Modeling and Analytical Methods in Tribology

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.

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.

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 SolidsSpatial Rough Contacts Modeled by Nonlinear CoatingAsymptotic Analysis of Plane Rough ContactsNumerical Methods and Results for Rough ContactsAnalysis of Axially Symmetric Rough ContactsAn Example of an Application to Roller Bearings Closure

Contact Problems with Friction Introduction Plane Frictional Contacts with Fixed BoundariesPlane Frictional Contacts with Free BoundariesPlane Frictional Rough Contacts Modeled by Nonlinear Coating Asymptotic and Numerical Analysis for Large Roughness Closure

Rheology of Lubricating OilsIntroduction Rheology Relationships for Lubricating OilsPolymer Thickening and Shear StabilityClosure

Properties of Multi-Grade Lubricating OilsIntroductionMulti-Grade Lubricating OilsViscosity ModifiersClosure

Degradation of Linear PolymersIntroduction 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 EquationsNumerical 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 TipsPerturbations for Multiple Cracks in a Half-PlaneContact Problem for a Cracked Elastic Half-PlaneDirections of Fatigue Crack Propagation Lubricant-Crack Interaction: Origin of FatigueTwo-Dimensional Statistical Model of Contact FatigueAnalysis of the Pitting ModelContact Fatigue of Rough SurfacesThree-Dimensional Model of Contact FatigueContact Fatigue of Radial Thrust BearingsClosure

Analysis of Fluid Lubricated Contacts Introduction Simplified Navier–Stokes and Energy Equations Lightly Loaded Lubrication RegimesPre-Critical Lubrication RegimesCompressible Fluids in Heavily Loaded Contacts Over-Critical Lubrication RegimesNumerical Solution for EHL Contacts Numerical Solution of Asymptotic EquationsAnalysis of EHL Contacts for Soft SolidsThermal EHL ProblemsRegularized Solution of Asymptotic Problems Regularization of the Isothermal EHL ProblemNumerical Validation of the Asymptotic Analysis Practical Use of the Asymptotic Solutions Approximations for Non-Newtonian FluidsTEHL Problems for Non-Newtonian LubricantsRegularization 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 ProblemsSolutions for Lubricants without Degradation EHL Solutions for Lubricants with Degradation Lubricant Degradation and Contact FatigueA Qualitative Model of Lubricant Life Closure
Non-Steady and Mixed Friction ProblemsIntroduction Properly Formulated Non-Steady EHL ProblemsNon-Steady Lubrication of a Journal BearingStarved Lubrication and Lubricant MeniscusFormulation and Analysis of a Mixed Lubrication ProblemDry Narrow Contact of Elastic SolidsClosure
Index
Exercises and Problems appear at the end of each chapter.