摘要
为求解粗糙表面弹性接触问题,将其转化为一个线性补余能问题,进而简化为一个二次函数的条件极值问题,利用共轭梯度法求解。算法实现了在共轭梯度方向上修正步长的优化,有效地提高了收敛效率。而占用大量计算时间的弹性变形求解采用快速傅里叶变换(Fast Fourier transform,FFT)技术,该算法有效地克服了传统傅里叶变换所引起的周期性误差。计算实例模拟了点接触单峰表面,正弦表面和真实粗糙表面的弹性接触以及有限长滚子线接触等接触问题。计算结果显示目前所用算法有效地缩短了干接触弹性接触问题的求解时间,对于不同的粗糙表面和接触类型都表现出一致的良好收敛性,同时计算精度对网格的依赖性很小,是工程中有效的分析设计工具。
In order to solve elastic contacts of rough surfaces, the problem is firstly formulated as a linear complement arity energy problem, and then converted into a quadratic programming problem with constrictions. A Conjugate gradient method （CGM） is used to solve the pressure distribution, whose correct factor in conjugate gradient direction is specially optimized to improve the convergence. A fast Fourier transform （FFT） based method for calculation of surface deformation is used to speed up the calculation of elastic deformation, which takes much computation time. The algorithm efficiently overcomes the periodical error caused by FFT. Several cases are presented for point contacts including single asperity, wavy surface and real engineering rough surfaces, and also for finite line contact, It can be found that present numerical algorithm is very efficient, and has consistently convergent property for different rough surfaces and contact types; meantime, its accuracy little depends on the mesh density. It appears to be a useful tool for engineers.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2006年第7期14-18,共5页
Journal of Mechanical Engineering
基金
国家自然科学基金(50135040)
中国博士后科学基金(2004035312)
清华-中大博士后基金资助项目。
关键词
干接触
线形补余
弹性变形
快速傅里叶变换
共轭梯度法
Dry contact Linear complementarity energy Elastic deformation Fast Fourier transform Conjugate gradient method
