Michael R. Hoeprich

Residual Stresses Due to Debris Effects in EHL Contacts

Debris in lubricated contacts significantly reduces the contact fatigue life. The life reduction is due to the surface damage caused by debris denting and the subsequent overrolling of the dent in the EHL contact. High pressure spikes are generated due to the dent which will modify the contact stress profiles, leading to stress concentration at or near the surface. In this paper, the residual stresses caused by debris effects are investigated. The residual stresses originate from the debris denting process and from the overrolling process of the dent in EHL contacts. The finite element method was used to investigate the residual stresses due to each process and their combined effects on the internal stress distribution of an EHL contact. It was found that the residual stress from debris denting will increase the internal stresses in an EHL contact. However, the residual stresses from overrolling of dent will reduce the internal stresses. The residual stresses are largely dependent on the plastic modulus of the contacting materials and need to be considered when investigating the internal stresses in heavily loaded lubricated contacts.

On Mechanisms of Fatigue Life Enhancement by Surface Dents in Heavily Loaded Rolling Line Contacts

This paper studies mechanisms of surface dents in enhancing the fatigue life of rolling bearings previously reported in Akamatsu et al. (1). First, transient micro-EHL analyses of heavily loaded contacts between rough surfaces with multiple dents are conducted under near rolling conditions. Contacts with various dent dimensions, dent arrangements under different loading and kinematic conditions are investigated. Results show that surface dents generate no favorable micro-EHL effects to enhance the contact fatigue life. Subsequent analyses, in conjunction with other published studies, suggest that the fatigue life enhancement likely comes from the reduced local traction at asperity contacts through the oil pots effects of the dents. The effects of the surface dents on contact fatigue life may depend on the lubrication regime in which the contact is operating, being favorable in poor lubrication conditions but adverse in well-lubricated contacts. Since rolling bearings are usually designed to operate in a healthy regime of lubrication, fatigue life enhancement by artificially introducing dents on bearing surfaces may not extend to field applications.

Dent initiated spall formation in EHL rolling/sliding contact

Dents in elasto-hydrodynamic lubricated (EHL) contacts will initiate spalls and shorten the fatigue life significantly. Experimental results are provided from a ball-on-rod rolling contact fatigue tester with the rod predented with a single large dent. The results indicate that the spall usually initiated at the trailing edge of the dent on the driving surface. These cracks and spalls can also be created in the absence of lubricant. Based on the accumulated plastic strain and damage mechanics concept, a line contact spall initiation model was developed to investigate the dent effects on spall initiation and propagation. The near surface volume of the contact solid was divided into many small metal cells and for each cell the damage law was applied to determine whether the cell is undergoing damage or not. If the cell on the surface is damaged, then it is removed from the surface and a spall will be formed. If the damaged cell occurs below the surface, then a subsurface void is generated, this void could grow to the surface depending on the running conditions. The spall will further modify the surface geometry and initiate a new spall, hence, the spall will propagate. The results indicate that the location of spall initiation depends on the EHL and dent condition. Spalls can initiate at either the leading or trailing edge of the dent depending on the surface traction.

A Numerical Model for Life Scatter in Rolling Element Bearings

Fatigue lives of rolling element bearings exhibit a wide scatter due to the statistical nature of the mechanisms responsible for the bearing failure process. Life models that account for this dispersion are empirical in nature and do not provide insights into the physical mechanisms that lead to this scatter. One of the primary reasons for dispersion in lives is the inhomogeneous nature of the bearing material. Here, a new approach based on a discrete material representation is presented that simulates this inherent material randomness. In this investigation, two levels of randomness are considered: (1) the topological randomness due to geometric variability in the material microstructure and (2) the material property randomness due to nonuniform distribution of properties throughout the material. The effect of these variations on the subsurface stress field in Hertzian line contacts is studied. Fatigue life is formulated as a function of a critical stress quantity and its corresponding depth, following a similar approach to the Lundberg-Palmgren theory. However, instead of explicitly assuming a Weibull distribution of fatigue lives, the life distribution is obtained as an outcome of numerical simulations. A new critical stress quantity is introduced that considers shear stress acting along internal material planes of weakness. It is found that there is a scatter in the magnitude as well as depth of occurrence of this critical stress quantity, which leads to a scatter in computed fatigue lives. Further the range of depths within which the critical stress quantity occurs is found to be consistent with experimental observations of fatigue cracks. The life distributions obtained from the numerical simulations are found to follow a two-parameter Weibull distribution closely. The L 10 life and the Weibull slope decrease when a nonuniform distribution of elastic modulus is assumed throughout the material. The introduction of internal flaws in the material significantly reduces the L 10 life and the Weibull slope. However, it is found that the Weibull slope reaches a limiting value beyond a certain concentration of flaws. This limiting value is close to that predicted by the Lundberg-Palmgren theory. Weibull slopes obtained through the numerical simulations ranee from 1.29 to 3.36 and are within experimentally observed values for bearing steels.

Evaluation of Stresses Around Inclusions in Hertzian Contacts Using the Discrete Element Method

Inclusions are the primary sites for subsurface fatigue crack initiation in bearing contacts. To understand the mechanisms of subsurface crack nucleation under contact loading, a detailed description of the stress field around these inclusions is necessary. This paper presents a new approach to computing stresses in an inhomogeneous medium where inclusions are treated as inhomogeneities in a homogeneous material matrix. The approach is based on the Discrete Element (DE) Method in which the material continuum is replaced by a set of rigid discrete interacting elements. The elements are connected to each other along their sides through springs and dampers to form the macro-continuum and undergo relative displacements in accordance with Newtons laws of motion under the action of external loading. The spring properties are derived in terms of the overall elastic properties of the continuum. The relative motion between elements gives rise to contact forces due to stretching or compression of the inter-element springs. These forces are evaluated at each time-step and the corresponding equations of motion are solved for each element. Stresses are calculated from the inter-element joint forces. A Hertzian line contact case, with and without the presence of subsurface inclusions, is analyzed using the DE model. The DE model was used to determine stresses for an inclusion-free medium that compares well with that obtained from the continuum elasticity models. Parametric studies are then carried out to investigate the effects of size, location, orientation, and elastic properties of inclusions on the subsurface stress field. Both inclusions that are stiffer and/or softer than the base material are seen to give rise to stress concentrations. For inclusions that are stiffer than the base material (semi-infinite domain), the stress concentration effect increases with their elastic modulus. The stress concentration effect of a softer inclusion is higher than that of a stiffer inclusion. Inclusions that are oriented perpendicular to the surface give rise to much higher von Mises stresses than the ones that are oriented parallel to the surface. There is little change in the maximum von Mises stress for inclusions that are located deep within the surface.

Lubricating Properties of Water in Oil Emulsions

In this study the effect of water as a contaminant in lubricated contacts was analytically, and experimentally investigated. A steel ball on glass disc apparatus was used to measure lubricant film thickness of pure oil and water in oil emulsions under various operating conditions. A steel ball on steel disc rig was used to measure friction as a function of various loads, slide to roll ratios and water in oil emulsions. A finite difference numerical model was developed using the continuum theory of mixtures and results were corroborated with the experimental measurements. Numerical results are in excellent agreement with the experimental results and indicate that water will flow around the contact. The experimental and analytical results suggest that for heavily loaded contacts water-in-oil emulsions perform essentially the same as pure oils.

Rolling-Element Bearing Internal Temperatures

The internal temperature distribution within tapered rolling-element bearings was investigated. A simple experimental procedure using thermocouples for the stationary outer race and a temperature-sensitive medium on the moving components was used to determine bearing operating component temperatures. Circulating oil was used to lubricate the bearings. Temperatures for two different loads and three taper conditions (simulating bearing misalignment) are given. Corresponding contact pressure distributions and the calculated EHL films are shown. The correlation between temperatures and changes in pressure distributions, as well as their calculated effects on the lubricant film, can be easily seen. Presented at the 51st Annual Meeting in Cincinnati, Ohio May 19–23, 1996

A Study on Rolling Element Skew Measurement in a Tapered Roller Bearing With a Specialized Capacitance Probe

This paper reports on roller skew in tapered roller bearings. The roller skewing of a tapered roller bearing is experimentally measured with a specialized capacitance probe (Kelvin contact potential difference, CPD, probe). The probe measures the electrochemical potential difference between the probe and roller surfaces. Two probes are inserted through holes in the housing and bearing outer race. The electrical signals from both ends of a roller are used to determine the skewing. The technique, as well as the effect of lubrication and rotational speed on the roller skewing, is presented. It is shown that the skewing increases with an increase in rotational speed, and the lubrication of the large end of the roller. A theoretical analysis has been developed to account for the experimental results.

EHL Modeling for Nonhomogeneous Materials: The Effect of Material Inclusions

Inclusions are common in bearing materials and are a primary site for subsurface fatigue crack initiation in rolling element bearings. This paper presents a new approach for computing the pressure, film thickness, and subsurface stresses in an elastohydrodynamic lubrication (EHL) contact when inclusions are present in the elastic half-space. The approach is based on using the discrete element method to determine the surface elastic deformation in the EHL film thickness equation. The model is validated through comparison with the smooth EHL line contact results generated using linear elasticity. Studies are then carried out to investigate the effects of size, location, orientation, and elastic properties of inclusions on the EHL pressure and film thickness profiles. Both inclusions that are stiffer than and/or softer than the base material are seen to have effects on the pressure distribution within the lubricant film and to give rise to stress concentrations. For inclusions that are stiffer than the base material (hard inclusions), the pressure distribution within the lubricant film behaves as though there is a bump on the surface, whereas for inclusions that are less stiff than the base material (soft inclusions), the pressure distribution behaves in a manner similar to that of a dented surface. Inclusions close to the surface cause significant changes in the contact stresses that are very significant considering the stress life relationship. For inclusions that are located deep within the surface, there is little change in the EHL pressure and film thickness.

Rolling Element Bearing Contact Geometry Analysis

Rolling element bearings are subjected to a variety of loads during the operation of machinery. Raceway contact geometries should be designed and analyzed in a manner which accurately models internal contact stress distributions for these different load cycle conditions. To properly determine contact stresses, analyses should determine the orientation of rolling elements relative to the raceways through consideration of load, bearing alignment and bearing internal geometry. Since design loads are not always well defined and machinery upgrades may increase loads, contact geometry designs should have sufficient flexibility to handle conditions differing from the initial design loads. An analytical procedure with examples is discussed. Presented at the 50th Annual Meeting in Chicago, Illinois May 14–19, 1995