Modeling and Analytical Methods in Tribology: 1st Edition (Hardback) book cover

Modeling and Analytical Methods in Tribology

1st Edition

By Ilya I. Kudish, Michael Judah Covitch

Chapman and Hall/CRC

928 pages | 308 B/W Illus.

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Hardback: 9781420087017
pub: 2010-07-20
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Improving our understanding of friction, lubrication, and fatigue, Modeling and Analytical Methods in Tribology presents a fresh approach to tribology that links advances in applied mathematics with fundamental problems in tribology related to contact elasticity, fracture mechanics, and fluid film lubrication. The authors incorporate the classical tenets of tribology while providing new mathematical solutions that address various shortcomings in existing theories.

From contact interactions to contact fatigue life, the book connects traditionally separate areas of tribology research to create a coherent modeling methodology that encompasses asymptotic and numerical techniques. The authors often demonstrate the efficacy of the models by comparing predictions to experimental data. In most cases, they derive equations from first principles. They also rigorously prove problem formulations and derive certain solution properties. Solutions to problems are presented using simple analytical formulas, graphs, and tables. In addition, the end-of-chapter exercises highlight points important for comprehending the material and mastering the appropriate skills.

Unlocking the secrets that govern the physics of lubricated and dry contacts, this book helps tribologists on their quest to reduce friction, minimize wear, and extend the operating life of mechanical equipment. It provides a real-world industrial perspective so that readers can attain a practical understanding of the material.

Table of Contents

Basics of Asymptotic Expansions and Methods


Ordering, Order Sequences, and Asymptotic Expansions

Asymptotic Sequences and Expansions

Asymptotic Methods

Contact Problems for Coated and Rough Surfaces


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


Contact Problems with Friction


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


Rheology of Lubricating Oils


Rheology Relationships for Lubricating Oils

Polymer Thickening and Shear Stability


Properties of Multi-Grade Lubricating Oils


Multi-Grade Lubricating Oils

Viscosity Modifiers


Degradation of Linear Polymers


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


Degradation of Star Polymers


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


Review of Data on Contact Fatigue


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


Fracture Mechanics and Contact Fatigue


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


Analysis of Fluid Lubricated Contacts


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


Lubrication by Greases


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


Lubricant Degradation in EHL Contacts


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


Non-Steady and Mixed Friction Problems


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



Exercises and Problems appear at the end of each chapter.

About the Authors

Ilya I. Kudish is a mathematics professor at Kettering University in Flint, Michigan. Dr. Kudish is a Fellow of the American Society of Mechanical Engineers (ASME) and Associate Editor of the ASME Journal of Tribology.

Michael J. Covitch is a Senior Fellow at the Lubrizol Corporation in Wickliffe, Ohio. Dr. Covitch is the Secretary of the Society of Automotive Engineers (SAE) Engine Oil Viscosity Classification task force and a recipient of the SAE Excellence in Oral Presentation and Forest R. McFarland awards.

About the Series

Modern Mechanics and Mathematics

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