FRICTION RND LUBRIC~llON IN MKHRNICRL D€SIGN MECHANICAL ENGINEERING A Series of Textbooks and Reference Books Editor L L Faulkner Columbus Division, Battelle Memorial Institute and Department of Mechanical Engineering The Ohio State University Colurnbus, Ohio 10 1 12 13 14 15 17 18 19 20 21 22 23 Spring Designer's Handbook, Harold Carlson Computer-Aided Graphics and Design, Daniel L Ryan lubrication Fundamentals, J George Wills Solar Engineering for Domestic Buildings, William A Himmelman Applied Engineering Mechanics: Statics and Dynamics, G Boothroyd and C Poli Centrifugal Pump Clinic, lgor J Karassik Computer-Aided Kinetics for Machine Design, Daniel L Ryan Plastics Products Design Handbook, Part A: Materials and Components; Part B: Processes and Design for Processes, edited by Edward Miller Turbomachinery: Basic Theory and Applications, Earl Logan, Jr Vibrations o f Shells and Plates, Werner Soedel Flat and Corrugated Diaphragm Design Handbook, Mario Di Giovanni Practical Stress Analysis in Enginee~ng Design, Alexander Blake An Introduction to the Design and Behavior of Bolted Joints, John H Bickford Optimal Engineeing Dmgn: pn'nc@lesand Applications, James N Siddall Spring Manufacturing Handbook, Harold Carlson Industrial Noise Control: Fundamentals and Applications, edited by Lewis H Bell Gears and Their Vibration: A Basic Approach to Understanding Gear Noise, J Derek Smith Chains for Power Transmission and Material Handling: Design and Applications Handbook, American Chain Association Corrosion and Corrosion Protection Handbook, edited by Philip A Schweitzer Gear Drive Systems: Design and Application, Peter Lynwander Controlhg In-Plant Airborne Contaminants: Systems Design and Calculations, John D Constance CAD/CAM Systems Planning and Implementation, Charles S Knox Probabilistic Engineering Design: Princbles and Applications, Jarnes N Siddall 24 Traction Drives: Selection and Application, Frederick W Heilich 111 and Eugene E Shube 25 Finite Element Methods: An Introduction, Ronald L Huston and Chris E Passerello 26 Mechanical Fastening of plastics: An Engineen'ng Handbook, Brayton Lincoln, Kenneth J Gomes, and James F Braden 27 Lubrication in Practice: Second Edition, edited by W S Robertson 28 Princ@lesof Automated Drafting, Daniel L Ryan 29 Practical Seal Design, edited by Leonard J Martini 30 Engineering Documentation for CAD/CAM Applications, Charles S Knox Design Dimensioning with Computer Graphics Applications, Jerome C Lange 32 Mechanism Analysis: Simplified Graphical and Analytical Techniques, Lyndon Barton 33 CAD/CAM Systems: Justification, Implementation, Productivity Measurement, Edward J Preston, George W Crawford, and Mark E Coticchia 34 Steam Plant Calculations Manual, V Ganapathy 35 Design Assurance for Engineers and Managers, John A Burgess 36 Heat Transfer Fluids and Systems for Process and Energy Applications, Jasbir Singh 37 Potential Flows: Computer Graphic Solutions, Robert H Kirchhoff 38 Computer-Aided Graphics and Design: Second Edition, Daniel L Ryan 39 Electronically Controlled Proportional Valves: Selection and Application, Michael J Tonyan, edited by Tobi Goldoftas 40 Pressure Gauge Handbook, AMETEK, U.S Gauge Division, edited by Philip W Harland 41 Fabric Filtration for Combustion Sources: Fundamentals and Basic Technology, R P Donovan 42 Design of Mechanical Joints, Alexander Blake 43 CAD/CAM Dictionary, Edward J Preston, George W Crawford, and Mark E Coticchia 44 Machinery Adhesives for Locking, Retaining, and Sealing, Girard S Haviland 45 Couplings and Joints: Design, Selection, and Application, Jon R Mancuso 46 Shaft Alignment Handbook, John Piotrowski 47 BASIC Programs for Steam Plant Engineers: Boilers, Combustion, Fluid Flow, and Heat Transfer, V Ganapathy 48 Solving Mechanical Design Problems with Computer Graphics, Jerome C Lange 49 Plastics Gearing: Selection and Application, Clifford E Adams 50 Clutches and Brakes: Design and Selection, William C Orthwein Transducers in Mechanical and Electronic Design, Harry L Trietley 52 Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, edited by Lawrence E Murr, Karl P Staudhammer, and Marc A Meyers 53 Magnesium Products Design, Robert S Busk 54 How to Integrate CAD/CAM Systems: Management and Technology, William D Engelke 55 Cam Design and Manufacture: Second Edition; with cam design software for the IBM PC and compatibles, disk included, Preben W Jensen 56 Solid-state A C Motor Controls: Selection and Application, Sylvester Campbell 57 Fundamentals of Robotics, David D Ardayfio 50 Belt Selection and Application for Engineers, edited by Wallace D Erickson 59 Developing Three-Dimensional CAD Software with the IBM PC, C Stan Wei 60 Organizing Data for CIM Applications, Charles S Knox, with contributions by Thomas C Boos, Ross S Culverhouse, and Paul F Muchnicki 61 Computer-Aided Simulation in Railway Dynamics, by Rao V Dukkipati and Joseph R Amyot 62 Fiber-Reinforced Composites: Materials, Manufacturing, and Design, P K Mallick 63 Photoelectric Sensors and Controls Selection and Application, Scott M Juds 64 Finite Element Analysis with Personal Computers, Edward R Champion, Jr., and J Michael Ensminger 65 Ultrasonics: Fundamentals, Technology, Applications: Second Edition, Revised and Expanded, Dale Ensminger 66 Applied Finite Element Modeling: Practical Problem Solving for Engineers, Jeffrey M Steele 67 Measurement and Instrumentation in Engineering: Princ@les and Basic Laboratory Experiments, Francis S Tse and lvan E Morse 60 Centrifugal Pump Clinic: Second Edition, Revised and Expanded, lgor J Karassik 69 Practical Stress Analysis in Engineering Design: Second Edition, Revised and Expanded, Alexander Blake 70 An Introduction to the Design and Behavior of Bolted Joints: Second Edition, Revised and Expanded, John H Bickford 71 High Vacuum Technology: A Practical Guide, Marsbed H Hablanian 72 Pressure Sensors: Selection and Application, Duane Tandeske 73 Zinc Handbook: Properties, Processing, and Use in Design, Frank Porter 74 Thermal Fatigue of Metals, Andrzej Weronski and Tadeusz Hejwowski 75 Classical and Modern Mechanisms for Engineers and Inventors, Preben W Jensen 76 Handbook o f Electronic Package Design, edited by Michael Pecht 77 Shock-Wave and High-Strain-Rate Phenomena in Materials, edited by Marc A Meyers, Lawrence E Murr, and Karl P Staudhammer 70 Industrial Refrigeration: Princ@les, Design and Applications, P C Koelet 79 Applied Combustion, Eugene L Keating 80 Engine Oils and Automotive Lubrication, edited by Wilfried J Bartz Mechanism Analysis: Simplified and Graphical Techniques, Second Edition, Revised and Expanded, Lyndon Barton 02 Fundamental Fluid Mechanics for the Practicing Engineer, James W Murdock 03 fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition, Revised and Expanded, P K Mallick 84 NumericalMethods for Engineen'ng Applications, Edward R Champion, Jr 85 Turbomachinery: Basic Theory and Applications, Second Edition, Revised and Expanded, Earl Logan, Jr 86 Vibrations of Shells and Plates: Second Edition, Revised and Expanded, Werner Soedel 87 Steam Plant Calculations Manual: Second Edition, Revised and Ex panded, V Ganapathy 88 Industrial Noise Control: Fundamentals and Applications, Second Edition, Revised and Expanded, Lewis H Bell and Douglas H Bell 89 finite Elements: Their Design and Performance, Richard H MacNeal 90 Mechanical Properties of Polymers and Composites: Second Edition, Revised and Expanded, Lawrence E Nielsen and Robert F Landel 91 Mechanical Wear Prediction and Prevention, Raymond G Bayer 92 Mechanical Po wer Transmission Components, edited by David W South and Jon R Mancuso 93 Handbook of Turbomachinery, edited by Earl Logan, Jr 94 Engineering Documentation Control Practices and Procedures, Ray E Monahan 95 Refractory Linings Thermomechanical Design and Applications, Charles A Schacht 96 Geometric Dimensioning and Tolerancing: Applications and Techniques for Use in Design, Manufactun'ng, and Inspection, James D Meadows 97 An Introduction to the Design and Behavior of Bolted Joints: Third Edition, Revised and Expanded, John H Bickford 98 Shaft Alignment Handbook: Second Edition, Revised and Expanded, John Piotrowski 99 Computer-Aided Design o f Polymer-Matrix Composite Structures, edited by Suong Van Hoa 100 Friction Science and Technology, Peter J Blau 101 Introduction to Plastics and Composites: Mechanical Properties and Engineering Applications, Edward Miller 102 Practical Fracture Mechanics in Design, Alexander Blake 103 Pump Characteristics and Applications, Michael W Volk 104 Optical Princr;Oles and Technology for Engineers, James E Stewart 105 Optimizing the Shape of Mechanical Elements and Structures, A A Seireg and Jorge Rodriguez 106 Kinematics and Dynamics of Machinery, Vladimlr Stejskal and Michael Val4Sek 107 Shaft Seals for Dynamic Applications, Les Horve 108 Reliability-BasedMechanical Design, edited by Thomas A Cruse 109 Mechanical Fastening, Joining, and Assembly, James A Speck 110 Turbomachinery Fluid Dynamics and Heat Transfer, edited by Chunill Hah 111 High- Vacuum Technology: A Practical Guide, Second Edition, Revised and Expanded, Marsbed H Hablanian 112 Geometric Dimensioning and Tolerancing: Workbook and Ans werbook, Jarnes D Meadows 113 Handbook of Materials Selection for Engineering Applications, edited by G T Murray 14 Handbook of Thermoplastic Ptping System Design, Thomas Sixsmith and Reinhard Hanselka 15 Practical Guide to Finite Elements: A Solid Mechanics Approach, Steven M Lepi 16 Applied ComputationalFluid Dynamics, edited by Vijay K Garg 1 Fluid Sealing Technology, Heinz K Muller and Bernard S Nau 18 Friction and Lubrication in Mechanical Design, A A Seireg Additional Volumes in Preparation Machining of Ceramics and Composites, edited by Said Jahanmir, M Ramulu, and Philip Koshy Heat Exchange Design Handbook, T Kuppan Couplings and Joints: Second Edition, Revised and Expanded, Jon R Mancuso Mechanical EngineeringSoftware Spring Design with an IBM PC, AI Dietrich Mechanical Design Failure Analysis: With Failure Analysis System Software for the IBM PC, David G Ullman Influence Functions and Matrices, Yuri A Melnikov FRICT'IONR" LUBRIC~ION IN M€CHANI(RL D€SIGN University of Wisconsin-Madison Madison, Wisconsin and University of Florida Gainesviiie, Florida a% MARCEL DEKKER MARCEL DEKKER, INC NEW YORK BASEL HONG KONG ISBN: 0-8247-9974-7 This book is printed on acid-free paper Headquarters Marcel Dekker, Inc 270 Madison Avenue, New York, NY 10016 tel: 12-696-9000; f a : 12-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 44-6 1-26 1-8482; f a : 44-6 1-26 1-8896 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities For more information, write to Special Saleflrofessional Marketing at the headquarters address above Copyright 1998 by Marcel Dekker, Inc All Rights Reserved Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher Current printing (last digit): PRINTED IN THE UNITED STATES OF AMERICA Preface The awareness of friction and attempts to reduce or use it are as old as human history Scientific study of the friction phenomenon dates back to the eighteenth century and has received special attention in modern times since it is one of the most critical factors in all machinery The increasing emphasis on material and energy conservation in recent years has added new urgency to the development of practical predictive techniques and information that can be used, in the design stage, for controlling friction and wear Advances in this field continue to contribute to improved energy efficiency, increased useful life of machines, and reduced maintenance costs This book treats friction, lubrication, and wear as empirical phenomena and relies heavily on the experimental studies by the author and his coworkers to develop practical tools for design Empirical dimensionless relationships are presented, whenever possible, that can be readily applied to a variety of situations confronting the design engineer without the need for extensive theoretical analysis or computation The material in the book has been used for many years in an interdisciplinary course on this subject taught at the University of WisconsinMadison, and can be used as a text for senior, graduate, or professional development courses It can also be used as a reference book for practical design engineers because the many empirical equations and design graphs can provide a fundamental parametric understanding to guide their design decisions Chapter gives a brief review of the history of this subject and sets the stage for the topics presented in the book Chapters 2, 3, and summarize 111 Introduction In any situation where the resultant of tangential forces is smaller than some force parameter specific to that particular situation, the friction force will be equal and opposite to the resultant of the applied forces and no tangential motion will occur When tangential motion occurs, the friction force always acts in a direction opposite to that of the relative velocity of the surfaces The friction force is proportional to the normal load The coefficient of friction is independent of the apparent contact area The static coefficient is greater than the kinetic coefficient The coefficient of friction is independent of sliding speed Strictly speaking, none of these laws is entirely accurate Moore indicated and (6) are reasonably valid for dry friction under the that laws (3), (4), (9, following conditions: For law (3), the normal load is assumed to be low compared to that causing the real area of contact to approach the apparent area For law (4), the materials in contact are assumed to have a definite yield point (such as metals) It does not apply to elastic and viscoelastic materials Law ( ) does not apply for materials with appreciable viscoelastic properties Law (6) is not valid for most materials, especially for elastomers where the viscoelastic behavior is very significant A number of workers also found some exceptions to the first friction law Rabinowicz [ 181 reported that Stevens [ 191, Rankin [20], and Courtney-Pratt and Eisner [21] had shown that when the tangential force F i s first applied, a very small displacement occurs almost instantaneously in the direction of F with a magnitude in the order of 10-5 or 10-6 cm Seireg and Weiter [22] conducted experiments to investigate the loaddisplacement and displacement-time characteristics of friction contacts of a ball between two parallel flats under low rates of tangential load application The tests showed that the frictional joint exhibited “creep” behavior at room temperatures under loads below the gross slip values which could be described by a Boltzmann model of viscoelasticity They also investigated the frictional behaviors under dynamic excitation [23, 241 They found that under sinusoidal tangential forces the “breakaway” coefficient of friction was the same as that determined under static conditions They also found that the static coefficient of friction in Hertzian contacts was independent of the area of contact, the magnitude of the normal force, the frequency of the oscillatory tangential load, or the ratio Chapter I of the static and oscillatory components of the tangential force However, the coefficient of gross slip under impulsive loading was found to be approximately three times higher than that obtained under static or a vibratory load at a frequency of l00Hz using the same test fixture Rabinowicz [25] developed a chart based on a compatibility theory which states that if two metals form miscible liquids and, after solidification, form solid solutions or intermetallic components, the metals are said to be compatible and the friction and wear between them will be high If, however, they are insoluble in each other, the friction and wear will be low Accordingly two materials with low compatibility can be selected from the chart to produce low friction and wear In the case of lubricated surfaces, Rabinowicz [26] found that the second law of friction was not obeyed It was found that the direction of the instantaneous frictional force might fluctuate by one to three degrees from the expected direction, changing direction continuously and in a random fashion as sliding proceeded The general mechanisms which have been proposed to explain the nature of dry friction are reviewed in numerous publications (e.g., Moore [17]) The following is a summary of the concepts on which dry friction theories are based: Mechanical interlocking This was proposed by Amontons and de la Hire in 1699 and states that metallic friction can be attributed to the mechanical interlocking of surface roughness elements This theory gives an explanation for the existence of a static coefficient of friction, and explains dynamic friction as the force required to lift the asperities of the upper surface over those of the lower surface Molecular attraction This was proposed by Tomlinson in 1929 and Hardy in 1936 and attributes frictional forces to energy dissipation when the atoms of one material are “plucked” out of the attraction range of their counterparts on the mating surface Later work attributed adhesional friction to a molecular-kinetic bond rupture process in which energy is dissipated by the stretch, break, and relaxation cycle of surface and subsurface molecules Efectrostaticforces This mechanism was presented in 1961 and explains the stick-slip phenomena between rubbing metal surfaces by the initiation of a net flow of electrons Welding, shearing and ploughing This mechanism was proposed by Bowden in 1950 It suggests that the pressure developed at the discrete contact spots causes local welding The functions thus formed are subsequently sheared by relative sliding of the surfaces Ploughing by the asperities of the harder surface through the matrix Introduction of the softer material contributes the deformation component of friction Dry rolling friction was first studied by Reynolds [27] in 1875 He found that when a metal cylinder rolled over a rubber surface, it moved forward a distance less than its circumference in each revolution of the cylinder He assumed that a certain amount of slip occurred between the roller and the rubber and concluded that the occurrence of this slip was responsible for the rolling resistance Palmgren [28] and Tabor [29] later repeated Reynolds’ experiment in more detail and found that the physical mechanism responsible for rolling friction was very different in nature than that suggested by Reynolds Tabor’s experiments showed that interfacial slip between a rolling element and an elastic surface was in reality almost negligible and in any case quite inadequate to account for the observed friction losses Thus he concluded that rolling resistance arose primarily from elastic-hysteresis losses in the material of the rolling element and the surface 1.3 BOUNDARY LUBRICATION FRICTION Hardy [30] first used the term “boundary lubrication” to describe the surface frictional behavior of certain organic compounds derived from petroleum products of natural origin such as paraffins, alcohols and fatty acids Since then, boundary lubrication has been extended to cover other types of lubricants, e.g., surface films and solid mineral lubricants, which not function hydrodynamically and are extensively used in lubrication In the analysis of scoring of gear tooth surfaces, it has been fairly well established that welding occurs at a critical temperature which is reached by frictional heating of the surfaces The method of calculating such a temperature was published by Blok [31], and his results were adapted to gears in 1952 [32] Since then, some emphasis has been focused on boundary lubrication Several studies are available in the literature which deal with the boundary lubrication condition; some of them are briefly reviewed in the following Sharma [33] used the Bowden-Leben apparatus to investigate the effects of load and surface roughness on the frictional behavior of various steels over a range of temperature and of additive concentration The following observations are reported: Sharp rise in friction can occur but is not necessarily followed by scuffing and surface damage Load affects the critical temperature quite strongly Chapter I Neither the smoother surface nor the rougher surface gives the maximum absorption of heat, but there exists an optimum surface roughness Nemlekar and Cheng [34] investigated the traction in rough contacts by solving the partial elastohydrodynamic lubrication (EHL) equations It was found that traction approached dry friction as the ratio of lubricant film thickness to surface roughness approached zero, load had a great influence on friction, and the roller radius had little influence on friction Hirst and Stafford [35] examined the factors which influence the failure of the lubricant film in boundary lubrication It is shown that substantial damage only occurs when a large fraction of the load becomes unsupported by hydrodynamic action It is also shown that the magnitude of the surface deformation under the applied load is a major factor in breakdown When the deformation is elastic, the solid surface film (e.g., oxide) remains intact and even a poor liquid lubricant provides sufficient protection against the buildup of the damage The transition temperature is also much lower They also discussed the effect of load and surface finish on the transition temperature Furey and Appeldoorn [36] conducted an experiment to study the effect of lubricant viscosity on metallic contact and friction in the transition zone between hydrodynamic and boundary lubrication The system used was one of pure sliding and relatively high contact stress, namely, a fixed steel ball on a rotating steel cylinder It was found that increasing the viscosity of Newtonian fluids (mineral oils) over the range 2-1 100 centipoises caused a decrease in metallic contact The effect became progressively more pronounced at higher viscosities The viscosity here was the viscosity at atmospheric pressure and at the test temperature; neither pressure-viscosity nor temperature-viscosity properties appeared to be important factors On the other hand, non-Newtonian fluids (polymer-thickened oils) gave more contact than their mineral oil counterparts This suggested that shear-viscosity was important However, no beneficial effects of viscoelastic properties were observed with these oils Friction generally decreased with increasing viscosity because the more viscous oils gave less metal-to-metal contact The coefficient of friction was rather high: 0.13 at low viscosity, dropping to 0.08 at high viscosity The oils having higher PVIs (pressure-viscosity index a) gave somewhat more friction which cannot be solely attributed to differences in metallic contact Furey [37] also investigated the surface roughness effects on metallic contact and friction in the transition zone between the hydrodynamic and boundary lubrications He found that very smooth and very rough surfaces gave less metallic contact than surfaces with intermediate roughness Friction was low for the highly polished surfaces and rose with increasing Introduction surface roughness The rise in friction continued up to a roughness of about 10 pin, the same general level at which metallic contact stopped increasing However, whereas further increases in surface roughness caused a reduction in metallic contact, there was no significant effect on friction Friction was found to be independent of roughness in the range of lopin center line average (CLA) He also used four different types of antiwearlantifriction additives (including tricresyl phosphate) and found that they reduced metallic contact and friction but had little effect on reducing surface roughness The additives merely slowed down the wear-in process of the base oil Thus he concluded that the “chemical polishing” mechanism proposed for explaining the antiwear behavior of tricresyl phosphate appeared to be incorrect Freeman [38] studied several experimental results and summarized them as follows: An unnecessarily thick layer of boundary lubricant may give rise to excessive frictional resistance because shearing and ploughing of the lubricant film may become factors of importance The bulk viscosity of a fluid lubricant appears to have no significance in its boundary frictional behavior Coefficients of friction for effective boundary lubricants lie roughly in the range 0.02 to 0.1 The friction force is almost independent of the sliding velocity, provided the motion is insufficient to cause a rise in bulk temperature If the motion is intermittent or stick-slip, the frictional behavior may be of a different and unpredictable nature In general the variables that influence dry friction also influence boundary friction Friction and surface damage depends on the chemical composition of the lubricant and/or the products of reaction between the lubricant and the solid surface Lubricant layers only a few molecules thick can provide effective boundary lubrication The frictional behavior may be influenced by surface roughness, temperature, presence of moisture, oxygen or other surface contaminants In general, the coefficient of friction tends to increase with surface roughness 1.4 FRICTION IN FLUID FILM LUBRICATION Among the early investigations in fluid film lubrication, Tower’s experiments in 1883-1884 were a breakthrough which led to the development of 10 Chapter I lubrication theory [6, 71 Tower reported the results of a series of experiments intended to determine the best methods to lubricate a railroad journal bearing Working with a partial journal bearing in an oil bath, he noticed and later measured the pressure generated in the oil film Tower pointed out that without sufficient lubrication, the bearing operates in the boundary lubrication regime, whereas with adequate lubrication the two surfaces are completely separated by an oil film Petrov [5] also conducted experiments to measure the frictional losses in bearings He concluded that friction in adequately lubricated bearings is due to the viscous shearing of the fluid between the two surfaces and that viscosity is the most important property of the fluid, and not density as previously assumed He also formulated the relationship for calculating the frictional resistance in the fluid film as the product of viscosity, speed, and area, divided by the thickness of the film The observations of Tower and Petrov proved to be the turning point in the history of lubrication Prior to their work, researchers had concentrated their efforts on conducting friction drag tests on bearings From Tower’s experiments, it was realized that an understanding of the pressure generated during the bearing operation is the key to perceive the mechanism of lubrication The analysis of his work carried out by Stokes and Reynolds led to a theoretical explanation of Tower’s experimental results and to the theory of hydrodynamic lubrication In 1886, Osborne Reynolds published a paper on lubrication theory [4] which is derived from the equations of motion, continuity equation, and Newton’s shear stress-velocity gradient relation Realizing that the ratio of the film thickness to the bearing geometry is in the order of 10-3, Reynolds established the well-known theory using an order-of-magnitude analysis The assumptions on which the theory is based can be listed as follows The pressure is constant across the thickness of the film The radius of curvature of bearing surface is large compared with film thickness The lubricant behaves as a Newtonian fluid Inertia and body forces are small compared with viscous and pressure terms in the equations of motion There is no slip at the boundaries Both bearing surfaces are rigid and elastic deformations are neglected Since then the hydrodynamic theory based on Reynolds’ work has attracted considerable attention because of its practical importance Most initial investigations assumed isoviscous conditions in the film to simplify the analysis This assumption provided good correlation with pressure distribution Introduction I1 under a given load but generally failed to predict the stiffness and damping behavior of the bearing A model which predicts bearing performance based on appropriate thermal boundaries on the stationary and moving surfaces and includes a pointwise variation of the film viscosity with temperature is generally referred to as the thermohydrodynamic (THD) model The THD analyses in the past three decades have drawn considerable attention to the thermal aspects of lubrication Many experimental and theoretical studies have been undertaken to shed some light on the influence of the energy generated in the film, and the heat transfer within the film and to the surroundings, on the generated pressure In 1929, McKee and McKee [39] performed a series of experiments on a journal bearing They observed that under conditions of high speed, the viscosity diminished to a point where the product of viscosity and rotating speed is a constant Barber and Davenport [40] investigated friction in several journal bearings The journal center position with respect to the bearing center was determined by a set of dial indicators Information on the load-carrying capacity and film pressure was presented In 1946, Fogg [41] found that parallel surface thrust bearings, contrary to predictions by hydrodynamic theory, are capable of carrying a load His experiments demonstrated the ability of thrust bearings with parallel surfaces to carry loads of almost the same order of magnitude as can be sustained by tilting pad thrust bearings with the same bearing area This observation, known as the Fogg effect, is explained by the concept of the “thermal wedge,” where the expansion of the fluid as it heats up produces a distortion of the velocity distribution curves similar to that produced by a converging surface, developing a load-carrying capacity Fogg also indicated that this load-carrying ability does not depend on a round inlet edge nor the thermal distortion of the bearing pad Cameron [42], in his experiments with rotating disks, suggested that a hydrodynamic pressure is created in the film between the disks due to the variation of viscosity across the thickness of the film Viscoelastic lubricants in journal bearing applications were studied by Tao and Phillipoff [43] The non-Newtonian behavior of viscoelastic liquids causes a flattening in the pressure profile and a shift of the peak film pressure due to the presence of normal stresses in the lubricant Dubois et al [44] performed an experimental study of friction and eccentricity ratios in a journal bearing lubricated with a non-Newtonian oil They found that a non-Newtonian oil shows a lower friction than a corresponding Newtonian fluid under the same operating conditions However, this phenomenon did not agree with their analytical work and could not be explained 12 Chapter I Maximum bearing temperature is an important parameter which, together with the minimum film thickness, constitutes a failure mechanism in fluid film bearings Brown and Newman [45] reported that for lightly loaded bearings of diameter 60 in operating under 6000 rpm, failure due to overheating of the bearing material (babbitt) occurred at about 340°F Booser et al [46] observed a babbitt-limiting maximum temperature in the range of 266 to 392°F for large steam turbine journal bearings They also formulated a one-dimensional analysis for estimating the maximum temperature under both laminar and turbulent conditions In a study of heat effects in journal bearings, Dowson et al [47] in 1966 conducted a major experimental investigation of temperature patterns and heat balance of steadily loaded journal bearings Their test apparatus was capable of measuring the pressure distribution, load, speed, lubricant flow rate, lubricant inlet and outlet temperatures, and temperature distribution within the stationary bushing and rotating shaft They found that the heat flow patterns in the bushing are a combination of both radial flows and a significant amount of circumferential flow traveling from the hot region in the vicinity of the minimum film thickness to the cooler region near the oil inlet The test results showed that the cyclic variation in shaft surface temperature is small and the shaft can be treated as an isothermal component The experiments also indicated that the axial temperature gradients within the bushing are negligible Viscosity is generally considered to be the single most important property of lubricants, therefore, it represents the central parameter in recent lubricant analyses By far the easiest approach to the question of viscosity variation within a fluid film bearing is to adopt a representative or mean value viscosity Studies have provided many suggestions for calculations of the effective viscosity in a bearing analysis [48] When the temperature rise of the lubricant across the bearing is small, bearing performance calculations are customarily based on the classical, isoviscous theory In other cases, where the temperature rise across the bearing is significant, the classical theory loses its usefulness for performance prediction One of the early applications of the energy equation to hydrodynamic lubrication was made by Cope [49] in 1948 His model was based on the assumptions of negligible temperature variation across the film and negligible heat conduction within the lubrication film as well as into the neighboring solids The consequence of the second assumption is that both the bearing and the shaft are isothermal components, and thus all the generated heat is carried out by the lubricant As indicated in a review paper by Szeri [50], the belief, that the classical theory on one hand and Cope’s adiabatic model on the other, bracket bearing performance in lubrication analysis, was widely accepted for a while A thermohydrodynamic hypothesis was Introduction 13 later introduced by Seireg and Ezzat [51] to rationalize their experimental findings An empirical procedure for prediction of the thermohydrodynamic behavior of the fluid film was proposed in 1973 by Seireg and Ezzat This report presented results on the load-carrying capacity of the film from extensive tests These tests covered eccentricity ratios ranging from 0.6 to 0.90, pressures of up to 750 psi and speeds of up to 1650 ftlmin The empirical procedure applied to bearings submerged in an oil bath as well as to pump-fed bearings where the outer shell is exposed to the atmosphere No significant difference in the speed-pressure characteristics for these two conditions was observed when the inlet temperature was the same They showed that the magnitudes of the load-carrying capacity obtained experimentally may differ considerably from those predicted by the insoviscous hydrodynamic theory The isoviscous theory can either underestimate or overestimate the results depending on the operating conditions It was observed, however, that the normalized pressure distribution in both the circumferential and axial directions of the journal bearing are almost identical to those predicted by the isoviscous hydrodynamic theory Under all conditions tested, the magnitude of the peak pressure (or the average pressure) in the film is approximately proportional to the square root of the rotational speed of the journal The same relationship between the peak pressure and speed was observed by Wang and Seireg [52] in a series of tests on a reciprocating slider bearing with fixed film geometry A comprehensive review of thermal effects in hydrodynamic bearings is given by Khonsari [53] and deals with both journal and slider bearings In 1975, Seireg and Doshi [54] studied nonsteady state behavior of the journal bearing performance The transient bushing temperature distribution in journal bearing appears to be similar to the steady-state temperature distribution It was also found that the maximum bushing surface temperature occurs in the vicinity of minimum film thickness The temperature level as well as the circumferential temperature variation were found to rise with an increase of eccentricity ratio and bearing speed Later, Seireg and Dandage [55] proposed an empirical thermohydrodynamic procedure to calculate a modified Sommerfeld number which can be utilized in the standard formula (based on the isoviscous theory) to calculate eccentricity ratio, oil flow, frictional loss, and temperature rise, as well as stiffness and damping coefficients for full journal bearings In 1980, Barwell and Lingard [56] measured the temperature distribution of plain journal bearings, and found that the maximum bearing temperature, which is encountered at the point of minimum film thickness, is the appropriate value for an estimate of effective viscosity to be used in load capacity calculation Tonnesen and Hansen [57] performed an experiment 14 Chapter on a cylindrical fluid film bearing to study the thermal effects on the bearing performance Their test bearings were cylindrical and oil was supplied through either one or two holes or through two-axial grooves, 180" apart Experiments were conducted with three types of turbine oils Both viscosity and oil inlet geometry were found to have a significant effect on the operating temperatures The shaft temperature was found to increase with increasing loads when a high-viscosity lubricant was used At the end of the paper, they concluded that even a simple geometry bearing exhibits over a broad range small but consistent discrepancies when correlated with existing theory In 1983, Ferron et al [58] conducted an experiment on a finite-length journal bearing to study the performance of a plain bearing The pressure and the temperature distributions on the bearing wall were measured, along with the eccentricity ratio and the flow rate, for different speeds and loads All measurements were performed under steady-state conditions when thermal equilibrium was reached Good agreement was found with measurements reported for pressure and temperature, but a large discrepancy was noted between the predicted and measured values of eccentricity ratios In 1986, Boncompain et al [59] showed good agreement between their theoretical and experimental work on a journal bearing analysis However, the measured journal locus and calculated values differ They concluded that the temperature gradient across and along the fluid film is the most important parameter when evaluating the bearing performance 1.5 FRICTIONAL RESISTANCE IN ELASTOHYDRODYNAMIC CONTACTS In many mechanical systems, load is transmitted through lubricated concentrated contacts where rolling and sliding can occur For such conditions the pressure is expected to be sufficiently high to cause appreciable deformation of the contacting bodies and consequently the surface geometry in the loaded area is a function of the generated pressure The study of the behavior of the lubricant film with consideration of the change of film geometry due to the elasticity of the contacting bodies has attracted considerable attention from tribologists over the last half century Some of the studies related to frictional resistance in this elastohydrodynamic (EHD) regime are briefly reviewed in the following with emphasis on effect of viscosity and temperature in the film Dyson [60] interpreted some of the friction results in terms of a model of viscoelastic liquid He divided the experimental curves of frictional traction versus sliding speed into three regions: the linear region, the nonlinear Introduction 15 (ascending) region, and the thermal (descending) region At low sliding speeds a linear relation exists, the slope of which defines a quasiNewtonian viscosity, and the behavior is isothermal At high sliding speeds the frictional force decreases as sliding speed increases, and this can be attributed to some extent to the influence of temperature on viscosity In the transition region, thermal effects provide a totally inadequate explanation because the observed frictional traction may be several orders of magnitude lower than the calculated values even when temperature effects are considered Because of the high variation of pressure and temperature, many parameters such as temperature, load, sliding speed, the ratio of sliding speed to rolling speed, viscosity, and surface roughness have great effects on frictional traction Thermal analysis in concentrated contacts by Crook [61, 621, Cheng [63], and Dyson [60] have shown a strong mutual dependence between temperature and friction in EHD contacts Frictional traction is directly governed by the characteristics of the lubricant film, which, in the case of a sliding contact, depends strongly on the temperature in the contact The temperature field is in turn governed directly by the heating function Crook [61] studied the friction and the temperature in oil films theoretically He used a Newtonian liquid (shear stress proportional to the velocity gradient in the film) and an exponential relation between viscosity and temperature and pressure In pure rolling of two disks it has been found that there is no temperature rise within the pressure zone; the temperature rise occurs on the entry side ahead of that zone When sliding is introduced, it has been found that the temperature on the entry side remains small, but it does have a very marked influence upon the temperatures within the pressure zone, for instance, the introduction of 400 cm/sec sliding causes the effective viscosity to fall in relation to its value in pure rolling by a factor of 50 It has also been shown that at high sliding speeds the effective viscosity is largely independent of the viscosity of oil at entry conditions This fact carries the important implication that if an oil of higher viscosity is used to give the surfaces greater protection by virtue of a thicker oil film, then there is little penalty to be paid by way of greater frictional heating, and in fact at high sliding speeds the frictional traction may be lower with the thicker film It has also been found that frictional tractions pass through a maximum as the sliding is increased This implies that if the disks were used as a friction drive and the slip was allowed to exceed that at which the maximum traction occurs, then a demand for a greater output torque, which would lead to even greater sliding, would reduce the torque the drive can deliver Crook [62] conducted an experiment to prove his theory, and found that the effective viscosity of the oil at the rolling point showed that the variation 16 Chapter I of viscosity, both for changes in pressure and in temperature, decreased as the rolling speed was increased Cheng [63] studied the thermal EHD of rolling and sliding cylinders with a more rigorous analysis of temperature by using a two-dimensional numerical method The effect of the local pressure-temperature-dependent viscosity, the compressibility of the lubricant, and the heat from compression of the lubricant were considered in the analysis A Newtonian liquid was used He found that the temperature had major influence on friction force A slight change in temperature-viscosity exponent could cause great changes in friction data He also compared his theoretical results with Crook’s [62] experimental results and found a high theoretical value at low sliding speed Thus he concluded that the assumption of a Newtonian fluid in the vicinity of the pressure peak might cease to be valid One of the most important experimental studies in EHD was carried out by Johnson and Cameron [64] In their experiments they found that at high sliding speeds the friction coefficient approached a common ceiling, which was largely independent of contact pressure, rolling speed and disk temperature At high loads and sliding speeds variations in rolling speed, disk temperature and contact pressure did not appear to affect the friction coefficient Below the ceiling the friction coefficient increased with pressure and decreased with increasing rolling speed and temperature Dowson and Whitaker [65] developed a numerical procedure to solve the EHD problem of rolling and sliding contacts lubricated by a Newtonian fluid It was found that sliding caused an increase in the film temperatures within the zone, and the temperature rise was roughly proportional to the square of the sliding velocity Thermal effects restrained the coefficient of friction from reaching the high values which would occur in sliding contacts under isothermal conditions Plint [66] proposed a formula for spherical contacts which relates the coefficient of friction with the temperature on the central plane of the contact zone and the radius of the contact zone There are other parameters which were investigated for their influence on the frictional resistance in the EHD regime by many tribologists [67-851 Such parameters include load, rolling speed, shear rate, surface roughness, etc The results of some of these investigations are utilized in Chapter for developing generalized emperical relationships for predicting the coefficient of friction in this regime of lubrication Introduction I7 REFERENCES 10 11 12 13 14 15 16 17 18 19 20 21 MacCurdy, E., Leonardo da Vinci Notebooks, Jonathan Cape, London, England, 1938 Amontons, G., Histoire de 1’AcadCmie Royale des Sciences avec Les Memoires de Mathematique et de Physique, Paris, 1699 Coulomb, C A., 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