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Frictional transition effects in unlubricated sliding Pomeroy, Richard James 1963

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FRICTIONAL TRANSITION EFFECTS IN UNLUBRICATED SLIDING by RICHARD JAMES POMEROY B.A.Sc., University of British Columbia, I961 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of Mechanical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July, 1963 i i In presenting this thesis -in par t ia l fulfilment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shall make i t freely available 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 publications of this thesis for f inancial gain shall not be allowed without my. written permission. Department of Mechanical Engineering, The University ef B r i t i s h Columbia, Vancouver 8, Canada. J u l y , 1963-i i i ABSTRACT The object of this research was to study the effect of i n i t i a l surface -finish and f in ish mark orientation on intermetallic f r i c t i on under unlubricated s l iding contact conditions. The metal used was mild steel and the parameters investigated were s l iding speed and load. Qualitative assessments of wear were also made. The basic apparatus consisted of a rotating disc and an e las t i ca l ly supported s l ider. The disc and sl ider each had the same-initial surface f in ish . Six different surface finishes were examined ranging in roughness from.a peak to valley distance of 6.9 thousandths of an.inch to 35 microinches R.M.S. Speed was varied from 1.25 to 60 inches per second and normal load from 1.025 to 3-075 pounds. No significant correlation was found, between the theory of Ernst and Merchant and the experimental results. Fr ic t ion was more dependent on surface parameters affecting load concentration than, on the particular details of each surface asperity. The effects of f in ish mark orientation were only significant when they produced appreciable load concentration. Fr ic t ion was found to increase as "wear-in" progressed and remain approximately constant once wear-in was complete. No relation between f r i c t i on and velocity could be deduced. Wear-in was found to be influenced by i n i t i a l surface geometry. The sufaces which gave high load concentration at sharp protuberances "wore-in" more quickly than those-with low load concentration. Smooth compatible surfaces which required l i t t l e surface alteration.also wore-in rapidly. Wear debris was found to influence both f r i c t i on and wear-in. i v Evidence of mechanical working of de"bris between the surfaces was obtained. A quasi-harmonic o s c i l l a t i o n of the s l i d e r supporting system was observed to r e s u l t from wear-in. The frequency of v i b r a t i o n was a function of disc speed and load. The amplitude of the v i b r a t i o n increased l i n e a r l y with disc speed up to>a maximum vaiue. The magnitude-of t h i s maximum was dependent on normal load. X ACKNOWLEDGEMENTS The author.is grateful for many helpful discussions with members of the faculty.and graduate students i n the-departments-of Mechanical Engineering and Metallurgy. Special thanks are due Dr. CA. Brockley, the research director, for his suggestions and encouragement. Research work was carried out i n the Lubrication Laboratory, Department of Mechanical Engineering, University of B r i t i s h Columbia. Financial assistance was provided by the Defence Research Board of Canada under Grant Number -751O-3I. V TABLE OF CONTENTS CHAPTER PAGE NO. I 1. Introduction 1 2. Literature Synopsis 2 3- Summary 7 II Theoretical Considerations 8 III 1. Apparatus, and Instrumentation 13 2. Specimens . 18 IV 1. Experimental Method 22 2. Types of Friction Record 23 3- Results and Discussion 26 A) Geometry versus Friction . . . 26 B) Velocity and Load Effects 30 C) Wear and Wear-In 33 D) Finish Mark Orientation 37 E) Wear Debris 39 F) Kinetic Aspects k2 V 1. Conclusion 53 2. Recommendations . 55 APPENDICES I Speed Calibration 56 II Load Calibration 57 III Friction Force Calibration 58 IV Instrumentation 59 V Surface Finish Measurement .61 BIBLIOGRAPHY 62 LIST OF FIGURES FIGURE PAGE 1. Enlarged Sketch of Surface -Asperity Contact 8 2. Graph of F r i c t i o n . C o e f f i c i e n t versus Angle of Asperity Contact 9 3- Graph of Stress Di s t r i b u t i o n for Hertzian Contact . . . .10 k. Photograph of the Apparatus -lk • 5- Diagram of the Self-Aligning Joint -15 6. Diagram' of Typical-Striae P r o f i l e 19 7. Three Types of Oscillograph Trace 25 . a) Steady Deflection . , . . . . b) Random O s c i l l a t i o n . . . c) Steady Vibration 8. Profile-View .of Contact'Between-Striae..at Interlock . . -26 9. Graph of F r i c t i o n Coefficient versus Contact'Angle . . • 27 10. Graph of F r i c t i o n Coefficient versus Disc Speed 31 11. Graph.of F r i c t i o n Coefficient.versus S l i d i n g Distance . . 32 12. Graph of Load versus S l i d i n g Distance Required.for Continuous Vibration 36 13. Graph of Coefficient of F r i c t i o n versus Finish Mark Orientation 3^ lk. Photographs of Wear Debris ^0 a) Cuttings from-a Jeweller's- Saw b) Cuttings After. About 1000 Inches of Sli d i n g . . c) 'Debris Formed by Wear-In . 15. Graph of Load and Disc Speed versus Frequency of Vibration-^3 16. Graph, of'Amplitude-of Vibration versus Disc Speed for Test k . . kk 17. Graph of Amplitude of Vibration versus Disc Speed for; Test 2 -U5 18. Graph of Amplitude of Vibration versus Disc Speed for Test 3 k6 v i i PAGE 19- Graph of Amplitude of Vibration versus Disc Speed.for Test. 6 ^7 20. Graph of Amplitude of Vibration versus Load for ..Test h . k-9 21. Graph of Amplitude of Vibration versus Normal Load for 50 Test ,6 22. Photographs of Striae Profi le 60 . a) Test One b) Test Two c) Test Three d) Test Four v i i i LIST OF TABLES TABLE . PAGE . 1 . Dimensions of•Striae Profi le 20 2. Surface Finish and Coefficient of Fr ic t ion at Interlock 28 • 3- Surface Finish and Sliding Distance for Continuous Vibration 35 i x LIST OF SYMBOLS A' - True area of contact A - True area of contact projected into the plane of contact a - Radius of the true contact, area of mating asperities d - Depth of striae cross-section E - Elast ic modulus F - Fr ic t ion force H - Surface hardness, .yield stress in compression L - Distance between para l l e l striae peaks N - Normal load S - Shear strength of a metal or a metallic junction x - Instantaneous position of vibrating sl ider X - Amplitude of quasi-harmonic vibration 0< - Angle between.A' and A ^ - Included angle of striae cross-section 0~ - Tensile or compressive stress CO - Frequency of vibration CHAPTER I 1. INTRODUCTION 2. LITERATURE, SYNOPSIS 3- SUMMARY 1 •1. INTRODUCTION The c lass ica l laws of f r i c t ion have long been known, but u n t i l . th i s century their physical basis, has been cause for l i t t l e more than speculation. About thirty years, ago,,as improved experimental equipment and techniques became available, concentrated study of friction.and.wear began. From this work the adhesion theory of f r i c t i o n , . which was based on plast ic deformation at points of surface contact, was evolved. This theory was found to be - inadequate in some respects.and recently.attempts have been made to present a theory.involving elastic deformations, which accounts not only for f r i c t i on but also to some extent for wear. ' There are many other phenomena which must be•accounted.for by.any theory, which claims generality. Among these-are thermal.effects,. and metallurgical considerations such as sol id solubil ity, and lat t ice parameter. It is-also fe l t that a general theory must consider both elastic and plastic deformations. The purpose of the present investigation centres on the close association of friction.and.wear. •The methods are wholly empirical and are devoted to the areas of i n i t i a l surface f inish and orientation of f in ish .marks which, i t i s felt , .have been largely overlooked by other workers. A bias has also been, preserved for situations which might,be encountered in engineering practice. 2 2. LITERATURE SYNOPSIS The c lass ica l laws of f r i c t i on were f i r s t described by Leonardo da Vinc i , Amontons and Coulomb. Their formulations were based ©n .observations, and the accompanying explanations ,of the cause of f r i c t i on were-vague .and unconvincing. Interest in these explanations persisted,. although i t was not u n t i l the 1930's that serious attempts were made to analyze the•details of surface contact and the basic mechanics of f r i c t ion and wear. -j ^ Bowden and Leben presented such an analysis in .1939> based on empirical evidence which suggested inter-metallic adhesion. In the same o year Bowden and Tabor published an. analysis of true-area of surface contact, comparing elastic and plast ic surface-deformation ,in the l ight of e l ec tr i ca l resistance measurements between.surfaces. One.of the f i r s t comprehensive papers dealing with f r i c t i on and wear, was by Ernst and Merchant in 19^ -0. Their study originated from problems encountered in the metal cutting process, and led to a postulation of the mechanism of contact and the presentation of a theory of static f r i c t ion which considered,.inter a l i a , . surface f in ish and metal sol id so lubi l i ty . The ideas of these and other workers, at the time-were essentially, identical , .and.led to what has been described.as the.adhesion theory of f r i c t ion . The crux of this theory l i e s in the postulation that surface contact deformations are p las t i c . Hertz,. in ,1886,. envisaged,.a spherical indenter pressed into a plane surface and produced equations for. the resulting k elastic deformations. His analysis was used by Timoshenko to show the * Numbers refer to the bibliography at the end of the-thesis •3 stress distribution on the point of plastic yielding. Bowden and co-workers, starting with these concepts, studied surface•asperity contact in deta i l . The Bowden group stated that in most pract ica l cases the area of real contact equals the normal load divided by, the;, y i e ld pressure. They suggested that the y ie ld "pressure, is a constant and that i t is related to the y i e ld point in pure compression'. These-workers found an approximate relationship between shear strength and hardness, which predicted unreal ist ical ly . low values of f r i c t ion coefficient. Further investigation^ pointed ..to inadequacies in the adhesion theory, although the ideas have remained popular. Brockley^-'T has. used model studies of plasticene and lead to•investigate load-area relationships and confirmed that these relationships are not as simple as the adhesion theory had predicted. A new.approach to the-question of surface interaction was a series of.investigations of large-scale model.asperities and junctions of various geometries. The intention was to obtain a better idea of the physical Q behaviour of asperities before attempting an analytical solution. Green , a pioneer in this method, experimented with plasticene- and developed plane stress and plane strain solutions for junctions, with different prof i les . Greenwood; and Tabor9>1(-) veri f ied some of Green1 s theory, experimentally and found.simulated f r i c t i on values for one-piece models to be much higher than those normally found ex vacuo. In the foregoing discussion no dist inction has been, made between static and.kinetic f r i c t i o n . A l l the studies described :apply, to situations of no motion tangent to the surfaces in contact,. or motion so slow that i t s kinetic effects can be ignored. In certain situations, however, changes in f r i c t i o n values bring about important consequences. k. For example, s t i ck-s l ip vibration, which involves an elast ical ly . supported s l ider on a slow moving surface, . is a direct result of the difference 11 12 between static and kinetic f r i c t i o n . Some-workers ' have also encountered a quasi-harmonic v ibrat ion,at .a frequency.near, the-natural frequency, of the-supporting system. This vibration occurs, at speeds above the maximum encountered in . s t ick-s l ip , but l i t t l e is. known of i t s character-i s t i c s . These vibration phenomena are greatly, influenced by.the elastic character of the s l ider supporting system. Other: factors not yet mentioned, such as. interface temperature and .rate of deformation become important surface contact parameters as velocity,increases. ' The dynamic, aspects of surface asperity encounters are most certainly, complicated and no satisfactory treatment of the problem has been offered aside from that of wholly plast ic deformation. There has been a growing awareness, that plast ic and elastic stresses 13 must-act together during surface contact. - Archard has shown that, even when contact deformation is entirely, e last ic , £ s i c ] area is very nearly proportional to load and-Amonton's law can be explained without the necessity of assuming that the. deformation is p las t ic . The dual.deformation approach is most promising and .in a recent paper ( l 9 6 l ) Archard X 4 reviews his rea l i s t i c assumption of multiple contacts between surface.-asperities. His-analysis shows that asperities may. bear much .larger loads e las t i ca l ly than was-thought possible. The theory suggests that most interaction-between, asperities involves elastic rather than plast ic deformation and although a single-asperity which is deformed e las t i ca l ly does not obey Amonton's law,.an assembly of protuberances should do so. In the analysis f r i c t i on force : i s taken to vary direct ly as the area of contact A, . and A o c N n . N is the load pressing the protuberances 5 together and n is an index which is shown to•approach 1.as the number of protuberances increases. Archard extends the analysis to a relation between fr i c t ion and wear, noting that the v i t a l difference between the two .is that a l l asperity encounters must contribute-to fr ic t ion , .but n o t . a l l contribute •15 to wear. He showed ..in .1953 that one asperity encounter in about a mil l ion produces a wear part ic le . The lat ter statements are of significance,.because-they represent one of.the few attempts to relate -friction.and wear direct ly . Up to the present, wear research has been largely concerned with empirical relationships. Burwell and Strang"^ found-that, under certain conditions wear rate varied l inearly, with distance travelled : and with normal load. Two dist inct values of wear rate were encountered and were attributed to low stress and high 17 stress at the interface. Archard affirms these results,•adding that l 8 wear.rate is independent of apparent area of contact. Kerridge studied metal transfer and wear,.and found a three-stage process•involving transfer of metal, conversion to metallic oxide,.and removal of oxide. However, generally applicable postulates are not yet possible , . largely due to a lack of knowledge of how. wear particles, are formed and detached. Various investigations have emphasized factors other than surface • i n geometry.and mechanics. Ling y and associates, have investigated the metallurgical aspects of f r i c t i o n a l adhesion. They have postulated that junction formation and growth.can.be explained in terms of recrystal l izat ion and grain growth. As might be expected,:interface-temperature-is of "fundamental importance-in this approach. A s ta t i s t i ca l bifurcation in values of static f r i c t i o n has also been encountered,. which indicates that two separate mechanisms contribute to f r i c t i o n ; one-is accounted for by.the weld junction theory, the other is not yet satisfactori ly, explained. This 6 bifurcation . suggests that two wear rates exist , and is perhaps an avenue for further association between f r i c t i on and wear. Other studies have been made at extremes of speed,•load, temperature and environment,' but in general the results are neither part icular ly revealing nor are they applicable to most engineering situations. The plast ic roughening theory 90 proposed by Feng is such a study, with application limited to high load situations. 7 3- SUMMARY In.summary then, research progress may be reviewed as follows: 1. The adhesion theory and other early theories are found...to. be over-simplified. 2. Mathematical and graphical model studies..are useful , : but the results cannot be applied.directly. to generalized surface contact. 3- .Studies of physical models are forced to idealize both the shape-of surface asperities and the manner in which they come together. In both these respects the random nature of true surface contact is lost . k. Thermodynamic and metallurgical considerations.•are important,. and must form part of every.rigorous, treatment of surface contact. 5-. Frict ion.and wear have most often been treated separately,.and yet the explanations for these phenomena must:be compatible. An.approach involving both plast ic and elastic surface deformations,.and.multiple encounters between .asperities, shows, the most promise. Many gaps exist in the store of empirical data,., and ..the present study concentrates on two - aspects;.the effect of i n i t i a l surface finish.and the action of wear debris. Ideas regarding surface geometry presented by Ernst and Merchant wil l :be examined.in greater deta i l . Also the multiple contact and elast ic deformation proposals of Archard w i l l be extended to a general application, involving surface f inish and.wear debris. CHAPTER II THEORETICAL CONSIDERATIONS 8 THEORETICAL CONSIDERATIONS' •3 The static f r i c t i o n .theory.of Ernst and-Merchant involved a model,.of surface asperity contact.as shown i n Fig . 1. N P L A N E OF CONTACT A Fig . 1. Enlarged-Sketch.of Surface Asperity Contact. The authors proposed that upon application of the load N the size-of the projected area of contact-A-is established by plast ic flow.of the metal and that a strong inter-metall ic junction exists along the interface-A'. Analysis of the model led:to the following expression for f r i c t i on coeff ic ient: /U = — + tan o< ( l ) where shear strength S and.surface pressure hardness H' are considered to be constants of the materials. H is. defined as'N/A. Equation ( l ) may be • investigated.at two l imit ing conditions. For a surface consisting of uniform high angle irregular i t ies tan OX w i l l be-large and w i l l be.constant. It is then possible to investigate f r i c t i o n coefficient-as .a function of the-angle cX • • A-study, of equation ( l ) suggests, that i f the f r i c t i on coefficient is plotted as. a function of angle oc ,. i t should, describe the-same curve-as tan &, , and be displaced a constant distance from.it .as shown in Fig . 2. Fig . 2. Graph of Fr ic t ion Coefficient Versus Angle of-Asperity Contact. When .the surfaces, are smooth or when the surface-irregularit ies do' not interlock, the tan o< term may be considered.negligible and equation ( l ) reduces to: This, la t ter case is the essence of the adhesion theory, and has been the S subject of much research. The constant term was. found to have an approximate value of 0;2 for a wide variety of materials'^. The commonest jus t i f i cat ion for.the a p r i o r i , assumption of plast ic deformation at points of contact has. been,the Hertz equation. Hertz considered a spherical indenter on a plane surface and solved for stress k and strain under elastic deformation. Timoshenko applies, the Hertz Theory •10 to the situation of impending plast ic deformation. For a sphere of.radius R loaded against a plane surface of material with identical elastic modulus E and Poisson's Ratio of 0 . 3 , the radius, of the contact.-area i s : 'MR 1.1/3 1.109 (3) Calculations of..the stress distribution .in the materials have been, made, and are shown in Fig . 3-0.5 <J0 <^o (Tr = Oo M A X I M U M SHEAR S T R E S S Fig . 3- Graph of Stress-Distribution ..for Hertzian Contact (after Timoshenko) The point of contact is 0,. and OZ is the axis of symmetry perpendicular to the plane of contact. Polar coordinates.r . and © describe the-plane of contact. From radial , symmetry the stresses are a maximum along the axis QZ,. and i t is these ..maximum stresses which are-displayed in F ig . 3- The unit of stress, ^ 0 > is the maximum pressure at 0. 'Ductile materials. such. as. steel, f a i l , in shear. The shear, stress, is proportional to ( (Ti - G"t" ) and. this difference determines the position .of the point of f i r s t plast ic yielding by the Maximum'Shear Theory. 11 Reference to Fig . 3 indicates, that the shear stress is a maximum at a point approximately. | ; below ©....-At the point 0,. shear stress, is • less than .1/3 of the maximum value,.while.at .a depth of V from the-surface the shear stress, .is ful ly. 3/)+ of the maximum. The - areas-.of highest, shear stress and.hence-the.areas, where plast ic yielding w i l l f i r s t occur, are definitely.subsurface. As N is. increased,. equation 2 predicts :that'""a" also increases-' Hence an.additional factor, which serves to prevent plast ic deformation from occurring at the surface of .contact is the-increase in depth.of. the point .of maximum shear, stress as normal load increases. -When subsurface plast ic yielding occurs the-equations quoted here are -invalidated; ; however., they, are s t i l l useful as :.a qualitative indication of stress distributions. • An analysis considering two contacting surface protuberances with general r a d i i of curvature-and planes of curvature-also yields the result that maximum shear stress is. some distance below the surface of contact, although the area of contact may be e l l i p t i c a l or rectangular instead of c i rcu lar . The fact that plast ic deformation.can occur while surface deformations remain elastic i s important f o r . i t offers, an alternative-to the concept of surface plast ic yielding and welding adhesion in areas .of contact. Archard has done a considerable .amount of work on this subject and has shown :that many.surface contact situations consist of a number of contact points which deform e las t i ca l ly . Further, he demonstrates that in, multiple contact'Amonton's law i s followed without the necessity.of postulating plast ic deformation and cold welding. 12 Elast ic deformation may also be assigned to wear debris, provided the loading on each p a r t i c l e : i s not too great. General ly . i t may be stated that plast ic deformation need not always be associated with surface deformations and adhesion. CHAPTER III 1. APPARATUS.AND INSTRUMENTATION 2. SPECIMENS 1. APPARATUS AND INSTRUMENTATION The apparatus i s shown, i n Fig. k. The drive unit•(A) consists of a variable speed servo-controlled dc motor,, with.a speed range of zero to 3600 rpm (see App.I). The drive unit i s coupled through a'^0:1 speed reducing worm gear and a U:3 r o l l e r chain drive to the horizontal.shaft (B). A set of 1:1 bevel gears transmit motion to the rotating head (c). A mechanical revolution counter (D) i s also driven by.the horizontal shaft. A disc specimen, : 10 inches i n diameter-and 3/^ inch thick, .-is shown mounted on the rotating head. The s l i d e r has .a rectangular bearing- face 3/^ inch. \>y'l/k- inch, and i s l/k inch thick. I t - i s mounted.in.a semi-cylindrical, s l i d e r mount. The s l i d e r mount,.as shown i n Fig. 5> forms part of.a s e l f ^ a l i g n i n g universal j o i n t . This j o i n t i s an important part of the-apparatus, for i t ensures that the s l i d e r surface l i e s f l a t on the-disc a t - a l l times during s l i d i n g . The s e l f - a l i g n i n g .joint permits f r i c t i o n and wear.to be related to the i n i t i a l f i n i s h : a n d prolonged alignment wear-in with associated destruction of the i n i t i a l surface i s thus obviated. The s e l f - a l i g n i n g j o i n t assembly.is mounted on the steel.beam, Fig. 1 ( E ) which i s four inches long, one and one-half inches deep.and one-eighth inch wide. The unit constitutes the e l a s t i c supporting system of xthe s l i d e r . The c i r c u l a r natural frequency of the system was found from free vibration tests to be-232 radians per second. The beam i s cantilevered from a steel bar and t h i s entire assembly i s pivoted on b a l l bearings. Normal:load i s applied to the s l i d e r by the knife edge (F) through the pulley system from the load pan (£). The load c a l i b r a t i o n i s detailed i n App.II. FIGA PHOTOGRAPH OF THE APPARATUS The r a d i a l p o s i t i o n ,.of the s l i d e r on the disc i s c o n t r o l l e d by the lead screw (H), which.moves the entire. assembly, described..,above. Four separate wear tracks can be made on..the-disc before the p i n .in.the s e l f -a l i g n i n g j o i n t i n t e r f e r e s with the ^ edge -of the d i s c S t r a i n gauges, (SR-U type C-7) were mounted on each side .of the s t e e l , beam and.measured the. s t r a i n induced b y . f r i c t i o n at the s l i d e r . The gauges were wired i n t o t h e - b r i d g e - c i r c u i t of a Brush Strain.Analyzer,. and the output from t h i s u n i t was. displayed on .one channel of an Edin two channel o s c i l l o g r a p h . The c a l i b r a t i o n of the beam f o r , . friction/measurement i s glyen.,:in: App. I I I . The other channel of the o s c i l l o g r a p h supplied a reference nark, : beside the f r i c t i o n ..trace,, so that.the e f f e c t of finish.mark :,orientation • could;be assessed. To .this l a t t e r end microswitch ( j ) was-mounted and when.closed by a p i n on. the -disc caused, a pulse of current t o . d e f l e c t the pen, .thus p r e c i s e l y . marking the reference o r i e n t a t i o n ..once every, disc revolution. Points on the o s c i l l o g r a p h paper corresponding to other f i n i s h mark ori e n t a t i o n s were located by a l i n e a r -transformation .of the f r a c t i o n ..of a rev o l u t i o n .to .the distance between .pulse marks. The c i r c u i t r y also•included a separate toggle switch which produced.a reference d e f l e c t i o n of d i f f e r e n t -.amplitude. This was used t o mark u n r e l i a b l e data; . f o r example, data recorded while the disc speed was -being changed. The-apparatus was designed f o r g e n e r a l . f r i c t i o n and wear studies, hence the f e a s i b l e range of. variables >.in t h i s study, was determined em p i r i c a l l y . A disc and s l i d e r with/ground surfaces were mounted-and the e f f e c t of disc speed ..and normal'load were observed. The governing ..factor was found to be the violence of v i b r a t i o n of the beam;:there were conditions of speed-and load which required.use of.the highest..amplifier' 17 attenuation .and produced.definite edge loading effects. •Edge loading could have been the result of high normal force upsetting ."the designed s tab i l i ty of the self-al igning .joint. • From these considerations, the range of normal loads selected..was 1.025 pounds to 3-075-pounds in three equal ..steps. The maximum disc speed was 122'.2 revolutions per minute; . the -minimum,;based on.motor s tab i l i ty , was 1.22 revolutions per minute. Eleven .intervening speeds were selected. An oscillograph paper speed.of five' millimeters per second was used for speeds up toV.33'3 .revolutions per minute. -Paper speed of ten millimeters per. second was-used at higher disc speeds. A Brush oscillograph ..with a paper, speed of. 125 millimeters per second was used to obtain expanded details of the f r i c t i o n trace under vibration .conditions. Further details of.the instrumentation are given^in Appendix IV. 18 2. SPECIMENS It was decided to make the discs and sliders from .identical material to avoid metallurgical complications. Mild .steel;was selected because of i t s wide application to engineering work in general. • ASTM ;283 -Grade C was•available in the stock size required, and was representative of intermediate tensile strength steel .of uniform structural quality. The steel contained.0.16 percent carbon,;0.010 percent phosphorous, .0.62 percent manganese, 0.05.percent s i l i con and: 0.021 percent sulphur. The discs-were flame-cut .from three-quarter inch thick hot ro l led plate with a peripheral machining allowance which ensured that the f ina l sizing to ten inches diameter removed any material chemically affected by.the flame cutting. •After annealing the disc had a hardness of Rockwell B6k. Notches were machined in.the edges of each, disc to permit •its being clamped to the table'':of a shaper. The s l iders were surface ground to f i t . snugly i n t o ; a slot in the sl ider mount. Hardness was Rockwell B75 and,.because no : flame cutting was involved,.annealing was not considered necessary. The final-surface f in ish process had the greatest -effect-on ..surface hardness and also i t was thought that a s l ight ly harder s l ider was desirable in order to prolong the wear-in period for purposes of study. The f i r s t four.test finishes were generated by means of a shaper, and considerable time was spent investigating tool materials :and tool geometry. It was found that both s t e l l i t e and carbide-tipped tools le f t the disc surface badly torn and ragged. Further investigation, .revealed that high speed,tool steel produced the best surface. The discs were machined without lubricant .at a cutting speed of seventy-five feet per minute. 19 The tool face was. in ;the form of a symmetrical V, with a range of included angle for three tools of 9h°, 1 2 6 ° and l U 6 ° and a rake angle of •25° throughout. The edges of the tool.were hand honed.to give an appearance, under 200 power magnification,.comparable to'that of•a razor blade edge. One disc and four sliders .could be finished with each, tool before re-honing of the tool edge was necessary. Prior to f ina l surface f inishing .the specimens, were thoroughly.washed in Varsol to remove o i ly or greasy surface contamination. The table of the shaper and the tool head were also washed down.to preclude the migration of contaminants to the specimen'surfaces. Fig . 6. Diagram of Typical-Striae Prof i le The tool was mounted to cut symmetrical grooves .and with an appropriate value of cross-feed and depth of cut, gave a striated surface with a general cross-section as shown, in F i g . 6. The f i r s t three surfaces were to have nominal values, of ^ of 9 0 ° 1 2 0 ° and.150° and a .constant value of L. The fourth f in ish .was. to have j3> .= 1 5 0 ° and one-half 20 of the previous value of L. Table 1 shows the.actual dimensions as measured from the specimens. After machining,.the surfaces, were buffed on a clean wire wheel to remove loose debris, .and then were mounted in the apparatus. Table-1. • Dimensions.of Striae Profi le 1 2 3 k 23.6xio"3 23.6xio" 3 23.6xiO"3 n.Oxio" 3 6.9xl0" 3 3.6xl0" 3 2;0xl0" 3 l . l 6 x i o " 3 102 131 157 153 Striae on the discs were para l l e l to a diameter.and were-uniform across, the face of the disc;.on the-slider.they.were para l l e l - to the - short side of the rectangular bearing face and similarly.uniform. •Thus, with : disc and s l ider mounted:in the.apparatus there -were two positions during . each revolution of the disc in .which ...straie of disc 'and.slider-interlocked, and two positions, in which they-were-mutually perpendicular. . • At , .a l l other disc positions the-striae were in some relative -orientation between .. these two extremes. The last two surfaces, were not finished on .the shaper. Test f in ish 5 was generated by.surface grinding, f in ish marks being orientated as described .previously. Although this surface was. not striated to the same -extent .as. the previous four,.there were definite-direct ional effects. Surface roughness values,-as. determined by, the Brush Surface; Analyzer were 100.micro-inches*:across the f in ish marks, and 25.micro-inches along the f in ish marks. * A l l surfaces described in micro-inches represent root mean square values of roughness. ' • Surface f in ish L.(inches) d (inches) 6(degrees) , 21 -Test surface 6 was a surface ground .finish which was hand lapped.with a cast iron plate, using 2^ 0 mesh;(Tyler Sieve s i ze ) , s i l i con .carbide powder in a pure l iqu id paraffin medium. The surface roughness was 35 micro-inches'with no discernible - directional effects. The wire-wheel buffing operation was omitted with..these last two surfaces,.although surface -6 was washed i n trichloroethylene to remove-all traces of lapping compound. As a f i n a l decontamination procedure before each test, .the disc•and s l ider were thoroughly, swabbed with .ethyl.alcohol and clean cotton wool after, having ;been mounted in the-apparatus. This procedure was, intended to 'remove- any, surface contamination.: acquired by .'specimens during handling. The a ir in the laboratory was b e t w e e n 6 0 ° F and 70°F throughout the testing, period. The low humidity of the atmosphere was demonstrated by the fact that no corrosion could.be .detected on ;the freshly,machined surfaces or even .in wear debris., after open exposure for days. Visual inspection and- x-ray .'diffraction photographs were used to test for. iron oxide. CHAPTER :IV EXPERIMENTAL METHOD TYPES OF FRICTION. RECORD • RESULTS, AND DISCUSSION A) . Geometry .ver su s Fric t i on B) 'Velocity, and Load Effects C) Wear, and Wear-In : D) Finish Mark Orientation E) Wear Debris F) •Kinetic Aspects 22 , 1 . EXPERIMENTAL METHOD. The tests on each surface f in ish were conducted according to:a standard procedure. The maximum radius of the -slider on .the.--disc was selected to:allow,a small clearance-at the edge of the disc. This clearance freed the s l ider from the effect of• any.surface f in ish irregular i t ies -at the edge of the d i s c The maximum :radius position was used.for normal load of 1.025 pounds, the next smaller.radius, for load of .2.050 pounds and the -third smallest radius for load of 3-075 pounds, with a small clearance allowed.between each wear.track. The.advantage of this procedure was that the smaller r a d i i gave'lower relative speed between ..the disc and the s l ider and part ia l ly , offset the increase in the rate of surface destruction and wear-in•resulting from higher.load. The inner-most s l ider position was' reserved for reproducibi l i ty .tests or other tests on ..wear, debris. Some further testing was done - in .the previously/worn • tracks,'but not u n t i l after, the standard testing procedure was completed. At each .load the speed .of rotation ,of the-disc was raised in increments from zero to. the maximum and reduced in the same steps.. Approximately six revolutions of the disc were allowed at each speed setting. However,- because of the slow maximum oscillograph paper speed, many more revolutions were required at high disc speeds before the resulting fr ic t ion , trace was long enough-to analyze. ' Wear debris was removed from .the disc with dry cotton wool after each load was tested, but the disc was not subjected to-additional cleaning with ethyl alcohol. 23 .2. TYPES'OF FRICTION RECORD . Three types of oscillograph trace-were observed,.corresponding to different behaviour of the friction.:.surfaces. ; The . f irs t '• type was. a constant or near, constant deflection such-as shown.in F i g . . 7 a . . This type-indicates that no vibration,existed.at the f r i c t i o n surface and is characteristic of the early/wearing-in.period of fresh surfaces (exclusive of the positions -at which striae interlock). The second t y p e , • F i g .ft, shows, an intermittant or random high amplitude osc i l la t ion; which has similar characteristics to'"st ick-s l ip" osc i l la t ion . The basis of this type of trace is, a stick period during which the s l ider is deflected with the velocity, of the disc. Then when .the restorative force exceeds the force of adhesion the s l ider sl ips towards the undeflected posit ion, with the form of a one-half wave at -the damped natural frequency. The s l ider might stick again at some point and the cycle be repeated. This process occurred at the interlocking position .when interlocking striae created.high stick forces. ' Sometimes at high speeds and loads the-osci l lations were -frequent and violent. 'Under these conditions the-behaviour was, attributed to edge loading of the s l ider . The application of loose wear debris to the wear track also produced this form of osc i l la t ion . The th ird type of trace was..a continuous, constant amplitude v ibrat ion , •F ig . 7c) which might .be described as a quasi-harmonic osc i l la t ion at the damped natural frequency,of the elastic supporting system. The vibration appeared only,after a definite wear-ih period. The, transit ion from steady deflection ;Was often .abrupt, but the vibration was uniform and 2k In the subsequent discussion :the three types .of f r i c t i on behaviour • w i l l be referred to .as steady.deflection, random 'osci l lat ion ,and continuous vibration. • With this nomenclature ' i t . i s now convenient to examine the results in deta i l . 25 FIG.7 THREE TYPES OF OSCILLOGRAPH TRACE 26 3- RESULTS AND -DISCUSSION A. GEOMETRY versus FRICTION .The geometry of the surface finishes was measured.by. the-optical:and photographic techniques outlined i n Appendix V. It is-thus .possible to'treat the surfaces as an array, of model asperities. Fig. 8. Profile View of Contact Between Striae at Interlock The model asperities contacted one - another in a variety.of different orientations-as the disc rotated ..and-at .the interlocking position they met-as shown in Fig. 8.- The work of Ernst and Merchant suggests that j£ i s expected to vary with o< in a form expressed by. equation ..(l). Fig.9 shows coefficient of f r i c t i o n versus the complement of the striae half angle on . If i t - i s , assumed that the interlocking effect..for finish 6 is negligible ( CK m O ) then we may assign the value O.U to the •adhesion term = . This value, i t might be noted, is considerably.higher than the value predicted by Bowden and Tabor. Experimental: evidence• agrees with theory from the point <X,= 0 to .an .angle of about oc = 25°-z o I u. li. o \~ z UJ g U. U-UJ o o SURFACE FlMlSH FIG. 9 G R A P H OF COEFFICIENT OF FRICTION VERSUS C O N T A C T A N G L E 28 At greater angles, experiments indicate that ytf increases .more rapidly, than •the tangent function. This behaviouris unexpected .since the theory implies that as ot increases,.tan oC becomes more significant, and should completely , control the f r i c t i o n coefficient. Further evidence of complexity-is provided by.additional.anomalies. F r i c t i o n coefficients for surface f in ish 3 were consistently.higher than those of f in ish h,-whereas by. a comparison of ex. values they should.have been sl ightly, lower. Although the angle o< cannot be deduced for finishes • 5: and 6, ..roughness measurements Indicate that the ground surfaces had a greater capacity, for.-interlocking than the lapped surfaces. Yet the ground surfaces showed consistently .'lower values of JUL than the lapped surfaces-as seen . in Table 2. This Table is a summary of Fig.9 showing.average f r i c t i on coefficient.for. each surface f in i sh . Surface Finish.and -Coefficient of Frict ion;at-Interlock 2 3 J+ 5 6 0.86 0.68 0.U5 0.25 -o.hi Loads) The question of the size-of surface .asperities-may be raised here,,and i t can be argued that the - asperities-which have been-investigated are themselves covered with smaller asperities which can : interlock. Consider the difference in f r i c t i on coefficient-between ..finishes.' 1j and..2." These finishes were generated by the same process and so the small scale asperities should influence f r i c t i o n equally. Therefore the observed difference in f r i c t i o n coefficient must be - attributed to macroscopic., surface geometry. Evidence shows that surface geometry, has an•increasing t Table-2. Surface Finish Coefficient of :. _ T> • u.- 2.3D Fric t ion I Avp-rncrp f n r 'Thrpp 29 effect.as the slope of.the sides ;of the asperities, becomes large, but in order to explain this adequately, the theory of Ernst :,and Merchant must be modified. The divergence- between-the experimental results, .and the tan ex relationship in the large angle range ( oC > 25°) suggests that -other factors become :important .-in this region. . One -explanation of this, increasing divergence is as. follows: I t . i s well known that .-a large.amount of plast ic deformation at the surface, . i .e . ;welding adhesion, greatly.increases fr ict ion.and in.,extreme cases may cause seizure. An increase'in the proportion .of elastic deformation.should correspondingly.reduce f r i c t i on . ' Considering the effects of surface geometry/it ,is clear that-a surface with a few sharp •peaks w i l l experience more plast ic deformation.through:load concentration than one with,.a greater number of shallow-peaks. Concentrated .loading should lead to greater surface, adhesion .and hence greater friction'. Reviewing Fig.9 with these considerations, . i t is. seen,:that as the sharpness of the surface•irregularities, decreases f r i c t i on decreases. Finish k, with i t s increase in the number of load-bearing peaks, produced a decrease in f r i c t i o n .although the peak .geometry/is essentially/unchanged from f inish 3- Finish 6 should display/the lowest values of JJ, ; but they are sl ightly.higher-than those o f . f in i sh 5. Two mechanisms are involved here which.are peculiar to f la t smooth surfaces. •Firs t .is adhesion which does not necessarily, involve plast ic deformation, - such as that' between very smooth gauge blocks. This adhesion has. been, attributed fco a combination of Van:.der Waals forces, and . atmospheric exclusion, . and i s . a possible explanation of fr ic t ional . force -in.elastic contact .situations where adhesion, due to cold welding i s ruled out. The second arises from 3D the small amount .of clearance between :the lapped surfaces. 'Wear partic les under these conditions would ..remain in ..contact, with the surfaces, and be subjected .to p l a s t i c deformation and cold.work, . thus, contributing to f r i c t i o n . B. VELOCITY & LOAD EFFECTS The effects of load and disc speed-were examined.,; at the f inish mark orientation .where striae were crossed. ' Consider"Fig.10.which Is a plot of fr ict ion, .coefficient versus disc speed.for test f inish-5- • Starting at point P, JJ•is lower than the generally.encountered values, for . s tee l on steel.and no -load effects, are discernible. As speed .increases, f r i c t i on coefficient rises gradually and.load effects become evident. The curves for the large loads rise more rapidly, than ..for the smallest load and also reach :higher-values of JJ . A general increase- inelast icdeformation and •welding adhesion which would occur, as load.increased offers a possible explanation of these effects. Microscopic examination revealed more evidence of surface plast ic deformation as lead increased. The values of JJ tend to stabil ize in the generally accepted range for steel .of 0.3 to 0 . 6 . The variation of JJL with disc :speed was not reversible however, • and as speed was reduced from the maximum a further, increase in JJL occurred. Some tests were made,.with test f in ish two,.which:deviated from the standard procedure. Tests, were started at high speed, - and, .changes in speed.were random rather than sequential. In these cases too,,the average coefficient of fr ict ion, increased with s l iding distance. Definite velocity effects were found at the interlocking posi t ion, • but these were due to an interaction between the natural frequency of the beam and the forcing frequency aris ing from successive iriterlockings of para l l e l striae. I.O Z o u o NOTE: : ARROWS I N D I C A T E INCREASE. IN SLID IMG DISTANCE TRAVELLED DATA FROM TEST 5 50 2 UJ 6 o o •as O- LOAD • - LOAD A - LOAD 1.025 POUNiDS 2-05O POUNDS 3.075 POUNDS — P O I N T S F O R O A N D • C O I N C I D E — ALL THREE POINTS COINCIDE FIG. IO o ao SO AO DISC SPEED ( INCHES/SECOND) GRAPH OF COEFFICIENT OF FRICTION VERSUS DISC SPEED I.O D A T A F R O M T E S T 5 O - LOAD POUNDS • - L O A D 2.05O P O U N D S A - LOAD 3 . 0 7 5 P O U N D S • — POINTS O AND A COINCIDE • - A L L POINTS COINCIDE 6 6 IO \Z SLIDING D I S T A N C E (THOUSANDS OF INCHES) 1 4 FIG. II G R A P H O F C O E F F I C I E N T OF FRICTION VERSUS SLIDING D ISTANCE 33 This behaviour leads to the interpretation that the variation,.in JJ^ i s due to effects of wear-in rather than velocity, and that the important variables are and s l iding distance. Fig.11 is a plot of these variables for test 5^  and supports the .above interpretation. The f r i c t i o n curves for 1.025 and 2.050 pounds normal load are seen, to r ise continually as s l iding distance increases. It. might"be assumed that f r i c t i on values should decrease,.for. as wear-in progressed the points of load concentration were flattened and hence the amount of plast ic deformation.should'be reduced. The increased f r i c t i o n may be accounted ..for: by the same explanation as was applied to.the high f r i c t i o n coefficients of f in ish 6. It was not possible to determine whether elastic adhesion or the cold working of wear debris was the dominant mechanism but as. wear-in rendered the peaks of the striae of sl ider.and disc compatible both of these mechanisms became feasible. Considerable plast ic surface deformation..undoubtedly occurs at jagged Irregular protuberances such -as might be lef t after, metal cutting operations. With, freshly prepared surfaces random osci l lat ions, were observed during the f i r s t one or'two revolutions. • As protuberances were flattened or worn away elastic contact deformation prevailed and f r i c t i on values became steady. C. WEAR: AND WEAR-IN . The concept of simultaneous elastic, and plast ic deformations has particular application to wear. Although empirical \ laws of wear.are ,, known, i t i s not explained why,variations in wear' rate may be orders of magnitude greater than corresponding variations • in f r i c t i o n . •For example experimental evidence shows that the coefficient, of f r i c t i on is generally constant whereas comparison ,of the wear tracks and visual observation of • 3^ the amount of wear debris formed, indicate a much greater variat ion- in wear rate. The amount .of subsurface plast ic deformation may.vary. widely while surface deformation s t i l l remains e last ic . • Subsurface -plastic deformation would contribute less to f r i c t i on force than would welding adhesion, because the subsurface, deformation arises directly,from the action of normal load but welded-junctions must be sheared wholly by a force tangent to the surface, . i . e . f r i c t i on force. However subsurface •deformation ..could s t i l l . contr ibute .to the production .of wear .debris. Repeated loading. :and unloading of .asperit ies would create-a fatiguing situation and eventually a wear part ic le , - highly.work hardened,.would.become detached. The f i r s t .appearance of the fatigue crack w i l l be below .the surface of contact in,:the region .of maximum.shear, stress. Of course any plast ic deformations occurring at the - surface would contribute to wear and f r i c t i o n through welding adhesion. Such adhesions are-inevitable, but may occur to only, a. l imited extent. Frict ion, then may ."be attributed to a-large term due to non-welding ;adhesion,. a term resulting from .subsurface plast ic deformation, which varies, widely, but has relatively, small influence on the tota l f r i c t i on ..force, . and a small term resulting from surface welding adhesion. Wear, on the other hand, may-arise mainly,from the widely ' varying plast ic deformation term, with a small contribution :from surface welding adhesion. With these considerations in mind experimental results can be examined. The appearance of the continuous vibration ..type of frict ion, trace-was a function of wear-in; F i g .12 shows wear-in distance -against load for the six surfaces tested. It is seenthat finishes 1.and 2,.with the greatest poss ib i l i ty of plast ic deformation through load'concentration, displayed continuous vibration most .rapidly. Finish 1.3 was. a transit ional ..case between, rapid wear-in and slow wear-in and.never, produced the very, stable 3''5 vibration common to-the other surfaces. 'Points underlined on. this-figure •indicate that the test .was terminated before continuous•vibration was observed. Finish 6-would be expected to wear-in very,sloWly, yet continuous vibration , appeared-..after s l iding a distance comparable -to the roughest finishes. Wear rate was indeed .low, as was .evidenced by.the appearance of the wear track,-but the surfaces,.being lapped,.required l i t t l e wear to produce surface compatibility. I t . i s evident that lapped surfaces have pecul iar i t ies which-are not common to the other machined finishes. Table 3 i s a summary of ; F ig . 12-in..which wear-in. .distances for the three loads are. .averaged to give one wear-in :distance for each surface f in i sh . Table 3' Surface Finish.and Sl iding Distance for Continuous Vibration • Surface Finish Sliding Distance (inches) '^ .Remarks ,. (Average for Three Loads Unless Noted) 1 ,3700 2 -3500 3 5300 k l l 6 0 0 No vibration k 2U5OO - One test only ,5 .12^00 - - - - - Two tests •6 6100 o— T E S T FINISH 1 • — TEST FINISH 2 A — TEST FINISH 3 V — T E S T FINISH 4 o — T E S T FINISH 5 • — T E S T FINISH 6 POINTS UNDERLINED INDICATE TWAT TESTING WAS T E R M I N A T E D BEFORE CONTINUOUS VIBRATION APPEARED 5 IO 15 20 SLIDING D I S T A N C E ( T H O U S A N D S OF I N C H E S ) 25 L O O N FIG. 12 G R A P H O F L O A D VERSUS SLIDING DISTANCE REQUIRED FOR CONTINUOUS VIBRATION 37 •D FINISH MARK ORIENTATION It is now possible to discuss the .effects of variations, in .finish mark orientation. Fig.13 shows.friction -force versus orientation, .of f in i sh marks for Test .3- The information ..for Fig . 13 was obtained- after .about..i+00-inches of. s l iding had occurred. • At this stage, noticeable changes in surface geometry due to ,wear-in-were-evident. 0 = 0 and 0 ,= TT represent.the two positions of striae interlock which occurred during-each revolution. It,.is seen that at these positions f r i c t i on is re lat ive ly .high. This case was discussed under geometry versus f r i c t i o n . For.almost . a l l of the remaining disc rotation f r i c t i o n has a uniform low value with.a sl ight minimum at 0 ,= ^ and • Orientation of f in ish marks then has a pronounced effect where surface geometry gives high:load concentration,but for most reasonably smooth surfaces the effect w i l l be small. Microscopic examination of the wear tracks revealed that-.wear was highest ;at © •= 0 and TT ., , and lower at ©,,= and' . . The drop in f r i c t i o n coefficient with :.load-; at orientations of © = 0 and TC i s attributed to faster wear-in .at high loads. It was found generally that as wear-in progressed f r i c t i o n coefficients.at © .= 0 .and Tt decreased but at © .= and they, increased. The explanation of these findings i s outl ined.in the sections covering Fr ic t ion versus Geometry and Velocity.and Load Effects. N O T E : S T R I A E . A R E INTERLOCKED A T 9 - O A N D TT D^SC WITH STRIAE D A T A F R O M T E S T 3 O — L O A D 1.02.5 POUNDS • — L O A D 2..050 POUNDS A — LOAD 3 -075 POUNDS — POINTS • AND A COINCIDE — A L L POINTS COINCIDE 7T/2 "TC 3TT/2 F IN ISH M A R K O R I E N T A T I O N 9 (RADIANS) F \ G . 13 GRAPH OF COEFF\C\ENT OF FRACTION VERSUS FINISH MARK OR\ENTAT\ON 2.T 00 39 E. WEAR DEBRIS The role of. wear debris in .surface -interaction was..investigated in deta i l . Tests carried out on surfaces 5 and 6 by adding wear-debris to fresh surfaces indicated that two mechanisms exist with respect to wear debris. One -is an increase in f r i c t i o n through deformation,. cold work and possibly adhesion of the-debris,.which has..already, been .discussed. The other mechanism i s concerned with a drop .in friction,.which. ;suggests that.the -wear part ic les may carry.load l i k e miniature '"ball-bearings". Referring to Flg.lh, the rounded .appearance of . the-particles supports . this suggestion,.and such a mechanism would.most.probably, result ' in:the sudden.and substantial drops in f r i c t i o n which, were-sometimes observed. • A simple experiment of r o l l i n g plasticene f i r s t . l ight ly and then with considerable force between the - fingers can demonstrate these two mechanisms. A large number of part ic les would be-required before the second mechanism could operate. However the'high wear rate resulting from a normal load of 3-0?5 pounds could produce t^hem. The values of JX found in Fig.11 for a load of 3.075.pounds, varied widely as. s l iding distance increased. At this ' load random osc i l la t ion predominated .and the.amount of debris was large. A combination of the two debris mechanisms is .the most • l ike ly explanation f o r the variation in jj. . It has been mentioned that wear .'debris,. inter.-al ia, , caused- and promoted random osc i l la t ion . The corollary/that removal of wear.:debris reduces the incidence of random osc i l la t ion ;,was • also true, . and in this, respect.-a thorough cleaning with ethyl alcohol proved.more effective than a dry wipe with cotton wool. These results were qualitative only, but they do underline the importance of the action :.of wear/debris. lUa Cuttings from a Jeweller's Saw X210 lUb Cuttings After About 1000 i n . Sl iding X210 ihc Debris Formed by Wear-in X290 FIG.lh PHOTOGRAPHS OF WEAR DEBRIS •1+1 • The effect of.debris on wear-in and the.appearance-of continuous vibration .were also assessed. •The 1.025 load was, applied to test .finish .5 . f or: 11,1+80 inches'before continuous vibration .appeared. This, vibration •was not stable above a disc speed of .2. lh-. inches per second. A further test ;.was made using a fresh..track and s l ider , with wear debris being added to the track. In the lat ter case continuous vibration appeared after only--8665 inches, and was stable up 'to;at"leastU.U inches per second, . although i t was not tested,- above this, speed. Debris was deposited on a track on test .finish 6 ^while continuous vibration was occurring. Vibration immediately, ceased,.and a steady deflection was observed. • Considering the 'lack of clearance between .the f la t surfaces of f in i sh 6, i t i s probable that the second wear debris mechanisms, had become dominant. Clearly wear debris has ,an ..important .influence on .the behaviour at the s l iding surfaces;.undoubtedly.in conjunction with the geometry,at the surfaces themselves. X-ray powder patterns were made of debris from tests, two.and four. The debris was found to be in ,a highly work-hardened state.and.line broadening of the 'powder pattern occurred to such.an .extent that annealing of the debris was necessary. Care was taken to anneal at a temperature at which iron • oxides, 1.'if ^present': in thecdebris:,:. wbuld:'not^be' reduced.':." • It was found that the debris consisted of pure iron. This is contrary to the findings of Kerridge, who encountered much iron oxide in wear debris. F. KINETIC ASPECTS "Discussion of the continuous vibration.•;involves some pecul iari t ies of a dynamic nature. Fig.15 shows the change in vibration frequency with disc speed-and w i t h . . l o a d . A t high disc speeds the frequency appears to be ;asymptotic to..a frequency-near that of free vibration, .while at low .speeds a stick period w i l l greatly alter .the vibration frequency.. - As load increases the observed frequency.of v ibrat ion . fa l l s -almost l inearly but changes slope abruptly at a normal load of 2.050 pounds. Figs. l6,.17,•18 .and 19.show the amplitude of the continuous . vibration ..versus disc speed, at. the three test'loads. F ig .l6 . i l lus trates the method used to plot.these curves. •Curve-A represents the maximum . s l ider displacement .as measured on the oscillograph chart.. Curve !B is the, average displacement, ;being one-half the-sum .of the-maximum-and the minimum sl ider displacement on'.the chart. Curve C is the: difference between maximum and average displacements, taken graphically. Curves 17,.l8 and 19 represent only/the-derived curve C for each of the three loads applied to surface finishes 2, ,. 3 .and .6 respectively. These curves -are i n i t i a l l y .'linear, with.:a slope between 0.29. and O.UU.- At some speed the slope-becomes zero and amplitude of vibration versus disc speed becomes invariant for,higher speeds. The Figures i l lus tra te that the amplitude curves for various loads are .asymptotic to the i n i t i a l straight •line. Qualitatively the maximum amplitude i s greater i f the load is greater but the values are not proportional-to load nor do .-they, correspond for ..different surface finishes. In ..view of the near harmonic characteristics of the continuous vibration a solution may be written defining the s l ider position to a _ 0 — r» o» C O | I i 1.0 09 (P Ui I o ^ . 0 8 Z 0 F < CC fl) > o UJ o h ~j a < <07 .06 .05 .02 .01 T E S T FINISH 4-L O A D L02.S POUNDS -B- • B A A - M A y I M U M D I S P L A C E M E N T B - A V E R A G E D \ S P L A C E M E N T C - AMPLITUDEC O F V I B R A T I O N TT F I G . I© 5 IO . IS D I S C S P E E D ( I N C H E S / S E C O N D ) GRAPH OF AMPLITUDE O F VIBRATION VERSUS DISC SPEED 2 0 4^  .16 CO O 5 10 15 20 25 30 35 40 45 D I S C S P E E D ( I N C H E S / S E C O N D ) F I6 . 17 GRAPH OF AMPLITUDE OF VIBRATION VERSUS DISC SPEED FOR TEST T W O LOAD 3 .075 POUNDS L O A D S .05O P O U N D S L O A D I.OE5 POUNDS 15 ZO 25 30 35 D\5C S P E E D ( INCHES/SECOND) 40 45 FIG. 18 GRAPH OF AMPLITUDE OF VIBRATION VERSUS DISC SPEED FOR T E S T T H R E E O S 10 13 20 25 30 35 40 45 DISC S P E E D ( I N C H E S / S E C O N D ) FIG. 19 GRAPH OF AMPLITUDE OF VIBRATION V E R S U S DISC SPEED FOR T E S T SIX HQ-f i r s t ..approximation,. as: x = X sin oo t •' ( M • and differentiating, t h i s expression to obtain velocity: — .= X OO cos ojt (5) dt k ..For a given disc speed- and' load X was obtained from Figs. 16 to 19- and LO could be assigned in accordance with F ig i l5 - It was. then possible to evaluate the expression for maximum sl ider velocity: =Xo) (6) dt I max Under conditions in which the amplitude of vibration ..increased l inear ly with.disc speed:it was found that .the maximum velocity • X CO was .approximately, equal to ..the-disc speed. This finding .introduces the poss ib i l i ty of a stick period at low disc ve loc i t ies , during which the relative velocity between the-disc and the s l ider i s zero. In the horizontal portions of the curves of Figs. 16 to 19 the disc - speed was always larger than the maximum sl ider velocity and there was no poss ib i l i ty of a st ick period. Referring to Fig.15, the existence of -a stick period would serve to reduce vibration frequency In the range of low disc speeds, but this mechanism is not applicable at high disc speeds. The abrupt change in slope of the load versus frequency.of vibration curve of F ig . 15 . indicates that some change has occurred ..at. the - s l iding ..surfaces and suggests that stick should be - investigated through considerations of load as well as disc speed. Fig . 20 shows amplitude of vibration against normal:load for surfaces ' which had previously'run-in' a distance of 60,000 inches. As in Fig.l6, 0 1.0 2.0 NORMAL LOAD (POUNDS) PIG. 2 0 " GRA.PH OP" AMPLlTUDE, OF V IBRATION VERSUS LOAD FOR T E S T FINISH FOUR A- MAXIMUM DISPLACEMENT O I 2 3 NORMAL LOAD (POUMOS) FI6. 21 G R A P H O F AMPLITUDE O F VIBRATION VERSUS LOAD FOR TEST FINISH SIX 51 curve A is maximum displacement, curve B .is average displacement, and curve C i s amplitude of: vibration. . • Average displacement rises/with normal force although the relationship i s not linear. Maximum-displace-ment ..also rises, reaching a peak -.at - a normal load of approximately .1. 3 pounds, and drops slightly.thereafter. The resulting amplitude of oscillation curve shows a maximum at 1.1 pounds normal load, . and drops smoothly.to .a value of. 0.35 inches at-1.52 pounds. Here continuous vibration ceases abruptly, and a steady deflection of .0.015.inches, .equivalent t o : a f r i c t i o n coefficient-of 0.7Q, is encountered.' The surfaces used to obtain Fig.20 were 'run-in with :a normal-load of 1.025 pounds and continuous vibration began after 2^,350 inches of sliding. At 32,100 inches,,the normal'load was increased to - 2 . 0 5 0 'pounds, which caused continuous vibration to cease. The surfaces were run at this new loading for an additional.2k f320 inches but continuous vibration did not reappear. Load was then reduced to -1.020'pounds and in 30 inches of sliding continuous vibration. iwaa-re-established. Load was varied in smaller increments and the results yielded Fig.20. Other ;tests confirmed that continuous vibration, i s stable at normal loads less than that at which surfaces .are run-in. Fig.21, for surfaces run-in at 3*075 pounds normal load, indicates that.;a straight-line relationship exists between the displacement parameters and normal:load. Such straight lines could be drawn on Fig.20 in the range of normal loads up to that used for run.-in. Details of the behaviour at the slider-disc interface are-obscure, but wear debris was found to be an important factor. It has already been pointed out that the application of wear debris hastened the ;appearance of continuous vibration,,and yet the. application of wear 52 debris to surfaces displaying vibration caused i t to cease. 21 22 Papenhuyzen, and S inc la ir . have encountered this vibration ..while studying other phenomena, and Cooic^ ""'" has commented on the general complexity of the variables involved in quasi-harmonic vibration. CHAPTER V CONCLUSIONS RECOMMENDATIONS 53 1. CONCLUSIONS Investigations, have .been conducted with particular reference to surface finish and fin i s h mark orientation,.although considerations of speed, load and wear .debris were found to be indispensible. Results of geometry versus f r i c t i o n studies were compared with the theory of Ernst and Merchant.and the discrepancies which were encountered indicate the presence of factors not noted in the theory. It has been proposed that these factors may be accounted for by a concept of dual deformation. Surface contact deformation .is f e l t to be basically elastic; and surface plastic deformation i s considered to be an exceptional situation resulting from high load concentration. Plastic deformation can occur a small distance below the surface while contact deformation remains elastic. The rise in f r i c t i o n with velocity was found to be explicable by a rise in .friction with wear-in. Load was found to affect the results in a manner compatible with the dual deformation concept. As association was found between rate of wear-in ;and surface finish, and this association was qualitatively similar to that between f r i c t i o n and surface finish, i.e. for a surface finish giving high f r i c t i o n values, rapid wear-in can be expected. Finish mark orientation was found to be of consequence only when the finish marks interlock,,and i s considered to be important only in rather extreme cases. Two mechanisms were attributed to wear debris. Small numbers of wear particles evidently suffered plastic deformation through load concentration, but in.large numbers they appeared to carry load like 5h miniature b a l l bearings. Debris was found to hasten wear-in and ..influence vibration behaviour. The debris was found by x-ray; analysis to contain no iron oxides. The quasi-harmonic oscillation was found to depend on surface finish, disc speed and normal load. •A definite wear-in .period always preceeded the vibration but the prerequisite, surface contact conditions were obscure. Significant variations in amplitude-and frequency of vibration with speed and load were found, but no comprehensive theoretical analysis of the vibration was attempted on the basis of the data.available. The dynamics of the vibration : w i l l require further study. The research has touched on ,a wide variety of topics.• The fact that a generalized study was possible muet be considered as.an indication that the design and construction of the apparatus was successful. 5 5 2. RECOMMENDATIONS Future studies of i n i t i a l surface finish effects should concentrate on overall quality of finish,rather than .the precise geometry of individual asperities. Specifically the following items could be investigated: (1) Surfaces without orientation•effects should be studied,.and quantitative measurements of wear rate versus surface finish obtained. (2) Different materials could be tested, with particular attention ,to variations in elastic properties. (3) ,• Further study of the effect of debris may.be made using hard and soft particles and particles of different materials. (k) The continuous vibrationals-a separate study which warrants an entire project. The f i r s t problem to solve : i s that of in i t i a t i o n of the vibration. The vibration i s a result of wear-in of clean,. freshly prepared surfaces,- but l i t t l e else is known. APPENDICES I. Speed Calibration II. Load Calibration III. Friction Force-Calibration IV. Instrumentation V.. • Surface Finish Measurement 56 . APPENDIX I Speed-Calibration •Speed of the dc driving motor was regulated by a control head. Ten turns of the control knob increased speed from zero to the maximum, 'and each turn was marked into 100 divisions. The f i r s t 3© divisions gave no motor rotation,.and therefore the remaining .970 divisions were equivalent-to a change in disc speed from zero to= 1^5 - revolutions per minute, the maximum disc speed. An .acceptable accuracy.of setting was -.1 + 0.5 division,.so the speed.settings were accurate to +_ 0* 5 x 0,70 X 1U5 = + O.O75 -r.p.m. At an average radius on the disc of h.5 inches, the variation in speed would be + O.O35 inches per second, or + 1 percent at the lowest speed and very much less, at other speeds. The true speed of the rotating head was determined at low speeds with .a Smith Tachometer and.at higher speeds with a Strobotac. Good agreement was obtained and the resulting plot of disc speed in revolutions per minute against control, head setting was linear, with ,a slope of lU.80 r.p.m./division arid; an .intercept of -3.62 r.p.m. 57 APPENDIX II Load Calibration •The system which served to load the "slider against the .disc was calibrated with a strain .ring. The strain ring was f i r s t connected to the bridge c i r c u i t of the Strain Analyzer,.and known loads were applied to calibrate load .against pen deflection. Four calibrations .were taken and the results plotted to obtain the best straight l ine . The ring was then clamped to the housing of the rotating head in such a way-that when the s l ider mount rested on .a small.steel b a l l on the top of the r ing, the pivoted bar was horizontal and the s l ider mount was, at .a radius of about inches from :the centre of the rotating head. This is the approximate configuration in which the actual tests were made. In. this position calibrations were made and the results plotted to give the best straight l ine . Both of the-above calibrations showed l i t t l e deviation ..from l inear i ty . From the cal ibration curves i t was possible to determine that a graph of normal load at s l ider versus load on weight pan was a straight l ine with a slope o f 0.5125 pounds at slider/pound on pan. For convenience during experimentation, normal loads were referred to by.the load on the weight pan, as L2, lh. and L6 for 1^025 pounds, .-2.050 pounds and 3-075 pounds respectively. •59 : APPENDIX III Fr ic t ion Force Calibration A special dummy sl ider mount was made to fac i l i ta te cal ibration. It was semi-cylindrical with a longitudinal groove:in the f lat side to •accommodate a loading knife edge. The pivoted bar was clamped to the table edge and pen deflections were noted as the beam was loaded and then unloaded. Four separate calibrations were made, results plotted and a straight l ine drawn. The points near zero were not obtained,.as the beam deflected under, i t s own weight and the weight of the self-al igning joint even with no load applied. However,.as no evidence of non-linearity was observed,•the results were extrapolated to zero. The slope of force at s l ider against pen deflection was found to be 0^0375 ^°s>' • m.m 59 APPENDIX IV .'Instrumentation Attenuation factor settings of 1, . 2, . 5 , -10 , .20 , 50, 100 and 200 .were provided on the amplifier. These settings were checked by .applying the cal ibration pulse from the amplifier, changing the attenuation factor settings and noting the resulting change-in pen deflections. From this information the true attenuation values were -deduced. The Edin oscillograph had-a paper width of h centimeters on .each channel,. with one millimeter divisions. This permitted,.a maximum pen deflection of 2 centimeters in either direction. The Brush oscillograph paper was s imilarly divided,; but. allowed a deflection of 2;5 centimeters in ..either direction. ' Pen deflection was calibrated to give f u l l ; scale deflection on the Edin Oscillograph with an attenuation factor of 5-These conditions.represent.the-highest gain setting and lowest attenuation factor: combination for f u l l scale deflection,.and.thus gave maximum sensit iv i ty . Ful l . sca le response of both the oscillographs was found to be ident ical , which meant that the Brush ..instrument was 1.25 times as sensitive as the Edin. The pen deflection .could be read: accurately, to at-least one-half of a div is ion, which gave-an .error of 2.5 percent with .the Edin instrument and 2 percent with the Brush instrument a t , f u l l scale deflection. 22a Test One 22d Test Four FIG.22 PHOTOGRAPHS OF STRIAE PROFILE X210 6 l APPENDIX. V Surface Finish:Measurements The prof i le of the f i r s t four surface finishes.was measured by two methods. F i r s t , . t h e surfaces were viewed at -200 power with a Reichert Binocular Microscope- A graticle with 0.01 millimeter divisions, placed in one eyepiece, permitted measurement of peak to peak distance between striae by superposition :of the graticle on the -image of the surface. The second method-was used only, for.the s l ider specimens, but the results were applicable to the discs as well . •Photographs of the prof i le of the s l ider f in ish were taken at 210 power,.and on these photographs included-angle and height of the striae were measured. The lat ter method was considered to be the -most -accurate,.although measurements by.the microscope technique were within .10 .or 15.percent. The photographic technique showed the straie prof i le to be uniform and .straight, : and the angles corresponded closely.with the "tool.angles. Roughness measurements made with the Brush Surface Analyzer had- an estimated precision of.+ 10 percent. Readings taken- at.different-points on the specimens indicated.that the surfaces were uniform in f in ish .roughness within the range of precision, noted-above. 62 BIBLIOGRAPHY 1. F .P . Bowden-and L. Leben,- Proceedings of the Royal Society:(London), Series A, Volume 169,•1939, pp.371-391-2. F .P. Bowden.and D. Tabor,- Proceedings of the Royal Society;(London), • Series A, Volume-169,.1939/pp.391-^ 05- ' 3- H. Ernst and M.E. Merchant,•"Surface Fr ic t ion of Clean Metals,— A -Basic Factor'in/the Metal Cutting Process", :Proceedings of the Summer Conference on Lubrication and. Wear,'Massachusetts Institute of Technology Bulletin,.-19^0, pp.76-IOI. k. Timoshenko, •"Theory of Elas t ic i ty" , - Second Edit ion, McGraw-Hill, New York,;1951, pp.372-382. 5- F .P . Bowden.and D. Tabor,"The Fr ic t ion and Lubrication of Solids", Clarendon Press, Oxford, • 195I+. 6. C A . Brockley,•"Modern Development in Fr ic t ion ,and Wear Research", • NRC Fric t ion .and Wear- Conference, June 1962. 7. C A . Brockley,. Annual Report to DRB, October,.1962. 8. A.P. Green,^"Friction Between Unlubricated Metals - A'Theoretical Analysis of the Junction Model",- Proceedings of the' Royal Society (London), Series A, Vol:228, 1955, pp.191-20^ . 9- J .A . Greenwood-and D. Tabor, .-"Deformation Properties of Fr ic t ion Junctions", Proceedings of the Royal-Society (London), - Series B, - Part 9, Vol.69, Sept.•1955, pp.609-619. 10. J . A . Greenwood and D. Tabor, • "The 'Properties of Model: Fr ic t ion Junctions", Transactions of Conference -on Lubrication and Wear, 1957, PP.31^ -317. 11. E. Rabinowicz, "A Study, of the St ick-Sl ip Process", Fr ic t ion .and Wear, ; Elseview Publishing Company, Amsterdam,-1959* PP•1^9-l6l• 12. S N . H . Cook, ASME,paper 58-A-257-13. J . F . Archard,•Proceedings of the Royal Society (London), Scries A, -Vol . 2k3, 1951, pp.190-205. lh. J . F . Archard, :-"Single Contacts and Multiple Encounters", - Journal of Applied Physics, Vol . 32, Number 8, August I 9 6 I , pp. 11+20-1^25. 15. J . F . Archard and W.•Hirst , Proceedings of the Royal Society (London), Series A, Vol.236,-1956, pp-397-UlO. 16. J . T . Burwell.and C D . Strang, : "On the Empirical Law of Adhesive Wear", Journal of Applied Physics, Vol.23, Number 1, January. 1952, pp. 18-28. 63: 17- J . F . Archard, "Contact and Rubbing of Flat Surf aces", - Journal of Applied Physics, Vol . •2k, Number 8,.August .1953,.pp.981-988. 18. M. Kerridge, "Metal Transfer and. the Wear Process",-.Proceedings of the;:Phy'sics Society, Series B, Vol.68, '.1955, pp.^OO-UOft. • • 19. F . F . Ling,•"Welding Aspects of - Sl iding Fr ic t ion between Unlubricated Surfaces", Final Report t o ; A i r Research and Development Command, Washington, June i960. 20. J .M. ' Feng, .• "Metal Transfer and Wear", Journal of Applied Physics, Vol.23, 1952, pp.1011-1019. 21. B. Blok, "Fundamental Aspects of Boundary Lubrication", Journal of the Society of Automotive'Engineers, Vol . k6, 19^ 0, pp.5^ -68. 22. D.' S inc la ir , "Frict ional Vibrations", Journal of. Applied Mechanics, ; June 1955} PP• 207-21^ , ' 

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