Farshid Sadeghi

A Review of Rolling Contact Fatigue

Ball and rolling element bearings are perhaps the most widely used components in industrial machinery. They are used to support load and allow relative motion inherent in the mechanism to take place. Subsurface originated spalling has been recognized as one of the main modes of failure for rolling contact fatigue (RCF) of bearings. In the past few decades a significant number of investigators have attempted to determine the physical mechanisms involved in rolling contact fatigue of bearings and proposed models to predict their fatigue lives. In this paper, some of the most widely used RCF models are reviewed and discussed, and their limitations are addressed. The paper also presents the modeling approaches recently proposed by the authors to develop life models and better understanding of the RCF.

Finite element modeling of engagement of rough and grooved wet clutches

A finite element model has been developed to investigate the engagement of rough, grooved, paper-based permeable wet clutches. The finite element (Galerkin) approach was used to discretize the modified Reynolds and force balance equations, and the solution domain geometry was described using an isoparametric formulation. Surface roughness effects were modeled via the Patir and Cheng (1978) average flow model, while asperity load sharing was calculated using the Greenwood and Williamson (1966) approach. The finite element model developed was used to investigate the effects of applied load, friction material permeability, and groove size on the engagement characteristics of wet clutches (i.e., torque, pressure, engagement time, and film thickness). The results indicate that the applied load, friction material permeability, and groove width significantly influence the engagement characteristics. Higher facing pressures increase peak torque and decrease engagement time. Higher permeability of the friction material significantly decreases engagement time but dramatically increases peak torque. Wider grooves decrease the peak torque and increase the engagement time. Groove depth does not significantly affect engagement characteristics for this model.

Thermal EHL Analysis of Circular Contacts With Measured Surface Roughness

Time dependent thermal EHL circular contact results with measured surface roughness were obtained to analyze the effects of roughness on pressure, film thickness, temperature, and coefficient of friction. Both contact surfaces are considered to be rough. Multilevel multigrid techniques (with multigrid integration) were used to solve the system of two dimensional Reynolds, elasticity and three dimensional energy equations simultaneously. The effects of surface roughness under various loads, speeds, and slip conditions have been studied. Surface roughness causes pressure and temperature spikes and increases the coefficient of friction, and surface roughness flattens due to the high pressure in EHL contact. The higher the load, speed and slide to roll ratio, the more significant the effect of the surface roughness. A comparison between rough EHL and smooth EHL results indicates that surface roughness cannot be ignored in EHL analysis.

Thermal Elastohydrodynamic Lubrication of Rolling/Sliding Contacts

A complete numerical solution of thermal compressible elastohydrodynamic lubrication of rolling/sliding contacts has been obtained. The Newton-Raphson technique is used to solve the simultaneous system of Reynolds and elasticity equations. The control volume finite element modeling was employed to solve the energy equation and its boundary conditions. The effects of various loads, speeds, and slip conditions on the lubricant temperature, film thickness, and friction force have been investigated. The results indicate that the temperature effects are significant and cannot be neglected.

Analytical and Numerical Modeling of Engagement of Rough, Permeable, Grooved Wet Clutches

A simple mathematical model for the engagement of rough, permeable, grooved wet clutches has been developed and used to determine the effect of various input parameters (applied load, grooved area, and friction material permeability) on engagement. The model includes the effects of surface roughness according to Patir and Cheng (1978), friction material permeability according to Natsumeda and Miyoshi (1994) and Beavars and Joseph (1967), and grooving in the friction material according to a new approximation. The approach reduces the system ofReynolds and force balance equations to a single, first-order differential equation in film thickness and time. A line searching algorithm, exploiting the low computational cost of function evaluations for the new model, is used to find the set of input parameter combinations yielding the same engagement characteristics. This set of design points is presented as an engagement isosurface in the parameter space (F app , Φ, A red ). The isosurface implicitly gives information about engagement time, and it shows regions in which the desired engagement characteristics cannot be achieved. The input parameters are classified as those affecting the transient portion of engagement and those affecting the steady-state portion.

Lubrication regime transitions at the piston ring-cylinder liner interface

Abstract An experimental apparatus and an analytical model have been developed to investigate and determine the lubrication condition and frictional losses at the interface between a piston ring and cylinder liner. In order to obtain a solution for the lubrication condition between the piston ring and cylinder liner, the system of Reynolds and film thickness equations subject to boundary conditions were simultaneously solved. The effects of boundary and mixed lubrication conditions were implemented using the Greenwood-Tripp stochastic approach. The Elrod cavitation algorithm was used to investigate the effects of fluid rupture and reformation at the top and bottom dead centres. The experimental results indicate that the piston ring and liner experience all the different lubrication regimes (i.e. boundary, mixed, and hydro-dynamic lubrication) during a stroke. A comparison between experimental and analytical results indicated that they are in good agreement and the analytical model developed for this study can capture the different lubrication regimes that the piston ring and liner experience.

Cage Instabilities in Cylindrical Roller Bearings

A six-degree-of-freedom model was developed and used to simulate the motion of all elements in a cylindrical roller bearing. Cage instability has been studied as a function of the roller-race and roller-cage pocket clearances for light-load and high-speed conditions. The effects of variation in inner race speed, misalignment, cage asymmetry, and varying size of one of the rollers have been investigated. In addition, three different roller profiles have been used to study their impact on cage dynamics. The results indicate that the cage exhibits stable motion for small values of roller-race and roller-cage pocket clearances. A rise in instability leads to discrete cage-race collisions with high force magnitudes. Race misalignment leads to a rise in instability for small roller-cage pocket clearances since skew control is provided by the sides of the cage pocket. One roller of larger size than the others causes inner race whirl and leads to stable cage motion for small roller-race clearances without any variation in roller-cage pocket clearance. Cage asymmetry and different roller profiles have a negligible impact on cage motion.

Analysis of EHL Circular Contact Start Up: Part I—Mixed Contact Model With Pressure and Film Thickness Results

In this paper a model is presented to investigate the start up condition in elastohydrodynamic lubrication. During start up the lubrication condition falls into the mixed lubrication regime. The transition from solid contact to lubricated contact is of importance when investigating the start up process and its effects on bearing performance. The model presented uses the multigrid multilevel method to solve the lubricated region of the contact and a minimization of complementary energy approach to solve the solid contact region. The FFT method is incorporated to speed up the film thickness calculation. An iteration scheme between the lubrication and the solid contact problems is used to achieve the solution of the mixed lubrication contact problem. The results of start up with smooth surfaces are provided for the case when speed increases from zero to desired speed in one step and the case when speed is linearly increased to desired speed. The details of the transition from full solid contact to full lubricated contact in EHL start up are presented. The change of pressure and film thickness as well as contact forces and contact areas are discussed.

A Statistical Damage Mechanics Model for Subsurface Initiated Spalling in Rolling Contacts

Fatigue lives of rolling element bearings exhibit a wide scatter due to the statistical nature of the rolling contact fatigue failure process. Empirical life models that account for this dispersion do not provide insights into the physical mechanisms that lead to this scatter. One of the primary reasons for dispersion in lives is the stochastic nature of the bearing material. Here, a damage mechanics based fatigue model is introduced in conjunction with the idea of discrete material representation that takes the effect of material microstructure explicitly into account. Two sources of material randomness are considered: (1) the topological randomness due to geometric variability in the material micro-structure and (2) the material property randomness due to nonuniform distribution of properties throughout the material. The effect of these variations on the subsurface stress fields in rolling element line contacts is studied. The damage model, which incorporates cyclic damage accumulation and progressive degradation of material properties with rolling contact cycling, is used to study the mechanisms of subsurface initiated spalling in bearing contacts. Crack initiation as well as propagation stages are modeled using damaged material zones in a unified framework. The spalling phenomenon is found to occur through microcrack initiation below the surface where multiple microcracks coalesce and subsequent cracks propagate to the surface. The computed crack trajectories and spall profiles are found to be consistent with experimental observations. The microcrack initiation phase is found to be only a small fraction of the total spalling life and the scatter in total life is primarily governed by the scatter in the propagation phase of the cracks through the microstructure. Spalling lives are found to follow a three-parameter Weibull distribution more closely compared to the conventionally used two-parameter Weibull distribution. The Weibull slopes obtained are within experimentally observed values for bearing steels. Spalling lives are found to follow an inverse power law relationship with respect to the contact pressure with a stress-life exponent of 9.35.

Spall initiation and propagation due to debris denting

An analytical model has been developed to investigate the effects of dent on spall initiation and propagation in lubricated contacts. The model is based on the damage mechanics concept that the fatigue spall initiation and propagation is due to the accumulated plastic strain process rather than the stress intensity at the tip of the crack. The contact surface layer was divided into small metal matrix (cell) and for each cell a damage law was applied to determine whether the cell is undergoing damage or not. In this model, spall will be formed when a cell is damaged. A dent profile from finite element analysis for a spherical debris denting the contact surface was used in a point EHL model. The pressure and traction profiles were then used to obtain the internal stresses and accumulated plastic strain for each cell. A damage variable was calculated for each cell based on the accumulated plastic strain. When the damage in a cell reaches a certain level, the cell is damaged and is assumed to fall off the contact surface layer, hence, spall is generated. The spall will further modify the contact surface resulting in new pressure and traction profiles. The accumulated plastic strain and damage are calculated again based on which new spalls may be generated. The entire procedure is repeated which allows the spall to propagate. Spall size and growth rate versus cycle number are presented. The results indicate that spall will always initiate at the dent edge.