考虑摩擦的滚珠丝杠式惯容器惯质系数修正方法

Correction of inertance of ball-screw inerter considering friction

为了得到更加精确的滚珠丝杠式惯容器惯质系数,基于Frenet标架理论和赫兹接触理论,研究滚珠丝杠式惯容器中滚珠与滚道之间的差动速度,推出滚珠与滚道之间的摩擦效率,得到摩擦惯质系数进行计算方法.对滚珠丝杠式惯容器惯质系数进行实验研究,结果表明摩擦惯质系数更加接近实验值,证明该计算方法的准确性.此外,分析滚珠丝杠副的参数对惯质系数的影响,分析结果表明导程越小、公称半径越小、滚珠半径越大、滚珠数量越小、接触角越小,惯质系数越大.研究结果有利于滚珠丝杠式惯容器的精准化设计及其在工程减振系统中的应用.

In order to obtain the accurate inertance of a ball-screw inerter,an inertance calculation method of the ball-screw inerter considering frictional factors was proposed in this paper.Based on Frenet frame theory and Hertz contact theory,the relative sliding speed and the sliding friction torque between balls and raceways of the ball-screw inerter have been deduced,the sliding friction efficiency of the balls is derived,and finally the method of calculating the friction inertance is obtained after considering friction.An experimental study on the inertance of ball-screw inerter has been carried out,and the results show that the frictional inertance is more close to the experimental value;it demonstrates the accuracy of the calculation method proposed in this paper.Besides,the influences of other parameters of the ball-screw mechanism on the inertance are also analyzed,and the results show that the smaller the lead,the smaller the nominal radius,the greater the ball radius,the smaller the number of balls,the smaller the contact angle,the greater the inertance.These results are favorable to the precise design of ball-screw inerter and its application in engineering anti-vibration systems.