1st Edition

Elastohydrodynamic Lubrication for Line and Point Contacts Asymptotic and Numerical Approaches

By Ilya I. Kudish Copyright 2013
    712 Pages 153 B/W Illustrations
    by CRC Press

    712 Pages 153 B/W Illustrations
    by CRC Press

    Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches describes a coherent asymptotic approach to the analysis of lubrication problems for heavily loaded line and point contacts. This approach leads to unified asymptotic equations for line and point contacts as well as stable numerical algorithms for the solution of these elastohydrodynamic lubrication (EHL) problems.

    A Unique Approach to Analyzing Lubrication Problems for Heavily Loaded Line and Point Contacts

    The book presents a robust combination of asymptotic and numerical techniques to solve EHL problems for lightly and heavily loaded line and point contacts. It also proposes a reasonably simple and naturally based regularization approach that produces stable solutions in heavily loaded EHL contacts. The book offers a clear understanding of the processes taking place in heavily loaded line and point EHL contacts as well as of the proper solution structure for EHL problems. It outlines concrete ways to determine important design parameters such as lubrication film thickness and frictional stresses and forces. The book establishes a close link between EHL problems for heavily loaded point and line contacts.

    Fine Tune Your Methods for Solving Elastohydrodynamic Lubrication Problems

    In most cases, the equations in the book are derived from first principles. The author describes each of the asymptotic and numerical methods in detail, making it easier for readers to apply them to various problems. The problem solutions are presented in the form of simple analytical formulas, graphs, and tables. Almost all the chapters include exercises that highlight key points and skills. Suitable for engineering and applied mathematics students, this is also a unique resource for researchers and practitioners who want to fine tune their solution methods and design better numerical methods to tackle elastohydrodynamic lubrication problems.

    I Basic Properties of Solids and Fluids Involved in Lubricated Contacts

    Basic Properties and Rheology of Lubricating Oils
    Introduction
    Rheology Relationships for Lubricating Oils
    Polymer Thickening and Shear Stability
    Closure
    Exercises and Problems
    References

    Basic Properties of Elastic Solids
    Introduction
    Material Density
    Material Elastic Properties
    Material Thermal Diffusivity and Specific Heat Capacity
    Closure
    References

    II Asymptotic Methods and Relationships Relevant to Elastohydrodynamic Lubrication Theory

    Basics of Asymptotic Expansions and Methods
    Introduction
    Ordering, Order Sequences, and Asymptotic Expansions
    Asymptotic Sequences and Expansions
    Asymptotic Methods
    Closure
    Exercises and Problems
    References

    Basics of the Theory of Elastohydrodynamically Lubricated (EHL) Contacts
    Introduction
    Simplified Navier-Stokes and Energy Equations
    Some Classic Results for Smooth Elastic Solids
    Closure
    Exercises and Problems
    References

    III EHL Problems for Lightly Loaded Line and Point Contacts

    Lightly Loaded Lubrication Regimes for Line and Point Contacts
    Introduction
    Lightly Loaded Lubrication Regimes for Line Contacts
    Asymptotic Approach to Lightly Loaded Point EHL Problems
    Closure
    Exercises and Problems
    References

    IV Isothermal EHL Problems for Heavily Loaded Line Contacts with Newtonian Lubricant

    Asymptotic Approaches to Heavily Loaded Lubricated Line Contacts
    Introduction
    Numerical Solution for EHL Contacts
    Pre-Critical Lubrication Regimes
    Practical Use of the Asymptotic Solutions
    Compressible Fluids in Heavily Loaded Contacts
    Over-Critical Lubrication Regimes
    Choosing Pre- or Over-Critical Lubrication Regimes
    Analysis of the Ertel-Grubin Method
    Numerical Solution of Asymptotic Equations
    Numerical Validation of the Asymptotic Analysis
    Numerical Precision, Grid Size, and Stability Considerations
    Closure
    Exercises and Problems
    References

    V Isothermal and Thermal EHL Problems for Line Contacts and Lubricants with Newtonian and Non-Newtonian Rheologies

    Thermal EHL Problems for Line Contacts
    Introduction
    Formulation of TEHL Problem
    Analytical Approximations for Newtonian Fluids in TEHL Contacts
    Numerical Solutions of Asymptotic TEHL Problems for Newtonian Lubricants
    Closure
    Exercises and Problems
    References

    Regularization of the Isothermal EHL Problems
    Introduction
    Regularized Solution of Asymptotic Problems
    Numerical Method for the Isothermal EHL Problem
    Some Numerical Solutions of the Regularized Isothermal EHL Problem
    Closure
    Exercises and Problems
    References

    Approximations for Non-Newtonian Fluids in Line Contacts
    Introduction
    Formulation of Isothermal Line EHL Problem for Non-Newtonian Fluids
    Isothermal Line EHL Problem for Pure Rolling. Pre- and Over-Critical Lubrication Regimes. Some Numerical Examples
    Isothermal Line EHL Problem for Relatively Large Sliding. Pre- and Over-Critical Lubrication Regimes
    Choosing Pre- and Over-critical Lubrication Regimes for Non-Newtonian Lubricants
    Closure
    Exercises and Problems
    References

    TEHL Problems for Non-Newtonian Lubricants in Line Contacts
    Introduction
    TEHL Problem Formulation for Non-Newtonian Fluids
    Asymptotic Analysis of the Problem for Heavily Loaded Line Contacts
    Heat Transfer in the Contact Solids
    Regularization for Non-Newtonian Fluids
    Friction in Heavily Loaded Lubricated Contacts
    Closure
    Exercises and Problems
    References

    VI Stress-Induced Lubricant Degradation in Line EHL Contacts

    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
    Closure
    Exercises and Problems
    References

    VII Isothermal and Thermal EHL Problems for Point Contacts and Lubricants with Different Rheologies

    Isothermal EHL Problems for Heavily Loaded Point Contacts with Newtonian Lubricants
    Introduction
    Problem Formulation
    Pre-Critical Lubrication Conditions
    Over-Critical Lubrication Conditions
    Discussion and Validation of Results
    Closure
    Exercises and Problems
    References

    Isothermal EHL Point Contacts with Skewed Direction of Entrained Lubricant
    Introduction
    Problem Formulation
    Pre-Critical Lubrication Conditions
    Over-Critical Lubrication Conditions
    Closure
    Exercises and Problems
    References

    Lubricated Heavily Loaded Rolling and Spinning Ball in a Grooved Raceway
    Introduction
    Problem Formulation
    Case of Pure Spinning
    Pre-Critical Lubrication Conditions
    Over-Critical Lubrication Conditions
    Closure
    Exercises and Problems
    References

    Thermal EHL Problems for Heavily Loaded Point Contacts with Newtonian Lubricants
    Introduction
    Problem Formulation
    Asymptotic Solution for the Lubricant Temperature T. Case of Not Spinning EHL Contact
    Approximations of Sliding Frictional Stresses. No Spinning EHL Contact Case
    Asymptotic Solution for the Lubricant Temperature T. Case of EHL Contact with Spinning
    Regularization Approaches to Solution of Isothermal Point EHL Problems
    Closure
    Exercises and Problems
    References

    Isothermal EHL Problems for Heavily Loaded Point Contacts. Non-Newtonian Lubricants
    Introduction
    Problem Formulation
    Case of Pure Rolling
    Case of High Slide-to-Roll Ratio. Approximation of the Reynolds Equation
    Closure
    Exercises and Problems
    References

    Thermal EHL Problems for Heavily Loaded Point Contacts. Non-Newtonian Lubricants
    Introduction
    Problem Formulation
    Solutions for fx and fy. High Slide-to-Roll Ratio
    Solution for Lubricant Temperature T. High Slide-to-Roll Ratio
    Approximate Reynolds Equation. High Slide-to-Roll Ratio
    Straight Lubricant Entrainment. High Slide-to-Roll Ratio
    Skewed Lubricant Entrainment without Spinning. High Slide-to-Roll Ratio
    Skewed Lubricant Entrainment with Spinning. High Slide-to-Roll Ratio
    Regularization Approach
    Closure
    Exercises and Problems
    References

    VIII Some Other Topics in Elastohydrodynamic Lubrication

    Analysis of EHL Contacts for Soft Solids
    Introduction
    Formulation of an EHL Problem for Soft Solids
    Qualitative Analysis of the EHL Problem
    Surface Velocities for Soft Solids
    Dimensionless Variables and Numerical Method
    Numerical Results and Discussion
    Closure
    Exercises and Problems
    References

    Non-Newtonian Lubricants and Scale Effects
    Introduction
    Results of Perturbation Analysis
    Application of Analytical Result to an EHL Experiment
    Numerical Solution
    Application of Numerical Results to an EHL Experiment
    Closure
    Exercises and Problems
    References

    Lubrication of Line Contacts 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
    Exercises and Problems
    References

    Non-Steady EHL Problems
    Introduction
    Properly Formulated Non-Steady EHL Problems
    Non-Steady Lubrication of a Journal Bearing
    Closure
    Exercises and Problems
    References

    Lubricant Starvation and Mixed Friction Problems for Point Contacts
    Introduction
    Starved Lubrication and Lubricant Meniscus
    Formulation and Analysis of a Mixed Lubrication Problem
    Dry Narrow Contact of Elastic Solids
    Closure
    Exercises and Problems
    References

    Final Remarks
    Introduction
    EHL Contacts for Rough Surfaces
    Lubricant Degradation
    Contact Fatigue
    References

    Biography

    Ilya I. Kudish is a professor of mathematics at Kettering University in Flint, Michigan. He is a recipient of all Kettering University research awards—Outstanding New Researcher, Outstanding Applied Researcher, Outstanding Researcher, and Distinguished Researcher Awards—as well as of Rodes and Oswald Professorships. Dr. Kudish is a Fellow of the American Society of Mechanical Engineers (ASME). He has served as a consultant to Caterpillar, Inc. and as a visiting professor at Purdue University (USA), Cardiff University (UK), and INSA (France). Dr. Kudish’s main interests are in the sphere of application mathematical methods to various problems of tribology. Over the years he has made theoretical contributions to the fields of elastohydrodynamic lubrication, stress-induced lubricant degradation, contact problems for coated/rough elastic solids, fracture mechanics, and fracture mechanics-based contact and structural fatigue modeling.

    "Elastohydrodynamic lubrication (EHL) is a relatively new area in the development of lubrication theory and practice. This monograph is devoted to selected performances of liquid lubricants, particularly mineral oils and synthetic fluids. … combines asymptotic and numerical techniques to solve EHL problems for line and point contacts. Most chapters include exercises with different levels of difficulty."
    Mathematical Reviews, January 2015

    "… the present work uses completely different mathematical tools represented by asymptotic methods. … they enable to obtain very elegant and useful limiting solutions that accompany numerical methods or gave answers to stiff problems where these later techniques converge with difficulty or fail. The book is very well written, with an excellent mathematical background and bridges in a successful manner the gap between mathematics and technology. The reviewer strongly recommends the book to all lubrication scientists from academy or industry."
    —Mihai ARGHIR, Université de Poitiers, France

    "This book offers a comprehensive approach to the solution of the elastohydrodynamic lubrication (EHL) problem under a wide variety of operating conditions/regimes using a combination of asymptotic and numerical techniques. It also offers insight into physical aspects and phenomena governing the EHL problem such as lubricant rheology (Newtonian and non-Newtonian), solid properties, lubricant degradation, kinematic considerations, soft solids, grease lubrication, non-steady operation, starvation, [and] mixed friction … In addition, a variety of problems are offered at the end of each chapter, helping readers reach a higher level of understanding of the complex nature of the EHL problem."
    —Wassim Habchi, Lebanese American University, Byblos, Lebanon

    "This book introduces to the tribology community the application of asymptotic methods to solve an important and difficult class of problems in lubrication. These analytical techniques overcome some limitations of traditional numerical schemes for determining EHL film thickness and, moreover, aid in the development of insight as to the physical mechanisms at play. …like the comprehensive coverage of EHL regimes: line and point contacts, lightly and heavily loaded conditions, Newtonian and non-Newtonian rheology, isothermal and thermal behavior, steady-state and transient conditions. I also like that the author provides a detailed introduction to lubricant rheology. …I am confident that the work is both technically sound and practically relevant. The author appears to take care in providing a systematic and rigorous treatment and conveys a good appreciation for the engineering implications of his work. …This book provides a welcome contribution to the topic of elastohydrodynamic lubrication (EHL), which is critically relevant to the operation of gears, rolling element bearings and several other machine components. The author demonstrates pitfalls associated with traditional numerical approaches and effectively applies analytical asymptotic methods to develop solutions for various EHL regimes, including those with thermal, non-Newtonian and transient effects. …This book introduces researchers in tribology to a powerful mathematical technique that promises to advance lubrication theory."
    ––Jeffrey L. Streator, G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, USA