Abstract
The paper presents an explicit matrix algorithm to solve the problem of an elastic wedge with three loaded surfaces. The algorithm makes use of a recently published concept of transformation matrix, by which the original surface loads are converted to equivalent loads in half-space. The three loaded edges are considered simultaneously. The developed algorithm is used to study the effects of two free edges of a steel block and tapered rollers with different contact angles. The two load-free edges can substantially increase deformation if the two edges are close in distance. The results of the tapered roller simulation show that deformation is considerably sensitive to the contact angle of the tapered roller. The largest deformation appears at the big end of the roller. Furthermore, empirical formulae for correction factors for the calculation of block or quarter-space deformation based on half-space solutions are summarized.
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This research is completely supported by the Research Grants Council of Hong Kong (Project No. CityU11213914).
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Liang GUO. He received his Ph.D. degree from the Department of Mechanical and Biomedical Engineering, City University of Hong Kong in 2016. He is currently a postdoctoral fellow in the same department. His research interests include interfacial effect in hydrodynamic lubrication and contact mechanics.
Patrick WONG. He obtained his Ph.D. degree from the University of Hong Kong in 1990, and his BSc degree from City University, London in 1983. Dr. Wong started his academic career in the City University of Hong Kong since 1990. He is currently an associate professor in the Department of Mechanical Engineering in the City University of Hong Kong. His research interests include rolling element bearings, interfacial phenomena, and lubrication.
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Guo, L., Zhang, Z.M., Wang, W. et al. An explicit solution to a three-dimensional wedge problem considering two edges effect. Friction 8, 370–383 (2020). https://doi.org/10.1007/s40544-019-0265-7
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DOI: https://doi.org/10.1007/s40544-019-0265-7