摘要
针对传统方法在求解滑动摩擦条件下弹性非相似接触问题时存在多项式积分过多的问题,提出了一种直接求解方法。建立了弹性非相似体接触问题的模型,用修正的高斯-雅可比积分公式求解奇异积分方程,可求得接触表面上的接触应力和与疲劳相关的平面应力。因计算中不含积分过程,所提方法能更有效、更直接地求解滑动摩擦条件下弹性非相似接触问题,且计算过程可用于其他类型的接触问题。用一个算例,通过与精确解的比较验证了方法的有效性。计算了圆柱型压头与弹性半平面在滑动摩擦条件下的接触应力分布实例,分析了摩擦因数对接触表面应力分布的影响规律,探讨了接触表面产生裂纹的可能原因。结果发现:接触面的摩擦效应导致接触区质心向接触区尾翼偏移,偏移量随摩擦因数增大而变大,这会产生偏移力矩,而法向接触力与接触区长度近似呈抛物线型的变化关系。研究对设计实际工程中具抗疲劳性能的零部件有理论价值和指导意义。
An efficient and straightforward technique based on the improved Gauss-Jacobi quadrature rule was studied for solving elastically dissimilar contact problems under sliding condition in the paper.The model of contact problem for elastically dissimilar contact problems was established.The singular integral equation was solved by the improved Gauss-Jacobi quadrature rule.The contact stress on the contact surface could be obtained,and so was the plane stress which was related to the fatigue.Because there is no integration process in the computation,the elastically dissimilar contact problem can be worked out by the method proposed more efficiently and directly.The computation can be applied to other types of contact problems.The effectiveness of the method proposed was proved by comparing with the exact value for some computation sample.The real contact problem for a cylindrical stamp sliding on a half-plane was calculated.The effect of frictional coefficient on the contact pressure distribution was analyzed.The possible reasons for crack initiation associated with fatigue and fracture of the contacting components were also discussed.It finds that the frictional effect on the contact surface will cause the centre of the contact area migrating to the end of the contact area.The migration will become bigger when the frictional coefficient is bigger.It will form migration moment.And the relationship of the normal contact force and the length of the contact area can be characterized by paracurve.This study has its theoretically value and reference meanings in designing the anti-fatigue parts in engineering.
出处
《上海航天》
CSCD
2017年第3期66-72,共7页
Aerospace Shanghai
作者简介
陈汀（1984-）,男,博士,主要研究方向为卫星总体设计、机械系统动力学.
