Fig. 11 Empirical wear mechanism map for steel (pin-on-disk configuration) References 1. N.P. Suh, Tribophysics, Prentice-Hall, 1986, p 73 2. P.J. Blau, Friction and Wear Transitions of Materials, Noyes Publications, 1989 3. H. Czichos, Tribology A Systems Approach to the Lubrication and Wear, Elsevier, Amsterdam, 1978, p 195, 196 4. K H. Zum Gahr, Microstructure and Wear of Materials, Elsevier, Amsterdam, 1987, p 379 5. N.C. Welsh, The Dry Wear of Steels, Philos. Trans. R. Soc. (London) A, Vol 257, 1965, p 31-70 6. K H. Habig, Wear and Hardness of Materials, Hanser-Verlag, München, 1980 (in German) 7. T.F.J. Quinn, D.M. Rowson, and J.L. Sullivan, Applications of the Oxidational Theory of Mild Wear to the Sliding Wear of Low Alloy Steel, Wear, Vol 65, 1980, p 1-20 8. M. Woydt, D. Klaffke, K H. Habig, and H. Czichos, Tribological Transition Phenomena of Ceramic Materials, Wear, Vol 136, 1990, p 373-380 9. H. Czichos, Influence of Adhesive and Abrasive Mech anisms on the Tribological Behaviour of Thermoplastic Polymers, Wear, Vol 88, 1983, p 27-43 10. M. Godet, Third Bodies in Tribology, Proceedings of EUROTRIB 1989, K. Holmberg and I. Nieminen, Ed., The Finnish Society for Tribology, ESPO, Vol 1, 1989, p 1-15 11. H. Czichos and K. Kirschke, Investigations into Film Failure (Transition Point) of Lubricated Concentrated Contacts, Wears, Vol 22, 1972, p 321-336 12. C.M. Lossie, J.W.M. Mens, and A.W.J. de Gee, Practical Applications of the IRG Transition Diagr am Technique, Wear, Vol 129, 1989, p 173-182 13. H. Czichos, Failure Criteria in Thin Film Lubrication: The Concept of a Failure Surface, Tribol. Intl., Vol 7, 1974, p 14-20 14. S.C. Lim and M.F. Ashby, Wear-Mechanism Maps, Acta Metall., Vol 35, 1987, p 1-24 15. S.C. Lim, M.F. Ashby, and J.H. Bruton, Wear- Rate Transitions and their Relationship to Wear Mechanisms, Acta Metall., Vol 35, 1987, p 1343-1348 Concepts of Reliability and Wear: Failure Modes Horst Czichos, BAM (Germany) Introduction METHODS TO CHARACTERIZE THE RELIABILITY of mechanical equipment on the basis of measurements or estimations of wear are often tried in mechanical engineering applications (Ref 1). In this article, statistical techniques and probability concepts for the evaluation and presentation of wear and reliability data are briefly outlined. More detailed information on reliability analysis can be found in the references provided as well as Vol 17 of ASM Handbook (formerly 9th Edition Metals Handbook). Acknowledgements The author would like to thank his tribology colleagues at BAM, and in particular Karl-Heinz Habig and Erich Santner for their help in the preparation of this Section. Special thanks are also due to BAM mathematicians. Wolfgang Gerisch and Thomas Fritz for their review and valuable contributions. Characteristics of Reliability Reliability is defined as "the probability of a device performing its purpose adequately for the period of time intended under the operating conditions encountered." (This is the classic definition of reliability given by the Radio Electronics and Television Manufacturers Association in 1955.) In a quantitative way, the reliability of systems, devices, or products may be characterized by the probability concepts outlined in Table 1. Table 1 Reliability probability concepts Relationship Between Wear and Reliability Consider as a starting point for the reliability considerations of tribosystems that wear behavior is a function of time (Ref 2). In the previous article on "Presentation of Friction and Wear Data," it was explained that for time-dependent wear of a tribosystem, three different wear stages can be distinguished: • Self-accommodation or running-in wear • Steady-state wear • Self-acceleration (catastrophic damage) of wear These wear mode changes in the system behavior may follow each other with time, as indicated in Fig. 1. In this figure, W lim denotes a maximum admissible level of wear losses. At this level the system structure has changed in such a way that the functional input-output relations of the system are disturbed severely. Repeated measurements show random variations in the data, as indicated by the dashed lines in Fig. 1. Fig. 1 Simple curves of wear and failure and reliability functions From sample curves of wear, a probability density function, f(t), of the time for reaching the maximum admissible level of wear (W lim = constant) is obtained. For a given time, t 0 , the shaded area under the curve f(t), that is, the value of F(t 0 ), is a measure of the probability that the system fails within the time t < t 0 . Statistical Distributions of Wear and Reliability For the modeling of the distribution of measured wear data and the estimation of reliability data, statistical distributions may be used. In the following paragraphs, some of the statistical distributions that have been applied for these purposes are briefly reviewed in a highly simplified manner in order to illustrate the given probability concepts. With respect to the estimation of the occurring parameters, the calculation of confidence intervals, and related subjects, the reader is referred to Ref 3, 4, 5, 6. For exponential distribution: (t) = = const f(t) = · exp (- t) R(t) = exp (- t) MTTF = 1/ (Eq 1) In this case, the failure rate is constant, which means that failure occurs accidentally without an accumulation of fatiguelike effects during service time. Components in a machine fail in this mode, for example, when the failure is brittle fracture. In Fig. 2 the density function of the failure of a diesel engine control unit is plotted showing an exponential distribution (Ref 7). Fig. 2 Failure density function of diesel engine control units For normal distribution: (Eq 2a) where is the standard normal distribution function, and R(t) = 1 - ((t - )/ ) MTTF = (Eq 2b) Many machine components obey this distribution, especially if the failure occurs due to wear processes. For lognormal distribution: (Eq 3) This distribution is concentrated on the positive t-axis. Its failure rate increases to a maximum and then decreases to zero. Therefore, it can be used for modeling survival times after extreme stress. For the Weibull distribution: (Eq 4) In its simplest form, this is a distribution with two key parameters: t 0 , the nominal life, and the constant C. This distribution is found to represent failure of many kinds of mechanical systems, such as fatigue in ball bearings. As an example, Fig. 3 shows the probability distribution function of the time to failure, F(t), as determined by testing 500 grease-lubricated ball bearings at 1000 rpm (Ref 8). Fig. 3 Failure distribution function of ball bearings For the Gamma distribution: (Eq 5a) where (a,z) is the standard incomplete gamma function, and R(t) = ( (x) - (x,Ct))/ (x) MTTF = x/C (Eq 5b) where (x) is a Gamma function. This is also a distribution with two parameters. Theoretically, the importance of this distribution is attributed to the fact that the equation is an x-fold convolution of the exponential function. It means physically that a component fails at xth shock which occurs as a Poisson statistical process with parameter C. In Fig. 4, the density function of the failure of a piston in a diesel engine is plotted showing a Gamma distribution with x = 2 (Ref 7). Fig. 4 Failure density function of diesel engine pistons Wear and Failure Modes The aforementioned examples of statistical distributions indicate that different failure modes and different elementary failure processes are associated with different types of failure distribution functions. It follows that from the experimental determination of failure distribution curves, conclusions may be drawn as to the type of failure mechanism. For most tribosystems failing as a consequence of wear processes, the failure behavior is characterized by the normal distribution or the Weibull distribution. If for a given type of tribosystem the failure mode and the type of failure distribution are known, this knowledge can be used to improve the reliability of the system (Ref 9). For instance, this approach can be used to select the type of a ball or roller bearing system to operate under a given set of operating conditions with high operational safety (Ref 10). More general treatments concerning correlations between life data, statistical lifetime distribution, and failure models can be found in Ref 3, 4, 5, 6, 11 and 12. Dependence of Failure Rate on Operating Duration To conclude the brief discussion on the failure and reliability of tribosystems, and dependence of the failure rate on the operating duration of a system should be considered. If the failure rate is plotted as a function of time, a curve known as the "bathtub curve" is generated (Fig. 5). Fig. 5 "Bathtub" failure rate curve In this curve, three regimes can be distinguished: (1) early failures, (2) random failures, and (3) wear-out failures. None of the distribution curves discussed above have this bathtub-shaped failure curve, but an approximation can be obtained by selecting an appropriate probability density function for each of the three regimes. Regime (1) describes the region of the "infant death" of the system. This regime is characterized by a decrease of the failure rate with time during running-in wear. Regime (2), which exhibits a constant failure rate, is the region of normal running. Here failure occurs as a consequence of statistically independent factors. Regime (3) is characterized by an increase of the failure rate with time. Here failure may be due to aging effects. As described above, for a great deal of tribo-induced failures, the failure rate increases with time. Thus region (3) of the bathtub curve of Fig. 5 appears to be relevant for the normal mode of wear- induced failure of mechanical systems. References 1. G. Fleischer, H. Gröger, and H. Thum, Wear and Reliability, VEB Verlag Technik, Berlin, 1980 (in German) 2. H. Czichos, Tribology A Systems Approach to the Science and Technology of Friction, Lubrication and Wear, Elsevier, Amsterdam, 1978, p 234-240 3. W. Nelson, Applied Life Data Analysis, John Wiley, 1982 4. J.F. Lawless, Statistical Models and Methods for Lifetime Data, John Wiley, 1982 5. N.R. Mann, R.E. Schafer, and N.D. Singpurwalla, Methods for Statistical Anal ysis of Reliability and Life Data, John Wiley, 1974 6. J. McCormick, Reliability and Risk Analysis, Academic Press, 1981 7. G. Fleischer, Problems of the Reliability of Machines, Wiss. Z. Tech. Univ. Magdeburg, Vol 16, 1972, p 289 (in German) 8. G. Bergling, Reliability of Rolling Bearings, Kugellager-Zeitschrift, Vol 51, 1976, p 1 (in German) 9. A. Holfeld, Wear and Life Time Determination on a Statistical Basis, Schmierungstechnik, Vol 20, 1989, p 167-171 (in German) 10. A. Sturm, "Rolling Bearing Di agnosis in Machines and Plants," Verlag TÜV Rheinland, Cologne, 1986 (in German) 11. H.F. Martz and R.A. Walter, Bayesian Reliability Analysis, John Wiley, 1982 12. A.E. Green and A.J. Bourne, Reliability Technology, Wiley-Interscience, London, 1972 Friction and Wear of Rolling-Element Bearings Tedric A. Harris, Pennsylvania State University Introduction ROLLING-ELEMENT BEARINGS, also called rolling bearings and antifriction bearings, are among the most common machine elements. The basic design of the current ball bearings was devised by Leonardo da Vinci in the 15th century. (See Ref 1 for a history of lubrication and bearings.) The term rolling element refers to the ball or roller components that are used to separate the inner and outer rings. The term antifriction is used because the bearings tend to have very low friction characteristics compared to fluid film bearings or simple sliding bearings. In addition to the components cited above (that is, balls or rollers, inner rings, and outer rings), most rolling bearing have a cage (also called a separator or retainer) that spaces the rolling elements during operation. The cage also serves to retain the rolling elements in the bearing prior to assembly and also in the subsequent application. Figure 1 illustrates the components in a typical ball bearing. Note that the rolling elements run on an inner ring track called the inner raceway; similarly, the outer ring track is called the outer raceway. Fig. 1 Cutaway view of radial ball bearing showing inner ring, outer ring, balls, and cage assembly Rolling bearings have much less friction torque than conventional hydrodynamic bearing types, and starting friction torque is only marginally greater than operating friction torque. In addition, rolling-element bearing deflection is not as sensitive to load fluctuation as is deflection in a hydrodynamic bearing. In most applications, only a small quantity of lubricant is required for satisfactory operation, eliminating the need for expensive and space-consuming lubricating systems. Moreover, rolling-element bearings require less space than corresponding hydrodynamic bearings, and they can be selected or designed in compact units to support combination loads (for example, radial, thrust, and moment loads). The load and speed ranges to which a given rolling-element bearing may be subjected and function efficiently under each condition are significantly wide. In general, if a rolling-element bearing can satisfy the operating conditions for a given application, it represents the economical choice. Types of Rolling-Element Bearing There are two basic rolling-element types: balls and rollers. Ball bearings enjoy the most universal usage. However, for applications in which very heavy loads must be supported, roller bearings find extensive usage. In addition to categorizing rolling bearings according to rolling-element type, such bearings are also identified according to the predominant loading they are designed to support (for example, radial load or thrust load [also called axial load]). Within each subcategory type (for example, radial ball bearings, thrust ball bearings, radial roller bearings, and thrust roller bearings), there are several different basic variations, the usage of each depending on the load and speed conditions to be accommodated. Ball Bearings Ball bearings can be further classified as either radial ball bearings, angular-contact ball bearings, or thrust ball bearings. Radial Ball Bearings. The most common ball bearing type is the nonseparable Conrad assembly (Fig. 2). The nominal contact angle between a ball and a raceway is 0° (the contact angle is defined as the angle the ball-raceway load vector makes with the bearing radial plane). The bearing is designed to carry moderate radial road. The bearing can, however, support some thrust (axial) and moment load in addition to the radial load. In this case, the contact angles between balls and raceways increase beyond 0° with the application of thrust. In most cases, the bearings can operate at high speeds of rotation ( 5 × 10 5 n · d m , where n is the speed of rotation in rev/min and d m is the pitch diameter, above which special cooling is often required to keep operating temperatures at <170 °C, or 338 °F). Because the bearing balls and rings form an inseparable unit when assembled, cages are either two-piece riveted assemblies or one-piece snap-on plastic (generally fiberglass-filled polyamide [nylon]) units. When using bearings with plastic cages, care must be exercised to ensure the compatibility of the cage material with the bearing lubricant and operating temperatures. The latter must not be >120 °C (>248 °F). Fig. 2 Schematic showing assembly process for a nonseparable Conrad-type ball bearing. , assembly angle Self-aligning ball bearings are principally double-row radial bearings that can accommodate radial load simultaneously with substantial misalignment (for example, from 1.5 to 3° depending on internal design), without detriment to bearing endurance. In conjunction with the principal radial load, they can also support some axial loading. Because the outer raceway is a portion of a sphere (Fig. 3), the conformity of the outer raceway to the ball is not close. Accordingly, the outer raceway has less load-carrying capacity than does the inner raceway. The reverse is true for almost all other basic types of radial rolling-element bearings. [...]... 0.22 0.23 0.24 0.25 0.26 fc = 50°(b) 109.7 127.8 139 .5 148.3 155.2 160.9 165.6 169.5 172.8 175.5 177.8 179.7 181 .1 182 .3 183 .1 183 .7 184 184 .1 184 183 .7 183 .2 182 .6 181 .8 180 .9 179.8 178.7 = 65°(c) 107.1 124.7 136 .2 144.7 151.5 157 161.6 165.5 168.7 171.4 173.6 175.4 176.8 177.9 178.8 179.3 179.6 179.7 179.6 179.3 = 80°(d) 105.6 123 134 .3 142.8 149.4 154.9 159.4 163.2 166.4 169 171.2... lubricant is required to: • Form fluid films between the rolling elements and raceways, rolling elements and cage pockets, cage rails and ring lands, roller ends and abutting flanges, thereby minimizing metal-to-metal contact, • • friction, and wear Contain chemical additives to minimize rolling-contact surface corrosion and wear Transport friction heat away from the bearing In general, only a small... Fig 4 Key components of an angular-contact ball bearing Fig 5 Duplex angular-contact ball bearing arrangements used to accommodate thrust loading induced by applied radial loading (a) Face-to-face mounting (b) Back-to-back mounting Fig 6 Pair of angular-contact ball bearings mounted in tandem The bearings may be assembled with one-piece pressed (stamped) or precision-machined cages fabricated from steel,... fc factors for radial ball bearings and angular-contact ball bearings (D · cos d(a) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0 .13 0.14 0.15 0.16 0.17 0 .18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 (a) )/ fc Single-row radial contact groove ball bearings and single-row and double-row angular contact groove ball bearings... indicated above, then the standard load rating formulas cannot be used If the raceway curvature radius is greater than standard, normal stresses will be greater than standard and the basic load rating can be considerably less than standard Also, if a bearing has an internal radial clearance greater than standard, maximum rolling-element load will be greater than standard, and the basic load rating will... 0.11 0.12 0 .13 0.14 0.15 0.16 0.17 0 .18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 fc, = 90° 105.4 122.9 134 .5 143.4 150.7 156.9 162.4 167.2 171.7 175.7 179.5 183 186 .3 189 .4 192.3 195.1 197.7 200.3 202.7 205 207.2 209.4 211.5 213. 5 215.4 217.3 219.1 220.9 222.7 224.3 (D · cos )/d(a) 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0 .13 0.14 0.15 0.16 0.17 0 .18 0.19 0.20... misalignment of ±3° Bearing Component Materials Rolling-Contact Component Steels Most modern ball and roller bearing rings, balls, and rollers are manufactured from vacuum-processed AISI 52100, a high-carbon through-hardening steel, heat treated to at least 58 HRC High-quality grades of this steel are required for ball and roller bearings to achieve the standard load rating generally published in the catalogs... loading; they may be mounted in back-to-back or face-to-face duplex arrangements (Fig 5) The former provides substantial resistance to moment loading (that is, high stiffness), whereas the latter provides greater ability to accommodate misalignment In addition, angular-contact bearings can be mounted in tandem for increased axial load-carrying capacity (Fig 6) Duplex angular-contact ball bearings can be... (in mm) The tabular data pertain strictly to radial and angular-contact bearings having inner ring groove radii 0.52D and outer ring groove radii 0.53D and to self-aligning bearings having inner ring groove radii 0.53D Table 1 bm factors for selected rolling bearing types Bearing type Ball bearings Radial and angular-contact ball Filling slot ball Self-aligning ball Thrust ball Roller bearings Cylindrical... operate with slightly less friction and can therefore achieve higher operating speeds without special attention to friction heat removal Precision-machined cages are manufactured from steel (for example, AISI 4349, brass, bronze, and variations such as silicon-iron-bronze and alcop (aluminum-copper bronze) Bearings with such machined cages are either inner or outer ringland riding (Fig 17) Bearings with . 1 4-2 0 14. S.C. Lim and M.F. Ashby, Wear- Mechanism Maps, Acta Metall., Vol 35, 1987, p 1-2 4 15. S.C. Lim, M.F. Ashby, and J.H. Bruton, Wear- Rate Transitions and their Relationship to Wear. Friction and Wear Data," it was explained that for time-dependent wear of a tribosystem, three different wear stages can be distinguished: • Self-accommodation or running-in wear • Steady-state. Gröger, and H. Thum, Wear and Reliability, VEB Verlag Technik, Berlin, 1980 (in German) 2. H. Czichos, Tribology A Systems Approach to the Science and Technology of Friction, Lubrication and Wear,