论文标题
分析全滑动状态下线性弹性半空间上的刚性缸体滚动
Analysis of a Rigid Cylinder Rolling over a Linear Elastic Half-space in the Full-slip Regime
论文作者
论文摘要
本文为圆柱辊引起的弹性半空间的变形提供了分析解决方案。该滚筒被认为是刚性的，被迫进入半空间并在其表面上滚动，并通过库仑摩擦建模。通常，与半空间接触的滚筒表面的一部分可能会在半空间的表面上滑动，或者可能粘在其上。在本文中，我们仅考虑所有滚筒接触表面滑动的制度。这会导致混合边界价值问题，该问题被称为$ 2 \ times 2 $矩阵Wiener-Hopf问题。 Wiener-HOPF矩阵中的指数因素可以通过遵循Priddin，Kisil和Ayton的迭代方法（Phil。Trans。Roy。Soc。A378，p。20190241，2020）进行数值实现，该方法是通过计算Cauchy在使用Sleepral sleevinsky和olver的频谱方法来计算的。 2017）。接触区域的限制是通过应用优化方法定位的后验。用几个示例说明了该解决方案，并且在补充材料中包括计算解决方案的数值代码。
This paper provides an analytical solution for the deformation of an elastic half-space caused by a cylindrical roller. The roller is considered rigid, and is forced into the half space and rolls across its surface, with contact modelled by Coulomb friction. In general, portions of the surface of the roller in contact with the half space may slip across the surface of the half space, or may stick to it. In this paper, we consider only the regime where all of the rollers contact surface is slipping. This results in a mixed boundary value problem, which is formulated as a $2\times 2$ matrix Wiener-Hopf problem. The exponential factors in the Wiener-Hopf matrix allows a solution by following the iterative method of Priddin, Kisil, and Ayton (Phil. Trans. Roy. Soc. A 378, p. 20190241, 2020) which is implemented numerically by computing Cauchy transforms using a spectral method following Slevinsky and Olver (J. Comput. Phys. 332, pp. 290-315, 2017). The limits of the contact region are located a posteriori by applying an optimisation method. The solution is illustrated with several examples, and numerical code to compute the solutions in general is included in the supplementary material.
