液力变矩器轴面流线数值计算及分段最佳圆弧逼近

Numerical Calculation of Meridional Path Line and Optimum Approximation with Multi-segment Arc of Hydrodynamic Torque Converter

对液力变矩器建模精度进行了研究,分析了影响建模精度的各种因素,提出了一种提高建模精度的新方法。基于轴面流线方程,推导了曲率半径和曲率中心坐标的计算公式,采用数值计算方法得到了曲率半径和曲率中心坐标随极角变化的规律。依据这种规律,采用非初等函数—分段圆弧一致逼近,使逼近最大绝对误差达到最小。编制了参数化程序,对所有方程进行了验证。利用程序不仅可以直接得到各段圆弧的圆心坐标、圆弧半径和圆弧起止点的极角,还可以直接得到分段圆弧逼近的最大绝对误差和最大相对误差,便于对结果是否满足精度要求做出判别。研究结果表明,该方法是可行的,可以显著地提高建模精度,具有工程使用价值。

The modeling precision of hydraulic torque converter is investigated and various factors affect the modeling precision are analyzed,a new high precision modeling method is proposed. Based on the meridional path line equation,the calculation formula of curvature radius and curvature center coordinates is derived.By using numerical calculation method,the curves of curvature radius and curvature center coordinates versus the polar angle are obtained. According to this law,by using a non-elementary function multi-section circular arcs uniformly approximation,the maximal absolute error of approximation reaches a minimum. A parametric program code is developed and all equations are verified. By using the program,the radius and center coordinates of each circular arc,and polar angle of each arc joining point are obtained directly. In addition,the absolute error and percentage error of approximation can be obtained as well,which is convenient to discriminate if the approximation meets the precision requirement. The investigation results indicate that the method is feasible,can improve modeling accuracy significantly,and is of engineering application value.