perpendicular - parallel. 2. Target contact pressures: 23 Pa, 47 Pa, 94 Pa, 188 Pa, 375 Pa, 750 Pa, and 1500 Pa.  2 1 3 6 7 7 4 2 5 -22- For each orientation the primary surface strand was attached to the raised primary platform using double-sided tape.  The platform was then placed on the inclined plane in contact with the stop block.  The secondary surface strand was attached to one of two sled designs (Figure 10) also using double-sided tape.  For the first two strand orientations the sled equipped with dowel extensions was used for contact pressures greater than, and including, 188 Pa.  Weights were hung from the extensions to adjust the contact pressure (Figure 11).  For contact pressures less than 188 Pa, the sled equipped with an adhesive surface was used.  This was necessary as the first sled produced a contact pressure that was greater than 94 Pa without the addition of any weights.  Small weights were attached to the adhesive surface of the second sled to adjust the contact pressure.  For the third strand orientation the second sled was used exclusively.  Because the contact surface area was significantly less for the third orientation, the weights had to be reduced accordingly to achieve the appropriate contact pressure.  For each pair of strands the same surfaces were in contact for the three orientations tested.   Figure 10.  Two sleds used for the inclined plane test, (left) sled equipped with dowels for larger contact pressures and (right) sled equipped with adhesive surface for lower contact pressures.  1-inch -23- Figure 11.  Photograph of the testing procedure for the coefficient of static friction of wood strands using the inclined plane technique, showing a parallel – parallel orientation.  For the coefficient of static friction tests involving wood strands and HDPE the same test format was followed, including three orientations and seven contact pressures.  Instead of using a variety of HDPE samples however, only two were used.  The larger HDPE sample was used for the first two orientations and the smaller sample was used for the third orientation.  In all three cases the HDPE was the primary surface and the wood strand was the secondary surface.  The HDPE sample was placed directly on the inclining plane in contact with the stop block for the first two orientations.  For the third orientation the HDPE was attached to the raised platform, which was then placed on the inclined plane.  The raised platform added stability to the HDPE sample, preventing it from shifting during the tests.  The same secondary surface strands from the first set of tests were used for this second set of tests.  The secondary surface was prepared identically as before using the two sleds.  After the strands were mounted to the respective surfaces the testing apparatus was leveled using the adjustable glides.  The appropriate weight was then added to the sled. The angle of inclination was slowly increased until the secondary surface began to slip along the primary surface.  The heights from the base of the apparatus to two predetermined points along the inclined plane as well as the distance between those two points along the inclined plane, the -24- hypotenuse, were recorded when the sled began to slip.  These measurement points remained constant across all of the tests.  The coefficient of static friction was then determined according to Equation 5.  This procedure was repeated for each contact pressure, strand orientation, and system of materials.   The complete set of results were then analyzed using SAS version 9.1 to develop a model that predicted the coefficient of static friction based on the material combination, orientation, and contact pressure.  ⎟⎠ ⎞⎜⎝ ⎛ −= l hh 12arcsintanμ          [5]   Figure 12.  Schematic of inclined plane jig showing measurement locations for Equation 5.   3.4 Results The test results aimed at determining the coefficients of static friction for strand to strand and strand to flight interactions clearly showed a decreasing coefficient of static friction value for increasing contact pressures (Table 4, Figure 13, Table 5, and Figure 14).  This is particularly apparent when increasing from 23 Pa to 94 Pa.  The coefficient of static friction appears to be constant for pressures greater than and including 94 Pa.  These results are consistent with α hypotenuse, l height 2, h2 height 1, h1 -25- those obtained by Bejo et al. (2000).  Bejo found that as the contact pressure decreased below approximately 5 kPa the coefficient of static friction increased substantially. Above 5 kPa the static friction coefficient began to stabilize. It was also found that the grain orientation had a considerable impact  Table 4.  Summary of test results for the coefficient of static friction between two wood strands at 22°C and 55% relative humidity1.  Approximate contact pressure (Pa) Primary strand orientation Secondary strand orientation  23 47 94 188 375 750 1500 Parallel Parallel Mean 0.63 0.55 0.53 0.49 0.41 0.44 0.41   COV % 24 21 19 17 26 20 25 Perpendicular Perpendicular Mean 0.88 0.81 0.77 0.66 0.64 0.63 0.70   COV % 13 12 19 12 12 18 6 Parallel Perpendicular Mean 0.89 0.60 0.50 0.51 0.41 0.36 0.35   COV % 28 11 20 15 10 12 11 1Average ambient strand moisture content was 9.2%.  0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 Contact Pressure (Pa) S ta tic  C O F PERP/PERP PAR/PERP PAR/PAR  Figure 13.  Static coefficient of friction between two wood strands for increasing contact pressures and different strand sample orientations. Perpendicular - Perpendicular Parallel - arallel Parallel - Perpendicular -26-  Table 5.  Summary of test results for the coefficient of static friction between a wood strand and HDPE at 22°C and 55% relative humidity2.  Approximate contact pressure (Pa) Primary strand orientation Secondary strand orientation  23 47 94 188 375 750 1500 Parallel Parallel Mean 0.31 0.30 0.26 0.22 0.24 0.25 0.24   COV % 16 23 12 12 8 6 16 Perpendicular Perpendicular Mean 0.38 0.31 0.29 0.29 0.29 0.28 0.28   COV % 18 10 9 6 1 8 5 Parallel Perpendicular Mean 0.39 0.40 0.32 0.29 0.26 0.26 0.27   COV % 20 20 12 20 27 12 17 2Average ambient strand moisture content was 9.2%.  0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 Contact Pressure (Pa) S ta tic  C O F PERP/PER P PAR/PERP PAR/PAR  Figure 14.  Static coefficient of friction between a wood strand and HDPE for increasing contact pressures and different strand and HDPE sample orientations.  The test results were analyzed using multiple regression analysis in SAS version 9.1.  A logarithm transformation was necessary to normalize the data so that a model could be fit that accurately predicted the static friction coefficient (Equation 6), while meeting the assumptions of multiple linear regression analysis at a α = 0.05 (Kleinbaum 1988).   Perpendicular - Perpendicular Parallel - Parallel Parallel - Perpendicular -27- )()( 2101010 xbxLogbbs ++=μ           [6] where: µs is the predicted static friction coefficient, x is the contact pressure in pascals, and bi is the predicted parameters for i = 0 to 2.  The appropriate coefficients for the respective systems of materials and orientation are shown in Tables 6 and 7.  In general, these results show an approximate 2:1 ratio between the static coefficient of friction for wood to wood and wood to HDPE.  The complete SAS analysis is included in Appendix A.  It is important to note that this relationship has only been verified for the range of data presented above and at the ambient temperature and relative humidity encountered during the test, i.e. approximately 21oC and 50% respectively.  Table 6.  Regression parameters for determining the coefficient of static friction between two wood strands at 22°C and 55% relative humidity. Primary strand orientation Secondary strand orientation b0 b1 b2 Parallel Parallel 4.242 x 10-2 -1.748 x 10-1 8.835 x 10-5 Perpendicular Perpendicular 1.112 x 10-1 -1.290 x 10-1 8.835 x 10-5 Parallel Perpendicular 2.454 x 10-1 -2.634 x 10-1 8.835 x 10-5  Table 7.  Regression parameters for determining the coefficient of static friction between a wood strand and HDPE at 22°C and 55% relative humidity. HDPE orientation Strand orientation b0 b1 b2 Parallel Parallel -3.530 x 10-1 -1.222 x 10-1 8.835 x 10-5 Perpendicular Perpendicular -2.842 x 10-1 -1.216 x 10-1 8.835 x 10-5 Parallel Perpendicular -1.500 x 10-1 -1.179 x 10-1 8.835 x 10-5   3.5 Conclusions The coefficient of static friction tests confirmed previous work by Bejo et al. (2000) where it was found that, contrary to classical theoretical research pertaining to friction, the coefficient of static friction is in fact dependent on the contact pressure between surfaces when at least one surface is wood.  In general, the contact pressure and coefficient of friction were inversely related, as the contact pressure decreased the friction coefficient increased and vice-versa.  It was also found that the coefficient of friction was highest when the wood grains were aligned perpendicular - perpendicular and least when they were aligned parallel - parallel to the sloped plane.  Finally, the relationship between the coefficient of friction between two aspen strands versus that between an aspen strand and HDPE was found to be approximately 2:1. -28-  These findings suggest that knowledge of the contact pressures encountered during the blending operation is necessary to fully describe the slipping of strands in the RDBM. Because the currently available discrete element modeling software packages are unable to accommodate for a variable coefficient of static friction, a value must be selected that results in the most accurate resemblance between the RDBM simulations and the actual observed dynamics.  As an initial starting point for the model validation process, the average of the two extreme strand orientations will be used together with the average of the higher, more rapidly changing friction coefficients (contact pressure ≤188 pa) and the lower, more stable friction coefficients (contact pressure >188 pa).  -29- CHAPTER 4  DETERMINATION OF SUITABLE MATERIAL AND INTERACTION PROPERTIES FOR USE AS INPUT PARAMETERS IN THE RDBM  4.1 Introduction The RDBM required the input of three mechanical properties for each material used in a simulation and three interaction properties for each pair of materials that may come in contact during a simulation (Tables 8 and 9).  While all of these properties must be included for a simulation to be initiated, not all of them have a significant effect on the bulk strand dynamics.  Instead, some of these properties are only significant outside of the tested ranges and/or are used for measuring incidents of little consequence to this study, such as compressive forces acting on the particles.  Because this research is focused predominantly on measuring the bulk strand flow within a rotary drum blender, it is only necessary to select representative values for those factors that are vital to the accurate representation of said strand flow.  Table 8.  Required material and interaction properties for the RDBM. Material properties  Interaction properties    Modulus of rigidity (G)     Coefficient of restitution    Poisson’s ratio (ν)     Coefficient of rolling friction    Density (ρ)     Coefficient of static friction  Table 9.  Materials used and materials that may come in contact in the RDBM. Materials  Interactions    Aspen wood strands     Strand - Strand    Polyethylene1     Strand - Polyethylene 1 Polyethylene (PE) has been used here to describe both the high density polyethylene flights (HDPE) and the ultra high molecular weight polyethylene drum liner (UHMW).  This will be discussed further in section 4.2.1.  Focusing on the behavior of the overall system introduces several inherent challenges.  First, published values for these properties are typically based on measurements taken of individual pieces of clear wood samples.  These values may or may not be accurate for characterizing the behavior of large collections of strands. They do however provide a useful foundation for beginning such research.  Second, these properties must also incorporate other events that are occurring in an actual rotary drum blender but are not able to be incorporated into the model -30- because of constraints, such as the representation of strands using a series of spheres or the lack of any air flow dynamics in the model.  In addition to potentially affecting the strand dynamics, preliminary simulations and literature (DEM Solutions 2008) have also shown that the material properties have a significant impact on the processing time for a simulation.   The processing time increases with increasing shear modulus of rigidity and decreases with increasing density and Poisson’s ratio.  If it can be found that any of the above listed material properties do not significantly impact the bulk material dynamics then values may be chosen that minimize the time required for processing a simulation. The relationship between the density, ρ; modulus of rigidity, G; Poisson’s ratio, ν; particle radius, R; and processing time as represented by the idealized time step, TR is (DEM Solutions 2008):  ⎟⎠ ⎞⎜⎝ ⎛ += G RTR ρ ν π 8766.01631.0 .        [7]  In this case where strands are being modeled, the particle radius refers to the individual particles, or spheres, that are joined to form a strand.  As a result, the particle radius is ½ inch as will be discussed further in Section 4.2.2.  This study was therefore divided into two distinct phases.  The first phase consisted of two 2- level, full factorial experimental designs aimed at determining which material properties and interaction properties were in fact significant to the overall strand dynamics.  The second phase consisted of a systematic series of simulations aimed at determining suitable values for those properties that were deemed significant during phase 1.  Published values and experimental results from section 3.4 were employed as initial values from which these values were improved upon.  In order to assess the effectiveness of the tested values at accurately simulating the bulk strand flow, a series of experiments were simultaneously conducted and video recorded in a 6 foot laboratory blender for validation purposes.  It was hypothesized in this leg of the project that there is a particular set of input parameters that produces simulated bulk strand flow that is reasonably similar to reality.  Although there are several materials involved in this process (HDPE, UHMW, and Aspen wood strands), this study focused exclusively on the material properties of Aspen wood -31- strands for several reasons.  First, because of the large quantity of strands used in the simulation, it was assumed through consultation with the software providers that changes made to the material properties of the strands has a significantly larger impact than changes made to the material properties of either the blender liner or flights.  And second, the software package assumes the materials to be isotropic.  Wood strands are highly anisotropic and therefore there is not a single value for each of the mechanical properties available in the public literature (USDA, Forest Products Laboratory 1999).  Instead, these values were selected based on exploratory simulations using published ranges.  Objectives: 1. To determine which material and interaction properties are significant to the bulk strand flow, and 2. To assign suitable values to those properties deemed to be significant.  4.2 Procedure 4.2.1 Screening design The significance of the six factors listed in Table 8 was determined using a full factorial, 2k design for each the material and the interaction properties (Montgomery 2005; Pyzdek 2003). Two individual 2k designs were followed to minimize the required number of runs and to facilitate clarity in the results (Table 10).  This required that it be assumed there would not be any significant interactions between the two groups.  In total, 16 simulation runs were required.  Table 10. (Left) Aspen wood strand material properties and (right) interaction properties simulation design. Simulation Factors Run Modulus of rigidity Poisson’s ratio Density 1 -1 -1 -1 2 -1 -1 1 3 -1 1 -1 4 1 -1 -1 5 1 1 -1 6 1 -1 1 7 -1 1 1 8 1 1 1 Simulation Factors Run Coefficient of restitution Coefficient of rolling friction Coefficient of static friction 1 -1 -1 -1 2 -1 -1 1 3 -1 1 -1 4 1 -1 -1 5 1 1 -1 6 1 -1 1 7 -1 1 1 8 1 1 1 -32-   The aspen strand material property levels were selected based on published ranges (USDA, Forest Products Laboratory 1999), recommendations made by representatives from DEM Solutions, laboratory results, and preliminary modeling results (Tables 11 and 12).   For the blender liner and flights, which are constructed of UHMW and HDPE respectively, the material properties were provided by Coil Manufacturing and are listed in Appendix B.  To facilitate the model setup, the averages of these values were used for both components and this set of values will be referred to as simply polyethylene (PE) for the duration of this report (Table 13).  Because the material properties differ by less than 20% and they are not the focus of this study it was felt that this was a reasonable simplification to the model.  As a means of further streamlining this portion of the study, the linear interaction factors, which include wood to wood and wood to PE material contacts, were tested using the same value for both material contacts.  This was largely done to allow for a clearer understanding of the results.  Table 11.  Factor levels for Quaking Aspen material properties. Material properties (Quaking Aspen) Low level High level Modulus of rigidity (G) 1 x 108 Pa 1 x 109 Pa Poisson’s ratio (ν) 0.038 0.453 Density (ρ) 123.3 kg/m3 (7.7 pcf)  379.6 kg/m3 (23.7 pcf)  Table 12.  Factor levels for interaction properties. Interaction properties Low level High level Coefficient of restitution (wood-wood & wood-PE) 0.01 0.10 Coefficient of rolling friction (wood-wood & wood-PE) 0.01 1.00 Coefficient of static friction (wood-wood & wood-PE) 0.24 0.64  All operating and blender design factors, aside from the six specified, were fixed for the duration of this project.  This included the blender rotation speed, the number of and the shape of the flights, the blender diameter, and the flight and liner material properties.  These fixed values were selected based on industry standards and limitations of the laboratory blender (Table 14).  -33-  Table 13.  Fixed factor levels for the liner and flights. Material properties (liner and flights) Value Modulus of rigidity (G) 3.39 x 108 Pa Poisson’s ratio (ν) 0.42 Density (ρ) 935 kg/m3  Table 14.  Fixed factor levels for the blender operation and design. Fixed blending factors Value Blender diameter 6.04 ft (1.840 m) Blender length 1 ft (304.8 mm) Drum rotation speed 25.5 rpm Number of flights 8 Flight height 4 in. (101.6 mm) Flight shape L-shaped Fill level 1/8th  In addition, the strands were represented using ‘sticks’ of the following dimensions: length = 6 inches, width = 1 inch, and thickness = 1 inch (Figure 15).  Simplification of the strand dimensions was necessary because of computing and software limitations.  If the actual strand dimensions were used then the maximum sized sphere possible would be 0.030 inches, or equivalent to the strand thickness.    Consequently, more than 6500 spheres would be required to represent each 6 inch long by 1 inch wide strand.  Because the software is limited to approximately 100 000 to 200 000 spheres, using 0.030 inch spheres would significantly reduce that amount of strands that could be simulated. The key assumption is that the motion of actual wood strands in a blender does not differ significantly from the sticks.  The simulator settings have been included below in Table 15.  For each simulation the first 2 revolutions (approximately 6 seconds) were discarded.  Visual interpretation of the bulk strand flow revealed that the strands behaved erratically during this time, and this period was not representative of the actual blending dynamics.  Table 15.  Simulation settings. Fixed simulator settings Value Time step 40% of TR Write-out every frequency 0.01 sec Simulation time 24 sec (8 revs)  -34- Further, the sticks were generated inside the drum throughout the first revolution.  Gradually creating the sticks during a complete revolution facilitated the dispersion of sticks around the drum and resembled the feeding of strands into an industrial blender.  4.2.2 Strand representation in EDEM The wood strands were represented using a series of six, 1 inch diameter spheres.  The spheres were rigidly connected at their points of contact (Figure 15).  Within EDEM, the six spheres are treated as an individual body with measures, such as its location, being related to its center of mass.  In most cases a 6 inch by 1 inch by 1 inch stick template was placed over each of the sphere groupings.  This helped to distinguish between the sticks.  It is important to recognize that the template is not the interaction surface of the particles; it is merely applied during post-processing to aid in identifying the individual strands.  As a result, the sticks can overlap at their edges when the maximum diameter of a sphere protrudes into the valley between adjacent spheres.  The stick template is best thought of as a virtual surface.  Figure 15. Schematic showing the representation of sticks using a series of six spheres (left) and a schematic showing the placement of a template over top of the six spheres to aid in the visual analysis process (right).  4.2.3 Characterization of resination potential A subgroup of 150 strands of the 1 027 in the blender were tracked as they passed through the resination region (Figure 16).  The resination region is based on an atomizer spray pattern provided by Coil Manufacturing Ltd (Appendix C) and includes an 11-inch tall region located at the center of the drum.  The width of the resination region is 1840 mm and it covers the entire drum length.  While in this region within an industrial blender equipped with atomizers, strands have the best opportunity to make contact with resin directly leaving the atomizers.   Ideally, all of the strands in the system would have been tracked; however, -35- because of computing, software, and time constraints, tracking all 1 027 strands was not practical.   Figure 16.  Blender schematic showing the resination region outlined in blue.  Three parameters were recorded for each strand while in the resination region: simulation time, x-location (across the diameter of the blender), and vertical velocity.  The vertical velocity was used solely for determining which strands were being lifted by the flights and which strands were in free-fall.  These parameters were recorded at a set time-interval of every 0.01 seconds.  This interval ensured that at least 91% of the time a strand was within the region it was recorded.  The complete details of this analysis are given in Appendix D. These data were then used for computing a set of response variables.  Three response variables were selected for characterizing the strand flow through the resination region: skewness, kurtosis, and count.  All three of these measures were applied to the x-location data.  In this analysis the skewness (Equation 8 and Figure 17) and kurtosis (Equation 9) characterize the distribution of the strands across the diameter of the drum as they descend.  Skewness is an indicator of the central tendency of the strand distribution and kurtosis is an indicator of the uniformity of the strand distribution.  Ideally, the strands should be dispersed evenly, or uniformly across the diameter in order to maximize the opportunity for an even resin distribution (Figure 17).  A uniform distribution is described by a skewness of 0.0 and a kurtosis of -1.2 (Snedecor and Cochran 1980). Resination region z x y -36-  ( )( )∑ ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ − −−= 3 21 s xx nn nskewness i            [8]  ( ) ( )( )( ) ( ) ( )( )32 13 321 1 2 4 −− −− ⎪⎭ ⎪⎬ ⎫ ⎪⎩ ⎪⎨ ⎧ ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ − −−− += ∑ nn ns xxnnn nnkurtosis i       [9]    where:    n is the sample size,    xi is the value of the ith sample,    x  is the average x value, and    s is the sample standard deviation.    -37-    Skewness = -0.3983   Skewness = -0.3024   Skewness = -0.0451  Figure 17.  Simulation and photographed examples of increasing skewness caused by increasing rotational speeds from 15.5 RPM to 25.5 RPM.  Note that the skewness results are based on entire simulation, not the individual still image.  The illustrated blenders have 8-4" flights and are 1/8th full.  15.5 RPM 25.5 RPM 20.5 RPM -38- The count is an indicator of the average total time the strands, or sticks, spent in the resination region.  When any of the 150 strands were within the resination region a timestamp was recorded every 0.01 seconds for each strand.  These timestamps were then accumulated to determine the total time that the overall subset of strands was within the resination region.  The count is significant because it measures the opportunity the wood strands have to come into contact with the resin, and therefore should be maximized.  In addition to determining the total time spent in the resination region, a histogram of the count data was also generated to visually interpret the x-position results. The histogram consisted of 32 intervals, or bins, where each bin was 57.5 mm wide (Figure 18). Cumulatively, the bins form the width of the resination region, 1840 mm.  In order to post- process the data files produced by the RDBM, a macro was written in VBA to parse out the needed data and compute the required statistics. A listing of the VBA code for the macro, called “Histogram_And_Commulative_Graph,” is given in Appendix E.   Figure 18.  Sample histogram with a respective skewness, kurtosis, and count of -0.3024, - 0.2794, and 22 453.     0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 Bin C ou nt  1 27 29 3121 23 25 15 17 199 11 135 7 3 -39- 4.3 Validation process – selection of appropriate input parameters Validation of the discrete element model was completed using three techniques.  These techniques were performed in the order listed below.  The first technique acted as a screening test because of its relative speed and simplicity in performing.  The second and third techniques were only performed if the previous test was successful.  The first technique is a visual comparison between a one minute video recording of the lab blender and an animation created from the simulation results.  Validation by means of a visual comparison has been the most common approach taken for discrete element modeling because of its inherent simplicity (Rajamani et al. 2000; Yang et al. 2006).  While these previous papers used still images for comparison, a video recording was used in this study because it resulted in a better understanding of the bulk strand dynamics; in particular strand surging, a common phenomenon in rotary drum blending.  It is important to recognize that one of the shortcomings of this approach is that it is a purely qualitative measure and is therefore subjective.  In order to observe and record the strand dynamics in a rotary drum blender, a custom built, 6 foot diameter by 3 foot deep Coil laboratory-scale blender was used.  This blender is unique in that it is outfitted with a tempered glass front that enables the motion of the strands inside the blender to be easily observed, photographed, or videotaped.  The bulk dynamics of the strands was recorded using a Sony Handycam, model DCR- DVD108, mounted on a tripod in line with the axis of rotation of the drum and 156 inches back from the front of the glass blender face. The blender was illuminated with two pairs of tripod mounted, 500 watt halogen lights positioned to minimize dark regions inside the blender drum and to avoid reflections (Figures 19 and 20).  Black tarpaulins were draped behind and around the video camera to reduce any reflections on the tempered glass front.  Five minutes of strand tumbling was recorded for 16 different combinations of fill level and drum speed (Table 16).  This video footage was transferred from the video camera to the computer using Picture Motion Browser Disc Importer Version 1.1.01.01170.  Once downloaded, a 1 minute interval beginning at the 3 minute mark was extracted and saved to be used for the validation process. This time interval was selected because visually it appeared that steady state had been reached in the blender. -40-  Figure 19. Schematic showing the placement of the lights and camera/video camera relative to the laboratory blender, with the axis indicated in blue.    Figure 20. Photograph showing the placement of the lights and camera/video camera relative to the laboratory blender.    Still camera / video camera Halogen lights 6′ Laboratory Blender yx z Halogen lights 156" 51" 67" 67" 51 72" -41- Table 16.  Blender rotational speed and fill level combinations for laboratory video recordings. Fill level (%) Drum speed (RPM) 1/64th 15.5 20.5 25.5 30.5 1/32nd 15.5 20.5 25.5 30.5 1/16th 15.5 20.5 25.5 30.5 1/8th 15.5 20.5 25.5 30.5  The simulated strand flow footage from the RDBM was converted into GIF animations.  The GIF was created by first exporting still images every 0.1 seconds from EDEM under the Analyst tab.  A detailed description on how to perform this task is presented in the EDEM 1.3 User Guide (DEM Solutions 2008).  The still images were then strung together as frames using the Animation Wizard in Jasc Animation Shop 3 and saved as a GIF.  The RDBM GIF and the video footage of the blender drum were put side by side in a Microsoft PowerPoint slide and their strand flows compared by visual inspection (Figure 21).  At this stage of the validation, the objective was to determine whether or not the strand flows appear to be similar based on the strands’ approximate point of detachment from the drum and their ultimate point of collision.  In addition, the patterns of strand detachment should have been similar.  Subsequent validation stages compared the simulated and laboratory results more thoroughly using quantitative techniques.    Figure 21. Example of (left) a screen shot taken of an animated GIF illustrating the simulation results and (right) a screen shot taken of the video footage taken in the laboratory.   The second technique, and less often employed, compares the shoulder and toe angles from a series of still images taken of the laboratory blender with the graphical simulated results.  As Cleary (2003) stated, “the shoulder and toe locations are the primary quantitative information available from [an experiment] for comparison with the DEM results.” The principle -42- advantage of this approach over the visual comparison is the fact that this is a quantitative measure, and as a result, reduces the degree of subjectivity and bias.  The definition of the shoulder and toe angle and the measurement approach is described in detail by Cleary (2003), and therefore, is only briefly summarized here.  The shoulder angle is the maximum vertical height reached by the bulk of the strands after detaching from the drum liner.  Conversely, the toe angle is the impact point of the bulk of the strands that move through the shoulder and land on the drum (Figure 22).  The term ‘bulk’ is used here to differentiate between the mass flow of the majority of strands and the sporadic flow of individual, rogue strands.  Because this research is focused on the overall bulk strand dynamics, the movement of individual strands is of little interest.   Figure 22.  Schematic showing the shoulder, σ, and toe, τ, angles for two points of detachment. The 0o and 90o reference angles are shown in blue.  The strand volume and drum rotational speed have a significant effect on the ability to accurately determine the shoulder and toe angles through visual inspection.  For instance, with volumes less than 1/8th full and with speeds greater than 25.5 RPM it is very difficult to locate the shoulder and toe angles and to identify them both on the same image.  As a result, -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 x-position (m) y- po sit io n (m ) (a) drum liner direction of rotation 0o 90o σA σB τB τA Shoulder Toe -43- for this analysis only three speeds were chosen: 15.5 RPM, 20.5 RPM, and 25.5 RPM.  All of the experiments were conducted at a 1/8th fill level.  The still images were taken using a tripod mounted, Nikon Coolpix S3 digital camera.  The lighting and camera to blender configuration was the same as for the previous analysis (Figure 19).  With the blender running at steady state, forty to fifty pictures were taken in the standard camera mode over approximately two minutes.  As described by Cleary (2003), by leaving the shutter open for a prolonged period a streaking effect is obtained, making it easier to identify the relevant angles (Figure 23).  However, because this particular camera model does not allow for the shutter speed to be set directly, leaving the camera in the default standard mode, instead of using a high speed or sports mode, it was possible to achieve the desired outcome.  In this case the shutter speed, as recorded in the image file, varied between 1/10th and 1/11th of a second.  The shoulder and toe location were then determined for each image.  The first 30 images that clearly showed both the shoulder and toe location were selected for analysis.  As one can imagine from viewing the still image of the blender in Figure 23, determining the precise location of these locations is not without some error.  Because of this, 30 images were included in the analysis to reduce the significance of any erroneous measurements.  In measuring the shoulder and toe locations, the angles were measured to the nearest degree.  -44-   Figure 23. Illustration showing the identification of the shoulder and toe angle from the laboratory video footage.  A similar approach was taken with the graphical simulation to facilitate the location of the shoulder and toe angles.  Instead of representing the strands using the stick template, EDEM’s streaming effect was used (DEM Solutions 2008).  The streaming effect draws a straight line between the respective strand’s last positions.  For this analysis the software was set to connect the last two positions (Figure 24).  As with the visual validation, still images were exported every 0.1 seconds from EDEM. The first two blender revolutions were not included because steady state had not been reached.  35 random images were then selected and the shoulder and toe angles determined.  Again, the first 30 images that clearly showed the shoulder and toe location in the same picture were selected for analysis.   Shoulder Toe τ σ -45-   Figure 24. Illustration showing the identification of the shoulder (σ) and toe (τ) angle from the simulation results using the streaming effect.  Once the shoulder and toe angles were compiled from the pictures and simulation results they were compared using a student t-test to determine if the mean shoulder and toe values were similar.  The third technique relied on grayscale, or light intensity measures to determine the presence of wood strands in the laboratory drum.  This is a relatively new technique and has only been found once in the literature as a model validation tool (Nakamura et al. 2007).  This method is based on the premise that the back of the blender drum is black, or low intensity and grayscale values, and that the strands are relatively light, or higher intensity and grayscale values.  As a result, as the strands travel through the line of sight in front of the drum back they are recorded as relatively high intensity regions. This approach removes nearly all subjectivity, which is its primary advantage over the previous two methods.  However, there are several inherent challenges associated with its use.  First, although it is simple to determine the presence of at least one strand in any y-z plane (Figure 25) it is unable to determine the degree of strand saturation. For instance, it is unable to decipher between a τ σ -46- single strand blocking the sight of the blender back or multiple strands blocking the sight of the blender back.  In addition, this technique is unable to account for parallax, and because the drum is 3 feet deep this can be significant at the outer edges of the drum.   Figure 25. Schematic of the x, y, z coordinate system relative to the blender.  The laboratory images used for this analysis were extracted from the one minute video clip used for the visual validation.  The video was converted from an MPG format to an AVI format using Cyberlink PowerDirector v6 (Anonymous 2007).  The AVI version was then imported into Adobe Premiere Pro CS3 and exported as individual still images (Adobe Systems Incorporated 2007).  This step was completed with the Export Frame Settings shown in Table 17.  Table 17.  Frame export settings used in Adobe Premiere Pro CS3. General:    File Type TIFF Video:    Frame Size 640 x 480    Frame Rate 29.97    Pixel Aspect Ratio 1.0 Keyframe and Rendering:    Deinterlace video footage ‘select’ Note: with the exception of the above listed settings, all other parameters were left at their respective default settings.  x z y -47- Using Image Pro Plus v6 (IPP), the still images were converted into 8-bit grayscale images. With 8-bit grayscale, 0 corresponds to black and 255 corresponds white. The intensity, or grayscale value, was determined for each column of pixels across the width of the resination region.  This is done using the Line Profile command in IPP, selecting Thick Horz under the report options, and then positioning the boundaries of the resination region (Figure 26).  This was performed for every third image of the 1 800 that were extracted.  The average grayscale value and associated variance was determined for each column of pixels.  A macro was written in VBA to perform this operation and is listed in Appendix F. -48-     Figure 26. Screen shot taken in Image Pro Plus v6 showing the placement of the thick, line profile and the cooresponding grayscale values.  The indicated grayscale values are an average of each column of pixels across the width of the resination region.  The histogram data from the RDBM simulations were then overlaid on top of the light intensity data to determine the degree of similarity (Figure 27).  To facilitate the direct comparison of the RDBM histograms with the light intensity data, the light intensity data was grouped and averaged according to the same 51 mm bin size as the histograms.  A critical assumption in this analysis is that the light intensity values are directly related to the count values from the simulation results. Resination region -49-   Figure 27. Example of simulation results overlaid on top of grayscale results.  The bin id’s are shown on the x-axis.  4.4 Results 4.4.1 Screening design – material properties After completing the full factorial simulation design the respective factor levels and response variables were compiled (Table 18) to be analyzed in SAS version 9.1 using an analysis of variance (ANOVA).  In addition to the three response variables previously mentioned: skewness, kurtosis, and count; the required processing time was also included.  The processing time was included because one of the objectives of this initial study was to determine a suitable combination of material properties that would minimize the required processing time without compromising the quality of the simulation results.  Therefore, the results for the processing time will only be used for determining, if appropriate, where assumptions could be made to reduce the time required to run subsequent simulations.       20.5 RPM - 1/32nd Full -50 0 50 100 150 200 250 300 350 400 450 500 550 Bin C ou nt  (S im ul at io n)  60 70 80 90 100 110 120 130 140 150 160 170 180 190 G ra ys ca le  (I m ag in g)  1 27 29 3121 23 25 15 17 199 11 135 7 3 Simulation Imaging -50- Table 18.  Factors and response variables for simulations investigating the impact of the material properties. Factors Response variables Run Shear modulus (psi) Poisson’s ratio Density (kg/m3) Skewness Kurtosis Count Proc. Time (hrs) 1 1 x 108 0.038 62.208 -0.0744 -1.0043 14267 11.10 2 1 x 108 0.038 380.000 -0.1921 -1.1023 15027 4.73 3 1 x 108 0.453 62.208 -0.1704 -1.0837 15063 11.70 4 1 x 109 0.038 62.208 -0.0544 -1.0776 14305 34.30 5 1 x 109 0.453 62.208 -0.2613 -1.1146 15352 37.00 6 1 x 109 0.038 380.000 -0.2429 -1.0365 15160 14.20 7 1 x 108 0.453 380.000 -0.1068 -1.0940 14902 5.03 8 1 x 109 0.453 380.000 -0.1537 -1.0274 14772 15.10   The ANOVA results showed that none of the material properties: shear modulus, Poisson’s ratio, or density; had a significant impact on the skewness, kurtosis, or count at a 95% confidence level (α = 0.05) (Appendix G).  This is demonstrated by the p-values consistently being greater than 0.05.  As expected from Equation 7, the processing time was significantly affected by the material properties, specifically by the shear modulus and density.  4.4.2 Screening design – interaction properties The results from the simulations investigating the impact of the interaction properties were also analyzed using an ANOVA in SAS version 9.1 (Table 19).  Table 19.  Factors and response variables for simulations investigating the impact of the interaction properties. Factors Response variables Run Coef. of restitution Coef. of rolling friction Coef. of static friction Skewness Kurtosis Count Proc. Time (hrs) 1 0.01 0.01 0.24 -0.5587 -0.8274 16863 5.24 2 0.01 0.01 0.64 -0.2302 -1.0118 15260 4.79 3 0.01 1.00 0.24 0.3976 -0.8940 13569 5.18 4 0.10 0.01 0.24 -0.4195 -0.9959 15671 5.18 5 0.10 1.00 0.24 0.4187 -0.7253 13429 5.25 6 0.10 0.01 0.64 -0.1145 -0.9241 14487 4.72 7 0.01 1.00 0.64 1.2969 0.9665 12855 4.4 8 0.10 1.00 0.64 1.2521 0.8854 12749 4.35   The ANOVA results (Appendix H) showed that the coefficient of rolling friction and the coefficient of static friction had a significant effect on the skewness of the data at a 95% confidence level, while only the coefficient of rolling friction had a significant effect on the count.  None of the factors significantly impacted the kurtosis.  Based on these results, it was necessary to complete additional simulations and research to determine appropriate coefficients of rolling and static friction. -51- 4.4.3 Coefficient of rolling friction An appropriate coefficient of rolling friction value for this project was determined by completing a series of simulations at both the upper and lower static friction coefficient values measured in the laboratory for seven different values of rolling friction (Table 20 and Figure 28). This provided insight into the affect of rolling friction on the bulk dynamics of the strands.  Common sense suggested that because strands do not roll, but instead slide along the liner, flights, or adjacent strands in an actual rotary drum blender, the coefficient of rolling friction should be set as high as possible to prevent the strands from rolling. However, the impact of the rolling friction on the strand dynamics was not completely known and therefore these simulations were necessary.  For these studies the coefficient of static friction was set independently for wood to wood and wood to PE (Table 20).  Table 20.  Rolling and static friction coefficients for the simulations aimed at determining a suitable coefficient of rolling friction. Static friction Run Wood to Wood Wood to PE Rolling friction x-position skewness 1 0.66 0.3 0.010 -0.22873 2 0.66 0.3 0.175 1.18975 3 0.66 0.3 0.340 1.49009 4 0.66 0.3 0.505 1.06571 5 0.66 0.3 0.670 0.71122 6 0.66 0.3 0.835 0.51079 7 0.66 0.3 1.000 0.59923 8 0.54 0.26 0.010 0.03421 9 0.54 0.26 0.175 1.22647 10 0.54 0.26 0.340 1.31727 11 0.54 0.26 0.505 0.83199 12 0.54 0.26 0.670 0.57810 13 0.54 0.26 0.835 0.53392 14 0.54 0.26 1.000 0.51188  -52-  Figure 28.  Skewness as a function of the coefficient of rolling friction (CRF).  In both cases the simulation results showed that the rate of change of skewness with rolling friction is smallest above 0.7.  It would therefore be ideal to operate in this range. However, in order for the simulation to remain stable the rolling friction coefficient should not be more than 0.7 (Cook 2008).  Thus for the purposes of this research a value of 0.67 was used to ensure model stability.  A disadvantage of this approach is that it removes some of the control we have over the bulk dynamics of the strands, only leaving the coefficient of static friction for controlling the simulated strand flow.  4.4.4 Validation - coefficient of static friction Once a suitable coefficient of rolling friction was determined, attention was focused on the coefficient of static friction.  As previously indicated, the static friction coefficients used in the model may not be necessarily the same as those values found in the laboratory experiments.  This is largely because of assumptions that were made in the model.  For instance, the bulk flow of strands in an actual blender is much more complicated than individual specimen tests.  There are many factors that impact specimen interactions, such as air flow or the presence of fine particles acting as lubricant on the material surfaces.  As a -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 CRF S ke w ne ss µwood/wood = 0.66 µwood/PE = 0.30  µwood/wood = 0.54 µwood/PE = 0.26  -53- result, a series of simulations were carried out in a systematic manner to narrow in on a pair of static friction coefficients that best produces realistic strand flow.  The validation techniques outlined in the Methodology section were used to understand whether or not the simulation results were improving with each successive simulation.  Six static friction levels were required to narrow in on a suitable combination of values (Table 21).  Runs 1 and 2 used the upper and lower laboratory determined values.  Neither of these runs agreed using visual validation.  The strands were lifted too high up on the drum wall before detaching and impacted the drum at too small an angle on their decent.  Table 21.  Pairs of static friction coefficients used to identify a suitable set of values. Static coefficient of friction Run Wood to wood Wood to HDPE 1 0.66 0.30 2 0.54 0.26 3 0.02 0.01 4 0.14 0.07 5 0.10 0.05 6 0.12 0.06  Runs 3 to 6 used values that were considerably less than the laboratory determined coefficients, however were necessary to correct for the disparity between runs 1 and 2 and the video footage taken in the laboratory.  Throughout these runs a ratio of approximately 2:1 was maintained between the wood to wood and the wood to PE coefficient values.  This ratio was found to be reasonably accurate from the laboratory results in Section 3.4.  Run 3 was an extreme case.  This simulation tested the lowest levels possible while maintaining a 2:1 ratio.  The visual results of this run showed that the point of detachment and collision were both too low on the drum, indicating that the optimal static friction coefficients were between the levels used in runs 2 and 3.  The visual results of run 4 were promising.  The point of detachment and collision both appeared to be similar to the laboratory video footage; as a result, validation using the shoulder and toe angle measurements was also completed (Table 22).  The results of the student t-test suggested that there was not a significant difference between the shoulder angle -54- in the simulated and laboratory results assuming a 95% confidence level.  The toe angles were however significantly different, with the simulated toe angle being lower.  Table 22. Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 4 and the laboratory results. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 55.8 53.9 247.7 256.2 Variance 38.90 20.53 44.42 29.98 Observations 30 30 30 30 Hypothesized mean dif. 0  0 Degrees of freedom 53  56 t-statistic 1.397  -5.419 P(T≤ t) two-tail 0.168  1.313 E-6 t-critical two-tail 2.006  2.003  Runs 5 and 6 were completed to determine if the results of run 4 could be improved upon. Again, visually both of these runs were promising, warranting validation by means of the shoulder and toe angles (Tables 23 and 24).  With run 5 the toe angle was closer to the laboratory results; however, the simulation shoulder was again lower.  In run 6, the shoulder and toe angles were both significantly lower than the laboratory results.  Table 23. Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 5 and the laboratory results. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 45.2 53.9 255.6 256.2 Variance 20.39 20.53 34.79 29.98 Observations 30 30 30 30 Hypothesized mean dif. 0  0 Degrees of freedom 58  58 t-statistic -7.392  -.408 P(T≤ t) two-tail 6.438 E-10  0.685 t-critical two-tail 2.002  2.002           -55- Table 24. Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 6 and the laboratory results. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 47.7 53.9 251.4 256.2 Variance 44.98 20.53 53.90 29.98 Observations 30 30 30 30 Hypothesized mean dif. 0  0 Degrees of freedom 51  54 t-statistic -4.173  -2.911 P(T≤ t) two-tail ≤0.001  0.005 t-critical two-tail 2.008  2.005  A summary of the shoulder and toe angle results from runs 4 to 6 and the results from the images taken of the laboratory blender is shown in Table 25.  The italicized values indicate those angles that are significantly different from the laboratory results at the 95% confidence level (α = 0.05).  These results show a decline in the shoulder angle with a decreasing coefficient of static friction.  At the same time, the toe angle steadily increased with decreasing friction values.  Table 25. Summary of runs 4 to 6 and the laboratory taken shoulder and toe angle results. Italicized values indicate those angles that are significantly different (α = 0.05) from the image results.  Shoulder Toe Lab images 53.9 256.2 Coefficient of static friction1:    Run 4 (0.14/0.07) 55.8 247.7    Run 5 (0.10/0.05) 45.2 255.6    Run 6 (0.12/0.06) 47.7 251.4 1The values are shown as the wood to wood and the wood to PE coefficient of static friction respectively.  Of these three runs, it was determined that run 4 resulted in simulation results that most closely resembled the laboratory results.  This decision was based on the close resemblance of the shoulder angles obtained in run 4 and the laboratory images.  Although the toe angle was significantly different from the laboratory results, it was ultimately decided that an accurate shoulder angle was more important than an accurate toe angle.  If the shoulder angle was incorrect it would more negatively impact subsequent simulations that included an atomizer boom in the middle of the blender, the which the strands would ultimately interact.  The results of runs 4 to 6 were expected based on previous work by Smith and Davis (Davis 1919; Smith and Gutiu 2002).  As the coefficient of friction increases so does the angle of -56- detachment from the drum wall.  In the simplest case, with a flight of zero height, this angle is predicted by (Smith and Gutiu 2002):  2 22 2 1 4arcsin 1 1arcsin ss g rn μ π μα +−⎟ ⎟ ⎠ ⎞ ⎜⎜⎝ ⎛ + =                                   [10]  where:   α is the detachment angle relative to the vertical axis, µs is the static friction coefficient, r is the radius of the drum, and n is the rotational speed.    To further verify these results, run 4 was re-run at 15.5 RPM and 25.5 RPM.  Using a higher and lower speed was expected to show a clear movement in the shoulder and toe angles. The results of these additional simulations showed that the shoulder and toe angles had a clear dependency on the rotational speed.  A summary of the results for run 4 at the various speeds is shown below (Table 26).  The detailed t-test results for 15.5 and 25.5 RPM are shown in Appendix I.  Table 26. Summary of shoulder and toe angles obtained at 15.5 to 25.5 RPM with the coefficients of static friction set at 0.14 and 0.07.  Italicized values indicate those angles that are significantly different (α = 0.05) from the image results. Shoulder angle Toe Angle RPM Simulation Laboratory Simulation Laboratory 15.5 40.4 38.9 258.0 259.0 20.5 55.8 53.9 247.7 256.2 25.5 67.0 63.1 217.9 227.4  Although both the simulated shoulder and toe angle were significantly different from the laboratory results at 25.5 RPM, the values were close enough to be satisfied with using 0.14 and 0.07 as the coefficient of static friction for wood to wood and wood to PE respectively.  As a final confirmation, the third validation technique relying on light intensity was also completed for 0.14 and 0.07 static friction values.  This validation was completed for a blender fill level of 1/8th at speeds of 15.5 RPM, 20.5 RPM, and 25.5 RPM.  Before completing this analysis a baseline test was completed to determine the light intensity of the blender without the presence of strands.  -57- For the baseline test the light intensity was measured across the resination region with the blender empty (Figure 29). The adjusted average grayscale value was then calculated and subtracted from subsequent analyses. Because of the occurrence of parallax the region of interest was narrowed to avoid inclusion of the drum liner for this validation technique.  The drum liner is nearly white and would have caused the results to be false near the left- and right-hand extents of the resination region.  The thatched regions, or first and last 4 bins, in the following graphs were not included in the analysis.  The average grayscale value for the region between the two cut-off points was found to be 66.2.  0 50 100 150 200 250 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Bin G ra y- sc al e Cut-off Cut-off Average = 66.2  Figure 29.  Baseline grayscale results for the laboratory blender running empty.  The cut-off points are indicated by the solid, vertical red lines.  The drum liner is contained in the thatched region. Note that the width of each bin is 57.5 mm.  The light intensity analyses showed close correspondence with the simulation results (Figures 30 to 32).  In particular, the initial points of inclination (middle to left side of graphs) and the peaks appear to be reasonably aligned.  This is especially true at 20.5 RPM and 25.5 RPM.  At 15.5 RPM the laboratory data are skewed slightly further to the right, or negatively skewed.  This disparity is difficult to interpret however.  Because the peak of the -58- laboratory data are contained within the cut-off region it is likely impacted by the lightness of the drum liner and therefore the precise location of the peak is not known.  Although the graphs of the simulation results appear to resemble the laboratory images for the entire region between the cut-off points, the region to the right of the graphs’ peak is less capable of accounting for changes in strand volume.  This is because at a 1/8th fill level the drum tends to become saturated with strands fluttering beneath the cascading stream of strands.  This blocks the view of the drum back, inhibiting the Image Pro Plus software from observing differences in the grayscale level. The simulation and laboratory results contained here are for a blender running counter-clockwise; and therefore, the this region is to the right of the peak in these graphs.  0 500 1000 1500 2000 2500 3000 3500 4000 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Bin C ou nt  (S im ul at io n) 66.0 86.0 106.0 126.0 146.0 166.0 186.0 206.0 G ra y- sc al e (L ab or at or y) Laboratory results Simulation results  Figure 30. Grayscale results for the blender running at 15.5 RPM and 1/8th full.  -59- 0 200 400 600 800 1000 1200 1400 1600 1800 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Bin C ou nt  (S im ul at io n) 66.0 86.0 106.0 126.0 146.0 166.0 186.0 G ra y- sc al e (L ab or at or y) Laboratory results Simulation results  Figure 31. Grayscale results for the blender running at 20.5 RPM and 1/8th full.  0 100 200 300 400 500 600 700 800 900 1000 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Bin C ou nt  (S im ul at io n) 66.0 76.0 86.0 96.0 106.0 116.0 126.0 136.0 146.0 156.0 166.0 G ra y- sc al e (L ab or at or y) Laboratory results Simulation results  Figure 32. Grayscale results for the blender running at 25.5 RPM and 1/8th full.  Based on the validation results the coefficients of static friction were similarly determined to be 0.14 and 0.07 for wood to wood and wood to PE respectively.  Using this combination of -60- coefficients produced simulation results that closely mimicked those obtained in the laboratory blender.  The final coefficient of static friction values for use in EDEM are considerably lower than the 0.66 and 0.30 values obtained through the bench-top laboratory experiments.  Much of this difference is likely a result of the choice in strand representation.  Because the sticks are composed of a series of spheres the contact surfaces between sticks have ridges that the adjacent surfaces must slide over.  This results in mechanical interlocking between the sticks. Reducing the friction coefficient acts as a lubricant for the surfaces, allowing them to more easily slide along each other or separate if necessary.  A second explanation for this disparity is the lack of fine particles in the model.  In an actual rotary drum blender, including the one used for validating this model, fine particles are generated within the process.  These fine particles coat the surfaces of the strands, flights, and drum liner and ultimately behave similar to very small ball bearings and effectively reduce the friction between surfaces.  4.5 Conclusions The selection of suitable material and interaction parameters has been shown to be critical to the successful implementation of a discrete element model for two principal reasons. First, the accuracy of the simulation results is largely determined by the input parameters.  The adage “garbage in, garbage out” has been shown to be particularly relevant here (Hirsch et al. 2002).  The findings of this study show that many of the parameters listed in Table 8 have no significant impact on the bulk dynamics of wood strands in the RDBM.  The only parameters that did have a significant impact were the coefficients of rolling friction and static friction.  Second, the combination of parameters may significantly impact the processing time required for an individual run.  During this project, processing times for a 24 second simulation ranged from as low as 4.7 hours to as high as 34.3 hours.  Accuracy of the simulation results being equal, shorter processing times are preferred.  Shorter processing times are achieved by using relatively high material densities or low shear moduli.  -61- Based on the findings of these simulations and analyses the complete set of material and interaction properties for this particular project is shown below in Table 27.  By using these input parameters the RDBM accurately, and processor efficiently, predicts the bulk dynamics of wood strands in a 6 foot rotary drum blender.  Table 27. Summary of material and interaction properties for use with EDEM. Material Properties Shear modulus 1x108 psi Poisson’s ratio 0.453 Density 380 kg/m3 Interaction Properties Coefficient of rolling friction 0.67 Coefficient of static friction:      Wood on wood 0.14      Wood on HDPE 0.07 Coefficient of restitution 0.01    -62- CHAPTER 5  MEASURING THE EFFECT OF ROTARY DRUM BLENDER DESIGN AND OPERATING PARAMETERS ON THE BULK STRAND FLOW USING A RESPONSE SURFACE DESIGN  5.1 Introduction Until this point the research project was largely focused on calibrating the RDBM with laboratory results.  This was necessary before exploratory studies could be completed using the model.  This next portion of the research therefore relies on these calibration results for conducting an exploratory study aimed at understanding the design and operation of rotary drum blenders.  This work utilizes the quantification techniques used in Chapter 4, together with a response surface design, to determine the relationship between four operating and blender design parameters and the distribution of strands across the blender diameter as well as the average time a strand spends in the resination region.  The four factors of interest are specific to the Coil Manufacturing, long-retention blenders, and include: the flight height, number of flights, blender fill level, and blender rotational speed.    This is not an exhaustive list of factors; however, they are the few parameters that do not require fundamental or significant changes to the current blending process. It is hypothesized that there are ideal combinations of blender design and operating parameters that results in the optimal blending environment.  Objective: 1. To understand the impact of blender design and operating parameters on the strand distribution across the drum diameter and the average time a strand spends in the resination region.  5.2 Methodology A response surface design was selected for determining the impact several of the rotary drum blender design and operating parameters have on the distribution of strands across the drum diameter, as described by the skewness and kurtosis, as well as the average time a strand spends in the resination region.  Response surface methodology (RSM) was followed -63- because it provides an efficient means of determining the relationship between several factors and response variables.  For this reason, RSM has been used extensively for product and process optimization (Myers and Montgomery 2002).  A modified four factor, Box-Behnken response surface design was followed for these simulations (Tables 28 and 29).  How this design differs from a traditional Box-Behnken design is that the number of flights and fill level increase geometrically.  Consequently, the median value, or factor level, is not equal to the mean value, as is the case with traditional Box-Behnken designs (SAS Institute Inc.).  The design scheme was altered in response to limitations with the design of the laboratory blender.  In particular, additional flights could only be positioned at set locations.  The laboratory blender was pre-drilled for 16 flights; therefore, in order to maintain a symmetric flight placement along the blender circumference, the number of flights was increased from 4 to 8 to 16.  Although it was ultimately decided that the laboratory blender was not required for further validation of the RDBM, at the onset of this analysis it was desired to maintain that option. -64- Table 28.  Response surface design matrix. Run Number of flights Flight height Fill level Rotational speed 1 -1 -1 -0.33 0 2 -1 1 -0.33 0 3 1 -1 -0.33 0 4 1 1 -0.33 0 5 -0.33 0 -1 -1 6 -0.33 0 -1 1 7 -0.33 0 1 -1 8 -0.33 0 1 1 9 -1 0 -0.33 -1 10 -1 0 -0.33 1 11 1 0 -0.33 -1 12 1 0 -0.33 1 13 -0.33 -1 -1 0 14 -0.33 -1 1 0 15 -0.33 1 -1 0 16 -0.33 1 1 0 17 -1 0 -1 0 18 -1 0 1 0 19 1 0 -1 0 20 1 0 1 0 21 -0.33 -1 -0.33 -1 22 -0.33 -1 -0.33 1 23 -0.33 1 -0.33 -1 24 -0.33 1 -0.33 1 25 -0.33 0 -0.33 0 26 -0.33 0 -0.33 0 27 -0.33 0 -0.33 0  Table 29.  Response surface design factor levels. Factor Units Low level (-1) Mid level (0 or -0.33) High level (1) Number of flights - 4 8 16 Flight height inches 2 4 6 Fill level1 % 6.25 12.50 25.00 Rotational speed rpm 18.71 23.39 28.07 1Fill level is represented as the fraction of blender volume occupied by strands if the blender drum was stopped during operation and the strands settled on the base of the drum.  The factor levels were selected based on discussions with Coil Manufacturing (Coil 2007b; Coil 2008) and by balancing computational and physical limitations, as previously mentioned.  For instance, the fill level of an industrial blender is typically 25% to 50%.  This level is based on the fraction of the blender volume occupied by strands when the blender is not rotating and the strands are resting on the bottom of the blender drum under self-weight. -65- Because of computing limitations, which include both the speed in which the software can solve a simulation and the speed in which the computer can run the software, the maximum fill level simulated was 25%.  The results show distinct trends however, which may be useful for extrapolating towards the higher fill levels.  In addition, the simulated blender diameter was limited to 1.84 meters (6.04 feet).  This corresponds to the laboratory blender and minimizes the computational requirements.  Industrial blenders are as large as 11 feet in diameter; however, it is anticipated that results from the 6 foot blender will provide valuable insight into the strand dynamics.  Further, it is assumed that many of the effects caused by the design and operational parameters will be relevant regardless of the blender diameter.  As will be outlined in the Future Work section, it is recommended that future experiments be conducted that investigate the validity of scaling the model results for an industrial blender. The selected blender rotational speeds were 60, 75, and 90% of the calculated critical speed (Smith and Gutiu 2002).  It is important to note that instead of reporting the total number of 0.1 second time steps that the 150 tracked strands spent in the resination region, as was the case with the sensitivity study (Chapter 4), the average time an individual strand spent in the resination region was reported in this study.  The reason for this slight change in the reporting format is because of the varying blender fill levels investigated in this study.  Reporting the average time helps avoid misinterpretation of the results and relates directly to the overall objective, which is to maximize the time spent in the resination region.  Throughout this study, a tracked sample size of 150 strands was maintained.  For all of the simulations, the number of recorded revolutions was maintained at 10; however, the first 2 revolutions were discarded to allow the model to reach steady state.  Consequently, 8 complete revolutions were included in the analysis for each simulation.  The response surface design was completed twice, once without an atomizer boom and once with a single atomizer boom (Figure 33).  The location of the boom was selected based on drawings provided by Coil Manufacturing (Coil 2007b).  As an initial investigation of the dynamics and the role design and operational parameters have on it, most of the attention was focused on the scenario without an atomizer boom.  This would allow for an optimal boom location to be selected based on the strand flow, while still providing some insight into the impact the boom will have on the resulting strand flow. -66-   Figure 33.  Schematic of a blender fitted with an atomizer boom, shaded grey.  The upward and downward rotating sides of the blender are also indicated.  All of the simulations were run using EDEM version 1.3.1 and post processed and sorted in Microsoft Excel using the VBA script listed in Appendix E.  The results were subsequently analyzed using SAS version 9.1’s response surface design tools.  Quadratic models were fit in SAS using the ANOVA selection method at a 95% confidence level (α = 0.05).  For the skewness and kurtosis it was necessary to include several of the insignificant effects to maintain the model hierarchy.  These effects are indicated in the Results and Discussion section.  5.3 Results and discussion 5.3.1 Overall predictive trends The results of the study using a 6 foot RDBM (Appendix J) show that all three response variables were significantly affected by at least two of the four factors, either as a main effect or as an interaction effect.  The skewness was impacted most, being affected by all four factors. Kurtosis was affected by the number of flights and flight height, while the average time spent in the resination region was affected by the flight height and rotational speed. The relationships between the response variables and the significant factors are presented in the following sections. Atomizer boom CCW Rotation Downward rotating side Upward rotating side -67-  These relationships are shown in the prediction profile graphs that were generated in SAS (Figures 34, 40, 43, and 44 to 47).  The factors are shown on the x-axes and the response variables on the y-axes.  These relationships are unique to the factor levels employed and may change accordingly if the factor levels were to change.  For the graphs included in this study, factor levels representative of industry norms were used for the skewness and average time spent in resination region analyses (Table 30) (Coil 2008; Smith 2005).  Table 30.  Factor levels used in the skewness and average time spent in resination region analyses. Factor Factor level Number of flights 14 Flight height (inches) 4 Fill level (fraction) 0.25 Rotational speed (rpm) 24.0  The factor levels used for the kurtosis analyses are described in Section 5.3.1.3.  The factor levels are indicated by a vertical line and accompanying x-axis label on the respective graphs.  In order to facilitate comparison of the simulation means, 95% confidence intervals are included on each of the following graphs.  5.3.1.1 Skewness All four factors had a significant effect on the skewness (Table 31 and Figure 34).  The skewness increased with an increasing rotational speed and number of flights and a decreasing fill level.  The skewness increased with an increasing flight height from 2 to 4 inches and then began to decrease.  The model for predicting the skewness is shown in Equation 11.  This model yields an F-value of 27.1357 (p-value < 0.0001), which is significant at a 95% confidence level (α = 0.05).        -68- Table 31.  List of effects for the skewness showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. Factor p-value Number of flights 0.0093 Flight height 0.0092 Fill level 0.0232 Rotational speed 0.0032 Number of flights x Flight height 0.0121 Flight height x Fill level 0.0051 Rotational speed2 0.0237 Flight height2 x Rotational speed 0.0410 Factor p-value Number of flights 0.0093 Flight height 0.0092 Fill level 0.0232 Rotational speed 0.0032 Number of flights x Flight height 0.0121 Flight height2 0.1106 Flight height x Fill level 0.0051 Flight height x Rotational speed 0.0516 Rotational speed2 0.0237 Flight height2 x Rotational speed 0.0410  4 2 2 2 44232 2 2 214321 0144.001145.01409.04520.22652.0 0282.07499.04648.66325.12006.03128.5 XXXXXXXX XXXXXXSk −++−+ −−+−+=             [11] where: Sk is the predicted skewness, X1 is the number of flights, X2 is the flight height in inches, X3 is the blender fill level as a fraction of the total blender volume, and X4 is the blender rotational speed in rpm’s.   Figure 34.  Prediction profiles generated in SAS showing the relationship between the skewness and the (top-left) number of flights, (top-right) flight height, (bottom-left) fill level, and (bottom-right) blender rotational speed.  The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs.  fr -69- Skewness was shown to increase with an increasing number of flights and decrease with an increasing blender fill level.  Recall that a positive skewness implies that the majority of the strands passed through the resination region on the downward rotating side of the drum, while a negative skewness implies that the majority of the strands passed through the resination region on the upward rotating side of the drum as they descended (Figure 33). Ideally the strands would be symmetrically distributed, which would be identified by a skewness of 0.  The impact of flight height and fill level is best described by considering the angle of repose. Although this measure is most applicable for granular material, it is also relevant for wood strands.  The angle of repose refers to the internal angle formed between a horizontal surface and a pile of granular material (Figure 35).  This angle is largely influenced by the coefficient of static friction and determines the height and width of the resulting pile for a given volume of material (Smith 2006).   Figure 35.  Schematic showing the angle of repose, α, for a pile of wood strands on a horizontal surface.  With fewer flights the loading per flight was relatively high, causing the strands to pile higher atop of each flight.  This is easily seen for the flight identified by the arrow in Figure 36a.  In this case, where there are only 4 flights, the amount of strands that the flight is able to carry is determined by the angle of repose.  As the flight moves along the drum circumference the angle of the flight relative to the horizontal axis increases.  This causes some of the strands to detach and slough off of the flight because the angle of repose has been exceeded, as shown in Figure 36b.  This is particularly relevant for the strands furthest away from the flight where the angle is greatest and the strands are less supported.  Once the flight reaches the location shown in Figure 36e the strands begin to slough off of the flight in a continuous flow.  With only 4 flights the strands slough off of the flight while the flight passed through the entire right half of the blender.   α furnishfurnish -70-           Figure 36.  Simulation images showing the charge level per flight and the discharge pattern when a relatively small number of flights are employed. The simulated blender has 4-6 inch flights and is rotating at 23.39 RPM and is 1/8th full. The arrow indicates the position of a specific flight as the drum rotates.  As the number of flights increased the loading of strands per flight diminished, reducing the height of the strand pile atop of each flight.  This is seen in Figure 37a.  As a result, the distance between the strands nearest to the flight and the strands furthest from the flight has decreased. In this case, the flights need to travel further along the drum circumference before the angle of repose is overcome.  This is illustrated in the following example where the strands do not begin detaching until the flight reaches the location shown in Figure 37d. Consequently, the strand piles sloughed off of their respective flight within a narrow timeframe.  With 16 flights, most of the strands detached as the flight passed through the upper-right drum quadrant.  A smaller loading per flight would be the preferred scenario for an industrial operation as it results in better control over the moment of detachment from the flight and the strand trajectory.        (a) (b) (c) (d) (h) (g) (f) (e) -71-       Figure 37.  Simulation images showing the charge level per flight and the discharge pattern when a relatively large number of flights are employed. The simulated blender has 16-6 inch flights and is rotating at 23.39 RPM and is 1/8th full. The arrow indicates the position of a specific flight as the drum rotates.  As anticipated, increasing the fill level caused the skewness to decrease.  As more strands were loaded into the blender the flights tended to become overloaded, causing the strands to slough off the flights relatively early.  This placed downward pressure on the skewness.  Similar to the effect of the number of the flights, increasing the rotational speed also caused the skewness to increase.  At less than approximately 21 RPM however, the speed appeared to have only a minimal impact on the skewness.  One explanation for this is that as the speed decreased the strands became less dispersed across the drum diameter.  This consolidation of strands continued until the strands were packed in the lower-right drum quadrant, rolling amongst themselves (Figure 38). 21 RPM could be the speed at which point there is only minimal free fall of strands and the majority of strands are rolling in this region.  Figure 38.  Simulation image showing strands rolling in the corner of the drum, where there are 8-4 inch flights and the blender is rotating at 18.71 RPM and is 1/4 full. (a) (b) (c) (d) (h) (g) (f) (e) -72- A positive relationship between the skewness and rotational speed was expected based on previous work (Davis 1919; Smith and Gutiu 2002).  As the rotational speed, n, increased so to did the centrifugal force, FC (Equation 12).  This caused the strands to stay in contact with the flights or drum wall longer as the centrifugal force caused detachment to occur at a higher angle. gr F F gC 2ω=                          [12] nrπω 2=                          [13] where:  ω is the angular velocity,  r is the distance from the center of the drum, g is gravitational acceleration, and  n is the rotational speed in rpm.  This effect is magnified by the fact that as the flow of strands moves further across the drum the falling strands are dispersed amongst a larger number of flights.  This reduces the likelihood of strands piling in the lower-right drum quadrant waiting to be collected by a passing flight.  Figure 39 shows an example of flight utilization.  At 18.71 RPM the strands are dispersed across only 9 flights, compared to 14 at 28.07 RPM.   Figure 39.  (Left) Simulation image showing the dispersion of strands across relatively few flights when the blender is rotating at 18.71 RPM and (right) across many flights when the blender is rotating at 28.07 RPM.  In both cases the blender has 16-4 inch flights and is 1/8th full.  The piling of strands in the blender and the movement of the passing flights through the pile is a possible contributor to strand attrition caused by the grinding of strands.  It may also result in poorly aligned strands on the flights as the strands become interlocked.  Poor alignment creates challenges for predicting when the strands will detach from their respective -73- flight.  Generally, the results show that poorly aligned strands detach prematurely, placing downward pressure on the skewness.  Flight height had an interesting effect on the skewness.  Between 2 and 4 inches a positive relationship was anticipated.  This is because as the flight height increased each flight was capable of carrying a larger number of strands, resulting in an increased overall system capacity.  As seen prior, with a fixed volume of strands, the capacity had a direct impact on the skewness.  Beyond 4 inches however, the relationship between the flight height and skewness became negative.  This was not foreseen but can be explained by examining the forces acting on the strands.  As the flight height increased the edge of the flights were closer to the center of rotation of the blender, resulting in a lower centrifugal force acting on those strands located nearer the edge of the flights.  This caused the strands to begin detaching and descending sooner than with shorter flights that were further from the center of rotation.  This same trend may not have been seen with flights between 2 and 4 inches because the shorter flights were incapable of lifting an adequate amount of strands.  As a result, the quantity of strands that prematurely fell from the shorter flights had less impact on the overall strand flow statistics.   Based on these findings, it appears that flights that are between 4 and 5 inches in height strike a good balance between capacity and control over the strand detachment point for this particular 1.840 meter (6.04 feet) diameter blender.  It is important to recognize however that the difference in the predicted skewness for flights that are 4 inches and larger in height in not significant.  5.3.1.2 Effect of an atomizer boom on the skewness results The significant main effects that were determined according to the ANOVA selection method, using a 95% confidence level, was reduced from all four factors to only two factors when the atomizer boom was included. These factors were the fill level and the blender rotational speed.  All four factors were ultimately included however in order to maintain the skewness model hierarchy.  The inclusion of an atomizer boom in the simulations had a slight impact on the overall relationship between two of the main effects and the skewness (Table 32).  While in general -74- these relationships did not drastically change over the tested ranges (Figures 34 and 40), they are worth evaluating in order to better understand the bulk strand dynamics and the impact the atomizer boom placement has on it.  The model for predicting the skewness is shown in Equation 14.  This model yields an F-value of 18.3728 (p-value < 0.0001), which is significant at a 95% confidence level (α = 0.05).  Table 32.  List of effects for the skewness when an atomizer boom is present, showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. Factor p-value Fill level 0.0126 Rotational speed 0.0023 Number of flights x Rotational speed 0.0127 Flight height x Fill level 0.0463 Flight height x Rotational speed 0.0046 Fill level2 0.0070 Rotational speed2 0.0443 Number of flights2 x Rotational speed 0.0419 Factor p-value Number of flights 0.1720 Flight height 0.1517 Fill level 0.0126 Rotational speed 0.0023 Number of flights2 0.6020 Number of flights x Rotational speed 0.0127 Flight height x Fill level 0.0463 Flight height x Rotational speed 0.0046 Fill level2 0.0070 Rotational speed2 0.0443 Number of flights2 x Rotational speed 0.0419  421 2 4 2 3423241 2 14321 0024.0 0149.04595.760764.06584.10664.0 0536.02556.10559.221450.14394.11295.19 XXX XXXXXXXX XXXXXSk − +++−+ +−−−−=                 [14] where: Sk is the predicted skewness, X1 is the number of flights, X2 is the flight height in inches, X3 is the blender fill level as a fraction of the total blender volume, and X4 is the blender rotational speed in rpm’s.     -75-   Figure 40.  Prediction profiles generated in SAS showing the relationship between the skewness and the (top-left) number of flights, (top-right) flight height, (bottom-left) fill level, and (bottom-right) blender rotational speed when an atomizer boom is included in the simulation.  The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs.  The main effect and skewness relationships that changed involve the flight height and blender fill level.  In both cases it was in the upper portion of the tested ranges where a deviation in the results was observed.  When the atomizer boom was not included in the simulations the skewness was not significantly affected by flights greater than 4 inches. With the atomizer boom in place however skewness increased with flight height across the entire tested range.  Recall that an increasing skewness is an indicator of more strands being concentrated on the downward rotating half of the drum.  A possible explanation for this discrepancy is that the strands that detached prematurely from the longer flights tended to contact the top of the atomizer boom.  These strands then traveled over the boom and descended on the downward rotating half of the drum, instead of the upward rotating half or near the drum center.  This had a positive impact on the skewness.   Conversely, when the flights were relatively short and the strands were not carried as far up the blender wall before detaching, many of the strands collided with the side of the atomizer boom during their decent.  These strands were unable to travel as far across the blender drum, resulting in a lower, or more negative, strand distribution (Figure 41). fr -76-  2-inch flights   6-inch flights   Figure 41.  Simulation images showing the dispersion of strands across the blender diameter when there is (top-left) no atomizer boom and there are 2 inch flights, (top-right) no atomizer boom and there are 6 inch flights, (bottom-left) an atomizer and there are 2 inch flights, and (bottom-right) an atomizer boom and there are 6 inch flights.  In all cases there were 16 flights and the blender rotated at 23.39 RPM.  The skewness decreased consistently with an increasing fill level when the atomizer boom was not present.  This was a result of the fixed blender capacity and the inability of the blender to lift, carry, and disperse the increasing amount of strands across the blender diameter.  With the atomizer boom in place this same trend was not observed across the tested range.  In fact at a 20% fill level the relationship between the predicted skewness and fill level became positive.  This change in behavior is a result of strands becoming wedged between the atomizer boom and the blender wall.  When the fill level reaches a particular point, in this case around 20%, there is a chance that collections of strands will become wedged in this region (Figure 42).  The collection of strands is then carried over the atomizer boom and deposited on the opposite side of the drum, positively affecting the skewness. Because these strands are forced together between the boom and blender wall, there is also a greater chance that they will become interlocked and move as a clump through the drum, No atomizer boom Atomizer boom -77- causing the phenomenon to repeat itself.  This strand behavior may be a contributing factor to surging in blenders.  Figure 42.  Simulation image showing strands as they become wedged between the atomizer boom and blender wall when operating at elevated fill levels, indicated by the dashed oval. In this case the blender is ¼ full and is equipped with 8, 4 inch flights and is rotating at 28.07 RPM.  Surging occurs when a large number of strands become mechanically interlocked and a portion of these strands are lifted by the flights.  Those strands that are not supported by the flights, but instead are being lifted because they are mechanical interlocked with those strands that are supported, eventually break free and descend as a clump of strands.  This clump of strands overwhelms the flights that they fall upon and the process continues.  Once this process begins it will typically perpetuate until there is a disruption, for example when the affected strands are discharged from the blender.  Unfortunately, the resin distribution amongst those strands will be generally poor.  5.3.1.3 Kurtosis In addition to skewness, kurtosis was also used to describe the distribution of strands across the drum diameter.  While skewness is an indicator of how symmetric the strand distribution is between the upward rotating and downward rotating half of the blender, kurtosis is an indicator of the uniformity of the strand distribution across the blender diameter.  If the strands were normally distributed the kurtosis would be 0.  For these simulations however, a uniform distribution is sought and is obtained for a kurtosis value of –1.2.  Wedge region -78- Using an ANOVA to determine the significant effects it was found that none of the main effects were significant; however, three of the interactions were (Table 33).  The most notable interaction was between the number of flights and the flight height.  This combination is present in all three of the significant interactions shown in Table 33.  The model for predicting the kurtosis is shown in Equation 15 and yields an F-value of 17.8156 (p-value < 0.0001), which is significant at a 95% confidence level (α = 0.05).  Table 33.  List of effects for the kurtosis showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. Factor p-value Number of flights x Flight height 0.0056 Number of flights2 x Flight height 0.0243 Number of flights x Flight height2 0.0442 Factor p-value Number of flights 0.7843 Flight height 0.5681 Number of flights2 0.1128 Number of flights x Flight height 0.0056 Flight height2 0.1041 Number of flights2 x Flight height 0.0243 Number of flights x Flight height2 0.0442  2 212 2 1 2 2 21 2 121 0770.004115.01599.1 6924.11999.08225.153111.68071.47 XXXXX XXXXXK −− +++−−=               [15] where: K is the predicted kurtosis, X1 is the number of flights, and X2 is the flight height in inches.  In order to facilitate the interpretation of these results the graphs shown in Figures 43 and 44 were generated in SAS.  These graphs present four combinations of the number of flights and the flight height.  Figure 43 shows kurtosis with the flight height fixed at 4 inches and the number of flights at 4 and 16, while Figure 44 shows kurtosis with the number of flights fixed at 14 and the flight height at 2 and 6 inches.  As shown in the graphs, the combination of effects had a considerable impact on the kurtosis trends.  Note that the y-axis scale is not the same for the top and bottom sets of graphs in both figures; however, the graphs showing the relationship between the kurtosis and number of flights (left) in Figure 43 are in fact the same except for the 95% confidence interval, which is unique to the chosen factor level.  This is also true for the graphs showing the relationship between the kurtosis and the flight height (right) in Figure 44. -79-   Figure 43.  Prediction profiles generated in SAS showing the impact of the (left) number of flights on the relationship between (right) the kurtosis and the flight height.  The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs.    Figure 44.  Prediction profiles generated in SAS showing the impact of the (right) flight height on the relationship between (left) the kurtosis and the number of flights.  The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs.  -80- As the number of flights increased from 4 to 16 the significance of flight height quickly diminished.  With only 4 flights, the kurtosis decreased quickly with increasing flight height. With 16 flights however, kurtosis increased slowly with increasing flight height, but overall the trend was insignificant.  Building upon the skewness discussion and interpretation, these results were likely caused by the combination of the blender fill level and the capacity of the blender to lift and disperse strands.  With only a few relatively short flights, the blender capacity was low.  As a result, the majority of the strands remained in the lower-right quadrant of the drum and the quantity of strands that were lifted out of this quadrant and dispersed was insignificant.  With only 4 flights, increasing the length of the flight had a large impact on the capacity and the resulting kurtosis.  As one might expect, increasing the number of flights diminished the impact of increasing flight height due to the strands being spread across more flights.  Focusing now on the scenario where the number of flights was fixed at 14, as the flight height increased from 2 to 6 inches the impact of the number of flights on the kurtosis changed considerably.   With 2 inch flights, increasing the number of flights caused the kurtosis to decrease. This was true up until 13 flights, after which the kurtosis stabilized at around –1.4.  With 6 inch flights the kurtosis increased when there were 4 to 10 flights and then decreased when there were 13 to 16 flights; however, the difference was only minimally significant across this latter range.  This was consistent with the previous scenario and the skewness findings.  With 2 inch flights, increasing the amount of flights had a significant impact on the capacity of the blender to lift and disperse strands. With 6 inch flights the relationship between kurtosis and the number of flights became considerably less significant as the demand for additional capacity decreased.  5.3.1.4 Effect of an atomizer boom on the kurtosis results The presence of an atomizer boom in the simulations did not impact those effects that were found to be significant according to the ANOVA selection method. It did however impact the significance of the number of flights – flight height interaction on the kurtosis (Table 34, Figures 45 and 46).  With 16 flights the relationship between the flight height and kurtosis went from marginally positive to significantly negative (Figure 45).  One explanation for this occurrence is that the atomizer boom helps disperse strands more evenly on either side of the drum.  This is because as the strands fall on top of the boom they slide off on both sides. -81- However, in order for this to occur, the detachment point of the strands must be higher than the boom so that they may fall on top of it.  This is why the kurtosis became highly positive with shorter flights.  As discussed previously, with shorter flights the strands collide with the side of the boom and then fall in a near perfect vertical direction to the bottom of the drum. This caused a spike in the frequency of strands falling within a narrow region on the upward rotating side of the atomizer boom.  The relationship between the number of flights and kurtosis remained relatively unchanged with the inclusion of the atomizer boom when the flight height was set at 2 and 6 inches. The model for predicting the kurtosis is shown in Equation 16 and yields an F-value of 11.0681 (p-value < 0.0001), which is significant at a 95% confidence level (α = 0.05).  Table 34.  List of effects for the kurtosis when an atomizer boom is present, showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. Factor p-value Number of flights x Flight height 0.0106 Flight height2 0.0279 Number of flights2 x Flight height 0.0070 Number of flights x Flight height2 0.0438 Factor p-value Number of flights 0.6595 Flight height 0.6766 Number of flights2 0.0880 Number of flights x Flight height 0.0106 Flight height2 0.0279 Number of flights2 x Flight height 0.0070 Number of flights x Flight height2 0.0438  2 212 2 1 2 221 2 121 0503.00413.0 9161.03854.11921.03962.133881.53048.42 XXXX XXXXXXK −− +++−−=             [16]  where: K is the predicted kurtosis, X1 is the number of flights, and X2 is the flight height in inches.     -82-   Figure 45.  Prediction profiles generated in SAS showing the impact of the (left) number of flights on the relationship between (right) the kurtosis and the flight height when an atomizer boom is present.    Figure 46.  Prediction profiles generated in SAS showing the impact of the (right) flight height on the relationship between (left) the kurtosis and the number of flights when an atomizer boom is present. -83- 5.3.1.5 Average time a strand spent in the resination region The average time a strand spent in the resination region for a fixed number of revolutions was shown to be strongly related to the flight height and the blender rotational speed (Figure 47).  The average time decreased with both increasing flight height and rotational speed.  The model for predicting the average time a strand spends in the resination region is shown in Equation 17 and yields an F-value of 33.8102  (p-value < 0.0001), which is significant at a 95% confidence level (α = 0.05).  42 0794.01124.05407.3 XXt −−=                 [17] where: t is the predicted average time in seconds, X2 is the flight height in inches, and X4 is the blender rotational speed in rpm’s.    Figure 47.  Prediction profiles generated in SAS showing the relationship between the average time spent in the resination region and the (left) flight height and (right) blender rotational speed.  The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs.  As demonstrated in Figure 48, the negative relationship between the flight height and the average time spent in the resination region as well as the rotational speed and the average time was caused by similar phenomena.  With relatively small flights and/or low rotational speeds the strands tended to cluster and roll amongst themselves in the lower-right drum quadrant.  These strands fell slowly through the resination region as they moved within the cluster.  In addition, because they were clustered within a small area the strands did not have to travel far before making a complete revolution.  The strands therefore passed more frequently through the resination area. As the flight height and/or rotational speed increased the rolling motion decreased as a greater fraction of the strands were lifted by the flights and A ve ra ge  ti m e in  re si na tio n re gi on  (s ec ) A ve ra ge  ti m e in  re si na tio n re gi on  (s ec ) -84- dispersed across the blender.  These strands passed relatively quickly through the resination region on their descent and made fewer revolutions.  Low speed   High speed   Figure 48.  Simulation images showing (top-left) the clustering of strands at relatively low speeds with 2-inch flights, (top-right) the dispersion of strands at relatively high speeds with 2-inch flights, (bottom-left) the clustering of strands at relatively low speeds with 6-inch flights, (bottom-right) the dispersion of strands at relatively high speeds with 6-inch flights. Note that strands cluster more with shorter flights and/or slower blender rotational speeds. The blender rotational speeds were 18.71 RPM and 28.07 RPM respectively.  Although the overall objective of an operation is to devise a set of operating and design parameters that results in the strands spending the maximum time possible in the resination region, there are other criteria that must first be met.  For instance, the strands should be well dispersed across the blender diameter.  Scenarios where there is clustering and rolling of strands (Figure 48) is not desirable because only the strands on the surface of the cluster would become resinated.  As reported by Smith (2006), PF-resin does not spread well after its initial contact with the wood substrate.  Therefore, blending operations cannot rely on the smearing and transfer of resin between strands for resination purposes, as is the case with particleboard blending (Maloney 1993).  PMDI-resin is able to transfer; however, this 2-inch flights 6-inch flights -85- scenario is still not desirable as it is not an efficient use of resin and the blender (Smith 2006).  5.3.1.6 Effect of an atomizer boom on the average time a strand spent in the resination region The inclusion of an atomizer boom in the simulations had an effect on the selection of significant factors, ultimately reducing the number of factors that impacted the predicted average total time a strand spends in the resination region from two to one.  The model for predicting the average time a strand spends in the resination region is shown in Equation 18 and yields an F-value of 33.4386  (p-value < 0.0001), which is significant at a 95% confidence level (α = 0.05).  40772.00912.3 Xt −=                   [18] where: t is the predicted average time in seconds, and X4 is the blender rotational speed in rpm’s.  With the atomizer boom present only the blender rotational speed was significant.  It is not surprising that the flight height was no longer significant.  As was shown before, the principal difference between the flow pattern of the strands when the blender is equipped with long flights versus short flights is which side of the atomizer boom the majority of strands fall on.  With longer flights the strands are more likely to fall on top of the atomizer boom and slide off on either or both sides of the blender.  With shorter flights the strands tend to collide with the side of the boom and fall almost entirely on the upward rotating side of the blender.  In either case the strands fall near vertically to the bottom of the drum after collision with the boom.  This near vertical drop of the strands through the resination region for both scenarios resulted in a relatively short period of time spent in that region.  This is compared to the case where there is no atomizer boom and the associated longer parabolic trajectory of a strand that detaches from the drum and does not collide with a boom.  5.3.1.7 Discussion The results showing the general relationship between the factors and response variables confirmed many of the previous speculations regarding the operation of rotary drum blenders.  In particular, the results show that the skewness increased with an increasing -86- number of flights, flight height, and blender rotational speed within the tested ranges.  The impact of flight height on the skewness diminished as the flight height increased, likely due to early detachment that is a result of the strands being closer to the axis of rotation of the drum.  Increasing the blender fill level had the opposite effect on the skewness, causing it to decrease.  These interactions are largely related to the overall capacity of the blender to lift, carry, and finally disperse a fraction of the total strands across the blender diameter.  The capacity is broadly determined by two factors, the size of the individual flight and the number of flights that the strands are spread across.  In addition to confirming some previous thoughts regarding blending dynamics, the results also presented several interesting findings.  Most notable was the significance of the interaction between the flight height and the number of flights on the kurtosis.  This suggests that during the manufacturing of blenders it is vital that care and attention be focused on the selection and placement of flights.  Once the blender is in operation it is very difficult to change either of these parameters.  Further, it was shown that the average time a strand spent in the resination region was negatively related to the flight height and the rotational speed. Upon visual inspection of the results it was determined that, although strands spent more time in the resination region with smaller flights and/or at lower speeds, the additional time spent in the region was not beneficial because a considerably smaller percentage of the strands were actually exposed to the atomized resin.  The impact of the atomizer boom on the strand dynamics was largely dependent on whether or not the strands were carried high enough by the flights to cascade over top of the atomizer boom.  In either case the strands tended to stream off of the respective side(s) of the boom. In several extreme cases where the blender was filled ¼ full the strands became wedged between the atomizer boom and the drum wall, resulting in a surging effect.  5.3.2 Research applications These results were further analyzed based on two perspectives: the wood strand-based product manufacturers (end-users), and the blender manufacturers.  This work focused on the opportunities both groups have for optimizing their blenders given the available resources, such as the ability for an operation to make changes within a short timeframe.  The goal is to -87- gain unique insight into the impact each of the aforementioned segments may have on the bulk strand dynamics by making changes to the blender design and/or operating parameters.  5.3.2.1 Wood strand-based product manufacturers For existing operations it may not be possible or practical to change the number of flights or flight height.  While the flight height can be changed by purchasing new flights and installing them during an extended downtime, the number of flights is determined by the drilled hole pattern in the blender drum and would require considerable time to change.  Generally however, neither alteration is desirable. In addition, the blender fill level is largely determined by the demand from the proceeding process and the feed rate from the dry strand bins.  While there is a target fill level, this level can fluctuate during disturbances in the manufacturing process. This leaves the blender rotational speed as the only factor that can be changed accordingly while the process is running.  Figure 49 shows the contour graph for the skewness based on the fill level and simulated blender rotational speed for four common flight heights: 3, 4, 5, and 6 inch with no boom present.  The number of flights was fixed at 14, or approximately every 16 inches along the circumference, which is typical for an industrial blender (Coil 2007b; Coil 2008).   In addition to the skewness, the predicted average time a strand spends in the resination was also included in the graphs.  The aim is to select operating parameters that result in a skewness of 0 while maximizing the average time spent in the resination region.  All of the contour graphs are for a 6 foot simulated blender.  Although this diameter is smaller than that of typical industrial blenders, as outlined in Section 5.2 it is anticipated that the results of this study can be scaled for use on an industrial blender.   -88-    Figure 49.  Contour graphs for the skewness based on the fill level and blender rotational speed using 3, 4, 5, and 6-inch flights.  The number of flights has been fixed at 14.  The graphs suggest that as the fill level decreases the rotational speed must also decrease to maintain a skewness of 0.  This relationship becomes more apparent as the flight height increases.  For example, with 3 inch flights, a drop in the fill level from 25% to 7% only requires a slight reduction in speed from 25.5 RPM to 24 RPM.  However, with 6 inch flights, a drop in the fill level from merely 25% to 19% requires a reduction in speed from 25 (sec) (sec) (sec) (sec) -89- RPM to 18.9 RPM.  Throughout the wood strand-based product industry, the growing trend has been to use higher flights in conjunction with larger diameter blenders to increase capacity.  Consequently, if it is assumed that this relationship between the blender fill level and rotational speed remains true as the drum diameter increases, operations run the risk of operating their blenders sub-optimally with only slight fluctuations in the blender feed rate. Therefore, it is imperative that operations link the blender rotational speed with the blender feed rate.  This way the process could adapt accordingly to changes in the strand flow and the resulting blender fill level.  Alternatively, shorter flights could be employed if blender capacity is not a concern.  This would reduce the impact strand flow fluctuations have on the blending environment.  5.3.2.2 Effect of the atomizer boom for wood strand-based product manufacturers The contour graphs indicate a sizeable shift in the required rotational speed given a specific fill level when an atomizer boom is present (Figure 50). In addition to this, the relationship between the blender fill level and the blender rotational speed was no longer strictly positive, instead all four of the flight heights included exhibit a negative relationship above a particular fill level.           -90-   Figure 50.  Contour graphs for the skewness based on the fill level and blender rotational speed using 3, 4, 5, and 6-inch flights when an atomizer boom is present.  The number of flights has been fixed at 14.  Until the point of inflection where the required rotational speed begins to decrease for an increasing fill level, the required rotational speed to achieve and maintain a skewness of 0 is considerably higher when the atomizer boom is present.  As an example, with 14-4 inch flights, and operating at 18% full, the required rotational speed when an atomizer boom is present is 27 RPM, versus less that 22 RPM when the atomizer boom is not present.  The (sec) (sec) (sec) (sec) -91- reason for this necessary increase in rotational speed is because the boom impedes on the trajectory of strands.  When the atomizer boom is not present the strands can travel unobstructed through the center of the blender after detaching from the flights.  When the atomizer boom is included however, many of those strands collide with the side of the boom. As a result, the blender must rotate faster to increase the centrifugal force acting on the strands so that they detach at a later point and fall on top of the atomizer boom, or at least so that the strands are dispersed more evenly on either side of the boom.  Interestingly, above a certain fill level the required rotational speed begins to decrease.  This was not observed when the atomizer boom was not present.  This change in behavior is due to the phenomenon first discussed when investigating the impact of the atomizer boom on the skewness, where it was found that strands became wedged between the atomizer boom and blender wall at elevated fill levels.   As the cluster of strands travels over top of the atomizer boom they eventually descend on the downward rotating side of the blender, increasing the skewness.  The easiest way to avoid this from occurring is to reduce the blender rotational speed.  Unfortunately, this results in considerably fewer strands being lifted and dispersed by the flights, instead the strands cluster in the lower-right drum quadrant (Figure 38).  As shown in the contour graphs presented in Figure 50, an alternative solution is to use higher flights.  Higher flights reduce the dependency of the fill level on the required rotational speed.  5.3.2.3 Blender manufacturers Unlike the end users of rotary drum blenders, blender manufacturers have nearly complete flexibility on the blender design.  Given a specific set of operating parameters, they can prescribe a specific flight design and drill the holes for a particular number flights that would result in the optimal strand distribution. As a result, blender manufacturers should be most interested in knowing the relationship between flight height and the required number of flights and its impact on the strand distribution.  This interaction was shown previously to have a significant impact on the strand distribution.  Blenders are designed and sourced based on the required maximum throughput (Coil 2008). The combination of the required throughput and the design and operating parameters will ultimately determine the blender fill level.  Once the blender design and operating parameters -92- have been established for this maximum fill level, it was shown that the strand distribution can be controlled by reducing the rotational speed accordingly as the fill level fluctuates below this maximum point.  During the initial sourcing stage however, it is necessary to first establish the maximum fill level and rotational speed so that the flight height and placement can be determined accordingly.  The graphs shown in Figure 51 were generated assuming the maximum fill level was 25%. They illustrate the impact various rotational speeds and combinations of flight height and number of flights have on the predicted skewness and kurtosis of the strand distribution and the predicted average time a strand spends in the resination region.  While blender manufacturers should strive to achieve a kurtosis of -1.2 and to maximize the average time a strand spends in the resination region, balancing the distribution of strands on either side of the blender is perhaps the most important characteristic to accomplish as an initial step.  A balanced distribution is identified by a skewness of 0.  Figure 51 suggests that the required number of flights and flight height are largely dependent upon each other as well as the rotational speed.  Generally, as the number of flights increases the flight height that maintains a skewness of 0 decreases.  Further, the required number of flights and/or flight height also decreases with increasing rotational speeds.  From previous work it has been shown that flights between 4 and 5 inches in height appear to strike the optimal balance between capacity and control over strand placement.  Based on this target flight height, the required number of flights ranges from approximately 15 at 23 RPM to 4 at 28 RPM.   When the kurtosis is included in this analysis however, it is shown that there must be at least 11 flights present to achieve a kurtosis of -1.2.  This creates an upper bound for the rotational speed of between 25 and 26 RPM.  Note that the average total time that a strand spends in the resination region has not been included in these graphs to improve legibility.  In all cases, the average total time increases from right to left on the graphs.       -93-    Figure 51.  Contour graphs based on number of flights and flight height.  The rotational speed ranged from 23 to 28 RPM and the fill level was fixed at 25%.  fr fr fr fr fr fr -94- 5.3.2.4 Effect of the atomizer boom for blender manufacturers The atomizer boom had a significant effect on the resulting contour graphs.  Given the specified boom location it is virtually impossible to achieve a kurtosis of -1.2, or at least a relatively even strand distribution, without using either 4 or 16, 6 inch flights.  This is consistent with the findings of the Overall Predictive Trends.  However, with 4 flights the strands are not well positioned to come into contact with the resin discharging from the atomizers (Figure 38).  The general relationship between the number of flights and the flight height that maintained a skewness of 0 remained similar with and without the atomizer boom.  However, the required flight height that corresponds to a particular number of flights increased across all of the tested rotational speeds when the fill level was fixed at 25%.  For example, at 26 RPM and with 11 flights, the required flight height increased from approximately 3.8 inches to 4.6 inches when the boom was included.  This increase was necessary because the strands needed to be lifted higher, or to a larger angle, before detaching from the flights.  This caused more of the strands to fall on top of the atomizer boom and disperse into the downward rotating half of the blender.          -95-    Figure 52.  Contour graphs for the inclusion of an atomizer boom based on number of flights and flight height.  The rotational speed ranged from 23 to 28 RPM and the fill level was fixed at 25%. fr fr fr fr fr fr -96- In addition to an increased required flight height, the results also show opportunity for optimizing the configuration of the atomizer mounts.  The alignment of the mounts ultimately determines the alignment of the atomizers, whether they be vertical or at an angle.  Most existing operations have their atomizer mounts oriented vertically. While the option is now available for a staggered mount design (Appendix C), it is still relatively uncommon for atomizer mounts to be positioned at an angle.  The simulation images show however that the angle in which the strands stream off of the atomizer boom, or in front of the atomizer itself, is largely dependent on the rotational speed (Figure 53).  In fact, this angle ranged from 14° at 18.71 RPM to 7° at 28.07 RPM.  This suggests that the angle of the atomizer mount should be adaptable to changes in the rotational speed of the blender.  If the strands collide with the atomizer, or come within close proximity, individual strands will collect a disproportionate amount of resin, starving other strands of resin.   Figure 53.  Simulation images showing the streaming of strands off of the atomizer boom at (a) 18.71 RPM, (b) 23.39 RPM, and (c) 28.07 RPM.  The simulated blenders were each equipped with 8-4 inch flights and filled 1/4 full.  The angles that the strands stream off of the boom are approximately 14°, 12°, and 7° from vertical respectively. 14° 12°  7° (a) (b) (c) 18.71 RPM 23.39 RPM 28.07 RPM -97- 5.3.2.5 Discussion The analyses focused on the end users of rotary drum blenders and the blender manufacturers presented several considerable implications and opportunities. First, these findings reveal whether or not an operation is even capable of achieving the desirable strand distribution. For instance, with 14-4 inch flights and operating with fill levels much less than 14%, it is unlikely that a skewness of 0 can ever be achieved, and the minimum fill level whereby this target can still be reached only increases with increasing flight heights.  Fortunately, most operations tend to run their blenders between 25% and 50% full anyways, so this may only be an issue during severe disruptions in the process.  Second, these findings suggest that operations should link the blender rotational speed with the factors that impact the blender fill level, such as the feed rate and blender tilt angle.  As the fill level increases the rotational speed should also increase to maintain the optimal blending dynamics.  Because of the extent of automation that is present in most operations, linking these processes would not be an insurmountable challenge.  The challenge is knowing the relationship between the factors; however, based on the results with 5 and 6 inch flights, this challenge is certainly worth overcoming because of the significant impact changes to the fill level have on the skewness when the rotational speed remains unchanged.  Third, this modeling approach could be used for determining when blender maintenance is required.  During normal operation the inside of a blender drum becomes coated with strands, effectively reducing the inside drum diameter and changing the flight profile.  By modeling the strand dynamics with different drum diameters and flight shapes, it would be possible to develop a threshold for an acceptable amount of strand build up before it will begin significantly affecting the strand dynamics.  Fourth, as was seen in the Overall Predictive Trends, the interaction between the flight height and the number of flights had a significant impact on the strand dynamics.  This is where considerable implications lie for the blender manufacturers.  The optimal combination of flight height and number of flights is dependant on the maximum fill level and rotational speed.  The results show that if the blender is sourced and designed using these expected maximum values, then the rotational speed alone can be used for counteracting any downward fluctuations in the fill level during operation. -98-  Finally, the inclusion of an atomizer boom proved to have a significant impact on the strand dynamics.  Diligence must be practiced when selecting the position for the atomizer boom(s) and selecting a maximum fill level.  As was demonstrated, when the fill level exceeds a particular point there is an increased risk that the strands will begin traveling as clusters over top of the atomizer boom, resulting in surging.  Also, the angle that the strands stream off of the boom, or immediately in front of the atomizers, should be taken into consideration when the orientation of the atomizer mounts is decided.  The results suggest that this angle should be adjustable to cope with changes to the blending conditions.  5.4 Conclusions Response surface methodology proved to be an effective method for reviewing the impact multiple blender design and operating parameters have on the wood strand dynamics, as described by the skewness and kurtosis of the strand distribution and the average time a strand spent in the resination region.  This technique was used for evaluating the results on three levels: an overview of the general relationship between the factors and response variables, the implications this research has for end users of rotary drum blenders, and finally the implications this research has for blender manufacturers.   The findings of this research are summarized below:  General • All four blender design and operating parameters significantly affected the skewness, o With increasing the number of flights or blender rotational speed the skewness increased, o With increasing the fill level the skewness decreased, and o With increasing the flight height between 2 and 3 inches the skewness increased, otherwise the skewness stabilized for flights 4 inches or more in height. • Only the interaction between flight height and the number of flights had a significant effect on the kurtosis, • Increasing the flight height and blender rotational speed both caused the average time a strand spent in the resination region to decrease, and -99- • The inclusion of an atomizer boom had a significant effect on the bulk strand dynamics, particularly at elevated fill levels.  Specific • The blender rotational speed and tilt angle should be linked to the blender feed rate to autocorrect for disruptions in the process, • Considerable attention should be made during the initial sourcing and design of a blender to find the optimal combination of flight height and number of flights for a specific maximum rotational speed and fill level, and • An adjustable atomizer mount angle would create a significant benefit when/if changes in the blending conditions occur.  This angle should be linked to the blender rotational speed.       -100- CHAPTER 6  SUMMARY AND FUTURE WORK.  This research project was divided into three distinct phases.   The first phase laid the groundwork before work could begin using the RDBM.  Perhaps the most critical input parameter for a model that simulates the rotary drum blending process is the static friction coefficients.  Because of the challenges associated with systems of material surfaces where at least one wood surface is present (as discussed in Section 2.3), specific static coefficient of friction values are not readily available in the published literature.  As a result, a series of laboratory experiments were conducted.  The objectives were to first determine the impact of contact pressure and grain alignment on the coefficient.  And second, to determine the relationship between the static coefficients of friction for systems involving two wood strand surfaces versus systems involving a single wood strand surface and a HDPE surface.  The findings of this work suggested that the contact pressure has a significant effect on the coefficient of static friction.  It also found that the two systems were related by a ratio of approximately 2:1 respectively.  Although the absolute coefficient of friction values were ultimately adjusted for the final RDBM, this 2:1 ratio remained in effect.  During the second phase of the project it was determined which of the six material and interaction input parameters were significant to the bulk strand dynamics in the RDBM. Together with software literature (DEM Solutions 2008), it was shown that the optimal combination of input parameters will not only result in representative strand flow dynamics, but will also minimize the overall required processing time for a simulation.  A series of simulations were conducted in a systematic manner to find the combination of those significant parameters where the simulated results closely resembled those obtained using a 6 foot laboratory blender.  It was also during this phase that three quantification techniques were decided upon for measuring the strand flow.  Skewness and kurtosis were used for quantifying the strand distribution across the drum diameter, and the average time a strand spent in the resination region was used for quantifying the opportunity a strand had to become resinated.  -101- After the RDBM had been calibrated for this particular model setup (including the strand size and shape and blender diameter) and the effectiveness of the quantification techniques had been tested, an exploratory study was designed to investigate the significance of several blender design and operating parameters on the bulk strand flow.  These parameters included: the flight height, number of flights, blender rotational speed, and blender fill level on the bulk strand flow.  In general the impact of these properties on the bulk strand flow, as described by the skewness and kurtosis of the strand distribution across the drum diameter, could be explained by focusing on their influence on the blending system capacity, or the ability of the blending system to lift, carry, and disperse strands across the blender.  As the capacity increased the strands detached from the drum circumference later and traveled further across the diameter on their decent.  As the capacity decreased, or the strand volume increased, the strand loading per flight increased resulting in a relatively early detachment point for a large quantity of strands.  Increasing the flight height, number of flights, and/or rotational speed all resulted in an increased blender capacity.  6.1 Future Work The exploratory component of this research was relatively limited, only focusing on two blender design and two operational parameters.  A more thorough investigation of a broader range of parameters would be a significant contribution to both industry and academia.  The range of possible factors to consider has increased substantially since the beginning of this project.  This is because of advancements in both the software and computing capabilities.  The most obvious and probably worthwhile factors to consider are the flight shape and blender diameter.  This research only focused on flights that were 90o to the drum wall.  In reality, flights are typically purchased bull-nosed or become bull-nosed while in service due to the buildup of strands along the surfaces.  The effect of flight shape is likely significant to the strand flow.  The angle of the leading face of the flight would effectively cause the strands to detach earlier.  Examining the effect of the drum diameter would also be worthwhile.  This research only focused on a 6 foot diameter blender.  This was partially due to software and computing limitations, but mostly because it coincided with the size of the laboratory blender. Simulating a 6 foot blender therefore allowed for validation experiments to be carried out as -102- required.  Industrial blenders range in size from 8 to 11 feet however.  As a result, focusing on larger diameter blenders would certainly be worthwhile from an industrial perspective. Fortunately, software and computing capabilities will now permit simulating larger diameter blenders in a timely manner.  Because of these software and computing advancements it is also now possible to extend the length of the simulated blender.  This research relied on a 1 foot section of blender. Extending the length to even 6 feet would enable one to examine the effect of blender tilt angle on the residence time.  Residence time, or the time that a strand spends in the blender, ultimately affects the opportunity strands have to become resinated.  If the residence time must be increased the blender tilt may be either decreased or the drum lengthened.  In addition to scaling the model towards a full sized, industrial blender, it would also be worthwhile to examine the impact the atomizer boom location has on the strand flow.   For the study presented in Chapter 5 the atomizer boom was placed in a position typical of today’s industrial blenders.  This location may not be the optimal solution however.  Ultimately, future research should focus first on determining the validity of scaling the 6 foot by 1 foot RDBM to an industrial blender.  Additional research can then be pursued to investigate the effect of flight shape and atomizer boom location on the strand flow. -103- LITERATURE CITED Adobe Systems Incorporated. 2007. Adobe® premiere® pro CS3 user guide for windows® and mac OS. California, USA. American Standards for Testing and Materials. 2002a. Standard guide for measuring and reporting friction coefficients. ASTM G 115-04. In . West Conschohocken, Pa: ASTM. ———. 2002b. Standard test method for coefficient of static friction of uncoated writing and printing paper by use of the inclined plane method. ASTM D 4918-97. In. West Conschohocken, Pa: ASTM. Anonymous. 2007. Convert MOD files to MPG or AVI - JVC Everio HDD camcorder. [cited March 5 2008]. Available from http://i.nconspicuo.us/2007/01/26/convert-mod-files-to- mpg-or-avi-jvc-everio-hdd-camcorder/ Beattie, N. W. 1984. The lignex spinning disc blender. Paper presented at Proceedings of the Eighteenth Washington State University International Particleboard/Composite Materials Series Symposium, Pullman, WA. ———. 1981. Improved blending capabilities for waferboard. Paper presented at 1980 Canadian Waferboard Symposium Proceedings - Special Publication SP505E. Bejo, Laszlo, Elemer M. Lang, and Tamas Fodor. 2000. Friction coefficients of wood-based structural composites. Forest Products Journal 50, (3): 39-43. Bertrand, F., L. -A Leclaire, and G. Levecque. 2005. DEM-based models for the mixing of granular materials. Chemical Engineering Science 60, (8-9): 2517-31. Bicanic, Nenad. 2004. Discrete element method. In Encyclopedia of computational mechanics., eds. Erwin Stein, Rene de Borst and Thomas J. R. Hughs. Vol. 1. Chichester, West Sussex: John Wiley & Sons. Chiu, S. T., and W. B. Scott. 1981. A liquid phenolic resin for waferboard manufacture. Paper presented at 1980 Canadian Waferboard Symposium Proceedings - Special Publication SP505E. Cleary, Paul W. 2006. Axial transport in dry ball mills. Applied Mathematical Modelling 30, (11): 1343. ———. 1998. Predicting charge motion, power draw, segregation and wear in ball mills using discrete element methods. Minerals Engineering 11, (11): 1061. Cleary, Paul W., Rob Morrisson, and Steve Morrell. 2003. Comparison of DEM and experiment for a scale model SAG mill. International Journal of Mineral Processing 68, (1-4) (1): 129-65. -104- Coil, G. K., and J. B. Kasper. 1984. A liquid blending system developed by Mainland Manufacturing. Paper presented at Proceedings of the Eighteenth Washington State University International Particleboard/Composite Materials Series Symposium, Pullman, WA. Coil, Gerald K. 2002. Advantages of precision atomization. Paper presented at Washington State University Thirty-Sixth International Wood Composite Materials Symposium Proceedings, Pullman, WA. Coil, Mike. 2008. Typical blender volume and drum speeds. Personal communication. April 17. ———. 2007a. Mechanical properties of UHMW and HDPE. Personal communication. July 29. ———. 2007b. Schematic of atomizer spray pattern. Personal communication. September 20. Collop, Andrew C., Glenn R. McDowell, and York Lee. 2004. Use of the distinct element method to model the deformation behavior of an idealized asphalt mixture. International Journal of Pavement Engineering 5, (1). Cook, Mark. 2008. Case 00001154: Rolling friction. Cundall, P. A. 1989. Numerical experiments on localization in frictional materials. Archive of Applied Mechanics 59, (2): 148-59. ———. 1971. A computer model for simulating progressive large scale movements in blocky rock systems. Nancy, France. Cundall, P. A., and O. D. L. strack. 1979. A discrete numerical model for granular assemblies. Geotechnique 29, (1): 47-65. Davis, E. W. 1919. Mechanics of the ball-mill. AIME Transactions 61: 250-96. DEM Solutions. 2008. EDEM 1.3 user guide, revision 12B. [cited March 5 2008]. Available from http://www.dem- solutions.com/downloads/manuals/edem131/EDEM1.3.1_user_guide.pdf. Dixon, Audrey. 2008. Focus on OSB north america. Wood Based Panels International. February/March 2008. Djordjevic, N., F. N. Shi, and R. Morrison. 2004. Determination of lifter design, speed and filling effects in AG mills by 3D DEM. Minerals Engineering 17, (11-12): 1135. Domenech, A., T. Domenech, and J. Cebrian. 1987. Introduction to the study of rolling friction. American Journal of Physics 55, (3): 231-5. -105- Gunn, John M. 1972. New developments in waferboard. Paper presented at Proceeding of the Sixth Washington State University Symposium on Particleboard, Pullman, WA. Higgs, Richard. 2008. Focus on OSB rest of the world. Wood Based Panels International. February/March 2008. Hirsch, E. D., Joseph F. Kett, and James Trefil. 2002. The new dictionary of cultural literacy. 3rd ed. Boston: Houghton Mifflin Company. Industry Canada. 2007. Wood-based panel products: Technology roadmap - oriented strand board. [cited March 26 2007]. Available from http://strategis.ic.gc.ca/epic/site/fi- if.nsf/en/oc01511e.html. International Wood Markets Group. 2006. 2006 edition wood markets: The solid wood products outlook 2006 to 2010. Vancouver, Canada: International Wood Markets Group Inc. Kaneko, Yasunobu, Takeo Shiojima, and Masayuki Horio. 2000. Numerical analysis of particle mixing characteristics in a single helical ribbon agitator using DEM simulation. Powder Technology 108, (1) (3/1): 55-64. Kleinbaum, David G. 1988. Applied regression analysis and other multivariable methods. Duxbury series in statistics and decision sciences. 2nd ed. Boston, Mass.: PWS-Kent Pub. Co. Lin, F. S. 1984. The globe blending system. Paper presented at Proceedings of the Eighteenth Washington State University International Particleboard/Composite Materials Series Symposium, Pullman, WA. Louisiana-Pacific Corporation. Investor presentation spring 2008. [cited July 23 2008]. Available from http://library.corporate- ir.net/library/73/730/73030/items/296211/InvestorPresentationSpring2008.pdf. Maloney, Thomas M., and E. M. Huffaker. 1984. Blending fundamentals and an analysis of a short-retention-time blender. Paper presented at Proceedings of the Eighteenth Washington State University International Particleboard/Composite Materials Series Symposium, Pullman, WA. Maloney, Thomas M. 1993. Modern particleboard & dry-process fiberboard manufacturing. Updated ed. San Francisco: Miller Freeman. McIvor, R. E. 1983. Effects of speed and liner configuration on ball mill performance. Mining Engineering 35, (6): 617-22. Mishra, B. K., and R. K. Rajamani. 1992. Discrete element method for the simulation of ball mills. Applied Mathematical Modelling 16, (11): 598. -106- Moakher, Maher, Troy Shinbrot, and Fernando J. Muzzio. 2000. Experimentally validated computations of flow, mixing and segregation of non-cohesive grains in 3D tumbling blenders. Powder Technology, 109, (1-3) (4/3): 58-71. Moeltner, Helmut G. 1980. Structural boards for the 1980's. Paper presented at Proceeding of the Fourteenth Washington State University International Symposium on Particleboard, Pullman, WA. Montgomery, Douglas C. 2005. Introduction to statistical quality control. 5th ed. United States: John Wiley & Sons. Mustoe, G. G. W. 2001. Material flow analyses of noncircular-shaped granular media using discrete element methods. Journal of Engineering Mechanics 127, (10): 1017-26. Myers, Raymond H., and Douglas C. Montgomery. 2002. Response surface methodology: Process and product optimization using designed experiments. Wiley series in probability and statistics. 2nd ed. New York: J. Wiley. Nakamura, Hideya, Takayuki Tokuda, Tomohiro Iwasaki, and Satoru Watano. 2007. Numerical analysis of particle mixing in a rotating fluidized bed. Chemical Engineering Science 62, (11) (6): 3043-56. Powell, M. S. 1991. The effect of the liner desgin on the motion of the outer grinding elements in a rotary mill. International Journal of Mineral Processing 31, (3): 163. Pyzdek, Thomas. 2003. The six sigma handbook, revised and expanded. United States: The McGraw-Hill Companies. Rajamani, R. K., B. K. Mishra, R. Venugopal, and A. Datta. 2000. Discrete element analysis of tumbling mills. Powder Technology 109, (1-3) (4/3): 105-12. SAS Institute Inc. SAS OnlineDoc 9.1.3. [cited March 23 2007]. Available  from http://support.sas.com/onlinedoc/913/docMainpage.jsp. Schafer, Benjamin Carrion, Steven F. Quigley, and Andrew H. C. Chan. 2001. Evaluation of an FPGA implementation of the discrete element method. Paper presented at 11th International Conference, FPL, Belfast, Ireland. Serway, Raymond A. 2000. Physics for scientists and engineers, with modern physics. 5th ed. Fort Worth: Saunders College Publishing. Smith, G. D. 2006. Wood 487 glued wood products, course handout. ———. 2005. Direct observation of the tumbling of OSB strands in an industrial scale coil blender. Wood and Fiber Science 37, (1): 147-59. -107- Smith, G. D., and Catalin Gutiu. 2002. Mechanics of OSB rotary drum blender I. no flight vs. one flight at 'zero height'. Internal report. Snedecor, George Waddel, and William Gemmell Cochran. 1980. Statistical methods. 7th ed. Ames, Iowa: Iowa State University Press. Spelter, Henry, David McKeever, and Matthew Alderman. 2006. Status and trends: Profile of structural panels in the United States and Canada. USDA, FPL-RP-636. Stewart, R. L., J. Bridgwater, Y. C. Zhou, and A. B. Yu. 2001. Simulated and measured flow of granules in a bladed mixer—a detailed comparison. Chemical Engineering Science 56, (19) (10): 5457-71. Thibault, Scott. 2008. Telephone discussion related to EDEM renewal and similar applications where EDEM has been successful. May 18. USDA, Forest Products Laboratory. 1999. Wood handbook: Wood as an engineering material. Watkins, W. L. 1981. Some early headaches of the first waferboard plant in Canada. Paper presented at 1980 Canadian Waferboard Symposium Proceedings - Special Publication SP505E. Winchester, Guy. 2005. Cost of goods sold: An analysis of marketplace mechanics affecting resin costs and supply. APA/Engineered Wood Journal. [cited June 11 2008]. Available from http://www.apawood.org/level_b.cfm?content=pub_ewj_arch_f05_resin. World Forest Institute. Wood products trade: Europe. [cited March 25 2007]. Available from http://wfi.worldforestrycenter.org/trade-3.htm. Yang, R. Y., C. T. Jayasundara, A. B. Yu, and D. Curry. 2006. DEM simulation of the flow of grinding media in IsaMill. Minerals Engineering 19, (10) (8): 984-94. -108- APPENDIX A  COEFFICIENT OF FRICTION - SAS ANALYSIS AND RESULTS                              The GLM Procedure                        Class Level Information               Class                     Levels    Values               Orientation                    3    1 2 3               Material_Combination           2    1 2                 Number of Observations Read         210                Number of Observations Used         210                            The GLM Procedure  Dependent Variable: y3                                       Sum of Source                     DF        Squares    Mean Square   F Value Model                      10     6.17918736     0.61791874    134.36 Error                     199     0.91518322     0.00459891 Corrected Total           209     7.09437058                      Source                 Pr > F                     Model                  <.0001                     Error                     Corrected Total            R-Square     Coeff Var      Root MSE       y3 Mean           0.870999     -16.88059      0.067815     -0.401735  Source                     DF      Type I SS    Mean Square   F Value Orientation                 2     0.53410516     0.26705258     58.07 Material_Combination        1     4.31967482     4.31967482    939.28 x3                          1     0.78723955     0.78723955    171.18 x                           1     0.08728987     0.08728987     18.98 x3*Orientat*Material        5     0.45087795     0.09017559     19.61                      Source                 Pr > F                     Orientation            <.0001                     Material_Combination   <.0001                     x3                     <.0001                     x                      <.0001                     x3*Orientat*Material   <.0001  Source                     DF    Type III SS    Mean Square   F Value Orientation                 2     0.09711957     0.04855979     10.56 Material_Combination        1     0.52906674     0.52906674    115.04 x3                          1     0.45125425     0.45125425     98.12 x                           1     0.08342778     0.08342778     18.14 x3*Orientat*Material        5     0.45087795     0.09017559     19.61                      Source                 Pr > F                     Orientation            <.0001                     Material_Combination   <.0001                     x3                     <.0001                     x                      <.0001                     x3*Orientat*Material   <.0001  -109-                                                     Standard Parameter                        Estimate             Error    t Value Intercept                    -.1499945172 B      0.04380096      -3.42 Orientation          1       -.1342523657 B      0.04501753      -2.98 Orientation          2       -.2029989310 B      0.04501753      -4.51 Orientation          3       0.0000000000 B       .                . Material_Combination 1       0.3954160209 B      0.03686604      10.73 Material_Combination 2       0.0000000000 B       .                . x3                           -.1792096345 B      0.02150605      -8.33 x                            0.0000883487        0.00002074       4.26 x3*Orientat*Material 1 1     0.0501600042 B      0.02505086       2.00 x3*Orientat*Material 1 2     0.0576087429 B      0.01987184       2.90                  Parameter                    Pr > |t|                 Intercept                      0.0007                 Orientation          1         0.0032                 Orientation          2         <.0001                 Orientation          3          .                 Material_Combination 1         <.0001                 Material_Combination 2          .                 x3                             <.0001                 x                              <.0001                 x3*Orientat*Material 1 1       0.0466                 x3*Orientat*Material 1 2       0.0042                             The GLM Procedure                                                    Standard Parameter                        Estimate             Error    t Value x3*Orientat*Material 2 1     0.0043934394 B      0.02505086       0.18 x3*Orientat*Material 2 2     0.0569813680 B      0.01987184       2.87 x3*Orientat*Material 3 1     -.0841658662 B      0.01678230      -5.02 x3*Orientat*Material 3 2     0.0000000000 B       .                .                  Parameter                    Pr > |t|                 x3*Orientat*Material 2 1       0.8610                 x3*Orientat*Material 2 2       0.0046                 x3*Orientat*Material 3 1       <.0001                 x3*Orientat*Material 3 2        .  NOTE: The X'X matrix has been found to be singular, and a generalized       inverse was used to solve the normal equations.  Terms whose       estimates are followed by the letter 'B' are not uniquely       estimable. -110-        Plot of resid8*yhat8.  Legend: A = 1 obs, B = 2 obs, etc.  resid8 ‚        ‚   0.20 ˆ        ‚                                                 A        ‚              A        ‚        ‚   0.15 ˆ            A              AA        ‚                           A        ‚                      A        ‚               A       A       A                 A        ‚                                   A      A   0.10 ˆ                       A       AA     A        ‚           B    A                         A    A  A        ‚         A                           A        ‚          A        A A     A   A          A    A     A        ‚             A         B                          A   0.05 ˆ       D   B    A         BC    A  A                 A        ‚       A    AA  A     AA           A        A  A  A        ‚          A  CAA A    A                    CAA    A        ‚       A AA  B A           A          A    ABA       A        ‚             A D     A    A               B  A   0.00 ˆ         A   AAA   C   A        ‚       D A A     A B                      A      A        ‚         A     AAA   BAA  AA   B           B        ‚         A   A A               BA    AA     A        ‚           C  AB       A  AAB              A   A     A  -0.05 ˆ         ABB  AA A B      A                  A    A  A        ‚            A  A   A   A  AA         A            A        ‚            A        AA    A       A      A A        ‚         B     A A          A      A A    A        ‚                                      A    A A  -0.10 ˆ                A  A   A                   A        ‚                            A         A   A    A        ‚         A        ‚                           B         A        ‚            A  -0.15 ˆ                                          A      A        ‚        Šƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒ         -0.7    -0.6    -0.5    -0.4    -0.3    -0.2    -0.1     0.0                                      yhat8 -111-                         The UNIVARIATE Procedure                           Variable:  resid8                                Moments    N                         210    Sum Weights                210    Mean                        0    Sum Observations             0    Std Deviation      0.06617301    Variance            0.00437887    Skewness           0.22525581    Kurtosis            -0.1163466    Uncorrected SS     0.91518322    Corrected SS        0.91518322    Coeff Variation             .    Std Error Mean      0.00456637                        Basic Statistical Measures             Location                    Variability         Mean      0.00000     Std Deviation            0.06617         Median   -0.00250     Variance                 0.00438         Mode     -0.02963     Range                    0.34095                               Interquartile Range      0.09199                        Tests for Location: Mu0=0            Test           -Statistic-    -----p Value------            Student's t    t         0    Pr > |t|    1.0000            Sign           M        -3    Pr >= |M|   0.7302            Signed Rank    S    -275.5    Pr >= |S|   0.7555                           Tests for Normality       Test                  --Statistic---    -----p Value------       Shapiro-Wilk          W     0.993373    Pr < W      0.4714       Kolmogorov-Smirnov    D     0.042515    Pr > D     >0.1500       Cramer-von Mises      W-Sq  0.057665    Pr > W-Sq  >0.2500       Anderson-Darling      A-Sq  0.337946    Pr > A-Sq  >0.2500                        Quantiles (Definition 5)                       Quantile         Estimate                       100% Max       0.18973526                       99%            0.15372204                       95%            0.11689399                       90%            0.08794163                       75% Q3         0.04498097                       50% Median    -0.00249597                       25% Q1        -0.04701096                       10%           -0.08154204                       5%            -0.10513642                       1%            -0.13710322                       0% Min        -0.15121120                           Extreme Observations               ------Lowest------        ------Highest-----                   Value      Obs            Value      Obs               -0.151211      105         0.147689       18              -0.148265       49         0.149581      185              -0.137103      178         0.153722       19              -0.133042      210         0.180071      118              -0.129082        4         0.189735       91  -112-                        The UNIVARIATE Procedure                           Variable:  resid8          Stem Leaf                           #             Boxplot           18 00                             2                0           16                                                 |           14 3804                           4                |           12 142                            3                |           10 1338477                        7                |            8 036782458                      9                |            6 00078012235                   11                |            4 000455566788991111456         21             +-----+            2 002247788890011223469999      24             |     |            0 113689111233466777899         21             |  +  |           -0 997665443300009733210         21             *-----*           -2 98866542110007444431000       23             |     |           -4 76655211000088765443322100    26             +-----+           -6 9876542886642200              16                |           -8 3293321                        7                |          -10 42652210                       8                |          -12 73990                          5                |          -14 18                             2                |              ----+----+----+----+----+-          Multiply Stem.Leaf by 10**-2                               Normal Probability Plot          0.19+                                                 **              |                                                  +              |                                            ****++              |                                          ***++              |                                       ****+              |                                     ***+              |                                   ***              |                               *****              |                            ****              |                         ****              |                      +***              |                   +****              |                *****              |             ****              |          +**              |       ****              |   ****         -0.15+**++               +----+----+----+----+----+----+----+----+----+----+                   -2        -1         0        +1        +2  -113- APPENDIX B  MECHANICAL PROPERTIES OF UHMW AND HDPE    Poisson's ratio (Coil 2007a): UHMW - 0.46 HDPE - 0.38.  Table B1:  Mechanical properties of UHMW(Coil 2007a). English  Units SI Units Mechanical1 Tensile Strength @ Yield D638 3 600 psi 25Mpa Elongation @ break D638 700% 700% Flexural modulus D790 155 000 psi 1070 Mpa Tensile impact strength D1822 120 ft-lb/in2 25 J/cm2 Tensile impact @ -40°C D1822 110 ft-lb/in2 25 J/cm2 ESCR, F50 (a) D1693 > 800 hr > 800 hr Brittleness temperature D746 < -76°C <-105°F Hardness shore D D2240 68 68 Thermal Vicat softening temperature D1525 123°C 254°F Heat deflection temp., 66psi D746 < 69°C <157°F 123 degrees C, 50% relative humidity unless noted **Product properties represent average laboratory values and are intended as a guide line. Final testing is the responsibility of the end user. Typical Values ASTM (1)UHMW Product  Properties:    Table B2:  Mechanical properties of HDPE(Coil 2007a). English  Units SI Units Mechanical1 Density D792 0.930 - 0.940 g/cm3 Tensile Strength @ Yield D638 2 900 - 3 400 psi 20 - 23 Mpa Elongation @ break D638 300 - 450 % 300 - 450 % Flexural modulus D790 100 000 - 150 000 psi 689 - 1 033 Mpa Hardness shore D D2240 64 - 66 64 - 66 123 degrees C, 50% relative humidity unless noted HDPE Product  Properties: ASTM (1) Typical Values **Product properties represent average laboratory values and are intended as a guide line. Final testing is the responsibility of the end user.  -114- APPENDIX C BLENDER DRAWINGS PROVIDED BY COIL MANUFACTURING   Figure C1:  Schematic of blender layout and atomizer spray patter (Coil 2007b). R es in at in g re gi on  be in g co ns id er ed  -115- For the purposes of this project only the horizontal spray pattern will be considered.  The diagonal spray pattern is a relatively recent option and is not currently present in many existing industrial operations.  In addition, the EDEM software package is unable to restrict particle tracking to a diagonal region.  As a result, computing and software constraints would quickly be reached if the diagonal spray pattern was considered.  -116- APPENDIX D  WRITE-OUT EVERY TIME INTERVAL CALCULATION  In discrete element modeling the frequency that the particle position and velocity are calculated is referred to as the time-step, Δt. Because these values are extremely small, for example in the neighborhood of 4x10-5 seconds, data is typically recorded for future analysis using a considerably larger interval.  This interval is referred to as the “write-out every” interval, Δtw, in the software package.  The write-out every interval refers to how frequently the simulator records data for analysis purposes.  This is not related to the time-step used in the simulator in any way except for that it must be equal to or larger than the time-step used in the simulator.  The write-out every interval begins when the simulation starts; however, only the write-out every intervals that occur within the resination region are considered.  The selected interval may directly affect the simulation time; therefore, it is important to select a reasonable value.  When selecting the write-out every time interval one must be aware of the process and the desired information.  For instance, in this particular problem, where the objective is to record the x-position, velocity, and ID of the particles as they pass through the resinating region, the write-out every time interval must be small enough to capture this information while the particles are in the resinating region. Figure D1 shows an example of a situation where a particle passes through the resinating region but the write-out every interval is set too large, resulting in the exported data suggesting that the particle did not spend any time in the resinating region.  -117-   Figure D1:  Schematic of an example where the write-out time interval is set too large.   An appropriate write-out every time interval was determined for this problem based on kinematic equations for motion in a straight line under constant acceleration (Equation D2) (Serway 2000, 1551).  Assuming an object is dropped from the highest point in the blender, A, and allowed to fall through the diameter of the blender until is collides with the bottom of the drum, D, under constant acceleration, an extreme scenario, is shown in Figure D2.   2 2 1 tatvxx xxiif +=−                       [D1]    ( )txxx a t xiif −−= 2                [D2] where:      x is the position in meters,      t is the time in seconds, vxi is the initial velocity, and      a is the acceleration, assumed to be 9.81m/s2. Measurement at t Measurement at t + Δtw Resinating region Blender drum Path of object Measurement at t = 0 -118-   Figure D2:  Schematic of the extreme case scenario where an object falls from the top of the blender, A, through the resination region, B to C, and collides with the bottom of the blender, D.  In this case, the total time spent in the resinating region is 0.066 seconds.  Therefore, the write-out every time interval must be less than 0.066 seconds. However, because the time spent in the region will be estimated based partly on the write-out every time interval (Equation D3), its impact on the accuracy of the estimated time must also be considered. As a result the range in accuracy was tested for a proposed write-out every time interval of 0.01 seconds.  wtRR txt Δ=ˆ                       [D3]  where: RRt̂  is the estimated time spent in the resinating region, xt is the number of write-out every time intervals that occurs in     the resinating region, and wtΔ  is the write-out every time interval.  One of two scenarios will result in the largest underestimation of the actual time spent in the resination region. First, when a write-out time interval is less, for example 1%, than a full Δtw inside the top of the region (Figure D3).  And second, when a write-out time interval is less than a full Δtw inside the bottom of the region (Figure D4). In this analysis both scenarios result in the discrete element modeling software recording 6 write-out every intervals while B C Resinating region Blender drum Path of object A D -119- the particle is in the resinating region.  The estimated time spent in the resinating region is therefore 0.06 seconds, or 91% of the actual time.     Figure D3:  Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the first interval is located marginally less than one full Δtw from the top of the region.     Figure D4:  Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the last interval is located marginally less than one full Δtw from the bottom of the region.  Similarly, one of two scenarios will result in the largest overestimation of the actual time spent in the resination region. First, when a write-out every time interval is marginally below the top of the region (Figure D5).  And second, when a write-out every time interval is marginally above the bottom of the region (Figure D6).  In this analysis both scenarios result in the discrete element modeling software recording 7 write-out every intervals while the particle is in the resinating region.  The estimated time in the resinating region is therefore 0.07 seconds, or 106% of the actual time. A: 0.814 m B: 0.854 m C: 0.896 m D: 0.938 m E: 0.981 m F: 1.026 m A: 0.799 m B: 0.839 m C: 0.880 m D: 0.923 m E: 0.966 m F: 1.010 m 0.775 m 1.054 m 0.775 m 1.054 m Path of particle Path of particle Blender Blender Resinating region Resinating region 0.99 Δtw 0.99 Δtw -120-    Figure D5:  Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the first interval is located marginally below the top of the region.     Figure D6:  Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the last interval is located marginally above the bottom of the region.  It can therefore be concluded that under these idealized assumptions, the estimated time a particle spends inside the resinating region will be between 91% and 106% of the actual time. A write-out time interval, Δtw, 0.01 produces reasonably accurate results for the purposes of this project. In reality, the particles will be replaced by strands, most of which will fall through the resinating region along a parabolic path resulting in a larger fraction of their time in the region accounted for.    A: 0.775 m B: 0.815 m C: 0.855 m D: 0.896 m E: 0.939 m F: 0.982 m G: 1.027 m A: 0.799 m B: 0.839 m C: 0.880 m D: 0.922 m E: 0.965 m F: 1.009 m G; 1.054 m 0.775 m 1.054 m 0.775 m 1.054 m Blender Path of particle Path of particle Blender Resinating region Resinating region 0.01 Δtw 0.01 Δtw -121- APPENDIX E  VBA MACRO FOR SORTING, FILTERING, AND ANALYSING EDEM DATA  Option Explicit  Public Sub Histogram_And_Commulative_Graph()  Application.ScreenUpdating = False  Dim tmpSng As Single Dim aRow_SD As Long Dim aRow_RD As Long Dim aColumn_RD As Integer Dim aColumn_SD As Integer Dim aRow_CD As Long Dim aColumn_TD As Integer Dim aRow_TD As Integer Dim NumOfTrackedParticles As Integer Dim NumOfTrackedParticlesB As Integer  Dim LowerTimeRange As Single Dim UpperTimeRange As Single  Dim LowerRow_SD As Long Dim UpperRow_SD As Long Dim LowerTimeConst As Single Dim UpperTimeConst As Single Dim LengthofSimulationRecorded As Single Dim BinSizeCummDist As Single Dim NumBinsCummDist As Single Dim DrumDiameter As Single Dim DrumRadius As Single Dim BinSizeHist As Single  DrumDiameter = 1632     '(mm) MUST BE SET!!!! DrumRadius = DrumDiameter / 2 BinSizeHist = 102       '(mm) MUST BE SET!!!!  'Set bin size for cummulative distribution graph BinSizeCummDist = 0.5   'MUST BE SET!!!!  'Set time constraints for analysis 'Should be based on specific number of runs under steady-state LowerTimeConst = 4.71   'MUST BE SET!!!! UpperTimeConst = 23.53  'MUST BE SET!!!!  'Set number of tracked particles NumOfTrackedParticles = 150 'MUST BE SET!!!! NumOfTrackedParticlesB = NumOfTrackedParticles + 1  tmpSng = Timer  'rename raw data worksheet ActiveSheet.Name = "raw_data"  -122- 'add new worksheet "sorted_data" Worksheets.Add(After:=Worksheets("raw_data")).Name = "sorted_data"  'Find Particle ID's aRow_SD = 1 For aRow_RD = 1 To xlLastRow("raw_data") / 2    'divided by two to avoid overloading                                                 'Excel with data causing it to crash     If Worksheets("raw_data").Cells(aRow_RD, 1).Value = "TIME:" Then          'Transfers x-positions         For aColumn_RD = 2 To xlLastCol("raw_data")         If Worksheets("raw_data").Cells(aRow_RD + 1, aColumn_RD).Value <> "no data" Then             If Worksheets("raw_data").Cells(aRow_RD + 1, aColumn_RD).Value <> "" Then                 Worksheets("sorted_data").Cells(aRow_SD, 1).Value = Worksheets("raw_data") _                     .Cells(aRow_RD + 1, aColumn_RD).Value                 aRow_SD = aRow_SD + 1             End If         End If          Next aColumn_RD     aColumn_RD = 2     End If Next aRow_RD  'remove duplicate particle ID's and sort data Dim x As Long      For x = xlLastRow("sorted_data") To 1 Step -1         If Application.WorksheetFunction.CountIf(Range("A1:A" & x), Range("A" & x).Text) > 1 Then             Range("A" & x).EntireRow.Delete         End If     Next x      Range("A1:A30000").Select     Selection.Sort Key1:=Range("A1"), Order1:=xlAscending, Header:=xlGuess, _         OrderCustom:=1, MatchCase:=False, Orientation:=xlTopToBottom, _         DataOption1:=xlSortNormal  'transpose data     Worksheets("sorted_data").Range("$A$1:$A$250").Copy     Worksheets("sorted_data").Cells(2, 2).PasteSpecial Paste:=xlPasteAll, Operation:=xlNone, SkipBlanks:= _         False, Transpose:=True     Worksheets("sorted_data").Range("$A$1:$A$250").Clear  'Transfer times     Worksheets("sorted_data").Cells(2, 1) = "TIME"     Worksheets("sorted_data").Cells(1, 1) = "First Ent.:"  aRow_SD = 3 For aRow_RD = 1 To xlLastRow("raw_data")      If Worksheets("raw_data").Cells(aRow_RD, 1).Value = "TIME:" Then     Worksheets("sorted_data").Cells(aRow_SD, 1).Value = Worksheets("raw_data").Cells(aRow_RD, 2).Value     LowerTimeRange = Worksheets("sorted_data").Cells(3, 1)          'Transfer x-positions         For aColumn_RD = 2 To xlLastCol("raw_data")         For aColumn_SD = 2 To NumOfTrackedParticlesB  -123-         If Worksheets("raw_data").Cells(aRow_RD + 1, aColumn_RD).Value = Worksheets("sorted_data") _             .Cells(2, aColumn_SD).Value Then             'Lookup if particle velocity is negative (moving downward) and includes it in the analysis if it is             If Worksheets("raw_data").Cells(aRow_RD + 3, aColumn_RD).Value <= 0 Then             Worksheets("sorted_data").Cells(aRow_SD, aColumn_SD).Value = Worksheets("raw_data") _                 .Cells(aRow_RD + 2, aColumn_RD).Value             End If         End If          Next aColumn_SD         Next aColumn_RD          aColumn_RD = 2         aColumn_SD = 2         aRow_SD = aRow_SD + 1     End If Next aRow_RD  'Look-up first time when strands enter resination region for cummulative distribution graph aColumn_SD = 2 Do While Worksheets("sorted_data").Cells(2, aColumn_SD) <> ""     aRow_SD = 3     Do While Cells(aRow_SD, aColumn_SD) = ""         aRow_SD = aRow_SD + 1     Loop     Worksheets("sorted_data").Cells(1, aColumn_SD) = Worksheets("sorted_data").Cells(aRow_SD, 1)     aColumn_SD = aColumn_SD + 1 Loop  'String columns of data together 'add new worksheet "tmp_data" Worksheets.Add(After:=Worksheets("sorted_data")).Name = "tmp_data"  'Lookup rows that correspond to time constraints LowerRow_SD = 3 'If LowerTimeConst = 0 Then LowerRow_SD = 3 Else     Do While Worksheets("sorted_data").Cells(LowerRow_SD, 1) < LowerTimeConst         LowerRow_SD = LowerRow_SD + 1     Loop 'End If  UpperRow_SD = 3 Do While Worksheets("sorted_data").Cells(UpperRow_SD, 1) < UpperTimeConst     UpperRow_SD = UpperRow_SD + 1 Loop  If UpperTimeConst <> Worksheets("sorted_data").Cells(xlLastRow("sorted_data"), 1) _     Then UpperRow_SD = UpperRow_SD - 1  'transfer data to tmp_data Worksheets("sorted_data").Range("$B$" & LowerRow_SD & ":$IV$" & UpperRow_SD).Copy _     Destination:=Worksheets("tmp_data").Cells(1, 1)  'remove empty cells and shift left Worksheets("tmp_data").Range(Cells(1, 1), Cells(xlLastRow("tmp_data"), NumOfTrackedParticlesB)) _     .SpecialCells(xlCellTypeBlanks).Delete Shift:=xlToLeft 'remove empty cells and shift up Worksheets("tmp_data").Range(Cells(1, 1), Cells(xlLastRow("tmp_data"), NumOfTrackedParticlesB)) _     .SpecialCells(xlCellTypeBlanks).Delete Shift:=xlUp -124-  'add new worksheet "compiled_data" Worksheets.Add(After:=Worksheets("tmp_data")).Name = "compiled_data"  'Transfer x-positions aRow_CD = 1  For aColumn_TD = 1 To xlLastCol("tmp_data") For aRow_TD = 1 To xlLastRow("tmp_data")  If Worksheets("tmp_data").Cells(aRow_TD, aColumn_TD).Value <> "" Then     Worksheets("compiled_data").Cells(aRow_CD, 1).Value = Worksheets("tmp_data") _         .Cells(aRow_TD, aColumn_TD).Value     aRow_CD = aRow_CD + 1 End If  Next aRow_TD Next aColumn_TD  'Worksheets("tmp_data").Delete  ' Make a histogram from the selected values. ' The top value is used as the histogram's title. Dim selected_range As Range Dim title As String Dim r As Integer Dim score_cell As Range Dim num_scores As Integer Dim count_range As Range Dim new_chart As Chart  Dim Data_Range As Range Set Data_Range = Worksheets("compiled_data").Range(Cells(1, 1), Cells(65536, 1))  Worksheets.Add(After:=Worksheets("compiled_data")).Name = "Histogram"  Worksheets("Histogram").Cells(2, 2) = "HISTOGRAM" Worksheets("Histogram").Range("B2:B2").Select     With Selection         .HorizontalAlignment = xlLeft         .Font.Bold = True     End With      ' See how many bins we will have.      Dim num_bins As Integer     num_bins = DrumDiameter / BinSizeHist      ' Make the bin separators.     Worksheets("Histogram").Cells(3, 2) = "Bins"     For r = 1 To num_bins - 1         Worksheets("Histogram").Cells(r + 3, 2) = -DrumRadius + r * BinSizeHist - 0.1     Next r      r = num_bins '+ 1         Worksheets("Histogram").Cells(r + 3, 2) = -DrumRadius + r * BinSizeHist      ' Make the counts.     Worksheets("Histogram").Cells(3, 3) = "Counts" -125-     Set count_range = Worksheets("Histogram").Range("C4:C" & num_bins + 3)     count_range.FormulaArray = "=Frequency(sorted_data!B$" & LowerRow_SD & ":$IV$" & _         UpperRow_SD & ", B4:B" & num_bins + 3 & ")"      ' Make the range labels.     Worksheets("Histogram").Cells(3, 4) = "Ranges"     For r = 1 To num_bins - 1         Worksheets("Histogram").Cells(r + 3, 4) = "'" & _             -DrumRadius + BinSizeHist * (r - 1) & " to " & _             -DrumRadius + BinSizeHist * (r - 1) + BinSizeHist - 0.1         Worksheets("Histogram").Cells(r + 3, 4).HorizontalAlignment = _             xlRight     Next r     r = num_bins '+ 1     Worksheets("Histogram").Cells(r + 3, 4) = "'" & _         -DrumRadius + BinSizeHist * (r - 1) & " to " & DrumRadius     Worksheets("Histogram").Cells(r + 3, 4).HorizontalAlignment = xlRight      ' Make the chart.     Set new_chart = Charts.Add()     With new_chart         .ChartType = xlColumnClustered         .SetSourceData Source:=Worksheets("Histogram").Range("C4:C" & _             num_bins + 3), _             PlotBy:=xlColumns         .Location Where:=xlLocationAsObject, _             Name:=Worksheets("Histogram").Name     End With      ' Format chart     With ActiveChart         .HasTitle = True         .ChartTitle.Characters.Text = ActiveWorkbook.Name         .Axes(xlCategory, xlPrimary).HasTitle = True         .Axes(xlCategory, _             xlPrimary).AxisTitle.Characters.Text = "Scores"         .Axes(xlValue, xlPrimary).HasTitle = True         .Axes(xlValue, xlPrimary).AxisTitle.Characters.Text _             = "Count"          ' Display score ranges on the X axis.         .SeriesCollection(1).XValues = "='" & _             Worksheets("Histogram").Name & "'!R4C4:R" & _             num_bins + 3 & "C4"     End With     With ActiveChart.Axes(xlCategory)         .HasMajorGridlines = False         .HasMinorGridlines = False     End With     With ActiveChart.Axes(xlValue)         .HasMajorGridlines = False         .HasMinorGridlines = False     End With     ActiveChart.HasLegend = False     With ActiveChart.PlotArea.Border         .ColorIndex = 16         .Weight = xlThin         .LineStyle = xlContinuous     End With -126-     With ActiveChart.PlotArea.Interior         .ColorIndex = 2         .PatternColorIndex = 1         .Pattern = xlSolid     End With     With ActiveSheet.ChartObjects(1)         .Width = 500         .Height = 300         .Left = 400         .Top = 100     End With     With ActiveChart.Axes(xlCategory).TickLabels         .Alignment = xlCenter         .Offset = 100         .ReadingOrder = xlContext         .Orientation = 45     End With     ActiveChart.SeriesCollection(1).Select     With ActiveChart.ChartGroups(1)         .Overlap = 0         .GapWidth = 0         .HasSeriesLines = False         .VaryByCategories = False     End With  ' Place Skewness and Kurtosis titles Worksheets("Histogram").Cells(3, 7) = "Statistics"  Range("G3:H3", "B3:D3").Select     With Selection         .HorizontalAlignment = xlCenter         .Font.Bold = True     End With Range("G3:H3").Merge  Worksheets("Histogram").Cells(4, 7) = "Average" Worksheets("Histogram").Cells(5, 7) = "Std Dev" Worksheets("Histogram").Cells(6, 7) = "Skewness" Worksheets("Histogram").Cells(7, 7) = "Kurtosis" Worksheets("Histogram").Cells(8, 7) = "Count"  ' Calculate Skewness and Kurtosis Worksheets("Histogram").Cells(4, 8) = Application.Average(Data_Range) Worksheets("Histogram").Cells(5, 8) = Application.StDev(Data_Range) Worksheets("Histogram").Cells(6, 8) = Application.Skew(Data_Range) Worksheets("Histogram").Cells(7, 8) = Application.Kurt(Data_Range) Worksheets("Histogram").Cells(8, 8) = Application.Count(Data_Range)   'Cummulative frequency chart Worksheets("Histogram").Cells(36, 2) = "CUMMULATIVE FREQUENCY GRAPH" Worksheets("Histogram").Range("B36:B36").Select     With Selection         .HorizontalAlignment = xlLeft         .Font.Bold = True     End With      ' See how many bins we will have.     LengthofSimulationRecorded = Worksheets("sorted_data").Cells(xlLastRow("sorted_data"), 1) _ -127-         - Worksheets("sorted_data").Cells(3, 1)      NumBinsCummDist = LengthofSimulationRecorded / BinSizeCummDist      ' Make the bin separators.     Worksheets("Histogram").Cells(37, 2) = "Bins"     For r = 1 To (NumBinsCummDist - 1)         Worksheets("Histogram").Cells(r + 37, 2) = r * BinSizeCummDist + LowerTimeRange - 0.01     Next r      r = NumBinsCummDist         Worksheets("Histogram").Cells(r + 37, 2) = r * BinSizeCummDist + LowerTimeRange      ' Make the counts.     Worksheets("Histogram").Cells(37, 3) = "Counts"     Set count_range = Worksheets("Histogram").Range("C38:C" & NumBinsCummDist + 37)     count_range.FormulaArray = "=Frequency(sorted_data!B1:IV1, B38:B" & _             NumBinsCummDist + 37 & ")"      ' Make the range labels.     Worksheets("Histogram").Cells(37, 6) = "Ranges"     For r = 1 To NumBinsCummDist - 1         Worksheets("Histogram").Cells(r + 37, 6) = "'" & _             BinSizeCummDist * (r - 1) + LowerTimeRange & " to " & _             BinSizeCummDist * (r - 1) + BinSizeCummDist + LowerTimeRange - 0.01         Worksheets("Histogram").Cells(r + 37, 6).HorizontalAlignment = _             xlRight     Next r     r = NumBinsCummDist     Worksheets("Histogram").Cells(r + 37, 6) = "'" & _         BinSizeCummDist * (r - 1) + LowerTimeRange & " to 20"     Worksheets("Histogram").Cells(r + 37, 6).HorizontalAlignment = xlRight      ' Calculate cummulative values.     Worksheets("Histogram").Cells(37, 4) = "Cumm."     r = 1         Worksheets("Histogram").Cells(r + 37, 4) = Worksheets("Histogram").Cells(r + 37, 3)         Worksheets("Histogram").Cells(r + 37, 4).HorizontalAlignment = _             xlRight      For r = 2 To NumBinsCummDist         Worksheets("Histogram").Cells(r + 37, 4) = Worksheets("Histogram").Cells(r + 37, 3) + _         Worksheets("Histogram").Cells(r + 37 - 1, 4)         Worksheets("Histogram").Cells(r + 37, 5).HorizontalAlignment = _             xlRight     Next r      ' Calculate cummulative percentages.     Worksheets("Histogram").Cells(37, 5) = "Cumm.Per."     For r = 1 To NumBinsCummDist         Worksheets("Histogram").Cells(r + 37, 5) = Worksheets("Histogram").Cells(r + 37, 4) / _             (NumOfTrackedParticlesB - 1)         Worksheets("Histogram").Cells(r + 37, 5).HorizontalAlignment = _             xlRight         Worksheets("Histogram").Cells(r + 37, 5).NumberFormat = "0.0%"     Next r      Range("B37:F37").Select     With Selection -128-         .HorizontalAlignment = xlCenter         .Font.Bold = True     End With      ' Make the chart.     Set new_chart = Charts.Add     With new_chart         .ChartType = xlLine         .SetSourceData Source:=Worksheets("Histogram").Range("E38:E" & _             NumBinsCummDist + 37), PlotBy:=xlColumns         .Location Where:=xlLocationAsObject, _             Name:=Worksheets("Histogram").Name     End With      ' Format chart     With ActiveChart         .HasTitle = True         .ChartTitle.Characters.Text = ActiveWorkbook.Name & " - Cummulative Distribution"         .Axes(xlCategory, xlPrimary).HasTitle = True         .Axes(xlCategory, _             xlPrimary).AxisTitle.Characters.Text = "Time (seconds)"         .Axes(xlValue, xlPrimary).HasTitle = True         .Axes(xlValue, xlPrimary).AxisTitle.Characters.Text _             = "Commulative Percent"          ' Display time ranges on the X axis.         .SeriesCollection(1).XValues = "='" & _             Worksheets("Histogram").Name & "'!R38C6:R" & NumBinsCummDist + 37 & "C6"     End With     With ActiveChart.Axes(xlCategory)         .HasMajorGridlines = False         .HasMinorGridlines = False     End With     With ActiveChart.Axes(xlValue)         .HasMajorGridlines = False         .HasMinorGridlines = False     End With     ActiveChart.HasLegend = False     With ActiveChart.PlotArea.Border         .ColorIndex = 16         .Weight = xlThin         .LineStyle = xlContinuous     End With     With ActiveChart.PlotArea.Interior         .ColorIndex = 2         .PatternColorIndex = 1         .Pattern = xlSolid     End With     With ActiveSheet.ChartObjects(2)         .Width = 500         .Height = 300         .Left = 400         .Top = 450     End With     With ActiveChart.Axes(xlCategory).TickLabels         .Alignment = xlCenter         .Offset = 100         .ReadingOrder = xlContext         .Orientation = 45 -129-     End With Application.ScreenUpdating = True MsgBox "Total processing time:" & Round((Timer - tmpSng) / 60, 5) & " minutes" End Sub  'Find the last populated row in a specified worksheet Function xlLastRow(Optional WorksheetName As String) As Long      With Worksheets(WorksheetName)         On Error Resume Next         xlLastRow = .Cells.Find("*", .Cells(1), xlFormulas, _         xlWhole, xlByRows, xlPrevious).Row         If Err <> 0 Then xlLastRow = 0     End With  End Function  'Find the first populated row in a specified worksheet Function xlFirstRow(Optional WorksheetName As String) As Long      With Worksheets(WorksheetName)         On Error Resume Next         xlFirstRow = .Cells.Find("*", .Cells(.Cells.Count), xlFormulas, _         xlWhole, xlByRows, xlNext).Row         If Err <> 0 Then xlFirstRow = 0     End With  End Function  'Find the last populated column in a specified worksheet Function xlLastCol(Optional WorksheetName As String) As Long      With Worksheets(WorksheetName)         On Error Resume Next         xlLastCol = .Cells.Find("*", .Cells(1), xlFormulas, _         xlWhole, xlByColumns, xlPrevious).Column         If Err <> 0 Then xlLastCol = 0     End With  End Function    -130- APPENDIX F  MACRO FOR PERFORMING THE GRAYSCALE ANALYSIS IN IMAGE PRO PLUS    Option Explicit Sub setLineProfile()  ret = IpProfCreate()  ret = IpProfLineMove(133, 205, 503, 268)   ' opens line analysis operation  ret = IpProfSetAttr(LINETYPE, THICKHORZ) ' sets the line analysis operation to "Thick Horizontal"  ret = IpProfLineMove(133, 205, 503, 268)  ' positions the horizontal lines End Sub  Sub analyzeImagesUsingLineProfile()  Dim id As Integer For id = 0 To 1800 Step 3  ' cycles through images labelled 0 to 1800, skipping to every 3rd  Dim FileName As String  ' set file location and name  FileName = "C:\Documents And Settings\gdick\My Documents\My Videos\January 31 2008 Lab        Blender\Baseline\BW Images\Baseline ("  ret = IpWsLoad(FileName & id &").tif","tif")  Call setLineProfile()  ret = IpProfSave("", S_DDE+S_DATA+S_HEADER+S_LEGEND+S_X_AXIS+S_COORDS)  ret = IpProfSelect(0)  ret = IpProfDestroy()  ret = IpDocClose()  ret = IpAnShow(0)  ' run Excel macro    Dim exl As Object    Set exl = Get_Excel_Object    exl.Application.Run "ImageDataCompTMP.xls!AddWorksheet"  Next id    exl.Application.Run "ImageDataCompTMP.xls!deleteWorksheet"  End Sub  ' This function tries to find a running ' instance of Excel. If it can't find one ' it starts one:  Function Get_Excel_Object() As Object   Dim exl As Object    ' GetObject will fail if Excel is not running.   On Error GoTo start_excel   Set exl = GetObject(,"Excel.Application")   On Error GoTo 0   GoTo excel_running  -131- start_excel:   ' Start Excel via CreateObject. If this   ' fails, we exit the macro.   On Error GoTo error_excel   Set exl = CreateObject("Excel.Application")   exl.Visible = True   exl.Workbooks.Add  excel_running:   Set Get_Excel_Object = exl   Exit Function error_excel:   MsgBox "Can't find Excel" End Function        -132- APPENDIX G  ANOVA RESULTS FOR THE MECHANICAL PROPERTIES OF ASPEN STRANDS  Table G1:  ANOVA results for the impact the material properties have on the skewness of the resulting histogram. Source  DF  SS  MS  F  Pr > F Shear Modulus 1 0.003553 0.003553 2.156907 0.380567 Poissons Ratio 1 0.002061 0.002061 1.250968 0.464437 Density 1 0.002278 0.002278 1.382878 0.448632 Shear Modulus x Poissons Ratio 1 0.001431 0.001431 0.868728 0.522379 Shear Modulus x Density 1 0.00009 0.00009 0.054499 0.853996 Poissons Ratio x Density 1 0.028489 0.028489 17.29343 0.150235 Model 6 0.037902 0.006317 3.834568 0.37218 Error 1 0.001647 0.001647 Total 7 0.039549  Table G2:  ANOVA results for the impact the material properties have on the kurtosis of the resulting histogram. Source  DF  SS  MS  F  Pr > F Shear Modulus 1 0.000099 0.000099 0.459528 0.620747 Poissons Ratio 1 0.001225 0.001225 5.663485 0.253247 Density 1 0.00005 0.00005 0.231139 0.714702 Shear Modulus x Poissons Ratio 1 0.000233 0.000233 1.078402 0.48799 Shear Modulus x Density 1 0.006997 0.006997 32.34766 0.110801 Poissons Ratio x Density 1 0.002238 0.002238 10.34488 0.191901 Model 6 0.010843 0.001807 8.354182 0.258832 Error 1 0.000216 0.000216 Total 7 0.011059  Table G3:  ANOVA results for the impact the material properties have on the count of the resulting histogram. Source  DF  SS  MS  F  Pr > F Shear Modulus 1 13612.5 13612.5 0.412194 0.636651 Poissons Ratio 1 221112.5 221112.5 6.695408 0.234776 Density 1 95484.5 95484.5 2.891323 0.338442 Shear Modulus x Poissons Ratio 1 18 18 0.000545 0.98514 Shear Modulus x Density 1 13122 13122 0.397341 0.641941 Poissons Ratio x Density 1 693842 693842 21.00992 0.136746 Model 6 1037192 172865.3 5.234455 0.322657 Error 1 33024.5 33024.5 Total 7 1070216       -133- Table G4:  ANOVA results for the impact the material properties have on the processing time of the respective simulation. Source  DF  SS  MS  F  Pr > F Shear Modulus 1 578.6802 578.6802 2057.53 0.014033 Poissons Ratio 1 2.53125 2.53125 9 0.204833 Density 1 378.6752 378.6752 1346.401 0.017345 Shear Modulus x Poissons Ratio 1 0.91125 0.91125 3.24 0.322829 Shear Modulus x Density 1 104.8352 104.8352 372.7474 0.032945 Poissons Ratio x Density 1 0.55125 0.55125 1.96 0.394863 Model 6 1066.184 177.6974 631.8129 0.030444 Error 1 0.28125 0.28125 Total 7 1066.466   -134- APPENDIX H  ANOVA RESULTS FOR THE INTERACTION PROPERTIES OF ASPEN STRANDS AND POLYETHYLENE  Table H1:  ANOVA results for the impact the interaction properties have on the skewness of the resulting histogram. Source  DF  SS  MS  F  Pr > F CORestitution 1 0.006682 0.006682 29.6063 0.115709 CRFriction 1 2.74742 2.74742 12172.26 0.00577 CSFriction 1 0.699944 0.699944 3101.054 0.011431 CORestitution x CRFriction 1 0.009709 0.009709 43.01392 0.096326 CORestitution x CSFriction 1 0.000999 0.000999 4.425826 0.282484 CRFriction x CSFriction 1 0.151027 0.151027 669.1154 0.024599 Model 6 3.615781 0.60263 2669.912 0.014813 Error 1 0.000226 0.000226 Total 7 3.616007  Table H2:  ANOVA results for the impact the interaction properties have on the kurtosis of the resulting histogram. Source  DF  SS  MS  F  Pr > F CORestitution 1 5.51E-06 5.51E-06 0.000172 0.991647 CRFriction 1 1.991802 1.991802 62.2212 0.080279 CSFriction 1 1.410029 1.410029 44.04739 0.095206 CORestitution x CRFriction 1 0.003542 0.003542 0.110656 0.795559 CORestitution x CSFriction 1 5.01E-06 5.01E-06 0.000156 0.992039 CRFriction x CSFriction 1 1.605559 1.605559 50.15548 0.089302 Model 6 5.010942 0.835157 26.08918 0.148756 Error 1 0.032012 0.032012 Total 7 5.042954  Table H3:  ANOVA results for the impact the interaction properties have on the count of the resulting histogram. Source  DF  SS  MS  F  Pr > F CORestitution 1 611065.1 611065.1 32.98041 0.109754 CRFriction 1 11710380 11710380 632.0327 0.025309 CSFriction 1 2185095 2185095 117.934 0.058457 CORestitution x CRFriction 1 369370.1 369370.1 19.93565 0.140267 CORestitution x CSFriction 1 25651.13 25651.13 1.384443 0.448454 CRFriction x CSFriction 1 242556.1 242556.1 13.09124 0.171665 Model 6 15144118 2524020 136.2264 0.06549 Error 1 18528.13 18528.13 Total 7 15162646      -135- Table H4:  ANOVA results for the impact the interaction properties have on the processing time of the respective simulation. Source  DF  SS  MS  F  Pr > F CORestitution 1 0.001513 0.001513 1 0.5 CRFriction 1 0.070312 0.070312 46.4876 0.09271 CSFriction 1 0.838512 0.838512 554.3884 0.027022 CORestitution x CRFriction 1 0.002813 0.002813 1.859504 0.40282 CORestitution x CSFriction 1 0.002112 0.002112 1.396694 0.447071 CRFriction x CSFriction 1 0.074112 0.074112 49 0.090334 Model 6 0.989375 0.164896 109.022 0.07318 Error 1 0.001513 0.001513 Total 7 0.990888 -136- APPENDIX I  RESULTS FROM STUDENT T-TEST FOR SHOULDER AND TOE ANGLES  Table I1:  Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 4 and the laboratory results ran at 15.5 RPM. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 40.37 38.93 257.97 258.97 Variance 52.79 37.79 11.90 22.93 Observations 30 30 30 30 Hypothesized mean dif. 0  0 Degrees of freedom 56  53 t-statistic 0.825  -0.928 P(T≤ t) two-tail 0.413  0.358 t-critical two-tail 2.003  2.006   Table I2:  Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 4 and the laboratory results ran at 25.5 RPM. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 67.03 63.13 217.93 227.43 Variance 42.24 19.64 67.65 39.77 Observations 30 30 30 30 Hypothesized mean dif. 0  0 Degrees of freedom 51  54 t-statistic 2.716  -5.020 P(T≤ t) two-tail 0.009  5.960 E -6 t-critical two-tail 2.008  2.005    -137- APPENDIX J  RESULTS FROM THE EXPLORATORY STUDY WITHOUT AND WITH AN ATOMIZER BOOM  Table J1:  Results from exploratory study without an atomizer boom. Run # of Flights Flight height Fill level RPM Skewness Kurtosis Count 1 4 2 1/8 23.39 -2.796074 10.57709 14261 2 4 6 1/8 23.39 0.181865 -1.003007 16046 3 16 2 1/8 23.39 -0.411452 -0.432711 19656 4 16 6 1/8 23.39 1.055151 0.157969 13356 5 8 4 1/16 18.71 -0.343624 -0.724349 24282 6 8 4 1/16 28.07 1.1601 0.175024 11068 7 8 4 1/4 18.71 -0.773404 0.022419 26218 8 8 4 1/4 28.07 0.16858 -1.073637 14726 9 4 4 1/8 18.71 -0.710635 0.990473 25525 10 4 4 1/8 28.07 0.171931 -1.090594 13541 11 16 4 1/8 18.71 0.067189 -0.990335 21693 12 16 4 1/8 28.07 1.166465 0.8005 11497 13 8 2 1/16 23.39 -1.665463 3.232918 26819 14 8 2 1/4 23.39 -1.093679 2.099582 22917 15 8 6 1/16 23.39 1.336239 0.894518 12610 16 8 6 1/4 23.39 -0.020098 -1.059842 17494 17 4 4 1/16 23.39 -0.046351 -0.824065 16558 18 4 4 1/4 23.39 -1.064182 1.452961 21355 19 16 4 1/16 23.39 0.742821 -0.565052 13758 20 16 4 1/4 23.39 -0.178404 -1.142662 18609 21 8 2 1/8 18.71 -1.213237 2.456989 29897 22 8 2 1/8 28.07 -1.123317 0.773495 19346 23 8 6 1/8 18.71 0.149338 -0.887824 21209 24 8 6 1/8 28.07 1.192715 0.594237 11720 25 8 4 1/8 23.39 -0.107397 -0.533136 17952 26 8 4 1/8 23.39 -0.301508 -0.484515 18770 27 8 4 1/8 23.39 -0.156009 -0.852739 18410    -138- Table J2:  Results from exploratory study with an atomizer boom. Run # of Flights Flight height Fill level RPM Skewness Kurtosis Count 1 4 2 1/8 23.39 -2.753631 10.27182 17414 2 4 6 1/8 23.39 -0.544805 -0.912654 15773 3 16 2 1/8 23.39 -1.456965 2.43358 22188 4 16 6 1/8 23.39 0.500032 -1.177029 14287 5 8 4 1/16 18.71 -0.493197 0.475805 25009 6 8 4 1/16 28.07 1.127426 0.109028 11052 7 8 4 1/4 18.71 -1.617404 2.214585 26383 8 8 4 1/4 28.07 -0.098553 -1.577502 14992 9 4 4 1/8 18.71 -0.691708 1.882807 25275 10 4 4 1/8 28.07 -0.915169 -0.227513 15823 11 16 4 1/8 18.71 -1.232934 2.204677 24619 12 16 4 1/8 28.07 0.683892 -1.002647 12391 13 8 2 1/16 23.39 -1.541192 3.088706 25728 14 8 2 1/4 23.39 -1.520084 3.775611 23605 15 8 6 1/16 23.39 0.96552 -0.37011 13005 16 8 6 1/4 23.39 -0.435279 -1.347452 18236 17 4 4 1/16 23.39 -0.86338 0.100537 17349 18 4 4 1/4 23.39 -1.50092 1.824392 21616 19 16 4 1/16 23.39 0.427871 -1.184065 14658 20 16 4 1/4 23.39 -0.600083 -1.133607 19818 21 8 2 1/8 18.71 -1.229002 3.385995 28478 22 8 2 1/8 28.07 -1.830354 3.381662 20421 23 8 6 1/8 18.71 -1.536919 2.754155 22487 24 8 6 1/8 28.07 0.721061 -0.920876 12542 25 8 4 1/8 23.39 -0.987434 0.148008 19596 26 8 4 1/8 23.39 -0.973097 0.04603 18870 27 8 4 1/8 23.39 -0.877569 -0.298419 19043 

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