Mechano-Chemical Modelling of Boundary Lubrication By Ali Ghanbarzadeh Submitted in accordance with the requirements for the degree of Doctor of Philosophy The University of Leeds School of Mechanical Engineering Leeds, UK March, 2016 I The candidate confirms that the work submitted is his own, except where work which has formed part of jointly-authored publications has been included. The candidate confirms that appropriate credit has been given within the thesis where reference has been made to the work of others. In all the papers listed below, Ali Ghanbarzadeh completed all the numerical work. Pourya Parsaeian has carried out the wear and MTM/SLIM measurements and Elio Piras has conducted the experiments to validate the surface topography predictions. All authors contributed to proof reading of the articles prior to publication. Papers contributing to this thesis:  Ghanbarzadeh, A., Wilson, M., Morina, A., Dowson, D., & Neville, A. (2016). Development of a new mechano-chemical model in boundary lubrication. Tribology International, 93, 573-582.  Ghanbarzadeh, A., Parsaeian, P., Morina, A., Wilson, M. C., van Eijk, M. C., Nedelcu, I.. & Neville, A. (2016). A Semi-deterministic Wear Model Considering the Effect of Zinc Dialkyl Dithiophosphate Tribofilm. Tribology Letters, 61(1), 1-15.  Ghanbarzadeh, A., Piras, E., Nedelcu, I., Wilson, M., Morina, A., Dowson, D., Neville, A. Zinc Dialkyl Dithiophosphate Antiwear Tribofilm and its Effect on the Topography Evolution of Surfaces: A Numerical and Experimental Study. Submitted to Wear.  Ghanbarzadeh, A., Wilson, M., Morina, A., Dowson, D., & Neville, A., A New Boundary Element Method for Contact Mechanics of Moving Rough Surfaces, Submitted to European Journal of Computational Mechanics Conferences presented: • Ali Ghanbarzadeh et al. Mechano-Chemical Numerical Modelling of Boundary Lubrication, 41st Leeds-Lyon Symposium on Tribology, Leeds 2014. • Ali Ghanbarzadeh et al. Chemo-Mechanical Numerical Modelling of Boundary Lubrication, STLE 69th Annual Meeting, Orlando Florida, USA 2014. • Ali Ghanbarzadeh et al, Analytical and Experimental Study of Tribofilm Growth Generated by Zinc Dialkyl Dithiophosphate and its Effect on Wear 42st Leeds-Lyon Symposium on Tribology, Lyon 2015 • Ghanbarzadeh A et al, A Semi-deterministic Wear Model Considering the Effect of Zinc Dialkyl Dithiophosphate Tribofilm, TurkeyTrib 2015 II This copy has been supplied on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. Assertion of moral rights: The right of Ali Ghanbarzadeh to be identified as Author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. © 2016 The University of Leeds and Ali Ghanbarzadeh III Acknowledgements First of all, I would like to express my sincere gratitude and special appreciation to my great supervisors Dr Mark Wilson, Professor Ardian Morina and Professor Anne Neville for their help, guidance and also being supportive and encouraging through my PhD. They have been tremendous mentors and this work would not have been possible without their support. I would also show my appreciation to ENTICE consortium which gave a great opportunity to interact with experts in the field of tribology/tribochemistry. I would like to thank Professor Duncan Dowson for the time he has put on sharing his knowledge, experience and passion on my PhD. His advice and guidance have been invaluable. I am also thankful to the members of iFS research group, especially to Ali, Thibaut, Michael, Filippo, Erfan, Abdullah, James, Earle, Evan, Doris, Vishal, Shahriar, Joe, Pourya, Fredrick, Siavash, John, Rick, Fiona, Lukman, Mohsen, Zahra, Farnaz, Macdonald, Elio, Nadia and Wassim. I would also like to thank my friends, especially Pouya, Ali, Neda, Mostafa and Reza. I especially thank my mom (Roshanak Oliyaei), dad (Mehdi Ghanbarzadeh), brother (Khashayar) and grandparents (Fatemeh, Ehteram and Ramzanali) for their continuous support, encouragement and love. I am also thankful to Nasser and Nassim, my cousins, who gave me the opportunity to travel to UK and helped me with finding the suitable PhD. IV ABSTRACT Boundary lubrication is known to be significantly important in the design of machine parts. The decrease in the efficiency of the system as well as its durability when operating in boundary lubrication conditions highlights the importance of this regime. Boundary lubrication involves many different physical, chemical and mechanical phenomena which make it difficult to understand the real mechanisms of friction, wear and lubrication. Tribochemistry is undoubtedly one of the most important processes occurring in boundary lubrication. Modelling such a complicated process needs a robust physical and chemical modelling framework that is capable of capturing different phenomena. The majority of the modelling attempts in boundary lubrication covers the contact mechanics of rough surfaces with different numerical approaches. Despite the importance of the tribochemistry and its effect in reducing friction and wear of boundary lubricated contacts, there is no comprehensive modelling framework that considers tribochemistry into the boundary lubrication models. In this work, tribochemistry was implemented into the deterministic contact mechanics simulation for elastic-perfectly plastic contact of rough surfaces. A tribochemical model for the growth of the ZDDP antiwear additive was developed based on the thermodynamics of interfaces that combines formation and removal of the tribofilm. The tribochemical model was then coupled with the contact mechanics model which was developed based on potential energy principles. A modification to Archard’s wear equation was proposed which accounts for the role of ZDDP tribofilm V in reducing the wear. This model was proposed based on the experimental observations of ZDDP in reducing wear. The numerical framework was then validated against experiments. The wear prediction capability of the model was validated against experiments from Mini- Traction Machine in a rolling/sliding contact. The model is able to predict changes in the topography of the surfaces and this was validated with experiments on a Micro Pitting Rig (MPR). The model shows a good potential in capturing the behaviours in boundary lubrication and opens new ways for further developments and testing the effect of different parameters in tribochemistry and wear. It can give insights in better understanding the real mechanisms of tribochemistry and also help in optimizing boundary lubricated contacts. VI VII Table of Contents Acknowledgements .................................................................................................. IV ABSTRACT .............................................................................................................. V Table of Figures .................................................................................................... XIII List of Tables ......................................................................................................... XX Chapter 1. Introduction .................................................................................... 1 1.1 Motivation for Research ............................................................................ 1 1.2 Literature Gaps, Aims and Objectives ...................................................... 3 1.3 Structure of Thesis .................................................................................... 3 Chapter 2. Fundamentals of Tribology, Lubrication and Wear ................... 5 2.1 Introduction ............................................................................................... 5 2.2 What is Tribology? .................................................................................... 5 2.3 Lubrication, Friction and Wear ................................................................. 6 2.3.1 Wear Mechanisms .......................................................................... 11 2.3.1.1 Adhesive Wear ............................................................... 12 2.3.1.2 Abrasive Wear ................................................................ 13 2.3.1.3 Corrosive Wear .............................................................. 14 2.3.1.4 Fatigue Wear .................................................................. 14 2.3.1.5 Erosive Wear .................................................................. 15 2.3.2 Friction Mechanisms ...................................................................... 15 2.3.3 Running-in ..................................................................................... 16 2.3.3.1 Friction ........................................................................... 17 2.3.3.2 Wear ............................................................................... 17 2.3.3.3 Surface Roughness ......................................................... 18 2.3.3.4 Attempts at Modelling Running-in ................................ 19 2.3.4 Boundary Lubrication .................................................................... 19 2.3.4.1 Antiwear Additives ........................................................ 21 2.3.4.2 Friction Modifiers .......................................................... 21 2.4 Summary ................................................................................................. 21 Chapter 3. ZDDP as an Antiwear Additive: A Review of the Literature. ....................................................................................................... 23 3.1 Mechanical Properties ............................................................................. 25 3.2 Tribofilm Growth .................................................................................... 28 3.3 Tribochemistry of ZDDP ........................................................................ 31 VIII 3.4 Stability of ZDDP ................................................................................... 34 3.5 ZDDP on Non-Ferrous Surfaces ............................................................. 35 3.6 Summary ................................................................................................. 36 Chapter 4. Boundary Lubrication Modelling: A Review of the Literature ……………………………………………………….....................38 4.1 Introduction ............................................................................................. 38 4.2 Modelling Methods in Boundary Lubrication......................................... 43 4.2.1 Molecular Dynamics ...................................................................... 43 4.2.1.1 Simulation of Atomic Friction ....................................... 44 4.2.1.2 Simulation of Contact Mechanics .................................. 47 4.2.1.3 Tribochemical Aspects ................................................... 49 4.2.2 Finite Element Method (FEM) ....................................................... 53 4.2.3 Discrete Element Method (DEM) .................................................. 57 4.2.4 Boundary Element Method (BEM) ................................................ 58 4.2.5 Surface Generation ......................................................................... 60 4.3 Contact Mechanics .................................................................................. 61 4.3.1 Variational Principle ...................................................................... 65 4.3.2 Boussinesq Potential Solution ........................................................ 67 4.3.3 Tribofilm Properties ....................................................................... 71 4.3.4 Numerical Implementation............................................................. 75 4.3.5 Contact Mechanics Numerical Implementations ........................... 76 4.3.6 Fast Fourier Transformation (FFT) ................................................ 79 4.3.7 Frictional Heating and Flash Temperature ..................................... 80 4.3.8 Implementation of Wear Equation ................................................. 82 4.4 Tribochemistry and the Film Formation/Removal Effect on Wear and Friction ............................................................................................. 84 4.4.1 Tribofilm Growth ........................................................................... 85 4.5 Tribofilm Formation and Removal Models ............................................ 89 4.5.1 Spikes’ Model ................................................................................ 90 4.5.2 Andersson’s Model: ....................................................................... 92 4.5.3 Diffusion Model: ............................................................................ 93 4.5.4 Turing (Diffusion-Reaction) Systems: ........................................... 95 4.6 Thermodynamics of Friction and Wear: ................................................. 98 4.6.1 Thermodynamic Analysis of Tribofilm Growth: ........................... 98 4.6.2 Tribo-activation: ........................................................................... 101 IX 4.7 Summary ............................................................................................... 103 Chapter 5. Development of the Contact Mechanics Model ....................... 105 5.1 Boundary Lubrication Modelling and Tribochemistry ......................... 105 5.2 Introduction to the Contact Mechanics Model ...................................... 109 5.3 Rough Surface Generation .................................................................... 110 5.4 Contact of Rough Surfaces.................................................................... 114 5.5 Direct Quadratic Mathematical Programming ...................................... 119 5.6 Elastic-Perfectly Plastic Contact Model................................................ 122 5.7 Movement of the Contacting Surfaces .................................................. 123 5.8 New Surface Movement Strategy ......................................................... 123 5.9 Fast Fourier Transform (FFT) Implication ........................................... 128 5.10 Tribofilm Mechanical Properties .......................................................... 129 5.11 Flash Temperature Calculation ............................................................. 131 5.12 Results ................................................................................................... 133 5.12.1 Influence Matrix .................................................................. 133 5.12.2 Contact Pressure for Static Contact..................................... 134 5.12.3 Movement of the Surfaces .................................................. 134 5.12.4 Plastic Deformations ........................................................... 135 5.12.5 Flash Temperature ............................................................... 136 5.13 Summary ............................................................................................... 136 Chapter 6. Tribofilm Growth Model Development ................................... 140 6.1 Introduction ........................................................................................... 140 6.2 Thermodynamics of Interfaces .............................................................. 141 6.3 The Tribochemical Reaction Kinetics Model ....................................... 142 6.4 Tribofilm Formation Model .................................................................. 148 6.5 Tribofilm Removal ................................................................................ 150 6.6 Results ................................................................................................... 152 6.6.1 Calibration .................................................................................... 153 6.6.1.1 Effect of ZDDP Concentration on x ........................ 155 tribo 6.6.1.2 Effect of Temperature on x ..................................... 159 tribo 6.6.2 Tribofilm Growth ......................................................................... 161 6.6.3 Inhomogeneity of the Tribofilm ................................................... 163 6.6.4 Tribofilm Coverage ...................................................................... 164 6.6.5 Effect of Load .............................................................................. 166 X