A General Method for Multi-tooth Contact Analysis of Cycloid-pin Gear Transmission

Abstract

Abstract: In order to effectively reveal the influences of tooth profile modification, elastic contact deformation and load variation on multi-tooth meshing contact dynamic characteristics of cycloid-pin gear transmission, a general dynamics analysis method was proposed based on the multi-body dynamics theory and elastic contact theory, which might be used to exactly predict the engagement number in cycloid-pin gear transmission, locate the contact point and get the contact load. A multi-rigid-body system of cycloid-pin gear transmission was modeled firstly. Secondly, at any moment of numerical calculation, the contact conditions between the discrete points on cycloid gear profile and pins were checked to meet the requirements or not. Then, the maximum contact depth was determined and the normal contact force was calculated. Finally, the contact force was converted to the generalized force, and the dynamics equations of the cycloid-pin gear transmission system with multi-tooth meshing contacts were formulated. The effects of profile modification, elastic contact deformation and load variation on multi-tooth meshing contact dynamics characteristics of a specific cycloid-pin gear transmission system were analyzed. The results indicate that the real numbers of pins to transmit load are determined by the characteristics of tooth profile modification and external torque. For the cycloid-pin gear systems with different transmission ratios, the estimation of the numbers of pins to transmit load and the calculation of contact force can be finished efficiently and accurately by this approach.

Key words: cycloid-pin gear transmission, multi-tooth meshing, contact dynamics, multi-body dynamics

摘要： 为有效地揭示齿廓修形、弹性接触及负载变化对摆线针轮传动多齿啮合接触动态特性的影响规律，基于多体动力学和弹性接触理论提出了一种可精确预估摆线针齿动态啮合对数、确定接触点位置并获取接触载荷的动力学分析方法。首先，建立了摆线针轮系统刚体多体动力学模型；其次，在数值计算的任一时刻，循环判断摆线齿廓的离散点与各个针齿之间是否满足接触条件，确定最大接触深度并计算法向接触载荷；最后，将摆线针齿接触载荷等效为系统广义力，建立了含多齿啮合接触关系的摆线针轮传动系统动力学方程。在此基础上，以某一针摆传动系统为算例，分析齿廓修形、弹性接触及负载变化对摆线针轮传动多齿啮合接触动态特性的影响。研究结果表明，摆线针轮传动的实际传力针齿数由齿廓修形和负载特性决定。该方法对于具有不同传动比的摆线针轮传动系统，均能高效准确地完成齿廓修形和负载变化条件下的传力针齿数预估和接触载荷计算。

关键词: 摆线针轮传动, 多齿啮合, 接触动力学, 多体动力学

CLC Number:

TH113

Xu Lixin, Yang Yuhu. A General Method for Multi-tooth Contact Analysis of Cycloid-pin Gear Transmission[J]. China Mechanical Engineering.

许立新, 杨玉虎. 一种摆线针轮传动多齿啮合接触特性分析方法[J]. 中国机械工程.

References

[1]何卫东，李力行，李欣. 机器人用高精度RV传动中摆线轮修形对回差影响的研究[J].机械传动，1999，23(1)：24-25.

He Weidong，Li Lixing，Li Xin. The Influence of Modification of Cycloid Gear on the Lost Motion of High Precision RV Transmission Used in Robots[J]. Journal of Mechanical Transmission，1999，23(1)：24-25.

[2]关天民. 摆线针轮行星传动中摆线轮最佳修形量的确定方法[J].中国机械工程，2002，13(10)：811-815.

Guan Tianmin. The Optimum Profile Modification on Cycloid Disks in the Cycloid Gearing Mechanism with Small Teeth Difference[J].China Mechanical Engineering，2002，13(10)：811-815.

[3]关天民，张东生. 摆线针轮行星传动中反弓齿廓研究及其优化设计[J]. 机械工程学报，2005，41(1)：151-156.

Guan Tianmin，Zhang Dongsheng. Inverse Arch-shaped Teeth Profile and Its Optimization in a Cycloid Drive[J]. Journal of Mechanical Engineering，2005，41(1)：151-156.

[4]Chen Bingkui，Zhong Hui，Liu Jingya，et al. Generation and Investigation of a New Cycloid Drive with Double Contact[J]. Mechanism and Machine Theory，2012，49(4)：270-283.

[5]李充宁，刘继岩，孙涛. 2K-V型行星传动中摆线针轮啮合的传动精度研究[J]. 机械工程学报，2001，37(4)：61-65.

Li Chongning，Liu Jiyan，Sun Tao. Study on Transmission Precision of Cycloidal Pin Gear in 2K-V Planetary Drives[J]. Journal of Mechanical Engineering，2001，37(4)：61-65.

[6]韩林山，沈允文，董海军，等. 2K-V型传动装置动态传动精度理论研究[J]. 机械工程学报，2007，43(6)：81-86.

Han Linshan，Shen Yunwen，Dong Haijun，et al. Theoretical Research on Dynamic Transmission Accuracy for 2K-V Type Drive[J]. Journal of Mechanical Engineering，2007，43(6)：81-86.

[7]杨玉虎，张洁，许立新. RV传动机构精度分析[J]. 天津大学学报，2013，46(7)：623-628.

Yang Yuhu，Zhang Jie，Xu Lixin. Precision Analysis of RV Transmission Mechanism[J].Journal of Tianjin University，2013，46(7)：623-628.

[8]张大卫，王刚，黄田，等. RV减速机动力学建模与结构参数分析[J]. 机械工程学报，2001，37(1)：69-74.

Zhang Dawei，Wang Gang，Huang Tian，et al. Dynamic Formulation of RV Reducer and Analysis of Structural Parameters[J]. Journal of Mechanical Engineering，2001，37(1)：69-74.

[9]杨玉虎，朱临宇，陈振宇，等. RV减速器扭转刚度特性分析[J]. 天津大学学报，2015，48(2)：111-118.

Yang Yuhu，Zhu Linyu，Chen Zhenyu，et al. Analysis of the Characteristics of Torsional Stiffness of RV Reducer[J]. Journal of Tianjin University，2015，48(2)：111-118.

[10]Hsieh C F. Dynamics Analysis of Cycloidal Speed Reducers with Pinwheel and Nonpinwheel Designs[J]. Journal of Mechanical Design，2014，136(9)：543-552.

[11]Li Shuting. Design and Strength Analysis Methods of the Trochoidal Gear Reducers[J]. Mechanism and Machine Theory，2014，81(11)：140-154.

[1]	CHENG Jiayuan;REN Tingzhi;ZHANG Zilong ;LIU Dawei ;JIN Xin. Multi-body Dynamics Analysis and Test Verification for Inertia Cone Crushers [J]. China Mechanical Engineering, 2020, 31(19): 2322-2331.
[2]	GE Wentao;HUANG Hui;LIU Zhou;QIU Xing;JIA Huifang. Load Spectrum Development Methodology for Accelerating Dynamics Model Virtual Iteration [J]. China Mechanical Engineering, 2020, 31(12): 1504-1511.
[3]	CHEN Ziming1,2;XUE Zhigang1,2;ZHANG Song3;LI Luoxing1,2. Closing Effort Analysis of Sliding Doors Based on Co-simulation of ADAMS and Simulink [J]. China Mechanical Engineering, 2020, 31(08): 924-930.
[4]	LI Shuya1;GU Zhengqi1,2;HUANG Taiming3;LIU Jun1;ZHENG Ledian1. Two-way Coupling Analysis of Vehicle Stability in Different Crosswind Conditions [J]. China Mechanical Engineering, 2019, 30(19): 2276-2286.
[5]	HAO Bingfei;WANG Hongyan;RUI Qiang;WANG Qinlong. Dynamics Modeling and Model Test Verification of Tank Multi-body Systems [J]. China Mechanical Engineering, 2018, 29(04): 429-433,440.
[6]	LIANG Mingxuan1,2,3;LI Zhenggang2;TANG Renzhong1;CHEN Li2;HUANG Chuan2. Structure Optimization Design of Robot Arm Based on Flexible Multi-body Dynamics [J]. China Mechanical Engineering, 2017, 28(21): 2562-2566.
[7]	Liu Rongsheng, Li Hui, Gao Yingjie, Yang Yulin. Vibration Analysis and Experimental Test of a Boom System of Truck Mounted Concrete Pump [J]. China Mechanical Engineering, 2015, 26(15): 2125-2129.
[8]	Liu Tingwei, Zhang Ning, Liang Wei, Zhang Liang. Failure Simulation Analysis and Eexperimental Verification of Bearings for Spaceborne Moving Mechanism [J]. China Mechanical Engineering, 2014, 25(21): 2864-2868.
[9]	TANG Hao, DUAN Ji-An, ZHENG Yu, CHU Meng-Feng. Motion Error Sensitivity Analysis of Planar Optical Waveguide Precise Aligning Stage [J]. China Mechanical Engineering, 2012, 23(8): 888-892,896.
[10]	LIU Wen-Ji-1, SONG Chao-Sheng-2, HONG Yang-1. Meshing Impact Analysis and Profile Modification of Planetary Gear Drive with Small Tooth Number Difference [J]. China Mechanical Engineering, 2012, 23(4): 425-429.
[11]	TAO Ting-Jiang, TAN Yang, WANG Li-Da. Flexible Multibdoy Contact Dynamics Analysis on Angular Contact Ball Bearings [J]. China Mechanical Engineering, 2011, 22(9): 1054-1059.
[12]	JI De-Sheng, HUANG Xue-Gong, WANG Yong. Study on Modified Involute Profile Roller Chain Sprocket and Its Dynamic Features [J]. China Mechanical Engineering, 2011, 22(9): 1118-1122.
[13]	YANG Zhi-Jun, FENG Wen-Xian, CHEN Xin. Research on Equivalent Multi-body Dynamics Model for Nonlinear Cable Elements [J]. China Mechanical Engineering, 2011, 22(3): 262-265.
[14]	CHOU Wu-Qing, WANG Shuo. Research on Obstacle Avoidance by Virtual Force for Redundant Robot [J]. China Mechanical Engineering, 2011, 22(24): 2899-2902.
[15]	TUN Chun-Yan-1, 2, JIN Xin-1, HE Yu-Lin-1, WANG Lei-1, LIU Hua-1. Load Calculation of Wind Turbine Subjected to Earthquake and Wind [J]. China Mechanical Engineering, 2011, 22(18): 2236-2240.