Rothbart_CH07.qxd 2/24/06 10:37 AM Page 7.1 Source: MECHANICAL DESIGN HANDBOOK CHAPTER 7 FRICTION, LUBRICATION, AND WEAR David Tabor, Sc.D. Professor Emeritus Laboratory for the Physics and Chemistry of Solids Department of Physics Cambridge University Cambridge, England 7.1 INTRODUCTION 7.1 7.4.8 Shear Properties of Thin Polymer 7.2 DEFINITIONS AND LAWS OF FRICTION 7.2 Films 7.13 7.2.1 Definition 7.2 7.4.9 Kinetic Friction 7.14 7.2.2 Static and Kinetic Friction 7.2 7.4.10 New Tribological Materials: 7.2.3 Basic Laws of Friction 7.2 Composites, Ceramics 7.15 7.3 SURFACE TOPOGRAPHY AND AREA OF 7.5 LUBRICATION 7.16 REAL CONTACT 7.2 7.5.1 Hydrodynamic or Fluid Lubrication 7.3.1 Profilometry and Asperity Slopes 7.2 7.16 7.3.2 Elastic and Plastic Deformation of 7.5.2 Elastohydrodynamic Lubrication Conical Indenters 7.3 7.18 7.3.3 Elastic and Plastic Deformation of Real 7.5.3 Boundary Lubrication 7.18 Surfaces 7.4 7.6 WEAR 7.21 7.4 FRICTION OF CLEAN METALS 7.7 7.6.1 Laws of Wear 7.21 7.4.1 Theory of Metallic Friction 7.7 7.6.2 Mild and Severe Wear 7.21 7.4.2 Microdisplacements before Sliding 7.6.3 Effect of Environment 7.22 7.9 7.6.4 Effect of Speed 7.22 7.4.3 Breakdown of Oxide Films 7.10 7.6.5 Wear by Abrasives 7.23 7.4.4 Friction of Metals after Repeated 7.6.6 Wear Behavior of Specific Materials Sliding 7.11 7.23 7.4.5 Friction of Hard Solids 7.11 7.6.7 Identification of Wear Mechanisms 7.4.6 Friction of Thin Metallic Films 7.11 7.23 7.4.7 Friction of Polymers 7.12 7.1 INTRODUCTION Sliding friction is primarily a surface phenomenon. Consequently it depends very markedly on surface conditions, such as roughness, degree of work hardening, type of oxide film, and surface cleanliness.4,6,11 In general, in unlubricated sliding the rough- ness has only a secondary effect, but surface contamination can have a profound influ- ence on friction (and wear), particularly with surfaces that are nominally clean. Because of this the account given here concentrates mainly on the mechanisms involved in friction.4,11,20a In this way the reader may be better able to assess the main factors involved in any particular situation. Tables of friction values are given, but they must be used with caution. Very wide differences in friction may be obtained under apparently similar conditions, especially with unlubricated surfaces. 7.1 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Rothbart_CH07.qxd 2/24/06 10:37 AM Page 7.2 FRICTION, LUBRICATION, AND WEAR 7.2 MECHANICAL DESIGN FUNDAMENTALS 7.2 DEFINITIONS AND LAWS OF FRICTION 7.2.1 Definition The friction between two bodies is generally defined as the force at their surface of contact which resists their sliding on one another. The friction force F is the force required to initiate or maintain motion. If W is the normal reaction of one body on the other, the coefficient of friction ␮ϭF/W (7.1) 7.2.2 Static and Kinetic Friction If the force to initiate motion of one of the bodies is F and the force to maintain its s ␮ motion at a given speed is Fk, there is a corresponding coefficient of static friction s ϭ F /W and a coefficient of kinetic friction ␮ ϭ F /W. In some cases, these coeffi- s ␮k ␮ k cients are approximately equal; in most cases s > k. 7.2.3 Basic Laws of Friction The two basic laws of friction, which are valid over a wide range of experimental con- ditions, state that:4 1. The frictional force F between solid bodies is proportional to the normal force between the surfaces, i.e., ␮ is independent of W. 2. The frictional force F is independent of the apparent area of contact. These two laws of friction are reasonably well obeyed for sliding metals whether clean or lubricated. With polymeric solids (plastics) the laws are not so well obeyed: in particular, the coefficient of friction usually decreases with increasing load as a result of the detailed way in which polymers deform. 7.3 SURFACE TOPOGRAPHY AND AREA OF REAL CONTACT 7.3.1 Profilometry and Asperity Slopes When metal surfaces are placed in contact they do not usually touch over the whole of their apparent area of contact.4,11 In general, they are supported by the surface irregulari- ties which are present even on the most carefully prepared surfaces. Such roughnesses are usually characterized by means of a profilometer in which a fine stylus runs over the surface and moves up and down with the surface contour. The movement is measured electrically and may be recorded digitally for future detailed analysis by appropriate interfaced display units.28 These units can provide information (see below) concerning the mean asperity heights, the distribution of peaks, valleys, slopes, asperity-tip curva- tures, correlation lengths, and other features. Some commercial units display not only the essential parameters but also some which are redundant or even pointless. For visual- ization of the surface topography it is convenient to display the stylus movements on a chart. Since changes in height are generally very small compared with the horizontal Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Rothbart_CH07.qxd 2/24/06 10:37 AM Page 7.3 FRICTION, LUBRICATION, AND WEAR FRICTION, LUBRICATION, AND WEAR 7.3 distance traveled by the stylus, it is usual to compress the horizontal movement on the chart by a factor of 100 or more. As a result the chart record appears to suggest that the surface is covered with sharp jagged peaks.30 In fact, when allowance is made for the dif- ference in vertical and horizontal scales, the average slopes are rarely more than a few degrees (see Fig. 7.1).30 FIG. 7.1 Profilometry traces of surfaces16 showing the average surface slopes of the fine-scale asperities and of the coarser topography. Surface treatments are (a) ground; (b) shot peened; (c) turned; (d) diamond turned. 7.3.2 Elastic and Plastic Deformation of Conical Indenters The characterization of surface topographies and the detailed way in which the asperi- ties deform under contact have become the subject of a number of specialized studies of varying degrees of sophistication.28,30 We consider here the simplest case, in which the individual asperity is represented by a right circular cone of a slope ␪ (semiapical angle 90° Ϫ␪). If the cone is pressed against a smooth, flat, nondeformable surface Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Rothbart_CH07.qxd 2/24/06 10:37 AM Page 7.4 FRICTION, LUBRICATION, AND WEAR 7.4 MECHANICAL DESIGN FUNDAMENTALS and if it deforms elastically, the mean contact pressure p is independent of the load and is given by p ϭ (E tan ␪)/2(1 Ϫ v2) (7.2) where E is Young’s modulus and v is Poisson’s ratio of the cone material.29 Ignoring the problem of infinite stresses at the cone tip we may postulate that plastic deforma- tion of the cone will occur when p equals the indentation hardness H of the cone,* that is, when (E tan ␪)/H ϭ 2(1 Ϫ v2) ≈ 2 (7.3) Thus the factors favoring elastic deformation are (1) smooth surfaces, that is, low ␪, and (2) high hardness compared with modulus, that is, a low value of E/H.* We may at once apply this to various materials to show the conditions of surface roughness under which the asperities will deform elastically (Table 7.1). The results show that with pure metals the surfaces must be extremely smooth if plastic deformation is to be avoided. By contrast, ceramics and polymers can tolerate far greater roughnesses and still remain in the elastic regime. From the point of view of low friction and wear, elastic deformation is generally desirable, particularly if interfacial adhesion is weak (see below). Further, on this model the contact pressure is constant, either (E tan ␪)/2(1 Ϫ v2) for elastic deformation or H for plastic deformation. Thus the area of contact will be directly proportional to the applied load. TABLE 7.1 Mean Asperity Slope for Conical Asperity Marking Transition from Elastic to Plastic Deformation 7.3.3 Elastic and Plastic Deformation of Real Surfaces Real surfaces are conveniently described by two main classes of representation, each of which requires two parameters. Random or Stochastic Process. Here the profile is treated as a two-dimensional ran- dom process and is described by the root-mean roughness (see below) and the distance *The indentation hardness for a conical asperity depends on the cone angle, but for shallow asperities (80° < < 90°) the variation in H is small compared with E tan ␪ in Eq. (7.3). Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.