行星滚柱丝杠副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与运动的传动机构。基于多头螺纹结构特点，建立了丝杠、滚柱和螺母螺纹的曲面方程。利用啮合曲面的连续相切接触条件，通过引入丝杠、滚柱或螺母螺旋曲面沿轴线移动的矢量，提出一种行星滚柱丝杠副啮合点位置与轴向侧隙的计算方法。在此基础上，推导得出丝杠和滚柱与螺母和滚柱之间的啮合方程以及轴向侧隙公式，将该啮合方程与现有计算方法进行比较验证其正确性，并进一步分析了当丝杠、滚柱和螺母牙型角相同时行星滚柱丝杠副的啮合点位置、轴向侧隙以及啮合螺旋曲面之间的轴向间隙分布。结果表明：丝杠和滚柱的啮合点会偏向二者螺纹牙顶；螺母和滚柱的啮合点位于螺纹中径切点处；为实现无侧隙设计，丝杠、滚柱和螺母应具有不同牙厚。
Planetary roller screw mechanism (PRSM) transfers power and movement by the meshing of helical surfaces of a few rollers contacting with the screw and nut. The helical surface equations of roller, screw and nut thread surfaces are established based on the multi-start thread structural characteristics. According to the continuous tangency conditions of meshing surfaces, a method to calculate the meshing point positions and axial clearances of the PRSM is presented by utilizing the vectors described the translation of the screw, roller and nut thread surfaces along their axis. Then, the meshing equations and the axial clearances at the screw/roller and nut/roller interfaces are derived. By comparing the results obtained by existed calculation method with those by the presented meshing equations, the feasibility of meshing equations is validated. The meshing point positions, axial clearances of PRSM and axial gap distributions of two meshing surfaces are analyzed in the case that the screw, roller and nut’s flank angles are identical. The results show that the meshing point at screw/roller interface will incline to the top of the screw and roller’s thread; the meshing point at nut/roller interface will lie on the tangent point of pitch circles of the two meshing components; in order to eliminate the axial clearance during the design, the thread thickness of the screw, roller and nut should be different.
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