点接触弹流润滑问题的高效直接算法

在复合直接迭代法的基础上,运用分块迭代的思想将方程组降维,通过研究弹性变形影响因子对弹性变形的影响,将压力迭代矩阵由满元阵变为稀疏的带状阵,提出一种新的求解点接触弹流问题的高效直接迭代算法.与复合直接迭代法相比,该算法大大减少了计算量,计算效率至少提高20倍,并且可适用重载工况.将新算法计算结果与Hamrock-Dowson公式计算结果进行比较,并讨论迭代矩阵半带宽与收敛速度、载荷范围、计算精度以及数值稳定性的关系.结果表明,当压力迭代矩阵密度为满阵的22％～25％时,新算法具有最高的计算精度.

High Efficiency Direct Iterative Algorithm for Point Contact EHL Problems

Based on the composite direct iterative method,by changing two dimensional point contact EHL problem into a set of one dimensional problems with block iteration method,and changing the full elements pressure iterative matrix into a spare one through considering the effect of influence factor of elastic transformation on the elastic transformation,a new and high efficiency direct iterative algorithm for point contact EHL was proposed.Compared with the traditional direct iterative algorithm,the new algorithm method can reduce the computation greatly,can raise the computational efficiency at least 20 times,and can get convergence solution even if under the heavy load cases.The computational results of the new algorithm method were compared with those of Hamrock-Dowson formula,and the relationships of semi-band width of iteration matrix with convergence speed,load range,calculation precision and numerical calculation stability were discussed.The results show that the new algorithm method can get the best calculation precision when the density of the pressure iterative matrix is 22%~25% of its full elements matrix.