Modeling of repeated rolling contact of rigid ball on rough surface: residual stress and plastic strain analysis

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Procedia Engineering 68 ( 2013 ) 593 – 599

Selection and peer-review under responsibility of The Malaysian Tribology Society (MYTRIBOS), Department of Mechanical Engineering, Universiti Malaya, 50603 Kuala Lumpur, Malaysia

doi: 10.1016/j.proeng.2013.12.226

ScienceDirect

The Malaysian International Tribology Conference 2013, MITC2013

Modeling of repeated rolling contact of rigid ball on rough surface:

residual stress and plastic strain analysis

R. Ismail

a

, M. Tauviqirrahman

a

, E. Saputra

a

, J. Jamari

b,

* and D.J. Schipper

a

a_{Laboratory for Surface Technology and Tribology, Faculty of Engineering Technology,University of Twente}

Drienerloolaan5, Postbus217, 7500 AE Enschede, The Netherlands

b_{Laboratory for Engineering Design and Tribology, Department of Mechanical Engineering, University of Diponegoro}

Jl. Prof. Sudharto Kampus UNDIP Tembalang, Semarang, Indonesia 50275

Abstract

In this paper, a three-dimensional finite element model of rigid hemisphere repeatedly rolling over a rough flat surface under constant normal load is discussed. The aim of this research is to study the von Mises residual stress and plastic strain distribution and to determine the steady-state phase of the repeated rolling contacts. The results show that the change of residual stress distribution takes place in the first-two rolling cycles and there is no significant change for the residual stress from the second to third rolling cycle, i.e. the surface is run-in after a few cycles. The increase of the contact load affects the area of the von Mises residual stress at the surface and subsurface and also the number of the deforming asperities. The residual stress distribution is getting wider as the normal force increases. The plastic strain is captured after the third cycle of rolling. Small area of plastic strain is found for the rough surface for the low forces applied which indicates the surface deformed mainly elastically. The rough surface is predicted to be plastically deformed for the highest force applied.

Selection and peer-review under responsibility of The Malaysian Tribology Society (MYTRIBOS), Department of Mechanical Engineering, Universiti Malaya, 50603 Kuala Lumpur, Malaysia.

Keywords: Finite element analysis; plastic strain; residual stress; rolling contact; rough surface.

Nomenclature

F force (N)

E elastic modulus (GPa)

R ball radius (mm) Greek symbols ı stress (MPa) ȣ Poisson’s ratio (-) Subscripts Y yield stress

* Corresponding author. Tel.: +62-24-7460059; fax: +62-24-7460059

E-mail address: j.jamari@gmail.com

Selection and peer-review under responsibility of The Malaysian Tribology Society (MYTRIBOS), Department of Mechanical Engineering, Universiti Malaya, 50603 Kuala Lumpur, Malaysia

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1. Introduction

The problem of the contact stress, residual stress, plastic deformation and plastic strain of surfaces due to rolling contact is a major problem in a number of areas of engineering design. In metallic surfaces, rolling contact occurs in many types of roller bearings. Residual stress and plastic strain are presented due to repeated rolling contact between a ball and a surface, which is relatively rough on micro-scale. Surface failure due to rolling contacts is often associated with the accumulation of plastic strain near the surface.

The running-in phase is a transient phase where many parameters seek their stabilized form. Running-in takes place during the initial use of rolling components. A successful running-in phase contributes to enhancing the degree of conformity so that the performance of the contacting components improves. The rolling components can be utilized in an optimum condition when the running-in phase is successfully accomplished and the steady-state phase is obtained. Considering the significance of the running-in phase, the study of the running-in of rolling contacts becomes important.

Jamari [1] researched the running-in of rolling contacts by modeling (local) elastic-plastic deformation, which results in a topographical change of an engineering surface. He proposed a deterministic model [2] based on the elastic-plastic ellipsoid contact model [3] to predict the plastic deformation of the higher asperities and change in surface topography [1]. The analytical model has been validated with a number of experiments, good agreement was found between model and experiment. Taúan et al. [4] reported changes in micro geometry on asperity level in both lateral and longitudinal direction of the rolling direction. The change in surface topography, which is caused by plastic deformation, mainly took place in the first two cycles, after which the amount of deformation decreased and the surface topography started to reach its final form.

Both of Jamari [1] and Tasan et al. [4] experiments investigated the running-in to steady state phase based on the plastic deformation of the higher asperities resulting in a change in surface topography. The residual stress and plastic strain as the results of plastic deformation are difficult to be analyzed experimentally. An eơective way of investigating the residual stress and plastic strain due to rolling contact is to conduct finite element (FE) simulations. In the present simulations, a three-dimensional rough surface model is developed which considers the real rough surface of Jamari’s experiment [1]. The aim of the study is to observe the residual stress and plastic strain development to determine the steady state phase of a repeated rolling contact. Comparing to the previous FE simulation on rolling contacts [5-7], the novelty of the present study are combinations of: (i) repeated rolling contacts, (ii) real rough surface model based on experimental observation, (iii) running-in to steady state phase investigation based on the residual stress and plastic strain development and (iv) simplification of the simulation using the readily post-processing analysis.

2. Contact model and simulation procedures

2.1. Contact model

In the present study, finite element (FE) simulations are conducted using ABAQUS 6.11 [8]. A rigid hemisphere is rolled three times over a rough surface to calculate the residual stresses and plastic strains of repeated rolling contacts. The rough surface of Jamari’s experiment [1] is employed as input in the FE model using 24281 elements of Tetrahedron [8]. The contact model for the finite element simulation is depicted in Fig. 1(a). A rigid ball, with R = 5 mm, is rolled over a rough aluminum surface with elastic-perfectly plastic material behavior. The mechanical properties of the aluminum (obtained from Jamari [1]) in these simulations: the elastic modulus (E), yield strength (ıY) and Poisson’s ratio (ȣ) are 75.2 GPa, 85.72 MPa and 0.34 respectively. Details of the mesh of the finite element model are depicted in Fig. 1(b). A refined mesh, with the length of 8.8 μm, is applied with respect to the mesh sensitivity test and located along the rolling path of contact for increasing the accuracy of the parameters studied. The bottom nodes of the rough surface are constrained in all directions.

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Fig. 1. (a) The schematic illustration of the rolling contact simulation of rigid hemisphere on a rough flat surface and (b) the mesh generation on the rough surface model.

2.2. Simulation Procedures

Previously, repeated rolling contacts have been simulated using a two-dimensional model between a rigid cylinder rolling over an artificial rough surface [9-10]. The rolling contact in the present simulation is modeled as a ball in contact with a three-dimensional rough surface. Three normal forces are used to simulate the severity of the contact. The ball is pressed on the rough surface with a normal force of 0.05 N, 0.5 N and 5 N, followed by rolling along the rolling path, as depicted in Fig. 1(b), while maintaining the contact load. The ball is unloaded after reaching the end of the track. The schematic illustration of the repeated rolling contact is depicted in Figs 2(a) and (b). The rolling contact simulation is repeated for three times. Free rolling is assumed in these simulations and friction is neglected. The residual stresses as well as the equivalent plastic strain are calculated after the contact is unloaded.

Fig. 2. The schematic rolling contact simulation of a rigid ball against a rough flat surface: a) start, the static contact and (b) continued by rolling, maintaining the contact load and unloading.

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3. Results and discussions

The distribution of the equivalent plastic strain after unloading of the rolling contact on the rough surface is depicted in Fig. 3 (a-c) for the contact loads of 0.05 N, 0.5 N and 5 N, respectively. The equivalent plastic strain is captured after the third cycle. A small area of plastic strain is found for the rough surface for F = 0.05 N and 0.5 N where the value of the strain is rather low. It indicates that the rough surface deforms mainly elastically. A larger area and higher value of plastic strain is found on the rough surface for F = 5 N which indicates the elastic-plastic deformation.

Fig. 3. The equivalent plastic strain of repeated rolling contact after unloading for (a) F = 0.05 N, (b) F = 0.5 N and (c) F = 5 N after 3rd overrolling.

The calculated von Mises stress distributions are presented to analyze the residual stress. The von Mises residual stresses of the rough surface for the contact loads of 0.05 N, 0.5 N and 5 N are depicted in Figs. 4-6 in isometric view. In order to have a detailed observation of the residual stress distribution in the subsurface, the rough surface is cut along the rolling path in the X-Z plane. The von Mises residual stress for a contact load of 0.05 N for the first, second and third cycle of rolling contact, are depicted in Fig. 4 (a-c), showing that the residual stress field is getting larger as the number of rolling cycles increases. However, the contact spots are rather located and contribute only to a small residual stress field.

An increase in contact load to F = 0.5 N and 5 N affects the area of the von Mises residual stress field at the surface and subsurface and also the number of the deformed asperities as depicted in Fig. 5-6. As expected, the residual stress field increases as the normal load applied to the ball-rough surface contact increases. The residual stress field reaches subsurface for F = 5 N (Fig. 6).

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The results show that the change of residual stress distribution takes place in the first two rolling cycles and there is no significant change of the residual stress from the second to third rolling cycle. The residual stress stabilizes in the first two to three cycles of the repeated rolling contact. Kadin, et al. [11] who studied the multiple repeated static contact of a ball on a flat surface using the finite element method also reported a stability of the plasticity distribution in the second to third contact. They concluded that the strain hardening behavior induced this phenomenon. Bijak-Zachowski and Marek [12] who studied the repeated rolling contacts on flat surface also indicated that the stabilized residual stress occurred in the second to third cycles.

Fig. 4. The von Mises residual stress of repeated rolling contact after unloading for F = 0.05 N: (a) first; (b) second; and (c) third overrolling, the insert gives the stress in MPa.

The stabilized form of the residual stress and plastic strain in the first-three cycles of repeated rolling contact in the present simulation acts as a key to explore the running-in to steady-state phase of the contact. The surface is run-in after a few cycles of rollrun-ing contacts. The results have a good agreement with the previous works of frun-inite element analysis on two-dimensional finite element analysis of a rolling cylinder on artificial rough surface where contact stress, residual stress and plastic strain stabilized on the first three cycles [9-10].

The present FE simulations assume free rolling where friction force is neglected. Wear of the material is not calculated in this study. Elastic-plastic deformation is pointed as the main parameter in inducing plastic strain and changing the surface topography, particularly for F = 5 N. The discussions of surface topographical change will be presented in another paper.

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Fig. 5. The von Mises residual stress of repeated rolling contact after unloading for F = 0.5 N: (a) first; (b) second; and (c) third overrolling, the insert gives the stress in MPa.

Fig. 6. The von Mises residual stress of repeated rolling contact after unloading for F = 5 N: (a) first; (b) second; and (c) third overrolling, the insert gives the stress in MPa (continued).

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Fig. 7. The von Mises residual stress of repeated rolling contact after unloading for F = 5 N: (a) first; (b) second; and (c) third overrolling, the insert gives the stress in MPa.

4. Conclusions

The repeated rolling contact of a rigid ball on a three-dimensional rough surface was analyzed using finite element simulations. The results show that the change of residual stress distribution takes place in the first-two rolling cycles and there is no significant change for the residual stress from the second to third rolling cycle. The surface is run-in after a few cycles of rolling contacts. The stabilize form of the residual stress and plastic strain acts as a key to explore the running-in to steady-state phase of the contact. An increase in contact load affects the area of the von Mises residual stress at the surface and subsurface and also the number of the deformed asperities. The residual stress distribution is getting wider as the load increases. The equivalent plastic strain is captured after the third rolling cycle to observe the remaining strain. A small area of plastic strain is found, for both applied forces, which indicates that the surface deformed mainly elastically results a negligible topographical change of the asperities.

References

[1] Jamari, J., 2006. Running-in of Rolling Contacts, PhD Thesis University of Twente, The Netherlands.

[2] Jamari, J., Schipper, D.J., 2006. An Elastic-plastic Contact Model of Ellipsoid Bodies, Tribology Letters 21 (3), p. 262. [3] Jamari, J., Schipper, D.J., 2008. Deterministic Repeated Contact of Rough Surfaces, Wear 264, p. 349.

[4] Taúan, Y.C., de Rooij, M.B., Schipper, D.J., 2007. Changes in the Micro-geometry of a Rolling Contact, Tribology International 40, p. 672. [5] Kulkarni, S., Hahn, G. T., Rubin, C. A., Bhargarva, V., 1990. Elastoplastic Finite Element Analysis of Three-dimensional Pure Rolling

Contact above the Shakedown Limit, ASME Journal of Applied Mechanics 58, p. 347.

[6] Jiang, Y., Xu, B., Sehitoglu, H., 2002. Three-dimensional Elastic-plastic Stress Analysis of Rolling Contact, ASME Journal of Tribology 124, p. 699.

[7] Nelias D., Antaluca E., Boucly, V., 2007. Rolling of an Elastic Ellipsoid upon an Elastic-plastic Flat, ASME Journal of Tribology 129, p. 791.

[8] ABAQUS 6.11/Standard User’s Manual, 2011, Dassault Systèmes Simulia Corp., USA.

[9] Ismail, R., Tauviqirrahman, M., Jamari, J., Schipper, D.J., 2010. “Two-dimensional finite element analysis on running-in of elastic-plastic rolling contact,” American Institute of Physics (AIP) Conference Proceedings 1325, p. 190.

[10] Ismail, R., Tauviqirrahman, M., Jamari, J., Schipper, D.J., 2011. “The Observation of the steady state phase on rolling contact using finite element analysis,” American Institute of Physics (AIP) Conference Proceeding 1415, p. 136.

[11] Kadin, Y., Kligerman, Y., Etsion I., 2006. Multiple Loading–unloading of an Elastic–plastic Spherical Contact, International Journal of Solids and Structures 43, p. 22.

[12] Bijak-Zochowski, M., Marek, P., 1997. Residual Stress in Some Elasto-plastic Problems of Rolling Contact with Friction, International Journal Mechanical Science 39 (1), p. 15.