A SECOND APPROXIMATION SOLUTION ON THE ELASTIC CONTACT PROBLEM
A SECOND APPROXIMATION SOLUTION ON THE ELASTIC CONTACT PROBLEM出 版 物：《Science China Mathematics》 (中国科学:数学(英文版))
年 卷 期：1958年第12期
页 面：1235-1246页
主 题：A SECOND APPROXIMATION SOLUTION ON THE ELASTIC CONTACT PROBLEM body 一舒
摘 要：A second approximation solution for the pressure distribution between two elastic bodies in contact is presented. In addition to the terms used by Hertz as the description of a general surface of contact, the present theory will contain the next higher order terms of its Taylor’s series expansion, such that the coefficients of the Hertz second power terms as well as the dominent fourth power term are satisfied Hence, the second order effect is a correction to the Hertz theory, which increases both with, the increase of normal load and with the increase of eccentricity of the contact ellipse.Щтаерман’s method of change of variables is adopted in the process, of integration. The solution, thus obtained, agrees exactly with that obtained, by Cattaneo wher reduced to his special case of two solids of revolution in contact.To illustrate the usefulness of the present theory, the problem of contact between a ball and the outer race of a ball bearing is studied. Curves are plotted to show that the relative magnitude of the second order effect varies with the shape ratio of the contact ellipse at various normal loads.
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