Meshing Theory and Contact Characteristics Analysis of the Recirculating Planetary Roller Screw Mechanism

doi:10.3901/JME.2025.05.202

Abstract

Abstract: According to the structural characteristics of the recirculating planetary roller screw mechanism that the rollers have no helix angle, the spiral raceway surface equations of the screw, roller and nut are established, and the spatial meshing model of recirculating planetary roller screw mechanism is calculated. The meshing point position and axial clearance are formulated, and the influence of the flank angle and the pitch on the meshing point position and axial clearance are discussed, respectively. Besides, the main curvature of the recirculating planetary roller screw mechanism is derived based on the principle of differential geometry. The Hertzian contact theory is used to solve the main curvature difference, contact ellipse area and maximum contact stress between the roller and the raceway, and the influence of the flank angle and the pitch on the contact characteristics are investigated. The results show that the meshing point position on the screw-roller interface always deviates from the line between the screw and roller axis, and the meshing point on the screw and roller is located toward the top of their thread. If the flank angles of the roller and the nut are equal, the meshing point position on the roller-nut interface will be located at the tangent point of the pitch diameter of the two threads. The nominal radius of the part can be used instead of the meshing radius to approximately calculate the principal curvature of the recirculating planetary roller screw mechanism. With the flank angle increases, the principal curvature difference and the contact ellipse area of the two contact interfaces simultaneously decrease, and the maximum contact stress on the thread teeth gradually increases. Increasing the pitch causes the principal curvature difference to increase gradually. However, the contact ellipse area and maximum contact stress do not change significantly. Therefore, in order to achieve the optimal design of the recirculating planetary roller screw mechanism, it is not advisable to set an excessively large flank angle.

Key words: recirculating planetary roller screw mechanism, helical surface, meshing mechanism, contact characteristics

CLC Number:

TH132

QIAO Guan, LIU Fule, TANG Shufeng, LI Zongxue, FU Xiaojun. Meshing Theory and Contact Characteristics Analysis of the Recirculating Planetary Roller Screw Mechanism[J]. Journal of Mechanical Engineering, 2025, 61(5): 202-213.

References

[1] QIAO G，LIU G，SHI Z，et al. A review of electromechanical actuators for More/All Electric aircraft systems[J]. Proceedings of the Institution of Mechanical Engineers，Part C：Journal of Mechanical Engineering Science，2018，232(22)：4128-4151.
[2] GARCIA A，CUSIDO J，ROSERO J A，et al. Reliable electro-mechanical actuators in aircraft[J]. Aerospace and Electronic Systems Magazine，IEEE，2008，23(8)：19-25．
[3] XING M，ZHANG B，LIU S，et al. Elastohydrodynamic lubrication analysis with eccentric errors for planetary roller screw mechanism[J]. Tribology International，2024，193，109362.
[4] 董永，刘更，马尚君，等. 行星滚柱丝杠副滚柱的设计方法与虚拟装配[J]. 机械设计，2013，30(8)：53-58. DONG Y，LIU G，MA S J，et al. Design method and virtual assembly of the planetary roller screw mechanism roller[J]. Journal of Mechanical Transmission，2013，30(8)：53-58.
[5] MA S J，LIU G，TONG R T，et al. A new study on the parameter relationships of planetary roller screws[J]. Mathematical Problems in Engineering，2012，340437：1-29.
[6] VELINSKY S A，CHU B，LASKY T A. Kinematics and efficiency analysis of the planetary roller screw mechanism[J]. Journal of Mechanical Design，2009，131(1)：1-6.
[7] JONES M H，VELINSKY S A. Kinematics of roller migration in the planetary roller screw mechanism[J]. Journal of Mechanical Design，2012，134(1)：1-6.
[8] 马尚君，刘更，佟瑞庭，等. 考虑滚柱节圆偏移的反向式行星滚柱丝杠副运动学分析[J]. 中国机械工程，2014，25(11)：1421-1426. MA S J，LIU G，TONG R T，et al. Kinematic analysis of an inverted planetary roller screw considering roller pitch circle mismatch[J]. China Mechanical Engineering，2014，25(11)：1421-1426.
[9] FU X J，LIU G，MA S J，et al. A comprehensive contact analysis of planetary roller screw mechanism[J]. Journal of Mechanical Design，2017，139(1)：012302.
[10] SANDU S，BIBOULET N，NELIAS D，et al. An efficient method for analyzing the roller screw thread geometry[J]. Mechanism and Machine Theory，2018，126：243-264.
[11] YAO Q，LIU Y S，ZHANG M C，et al. Investigation on the uncertain factors of the elastic–plastic contact characteristics of the planetary roller screw mechanism[J]. Proceedings of the Institution of Mechanical Engineers，Part C：Journal of Mechanical Engineering Science，2019，233(5)：1795-1806.
[12] HU R，WEI P T，DU X S，et al. Investigation of loaded contact characteristics of planetary roller screw mechanism based on influence coefficient method and machine learning[J]. Advanced Engineering Informatics，2023，58：102146.
[13] DU X，CHEN B，ZHENG Z. Investigation on mechanical behavior of planetary roller screw mechanism with the effects of external loads and machining errors[J]. Tribology International，2021，154：106689.
[14] XIE Z J，WANG Y，NI J N，et al. Friction torque analysis of planetary roller screw based on the creepage theory[J]. Tribology International，2023，178：108059.
[15] CHENG Z，ZU L，XING M，et al. Effects of eccentric errors on sliding velocity and accumulative wear depth of planetary roller screw mechanism[J]. Journal of Tribology，2024：1-18.
[16] JONES M H，VELINSKY S A. Contact kinematics in the roller screw mechanism[J]. Journal of Mechanical Design，2013，135(5)：051003.
[17] LIU Y，WANG J，CHENG H，et al. Kinematics analysis of the roller screw based on the accuracy of meshing point calculation[J]. Mathematical Problems in Engineering，2015(1)：1.
[18] 付晓军，刘更，马尚君，等. 行星滚柱丝杠副螺旋曲面啮合机理研究[J]. 机械工程学报，2016，52(3)：26-33. FU Xiaojun，LIU Geng，MA Shangjun，et al. Studies on meshing mechanism of helical surfaces in planetary roller screw mechanism[J]. Journal of Mechanical Engineering，2016，52(3)：26-33.
[19] 付晓军，刘更，马尚君，等. 考虑零件偏斜的行星滚柱丝杠副啮合特性研究[J]. 机械工程学报，2017，53(3)：25-33. FU Xiaojun，LIU Geng，MA Shangjun，et al. Meshing properties of planetary roller screw mechanism within misalignments[J]. Journal of Mechanical Engineering，2017，53(3)：25-33.
[20] 徐强，王水铭，赵国平，等. PWG型差动丝杠的啮合干涉分析与消除[J]. 组合机床与自动化加工技术，2015(9)：107-109. XU Qiang，WANG Shuiming，ZHAO Guoping，et al. The analysis of meshing interference and elimination of PWG planetary roller screw[J]. Modular Machine Tool & Automatic Manufacturing Technique，2015(9)：107-109.
[21] 乔冠，刘更，马尚君. 行星滚柱丝杠副主曲率计算与接触特性分析[J]. 机械工程学报，2020，56(21)：140-148. QIAO Guan，LIU Geng，MA Shangjun. Principal curvature calculation and contact characteristics analysis of the planetary roller screw mechanism[J]. Journal of Mechanical Engineering，2020，56(21)：140-148.
[22] 吴林萍，马尚君，许千斤，等. 考虑弹性变形的行星滚柱丝杠接触特性[J]. 机械工程学报，2024，60(5)：130-141. WU Linping，MA Shangjun，XU Qianjin，et al. Contact characteristics of planetary roller screw mechanism considering elastic deformation[J]. Journal of Mechanical Engineering，2024，60(5)：130-141.
[23] LITVIN F L. Gear geometry and applied theory[M]. New Jersey：PTR Prentice Hall，1994.