Numerical analysis of steady thermo-elastic wear regimes induced by translating and rotating punches I. Páczelt a,⇑ , Z. Mróz b a Faculty of Mechanical Engineering, University of Miskolc, 3515 Miskolc Egyetemváros, Hungary b Institute of Fundamental Technological Research, Warsaw, Poland article info Article history: Received 7 April 2010 Accepted 14 June 2011 Available online 16 July 2011 Keywords: Contact problems Sliding wear Steady state Thermal distortion Optimal contact surface abstract The present work provides the analysis of coupled thermo-elastic steady wear regimes: wear analysis of a punch translating on an elastic strip and wear induced by a rotating punch on a toroidal surface. The con- tact pressure and temperature are speciﬁed from the stationary conditions of the wear dissipation power or from the contact-conformity-condition. The wear and friction parameters are assumed as ﬁxed or tem- perature dependent. Three transverse friction models are discussed for wear debris motion. The analysis and results presented can be used in design of optimal contact shapes assuring the steady wear regimes throughout the whole contact operation period. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The present paper provides the numerical analysis of steady wear regimes induced by relative sliding of two contacting bodies B 1 and B 2 and follows the previous works by Páczelt and Mróz [1– 4]. It was shown that the stationary conditions of the global wear dissipation power on the contact surface S c provide the pressure distribution. The shape of contacting bodies on S c associated with this distribution is next numerically speciﬁed. This approach pro- vides the possibility to predict the wear rate and contact shape evolution in the steady state. A related optimal shape design prob- lem of contacting bodies can then be considered by postulating the steady state regime throughout the whole contact operation peri- od, thus avoiding transient run-in periods of larger wear rates. The coupled temperature ﬁeld due to external boundary condi- tions or heat generation due to friction and wear induces thermal distortion and essentially affects the steady state shape of contact surface, however, the pressure distribution on S c remains un- changed. This class of problems was analyzed in Páczelt and Mróz [4] by applying the coupled thermo-mechanical approach and the minimum principle of the global wear dissipation power. The cases of drum and disk brakes were analyzed in detail. In the present paper the analysis of thermoelastic wear regimes in relative contact translation and rotation of two bodies is presented. Body B 1 is treated as a punch executing the relative sliding mo- tion on the substrate B 2 . The stress and temperature ﬁelds in the steady state are speciﬁed together with the shape of contact sur- face reached due to wear process. These two relative sliding modes are most important for engineering applications. The paper is organized as follows. In Section 2 the wear rule and the steady state conditions are presented. Three cases are distin- guished, namely the wear of punch, the wear of two bodies and the wear of substrate. The steady state conditions are formulated for each case. In Section 3 the thermo-mechanical analysis problem is formulated and the numerical procedure is described for coupled thermal and mechanical ﬁelds following the previous work [4]. The contact pressure distribution was speciﬁed for cases when wear parameters and coefﬁcient of friction are constant or temperature dependent. In the variational form of thermal equations the Pet- rov–Galerkin upwinding term [5,6] is introduced in order to avoid oscillatory solutions usually occurring for large sliding velocities and discontinuous boundary conditions. The numerical analysis of wear process induced by sliding punch on a ﬂat substrate is pre- sented in Section 4. The cases of wear of punch only and of com- bined wear of punch and substrate are treated numerically assuming the steady state condition requiring the uniform contact pressure distribution. The case of wear of substrate only is ana- lyzed numerically by applying the contact conformity condition. In Section 5 the general analysis of a rotating punch of an arbitrary axisymmetric shape on a ﬁxed substrate is analyzed. Three gener- alized transverse friction models are introduced with account for wear debris motion within the contact interface layer. The station- ary conditions of minimization of the global wear dissipation 0045-7949/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruc.2011.06.001 ⇑ Corresponding author. E-mail address: mechpacz@uni-miskolc.hu (I. Páczelt). Computers and Structures 89 (2011) 2495–2521 Contents lists available at ScienceDirect Computers and Structures journal homepage: www.elsevier.com/locate/compstruc