Hertz点接触问题求解方法的对比研究  

A Comparative Study of the Methods for Solving the Hertz Point Contact Problem

作　　者：关佩[1,2] 陈家庆[2] 

机构地区：[1]北京化工大学机电工程学院,北京100029 [2]北京石油化工学院机械工程学院,北京102617

出　　处：《机械科学与技术》2011年第7期1171-1178,共8页Mechanical Science and Technology for Aerospace Engineering

基　　金：2009年度国家自然科学基金项目(50874018);北京市属高等学校人才强教计划项目(PHR200906214)资助

摘　　要：两个弹性体之间的点接触问题是一个经典的弹性力学问题,国内外围绕此问题已提了出多种求解方法。通过C语言编程对Harmrock&Brewe法、Brewe&Hamrock法、Greenwood法、Markho法、单项均分法、Dyson法、Houpert法、Tanaka法、Antoine法与自行开发的完全数值算法进行了对比研究。结果表明,虽然Brewe&Hamrock法、Hamrock&Brewe法、Markho法、Houpert法的计算形式比较简单,但都有其适用范围,在没有计算机可供利用编程的情况下,可根据需要选用其中公式;Antoine法计算精确,适用范围广,但其计算过程将较为麻烦;Dyson法的求解结果极为精确而且编程较为简单,适用于精度要求较高的计算场合,在有计算机可供利用编程的情况下,可以推广使用。在这些求解方法中,完全数值算法无需对公式进行转化,完全遵从于原始计算公式,计算结果最为精确。The point contact between the two elastic bodies is a classical elastic mechanics problem.There are several methods for solving this problem.A comparative study of the methods of Harmrock Brewe,Brewe Hamrock,Greenwood,Markho,the single sharing,Dyson,Houpert,Tanaka,Antoine,and the self-developed full numerical method show that the calculation form of these methods of Harmrock Brewe,Brewe Hamrock and Markho is simple.However,these methods all have their application range.According to the need,we can select a method of these when there is no computer for programming.Although the Antoine′s method have high precision and wide application range,the calculation process is more complicated without computer.The Dyson′s method not only can obtain accurate results,but the programming is simple,which is applicable to the high precision calculation,and is suitable to be promoted when there is a computer for programming.In these algorithms,the full numerical method need not to transform the formulas,and completely rely on the original formula to solve the problem,with the most accurate results.

关 键 词：点接触 弹性力学 适用范围 完全数值算法 

分 类 号：TH123.1[机械工程—机械设计及理论]