考虑滚柱偏斜的行星滚柱丝杠载荷分布计算方法  

The Calculation Method for the Load Distribution in the Planetary Roller Screw Mechanism with the Roller Deviation

作　　者：付晓军[1] 徐烨 刘更[1] 李欣[1] 马尚君[1] FU Xiaojun;XU Ye;LIU Geng;LI Xin;MA Shangjun(Shaanxi Engineering Laboratory for Transmissions and Controls,Northwestern Polytechnical University,Xi’an 710072)

机构地区：[1]西北工业大学陕西省机电传动与控制工程实验室,西安710072

出　　处：《机械工程学报》2024年第13期247-256,共10页Journal of Mechanical Engineering

基　　金：国家重点研发计划(2023YFB3406401);国家自然科学基金(51905428)资助项目。

摘　　要：滚柱在实际工作状态下不可避免的偏斜,会引起螺纹严重承载不均,是导致螺纹发生严重压溃失效的主要原因之一。针对现有静力学模型均基于螺母、丝杠和滚柱轴线相互平行假设的不足,提出了一种考虑滚柱偏斜及螺纹牙脱啮现象的行星滚柱丝杠载荷分布计算方法。建立了包含滚柱相对螺母与丝杠偏斜的静力学模型,推导了计入各对螺纹牙啮合状态变化的刚度矩阵和平衡方程,给出多载荷步求解流程。通过与有限元模型在无误差及包含滚柱偏斜时的载荷分布计算结果对比,验证其正确性。分析了滚柱偏斜对行星滚柱丝杠螺纹牙啮合状态和载荷分布的影响规律。结果表明,滚柱偏斜角ϕq和ψq均会对螺纹牙间的载荷分布产生显著影响。合适的偏斜角ϕq能够改善螺纹牙之间的载荷分布。偏斜角ψq的增加会引起螺纹牙所受最大接触力的急剧增加。当|ψq|>1.0′时,螺纹牙会出现明显脱啮现象,且最大螺纹牙受力约为理想状态的3倍。The unavoidable deviation of the roller will cause the seriously uneven load distribution among threads.It is one of the main reason for the collapse failure of thread teeth at the single-sided of the roller.Nevertheless,the axes of the screw,roller and nut are assumed to be parallel to each other in the previously published static models.A method is proposed to calculate the load distribution of the PRSM with the deviation of the roller and mesh-apart of thread teeth.A static model of the PRSM with the roller deviation is proposed.The stiffness matrix and equilibrium equation are derived with consideration of the change of the meshing states of thread teeth.The flowchart to solve the equation is given by dividing the external load of the nut into multiple load steps.By comparing the load distribution of the PRSM without/with the roller deviation obtained from the finite element model with those from the proposed method,the feasibility of the proposed method is validated.The meshing state and load distribution of the PRSM with the roller deviation is analyzed.The results show that the roller deviation anglesϕq andψq have great influences on the load distribution.A proper deviation angleϕq could reduce the maximum contact force acting on threads.The maximum contact force on threads increases sharply with the increase of the deviation angleψq.When|ψq|>1.0′,the mesh-apart of thread teeth can be observed and the maximum contact forces on the thread teeth is about 3 times larger than that on the thread teeth without deviation.

关 键 词：行星滚柱丝杠 偏斜 脱啮 载荷分布 弹性变形 

分 类 号：TH132.1[机械工程—机械制造及自动化]