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Friction sawing of wood Yu, Kwei Cho 1966

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THE FRICTION SAWING OF WOOD by KWEI CHO YU B. Sc., National University of Chekiang, Hanchow, China, 1046. A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of Mechanical Engineering We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1966. In presenting this thesis i n pa r t i a l fulfilment of the requirements for an advanced degree at the University of Bri t i s h Columbia,, I agree that the Library shall, make i t freely avai]able for reference and study, I further agree that permission-.for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Mec/)Cff?/C<r / _j£a^AtE^r-J^ The University of B r i t i s h Columbia Vancouver 8 , Canada i ABSTRACT The f r i c t i o n sawing of wood by a high speed rotating disk has been studied. The present experiments were carried out by sawing two commonly used timbers; namely, Douglas f i r and Western red cedar of different mois-ture contents, A 14 inch diameter, 14 gauge steel disk with a smooth edge, driven at a rotating speed of 4,620 rpm was used for the research. A theo-retical analysis of heat transmission characteristics and temperature dis-tribution i n the sawing disk i s presented. Experimental results showed that the f r i c t i o n a l forces, power con-sumed and cutting temperatures increased as feed speeds increased. The results also showed that the moisture content of the wood had no noticeable influence on the sawing action. A narrow kerf, straight, smooth and po-lished cut surfaces are some of the advantageous features of the process. At low feed speeds the calculated cutting edge temperatures were well below the ignition temperature of the wood specimen. However at high feed speeds the experimental horse power values increased and high calcula-ted cutting edge temperatures consequently obtained. Excessive power con-sumption and high cutting edge temperatures were believed to be related to the d i f f i c u l t y of disposition of cut material with a smooth edge disk. Reasonably high feed speeds were evident i n cutting plywood and veneer. For these materials clean, smooth and polished cut surfaces were evident. The method may be advantageous i n the cutting of plastic sheets. When cutting thicker lumber with this method the feed speed was confined to an impractical low level and power consumed was far higher than that required for ordinary sawing. Thus, whether this method of sawing can be put into practical use or not is determined by the possibility of having i i an effective means to dispose of cut material. In this connection several methods of modifying the disk for more efficient cutting and waste disposal are presented. i i i NOMENCLATURE Preferred Symbol Quantity Units LETTER SYMBOLS A^ Cross section area of outer periphery of annulus sq. f t . Ag Cross section area of inner periphery of annulus sq. f t . b Thickness of sawing disk f t . , i n . D Disk diameter f t . , i n . Fj, F r i c t i o n force on the cutting edge l b . F„ Normal force exerted on the wood l b . F T Feed thrust l b . h . C o e f f i c i e n t of heat t r a n s f e r at the side surface „ of the disk B t u / f t -hr.-°F J Mechanical equivalent of heat 778 f t . - l b / B t u K a Thermal conductivity of surrounding a i r Btu/ft-hr-°F K Thermal conductivity of s t e e l Btu/ft-hr-°F s L^ Length of wood specimen F t . £ Distance between reaction R and axis Y-Y1 F t . £i Distance between t a i l edge of wood and axis Y-Y' F t . ^2 Distance between rea c t i o n R^ and axis Y-Y' F t . Distance between t a i l edge and centre of gra v i t y of wood specimen F t . X^z Distance between c u t t i n g edge and t a i l edge of the wood specimen F t . N Rotating speed of disk . rpm Q^ Rate of heat inflow through the outer circum-ference of annulus Btu/hr. Qg Rate of heat outflow through inner circumference of annulus Btu/hr. Symbol Quantity 4 R R R l R„ Rate of heat transfer by radiation Rate of heat convected through aide surfaces Table support s t r a i n r i n g reaction Reaction exerted by t a i l edge of wood specimen on the table Reaction exerted on the wood specimen by the r o l l e r on the upper guide block r Inner radius of an annulus of the disk r Q Radius of sawing disk 6 Increment of radius r S Area of two side surface of annulus T = T - T am T(r) Disk temperature, function of radius ^ab Absolute disk temperature Feed speed •W Weight of specimen W Weight of specimen after being cut and before being dried.?- . Oven-dried weight of wood specimen Preferred Units Btu/hr. Btu/hr. l b . l b . l b . f t . f t . , i n . f t . sq„ f t . °F °F (°*> in./min. l b . l b . l b . xv GREEK LETTERS e Angle between the axis Y-Ye and the radius of the disk passing through top of cutting edge Angle between the axis Y-Y* and the radius of the disk passing through bottom of cutting edge. Angle between normal force F N and axis Y-Y' D i f f u s i v i t y of steel lI'K b s Degree Degree Degree f t 2 / n r . f t . * 1 Symbol Quantity Preferred Units a max 2 2 Kinematic v i s c o s i t y of surrounding a i r f t /sec», f t /hr. Stefan - Boltzman constant Btu/hr,«ft - ( T B ) T Local temperature °F Ambient temperature °F A T Maximum temperature difference between disk temperature and ambient temperature °F Angular v e l o c i t y of saving disk rad/sec , rad/hr» DIMENSIONLESS GROUP & C 2 Constants i n the solution of Bessel Equation e Emissivity of sawing disk I Modified Bessel function, order 0. 1st kind o Modified Bessel function, order 1, 1st kind {^G'/1) W+13.95R K = 5.53 " K Modified Bessel function, order 0* 2nd kind* o N Nusselt number u P Prantdl number r Rfi Rotational Reynolds number (i C oefficient of f r i c t i o n between disk and wood v i ACKNOWLEDGEMENT This experimental work was carried out i n the Lubrication Labora-tory, Department of Mechanical Engineering, University of B r i t i s h Columbia. Financial assistance was received from the National Research Council of Canada under Grant Number A-1065. The author i s grateful to the MacMillan, Bloedel and Powell River (B.C.) Ltd., for the supply of woods for t h i s experimental work; to the Vancouver Laboratory, Forest Products Laboratories of Canada for the season-ing of wood specimens. The author wishes to thank the Staff of Mechanical Engineering Department and Mr. J.E. Jones of the Lubrication Laboratory for t h e i r valuable assistance. The author also thanks Dr. Z. Rotem for his constructive sugges-tions on heat transmission i n the development of the theory of t h i s thesis. P a r t i c u l a r thanks are due to Dr. C.A. Brockley, the author's research Superviser, for his sound di r e c t i o n and constant encouragement i n the course of developing t h i s t h e s i s . v i i TABLE OF CONTENTS Page Chapter I I . 1 Introduction .* . • 1 Chapter II I I . 1 Theory 3 Chapter III I I I . 1 Apparatus ••• 10 I I I . 2 Measurements 16 111.3 Specimens 24 111.4 Experimental Procedure '. 25 Chapter IV IV. 1 Results 27 Chapter V V. l Discussion ... 61 Chapter VI V I . 1 Conclusion 65 VI.2 Recommendations • 66 v i i i TABLE OF CONTENTS Contd. Page Appendix A C a l i b r a t i o n of Table Support S t r a i n Ring 89 Appendix B C a l i b r a t i o n of Feed Thrust Measuring S t r a i n Ring 70 Appendix C C a l i b r a t i o n of Chrome1 - Constantan Thermocouple f o r Measuring Cutting Temperature 72 Appendix D Seasoning of Wood Specimens * * • 73 Appendix E Force Analysis During Cutting 74 Appendix F Numerical Results Obtained from Th e o r e t i c a l Equations 79 Appendix G Comparison of Heat Transfer by Radiation with Convective and Conductive Processes 84 ix LIST OF FIGURES Figure Page 1 Sawing Disk and Collars. 4 2 Schematic Drawing of the General Arrangement of the Friction Saw 12a 3 General Arrangement of Instruments and the Friction Saw , ,. 12b 4 Sawing Disk and Table 12c 5 Guide Blocks 13 6 Position of Specimen During Sawing 14 7 Strain Ring 15 8 Instrument Connections Block Diagram ............................ 18 9 Carriage, Power Screw and Push Rod for Feeding 20 10 Detail of Temperature Measuring Probe 22 11 Forces on Wood Specimen 23 12 Wood Specimen and T a i l Piece 25 13 Graph of Frictional Force versus Feed Speed, 11$ Moisture Content 29 14 Graph of Normal Force versus Feed Speed, 11$ Moisture Content ... 30 15 Graph of Frictional Force versus Feed Speed, 19$ Moisture C ontent 31 16 Graph of Normal Force versus Feed Speed, 19$ Moisture Content ... 32 17 Graph of Frictional Force versus Feed Speed, 25$ Moisture Content 33 18 Graph of Normal Force versus Feed Speed, 25$ Moisture Content ... 34 19 Graph of Frictional Force versus Feed Speed, 32$ Moisture Content 35 20 Graph of Normal Force versus Feed Speed, 32$ Moisture Content ... 36 21 Graph of Frictional Force versus Feed Speed, 34$ Moisture Content 37 X LIST OF FIGURES Contd. Figure Page 22 Graph of Normal Force versus Feed Speed, 34$ Moisture Content !38 23 Graph of F r i c t i o n a l Force versus Feed Speed, 72$ Moisture Content 39 24 Graph of Normal Force versus Feed Speed, 72$ Moisture Content 40 25 Graph of C o e f f i c i e n t of F r i c t i o n versus Feed Speed, 11$ Moisture Content • 41 26 Graph of C o e f f i c i e n t of F r i c t i o n versus Feed Speed, 19$ Moisture Content • 42 27 Graph of C o e f f i c i e n t of F r i c t i o n versus Feed Speed, 25$ Moisture Content • ^3 28 Graph of C o e f f i c i e n t of F r i c t i o n versus Feed Speed, 32$ Moi sture C ontent • ;44 29 Graph of C o e f f i c i e n t of F r i c t i o n versus Feed Speed, 34$ Moisture Content !45 30 Graph of C o e f f i c i e n t of F r i c t i o n versus Feed Speed, 72$ Moisture Content • • 46 31 Graph of F r i c t i o n a l Force versus Moisture Content - Cedar Across Grain Cutting -47 32 Graph of F r i c t i o n a l Force versus Moisture Content - Cedar Along Grain Cutting (48 33 Graph of F r i c t i o n a l Force versus Moisture Content - F i r Across Grain Cutting • C49 34 Graph of F r i c t i o n a l Force versus Moisture Content - F i r Along Grain Cutting , 50 35 Graph of Power Consumed versus Feed Speed - 11/6 Moisture Content 51 36 Graph of Power Consumed versus Feed Speed - 19$ Moisture Content • (5.2 37 Graph of Power Consumed versus Feed Speed - 25$ Moisture Content • 53 38 Graph of Power Consumed versus Feed Speed - 32$ Moisture Content (54 39 Graph of Power Consumed versus Feed Speed - 34$ Moisture Content '55 LIST OF FIGURES Contd. Figure Page 40 Graph of Power Consumed versus Feed Speed - 72$ Moisture Content 56 41 Graph of Cutting Temperature versus Feed Speed (57 42 Graph of Power Consumed versus Moisture Content - 8 in./min. Feed Speed 58 43 Graph of Power Consumed versus Moisture Content - 12 in./min. Feed Speed 59 44 Appearance of Cut Faces - Five D i f f e r e n t Feed Speeds ........ 60 45 Comparison of Cut Faces Between Ordinary Sawing and F r i c t i o n Sawing • 60 46 Recommended Saw Blade with Inner Teeth to Dispose of Wood Waste 67 47 Recommended Saw Blade to Eliminate Pinch A c t i o n 67 48 F i x t u r e f o r "Daytronic" 103A - 80 Linear Transducer C68 49 C a l i b r a t i o n of Table Support S t r a i n Ring (Tension) L69 50 C a l i b r a t i o n of Thrust Measuring S t r a i n Ring -71 51 Forces on Sawing Disk and Table • -74 52 Free Body of Wood Specimen • 75 53 D i r e c t i o n of Normal Force Acting on the Specimen L77 1 I C H A P T E R I . 1.1 I N T R O D U C T I O N F r i c t i o n a p p e a r s a s a r e s i s t a n c e t o t h e r e l a t i v e m o t i o n o f t w o s o l i d b o d i e s i n c o n t a c t . F r i c t i o n a l e n e r g y m a y b e c o n v e r t e d i n t o h e a t t h u s r a i s i n g t h e t e m p e r a t u r e o f t h e c o n t a c t i n g s u r f a c e s . I n m o s t e n g i n e e r i n g a p p l i c a t i o n s t e m p e r a t u r e e f f e c t s a s s o c i a t e d w i t h f r i c t i o n a r e c o n s i d e r e d t o b e u n d e s i r a b l e b u t f o r f r i c t i o n s a w i n g t h e h e a t m a y b e u s e f u l l y e m p l o y e d f o r c u t t i n g m a t e r i a l s . F r i c t i o n s a w i n g o f m e t a l s h a s b e e n s u c c e s s f u l l y a p p l i e d b y u t i l i -z i n g t h e f r i c t i o n a l h e a t t o s o f t e n t h e m e t a l a n d t h e n s w e e p i t a w a y b y t h e s a w b l a d e [ ! ] . F r i c t i o n s a w i n g o f w o o d i s b a s e d o n s i m i l a r p r i n c i p l e s , A t h e o r e t i c a l a n a l y s i s o f t e m p e r a t u r e d i s t r i b u t i o n i n t h e s a w i n g d i s k a n d t h e r e l a t i o n b e t w e e n t h e c u t t i n g e d g e t e m p e r a t u r e a n d p o w e r c o n s u m e d c a n b e m a d e b y c o n s i d e r i n g h e a t t r a n s m i s s i o n i n a r o t a t i n g d i s k w i t h h e a t g e n e r a t e d a t t h e p e r i p h e r y . T o r a i s e t h e c u t t i n g e d g e t e m p e r a t u r e a n d t h e n m a i n t a i n i t , 2 a s u f f i c i e n t amount of heat must be generated i n order to balance the l o s s e s . Heat loss through the wood specimen i s n e g l i g i b l e . This method of sawing wood by the use of f r i c t i o n a l heat, insofar as can be determined, has not been previously studied. The f r i c t i o n a l heat u t i l i z e d f o r sawing i s r e l a t e d to the c o e f f i -c i e n t of f r i c t i o n at the cutting edge. Furthermore, the feed speed may influence the values of the forces involved. Therefore the f i r s t purpose of the experimental i n v e s t i g a t i o n was to e s t a b l i s h the force values and t h e i r i n t e r r e l a t i o n s h i p s during actual c u t t i n g . The measurement of the temperature near the c u t t i n g edge was also included i n the i n v e s t i g a t i o n . Power con-sumed, wood saving and the condition of the cut surface are important economic factors and received a t t e n t i o n i n the present i n v e s t i g a t i o n . Mois-ture content a f f e c t s the strength of the wood and influences ordinary toothed sawing processes [2], hence i t was treated as a v a r i a b l e i n the present r e -search. 3 CHAPTER I I . I I . 1 . THEORY During f r i c t i o n sawing heat is generated at the interface between the edge of the sawing disk and the wood specimen. The amount of heat generated at the interface and the heat transmission characteristics deter-mine the temperature distribution i n the system. The majority of the heat generated is transmitted to the disk since the ratio of the thermal conduc-t i v i t y of wood to that of steel is as small as 1 ;13 to 1:26 (average thermal conductivity of Douglas f i r - 1 .0 to 2 .0 Btu./hr. f t , °F [3] and the thermal conductivity of steel - 26 Btu./hr. f t . °F [4,]*)--The system under consideration i s actually a rotating disk with heat generated at the periphery. As the amount of heat generated i s a function of the f r i c t i o n a l force the relation between the cutting tempera-ture and the f r i c t i o n a l force may be obtained as follows. 4 Assumptions: 1. The disk i s t h i n compared with i t s diameter; hence the temperature v a r i a t i o n normal to the plane of symmetry may be neglected. 2. Heat i s only generated at the portion of the disk where i t i s instan-taneously rubbing on the wood. However, with the disk rotating at high speed ( 4,620 rpm ) the period 2TT/CU i s only a small f r a c t i o n of a second ( 0.013 sec. or 3.6 x 10~ hr. ), the radius of the disk r Q = 7/12 f t . and d i f f u s i v i t y of steel K = 0.48 f t . /hr. [5j hence the product r o Therefore we may consider the periphery of the disk to be isothermal at a quasi-steady state condition. £8] 3. The amount of heat transfer by radiation i s small i n comparison with convective and conductive processes and may be neglected. A t h e o r e t i -c a l j u s t i f i c a t i o n i s given i n Appendix G. F i g . 1 Sawing Disk and C o l l a r s . Consider the heat balance i n an annulus having inner radius r and outer radius r + 6r ( F i g . l ) . Heat inflow through the outer circumference of the annulus per unit time i s given by: where K g = thermal conductivity of st e e l A^ = cross-section area of outer periphery of annulus = 2TT ( r + 6r)b T = l o c a l temperature b = thickness of disk Heat outflow through inner circumference per unit time: <*2 - + V 2 I ; •• <2-2> where Ag = cross section area of inner periphery of annulus = 2nrb Heat convected through side surfaces per u n i t time: Q = + Sh ( T - T ) (2-3) a N am7 v 7 where S = area of two side surfaces of annulus = 2TT [ ( r + 6 r ) 2 - r 2 ] h = c o e f f i c i e n t of heat trans f e r at the side surfaces a of the disk. T =ambient temperature am Under steady conditions the rate of heat inflow to the annulus must be equal to the heat outflow, and as defined i n the assumptions ( l ) , (2) and (3) we may neglect temperature v a r i a t i o n normal to the plane of symmetry; the p e r i o d i c i t y of heat input and transf e r of heat by r a d i a t i o n , we may have Q x = Q 2 + % (2-4) From equations (2-1), (2-2), (2-3) and (2-4) the d i f f u s i o n equation f o r the system i s obtained (neglecting (dr) --terms). 4 ' - ; ffl-A-o • ( 2 - 5 ) dr dr where T = T — T am /2h ' x s This i s the form of a modified Bessel equation of order 0 with parameter X. The complete s o l u t i o n of ( 2 - 5 ) i s T(r) = C ^ X r ) + C ^ o ( \ r ) (2-6) t i o n s . Where and Cg are constants to be determined by boundary condi-I = modified Bessel function, order 0, 1st kind K = modified Bessel function, order 0, 2nd kind o ' ' Boundary Conditions 1 im (a) Since r = 0 i s included i n the range, but _ Q K q(X) -• 0 0, we must have c 2 =0 giving T(r) = C j I ^ X r ) (b) At the outer periphery where the heat i s generated, the temperature i s a maximum T ( r ) = A T v o' max A T n max C l ~ I (Xr ) o x o' Hence I (\r) T(r) = T V J — V A T (2-7) v ' I (Ar ) max N ' o v o' Thus, for instance, I Q (Xr o ) = 2,200 (Appendix F ) , a t r = 0 T ( ° ) = ^ f o f l e s s t h a n Tmax At r = 3 inches, the part of the disk in contact with the col lar I Q(4.17) = 13.09 (Appendix F) T (3/12) =-|^g§§ i . e . s l ight ly more than 0.5$ A Tmax Differentiate (2-7) with respect to r S l i . «I . I j ^ . ^ ( M ) dr dr I (Xr ) max v ' os o# where 1^ = modified Bessel function, order 1, 1st kind Hence the temperature gradient at the disk periphery dT d r I,(Xr ) = ° K XAt (2-9) r I (A.r ) max N o 0 N 0' Substituting (2-9) in (2- l ) gives the expression for heat flux at the disk periphery o or q1 = — 2TK br 4l| r s odrIr o ' 0 I , (\rJ = - 2nK br T V 1 XAT (2-10) r s o l (Ar ) max x ' 0 o x o' Heat generated at the disk periphery i s 8 where |i = c o e f f i c i e n t of f r i c t i o n between the disk and the wood co = angular v e l o c i t y of disk J = mechanical equivalent of heat FJJ= normal force exerted on the wood f (Heat input to disk) = (Heat flux at periphery) |iFXTvOr I (Xr ) N o • n „ , o N o' , * + — = = + 2nK br T n 1 i XAT J s o I,(Xr ) max 1 x o' Rearranging terms, 2nJK b I,(Xr ) s l v o' M>F.T = — / • ° . \ A T (2-11) N cu I (Xr ) max N ' o v o' Evaluation of the Parameter X : The experiments were c a r r i e d out with a 14 inch diameter sawing disk r o t a t i n g at 4,620 rpm. (co = 483,9 r a d . / s e c ) . The r o t a t i o n a l Reynolds number i s given by cor 2 where r = radius of di s k o co = angular v e l o c i t y of disk v = kinematic v i s c o s i t y of surrounding a i r a In the present case r = 0.5835 f t . o CO = 483.9 rad./sec. v = 0.00018 f t 2 / s e c . {8] Hence R = 915,200 e * Results for the coefficient of heat transfer, at the side surface of the disk,h may be obtained from data by Cobb and Saunders [9], By the value of the Reynolds number we see that the present condition is at the tnjbulent end of the transition region. Thus using Cobb and Saunders' Fig.4 — 0 8 [9], we found that the mean Nusselt number (N = 0.15R W ,°) N = 875 u Since h r N u K Hence and since A o 41.83 , K br s o (2-12) Power Consumed: Power = JQ^ Power = 2nJK br T T T - T A A T (2-13) L D   /, \s ol (Ar ) ov o7 max and A T I (Ar ) Power (2-14) max I,Ur ) 2nJK br A l v o 7 s o 1 0 CHAPTER I I I . I I I . l . APPARATUS The apparatus consisted of three sub-assemblies: i . The sawing disk and dri v e ; i i . The table and guide; i i i . The feed mechanism. F i g s 2 and 3 show the general arrangement of these three sub-assemblies. The sawing disk and i t s shaft was driven by an induction motor through a V-belt d r i v e . The table carrying the wood specimen pivoted about the axis of the disk s h a f t . The specimen feed mechanism was driven by another induction motor through an hydraulic transmission u n i t . The wood specimen on the table was fed into the saw by the push rod of the feed mechanism. The feed speed of the specimen could be set to desired values by adjusting the hydraulic speed control u n i t . i . THE SAWING DISK AND DRIVE ( F i g . 2) ( i a ) The Sawing Disk and Shaft The 14 gauge sawing disk was made of SP plate s t e e l of hardness Rockwell C48. The outer periphery of the disk had a smooth surface without teeth. The disk had an outside diameter of 14 inches and an inner bore of i j - inches. The disk was mounted on an one inch diameter, SPS A t l a s s t e e l shaft between two supporting c o l l a r s 6 inches O.D. and 1% inches I.D. which were retained by a lock nut ( F i g . 4), The shaft was mounted on three bear-ings. ( i b ) The Motor and the V-Belt Drive A 15 H.P., 3,540 R.P.M. induction motor was used to drive the disk shaft. The power was transmitted by four size B, V - b e l t s . A 9-3/8 inches O.D. p u l l e y was attached to the disk shaft. With t h i s pulley arrangement the speed of the disk was stepped up to 4,620 R.P.M. giving a peripheral disk speed of 282 f t . / s e c . (16,920 ft./min). i i . THE TABLE AND GUIDE (Figs 4, 5, 6 & 7) ( i i a ) The Table The 30 inches x 16 inches x ^ inch aluminum table was mounted 4 inches above the centre l i n e of the d i s k . Along the l o n g i t u d i n a l centre l i n e a 14 inches by 3/8 inch s l o t was cut to permit the disk to emerge 3 inches above the table. The table was supported by two aluminum arms at each side of the disk ( F i g . 4). A short spindle was attached to each supporting arm. The spindle between the two l e f t hand bearings shown i n F i g . 4 was made hollow i n order to permit access f o r the disk shaft. The spindle bearings were flanged mounting b a l l bearings and were f i x e d on the two upper guard stands. The c o n c e n t r i c i t y of the disk shaft and the table supporting arm spindles simplified the calculation of the table forces by elimination of the moments of supporting reaction forces when taking moments about the axis of the disk shaft. (iib) Guide On the front part of the table a guide consisting of three aluminum blocks were attached (Fig. 5). The two side blocks with slots cut for the positioning bolts could be moved late r a l l y in order to compensate for the variation of specimen width. The upper block could be adjusted verti c a l l y to suit a variation of wood thickness. ( i i c ) Arrangements to Reduce Frictional Forces Between Wood Specimen and Table/Guide The f r i c t i o n a l forces between the wood specimen and the table and guide were reduced to negligible values. The inner walls of the two side blocks of the guide were lined with Arborite sheets. Fig. 6 shows that at the far end of the upper block of the guide a steel r o l l e r was installed in order to prevent the wood specimen from t i l t i n g up too far and to reduce the fri c t i o n a l force between the specimen and the upper guide block. A 9^ inches x 2 inches x l / l 6 inch Teflon strip was attached from the front edge along the centre line of the table. A t a i l piece with two Teflon rollers fixed at the rear corner was fastened to each specimen. Fig. 6 shows that during cutting the contact points between the specimen and the upper guide and between the specimen and the table were A and B respectively. (iid) Arrangement for Measuring Table Forces A strain ring was mounted on a stand under the table and was 13.95 inches in front of the vertical centre line of the sawing disk. The ring was made of mild steel with 3-3/16 inches O.D and 3 inches I.D. ( i . e . 3/32 inches thick). (Fig. 7). Fig. 3 General Arrangement of Instrument and the Friction Saw. J iTTl Upper Guard" S-Zond 7h&/& Styo//oor/-/r>g' /)r/n Upper Guard" tnr 1 sk and Table. 13 Fig. 5 Guide Blocks Fig, 6 Position of Specimen when Sawing is Proceeding. 15 F i g . 7 S t r a i n Ring 16 A weight pan at the rear end of the table was used f o r balancing. S u f f i c i e n t weights were applied to the pan i n order to give zero load on the table s t r a i n r i n g ( F i g . 2) iii . THE FEED MECHANISM ( i i i a ) The D r i v i n g Motor and the Transmission The feed mechanism was driven by an one horse power, 1,750 r.p.m., single phase induction motor through a hydraulic transmission u n i t . (Vickers Double Power Vnit9 Model AA-16801). The speed of the output shaft of the transmission could be var i e d continously from 0-550 r.p.m.. ( i i i b ) The Carriage and i t s Power Screw The output shaft of the hydraulic transmission was coupled to a single s t a r t 4 threads per inch power screw which i n turn drove the c a r r i a g e 0 A s p l i t nut on the carriage enabled i t to be engaged and disengaged from the power screw. The speed of the power screw and consequently the feed speed of the carriage could be changed by adjusting the output shaft speed of the hydraulic transmission. The speed of the output shaft of the hydraulic t r a n -smission had a continuous v a r i a t i o n i n the range from 0-550 r.p.m., hence the feed speed had a continuous v a r i a t i o n from 0 to 137.5 inches per minute. ( i i i c ) Push Rod and Thrust Measuring S t r a i n Ring The push rod was mounted on the fr o n t face of the carriage ( F i g , 9). The push rod M was r i g i d l y f i x e d to the lever arm K which was pivoted at 0, The reaction of the feed thrust, ,applied to the push rod, was transmitted through the lever arm K and the s t e e l b a l l J to the s t r a i n r i n g N, which measured the feed thrust F^. The mild s t e e l s t r a i n r i n g had the same dimen-sions as the table s t r a i n r i n g . ( F i g . 7) III.2 MEASUREMENTS _ _ _ _ _ _ _ _ The following quantities were measuredfjor c a l c u l a t e d from measured data; 1 7 i . D isk speed; i i . Table force; i i i . Feed Thrust; i v . Feed speed; v. Cutting temperature; v i . Specimen weight; v i i . Specimen centre of gravity; v i i i . C o e f f i c i e n t of F r i c t i o n between the Wood Specimen and the Sawing Disk. i . Disk Speed The disk speed was measured by a "Smith" tachometer. The ranges of the tachometer were 0-5,000 and 0-50,000 r.p.m. i i . Table Force A mild s t e e l s t r a i n r i n g was attached underneath the table 13.95 inches from the axis of the disk shaft. ( F i g . 2) The table was pivoted about the axis of the disk shaft, hence m u l t i p l i c a t i o n of the load at the s t r a i n r i n g by the distance between the r i n g and the disk centre l i n e gave the r e -sultant moment on the table about the a x i s . The d e f l e c t i o n of the s t r a i n r i n g was detected by a "Daytronic" 103A-80 l i n e a r displacement transducer. The transducer was c a l i b r a t e d to read d i r e c t l y the load applied to the r i n g i n pounds. The method of c a l i b -r a t i o n i s described i n Appendix A. E x c i t a t i o n of the transducer was supplied by a "Daytronic" d i f f e r -e n t i a l transformer i n d i c a t o r (Model 300BF). A v i s u a l d i splay of s t r a i n r i n g d e f l e c t i o n i n m i l l i - i n c h e s was shown by the i n d i c a t o r . ( F i g . 8) The centre of g r a v i t y of the wood specimen was moving during sawing; hence continuous v a r i a t i o n of forces resulted and thus a chart record of SRUSf/" Mode/ BL -332 "BRUSH" Mode/ RD-262Z-02 1 1 -—1 > • • • • S3 -o o o o ' /s/d/cafor-'(Mbd&30D8F} 1 £0/N Modu/crto* sBRUSH Osc/Z/ogrnph Mods/ F i g . 8 Instrument Connections B locK D i a g r a m . r -00 19 force versus p o s i t i o n or displacement of the specimen was required* The output from the d i f f e r e n t i a l transformer i n d i c a t o r was ampli-f i e d by an "Edin" modulator a m p l i f i e r * The amplified voltage was used to drive a "Brush" oscillograph (Model KD-2622-02) . A marker switch was f i t t e d to one side of the carriage. Along the surface of a s t r i p attached to the r a i l stand, buttons were f i t t e d at one inch i n t e r v a l s * The buttons actuated the marker switch which was connected to the marker recorder pen i n the o s c i l l o g r a p h . Hence a chart record of table force versus displacement of wood specimen could..be obtained* i i i . Feed Thrust Thrust was transmitted from the push rod to a mild s t e e l s t r a i n r i n g by a lever arm and a steel b a l l ( F i g . 9), The s t r a i n r i n g was mounted on the leading edge of the carriage* The d e f l e c t i o n of the r i n g was detec-ted by a "Daytronic" 103A-80 l i n e a r displacement transducer* The transducer was c a l i b r a t e d to read d i r e c t l y the force applied'on the push rod i n pounds. The method of c a l i b r a t i o n i s described i n Appendix B, In the same way as described i n the previous section, e x c i t a t i o n of the transducer was supplied by a "Daytronic" d i f f e r e n t i a l i n d i c a t o r (Model 300BF) which also gave a v i s u a l i n d i c a t i o n of the d e f l e c t i o n of the s t r a i n r i n g . The output of the "Daytronic" d i f f e r e n t i a l transformer i n d i c a t o r was amplified by a "Brush" D.C. a m p l i f i e r (Model BL-932) and was used to drive the other channel of the "Brush" o s c i l l o g r a p h described i n the pre-vious section. From the two channels of the oscillograph,chart records of feed thrust and table force versus displacement of wood specimen could be obtained ( F i g , 8), 21 i v . Feed Speed The feed speed was obtained by timing the carriage over a known t r a v e l distance, v. Cuttingj Temperature Temperature was measured by means of a measuring probe which con-s i s t e d of a 3/l6 inch 0„d., 11 inches long brass tube holding two chromel-constantan thermaeouples. The thermacouples were connected i n series with the cold junctions being placed i n an i c e bath. The t i p of the brass tube was insulated by a Teflon r i n g ( F i g . 10). A 9/32 inch diameter hole was d r i l l e d through each wood specimen along i t s l o n g i t u d i n a l a x i s . The probe was inserted through t h i s hole and was f i x e d i n p o s i t i o n by a copper clamp fastened to the f r o n t edge of the tab l e . The t i p of the probe was adjusted so that i t was l/8 inch from the cuttin g edge of the disk. Since the probe was f i x e d on the t a b e l , the hot junctions of the thermocouples remained i n the same p o s i t i o n during c u t t i n g . F i g . 10a shows that outer edge of the T e f l o n r i n g was tapered i n order to equalize the distance between the sawing edge and the two thermocouples. The signal from the thermocouples was amplified by a "Brush" D.C, ampli f i e r (Model BL-932) and the r e s u l t i n g voltage was used to drive a "Brush" o s c i l l o g r a p h (Model BD-2622-02). The marker switch on the push rod carriage was also connected to t h i s o s c i l l o g r a p h i n order to operate i t s marker recorder pen ( F i g . 8). By t h i s connection a chart record of c u t t i n g temperature versus displacement of the wood specimen could be obtained. The thermocouple chart was c a l i b r a t e d to give a d i r e c t reading of the cutting temperature i n degrees F. The method of c a l i b r a t i o n i s described i n Appendix C. However, i t should be stated that the temperatures measured were not e n t i r e l y representative of true i n t e r f a c e values. Fig. 1 0 Detail of Temperature Measuring Probe to ro 23 v i . Specimen Weight The weight was determined by a Howe scale having a range from 0 to 1 pound. v i i . Specimen Centre of Gravity The distance of the centre of gravity of a specimen from i t s rear edge was determined by the use of a knife edge. v i i i . C oefficient of F r i c t i o n (u) between the Wood Specimen and the Sawing  Disk (Fig.UT, ^on of D)sk F i g , 11 Forces on Wood Specimen. F = N F„ = F = T R = ¥ = l l = 1„ = Normal force on the cutting edge; F r i c t i o n force on the cutting edge; Feeding thrust; Table support s t r a i n ring reaction; Weight of specimen; Distance between t a i l edge of wood and y-y'» Distance between t a i l edge and centre of gravity of wood, 24 The c o e f f i c i e n t of f r i c t i o n between the wood specimen and the sawing disk was calculated by the following equations. The force analysis and d e r i v a t i o n of these equations are described i n Appendix E. (a) Normal force exerted on the cu t t i n g face of the wood specimen by the sawing disk: F N = 0.789 F T + 0.614 K i/r *"/)W + 1 3 ' 9 5 R Where K = — - 5.53 (b) F r i c t i o n a l force between the wood specimen and the sawing disk: F f = 0.614 F T - 0.789 K (c) The c o e f f i c i e n t of f r i c t i o n : F f 0.614 F T - 0.789 K ^ = F~ = 0.789 F m - 0.614 K N T III.3 SPECIMENS Edge grain green f i r and red cedar were selected f o r the specimens. The dimensions of each specimen were 8 inches x 2 inches x 1 inch. Half of the specimens of each type of wood were cut with the wood grain along the 8 inch side of the specimen. The remaining specimens were cut with the grain along the 2 inch side of the specimen. The former specimens were used f o r along-the-grain cutting and the l a t t e r were used f o r across-the-grain c u t t i n g . In order to investigate the influence of moisture content on sawing, the specimens were seasoned to s i x d i f f e r e n t moisture contents. The average moisture contents were 11$, 19$, 25$, 32$, 34$ and 72$. The method of sea-soning i s described i n Appendix D. A f t e r seasoning a 9/32 inch d i a . hole was d r i l l e d through each specimen along the l o n g i t u d i n a l axis ( F i g . 12). A t a i l piece was fastened to one end of the specimen. The t a i l piece was made of Formica f i b r e board with T e f l o n r o l l e r s a f f i x e d at the lower corner i n order to minimize the f r i c t i o n between the table and the specimen. f/o/e for /•etr7porc7Tiure o o rot/er F i g . 12 Wood Specimen and T a i l Piece III.4 EXPERIMENTAL PROCEDURE At the beginning of each set of experiments the el e c t r o n i c i n s t r u -ments were warmed up u n t i l they were s t a b l e . When there was no load on the table and the feeding push rod the correct reading of the force measuring instruments was zero; the reading of temperature measuring instruments was 32°F with the probe t i p being immersed i n i c e . The adjusting procedure was repeated every three hours i n order to correct f o r instrument d r i f t . Before each experiment the rim of the sawing disk was cleaned with a s t r i p of copper i n order to remove the residue composed of r e s i n , carbon and sawdust which had adhered.on the rim from previous c u t t i n g . The experiments were c a r r i e d out under f i v e d i f f e r e n t feeding speeds i n order to study the influence of feeding speed on cutting. The speeds used were 4, 8, 12, 16 and 18 inches per minute. 26 The specimen weight and centre of gra v i t y was determined immediately before each t e s t . The carriage was then engaged to the power screw and was stopped automatically a f t e r 5 inches of c u t t i n g by a stop switch. The cut specimen was detached from i t s t a i l piece and weighed, thus giving the weight Wc before k i l n drying. The specimen was then placed i n an oven maintained at a temperature of 250°F and was drie d u n t i l constant weight was obtained -t h i s weight was the oven drie d weight, W^ , of the specimen. The actual moisture content was determined as follows: Moisture Content = x 100$ Where weight of specimen a f t e r being cut and before being dried; Wn = oven-dried weight of specimen. 27 CHAPTER IV IV.1 RESULTS (l a ) F r i c t i o n Force (Fj) versus Feed Speed (V^) and Normal Force (F„) versus Feed Speed (V^) ( F i g . 13 to 24 inclusive) The forces increase as the feed speed increases independently of the moisture content. In general, cutting forces for f i r are greater than those for cedar. The slopes of the curves for the normal forces (FJJ) increase at a greater rate than the curves for f r i c t i o n a l forces (F^). (lb) Coefficient of F r i c t i o n versus Feed Speed ( F i g . 25 to 30 inclusive) There are two different shapes of curves. One group of the curves are concave upward, high values of LX occur at very low and very high feed speeds. Another group of curves are just the reverse — they are concave downward with low values of LI - t very low and very high feed speeds. ( l c ) F r i c t i o n a l Force (F^) versus Moisture Content ( F i g . 31 to 34 i n -__________________ ' No si g n i f i c a n t variations of f r i c t i o n a l force (F^) with moisture content are evident. However, i t may be stated that the forces are s l i g h t l y 28 smaller at the high moisture contents* (id) Power Consumed versus Feed Speed (Fig. 35 to 40 inclusive) The values of power consumed was obtained from the following equation: PfTfl>N H , P ' = 33,000 Where F^ = f r i c t i o n a l force i n lbs. D = disk diameter in f t . N = rotating speed of disk i n rpm. A l l the horsepower curves rise as feed speed increases, (le) Cutting Temperature versus Feed Speed (Fig. 4l) The cutting temperature rises as feed speed or thrust increases, ( i f ) Power Consumed versus Moisture Content (Fig. 42 and 43) There is no significant change in power consumed for variation in moisture content. (lg) Appearance of Cut Surfaces Examination of the wood specimens after being cut revealed that the width of the kerf was almost the same as the thickness of the disk. The cut surfaces were smooth and polished and were of a dark brown colour. Examina-tion of the cut surfaces at a magnification of lOx showed that the whole surface was covered with a layer of resin which appeared to have melted and then set. In comparison with the ordinary sawn surfaces the f r i c t i o n cut surface was far more smooth. (Fig. 44 and 45). 29 Fig. 13 Graph of Frictional Force versus Feed Speed with Moisture content 11$. 30 31 F i r along grain • F i r across grain V Cedar along grain Cedar across grain \ 1 I 1 1 1 1 1 1 f 1 / i J / < 1/ 1 / / / is 12 16 20 15 Graph of F r i c t i o n a l Force versus Feed Speed with Moisture Content=19$. 3 2 3 3 Feed Speed - /'r? Fig. 16 Graph of Normal Force versus Feed Speed with Moisture Content=19$ 34 35 36 F i r along grain a __________________ F i r across grain Cedar along grain • •Cedar across grain / ^ / i i / ' / '/ / I / / / 1 I , / / / i / / 1 I / / / / / (/ A c 1 / / / f A. < < yy c F&ecJ Speed" *f?//?7/ni , F i g . 20 Graph of Normal Force versus Feed Speed wxth Moisture Content = d_Jfe. F i r along grain F i r across grain Cedar along grain Cedar across grain I i i \ 1 i i i i // // V i y ^ -// / 7 / ^^^^ •• 7 ^—- < [>" ) 7 .^J < 4 12 16 20 Fig. 21 Graph of Frictional Force versus Feed Speed with Moisture Content=34#, 38 4 ! F i r along grain F i r across grain Cedar along grain Cedar across grain -• V / / / / > i / 1 / // / a 1 / . / / \ -i / 1 / / / ] C j , / / / ' i ( 1 1 / ) Fig. 22 Graph of Normal Force versus Feed Speed with Moisture Content = 34$, 39 F i r along grain F i r ; a c r o s s g r a i n V • Cedar along grain o • Cedar across grain 40 4 1 a o •H - P o • H U &< CH O - F Ct 0) •l-t o • H «H «H 01 o o 0 16 F i g , 4 8 12 Feed Speed - in/min 25 Graph of C o e f f i c i e n t of F r i c t i o n versus Feed Speed with 11$ mois-ture content. ;42 1.1 a o •H -P U •H H «H o -p d 0) •H U •H «W «H « o 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0 . 3 • F i r along grain a ———___-___________ F i r across grain V Cedar along grain Cedar across grain 1 1 1 \ \ \ \\ A \ / 1 V • \\ \ \ \ / / \ ^ '</.: \ \ \ 0 16 F i g . 4 8 12 Feed Speed - in/min 26 Graph of C o e f f i c i e n t of F r i c t i o n versus Feed Speed with Content. 20 19$ Moisture 43 1.1 o •H •P O •H (H PH O -P fl 0) •H O •rl «M <H 0) o o 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0. F i r along grain • F i r across grain Cedar along grain Cedar across grain \ • > \ • _ ' 7-— ' 7 0 4 8 12 16 20 Feed Speed in/min F i g . 27 Graph of C o e f f i c i e n t of F r i c t i o n versus Feeds SjJeed with 25$ Moisture Content. .44 1.1 a o •H -P o •H M PM «H O -P a O) •H U •H «H «H 0) O O L F i r along grain 0 F i r across grain V Cedar along grain Cedar across grain L) 9 , \ \ C c > \ c \ \ 't \ ( \ \ < j 5 A J 3 / y / / 7 12 16 20 Feed Speed in/min Fig. 28 Graph of Coefficient of Friction versus EeeddSpeed with 32$ Mois-ture Content. 45 8 12 16 20 Feed Speed in/min Fig. 29 Graph of Coefficient of Friction versus Feed Speed with 34$ Mois-ture Content. 46 4 8 12 Feed Speed in/min Fig. 30 Graph of Coefficient of Friction versus Feed Speed with 72$ Mois-ture Content. IV o o as d o u 50 40 30 20 10 10$ 20$ Feed Speed = 16 in/min o Fee( L Speed = 12 in/min • Feec. Speed = 8 in/min v * •• Fee(. Speed - 4 in/min y 30$ 40$ 50$ )isture Content ($) 60$ 70$ Fig. 31 Graph of Frictional Force Versus Moisture Content. Cedar Across Grain. 16 12 in/min Feed Speed O in/min Feed Speed v • — 8 4 c o D C V .__v _D •Or-? --• 1 —Jr-10$ 20$ 30$ ' 40$ 50$ 60$ 7P$ Moisture Content ($) F i g . 32 Graph of F r i c t i o n a l Force versus Moisture Content - Cedar Along Grain 50 20 10 0 16 in/min Feed SpeedO • L2 in/min Feed Speeda 8 in/min Feed Speedy" 4 in/min Feed Speedx _i_ n o o o ° Q ' " - - - Tr -— o • • " V V V X V v .. x — v —.)( —x-10$ 20$ 30$ 40$ 50$ 60$ 70$ 80$ ) Moisture Content ($) F i g . 33 Graph of F r i c t i o n a l Force versus Moisture Content - F i r Across Grain. 50 40 30 10 16 in/min Feed SpeeffO 12 in/min Feed " • 8 in/min Feed " V . . . 4 in/min Feed " y o 0 0 • • 6 • • ... _-o— V . . • — — X V X * " > X iO* 20$ 30$ 40$ 50$ 60$ 70$ 80$ Moisture Content ($) F i g . 34 Graph of F r i c t i o n a l Force versus Moisture Content- F i r Along Grain. Feed Speed in/min Fig. 36 Graph of Power Consumed versus Feed Speed with 19$ Moisture Content. 14 8 6 4 F i r along grain • F i r across grain V Cedar along grain O Cedar across grain A 1 / Ll / / / / / / / / / / / / / / / / / y^ / y^ y y T ^ y"^\^ 4 8 10 16 20 Feed Speed in/min Fig. 37 Graph of Power Consumed versus Feed Speed with 25$ Moisture Content. 8 2 0 F i r along grain 0 F i r across grain V Cedar along grain O . . . Cedar across grain V — ;  / / / / / / / / * 7 / / / _ / / 1 / / / / / / / ' / .X / A / / 0 4 8 12 16 20 Feed Speed in/min F i g . 38 Graph of Power Consumed versus Feed Speed with 32$ Moisture Content. Feed Speed in/min F i g . 39 Graph of Power Consumed versus Feed Speed with 34$ Moisture Content. 0 4 8 12 16 20 Feed Speed in/min Fig. 40 Graph of Power Consumed versus Feed Speed with 72$ Moisture Content. 500 300 20C F i r along grain • F i r across grain V Cedar along grain O Cedar across grain * » C • : L ( J ) 3 c [ C 1 > r 5? Room Temp Feed Speed in/min F i g . 41 Graph of Cutting Temperature versus Feed Speed. F i r along grain • • F i r across grain • v Cedar along grain o Cedar across grain X — -—V 5 7 () 3_ "80$ 10$ 20$ 30$ 40$ 50$ 70$ Moisture Content F i g . 42 Graph of Power Consumed versus Moisture Content(Feed Speed = 8 in/min} 20 r F i r along grain F i r across grain • v Cedar along grain o Cedar across grain >< —• m a o-o u SB o PH 10$ 20$ Fig. 43 Graph of Power Constuned versus 50$ 60$ 70$ ro 40$ Moisture Content Moisture Content(Feed Speed 12 in/min.) ax <£> 60 Fig.45 Comparison of Cut Faces Between Ordinary Sawing and Friction Sawing. 61 C H A P T E R V . V . l D I S C U S S I O N F r i c t i o n a l h e a t r a i s e s t h e t e m p e r a t u r e a t t h e c u t t i n g e d g e . E x p e r i -m e n t a l r e s u l t s s u g g e s t t h a t a t l o w f e e d s p e e d c u t t i n g t h e t e m p e r a t u r e m a y b e l e s s t h a n t h e i g n i t i o n t e m p e r a t u r e o f w o o d . H o w e v e r , a n e l e v a t e d t e m p e r a -t u r e , w h i c h i s l e s s t h a n t h e i g n i t i o n t e m p e r a t u r e , m a y s u b s t a n t i a l l y m o d i f y t h e s t r u c t u r e o f t h e w o o d , w h e r e b y i t b e c o m e s f r a g i l e a n d m a y b e r e m o v e d b y a t t r i t i o n . E x a m i n a t i o n o f F i g s . 13 a n d 14 a n d F i g s . 41 t o 5 2 i n d i c a t e s t h a t t h e f r i c t i o n a l f o r c e ( F ^ ) , t h e n o r m a l f o r c e ( F ^ ) , a n d p o w e r c o n s u m e d i n -c r e a s e a s t h e f e e d s p e e d ( V ^ ) i n c r e a s e s . T h e e x p l a n a t i o n i s r e l a t e d t o t h e d i s p o s i t i o n o f c u t m a t e r i a l . W h e n t h e f e e d s p e e d i s l o w t h e c u t m a t e r i a l r e m o v e d p e r u n i t t i m e i s s m a l l a n d t h e s m o o t h e d g e o f t h e s a w i n g d i s k c a n d i s p o s e o f t h e r e f u s e w i t h n o a c c u m u l a t i o n o n t h e k e r f . B u t w h e n t h e f e e d s p e e d i s h i g h t h e d i s p o s a l a c t i o n o f t h e s m o o t h d i s k e d g e i s n o t f a s t e n o u g h t o m e e t t h e r e q u i r e m e n t w i t h t h e r e s u l t t h a t c u t m a t e r i a l a c c u m u l a t e d on the kerf. The only way to dispose of the material i s to burn i t tho-roughly. From Graf's " I g n i t i o n Temperature of Various Papers, Woods and Fabrics" [ l O], the i g n i t i o n temperature of Douglas F i r i s 489°F and that of Western red cedar i s 468°F based on rates of temperature r i s e of 16°F per hour and 17°F per hour r e s p e c t i v e l y . The rate of temperature r i s e influences the i g n i t i o n temperature s i g n i f i c a n t l y ; the higher the rate of temperature r i s e , the higher the i g n i t i o n temperature. In the present work the rates of temperature r i s e were up to 3,000°F per hour or more, thus the i g n i t i o n temperature i n the cutting zone w i l l be higher than the above mentioned values. Therefore f a r greater power i s required when the wood i n the kerf has to be removed by i g n i t i o n . I t i s i n t e r e s t i n g to note that at low feed speeds, the values of f r i c t i o n a l force F^ are somewhat lower than the predictions of theory. Using the experimental r e s u l t s on power consumed and equation (2-14) from Chapter I I , i t was found that the temperatures near the cutti n g edge vary with the feed speed. Appendix F shows that at low feed speed (4 inches per minute) the cutt i n g edge temperatures are lower than the i g n i t i o n temperature of the wood while at high feed speeds, 8 inches per minute or higher, the cutting edge temperatures were extremely high. The low cutting edge temperatures at low feed speeds suggests that the wood becomes b r i t t l e and i s removed by a t t r i t i o n before the i g n i t i o n temperature i s reached. At high feed speeds the calculated cutting edge temperature exceeds the i g n i t i o n point of the wood. In some cases the c a l c u l a t e d temperatures exceed the melting point of s t e e l . Since no trace of molten metal was found on the rim of the disk i t appeared that the actual c u t t i n g temperature was below the melting point of s t e e l ( ca. 1,400°C [ l l ] . ) The r e s u l t s suggest that a part of the energy i s used to r a i s e the cutting temperature and some energy goes to fragmenting 63 and removal of material» There are two general types of curve for coefficient of f r i c t i o n versus feed speed (Fig. 25 to 30). One general form is concave upward and other form i s fl a t t e r and concave downward. The concave upward curves are due to pinching action which occurs when the wood bends inward after being cut, thus gripping the two side faces of the sawing disk and creating side fr i c t i o n a l forces. The additional f r i c t i o n a l forces add to the value of the cutting edge fri c t i o n a l forces and influence the shape of the p,- curves. This side fr i c t i o n a l force is a function of the spring constant of wood but independent of feed speed. Therefore i t may be considered to be constant through a l l changes of feed speed. Since the values of F^ and F^ at low feed speeds are far less than that at high feed speeds then the influence of side frict i o n a l force adding to F^ at low feed speed to increase the value of LI is far greater than i t s influence on high feed speed. This behaviour is revealed by the high values of coefficient of f r i c t i o n at low feed speeds. At high feed speeds another factor enters and causes the coefficient of f r i c t i o n to rise again. As previously mentioned the cutting temperature increases rapidly when the cut material in the kerf is burnt at high feed speed. The high cutting temperature melts the resin in the wood and causes i t to cover the contact surfaces between the specimen and the sawing disk, especially on the side faces. Consequently the value of the coefficient of fr i c t i o n increases. Examination of the cutting edge of the disk and the side faces of the specimen through a microscope clearly shows layers of resin (Fig. 44 and 45). At higher speeds the resin layers are thicker and darker. Wood is a natural product and i t s constituents are not homogeneous hence consistent results are hard to obtain. The fl a t t e r concave downward curves are produced by the wood bending outwards after being cut. At low feed speed, when the cutting temperature i s low, no melted r e s i n i s present to increase the f r i c t i o n a l f o r c e . When the feed speed increases the cutting edge temperature also increases and the wood r e s i n s t a r t s to melt. Further increase of feed speed causes higher c u t t i n g edge temperatures which melt the r e s i n with the r e s u l t that the f r i c t i o n a l force i s reduced. F i g s . 31 to 38 reveal that moisture content has l i t t l e e f f e c t on f r i c t i o n c u t t i n g . Generally the moisture i s only a small p o r t i o n of the t o t a l weight of the wood specimen. In f r i c t i o n cutting the energy required for c u t t i n g wood of d i f f e r e n t moisture content i s rel a t e d to the heat r e -quired f o r evaporating the d i f f e r e n t amount of moisture i n the wood. This difference of heat required f o r evaporating moisture i s i n s i g n i f i c a n t when compared with the t o t a l energy required for c u t t i n g . I t was i n t e r e s t i n g to note that the cut faces of the specimen were extremely smooth and polished. This f i n d i n g suggests that f r i c t i o n cut wood may not require a secondary planing operation. This smooth and polished cutting edge i s s p e c i a l l y noticeable i n plywood and veneer c u t t i n g . P l a s t i c can be softened at a c e r t a i n temperature hence i t may be possible to cut suc c e s s f u l l y by t h i s method. 6 5 CHAPTER VI. VI.1 CONCLUSION The research reveals that f r i c t i o n a l heat can be u t i l i z e d to saw wood. At low feed speed f r i c t i o n a l heat appears to raise the temperature to a level lower than the ignition temperature of wood. This finding sugg-ests that heat modifies the structure of the wood whereby i t becomes fragile and is removed by att r i t i o n . The sawing performance was repeatable i n the low feed speed cutting experiments. At high feed speed when waste was re-quired to be burnt and removed, very high power consumption was required and the calculated cutting temperature was then higher than the ignition tempera-ture of wood. The cutting of plywood was attempted with successful results. The faces after being f r i c t i o n cut were clean, unchipped and were of a far better finish than produced by planing. In a l l the experiments the cut edge was smooth, straight and the kerf was narrow. The narrow kerf indicates that wood waste is reduced by f r i c t i o n cutting. Unfortunately the saving of wood cannot cover the dis-advantages of high power consumption and low feed speed. These two dis-advantages arise from poor removal of cut material. A smooth disk edge re-quires excessive feed pressure and cannot dispose of the cut material effectively. If some means to reduce the cutting edge contact area and to dispose of the cut material effectively can be found then the feeding pressure and consequently the power consumed will be reduced and the feed speed may also be increased. In so doing the drawbacks of this method of sawing may be eliminated. Another factor giving excessive power consumption is related to the pinching action of the wood on the side faces of the disk. The two legs of the specimen after being cut bend inward and grip on the disk. If the outer rim i s made slightly thicker than the inner part of the disk the undesirable pinching action may be eliminated. VI.2 Recommendations The main disadvantages of f r i c t i o n cutting Df wood are high power consumption and low feed speed. These are probably caused by the smooth cutting edge of the sawing disk. Two types of cutting edge designed to reduce contact area and to give more effective disposal of cut material are recommended: ( l ) If several notches are introduced in the rim of the disk then the wood detritus can easily be carried away from the kerf by the notches and disposed of by centrifugal force. At the same time the notches would reduce the contact area of the cutting edge. (2) A second suggested type of sawing disk is shown in Fig . 46. Teeth are provided in the middle part of the rim having a diameter a l i t t l e smaller than that of the two side face edges. This arrangement w i l l greatly reduce the contact area of the 67 cutting Recommended Saw Blade to Reduce Contact Area F i g . 46 and with Inner Teeth to Dispose Wood Waste. edge while disposal of wood waste i s c a r r i e d out by the inner teeth. In order to eliminate the undesirable pinch action the outer rim of the disk should be made a l i t t l e t h i c k e r . ( F i g . 47) F i g . 47 Recommend Saw Blade to Eliminate Pinch A c t i o n . Fig. 48 Fixture of Daytronic 103A-80 Linear Transducer. CT> 00 69 APPENDIX A. CALIBRATION OF TABLE SUPPORT STRAIN RING (a) Compression. F i g . 48 shows the s t r a i n r i n g i n an upright p o s i t i o n with a "Daytronic" 103A80 l i n e a r displacement transducer being f i x e d on the trans-ducer support. The instrument connection has already been described i n Chapter I I I , Section 2, Load was placed on the top of the s t r a i n r i n g and increased gradually ( i n 4 oz. increments f o r the low range and i n 2 l b s . increments f o r the high range) u n t i l the maximum reading on the instrument was obtained. The load then was reduced i n the same increments as the load-ing sequence u n t i l a l l the load was removed. (b) Tension. The s t r a i n r i n g was c a l i b r a t e d f o r tension by the use of the pulley, s t r i n g and weight system shown i n F i g . 49. ////////////////^ F i g . 49 C a l i b r a t i o n of Table Support S t r a i n Ring (Tension) 70 APPENDIX B. CALIBRATION OF FEED THRUST MEASURING STRAIN RING A f t e r the table support s t r a i n r i n g was c a l i b r a t e d , i t was s o l i d l y clamped on one end of the carriage track ( F i g . 50). With the push rod and s t r a i n r i n g f i x e d i n p o s i t i o n the carriage was engaged with the power screw which was then turned slowly u n t i l the push rod ju s t contacted the table support s t r a i n r i n g . A gradual increase of the turning force on the power screw produced d e f l e c t i o n of both ri n g s . For each d e f l e c t i o n reading on one s t r a i n r i n g there would be a corresponding reading on the other. As the table support s t r a i n r i n g was already c a l i b r a t e d the c a l i b r a t i o n curves f o r the thrust measuring s t r a i n r i n g could then be plotted. Fig. 50 Calibration of Thrust Measuring Strain Ring. 72 APPENDIX C CALBRATION OF CHROMEL - CONSTANTAN THERMOCOUPLE FOR MEASURING CUTTING TEMPERATURE The thermocouple was connected as described i n Chapter III, Section 2. The cold junction (the t i p of the probe) was placed i n a beaker contain-ing water. The water was then heated u n t i l i t was b o i l i n g and then cooled down to room temperature. The temperature of the water was measured by a mercury thermometer and the chart record was read at 10°F i n t e r v a l s * ( f o r increasing and decreasing temperatures) F i g . 50ashows the c a l i b r a t i o n curve and the extrapolation employed. Data from [12] reveals that the e.m.f. versus temperature curves f o r chromel and constantan are l i n e a r over an extended range (0° - 800°C) ( F i g . 50b) - p 0 100 200 300 400 500 600 0 100 20D 300 400 500 600 700 800 Temperature F Temperature C F i g . 50a. F i g . 50b. Chromel-Constantan Thermocouple Thermal emf of Chromel-Constantan Thermocouple. C a l i b r a t i o n Curve (Data from W.D. Kingery: "Property Measurement at High Temperatures.") 7^3 APPENDIX D. SEASONING OF WOOD SPECIMEN The seasoning of the wood specimens was c a r r i e d out i n the Vancouver Laboratory of the Forest Products Laboratory. The specimens were placed i n the k i l n s f o r one month. There were four k i l n s each with a d i f f e r e n t moist-ure content. They were: Room No.l Dry bulb temperature 30°F Re l a t i v e humidity 90$ Specimen average moisture content a f t e r seasoning 32$ Room No.2 Dry bulb temperature 75°F . Relative humidity 83$ Specimen average moisture content a f t e r seasoning 25$ Room No.3 Dry bulb temperature 70°F Relative humidity 65$ Specimen average moisture content a f t e r seasoning 19$ Room No.4 Dry bulb temperature 70°F Relat i v e humidity 30$ Specimen average moisture content a f t e r seasoning 11$ 74 APPENDIX E. FORCE ANALYSIS DURING CUTTING F i g . 51 Forces on specimen and Table. ;. From F i g . 51 : , 1 ss Distance between R and Y - Y ' = 13.95 inches Rj= Reaction exerted by t a i l edge of the wood specimen on the table; Rg= Reaction exerted on the wood specimen by the r o l l e r on the upper guide block; lg= Distance between Rg & Y - Y ' = 6 .39 inches. As the f r i c t i o n between wood specimen and table and guide was r e -duced to a minimum by using Teflon, A r b o r i t e and r o l l e r s , t h i s part of f r i c t i o n force may be neglected (Chapter I I I , Section i i c ) 75 =0 o Rx x 1 2 - R x 1 - R 2 x 1 2 = 0 (1) Taking the wood specimen as a free body (Fig. 52): L 1 Fig. 52 Free Body of Wood Specimen L w = Length of the wood specimen 1 = Distance between cutting edge and t a i l edge of the wood specimen 1^ = Distance between centre of gravity and t a i l edge of the wood specimen YE =0 x F X T Sin 6 + F„ Cos 6 - F m = 0 N i T (2) EF =0 y F X T Cos 6 _ p Sin 6 + R1 - R_ - W = 0 N f 1 2 (3) m. = o A Vw C ° S 9 " F f 1 w S i n 9 " R 2 ^ 1 " X 2 ) " W 1 £ = 0 (4> 76 ( 4 / l w F N C o s 6 - p f S i n 6 - ( — i j L.) R2 _ _ J V = o ...(5) ' ttf TIT W W (3) - (5) ; Rx - R 2 - W + \ a Rg + W = 0 (6) w w (1 - 1 + 1 )R + (1 - 1 )W Rx = • j—= (7) S u b s t i t u t i n g (7) i n ( l ) , we have ( l - 1, + l j R o l , + ( l - 1 )W1, v w 1 2' 2 I v w g' 1 1 - R 1 - R 2 1 2 = 0 w Arranging terms; 11 R - ( l - 1 )1,W S u b s t i t u t i n g (8) i n (6) and arranging terms; IR - ( l - 1 )W R l - R 2 - W = ( 1 , - 1 ) ' " ( 9 ) (2) x Cos 6; F N S i n fi Cos 6 + F f C o s 2 9 - F^ Cos 9 = 0 .. (lO) (3) x S i n 9; F N S i n 9 Cos 9 - F f S i n 2 9 + (R -B 2 -W)Sin 9 =0.. ( l l ) (10) - (11) F f = F T Cos 9 + (RX - R 2 _ W) S i n 9 (12) (2) x S i n 9 F N S i n 2 9 + F f S i n 9 Cos 9 _ F T S i n 9 = 0 (13) (3) x Cos6 F NCos 6 - F fSin6Cose + - R g - Uf) Cos6 =0 .... (14) (13) + (14) F N = F.SinQ - (R x - R 2 - W) Co Se (15) Fig. 5 3 Direction of Normal Force Acting on the Specimen From Fig. 5 3 we see that 0 = Cos" 1 - ^ — i = c o g " 1 0 . 5 4 0 1 .'. p = 5 7 ° 1 8 ' a = Cos" 1 4 : ' 1 7 8 1 _ Cos" 1 0 . 6 8 3 0 .'. oc = 4 6 ° 5 5 ' e - c r + H M = i L f -e = 52° 6 i « Sine = 0.789 Cos6 = 0 . 6 1 4 • 1 , - 1 = 7Sin6 =5.53 inches 1 w Let K = R, - R„ - W (1 - 1X)W + IR 1 2 1, - 1 1 w K = ( l - 1,)W + 13.95R 1_S_ 1 5.53 Sub s t i t u t i n g the above i n (12) and ( l 5 ) , we have F f = 0.614 F_ + 0.789 K and . F = 0.789 F_ - 0.614 K APPENDIX F. NUMERICAL RESULTS OBTAINED FROM THEORETICAL EQUATIONS The following calculation i s based on equations ( 2 - l l ) , (2-12), (2-13) and (2-14) from Chapter I I : /2TUK b v I.(Xr ) - < — ± > T ^ T T t 2 (2-11) N " ~ TTTT") A a ' m a i 0 * 0' X = 41.83 .. (2-12) r a o lAXr ) Power = 2TiK sbr o JJ^ A t f ^ (2-13) o o' A«- I o ^ r o / . Power / 0 u \ 1 N 0 ' s o Now J = 778 f t . lb./Btu r Q = 7/12 = 0,584 f t . (Actual disk radius) b = °*°^ 6 6 = 0.00638 f t . (Actual disk thickness, 14 gage) ID = 4,620 x 60 x 27T = 1,741,700 rad/hr, (Actual disk speed) K = 26 Btu/hr, f t . °F (Thermal conductivity of steel) [8] Physical properties of a i r at 100°F (Prantdl number P r = 0,72) [8]: Thermal conductivity K = 0,0154 Btu/hr. f t . °F Kinematic v i s c o s i t y v = 0,00018ft. /sec. =0.648 f t 2 / h r . 80 Thus - 41.83^ 0.0154 26x0.00638x0.584 .'. \ - 16.68 f t * * 1 \ r 0 - 9.74 I Q(9.74) - 2,200 1^9.74) - 2,084 When r = 3 inches Xr(r=3") =4.17 I Q(4.17) • 13.09 I 1(4.17) = 11.39 Hence substituting the numerical values into (2-11) we have _ / 2TTX778X26KO.00638,, 2,084, C O A _ ^ N = < 1,741,700 ^2^200' X 1 6' 6 8 A Tmax = °- 0 0 7 3 6 A Tmax Graf's data [10] shows that the i g n i t i o n temperature of Western red cedar i s 468°F and that of Douglas f i r i s 489°F with moisture content 7$ and a rate of temperature r i s e of 15°- 17°F/hr. The rates of temperature r i s e i n the present system are much greater. Graf also found that the i g n i t i o n temperature was higher when the rate of temperature r i s e was greater. The cutting temperature i s d i f f i c u l t to assess but evidently i t should be below the melting point of steel (_ 1,400°C? [ l l ] ) . For i l l u s t r a t i v e purpose we assume the cutting temperature to be 900°F, then we have AT = 900 - 70 - 830°F (T = 70°F) max am ' HFXT = 0.00736 x 830 - 6.11 l b s . 81 From (2-13) 2nJK br I (Xr ) " 8 0 Q X Q 7 . = 60x33,000 I ^ r ) AVx 2nx778x26x0.00638x0.584 v 2,084 v ,- ft~Q,A 60x33,000 X 2^200 X 1 6 * 6 8 x 8 3 0 .'. HP = 3.15 h.p. I t i s i n t e r e s t i n g to note that at low feed speeds, the values of f r i c t i o n a l force F^ are somewhat lower than the predictions of theory. Using the experimental r e s u l t s on power consumed and equation (2-14) we found that the cutting edge temperatures are as shown i n the following tables: From (2-14) AT 6OK33,0Q0 max 2TTX778X26X0,00638x0,584x16.68 v2,084 AT = 264.6*HP max 32$ moisture content 1. Douglas F i r , along grain cutting Feed Speed (V f) ( i n . / min, ) 4 8 12 16 Power Consumed (Horse power) 1.235 2.93 5.4 10.12 AT (°F) max x ' 327 774 1,423 2,675 T = AT max + T (°F) am,v ' 397 844 1,493 2,745 8 2 2 , D o u g l a s F i r , a c r o s s g r a i n c u t t i n g F e e d S p e e d ( V f ) ( i n . / m i n . ) 4 8 12 16 Power Consumed ( H o r s e power) 1 .028 3 . 5 7 .57 12 .85 A T ( ° F ) max^ ' 272 926 1 ,998 3 ,385 T = AT max + T (op) a m , v ' 342 996 2 ,068 3 ,455 3 . W e s t e r n r e d c e d a r , a l o n g g r a i n c u t t i n g : F e e d S p e e d ( V f ) ( i n , / m i n . ) 4 8 12 16 Power Consumed ( H o r s e power) 0 .925 2 .06 3 j 5 5 . 66 A T ( ° F ) max 244 543 922 1 ,492 T = AT max + T ( ° F ) am ' 314 613 992 1 ,562 83 4. Western red cedar, across grain c u t t i n g : Feed Speed (V f) (in./min) 4 • ••; 8 : 12 16 Power Consumed (Horse power) 1.028 2.105 3.6 5.56 327 555 048 1,466 T - AT +T max am (OF) 342 625 1.018 1.536 . L 84 APPENDIX G. Comparison of Heat Transfer by Radiation with those by Convective  and Conductive Processes Heat transfer by radiation per uni t area [Q]« where e = emissivity of saw disk = 0.066 (the surface of the disk i s polished) [4] a =-Stefan - Boltzmann constant = 0.1714 x 10" 8 Btu./hr. f t 2 (°») 4 T ^ = absolute disk temperature (°R) T = absolute ambient temperature ( ° B ) An upper bound upon the radiation flux w i l l be obtained by taking the temperature of the disk adjacent to the rim to be 500°F and the ambient temperature to be 70°F. Then the heat loss per unit area i s QRad S = 0.066X0.1714 [ © - ( f f ) ] .'. -£f£ = 87.12 Btu/hr. f t . 2 From Chapter I I and Appendix F, we have heat loss per unit area due to convection Conv. . , \ — = — = h (T — T ) S a N am' K a where h f t = 875 ~ = " 8 7 5 x 0.584 = 23.1 Btu./hr. f t 2 °F 85 -£§22* = 23.1 x (500^-70) = 9,990 Btu./ hr. f t . 2 Also from Chapter II and Appendix F, we have the heat loss by con-duction *Cond. =fK = + 2 6 x _ t _ H x l 6 - 7 3 x 4 3 0 QCond. =+177,000 Btu./hr. f t . 2 A hence we have 4 s r ' =i§o = 0 ' 0 0 8 7 5 < 1^ ^Conv. -sr: ' m m ' 0 - 0 0 ™ 2 * 0 ' 1 * 9 ^Cond, ' 86 BIBLIOGRAPHY 1. " F r i c t i o n Sawing" Band Machining Handbook DoAll Co. 2. Koch, P, "Wood Machining Processes" The Ronald Press Company 1964 3. "Computed Thermal Conductivity of Common "Woods" United States Dept. of Agriculture, Forest Products Lab. Technical Note No. 248, Dec. 1952 4. McAdams, W»H. "Heat Transmission" McGraw - H i l l , 1954 3rd Ed. 5. In g e r s o l l , L.R., Zobel, O.J. and Ing e r s o l l , A.C. "Heat Conduction with Engineering and Geological Applications" McGraw - H i l l , 1954 6. Carslaw, H.S. and Jaeger, J.C. "Conduction of Heat i n Solids" Oxford Clarendon Press f 1960 7. Bowden, F.P. and Tabor, D. "The F r i c t i o n and Lubrication of Solids" : ,Volume 1, Oxford Clarendon Press ? 1960 8. K r e i t h , F, "Prin c i p l e s of Heat Transfer" International Textbook Co. 9 1962 9. Cobb, E.C, and Saunders, 0,A. "Heat Transfer from a Rotating Disk" Proceedings of the Royal Society„A, 236, P. 343, 1956 10. Graf, S.H. "Ignition Temperature of Various Papers, Wood and Fabrics" Engineering Experimental Station, Oregon State College Bulletin No. 26, March 1949 11. Hodgman, CD. "Handbook of Chemistry and Physics" Cleveland, Chemical Rubber Pub. Co. 46th Ed. 1966 p. 1269 - 1270 12. Kingery "Property Measurements at High Temperatures" John Wiley & Sons, Inc., 1959 

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