面向结构参数的滚珠丝杠副动态接触角建模

    Modeling for dynamic contact angle of ball screw mechanism aimed to structural parameters

    • 摘要: 为研究滚珠丝杠副结构参数对接触角的影响,基于Hertz理论和滚道控制理论,综合考虑滚珠、螺母和丝杠滚道的结构参数,以间隙、公称直径、滚珠直径、螺旋升角及滚珠数量作为变量,建立滚珠丝杠动态接触角模型,得到面向结构参数的接触角非线性方程组,给出采用Newton-Raphson法进行迭代求解的流程。基于动态接触角模型进行讨论和实例分析,研究不同工况下的结构参数对滚珠丝杠副动态接触角的影响规律。结果表明:工作中的滚珠丝杠副丝杠侧的内接触角始终大于螺母侧外接触角;滚珠与滚道间隙量增大0.1 mm,内、外接触角增大约7°;公称直径增加则外接触角减小、内接触角增大;滚珠直径和滚珠数量的增大会导致外接触角减小、内接触角先减小后增大;螺旋升角对接触角影响很小,内、外接触角变化幅值均不到0.006°。该研究为滚珠丝杠副结构尺寸优化、动态特性分析、提高设计精度提供了参考。

       

      Abstract: Abstract: Ball screw mechanism is one of the key parts in mechanical and electronic products especially in precision machineries due to its high transmission efficiency, long service life and high precision, high carrying capacity and positioning accuracy, which is determined by the contact angle formed between nut and screw. Aimed at the current problems in universal and limited application, which resulted from the specific structure parameters, this paper establishes the relationship between contact angle and ball screw's structure parameters, as well as the model of the dynamic contact angle of ball screw mechanism combined with the geometric parameters of the ball and the raceway between nut and screw. The relationship between force and deformation in ball and raceway is got by using the Hertz contact theory, which is used to solve the stiffness in contact area between screw and nut. The relationship between ball's rotation and revolution speed and screw's rotation speed is got by using the raceway control theory, which is used to solve the centrifugal force and gyroscopic moment formed under working conditions. The structural model of the nonlinear equations of contact angle is got, in which the variable includes clearance, nominal diameter, ball diameter, helix angle and ball number. The solving procedure of dynamic contact angle is given based on the Newton-Raphson method. The influence of structure parameters on contact angle of ball screw mechanism under different working conditions is studied through the example analysis, and verified by contrasting the influence of ball screw's rotational speed on contact angles with a specific structure. The results show that the inner contact angles in screw raceway are always greater than the external angles in nut raceway under working conditions. The inner contact angles increase with the increasing of screw's rotational speed, and in contrast, the external contact angles decrease. Both the values of inner contact angles and external contact angles increase with the load increasing under the low speed working condition, but the difference of the 2 values decreases. Under the working condition with high speed and low load, the inner contact angle decreases at first and then increases with the load increasing, while the external contact angle only increases, and the difference value of them still decreases. As for the influence of structure parameters on contact angles, the inner contact angle is always bigger than the external contact angle; both the inner contact angle and the external contact angle increase by about 7° while the clearance between ball and raceway increases by 0.1 mm; increasing the nominal diameter can lead to an increase on the inner contact angle and a decrease on the external contact angle; the ball's diameter and number have the familiar influence on the contact angle, the external contact angle can decrease with the increasing of the ball's diameter or number, but the inner contact angle decreases at first and then increases with the increasing of the ball's diameter or number; the helix angle has little influence on both the inner contact angle and the external contact angle, and the change values of both contact angles are less than 0.006° when the helix angle increases by 1°. Research results would provide the reference for the optimal design, dynamic characteristics analysis and accuracy improvement of ball screw mechanism.

       

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