A tutorial is presented outlining the evolution, theory, and application of rolling-element bearing life prediction from that of A. Palmgren, 1924; W. Weibull, 1939; G. Lundberg and A. Palmgren, 1947 and 1952; E. Ioannides and T. Harris, 1985; and E. Zaretsky, 1987. Comparisons are made between these life models. The Ioannides-Harris model without a fatigue limit is identical to the Lundberg-Palmgren model. The Weibull model is similar to that of Zaretsky if the exponents are chosen to be identical. Both the load-life and Hertz stress-life relations of Weibull, Lundberg and Palmgren, and Ioannides and Harris reflect a strong dependence on the Weibull slope. The Zaretsky model decouples the dependence of the critical shear stress-life relation from the Weibull slope. This results in a nominal variation of the Hertz stress-life exponent. For 9th- and 8th-power Hertz stress-life exponents for ball and roller bearings, respectively, the Lundberg- Palmgren model best predicts life. However, for 12th- and 10th-power relations reflected by modern bearing steels, the Zaretsky model based on the Weibull equation is superior. Under the range of stresses examined, the use of a fatigue limit would suggest that (for most operating conditions under which a rolling-element bearing will operate) the bearing will not fail from classical rolling-element fatigue. Realistically, this is not the case. The use of a fatigue limit will significantly overpredict life over a range of normal operating Hertz stresses. Since the predicted lives of rolling-element bearings are high, the problem can become one of undersizing a bearing for a particular application. Zaretsky, Erwin V. Glenn Research Center BALL BEARINGS; CRITICAL LOADING; LIFE (DURABILITY); PREDICTION ANALYSIS TECHNIQUES; WEIBULL DENSITY FUNCTIONS; ROLLER BEARINGS; SHEAR STRESS; STEELS; FAILURE; PREDICTIONS

This book highlights recent findings in industrial, manufacturing and mechanical engineering, and provides an overview of the state of the art in these fields, mainly in Russia and Eastern Europe. A broad range of topics and issues in modern engineering is discussed, including the dynamics of machines and working processes, friction, wear and lubrication in machines, surface transport and technological machines, manufacturing engineering of industrial facilities, materials engineering, metallurgy, control systems and their industrial applications, industrial mechatronics, automation and robotics. The book gathers selected papers presented at the 7th International Conference on Industrial Engineering (ICIE), held in Sochi, Russia, in May 2021. The authors are experts in various fields of engineering, and all papers have been carefully reviewed. Given its scope, the book will be of interest to a wide readership, including mechanical and production engineers, lecturers in engineering disciplines, and engineering graduates.

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Few rolling bearing users realize that the fundamentals of bearing life predictions are based on experimental data derived under conditions very different from the ones generally used in RCF testing today. The basic life formulas derived in the 1940s largely were based on tests run on steel with very different characteristics than the materials used to produce bearing components today. Still, the fundamental life calculations are based on the (C/P)n concept, which was experimentally derived by Lundberg and Palmgren (Lundberg, G. and Palmgren, A., "Dynamic Capacity of Rolling Bearings," Acta Polytech. Scand., Mech. Eng. Ser., Volume 1, No. 3, 1947), even if the basic equation has been expanded and adjusted to reflect the lives recorded for modern bearings and to incorporate the concept of a fatigue limit (Ioannides, E., Bergling, G., and Gabelli, A., "An Analytical Formulation for the Life of Rolling Bearings," Acta Polytech. Scand., Mech. Eng. Ser., Volume 137, 1999, pp. 9-12, 21-24). In an attempt to better understand the premature and unpredictable failures that sometimes occur in certain industrial applications today, the test procedures used by Lundberg and Palmgren have been revisited, and data have been derived that might contribute to an understanding of the short lives sometimes experienced in certain industrial bearing applications. Based on this test procedure, a better understanding of the development of micro-crack associated plastic deformations at non-metallic inclusions also has been gained. The propensity of different non-metallic inclusions to drive the formation and growth of micro-cracks has been studied in detail, and this knowledge has been used to develop steel that is less prone to butterfly development and micro-crack growth under very high contact stress conditions. Today's bearing life prediction models presume that the Palmgren-Miner rule of accumulated damage is globally applicable. Experimental data questioning this assumption are presented.

The most widely used steel grade for rolling bearings is based on a steel composition first used almost a hundred years ago, the so-called lC-1.5Cr steel. This steel is used either in a selective surface induction hardened condition or in a through hardened heat treated condition, both yielding exceptional structural and contact fatigue properties. The Lundberg and Palmgren rolling bearing life prediction model, published in 1947, was the first analytical approach to bearing performance prediction, subsequently becoming a widely accepted basis for rolling bearing life calculations. At that time the fatigue life of rolling bearings was dominated by the classical sub-surface initiated failure mode. This mode results from the accumulation of micro-plastic strain at the depth of maximum Hertzian stress and is accelerated by the stress concentrations occurring at the micro internal defects. In common with all fatigue processes, rolling bearing failure is a statistical process: the failures of bearings with high inclusion content tested at high stress levels belong to the well-known family of "Weibull" distributions. Steady improvements in bearing steel cleanliness due, amongst other things, to the introduction of secondary metallurgy steel making techniques, have resulted in a significantly increased rolling bearing life and load carrying capacity. In recognition of this, in 1985 Ioannides and Harris introduced a new fatigue life model for rolling bearings, comprising a more widely applicable approach to the modelling of bearing life based on the relevant failure mode. Subsequently this has been extended to include effects of hardness and of micro-inclusion distributions in state-of-the-art clean bearing steel.