Effects of tilt moment on the contact stresses for a wedge under sliding condition
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Effects of tilt moment on the contact stresses for a wedge under sliding condition Ting Chen • Qibai Huang
Received: 2 February 2012 / Accepted: 30 April 2012 / Published online: 17 May 2012 Ó Springer Science+Business Media, B.V. 2012
Abstract The contact stresses between a tilted, shallow wedge and half-plane, under frictional sliding condition, are investigated analytically. The closedform of contact law itself, together with the contact tractions and the size of the contact segments are explicitly found. The effects of tilt moment, material property, geometry variation and the applied loads on the contact pressure distributions are investigated. By making use of the Muskhelishvili’s potential function and the Plemelj formulae, the analytically derived contact pressure is the same as that obtained based on the singular integral equations. The result is verified by comparing with that in the literature. The in-plane stress field is evaluated from the standpoint of fatigue. It is shown that the Muskhelishvili’s potential function and the Plemelj formulae can be also used to solve this type of contact problem. This study is helpful for understanding the mechanism of frictional sliding contact problem with singular point and designing better high precision instruments and devices.
T. Chen Q. Huang (&) State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China e-mail: [email protected] T. Chen e-mail: [email protected]
Keywords Frictional contact Tilt moment Sliding wedge Plemelj formulae
1 Introduction In design of precision instruments such as surface profilometers and hard disk devises, wedge indenter is frequently used as a probe to contact with other surfaces. While some of the failure modes may be relatively easy to design in these conditions, design against fracture is generally very complicated. The reason is that not only the stress state of the body needs to be determined but also the possible location of initial defects has to be predicted. The wedge indenter has linear profile and sharp apex. The state of stress adjacent to the discontinuity in gradient present along the face of a contacting body is of great concern. The region near the apex is of localized stress concentrations, which would be most likely to result in some undesirable contact fatigue. In order to design against fracture of the contact surface, some detail of the nature of stress concentration arising at the apex needs to be investigated. The contact problem of a wedge indented into a half-plane has been studied for a considerable long time (Gladwell 1980; Johnson 1985; Hills et al. 1993). It has become clear that the contact pressure adjacent to the apex adopts the form of a weak (logarithmic) singularity. This was studied by Hall (1989) and Hall and Savage (1988) with particular reference to the
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development of the pressure spike in elastohydrodynamic lubrication. It should be noted that the wedge was as
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