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UBC Theses and Dissertations

Development of a lead spring u-bolt load transducer : part of an onboard weighing system for off-highway… Shetty, Mithun Karunakar 2006

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D E V E L O P M E N T OF A L E A F SPRING U - B O L T L O A D T R A N S D U C E R : P A R T OF A N ONBOARD WEIGHING S Y S T E M FOR OFF-HIGHWAY L O G T R U C K S by MITHUN K A R U N A K A R SHETTY B.E., The University of Mumbai, 2002  A THESIS S U M I T T E D IN P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S FOR T H E D E G R E E OF M A S T E R OF A P P L I E D S C I E N C E  in T H E F A C U L T Y OF G R A D U A T E S T U D I E S (Forestry)  T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A M a y 2006  © Mithun Karunakar Shetty, 2006  ABSTRACT This thesis was motivated by the current concern of brake failure in off-highway log trucks descending steep grades.  In order to utilise a guideline being developed for the  prediction of safe maximum grades for descent under a range of truck payloads, it is necessary to measure axle weights during loading. A background review found that there are no commercially available on-board weighing systems that can be retrofitted to the drive axles of an off-highway tractor. Therefore, an investigation into the development of an on-board weighing system for the off-highway log trucks was initiated. This research was divided into two stages: preliminary strain measurement with a loaded off-highway tractor, and finite element modelling of a U-bolt from the tractor's leaf spring suspension. A preliminary measurement test was carried out to identify potential suspension components that could act as load transducers for measuring axle weight.  The  preliminary results showed that incremental strain at two locations on the U-bolt varied linearly with payload, for an incremental load of 22.5 k N . Finite element modelling of the U-bolt was carried out to predict the maximum incremental strain occurring on the U-bolt surface. The model was calibrated with the measured data and a sensitivity analysis was done on key modelling parameters to determine the most suitable level of leaf spring block length, preload and U-bolt-to-leaf spring friction coefficient. Incremental strain on the top of the curved portion of the U-bolt was found to be relatively consistent and close to the maximum level of incremental strain and is recommended as a preferred position for strain gauging.  ii  T A B L E OF CONTENTS ABSTRACT  :  TABLE OF CONTENTS  iii  LIST OF TABLES  '.  iv  LIST OF FIGURES  v  ACKNOWLEDGEMENTS  vii  CHAPTER 1 INTRODUCTION 1.1 1.2 1.3 1.4  1  Need for investigation Background review Objectives Organisation of the thesis  1 4 10 11  CHAPTER 2 PRELIMINARY STRAIN MEASUREMENTS 2.1 2.2 2.2 2.3  12  Sensor location on the HDX suspension Instruments used Methodology Results and Discussion  •  CHAPTER 3 FINITE ELEMENT MODEL CONSTRUCTION 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9  ii  12 13 14 15 21  Overview Background of U-bolt modelling FEM description Meshing of the FEM Boundary conditions Preload modelling External load Contact modelling Postprocessing  21 22 25 29 30 31 32 32 34  CHAPTER 4 FINITE ELEMENT MODELLING RESULTS  35  4.1 4.2  Overview Sensitivity Analysis 4.2.1 Leaf spring block length 4.2.2 Preload 4.2.3 Coefficient of friction 4.3 Analysis of incremental strain 4.4 Possible causes of bending in the U-bolt shank 4.5 Limitations of the empirical measurements and finite element modelling  35 35 36 38 41 .42 47 52  CHAPTER 5 SUMMARY, CONCLUSION AND RECOMMENDATION  54  REFERENCES  56  APPENDIX I  .'  APPENDIX II  — 58 60  iii  LIST OF T A B L E S  Table 2-1: Estimated weight of water added and resulting drive axle group weights  16  Table 3-1: FEM component physical properties  29  Table 4-1: Run sequence inputs to evaluate leaf spring block length....  37  Table 4-2: Run scenario for the different levels of preload and coefficient offrictionbetween the curved portion of U-bolt and leaf spring 39  iv  LIST OF FIGURES  Figure 1.1: Typical off-highway log truck  1  Figure 1.2: Off-highway log truck axle weights used in forest road bridge design  2  Figure 1.3: Walking beam load transducer  4  Figure 1.4: Log bunk assembly on a highway log truck  5  Figure 1.5: Beam load cell mounted on a highway log truck  5  Figure 1.6: Trailer suspension assembly with SI beam load cell  6  Figure 1.7: Bunk assembly on an off-highway log truck  6  Figure 1.8: Leaf spring suspension of an off-highway tractor  7  Figure 1.9: Load cells mounted between a drive axle and its leaf spring suspension  9  Figure 2.1: Strain gauge locations  13  Figure 2.2: Measuring drive axle weights with portable pad scales  15  Figure 2.3: Incremental leaf spring strain response to unloading the tractor with strain gauges applied when tractor was loaded 17 Figure 2.4: Incremental axial strain measured in two locations on a leaf spring U-bolt during unloading with strain gauges applied when tractor was loaded 18 Figure 2.5: Incremental axial strain at location 1 on the suspension U-bolt in response to an averaged drive axle group weight 20 Figure 3.1: FE modelling procedure for the U-bolt analysis  22  Figure 3.2: Finite element modelling of U-bolted assembly  23  Figure 3.3: FEM of a U-bolted leaf spring assembly...  24  Figure 3.4: Schematic of the U-bolt assembly  26  Figure 3.5: 3-D 10-node tetrahedral structural solid...  27  Figure 3.6: Location of contact elements  28  Figure 3.7: Surface-to-surface contact elements  28  V  Figure 3.8: FEM of the U-bolt assembly  30  Figure 3.9: Boundary condition  31  Figure 4.1: Incremental strain at gauge location 1 on the U-bolt for various leaf spring block lengths  37  Figure 4.2: Incremental strain at gauge location 2 on the U-bolt for various leaf spring block lengths  38  Figure 4.3: Incremental strain at gauge location 1 on the U-bolt for various preloads and coefficients of friction (u) between the U-bolt and the leaf spring 40 Figure 4.4: Incremental strain at gauge location 2 on the U-bolt for various preloads and coefficients of friction (u) between the U-bolt and the leaf spring 40 Figure 4.5: Simulated incremental strains at locations 1 and 2 on the U-bolt for different U-bolt-to-leaf spring coefficients of friction  42  Figure 4.6: Distribution of incremental strain along the outer edge of U-bolt surface  43  Figure 4.7: Incremental strain distribution along the inner and outer surfaces of the U-bolt shank  44  Figure 4.8: Bending strain distribution along the outer surface of the U-bolt shank  45  Figure 4.9: Recommended gauge location on the U-bolt  47  Figure 4.10: Bending in the U-bolt  48  Figure 4.11: Geometry of two-dimensional model  49  Figure 4.12: Contact elements in two cases  50  Figure 4.13: Deformed shape for case 1  50  Figure 4.14: Deformed shape for case 2  51  Figure 4.15: Defining U-bolt Volume in FEM Figure A.I: Strain transformation along the curved portion of the U-bolt  52 58  Figure A.II: Slip-on water tank dimensions  60  vi  ACKNOWLEDGEMENTS I would like to express my sincere gratitude and thanks to my supervisor Dr. K e v i n C. Lyons for financial support and his invaluable help over the whole course of my studies. M y special thanks to M r . A l l a n Bradley of Forest Research Institute of Canada ( F E R I C ) for his invaluable professional advice, time and effort spend on proofreading this report.  I  would also like to thanks his family for their support during my stay in Canada. My  sincere thanks to M r . Marv Clark of F E R I C for providing constructive  feedback, financial assistance and instruments used in the preliminary testing. I would also like to thank Dr. John Nelson for participating on the committee for this thesis. I would like to acknowledge M r . A l l a n Waugh of Hayes Forest Services (Hayes) for providing a truck and shop facilities for the preliminary testing, and M r . Jeff Layfield of Hayes for providing useful information required in this work.  Thanks to the Instrumentation Lab,  Dept. of Mechanical Engineering, U B C for providing instruments used in the preliminary testing. I would like to thank M r . Rob Jokai and M r . Seamus Parker of F E R I C for their help with using FERIC-supplied instruments. I owe my parents a special gratitude for their love, understanding and support during the course of the study.  M.K.S.  vii  CHAPTER 1 INTRODUCTION 1.1 Need for investigation Heavy-duty off-highway  log trucks, as shown i n Figure 1.1, have a very limited  population and now are mainly confined to use on the coast of British Columbia.  These  trucks are no longer manufactured and most are at least 30 years old. They have been kept in service because of their robust construction and high load carrying capacity. These log trucks commonly consist of a tandem drive axle tractor and a tandem axle pole trailer.  Figure 1.1: Typical off-highway log truck The typical loaded mass of these trucks is between 107 to 122 tonnes, with payloads of approximately 68 to 83 tonnes (Oakley and Marshall, 1989).  These trucks  were designed for off-highway operation where axle loads and vehicle dimensions are not subject to regulations applied to public roads. Figure 1.2 presents maximum axle loads for an off-highway log truck used for the design of forestry bridges in British Columbia.  1  In addition to the differences in size and weight between highway and off-highway log trucks; there are also structural differences.  Two of most common off-highway truck  models are considered in this study—the Hayes H D X and the Pacific P I 6 .  Steering axle  Drive axle group  Trailer axle group  kN  105  602  602  lb  23545  135320  135320  Figure 1.2: Off-highway log truck axle weights used in forest road bridge design (British Columbia Ministry of Forests 1999)  Because of the heavy payloads drivers of these off-highway log trucks may have difficulty braking on steep hills. Parker (2004) states that road grade, speed and mass of the truck must be carefully managed when descending steep grades so that the required retardation power does not cause excessive brake temperatures resulting in brake fade. The Workers Compensation Board of British Columbia ( W C B , 2004) reported a fatal accident for a truck driver descending a steep grade with a heavily loaded off-highway truck. The recommendations in the W C B report suggested loads should be reduced for steeper grades to ensure vehicle control can be maintained. Off-highway truck payloads are difficult to assess because these trucks are not equipped with on-board weighing systems and variations in wood density and load 2  dimensions make visual estimates highly inaccurate. To-date on-board weighing systems have not been developed for off-highway log trucks because it is common to load them until their volumetric capacity is reached rather than restricting loads to some maximum allowable axle weight. In 2004, the Workers Compensation Board of British Columbia asked the Forest Engineering Research Institute of Canada ( F E R I C ) to develop a guideline for predicting the safe maximum grade for descending with various off-highway truck payloads.  To  utilise the guideline w i l l require trucks to limit their load size by measuring their axle loads  during  .commercially  loading.  While  off-highway  available  non-load-bearing  pole trailers can be  transducers  (Figure  1.3)  equipped the  with  structural  differences between on- and off-highway tractor suspensions w i l l prevent the use of highway tractor scales with off-highway tractors.  3  Figure 1.3: Walking beam load transducer (Phillips 1990)  1.2 Background review Numerous on-board load-measuring systems are available for highway log trucks. These systems typically employ strain gauge technology or air pressure gauges mounted on the air suspension.  D u f f (2003) lists some common load measuring systems,  appropriate for use with highway log trucks. They include: 1)  mounting the log bunk support pedestal and bunk roller ring on beams instrumented as load cells (see Figures 1.4 and 1.5),  2)  mounting displacement transducers between the frame and an axle,  3)  plumbing air pressure gauges in the air bag suspension system,  4)  instrumenting the trunnion shaft to act as a load transducer in a suspension  4  having a single main trunnion shaft, and 5)  mounting beam load cells between the trailer frame and spring hangers (see Figure 1.6).  Figure 1.4: L o g bunk assembly on a highway log truck  Figure 1.5: Beam load cell mounted on a highway log truck (Phillips 1989)  The differences between off-highway and highway log trucks make it challenging to adapt highway type load-measuring systems for use on off-highway tractors. Specifically, when considering the load measuring systems listed above, the following can be noted: 1) the bunk roller ring diameter is much larger in the off-highway tractor and it is an integral part o f the tractor frame as seen in Figure 1.7. Therefore, it is not possible to mount the bunk pedestal and bunk roller ring on beams instrumented as load cells.  5  Figure 1.6: Trailer suspension assembly with SI beam load cell (adapted from www. sitechnologies. com)  2)  Figure 1.7: Bunk assembly on an offhighway log truck  Hayes H D X tractors have a leaf spring suspension, similar to as shown in Figure 1.8. The change in the clearance between a tractor frame and its drive axles is a nonlinear function of the payload carried by the leaf spring suspension and this would complicate calibration of a displacement transducer system. In addition, individual leaf springs may crack without the driver noticing and this could cause the displacement transducers to generate erroneous load readings.  6  Figure 1.8: Leaf spring suspension of an off-highway tractor (adapted from Lathan 1999)  3) Heavy duty off-highway tractors generally do not use air bag suspension systems. 4) Hayes H D X tractors use two short (140mm X 610mm) trunnion shafts. These short trunnion shafts are completely encased in their trunnion saddles. G i v e n the dimensions and confinement of the trunnion shafts, it is expected that the strains generated in these shafts due to bending or shear w i l l be small. Therefore, load measurements with the trunnion shafts would lack sufficient variation  to  achieve  adequate  resolution.  Further,  construction  and  instrumentation of specially designed trunnion shafts would be expensive, and replacement of damaged shaft gauges would be a complicated and lengthy repair.  7  5) For the off-highway tractors considered in, this study, the ends of the leaf springs are supported by metal pads mounted in brackets that are attached to the drive axle tubes. It might be possible to mount these brackets on shear load cells and then mount the load cells on the drive axle tubes as shown in Figure 1.9. Unfortunately, such an arrangement would require removal of the drive axles to fit the load cells between the brackets and the axle tube. A l s o , because of the heavy payloads, the load cells would have to be relatively thick. When installed, these load cells would raise the center of gravity of the tractor by an amount equal to their thickness and thereby reduce the tractor's roll stability. Finally, the axle tubes could be used as load transducer by applying strain gauges directly to the surface of the drive axle tubes. If strain gauges were to be placed directly on the top surface of the drive axle tubes they might be well protected, however, the stiffness of the robustly designed axle tubes may limit the range of strains to be measured, and also any differences of inflation pressure between the dual tires may affect the gauges' calibration (Newton 1987).  8  Frame  (  \{  ^  Leaf spring end support,  t  w  Figure 1.9: Load cells mounted between a drive axle and its leaf spring suspension  A review of the suspension components of a typical off-highway tractor revealed that it might be feasible to instrument its suspension to predict axle weights based on mechanical strain. The leaf springs and the U-bolts that fasten the leaf spring packs to the trunnion shaft saddles both offered candidate locations for mounting strain gauges.  In  order to be a useful indicator of payload the suspension component's strain should vary linearly with payload, vary in a repeatable manner, and vary sufficiently over the range of axle loads to provide adequate resolution. The main advantage of having a repeatable linear calibration curve is that this greatly simplifies calibration of the system. This could be an important consideration when off-highway log trucks are working in remote locations without ready access to technical support or weigh scale stations. O f the two candidate suspension locations, the U-bolt was preferred as a strain gauge location over the leaf spring because the latter is believed to have non-linear strain variation with load that may vary between successive load cycles (Newton 1987).  9  In  addition, ease of replacement of damaged strain gauges might prove important given the severe operating environment experienced by off-highway truck suspensions. However, suspension U-bolts are normally pre-stressed, and this creates high initial strains that could mask the incremental axial strains due to log loads. In order to measure a strong signal on the U-bolt, it may be important to locate the strain gauges where a combination of axial and bending strains occurs. 1.3 Objectives The objectives of this research were to: a) collect preliminary strain data from the suspension components of an offhighway log tractor; and, b) use a Finite Element M o d e l ( F E M ) of the trunnion saddle, U-bolt, and leaf spring system of the off-highway log tractor to determine the locations on the U-bolt surface that would provide the largest incremental strains when the truck is loaded. This objective w i l l require the following: i. ii.  Calibrate the F E M using the preliminary load and strain data; M o d e l the effect of preload on the incremental strain due to external loads; and,  iii.  Determine whether there is bending strain in the U-bolt that can be used to increase the measured incremental strain.  10  1.4 Organisation of the thesis The research has been carried out in two stages, namely  preliminary  strain  measurements and finite element modelling. Chapter 1 discusses the need for research and the difficulty of retrofitting commercially available on-board axle weighing system to an off-highway  tractor. Chapter 2 discusses the preliminary  testing and resulting  measurements from strain gauges placed on a leaf spring and a U-bolt of an off-highway tractor suspension in June 2004. Chapter 3 describes the F E M of the suspension built to evaluate strains along the entire U-bolt surface. Chapter 4 describes the effect of preload and bending strains in the U-bolt as well as the F E M ' s calibration using the preliminary test measurements. This chapter also describes how the calibrated F E M was evaluated for potentially suitable strain gauge mounting locations. Chapter 5 draws conclusions from this  work  and  makes  recommendations  for  improving  the  resolution  of  strain  measurements on U-bolts. Appendix I describes the transformation of the strains along the curved portion of the U-bolt from global to local coordinates. Appendix II includes the dimensions of the slipon tank used for preliminary strain measurement.  11  CHAPTER 2 PRELIMINARY STRAIN MEASUREMENTS  2.1 Sensor location on the H D X suspension In order to estimate wheel loads on a Hayes H D X heavy-duty off-highway log truck consideration was given to instrumenting load transducers on all of the truck's axles. Due to the front log bunk being located over the centre of the drive axles, however, the steering axle load is believed to be insensitive to payload changes and therefore may not need to be monitored.  The pole trailer w i l l need to be instrumented and it can be  equipped with commercially available non-load-bearing transducers of the type used for highway trucks (discussed in Chapter 1). The U-bolts that support the trunnion shafts on the leaf springs, and the bottom leaf spring were selected as mounting locations for load transducers on the drive axle suspension. It was not possible to instrument a trunnion shaft during these initial strain tests because they were fully encased in the trunnion saddles. The installation of strain gauges to the. Hayes H D X tractor and subsequent load testing was conducted in June 2004 at Hayes' service facility in Port Alberni, British Columbia.  One of eight U-bolt ends (four U-bolts) in the tractor suspension was  instrumented.  Two gauges were installed on the U-bolt and aligned to measure strain  along the axis of the U-bolt (Figure 2.1). These strain gauges were located on the shank portion of the U-bolt in order to avoid measurement variation caused by contact interaction between the U-bolt and the spring pad.  A third gauge was installed  longitudinally near the centre of the underside of the bottom-most leaf spring.  12  This  mounting location offered the best combination of ample mounting space and (expected) large bending strains, and it was far from any leaf spring stress concentrations.  U-bolt  Figure 2.1: Strain gauge locations  2.2 Instruments used The strain gauges used were type C E A - 1 3 - 240UZ-120, (uniaxial gauges) from Measurement Group, Inc. The stated gauge factor was 2.12 ± 0.5% at 24° C. Each strain gauge was connected to a channel box (an SB-10 Switch and Balance Unit) as a single active arm of a Wheatstone bridge (Figure 2.1). A Measurement Group System P3500 strain indicator was used to measure and record the strain values with a resolution of 1 microstrain. Four portable pad scales (model PT300) were used to measure the weight of each drive wheel assembly in response to different payloads.  13  2.2 Methodology The procedure for measuring tractor payload and load transducer output was as follows: 1.  a slip-on water tank was installed on the log bunk of the Hayes H D X tractor (Figure 2.2).  The dimensions of the slip-on tank are given in  Appendix II; 2.  strains were measured in the drive axle suspension members while the volume of water in the slip-on tank was varied from full to empty. The weight of water carried by the tractor at any time was calculated as the estimated volume of water in the tank multiplied by a density of 1000 kg per m ; and,  3.  the drive axle wheel loads were measured with the tractor parked on four portable pad scales on a level paved surface.  Incremental strains and the wheel loads were measured in response to different payloads carried by the tractor on a flat surface; no test loads were measured on a slope.  14  Figure 2.2: Measuring drive axle weights with portable pad scales  2.3 Results and Discussion The weight of water in the slip-on tank and the resulting weights for the drive axle group and for the right drive dual assembly are shown in Table 2-1. The maximum weight of water added to the tractor corresponded to approximately 2 5 % of a typical full drive axle group payload (i.e., 37 tonnes payload for a 55 tonne gross weight on the drive axle group) for a Hayes H D X . The incremental differences show a strong correlation between the weight of water carried by the truck and the total drive axle group weight. For example, a total of 90 k N of water were removed from the tank and the resulting decrease in total drive axle group weight was 87 k N . This indicates that additional payload added to the truck would be carried almost entirely by the drive wheels and little or none would be transferred to the steer wheels when the truck is on level ground. For travel on slopes,  15  the load shift onto or off of the steering axle could be estimated using a simple geometric relationship. Table 2-1: Estimated weight of water added and resulting drive axle group weights Weight of water  Total drive axle group weight  Total right hand side drive axle group weight  (kN) 121 110 101 93 85 78 69 61 54 48 37 31  (kN)  (kN) 144 140 135 131 127 123 119 115 111 107 103 99  279 270 261 254 246 238 230 223 214 207 198 192  Figure 2.3 illustrates the incremental strain response i n the leaf spring due to unloading a total o f 90 k N o f incremental load from the tractor; and, the negative incremental strains denote a relaxing of longitudinal strain as the load is decreased. The leaf spring packs are subject to bending moments when loaded and unloaded, and this bending generates relatively large strain responses (e.g., a 70 microstrain increase with a 90 k N load increment). The incremental strain in the bottom leaf was found to be linear over most o f the range o f incremental load evaluated. However, leaf spring deflection under a given load is known to be greatly affected by friction and may give variable results (Newton 1987). A l s o , multi-leaf spring suspensions have different spring rates at different load ranges, and the spring rate for intermediate loads is typically variable ( S A E 1999).  Another concern with locating load transducers on the leaf springs is that the  leaves are susceptible to cracking and this would effect transducer calibration. Finally,  16  locating load transducers on the bottom o f leaf springs exposes the instrumentation to road salt; aggregate and other debris thrown up by the tires while driving.  For these  reasons leaf springs are not preferred as an axle weighing system.  Incremental load carried by the tractor (kN) 90  80  70  60  50  40  30  20.  10  Figure 2.3: Incremental leaf spring strain response to unloading the tractor with strain gauges applied when tractor was loaded  Figure 2.4 presents the measured strains on the shank portion o f a leaf spring U-bolt i n response to different incremental loads. The load resolution was approximately ± 18 k N (1.8 tonnes) for the range o f incremental loads tested. If this resolution was consistent over the full range o f loading, the measurement error for a fully loaded drive axle group would be 3.0% (i.e., 18 k N / 602 kN).  17  Incremental load carried by the tractor (microstrain) 80 60 40 20  100  A Lower gauge location 1 • Upper gauge location 2  FT = 0 . 9 0 3 7  Figure 2.4: Incremental axial strain measured i n two locations on a leaf spring U-bolt during unloading with strain gauges applied when tractor was loaded.  The incremental strains from both strain gauges had very similar slopes for the range o f incremental loads measured.  The strain at location 2 on the U-bolt also was  consistently about 1 microstrain higher than at location 1 for the range o f incremental loads measured.  Given the limited amount o f testing it cannot be conclusively stated  whether the difference i n measured incremental strains at locations 1 and 2 was due to differences i n strain instrumentation or whether the leaf spring U-bolts are subjected to bending. In Figure 2.5 drive axle group weight was plotted against measured incremental strain. Each level o f incremental strain corresponded to two or three different drive axle group weights. These weights were averaged, therefore, and reported as a single average  18  value versus that level of incremental strain. The result shows the linear relationship with drive axle group weight and strain, however, the magnitude of the strain variation with payload was small (i.e., no more than 5 microstrains up to a maximum payload of 90 k N ) . U-bolts in the Hayes H D X suspension are normally tightened (preloaded) in order to ensure the leaf springs remain clamped, and therefore under high axial tension even when the truck carries no payload. The preload was not known and was indirectly estimated from the manufacturer's torque specification. The preload in the U-bolt could be estimated using the following formula that relates torque and bolt cross-sectional area (diameter) to preload (Dayton 2001): Preload = - I ^ H _ K x Diameter e  ( 1 )  The torque coefficient, K, is a measure of the friction between the nut and the U bolt threads.  A value of 0.2 was specified for K , as per conventional practise which  assumes that the bolt is new and lubricated (Dayton 2001). The torque for the leaf spring U-bolts was taken to be 1760 N - m , based on discussions with Hayes Forest Service about their torqueing practice. Using the above parameters, formula (1) estimates a preload of 231 k N for a 36.75 mm-diameter U-bolt.  The small strain variation for the range of  payloads tested may have been due to the large amount of preload in the U-bolt (Norton 1996) and because the maximum test payload was only about 2 5 % of a full payload. However, the linear relation in Figure 2.5 indicates that U-bolts have some potential as load transducers provided that their strain rate is repeatable.  19  310  170 -150  -I  0  :  1  0.5  ,  ,  1  1  1.5  2  1  2.5  1  3  ,  ,  3.5  4  1  4.5  Incremental strain (microstrain)  Figure 2.5: Incremental axial strain at location 1 on the suspension U-bolt i n response to an averaged drive axle group weight. Given the findings from the preliminary measurements, the following can be said about measuring drive axle group loading with U-bolt strain: 1. The entire U-bolt surface should be analysed to determine where incremental strains are largest and therefore would provide the greatest strain variation; 2.  Strain gauging locations should be selected to avoid contact interaction effects that could prevent measurement repeatability; and,  3.  Satisfactory weight measurements may be possible despite the limited strain variation observed in the U-bolt i f a higher resolution strain indicator and higher resistance strain gauges are used.  20  CHAPTER 3 FINITE E L E M E N T M O D E L C O N S T R U C T I O N 3.1 Overview The preliminary measurements (Chapter 2) indicated that the axial strain developed in the leaf spring U-bolts varied linearly with increasing payload.  A n F E M was created to  check strain distribution over the entire U-bolt surface in order to optimise the placement conditions of strain gauges. Due to their design U-bolts can be subject to a bending load. The F E M w i l l allow an examination of the U-bolt surface for areas subject to increased strain due to a combination of axial and bending strains. Two aspects of the U-bolt problem complicate the analysis. First the interaction between the U-bolt and leaf spring is a contact problem.  Second, the U-bolt is under a  significant preload. Thus, the U-bolt does not sustain the full effect of the applied load (Norton 1996). Both of these complicating aspects can be modeled using ANSYS®. The procedure for a typical structural analysis is to define the system's physical components, transform it into a structural model with meshing (i.e. descretization), apply appropriate load and boundary conditions until model predictions are comparable to measured strain responses, and finally interpret the F E M results. Figure 3.1 shows a framework used for modelling the U-bolt in this work. Section 3.3 describes the geometric model and F E M . Section 3.4 describes the boundary condition and modelling methodology. processing results are discussed in Chapter 4.  21  Post-  Define geometric model (geometry o f I -boh. leaf spring, and trunnion saddle)  O CO  o C i  D i s c r e t i z e the m o d e l  OH  (meshing  the m o d e l )  D e f i n e the b o u n d a r y c o n d i t i o n s (contact a n d displacement boundary conditions) tij 03  to  C  o  L o a d s t o p 1: p r e l o a d t h e I. -bolt ( a p p l y t e n s i o n w i t h a t h e r m a l >lrain)  o  r  V  Post-processor static  Load step 2: apply an external load (equal to the payload applied in testing)  )  Calculate strain distribution and interpret. Revise meshing, boundary conditions and preloading until outputs agree with measured test strains.  Figure 3.1: F E modelling procedure for the U-bolt analysis  3.2 Background of U-bolt modelling Considerable research has been devoted to analytical, mechanistic and numerical models simulating connections using standard bolts (i.e., straight, threaded bolts with a head).  22  V e r y little research on U-bolts, however, is documented in the literature. T w o studies involving U-bolts are discussed below. Diamantoudis and Apostolopoulas (2002) developed a three dimensional (3-D) model to determine whether the stress in two U-bolts, that secured a plate to a truck frame member, exceeded a limiting stress. The steel plate and the frame member of the truck were modeled with 3-D solid elements. The U-bolts, however, were modeled more simply with 2-D beam elements (the nodes have three degrees of freedom: translation along the X and Y axes and Z-axis rotation). Figure 3.2 illustrates the U-bolted plate and frame member obliquely and in cross-section. They found that the bending stresses in the C-channel were highest at its bottom corner where the influence of the eccentric vertical loading from the U-bolt shank was greatest.  Based on this an alternative mounting  connection was recommended. _  —  U-bolt  Figure 3.2: Finite element modelling of U-bolted assembly (Diamantoudis 2002)  K i r b y and Charniga (2005) modeled U-bolts clamping a leaf spring pack, axle seat and U-bolt lower bracket to an axle tube. This analysis was to investigate twisting of the leaf spring on the axle seat in order to address a noise concern with the suspension  23  system. The U-bolt was used only to simulate the structural response o f the leaf spring to preload.  The U-bolt shanks merely transferred preload to the curved portion and, i n  order to reduce computational time, were meshed with 2 - D beam elements (Figure 3.3). U s i n g this model the simulated load at critical points on the axle seat was correlated with measured loads for different coefficients of friction. Friction coefficients i n the range o f 0.1 to 0.15 were simulated.  Curved portion of U-bolt  Figure 3.3: F E M of a U-bolted leaf spring assembly (Kirby 2005)  It can be inferred from this review that little work has specifically concentrated on analysing incremental strain in the U-bolt. The objective o f the thesis is to analyse the maximum incremental strain along a U-bolt i n order to maximise strain resolution. Therefore, in this thesis the U-bolt was modelled completely with 3-D solid elements.  24  3.3 F E M description The F E M begins with the construction of a 3-D geometric model of the U-bolt, leaf spring pack and trunnion  saddle assembly based on physical measurements  of  components (Figure 3.4). Friction between the leaf spring leafs and between the leaf and the spring pad was assumed to be high enough to restrict differential motion between them in the region of the U-bolt.  Given this simplification and that our interest was  confined to the U-bolt and its zone of contact with the spring pad and leaf springs (hereafter called the leaf spring) the leaf spring was modelled as a single block. A similar assumption was made in the region of the U-bolt ends and nuts and this allowed them to be modelled as i f they were glued together and to the bottom of the trunnion saddle. In addition, the trunnion saddle had a complex geometry, however," it was modelled as a block to reduce its modelling requirements. The overall number of nodes available for modelling is limited by A N S Y S and these simplifications resulted in more nodes being available for modelling the U-bolt. More nodes were required for modelling the U-bolt because an accurate strain distribution was needed for comparison with the field measurements and for investigation of the U-bolt surface to identify suitable gauging locations.  25  Leaf spring block  152.4mm/ 6inch  436.75 mm / 1.5 inch  Nut  ?  27.56 mm/l.125 inch  T r u n n i o n Saddle  110.25 m m / 4 . 5 i n c h  Leaf spring block length (L)  Figure 3.4: Schematic of the U-bolt assembly Next a structural model was created with S O L I D 9 2 elements sourced from the A N S Y S element library. These quadratic 3-D tetrahedral elements were used instead o f simpler 3-D linear tetrahedral elements because the S O L I D 9 2 elements are more suitable for estimating strains i n curved sections and are generally more accurate ( A N S Y S 2004). The S O L I D 9 2 element has 10 nodes with three degrees o f freedom at each node (Figure 3.5).  26  Node  x  Figure 3.5: 3-D 10-node tetrahedral structural solid  In order to ensure compatibility of the mesh elements only one type of element (i.e. S O L I D 9 2 ) was used for modelling all components of the assembly. When loaded, the U-bolt assembly undergoes a relative displacement at the contact interface (Figure 3.6) and this must be accounted for in order to obtain an accurate predication of strain along the surface of the U-bolt. To model the relative displacement, surface-to-surface contact elements were placed between the curved portion of the U-bolt and leaf spring block, and also between the leaf spring block and the trunnion saddle (Figure 3.6). Surface-to-surface contact elements were modelled using A N S Y S contact 174 and target 170 elements. These types of elements are capable of transferring forces and stiffness between the surfaces. The contact elements take the shape of the underlying elements (10-node tetrahedron in this F E M ) and therefore appeared as triangular-shaped elements (Figure 3.7).  27  Contact elements  Contact elements  Figure 3.6: Location of contact elements  Surface contact element  Figure 3.7: Surface-to-surface contact elements  28  The material used in the F E M was assumed to be linear elastic. The physical properties of individual suspension components are listed in Table 3-1.  Table 3-1: F E M component physical properties Component  Type of steel  Property direction  U-bolt Leaf spring Trunnion saddle  4140 (Alloy) 5160 (Alloy) Cast  Isotropic Isotropic Isotropic  Modulus o f elasticity GPa 210 200 200 a  c  c  Poisson's ratio  Thermal expansion coefficient at 21 °C 10" m/m/°C 12 13.5° 13.5° 6  0.291 0.300° 0.300° a  b  Walsh 2000 Speck 1997 ° A S M 1994 a b  3.4 Meshing of the F E M The meshing algorithm i n A N S Y S allows the degree o f mesh coarseness to be selected by the analyst from a scale of 1 to 10, with 10 being coarsest. The entire U-bolt was meshed moderately densely (i.e., with a mesh coarseness o f 6). A denser mesh (i.e., with a line refinement level o f 2) was applied around the outside surface o f the curved portion o f the U-bolt and around the inside surface where the U-bolt contacted the leaf spring. A finer mesh results in the boundary of the body in the model being closer to the actual shape o f the body and this reduces the effect of stress concentrations due to meshing (Saravi and Lyons, 2004). The rest of the F E M components (i.e., leaf spring and trunnion saddle) were meshed coarsely (i.e., with a mesh coarseness o f 8) because the  29  overall number of nodes available was limited. Figure 3.8 illustrates the F E M o f the U-bolt assembly.  Figure 3.8: F E M of the U-bolt assembly  3.5 Boundary conditions The lower edges of the leaf spring were constrained to prevent translation in the X , Y and Z direction (Figure 3.9).  30  Leaf spnng edges constrained inX,Y,Z  Figure 3.9: Boundary condition  3.6 Preload modelling In the first loading step, the U-bolt was preloaded. The preload i n the U-bolt can be modeled using thermal strain or built-in A N S Y S P R E T S 1 7 9 elements (Imaoko 2000). Stalling (1992) simulated preload i n a bolt with thermal strain created by lowering the temperature of the components. The bolt was shrunk until the dimension changes created the desired level of tension in the bolt. In the analysis of the H D X truck suspension i n this thesis, the U-bolt preload was simulated using thermal strain. The basic procedure for modelling preload in the U-bolt was: 1) assign an appropriate coefficient o f thermal expansion to the suspension components,  31  2) specify a uniform temperature (21° C) to the components, 3) specify a subzero temperature for the shanks of the U-bolt (Figure A.I), 4) compute the U-bolt axial tension and, 5) iterate until the desired preload is achieved.  3.7 External load In the second loading step, an external load was applied to the bottom part of the trunnion saddle as a uniformly distributed pressure (Figure 3.9).  3.8 Contact modelling Contact element simulate contact between two surfaces by generating contact forces of finite stiffness value when two surfaces approach each other and by removing the contact forces  with stiffness as zero when the surfaces move away (Rizzo 1991).  simulates sliding with friction.  It also  There are two common algorithms to simulate this  contact element: 1) Penalty method. With this method, springs are placed in the contact interface. Some  finite amount of penetration is required  mathematically to  equilibrium; however, physical contacting bodies do not interpenetrate.  maintain Increasing  the stiffness of the element reduces the magnitude of the penetration, however, the condition of the stiffness matrix depends on the contact stiffness itself.  If the  contact stiffness is too large, it w i l l cause convergence difficulties. 2) Lagrange multiplier method. This method adds the extra degree of freedom to the stiffness matrix to satisfy the constraint exactly. In this method no imaginary  32  penetration is assumed, therefore error free solution is granted for sticking friction (Zahavi and Barlam 2001). The accurate strain distribution along the curved surface of the U-bolt was important in this analysis.  Therefore, a "Lagrange multiplier on contact normal and  penalty on tangent" algorithm ( A N S Y S 2004) was used for modelling the contact interaction between the curved surfaces of the U-bolt and the .leaf spring.  This option  uses a Lagrange multiplier on the contact plane and enforces zero penetration while a displacement penalty on the tangent plane limits slip for a sticking condition ( A N S Y S , 2004). A default algorithm, "Augmented Lagrange", was used for modelling the contact between the leaf spring and the trunnion saddle in order to save computational time. A N S Y S solves for displacement at contact surfaces by adding the stiffness matrix of the contact surface to the stiffness matrix of the bodies under consideration so that, for any load increment, equilibrium is achieved.  The equation that links force, displacement  and stiffness and has the following form: [K + K ]u=f b  where  (2)  c  Kb is an n x n stiffness matrix of the bodies under consideration, K is an n x n stiffness matrix of the contact surface, c  u and f are the displacement and the load vector respectively having an n x 1 form (Zahavi and Barlam 2001). When contact friction is introduced in an F E M the resulting slip can generate an unsymmetrical stiffness matrix (Burke and Olatunbosun, 1997).  A t higher coefficients  of friction, when slip is significant, a solution may not converge (that is, may not be possible). In such cases, A N S Y S recommends using an unsymmetrical stiffness matrix  33  to improve the likelihood of convergence.  Solving with an unsymmetric matrix,  however, is more computationally expensive than solving with a symmetric matrix.  A  symmetric matrix was used to solve equation (2) because of limited computing memory and because slip was assumed not to be significant in the region of U-bolt to leaf spring contact. Laursen and Simo (1994) developed a symmetrization algorithm by which most frictional contact problems can be solved using symmetric stiffness matrices.  ANSYS  features this symmetrization algorithm and this was used for the analysis.  3.9 Post processing The longitudinal strain was calculated along the U-bolt command ( A N S Y S 2004).  surface using the  PATH  This command interpolates stress, strain and displacement  results between adjacent nodes along a straight line between two specified end points. In order to estimate the strain distribution along the U-bolt surface the straight, shank portion was analysed separately from the curved portion.  The strains along the U-bolt  shank were expressed in conventional global coordinates: x, y, z (Appendix I).  To  simulate strains measurable on the curved surface, however, strains in the curved portion of the U-bolt were expressed in local coordinates (i.e., oriented in longitudinal, transverse and normal directions to the surface (Appendix I)). A macro was created to transform the strains along the curved portion of the U-bolt from global to local coordinates, and this is included in Appendix I.  Following these calculations, the incremental strain due to the  external load applied to the U-bolt was calculated as the difference between the strains obtained in load step 2 (i.e., preload and incremental load) and load step 1 (i.e., preload only).  34  CHAPTER 4 FINITE E L E M E N T M O D E L L I N G R E S U L T S  4.1 Overview Section 4.2 describes the sensitivity analyses that were performed to determine what leaf spring length was necessary to minimise the effect of the boundary conditions on the incremental strain along the U-bolt surface, and to determine the appropriate magnitude of the preload and the coefficient of friction.  Section 4.3 presents an evaluation of  incremental strain along the U-bolt under the loading conditions encountered in the preliminary field measurements. Based on the results recommendations were made for locating strain gauges on U-bolts for an axle weighing system.  Section 4.4 discusses  possible sources of bending in the U-bolt shank. Section 4.5 discusses the limitations of the empirical measurements and finite element modelling.  4.2 Sensitivity Analysis Although many variables affect U-bolt behaviour under load this analysis specifically investigated the effects of preloading and friction between the U-bolt and leaf spring block.  A range of typical friction coefficients (from 0.1 to 0.3) was considered because  the surface roughness was not known.  A range of preload value from 142 k N to 303 k N  was selected with the estimated preload from section 2.3 being mid range.  A n analysis  was also undertaken to find the minimum length of the leaf spring for which the incremental U-bolt strains did not change. The length of the leaf spring block was varied in order to reduce its modeling requirements and, at the same time, minimising boundary  35  condition effects. The mesh properties of the model, described in Section 3.4, were kept constant throughout the sensitivity analysis.  4.2.1 Leaf spring block length A leaf spring pack on a Hayes H D X is 1778 m m long. The leaf spring pack was modeled as a solid block (with the leaf springs glued to one another) and also was shortened in order to reduce the number of nodes required to model it.  The boundary condition used  at the bottom edge of the leaf spring (indicated in Figure 3.9) often creates stress concentrations ( A N S Y S 2002).  It was expected that these stress concentrations would  reduce the accuracy of strain estimates on the U-bolt, and that shortening the leaf spring block would exacerbate this effect.  Therefore, a sequence of analysis runs was  conducted in which the length of the leaf spring was increased until this boundary condition effect began to decrease. The parameters used in the analysis of leaf spring block length, and their values, are listed in Table 4-1.  A preload value of 142 k N  (corresponding to a torque of 1085 N-m) was used for this analysis. L e a f spring block length was varied between 165 and 521 mm.  For block lengths less than 165 mm, the  boundary condition effect adversely affected the strain estimates on the U-bolt. For leaf spring lengths greater than 521 m m the number of nodes required for modeling became a limitation.  The uniform load applied to the bottom of the trunnion saddle was equivalent  to 22.5 k N (i.e. the average difference between the right hand side drive wheel weights when fully loaded with water and when unloaded, refer to Table 2-1).  Friction  coefficient was taken to be 0.2 (i.e., a mid-point in the range of typical values (0.1 to 0.3).  36  Table 4-1: R u n sequence inputs to evaluate leaf spring block length Run sequence 1  1  Preload (kN) 142 .  1  Incremental load (kN) 22.5  1  Coefficient of friction 0.2  1  Leaf spring length* (mm) 165, 216, 267, 368, 419, 470, 521 :  _£  Figure 3.0.4 describes the physical dimensions of the leaf spring suspension  Figure 4.1 illustrates the relation between leaf spring block length and incremental strain at gauge location 1 on the U-bolt. It can be seen that variation in the incremental strain with respect to increasing spring block length is reduced for leaf spring block lengths of over 400 mm.  The same finding was true for incremental strains at gauge  location 2 (Figure 4.2). Therefore, a leaf spring block length of 470 m m was used in all subsequent analyses.  100  200  300 400 Leaf spring block length (mm)  500  600  Figure 4.1: Incremental strain at gauge location 1 on the U-bolt for various leaf spring block lengths (incremental load of 22.5kN, preload of 142 k N and U-bolt to leaf spring coefficient of friction of 0.2)  37  3.4  3.2 -  CD  3"  w  e  .9  £ c to  2 c  2.8 -2.6 -  CO  E CO  o 2.4 -  2.2 -  :  2 -0  100  200 300 400 Leaf spring block length (mm)  500  600  Figure 4.2: Incremental strain at gauge location 2 on the U-bolt for various leaf spring block lengths (incremental load of 22.5kN, preload o f 142 k N , and U-bolt to leaf spring coefficient of friction of 0.2) 4.2.2 Preload A sensitivity analysis was conducted on U-bolt preload to determine the most appropriate preload level for modelling. This analysis consisted o f evaluating preload at five levels and with five different coefficients o f friction, making for a total o f 25 observations. Table 4-2 summarises the input parameters used in this sensitivity analysis. The torque specification for the leaf spring U-bolts was 1630 N - m , however, this torque can vary i n practise by 270 N - m or more (Waugh 2005). Therefore, torque values between 1085 and 2310 N - m were considered i n the analysis. equation (1) for the given torque range.  38  The preload was calculated using  Table 4-2: R u n scenario for the different levels of preload and coefficient of friction between the curved portion of U-bolt and leaf spring Run sequence 2 3 4 5 6  Preload (kN) 142 196 231 267 303  Incremental load (kN) 22.5 22.5 22.5 22.5 22.5  Leaf spring block length (mm) 470 470 470 . 470 470  Coefficient of friction 0.1,0.15,0.2, 0.25,0.3 0.1,0.15,0.2, 0.25,0.3, 0.1,0.15,0.2, 0.25,0.3 0.1,0.15,0.2,0.25,0.3 0.1,0.15,0.2, 0.25,0.3  Figures 4.3 and 4.4 illustrate how U-bolt incremental strain varied with preload over the range of contact friction values, at an incremental load of 22.5kN.  The  simulated strains were compared to the measured incremental strains for the estimated U bolt preload. The preload value for the strain-gauged U-bolt in the preliminary test was estimated to be 231 k N (Section 2.3), The results of this sensitivity analysis indicated that: 1. U-bolt incremental strain was insensitive to preloads of between 140 k N and 231 kN; 2.  Incremental strain generally increased with preloads above 231 k N for all values of coefficient of friction;  3. Variation in incremental strain due to the coefficient of friction between the U-bolt and the leaf spring increased for preloads above 231 k N ; and, 4.  Variation in incremental strain with the coefficient of friction between the U-bolt and leaf spring was greater at gauge location 2 than at gauge location 1.  39  • 3 . 0 -I 140  preliminary strain m e a s u r e m e n t  ,  ,  ,  1  ,  ,  ,  160  180  200  220  240  260  280  ,—  300  P r e l o a d (kN)  Figure 4.3: Incremental strain at gauge location 1 on the U-bolt for various preloads and coefficients of friction (u) between the U-bolt and the leaf spring (incremental load of 22.5 k N and leaf spring length of 470 mm)  5.5  T  5.0  _  4.5  .£  4.0  3.5  3.0  -A-u-0.2 -e-u-0.25  2.5  -*-u-0.3 •  preliminary strain m e a s u r e m e n t  2.0 140  160  180  200  220  240  260  280  300  320  P r e l o a d (kN)  Figure 4.4: Incremental strain at gauge location 2 on the U-bolt for various preloads and coefficients of friction (u.) between the U-bolt and the leaf spring (incremental load of 22.5 k N and leaf spring length of 470 mm)  40  Although larger incremental strains were calculated for preload values in excess of 231 k N these may not be obtained, in practise, because of the relatively high level of preload required to generate them. The U-bolt preload from field testing was estimated to be 231 k N and this value was taken for all subsequent F E M analyses.  4.2.3 Coefficient of friction  The parameters given for run sequence 4 in Table 4.2 were used to estimate a suitable coefficient of friction between the U-bolt and the leaf spring block. Figures 4.5 shows the simulated incremental strain at locations 1 and 2 on the U-bolt for  different  coefficients of friction. N o clear trend for the relation between incremental strain and coefficient of friction was observed; different patterns are observed estimated preloads in Figure 4.3 and Figure 4.4.  for  different  Incremental strain at gauge location 1  was found to be relatively insensitive to coefficient of friction while incremental strain at gauge location 2 was a maximum at a coefficient of friction of 0.2. Due to the generally inconclusive results of the effect of coefficient of friction on the incremental strain a midrange value of 0.2 was selected for all subsequent analyses.  41  5.5  -i  o Simulated incremental strain at location 1 • Simulated incremental strain at location 2  c CD CO  P  •| 4.5 c to  £  4  CD  E  CD O  c  3.5  0.05  0.1  0.15  0.2 Coefficient of friction  0.25  0.3  0.35  Figure 4.5: Simulated incremental strains at locations 1 and 2 on the U-bolt for different U-bolt-to-leaf spring coefficients o f friction (incremental load o f 22.5 k N , preload o f 231 kN)  4.3 Analysis o f incremental strain Based on the results from the sensitivity analysis, the distribution o f incremental strain along the entire surface o f the U-bolt was calculated using a leaf spring block length o f 470 m m , an estimated preload o f 231 k N , external load o f 22.5 k N and a coefficient o f friction o f 0.2. Figure 4.6 shows the distribution o f incremental strain along the U-bolt surface. A s per the analysis objective, this distribution was examined to determine the best possible locations for mounting strain gauges on the U-bolt surface.  42  0  50  100  150  200  250  300  350  400  Distance along the U-bolt from the trunnion saddle (mm)  Figure 4.6: Distribution of incremental strain along the outer edge o f U-bolt surface (incremental load of 22.5 k N , preload of 231 k N and friction coefficient o f 0.2 between the U-bolt and the leaf spring)  Figure 4.6 indicates that the maximum incremental strain occurs close to the trunnion saddle and that it decreases uniformly from 0 m m to 220 mm. Where the U-bolt curved portion joins the straight, shank portion the incremental strain changes rapidly and reaches a minimum (0.1 microstrain) at 285mm. Incremental strain is relatively constant in the curved portion o f the U-bolt from 380 mm to 450 m m (i.e., within 70 m m o f either side of the apex of the curve). To investigate the source of bending the incremental strain on the inner surface o f the U-bolt was calculated and compared to that of the outer surface.  Figure 4.7 presents the incremental strain distributions along both inner and  outer surfaces o f the shank portion of the U-bolt. The increase in incremental strain on the inner surface towards the curved portion of the U-bolt was likely generated by a  43  superposition o f both axial and bending strains.  Therefore, where the strain curves  intersect the bending strain approaches zero as it changes sign and the incremental strain at this point (3.21E-06 microstrains) is solely due to axial load. The incremental strain due to bending can then be computed for any location on the shank by subtracting 3.21E-06 microstrains (the strain due to axial load) from the total incremental strain. Figure 4.8 shows the resulting strain distribution due to bending along the outer surface of the shank. The change in sign o f the incremental strain at 205 m m indicates that this is an inflection point for the displacement.  » Outer surface of U-taolt a Inner surface of U-bolt  54  O  D  £ • g £  outer Shank portion  2  0  50  100  150  200  Distance along the U-bolt shankfromthe trunnion saddle (mm)  Figure 4.7: Incremental strain distribution along the inner and outer surfaces o f the U-bolt shank (incremental load 22.5kN, preload of 231 k N and friction coefficient o f 0.2)  44  4 outer  -  S h a n k portion j N  h I •  "  •  —  • N \ 1 ;  «• •  •  •  * •  •  •  * •  •  •  •  *  *  50  (t  100  150  200  •  Distance along the U-bolt shank from the trunnion saddle (mm)  Figure 4.8: Bending strain distribution along the outer surface o f the U-bolt shank (incremental load o f 22.5kN, preload o f 231 k N and friction coefficient o f 0.2)  The F E M predicted that the largest incremental strains on the shank o f the U-bolt occur near the trunnion saddle (Figure 4.6), however, a more preferred location for the strain gauge would appear to be within 70 m m to either side o f the U-bolt apex because: 1. incremental strain values are relatively constant within this area and so w i l l be accurately read by strain gauges, 2.  incremental strain values are due to axial and bending strains that when combined generate close to the maximum incremental strain i n the U-bolt,  3. the gauge location is relatively far from stress concentrations created by the fixed end conditions at the trunnion saddle and nut, and 4.  the location is better protected from debris and spray than most other parts o f the U-bolt.  45  A s seen in the.field testing and in the F E M results, the incremental strain in the U-bolt was very small. The ability of strain gauges to detect small changes in strain is considered to be infinite, however, a resolution of 0.1 microstrain is the smallest practical value attainable because of the limitation of instrumentation and other  performance  factors (Window 1992). Acceptable weight measurement accuracy can be achieved with a strong signal strength, however, even i f strains are relatively small. The signal output of strain gauges can be improved by increasing the strain gauge sensitivity (Gauge Factor) or adding a signal amplifier.  Strain gauge sensitivity can be improved through  the use of higher resistance strain gauges supplied with higher input voltage. If an amplifier is used it should be located close to the strain gauges so that a minimum of noise from connecting wires is amplified. In order to convert the small change in resistance of the strain gauge(s) into voltage suitable for amplification and processing, a half bridge Wheatstone bridge can be used (Window 1992).  Figure 4.9 illustrates the recommended gauge location on the  U-bolt surface where the two uniaxial gauges are used in opposite arms of the bridge so that the signal measured is from the combined axial and bending strains and two more resistors are used to complete the half. Additionally a strong signal can be obtained through series of similar half bridge system installed near the U-bolt apex.  46  Figure 4.9: Recommended gauge location on the U-bolt  4.4 Possible causes of bending in the U-bolt shank  One possible source of the bending in the U-bolt shank observed in the F E M may be a result of the curved portion of the U-bolt trying to retain its curvature while it is pulled in the loading direction (Figure 4.10). In response, the shank portion of the U-bolt is bent inwards at the intersection with the curved portion. This inward deformation would be resisted by the fixed support at the bottom of the U-bolt shank. (The U-bolt end is considered to be fixed because the shank portion of the U-bolt and nut are glued to the trunnion saddle in the F E M ) . This deformation in the shank would create bending strain (that is, tension on the outer surface and compression on the inner surface of the shank).  47  curved portion of U-bolt  T- Tension C- Compression P- Axial force  Shank portion of U-bolt  T /////  Figure 4.10: Bending in the U-bolt A 2 - D model (Figure 4.11) was developed to check the above hypothesis. T w o cases were evaluated: case 1 (Figure 4.12 Case 1) defines contact elements on both the curved and straight portions; case 2 (Figure 4.12 Case 2) had contact only between the curved portions o f the U-bolt and leaf spring block.  In case 1 the U-bolt shank is  constrained against penetrating the leaf spring block; In case 2 the U-bolt shank is allowed to penetrate the leaf spring block.  Both cases were considered because, i n  practise, the shank portion o f the Hayes H D X suspension U-bolts is slightly wider than the leaf spring pack and may or may not be i n contact along the straight portion o f the  48  U-bolt when preloaded. Figure 4.13 shows the response to axial loading for case 1 when a 34.47 M P a (5000 psi) pressure was applied at the end of the curved portion of the U-bolt. The contact with the leaf spring block prevents inwards deformation of both the curved portion and the shank of the U-bolt. Thus, the shank deformation w i l l be purely axial and no bending moments w i l l be generated in the shank portion of the U-bolt. Figure 4.14 shows the deformed shape for case 2. The resulting deformation supports the hypothesis that the curved portion of the U-bolt w i l l tend to retain its curvature under an applied axial load.  14  2005  4 : IB : 59.  Figure 4.11: Geometry of two-dimensional model  49  Lines on the contact surface implies contact surface's outwan normal  >  1 Case 1 (a)  ,  Case 2 (b)  Figure 4.12: Contact elements in two cases  AN  DISPLACEMENT  NOV  DMX =.00183  Figure 4.13: Deformed shape for case 1  50  14  2005  ANSYS NOV  STE?=1 SUB =5  14 2005 14:18:23  i  Figure 4.14: Deformed shape for case 2 A second possible source of the bending in the shank could be the presence o f misalignment in the model. In finite element modelling, the alignment of the geometric model is confined to keypoints (Figure 4.15). In the process of model creation, the U-bolt shank was created by extruding the cross-sectional area (Areal) to the prescribed height (Figure 4.15) defined between keypoints 1 and 2. It was observed that these keypoints were slightly misaligned in the z direction (by an order of magnitude 10" mm). This 15  small misalignment is not a significant source of bending moment for the U-bolt shank FEM.  51  curved portion of U-bolt  j  keypoint 1 z  Area 1  |\shank portion of U-bolt  keypoint 2 Figure 4.15: Defining U-bolt Volume in F E M  4.5 Limitations of the empirical measurements and finite element modelling Empirical measurements were performed on the single truck parked on level ground. The load applied was comparable to about one third o f the full payload. Incremental strain was measured as load was removed from the truck and was measured i n only one  52  suspension U-bolt.  The strain measurements may differ for trucks having different  suspension arrangements.  Strains in the instrumented U-bolt would be expected to be  higher when the truck is on favourable grades because load shifts from the trailer to the tractor, however, this load shift may easily be predicted through geometric relations. Strains may also vary when load is added to the truck because of differences in the way the suspension moves during loading versus unloading.  The empirical data was not  checked for repeatability of incremental strains for payloads of similar magnitude. Finally, measured strains may vary between the four U-bolts. The F E M was correlated with only one set of load and incremental strain results from the preliminary strain measurements.  F E M inputs included assumed levels of U -  bolt preload and U-bolt-to-leaf spring coefficient of friction. A maximum U-bolt preload was estimated using a preload-torque relationship but preload may vary, i n practise, for different torque levels and torque coefficients. U-bolt-to-leaf spring friction may increase with corrosion (in-service life), however, the F E M found no trend for coefficient of friction so how this would influence strain measurements is unclear. A moderately fine mesh was used to model the U-bolt however more accurate results are not expected to be obtained with use of a finer mesh. This is because comparable results were obtained with a finer mesh (not reported in the thesis) but required much longer computational time. The U-bolt was modelled assuming that the straight shank portions were free to displace inwards in response to bending moment.  In practise, it is unclear whether the U-bolt  shanks could bend inwards and, i f they are prevented from this movement then the F E M w i l l slightly overestimate strain levels in the U-bolt shank.  53  CHAPTER 5 SUMMARY, CONCLUSION AND  RECOMMENDATION  One way to reduce the incidences of brake failure of off-highway log trucks when descending steep grades is to manage the trucks' load sizes.  This can be done by  measuring the axle weights during loading. A review of on-board weighing systems i n Section 1.2 reported that to-date no commercially available on-board technology exists for measuring drive axle weights of off-highway tractors. This is because none of the systems are made specifically for off-highway tractors and the on-highway truck systems are not readily adaptable to the structural differences present in off-highway log trucks. Due to the unsuitability of the existing technology, the suspension components of an offhighway log truck were evaluated for use as load transducers.  This evaluation was  conducted i n two stages: preliminary strain measurements were gathered from a loaded off-highway tractor; and, a U-bolt from the tractor's leaf spring suspension was analysed using finite element modelling. The preliminary strain measurements indicated that the load-strain response of the U-bolt was linear for unloading over the tested range of external loads. A three-dimensional F E M was created to check the outer surface of the U-bolt for locations that developed the largest strain responses.  The modelling was  carried out in two loading steps. First, the U-bolt was preloaded; and, second, an external load was applied to the bottom of the trunnion saddle.  A sensitivity analysis was  conducted to determine the appropriate level of preload, coefficient of friction, and leaf spring block length for use in modelling the U-bolt incremental strain.  The  FEM  predicted that U-bolt incremental strain was a maximum near the trunnion saddle and a  54  minimum at the intersection of the shank and curved portions, and again near the maximum at the top of the curved portion.  The predictions of strain in the U-bolt shank  could be less reliable because they assumed no contact between the leaf spring block and U-bolt shank. In practise, there may not be sufficient clearance to develop the bending forces that generated the predicted strains.  The incremental strains in the top of the  curved portion of the U-bolt were relatively constant and were close to the largest observed in the U-bolt.  Given the uniform strain distribution and the magnitude of the  incremental strains in the curved portion of the U-bolt it is the most promising location for strain gauging. The calibration of the F E M model constructed in this study was limited by the lack of empirical data. However, the results of the incremental strain analysis indicate it is unlikely that the incremental strain in the U-bolt w i l l be an order of magnitude greater than that found in the preliminary measurements. Thus the next stage in development of the U-bolt load transducer is to build a prototype that takes advantage of higher resistance strain gauges and amplifiers to produce a reliable signal.  55  REFERENCES  A N S Y S , 2002. Reference Manual A N S Y S Version 8.0. A N S Y S Inc., Pittsburgh, P A . A S M , 1999. Metals Reference Book. 2 (Metals Park, OH).  n d  ed. American Society of Metals International  Burke, A . M . and O. A . Olatunbosun, 1997. "Static tyre/road interaction modelling. " Meccanica journal, V o l . 32, pp 473-479, British Columbia Ministry of Forests, 1999. Forest Service Bridge Design and Construction Manual. B C M O F . . Victoria, BC (52p). Available online "http://www.for.gov.bc.ca/hth/engineering/documents/publications_guidebooks/manuals _standards/bridge_manual.pdf' last visited 03-11-2005. Diamantoudis, A . Th. and Ch. A . Apostolopoulas, 2002. " B o d y mounting and A D R requirement for tank vehicles carrying dangerous goods", Tech. Chron. Sci. Journal, V o l . 4, N o . 1-2, pp 19-25 (in Greek, extended summary in English). Duffy, D. P., 2003. "What you should know about weighing systems." Management magazine, V o l . 13 Issue, N o . 7 N o v / D e c 2003.  MSW  Dayton Parts Ltd., 2001. U-bolts Training and Technical Manual. Product Emphasis Program (PEP) N O . 8 (4p). Available online "http://www.daytonparts.com/_pdf/PEP08_U-Bolts.pdf' last visited 03-11-2005. Imaoka, S., 2000. "Modelling preloaded bolts". Memo from Collaborative Solution Inc, (1 lp). Available online " h t t p : / / A N S Y S . n e t / A N S Y S / t i p s / w e e k l 2-STI43_TNT_Bolt_preload.pdf' last visited 11-02-06. K i r b y , D. and R. Charniga, 2005. " A finite element and experimental analysis of a light truck leaf spring system subjected to pre-tension and twist loads." S A E Technical Paper 2005-01-3568, Society of Automotive Engineers. Warrendale, P A . (lOp). Lathan, C , 1999. Construction Mechanics Basic Volume 2. U S Naval Education and Training Professional Development and Technology Center. Laursen, T . A . and J.C. Simo, 1993, "Algorithmic Symmetrization of Coulomb Frictional Problems Using Augmented Lagrangians", Computers Methods in A p p l i e d Mechanics and Engineering, V o l . 108, N o . 1 & 2, pp 133-146 Newton, W . H . , 1987. Trials of Three On-board A x l e Weighing Systems for Heavy Goods. Research Report 103, Transport and Road Research Laboratory, U K . (24p).  56  Norton, R.L, 1996. Machine Design: A n Integrated Approach. Prentice-Hall, N e w Jersey. Parker, S., 2004. "Hauling safety on steep road grades in British Columbia" in Proceedings I U F R O 12 International Mountain Logging Conference. Vancouver, B C . June 2004, ( l i p ) . th  Phillips, E., 1989. On-board Weigh Scales for Logging Trucks and Loaders: Evaluation. F E R I C Technical Report T R - 9 1 . Vancouver, B C . (26p).  an  Oakley, P. and N . G . Marshall, 1989. Optimal Sizing of Off-highway Logging Trucks. F E R I C Technical Report TR-96. Vancouver, B C . (20p). Ragab, A . R . and S. E. Bayoumi, 1999. Engineering Solid Mechanics: Fundamentals and Applications. C R C Press. Florida. Rizzo, A . R . , 1991. " F E A Gap Element: choosing the right stiffness." Mechanical Engineering, V o l . 113, N o 6, pp 57-59. S A E , 1999. Manual on Design and Application of Leaf Springs, 4 Automotive Engineers. Warrendale, P A . (122 p).  th  edition. Society of  Saravi, A . and K. C. Lyons, 2004. "Finite element modelling of guyed backspars in cable logging." In Canadian Journal of Forest Research V o l . 34, pp 817- 828. Speck, J . A . , 1997. Mechanical Fastening, Joining and Assembly. Marcel Dekker Inc.. N e w York, N Y . Stalling, J . M . and D. Y . Hwang, 1992. "Modelling pretensions i n bolted connections." Computers and Structures, V o l . 45, N o . 4, pp 801-803. Walsh, R. A . , 2000. Electromechanical design handbook. M c G r a w H i l l , N e w York, N Y . Waugh, A . , 2005. Personal Communication, Hayes Forest Service. Window, A . L., 1992. Strain Gauge Technology, 2  n d  edition. Elsevier. Essex, U K .  Workers Compensation Board of British Columbia, 2003. Incident Bulletin IB2003NOA399. Vancouver, B C . (2p). Available online. "http://publications.healthandsafetycentre.org/PDFs/SafetyBulletins/IB2003NOA399.pdf " last visited 03-11-2005.  57  APPENDIX I Strain transformation along the curved part of U-bolt  Local  Shank portion  Global  Curved portion  x  Figure A.I: Strain transformation along the curved portion of the U-bolt  If s , s , e , y , Y x  y  z  xy  y z  and y  z x  are the three dimensional strain components aligned  with x y z coordinate system then the strain component e with respect to node aligned x  along with the xyz £  =J £  x  coordinate system (Ragab and Bayoumi, 1999) is  + e m + s n + y lm + y mn + y nl  2  2  y  2  z  yz  2X  where s , s , e are normal strain x  y  z  Yxy, Yyz and Yzx are engineering shear strain 1, m and n are the directional cosine vector which was calculated from the unit tangent vector in A N S Y S .  58  Note: A N S Y S reports the engineering shear strain which is twice the tensor shear strain  dv  r  y xy  —  dx  du^ \ = 2s xy dy  + -  r  dw  dv  dy V  dz  du dz  dw = 2e. dy j  r  r, y  2e  where u,v,w are the displacements at the x,y,z direction respectively  s ,s ,s xy  yz  zx  are the tensor shear strain  59  A P P E N D I X II The dimension of the slip-on water tank used in testing  All the Dimensions are in metres Plate thickness of 0.01m  M3 CD  FiotitViav  3£5  Top viav  Figure A.II: Slip-on water tank dimensions  60  

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