Simulations of Contact Mechanics and Wear of Linearly Reciprocating Block-On-Flat Sliding Test

Simulations of contact mechanics and wear of linearly reciprocating block-on-flat sliding test André Rudnytskyj Mechanical Engineering, master's level (120 credits) 2018 Luleå University of Technology Department of Engineering Sciences and Mathematics Simulations of contact mechanics and wear of linearly reciprocating block-on-flat sliding test AndréRudnytskyj Master programme in Tribology of Surfaces and Interfaces - TRIBOS 4th ed. Enrollment Semester Autumn 2016. Department of Engineering Sciences and Mathematics Lule˚aUniversity of Technology ©Lule˚aUniversity of Technology, 2018. This document is freely available at www.ltu.se Preface This master’s thesis was carried out at the Division of Machine Elements, Depart- ment of Engineering Sciences and Mathematics of Lule˚aUniversity of Technology (LTU), in Sweden. It was made possible through the Joint Erasmus Mundus Mas- ter Course (EMMC) TRIBOS (Tribology of Surface and Interfaces), of which I took part in its 4th generation between the years of 2016 to 2018. I would like to thank the Education, Audiovisual and Culture Executive Agency (EACEA) of the European Union and the TRIBOS programme coordinators, pro- fessors, tutors, lecturers, and everyone involved in the programme from the Uni- versity of Leeds (UK), the University of Ljubljana (Slovenia), the University of Coimbra (Portugal), and Lule˚aUniversity of Technology (LTU) for their support inside and outside the classroom. I also thank the people directly involved in the development of the thesis for their helpful support and discussions throughout the time of this work. AndréRudnytskyj Lule˚a,June 2018 I Abstract The use of computational methods in tribology can be a valuable approach to deal with engineering problems, ultimately saving time and resources. In this work, a model problem and methodology is developed to deal with a common situation found in experiments in tribology, namely a linearly reciprocating block-on-flat dry sliding contact. The modelling and simulation of such case would allow a better understanding of the contact pressure distribution, wear and geometry evolution of the block as it wears out during a test. Initially, the introduction and motivation for this work is presented, followed by a presentation of relevant scientific topics related to this work. Wear modelling of published studies are reviewed next, along with studies available in the literature and the goals for this thesis. The fourth section refers to the methodology used and the built-up of the model problem. In this work the Finite Element Method and Archard’s wear model through COMSOL Multiphysics® and MATLAB® are used to study the proposed contact problem. The construction of the model problem is detailed and the procedure for wear, geometry update and long term predictions, is presented inspired by the literature reviewed. Finally, the results are presented and discussed; wear increment and new ge- ometries evolution are presented in the figures, followed by pressure profile evolution at selected times. The final geometry is also compared for different time steps. At last, conclusions and recommendations for future work are stated. II Contents 1 Introduction1 1.1 Motivation................................1 2 Theory & Literature Review2 2.1 Tribology................................2 2.2 Friction.................................3 2.3 Wear...................................4 2.4 Factors affecting friction and wear...................5 2.4.1 Contact area..........................5 2.4.2 Load...............................6 2.4.3 Sliding velocity & Temperature................6 2.4.4 Running-in & Transfer-film..................7 2.5 Wear modelling.............................9 2.5.1 Contact modelling.......................9 2.5.2 Finite Element Method..................... 11 2.5.3 Archard’s wear equation.................... 12 2.5.4 Wear modelling in the literature................ 13 3 Research Gap 18 4 Model & Methods 19 4.1 Software................................. 19 4.2 Model problem............................. 19 4.2.1 Wear & Geometry update................... 24 4.3 Long term predictions......................... 26 4.4 Methodology overview......................... 27 5 Results & Discussion 29 5.1 Contact pressure............................ 29 5.2 Wear & Geometry........................... 31 5.2.1 Initial simulations........................ 32 5.2.2 Finer time steps......................... 34 5.2.3 Full-scale simulation...................... 39 6 Conclusions & Future works 43 III List of Figures 1 Stribeck curve showing the behaviour of friction for different lubri- cation regimes along with scheme of physical cases; I: Boundary, II: mixed, III: hydrodynamic, IV: EHL (non-conformal contact only). Adapted from [33]............................2 2 Representation of the real contact area of rough surfaces in contact, composed by a number of micro-contacts (in red) defined by ran- dom distribution of numerous small contact points, which prevents interlocking or meshing. Side view in square and contact surface view in circle. Adapted from [86]....................5 3 Schematics illustrating evolution of contact between a solid lubricant and a rough hard counterpart: from left to right - before sliding, gradual filling of the solid lubricant in the grooves of the counter-surface, buildup of the solid lubricant leading to self lu- brication. Note that there exists a change in roughness of both surfaces. Adapted from [81, 51].....................8 4 Point mass supported by spring system (a); illustration of the La- grange Multiplier Method (b); penalty spring due to penalty term (c). Adapted from [93]..........................9 5 A plate under uniaxial tension with a hole; finite element (FE) mesh of the model (middle) with finer (smaller) elements in regions where the fields and errors are expected to be high; typical visualization of a simulation. Adapted from [25]................... 11 6 Wear occurs when a fragment of material detaches from an asperity during contact. The shape is approximated as a hemisphere with radius a. Adapted from [86]....................... 12 7 Geometric model of disc brake assembly on which wear of the pad was modelled and numerically studied; Surface profile of brake pad for wear simulation. From [84]..................... 15 8 Left: illustration of block on plate experiment (from [28]); right: modelling of experiment - refer to text for numbered explanation.. 21 9 FE mesh for the counter surface showing finer refinement towards region where contact with the block occurs.............. 21 10 Finalized initial FE mesh showing zoomed-in details of finer refinement on destination boundary (block)................. 23 11 High peaks and gradients of contact pressure in the block’s edge region, leading to the set-up of finer FE mesh............. 24 12 Detail on the construction of the block’s contact boundary; higher density of points in the region of high pressure peaks and gradients. 25 13 Flowchart of wear computation methodology.............. 28 14 Pressure profile in elastic contact for different indenters (sphere, flat die and cone). From [96]......................... 29 15 Reference entities for non-dimensionalization of results........ 29 16 Contact pressure profile (top) normalized by the maximum pressure of the frictionless case, pr,fric (left) and x-component of the displacement field (bottom); frictional case with µ = 0.3 - chosen for visualization purposes only (right)................. 30 IV 17 General normalized dynamic pressure profile on the block’s contact boundary for unworn sliding (moving towards the right)....... 31 18 Dynamic contact pressure peaks behaviour with regards to coeffi- cient of friction µ changes........................ 31 19 Wear, ∆tg = 2s (“cycle-update”), A = 1000, 1st cycle......... 32 20 Wear, ∆tg = 2s (“cycle-update”), A = 1000, 2nd, 3rd and 4th cycles. 33 21 Wear, ∆tg = 2s (“cycle-update”), A = 500, 4th cycle......... 34 22 Wear, ∆tg = 0.05s, A = 1000, at different moments.......... 35 23 Maximum dynamic pressure during simulations of 4 cycles; “*” refers to inversion in the direction of motion when associated with a step “s”, or start of a new cycle when associated with a cycle “c”. 36 24 Dynamic pressure, ∆tg = 0.05s (named dt on the title), A = 1000, in the beginning and in the end of the same stroke moving to the right direction.............................. 37 25 Block’s edge final geometry after 4 cycles with A = 1000....... 38 26 Block’s edge final geometry after 4 cycles with A = 500........ 38 27 Block’s edge final geometry after 2 cycles with A = 1000....... 39 28 Maximum dynamic pressure during simulations of first 4 cycles with A = 4000; “*” refers to inversion in the direction of motion when associated with a step “s”, or start of a new cycle when associated with a cycle “c”.............................. 40 29 Maximum dynamic pressure during simulations of 4th to 9th cycles with A = 4000.............................. 40 30 Step showing non-smooth wear increment during the 6th cycle with A = 4000................................. 41 31 Wear, ∆tg = 0.05s, A = 4000, at different moments.......... 42 V 1 INTRODUCTION 1 Introduction Essentially all contacts of solid matter involve friction and wear, from modular junctions of hip replacement, to bearings in turbines of hydropower plants, and NASA’s Mars rover Curiosity’s wheels. Wear is a crucial factor that determines the service life-span and reliability of engineering systems, having enormous eco- nomical impact. In fact, a few decades

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