精密钢球传动啮合法向力与弹性回差

针对精密钢球传动法向力的传统求解方法和弹性回差对传动性能的影响,在分析啮合副弹性回差产生机理的基础上,提出利用啮合点刚度系数精确求解法向力和弹性回差的方法。建立啮合副力学模型,利用啮合点刚度系数并通过力矩平衡方程分别推导出减速啮合副和等速啮合副的弹性转角和啮合点法向力公式,应用啮合副弹性转角分别推出减速啮合副弹性回差、等速啮合副弹性回差和传动机构弹性回差的计算公式,并分析机构参数对弹性回差的影响规律。研究结果表明,减速啮合副和等速啮合副啮合法向力可用统一公式表示,传动机构弹性回差曲线呈周期性波动,机构参数变化对弹性回差影响较明显,减速钢球数对弹性回差影响最大。研究结果为精密钢球传动的传动精密性和运动平稳性分析及机构设计提供理论依据。

Engagement Normal Force and Elastic Backlash of Precision Ball Transmission

In view of usual resolved method of the engagement normal force and influence of the elastic backlash on the transmission performance of the precision ball transmission, based on mechanism analysis of the engagement pairs elastic backlash, the method to be resolved exact calculation engagement normal force and elastic backlash of engagement pairs is proposed by rigidity coefficient. The mechanical model of the engagement pairs is established. The formulas of the elastic turn angel and engagement normal force of the reduction speed engagement pair and equi-speed engagement pair are respectively deduced by the engagement point stiffness coefficient and torque balance equation. The elastic backlash formulas of the reduction speed engagement pair , the equi-speed engagement pair and the transmission mechanism are respectively deduced with the engagement pair elastic turn angel. The influence of the mechanism parameters on the elastic backlash is analyzed. The results show that engagement normal forces of the reduction speed engagement pair and the equi-speed engagement pair are represented by the unified formula. The elastic backlash curve of the transmission mechanism is changed periodically. It is obvious that mechanism parameters change affects the elastic backlash. The most important factor affecting the elastic backlash is the reduction of the number of steel balls. The research result provides theoretical basis for analysis of transmission accuracy, rotation smoothness and mechanical design of the precision ball transmission.