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Modeling of elastic finite-length space rolling-sliding contact problem.pdf

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Modeling of elastic finite-length space rolling-sliding contact problem.pdf

Tribology International xx (xxxx) xxxx–xxxx Contents lists available at ScienceDirect Tribology International journal homepage: /locate/triboint Modeling of elastic ?nite-length space rolling-sliding contact problem Haibo Zhang, Wenzhong Wang?, Shengguang Zhang, Ziqiang Zhao School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, PR China ARTICLE INFO Keywords: Finite-length space Overlapping method Matrix formulation Sliding contact ABSTRACT This paper presents a semi-analytical method (SAM) to solve sliding ?nite-length space contact problem with consideration of the e?ect of free end surface. The equation set based on the overlapping concept is analytically solved with tangential load considered and the explicit expressions for equivalent mirrored loads are obtained. Conjugate gradient method (CGM) is adopted to solve the pressure distribution and Fast Fourier transform (FFT) is used to speed up stress related calculation. The model is veri?ed by FEM and shows a high conformity. Di?erent line contact situations are discussed to explore the e?ect of free end surfaces. 1. Introduction It is quite common in industrial applications that there are two free end surfaces perpendicular to the axis of part, especially in some mechanical elements such as gears, cams and roller bearings, and in these contact situations, sliding motion usually exists that makes working condition more severe. The dimension of both the contacting parts along the axis are actually ?nite, however, the widely-used Hertz theory of contact is based on half space, through which only the approximate solution can be obtained, especially in the vicinity of the edge. For accurate application, it is desirable to consider the e?ect of the two free boundaries, i.e., ?nite-length space contact problem. Finite-length space contact problem is the extension of quarterspace contact problem, and many researchers have developed their study on the latter in the past decades. Among them a