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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 accuracy of the torque converter was studied, various factors affecting the modeling accuracy were analyzed, and a new method to improve the modeling accuracy was proposed. Based on the axial flow equation, the formulas of the radius of curvature and the center coordinates of the curvature are deduced. The curvature radius and the coordinate of the center of curvature with the change of polar angle are obtained by numerical calculation. According to this law, non-elementary functions-uniform approximation of segmented arcs are adopted to minimize the maximum absolute error of approximation. A parametric program has been developed that validates all the equations. The program can not only directly get the center coordinates of each arc, the radius of the arc and the polar angles of the starting and ending points of the arc, but also obtain the maximum absolute error and the maximum relative error of the approximated circular arc directly, so as to determine whether the result meets the accuracy Determined to make a judgment. The results show that this method is feasible, which can significantly improve the modeling accuracy and has the value of engineering use.