Electromechanically coupled dynamic modeling and analysis of a precision cycloidal reducer based on the small⁃vibration coordinate method

DU Wenwen; WEI Zuoxin; ZHANG Yinghui; HE Weidong

doi:null

您当前的位置：

首页 >

文章列表页 >

Electromechanically coupled dynamic modeling and analysis of a precision cycloidal reducer based on the small⁃vibration coordinate method

更新时间：2026-10-16

- Electromechanically coupled dynamic modeling and analysis of a precision cycloidal reducer based on the small⁃vibration coordinate method
- Journal of Mechanical Transmission Pages: 1-12(2026)
- 作者机构：
  
  大连交通大学机械工程学院，大连 116028
- 作者简介：
- 基金信息：
- DOI：
  CLC： TH132.46
- Received：21 July 2026，
  
  Revised：2026-08-11，
  
  Accepted：12 August 2026，
  
  Online First：15 October 2026，
- 稿件说明：
移动端阅览
杜文文，卫作鑫，张迎辉，等.基于小振动坐标法的精密摆线减速器机电耦合动力学建模与分析［J］.机械传动，XXXX，XX（XX）：1-12.

DU Wenwen，WEI Zuoxin，ZHANG Yinghui，et al.Electromechanically coupled dynamic modeling and analysis of a precision cycloidal reducer based on the small⁃vibration coordinate method［J］.Journal of Mechanical Transmission，XXXX，XX（XX）：1-12.
杜文文，卫作鑫，张迎辉，等.基于小振动坐标法的精密摆线减速器机电耦合动力学建模与分析［J］.机械传动，XXXX，XX（XX）：1-12. DOI：

DU Wenwen，WEI Zuoxin，ZHANG Yinghui，et al.Electromechanically coupled dynamic modeling and analysis of a precision cycloidal reducer based on the small⁃vibration coordinate method［J］.Journal of Mechanical Transmission，XXXX，XX（XX）：1-12. DOI：

摘要

目的

揭示误差激励与电动机输入共同作用下精密摆线减速器的耦合振动机制，为误差控制及机电参数优化提供理论依据。

方法

首先，以标准三曲柄双摆线轮精密摆线减速器为对象，基于小振动坐标法和拉格朗日方程，建立了包含输入轴、曲柄轴、摆线轮、输出行星架的11自由度平面弯扭耦合动力学模型，并结合伺服电动机电压-电流-电磁转矩增量关系构建了机电耦合动力学方程；其次，模型考虑了输入级齿轮副时变啮合、偏心轴承二维弹性支承及摆线针齿副单边接触特性，分析了误差激励、负载波动、电动机参数对系统动态响应的影响。

结果

输入端扭转振动经曲柄轴和偏心轴承转化为摆线轮平面振动，并通过偏心支承反力传递至输出行星架，形成输入扭转-摆线轮平面运动-输出扭转的耦合传递路径。输入级齿轮误差主要影响输入轴和曲柄轴的扭转响应，其影响沿传动链向输出端逐渐衰减；摆线针齿误差通过改变多齿接触状态和瞬时载荷分配，对输出动态传动误差影响更显著。与基准工况相比，输入级齿轮误差、摆线针齿误差和负载波动增大时，输出动态传动误差峰峰值分别提高12.37%、30.55%、7.96%。输入轴速度波动与电流扰动通过反电动势和电磁转矩形成双向机电耦合；增大机械阻尼可有效抑制输入端振动，而减小绕组电感会加剧电流纹波。

Abstract

Objective

To reveal the coupled vibration mechanism of a precision cycloidal reducer under the combined effects of error excitations and motor input

and to provide a theoretical basis for error control and coordinated optimization of electromechanical parameters.

Methods

Firstly

a standard three-crank double-cycloid precision cycloidal reducer was investigated. Based on the small-vibration coordinate method and Lagrange equations

an 11-degree-of-freedom planar bending-torsional coupled dynamic model incorporating the input shaft

crankshafts

cycloidal gears

and output carrier was established. The incremental relation among servo-motor voltage

current

and electromagnetic torque were further introduced to formulate an electromechanical coupled dynamic model. Then

time-varying meshing of the input-stage gear pair

two-dimensional elastic support of the eccentric bearings

and unilateral contact of the cycloid-pin tooth pairs were considered to investigate the effects of error excitations

load fluctuations

and motor parameters on the dynamic responses.

Results

Torsional vibration at the input side is converted into planar vibration of the cycloidal gears through the crankshafts and eccentric bearings and is subsequently transmitted to the output carrier through eccentric-support reaction forces

forming a coupled transmission path of input torsion-cycloidal-gear planar motion-output torsion. The input-stage gear error mainly affects the torsional responses of the input shaft and crankshafts

and its influence gradually attenuates toward the output side

whereas the cycloid-pin tooth error directly changes the multi-tooth contact state and instantaneous load distribution and therefore has a greater influence on the output dynamic transmission error. Compared with the baseline condition

increases in the input-stage gear error

cycloid-pin tooth error

and load fluctuation increase the peak-to-peak output dynamic transmission error by 12.37%

30.55%

and 7.96%

respectively. Input-shaft speed fluctuations and current disturbances form a bidirectional electromechanical coupling through back electromotive force and electromagnetic torque. Increasing mechanical damping effectively suppresses input-side vibration

whereas reducing winding inductance intensifies current ripple.

关键词

Keywords

references

Pham A D ， Ahn H J . High precision reducers for industrial robots driving 4th industrial revolution：state of arts，analysis，design，performance evaluation and perspective ［J］. International Journal of Precision Engineering and Manufacturing-Green Technology ， 2018 ， 5 （ 4 ）： 519 - 533 .

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］. Chinese Journal of Mechanical Engineering ， 2001 ， 37 （ 1 ）： 69 - 74 .

郑钰馨，奚鹰，卜王辉，等 . RV减速器5自由度纯扭转模型非线性特性分析［J］. 浙江大学学报（工学版）， 2018 ， 52 （ 11 ）： 2098 - 2109 .

Zheng Yuxin ， Xi Ying ， Bu Wanghui ， et al . Nonlinear characteristic analysis of 5-degree-of-freedom pure torsional model of RV reducer ［J］. Journal of Zhejiang University （Engineering Science）， 2018 ， 52 （ 11 ）： 2098 - 2109 .

Wang S ， Tan J ， Gu J J ， et al . Study on torsional vibration of RV reducer based on time-varying stiffness ［J］. Journal of Vibration Engineering & Technologies ， 2021 ， 9 （ 1 ）： 73 - 84 .

Yang Y H ， Chen C ， Wang S Y . Response sensitivity to design parameters of RV reducer ［J］. Chinese Journal of Mechanical Engineering ， 2018 ， 31 （ 1 ）： 49 .

孟聪，陈川，杨玉虎 . RV减速器模态特性分析［J］. 中国机械工程， 2018 ， 29 （ 1 ）： 8 - 13 .

Meng Cong ， Chen Chuan ， Yang Yuhu . Modal characteristic analysis of RV reducers ［J］. China Mechanical Engineering ， 2018 ， 29 （ 1 ）： 8 - 13 .

杨云，李朝阳，李轩 . 基于能量法的摆线针轮传动啮合刚度理论研究［J］. 机械传动， 2018 ， 42 （ 9 ）： 7 - 12 .

Yang Yun ， Li Chaoyang ， Li Xuan . Theoretical study on meshing stiffness of cycloid-pin gear drive based on energy method ［J］. Journal of Mechanical Transmission ， 2018 ， 42 （ 9 ）： 7 - 12 .

Xu L X ， Chen B K ， Li C Y . Dynamic modelling and contact analysis of bearing-cycloid-pinwheel transmission mechanisms used in joint rotate vector reducers ［J］. Mechanism and Machine Theory ， 2019 ， 137 ： 432 - 458 .

常安全，张迎辉，何卫东，等 . 基于多体动力学仿真的RV减速器角传动误差虚拟样机的建立［J］. 机械传动， 2018 ， 42 （ 9 ）： 168 - 172 .

Chang Anquan ， Zhang Yinghui ， He Weidong ， et al . Establishment of the virtual prototyping of angular transmission error of RV reducer based on multi-body dynamics simulation ［J］. Journal of Mechanical Transmission ， 2018 ， 42 （ 9 ）： 168 - 172 .

卢琦，何卫东 . RV减速器参数化建模及多体动力学仿真［J］. 机械传动， 2021 ， 45 （ 9 ）： 87 - 91 .

Lu Qi ， He Weidong . Parametric modeling and multi-body dynamics simulation of RV reducer ［J］. Journal of Mechanical Transmission ， 2021 ， 45 （ 9 ）： 87 - 91 .

Tung L C ， Chan Y J . A time-variant dynamic model for compound epicyclic-cycloidal reducers ［J］. Mechanism and Machine Theory ， 2023 ， 179 ： 105095 .

Li X ， Huang J Q ， Ding C C ， et al . Dynamic modeling and analysis of an RV reducer considering tooth profile modifications and errors ［J］. Machines ， 2023 ， 11 （ 6 ）： 626 .

丁国龙，詹明儒，赵大兴，等 . RV减速器的模态对其传动误差的影响规律研究［J］. 机械传动， 2023 ， 47 （ 1 ）： 27 - 34 .

Ding Guolong ， Zhan Mingru ， Zhao Daxing ， et al . Research on the influence of the RV-40E reducer modal on its transmission error ［J］. Journal of Mechanical Transmission ， 2023 ， 47 （ 1 ）： 27 - 34 .

苏建新，王东峰，徐家科，等 . 摆线针轮啮合刚度计算与仿真分析研究［J］. 机械传动， 2025 ， 49 （ 4 ）： 1 - 7 .

Su Jianxin ， Wang Dongfeng ， Xu Jiake ， et al . Research on calculation and simulating analysis of cycloidal pin wheel meshing stiffness ［J］. Journal of Mechanical Transmission ， 2025 ， 49 （ 4 ）： 1 - 7 .

Lin K S ， Chan K Y ， Lee J J . Kinematic error analysis and tolerance allocation of cycloidal gear reducers ［J］. Mechanism and Machine Theory ， 2018 ， 124 ： 73 - 91 .

Yang Y H ， Zhou G C ， Chang L ， et al . A modelling approach for kinematic equivalent mechanism and rotational transmission error of RV reducer ［J］. Mechanism and Machine Theory ， 2021 ， 163 ： 104384 .

许立新，夏晨，杨博 . 负载条件下RV减速器动态传动误差分析与试验［J］. 中国机械工程， 2023 ， 34 （ 18 ）： 2143 - 2152 .

Xu Lixin ， Xia Chen ， Yang Bo . Analysis and test on dynamic transmission errors of RV reducers under load conditions ［J］. China Mechanical Engineering ， 2023 ， 34 （ 18 ）： 2143 - 2152 .

Feki N ， Clerc G ， Velex P . An integrated electro-mechanical model of motor-gear units—Applications to tooth fault detection by electric measurements ［J］. Mechanical Systems and Signal Processing ， 2012 ， 29 ： 377 - 390 .

Jiang S ， Li W ， Wang Y Q ， et al . Study on electromechanical coupling torsional resonance characteristics of gear system driven by PMSM：a case on shearer semi-direct drive cutting transmission system ［J］. Nonlinear Dynamics ， 2021 ， 104 （ 2 ）： 1205 - 1225 .

Yao Z Y ， Lin T L ， Ren H L ， et al . Electromechanical coupling dynamic responses of motor-gear system under different motor control methods ［J］. Journal of Low Frequency Noise，Vibration and Active Control ， 2025 ， 44 （ 2 ）： 1020 - 1038 .

E Y K ， Feng Z P ， Chen X W ， et al . Electromechanical coupling dynamic modeling and motor current analysis for fault diagnosis of rotate vector reducers ［J］. Mechanical Systems and Signal Processing ， 2026 ， 246 ： 113903 .

Wang H ， Shi Z Y ， Yu B ， et al . Transmission performance analysis of RV reducers influenced by profile modification and load ［J］. Applied Sciences ， 2019 ， 9 （ 19 ）： 4099 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Simulation data-driven bearing fault diagnosis method under small sample conditions

Research on vibration response optimization of the urban rail vehicle traction gear transmission system based on combined surrogate model

Study on Electromechanical Coupling Dynamic Characteristics of Robot Joint Servo Transmission System

Research on Dynamic Characteristics of Robot Joint System Under Impact Load

Design methodology and numerical validation of the coaxial spherical parallel mechanisms

Related Author

TAO Yourui

YANG Yu

CHEN Yongchang

WU Jinhui

WU Yanan

YU Wennian

DAN Jiaguo

CHEN Kai

Related Institution

School of Mechanical Engineering, Hebei University of Technology

State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology

Chongqing Rail Transit (Group) Co., Ltd., Chongqing 400014, China］

State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University

College of Mechanical and Vehicle Engineering, Chongqing University

⁰