软轴摩擦力矩计算公式推导与优化

Derivation and Optimization of Calculation Formula for Flexible Shaft Friction Torque

通过采用回归分析的方法,结合软轴摩擦力矩的影响因素,推导和优化了结合软轴实际工作状况的摩擦力矩计算公式。首先,为了得到多组实验数据,将长度不同、轴芯半径不同的软轴作为实验对象,在不同的曲率半径下测量出软轴的摩擦力矩大小。实验结果表明:软轴的摩擦力矩受轴芯的长度、半径、及弯曲时的曲率半径的影响,呈现指数关系。其次,运用回归分析并采用最小二乘法推导出软轴的摩擦力矩经验公式。使用经验公式计算,所计算出的理论值的总体误差率为5.53%。最后,结合蒙特卡罗模拟和粒子群算法对经验公式进行优化,优化后的公式的总体误差率为5.37%,计算精度提高了0.16%。研究成果对软轴的系统设计和动态摩擦性能分析具有重要指导意义。

By adopting the regression analysis method and combining the frictional torque influence factors of the flexible shaft,the formula for calculating the frictional torque combined with actual working condition of the flexible shaft is deduced and optimized.Firstly,in order to obtain multiple sets of experimental data,flexible shafts with different lengths and different core radii are used as experimental objects,and the flexible shaft friction torque is measured under different curvature radi.The experimental results show that the frictional torque of the flexible shaft is affected by the length and radius of the shaft core and the radius of curvature during bending,showing an exponential relation.Secondly,the empirical formula for the friction torque of the flexible shaft is deduced using the regression analysis and the least square method.Using the empirical formula to calculate,the overall error rate of the calculated theoretical value is 5.53%.Finally,the empirical formula is optimized by combining Monte Carlo simulation and particle swarm algorithm.The overall error rate of the optimized formula is 5.37%,and the calculation accuracy is increased by 0.16%.The research results have important guiding significance for the system design and dynamic friction performance analysis of flexible shafts..