考虑径向间隙的非理想双圆弧滚道滚珠丝杠副接触角建模和分析

Modeling the elastic contact angle of preloaded ball screw pair with non-ideal double-arc raceway considering radial clearance

双圆弧(哥特式)滚道可以使滚珠丝杠副的承载能力、刚度和传动精度更加稳定,在精密型滚珠丝杠副结构中广泛采用,但是双圆弧滚道的制造和测量都比较困难,往往得到非理想滚道。由于滚道误差、径向间隙与滚珠丝杠副的主要性能指标-弹性变形接触角之间存在非线性关系,导致精密滚珠丝杠副装配后的性能不易控制。为了优化滚珠丝杠副的装配质量,考虑初始游隙和接触角变化等因素,基于赫兹弹性接触理论和变形协调原理建立了非理想滚道截形的滚珠丝杠副弹性变形接触角的计算模型,并通过对比双半内圈球轴承初始接触角的计算公式,验证了提出的计算模型的通用性和正确性。以精密滚珠丝杠副3210为例,分析了内外滚道误差、径向间隙及滚珠大小对弹性接触角的影响规律。研究结果可为滚珠丝杠副的装配方法和优化设计等提供理论参考和依据。

Double-arc raceway(Gothic raceway)is widely adopted in precision ball screw mechanism because it can made the ball screw’s mechanical properties such as bearing capacity,stiffness and transmission accuracy more stable.However,it is more difficult to manufacture and measure the double-arc raceway,and non-ideal raceway are often obtained in practical production.The geometric errors of raceway and radial clearance seriously affect the overall performance of the precision ball screw.In order to improve the assembling quality of ball screw pair,a mathematical model of elastic contact angle of double nut ball screw mechanism with non-ideal profile under pretention load was established based on the Hertz elastic contact theory and the deformation compatibility principle,considering initial radial clearance.The proposed model was verified by applying the model into the calculation of contact angle of split inner-ring ball bearing.Taking the example of double nut ball screw mechanism 3210,the influences of tolerance of raceway and ball diameter on elastic contact angle were analyzed.This method can provide a theoretical reference for optimization design of ball screw,and the intelligent optimization of assembly.