中文摘要：

丝杠、滚柱和螺母在实际工作状态下不可避免偏斜,会对行星滚柱丝杠副的承载、效率和寿命等传动性能产生重要影响。基于此问题,提出一种当零件出现偏斜时,丝杠、滚柱和螺母每对相啮合螺纹牙啮合位置以及间隙的计算方法。借鉴齿轮啮合原理,给出考虑零件偏斜的螺旋曲面相切接触条件,建立丝杠、滚柱和螺母的螺旋曲面方程,并应用坐标变换对零件的偏斜进行描述。在此基础上,推导出丝杠和滚柱以及螺母和滚柱存在相对偏斜时,不同螺纹牙啮合位置及间隙的求解方程。通过与已有模型在不考虑零件偏斜时的啮合位置计算结果对比,验证了其正确性。研究当滚柱相对丝杠发生偏斜时,两零件之间的啮合特性。结果表明,出现偏斜时,不仅丝杠或滚柱不同螺纹牙的啮合半径不同,而且各螺纹牙的啮合偏角也不再相同,同时丝杠和滚柱的多对螺纹牙不能够同时啮合。

英文摘要：

The unavoidable misalignments of the screw,roller and nut have great influences on the performances of planetary roller screw mechanism（PRSM） such as load carrying capacity,efficiency and lifetime.A method is proposed to calculate the meshing positions and clearances of each pair of thread teeth in the PRSM under the consideration of misalignments.The tangency conditions of mating thread surfaces within misalignments are developed by employing the theory of gearing and the tooth contact analysis.The vector functions of thread surfaces on the screw,roller and nut are developed and the misalignments of each component are described by coordinate transformations.Then,the equations to calculate the meshing positions and clearance of each pair of mating thread surfaces at screw/roller and nut/roller interfaces in the misaligned PRSM are derived.By comparing the meshing positions of the aligned PRSM obtained by the existed method with those by the proposed method,the feasibility of the proposed method is validated.The meshing properties at screw/roller interface are analyzed when misalignment occurs.The results show that the meshing radius of multiple thread teeth of the screw or the roller are not identical and the meshing angles of those thread teeth are also different;the multiple pairs of mating thread teeth at screw/roller interface cannot mesh with each other simultaneously.