反向式行星滚柱丝杠承载分布及寿命分析
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摘要
反向式行星滚柱丝杠是一种承载能力强,精度高、寿命长的直线传动机构。目前国内外对该机构的研究较少且不能综合分析不同承载条件下各结构参数对载荷分布及疲劳寿命的影响。因此,作者建立了其载荷分布、轴向变形和寿命的计算模型。在柱面坐标系中分别建立丝杠、滚柱和螺母的曲面方程;利用曲面啮合理论求出IPRS一个节距内滚柱分别与丝杠和螺母的啮合点;依据曲面方程和啮合点位置,利用赫兹接触理论建立啮合面接触变形的精确计算方式。根据赫兹变形、组件轴向变形及螺牙变形的几何关系建立载荷分布计算模型,并依据该模型得出特定参数下IPRS承载端的轴向变变形;依据求出的载荷分布、基于Lundberg–Palmgren方程建立寿命评估模型。将承载端轴向变形计算结果与实验数据对比,验证了该模型的准确性。针对关键参数于IPRS性能的影响进行分析,结果表明:载荷分布主要受螺牙数目、滚柱数目和螺旋角的影响,偏载率随着三者增加而增大;轴向刚度受滚柱数目、螺牙数目、螺旋角和螺母外径影响较大,其随滚柱数目和螺母外径的增大而增大,随螺牙数目和螺旋角的增大先增大后减小;接触疲劳寿命受滚柱数目、牙型半径、螺牙数目和接触角影响较大,其随着滚柱数目、牙型半径、螺牙数目的增大而增大,随着接触角的增大而减小。
Inverted planetary roller screw(IPRS) is a kind of linear transmission mechanism which has advantages of high load carrying capability, long fatigue life, high transmission accuracy and low noise. Due to these advantages, it has wide application prospect in the fields of aerospace, weapon equipment, CNC machine tools and petrochemical industry. Up to the present, there is little research about this mechanism.Therefore, a model was derived to calculate load distribution, axial deformation and contact fatigue life. Firstly, surface equation of screw, roller and nut was established. Based on Surface meshing theory, the meshing points of the roller with the screw and nut in a pitch were derived respectively. According to the surface equations and the location of contact points, an accurate method to calculate the elastic deformaion between the meshing surface was derived. Secondly, A model of IPRS's load distribution was obtained based on the geometric relationships between Hertz deformation, thread deformation and axial deformation. Based on its load distribution condition and motion principle, a fatigue life model was deduced using Lundberg–Palmgren equation. Then, a program was compiled in the MATLAB Environmet to calculate load distribution axial deformation and contact fatigue life. By comparing calculationg result with the expriments, the load distribution and axial deformation model was verified. The influence of the key parameters on the performance of IPRS was analyzed and the following results were derived. The load distribution was mainly influenced by the number of teeth, the number of rollers and the helix angle, and increased with the increases of these three factors. The axial stiffness was mainly influenced by the number of teeth, the number of rollers, the helix angle and the outer diameter of the nut,and increased with the increases of the number of rollers and the outer diameter of the nut, increased first and then decreased with the increase of the number of teeth and the helix angle. The contact fatigue life was mainly influenced by the number of teeth, the number of rollers, the contact angle and the radius of thread profile, and increased with the increases of the number of teeth, the number of rollers and the radius of thread profile, decreased with the increase of contact angle.
Inverted planetary roller screw(IPRS) is a kind of linear transmission mechanism which has advantages of high load carrying capability, long fatigue life, high transmission accuracy and low noise. Due to these advantages, it has wide application prospect in the fields of aerospace, weapon equipment, CNC machine tools and petrochemical industry. Up to the present, there is little research about this mechanism.Therefore, a model was derived to calculate load distribution, axial deformation and contact fatigue life. Firstly, surface equation of screw, roller and nut was established. Based on Surface meshing theory, the meshing points of the roller with the screw and nut in a pitch were derived respectively. According to the surface equations and the location of contact points, an accurate method to calculate the elastic deformaion between the meshing surface was derived. Secondly, A model of IPRS's load distribution was obtained based on the geometric relationships between Hertz deformation, thread deformation and axial deformation. Based on its load distribution condition and motion principle, a fatigue life model was deduced using Lundberg–Palmgren equation. Then, a program was compiled in the MATLAB Environmet to calculate load distribution axial deformation and contact fatigue life. By comparing calculationg result with the expriments, the load distribution and axial deformation model was verified. The influence of the key parameters on the performance of IPRS was analyzed and the following results were derived. The load distribution was mainly influenced by the number of teeth, the number of rollers and the helix angle, and increased with the increases of these three factors. The axial stiffness was mainly influenced by the number of teeth, the number of rollers, the helix angle and the outer diameter of the nut,and increased with the increases of the number of rollers and the outer diameter of the nut, increased first and then decreased with the increase of the number of teeth and the helix angle. The contact fatigue life was mainly influenced by the number of teeth, the number of rollers, the contact angle and the radius of thread profile, and increased with the increases of the number of teeth, the number of rollers and the radius of thread profile, decreased with the increase of contact angle.
引文
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[6]Yang Jiajun,Wei Zhenxing,Zhu Jisheng,et al.Calculation of load distribution of planetary roller screws and static rigidity[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2011(4):1-4.[杨家军,韦振兴,朱继生,等.行星滚柱丝杠副载荷分布及刚度计算[J].华中科技大学学报(自然科学版),2011(4):1-4.]
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[9]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.[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.]
[10]万长森.滚动轴承的分析方法[M].北京:机械工业出版社,1987.
[11]山本晃,郭可谦.螺纹联接的理论与计算[M].上海:上海科学技术文献出版社,1984.
[12]Aurégan G,Fridrici V,Kapsa P,et al.Experimental simulation of rolling-sliding contact for application to planetary roller screw mechanism[J].Wear,2015,332:1176-1184.
[13]Zhao Guoping,Dong Huili,Wang Chunming,et al.Whole fatigue life of helical gear covering crack initiation stage and propagation process[J].Tribology,2016,36(5):643-649.[赵国平,董辉立,王春明,等.斜齿轮疲劳裂纹萌生及扩展过程全寿命研究[J].摩擦学学报,2016,36(5):643-649.]
[14]Harris T A,Yu W K.Lundberg-Palmgren fatigue theory:Considerations of failure stress and stressed volume[J].Journal of Tribology,1999,121(1):85-89.
[15]Abevi F K,Daidie A,Chaussumier M,et al.Static analysis of an inverted planetary roller screw mechanism[J].Journal of Mechanisms&Robotics,2016,8(4):56-61.
[2]Lemor P C.The roller screw,an efficient and reliable mechanical component of electro-mechanical actuators[C]//Energy Conversion Engineering Conference.New York:IEEE,2002.
[3]Dang Jinliang,Liu Geng,Ma Shangjun.Motion principle and simulation analysis of inverted planetary roller screw mechanism[J].Journal of System Simulation,2013,25(7):1646-1651.[党金良,刘更,马尚君,等.反向式行星滚柱丝杠机构运动原理及仿真分析[J].系统仿真学报,2013,25(7):1646-1651.]
[4]Ma Shangjun,Liu Geng,Tong Ruiting,et al.Kinematic analysis of an inverted planetary roller screw considering roller pitch circle mismatch[J].China Mechanical Engineering,2014,25(11):1421-1426.[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.]
[5]Jin Qianzhong,Yang Jiajun,Sun Jianli.A comparative study of static stiffness between ball screw and planetary roller screw[J].Mechanical Science and Technology for Aerospace Engineering,1999(2):230-232.[靳谦忠,杨家军,孙健利.滚珠丝杠副和行星式滚柱丝杠副静刚度的比较研究[J].机械科学与技术,1999(2):230-232.]
[6]Yang Jiajun,Wei Zhenxing,Zhu Jisheng,et al.Calculation of load distribution of planetary roller screws and static rigidity[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2011(4):1-4.[杨家军,韦振兴,朱继生,等.行星滚柱丝杠副载荷分布及刚度计算[J].华中科技大学学报(自然科学版),2011(4):1-4.]
[7]Jones M H,Steven A V.Stiffness of the roller screw mechanism by the direct method[J].Mechanics Based Design of Structures&Machines,2014,42(1):17-34.
[8]Jones M H,Velinsky S A.Contact kinematics in the roller screw mechanism[C]//Proceedings of ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.Chicag:ASME 2013:451-459.
[9]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.[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.]
[10]万长森.滚动轴承的分析方法[M].北京:机械工业出版社,1987.
[11]山本晃,郭可谦.螺纹联接的理论与计算[M].上海:上海科学技术文献出版社,1984.
[12]Aurégan G,Fridrici V,Kapsa P,et al.Experimental simulation of rolling-sliding contact for application to planetary roller screw mechanism[J].Wear,2015,332:1176-1184.
[13]Zhao Guoping,Dong Huili,Wang Chunming,et al.Whole fatigue life of helical gear covering crack initiation stage and propagation process[J].Tribology,2016,36(5):643-649.[赵国平,董辉立,王春明,等.斜齿轮疲劳裂纹萌生及扩展过程全寿命研究[J].摩擦学学报,2016,36(5):643-649.]
[14]Harris T A,Yu W K.Lundberg-Palmgren fatigue theory:Considerations of failure stress and stressed volume[J].Journal of Tribology,1999,121(1):85-89.
[15]Abevi F K,Daidie A,Chaussumier M,et al.Static analysis of an inverted planetary roller screw mechanism[J].Journal of Mechanisms&Robotics,2016,8(4):56-61.