Ilya I. Kudish

Modern State of Experimentation and Modeling in Contact Fatigue Phenomenon: Part II—Analysis of the Existing Statistical Mathematical Models of Bearing and Gear Fatigue Life. New Statistical Model of Contact Fatigue

The paper presents a critical analysis of some existing statistical mathematical models of fatigue life applicable to bearings and gears, i.e. the assumptions, advantages, disadvantages and several contradicting aspects of these models. Some conclusions that adequately reflect the experimental and theoretical data discussed in Part I are drawn regarding the necessary features of a successful mathematical model of contact fatigue. Furthermore, such a new statistical model that will allow to predict fatigue life of machine parts is proposed in this paper. It is based on the first five parameters from the list compiled by Kudish and Burris (2000a) that are known to strongly affect contact fatigue. The other parameters from this list can be subsequently incorporated into the model. The paper also presents a theoretical analysis of the new model and some numerical results for contact fatigue life based on this model. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in Orlando, Florida, October 11–13, 1999

A new statistical model of contact fatigue

A detailed derivation of a new statistical model of contact fatigue life followed by its qualitative and quantitative analysis are presented. The model is based on contact and fracture mechanics and statistical treatment of the initial distribution of material defect. The model assumptions and their validation as well as the model properties are discussed. A parametric study of the model is performed. A generalization of the model for the case of stochastic residual stress or other contact parameters is proposed. Some analytical formulas for calculation of contact fatigue are proposed and analyzed. The validation of the model and its applicability to calculation of bearing fatigue life and some particular data are considered. A reflection of the quality of bearing manufacturing process on the contact fatigue model is discussed. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Seattle, Washington, October 1–4, 2000

Modeling and analytical methods in tribology

Basics of Asymptotic Expansions and Methods Introduction Ordering, Order Sequences, and Asymptotic Expansions Asymptotic Sequences and Expansions Asymptotic Methods Contact Problems for Coated and Rough Surfaces Introduction Some Classic Results for Smooth Elastic Solids Spatial Rough Contacts Modeled by Nonlinear Coating Asymptotic Analysis of Plane Rough Contacts Numerical Methods and Results for Rough Contacts Analysis of Axially Symmetric Rough Contacts An Example of an Application to Roller Bearings Closure Contact Problems with Friction Introduction Plane Frictional Contacts with Fixed Boundaries Plane Frictional Contacts with Free Boundaries Plane Frictional Rough Contacts Modeled by Nonlinear Coating Asymptotic and Numerical Analysis for Large Roughness Closure Rheology of Lubricating Oils Introduction Rheology Relationships for Lubricating Oils Polymer Thickening and Shear Stability Closure Properties of Multi-Grade Lubricating Oils Introduction Multi-Grade Lubricating Oils Viscosity Modifiers Closure Degradation of Linear Polymers Introduction Kinetic Equation for Degrading Linear Polymers Probability of Scission of Linear Polymer Molecules Conditional Probability of Scission for Linear Polymers Lubricant Viscosity and Polymeric Molecules Some Properties of the Kinetic Equation A Limiting Case of the Kinetic Equation Numerical Method for the Kinetic Equation Numerical Solutions of the Kinetic Equation Closure Degradation of Star Polymers Introduction System of Kinetic Equations for Star Polymers Probabilities of Scission Forming Star Polymeric Molecules Approximation of Star Polymer Initial Distribution Lubricant Viscosity and Polymer Distribution Some Properties of the System of Kinetic Equations Numerical Method for Kinetic Equations Numerical Results for Lubricants with Star Polymers Closure Review of Data on Contact Fatigue Introduction Contact and Residual Stresses Material Defects and Lubricant Contamination Bearing Fatigue Life and Contact Friction Crack Development and Material Microstructure Some Contemporary Contact Fatigue Models Closure Fracture Mechanics and Contact Fatigue Introduction Modeling the Vicinity of Crack Tips Perturbations for Multiple Cracks in a Half-Plane Contact Problem for a Cracked Elastic Half-Plane Directions of Fatigue Crack Propagation Lubricant-Crack Interaction: Origin of Fatigue Two-Dimensional Statistical Model of Contact Fatigue Analysis of the Pitting Model Contact Fatigue of Rough Surfaces Three-Dimensional Model of Contact Fatigue Contact Fatigue of Radial Thrust Bearings Closure Analysis of Fluid Lubricated Contacts Introduction Simplified Navier-Stokes and Energy Equations Lightly Loaded Lubrication Regimes Pre-Critical Lubrication Regimes Compressible Fluids in Heavily Loaded Contacts Over-Critical Lubrication Regimes Numerical Solution for EHL Contacts Numerical Solution of Asymptotic Equations Analysis of EHL Contacts for Soft Solids Thermal EHL Problems Regularized Solution of Asymptotic Problems Regularization of the Isothermal EHL Problem Numerical Validation of the Asymptotic Analysis Practical Use of the Asymptotic Solutions Approximations for Non-Newtonian Fluids TEHL Problems for Non-Newtonian Lubricants Regularization for Non-Newtonian Fluids Friction in Heavily Loaded Lubricated Contacts Closure Lubrication by Greases Introduction Formulation of the EHL Problems for Greases Properties of the Problem Solution for Greases Greases in a Contact of Rigid Solids Regimes of Grease Lubrication without Cores Closure Lubricant Degradation in EHL Contacts Introduction EHL for Degrading Lubricants Lubricant Flow Topology Numerical Method for EHL Problems Solutions for Lubricants without Degradation EHL Solutions for Lubricants with Degradation Lubricant Degradation and Contact Fatigue A Qualitative Model of Lubricant Life Closure Non-Steady and Mixed Friction Problems Introduction Properly Formulated Non-Steady EHL Problems Non-Steady Lubrication of a Journal Bearing Starved Lubrication and Lubricant Meniscus Formulation and Analysis of a Mixed Lubrication Problem Dry Narrow Contact of Elastic Solids Closure Index Exercises and Problems appear at the end of each chapter.

Scale Effects in Generalized Newtonian Elastohydrodynamic Films

The prediction of elastohydrodynamic lubrication (EHL) film thickness requires knowledge of the lubricant properties. Today, in many instances, the properties have been obtained from a measurement of the central film thickness in an optical EHL point contact simulator and the assumption of a classical Newtonian film thickness formula. This technique has the practical advantage of using an effective pressure-viscosity coefficient which compensates for shear-thinning. We have shown by a perturbation analysis and by a full EHL numerical solution that the practice of extrapolating from a laboratory scale measurement of film thickness to the film thickness of an operating contact within a real machine may substantially overestimate the film thickness in the real machine if the machine scale is smaller and the lubricant is shear-thinning in the inlet zone.Copyright

Modern State of Experimentation and Modeling in Contact Fatigue Phenomenon: Part I—Contact Fatigue. Normal and Tangential Contact and Residual Stresses. Nonmetallic Inclusions and Lubricant Contamination. Crack Initiation and Crack Propagation. Surface and Subsurface Cracks

The purpose of this paper is to describe the modern understanding of the contact fatigue phenomenon which occurs in different materials under various loading conditions. Part I presents experimental and theoretical knowledge of the influence of normal and factional contact and residual stresses on contact fatigue. It analyzes relationships between contact fatigue and material defects, inclusions, and lubricant contamination. Furthermore, it discusses crack initiation and crack propagation, the effect of material microstructure on contact fatigue life as well as some theoretical results for surface and subsurface cracks. Part II is devoted to reviewing the existing mathematical models of fatigue life for bearings and gears and to describing a new statistical model of contact fatigue based on contact and fracture mechanics. This new model is based on the assumptions derived from the analysis of the data presented in Part I. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference In Orlando, Florida, October 11–13, 1999

Formulation and Analysis of EHL Problems for Soft Materials

This paper presents a qualitative and numerical analysis of the new formulation of a steady problem for lubricated rollers made of elastic materials with low Youngs modulus. The feature that makes this formulation different from the classic one is that the linear velocities of the surfaces take into account tangential deformations of elastic materials. Therefore, in Reynolds equation, the surface linear velocities are represented by functions of the location in the contact region instead of constants. The new formulation predicts the formation of a significant depression (dimple) in the contact surfaces of soft materials as opposed to flat surfaces in the classic EHL theory, The paper also describes the dependence of dimple sizes on problem parameters.

Modeling of Kinetics of Stress-Induced Degradation of Polymer Additives in Lubricants and Viscosity Loss

A fundamental approach to the problem of modeling mechanically induced polymer degradation is proposed. The polymer degradation is modeled by a kinetic equation for the density of the statistical distribution of linear polymer molecules as a function of their molecular weight. The integrodifferential kinetic equation is solved numerically. A comparison of numerically calculated molecular weight distributions and lubricant viscosity loss caused by polymer degradation with experimental ones obtained in bench tests showed that they are in excellent agreement. The effects of pressure, shear, temperature, and lubricant viscosity on lubricant degradation are considered. The increase of pressure promotes fast degradation while the increase of temperature depending on other parameters may delay or promote degradation. In some cases, the density of the molecular weight distribution function maintained its initial single-modal shape and in other cases it changed with time from a single-modal shape to a multi-modal one. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Cancun, Mexico October 27–30, 2002

Lubricant-Crack Interaction, Origin of Pitting, and Fatigue of Drivers and Followers

A mechanical model for lubricated elastic solids weakened by cracks is studied. The model is used to explain mechanisms of surface and subsurface originated contact fatigue. Subsurface and surface cracks are considered including the interaction of lubricant with elastic solids within cavities of surface cracks. The adequate boundary conditions for the crack displacement jumps and normal stress applied to crack faces within the surface crack cavities fully or partially filled with lubricant as well as for subsurface cracks arc used. These boundary conditions include conditions that: prevent crack faces from overlapping, describe multiple surface crack cavities fully or partially filled with lubricant etc. Numerical results for surface and subsurface cracks are discussed, and numerical and asymptotic results for small subsurface cracks are compared. It is shown that stress intensity factors for surface cracks may be two orders of magnitude higher than those for subsurface cracks. Based on the crack analysis it is shown that pitting has predominantly subsurface origin. Moreover, an explanation of the difference in fatigue behavior of followers and drivers is presented. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Cancun, Mexico October 27–30, 2002

On Formulation of a Non-Steady Lubrication Problem for a Non-Conformal Contact©

A formulation of a non-steady problem for elastohydrodynamically lubricated (EHL) non-conformal contact is considered. It takes into account elasticity of contact bodies, lubricant viscosity and changing in time location of the inlet boundary, velocities of the contact surfaces and applied load. The main goal of this paper is to propose a “modified” formulation of the problem free of certain defects. A “traditional” and “modified” formulations of the problem, leading to discontinuous and smooth solutions in cases of abrupt changes in external load applied to a contact and linear velocities of its surfaces, are considered. For the case of purely squeezed lubrication film, an analytical and numerical analysis of the dynamic response of a lubricated contact to abrupt changes in external load is performed. It is shown that in the case of purely squeezed rigid surfaces it takes infinite time to bring the surfaces in direct contact, i.e. theoretically, the film thickness never reaches zero. Presented as a Socie...

Lubricants with non-Newtonian rheology and their degradation in line contacts

A plane isothermal elastohydrodynamic problem for a line contact lubricated by a degrading fluid with non-Newtonian rheology is studied. The lubricant is represented by a base stock with a polymer additive which undergoes stress-induced degradation caused by scission of polymer molecules. The polymer molecules are considered to be of linear structure. The effective lubricant viscosity experiences reversible and irreversible losses. The reversible loss of the effective lubricant viscosity (shear thinning) is due to the non-Newtonian rheology of the fluid and variations in the fluid shear rate. The irreversible loss of the effective lubricant viscosity is caused by the degradation process of the polymer additive dissolved in the lubricant. The degradation process of the polymer additive while it passes through the contact is described by a kinetic equation. The kinetic equation is solved along the lubricant flow streamlines. The solution of the kinetic equation predicts the density of the probabilistic distribution of the polymer molecular weight versus polymer molecule chain length. The changes in the distribution of polymer molecular weight affect local lubricant properties. In particular, the lubricant viscosity experiences reversible and irreversible losses and, in general, is a discontinuous function. The changes in the lubricant viscosity alter virtually all parameters of the lubricated contact such as film thickness, friction stresses, pressure, and gap. The considered non-Newtonian rheology of the lubricant causes a small reversible loss of its viscosity As a result of the polymer additive degradation the lubricant may experience a significant irreversible loss of its viscosity which, in turn, leads to a noticeable reduction in the lubrication film thickness in comparison with the case of a non-degrading lubricant with similar rheology. Some comparisons between the cases of lubricants with Newtonian and non-Newtonian rheologies with and without lubricant degradation are considered.