多工况多误差行星滚柱丝杠螺旋曲面弹性啮合传动机理研究

Planetary roller screw mechanism (PRSM) is a kind of rolling components, which transfers power and movement by the meshing of helical surfaces of several rollers contacting with the screw and nut. Aiming at revealing the transmission mechanism on the elastic meshing of the helical surfaces in the PRSM with multiple working conditions and errors, the theoretical and experimental studies of the PRSM will be performed, in which the coupling mechanism of the force equilibrium and the deformation compatibility of parts with multiple working conditions, and the interaction mechanism of the meshing–motion–force–deformation of the helical surfaces with multiple errors will be taken into consideration. Firstly, in order to analyze the motion, force and deformation of the parts with multiple working conditions accurately, an elasto-dynamic model of the PRSM will be developed, which includes the elastic deformation of the helical surfaces, the load distribution of thread teeth, the load sharing among rollers and the rotation of screw. Then, by using multi-step loading method and considering the floating and contact loss of rollers, an improved elasto-dynamic model of the PRSM with errors will be developed. The errors include position error, threads dividing error, run-out error and profile error, etc. The influence of the working conditions and errors on the elasto-dynamic characteristics of the PRSM will be investigated and discussed. Finally, the experimental test of the rotational angles of the screw and carrier, the torque of the screw and the force acting on the nut with different working conditions and errors will be carried out to testify the validity of the proposed models. The achievements of this project will provide a theoretical basis for the design of the PRSM with high dynamic transmission performance.

行星滚柱丝杠（PRSM）是一种通过多个滚柱与丝杠及螺母之间螺旋曲面啮合传递动力和运动的滚动功能部件。本项目以揭示多工况多误差PRSM螺旋曲面弹性啮合传动机理为目标，围绕多工况零件受力平衡与变形协调耦合机理、考虑误差的啮合-运动-受力-变形相互作用机制等科学问题，开展理论与试验研究。首先，建立计入螺旋曲面弹性变形、螺纹牙载荷分布、多滚柱载荷分配和丝杠旋转的PRSM弹性动力学模型，实现多工况条件下零件运动、受力和变形更为准确的求解。其次，采用分载荷步建模与求解方法，并考虑滚柱脱啮和浮动现象，将啮合方程、变形协调方程和运动方程相耦合，建立包含位置、偏心、螺纹分头和牙型等多种误差的PRSM弹性动力学模型，分析工况和误差对其弹性动力学特性的影响规律。最后，开展多种工况和误差条件下的丝杠与保持架转速、丝杠扭矩和螺母负载试验测试，验证所建模型的正确性。本项目研究成果将为高性能PRSM设计提供理论基础。

作为一种将旋转运动转化为直线运动的传动机构，行星滚柱丝杠（Planetary Roller Screw Mechanism, PRSM）由于承载力高、刚性强、寿命长、动态性能良好和安装及维护方便等优点，越来越成为机电伺服作动系统中的关键部件，具有广阔的应用前景。然而，我国对PRSM的基础理论和应用研究较为薄弱，制约着PRSM的广泛应用和发展。为此，本研究以揭示多工况多误差PRSM螺旋曲面弹性啮合传动机理为目标，对PRSM的运动和承载特性开展了系统深入的研究。.本研究将拉格朗日方法和牛顿第二定律相结合，提出了一种高效PRSM高效动力学特性分析方法。在此基础上，建立了多级PRSM零件运动及受力计算方法。利用广义有限元方法，实现了双螺母PRSM预紧力及其承载特性分析。进一步将广义有限元方法和动力学模型相耦合，建立了PRSM弹性动力模型。计入滚柱间载荷分配及零件位置和螺纹分头误差，实现了多滚柱承载模型的建立与求解。完成了PRSM承载与传动特性软件仿真及试验测试研究，并验证了理论模型的正确性。重要结果和关键数据有：.（1）在相同计算条件下，本研究所提出的PRSM刚体动力学特性高效计算方法所耗费的CPU计算时间仅为原有模型的4%。.（2）当丝杠转速为阶跃输入时，随着仿真进行，多级PRSM的效率呈“阶梯”式上升，内齿圈对滚柱接触力先减小后略有增加，保持架对滚柱接触力很快增加至稳态值。.（3）在双螺母PRSM中，使得螺母预紧力消失时的外载荷会远大于初始预紧力，且柱销剪切力远远小于外载荷。.（4）在双螺母PRSM运行过程中，丝杠和滚柱#1之间接触点处的滑滚比会与丝杠和滚柱#2之间接触点处的滑滚比具有很大的差异。由于摩擦力的影响，丝杠旋转方向的改变会引起行星滚柱丝杠各个零件运动、受力和变形的突变。.（5）零件位置误差对滚柱间载荷分配有着显著影响。丝杠和螺母轴线重合的装配状态能够改善滚柱间载荷分配不均。螺纹分头误差对螺纹牙载荷分布的影响远大于其对滚柱间载荷分配的影响。.本研究系统性地完成了不同结构、误差和工况条件下的PRSM运动、受力和变形计算与分析，对于研制高性能PRSM，促进PRSM在航空航天、船舶、智能装备等领域的应用具有重要的理论意义和工程应用价值。