Modification design of cycloidal gear based on contact stress optimization

doi:10.3785/j.issn.1006-754X.2022.00.084

Chin J Eng Design

2022, Vol. 29

Issue (6): 713-719 DOI: 10.3785/j.issn.1006-754X.2022.00.084

Optimization Design

Modification design of cycloidal gear based on contact stress optimization

Zhi-bo ZHAO¹(

),Da-qiang GU¹(

),Li-xin LI¹,Jing ZHANG²

^1.School of Mechanical Engineering, Zhejiang University, Hangzhou 310000, China
^2.Zhejiang Fine-motion Robot Joint Technology Co. , Ltd. , Taizhou 318000, China

Download:

HTML

PDF(1164KB)
Export: BibTeX | EndNote (RIS)

Abstract

Rational modification of cycloidal gear can greatly improve the transmission performance and bearing capacity of RV (rotary vector) reducer. In order to further optimize the contact stress of the "inverse arch-shaped " tooth profile, a two-stage modification method was proposed based on the comprehensive analysis of the influence of combined modification on the meshing force and contact stress of the inverse arch-shaped tooth profile. In this method, the cycloidal gear tooth profile was divided into two sections, and different modification quantities were adopted for different working sections according to the needs, so as to design the cycloidal gear tooth profile more flexibly. Taking RV-40E reducer as an example, the force analysis model of cycloidal gear was established by using MATLAB software, and the modification amount and equation of the new tooth profile were determined according to the two-stage modification method; then, the finite element model of contact between cycloidal gear and needle tooth was established by ANSYS software, and the contact stress between the new tooth profile and the inverse arch-shaped tooth profile was compared. The theoretical calculation results showed that the maximum contact stress of the new tooth profile was reduced by 8.34%; the finite element simulation results showed that the maximum contact stress of the new tooth profile was reduced by 4.39%, and the possible error sources were analyzed. The research shows that the two-stage modification method can improve the contact stress of cycloidal gear tooth profile and prolong the service life of cycloidal gear, which provides a certain reference for the modification design of cycloidal gears.

Key words： cycloidal gear contact stress combined modification two-stage modification finite element analysis

Received: 12 April 2022 Published: 06 January 2023

CLC:

TH 132

Corresponding Authors: Da-qiang GU E-mail: 22025111@zju.edu.cn;gudq@zju.edu.cn

	Service
	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Zhi-bo ZHAO
	Da-qiang GU
	Li-xin LI
	Jing ZHANG

Cite this article:

Zhi-bo ZHAO,Da-qiang GU,Li-xin LI,Jing ZHANG. Modification design of cycloidal gear based on contact stress optimization. Chin J Eng Design, 2022, 29(6): 713-719.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2022.00.084 OR https://www.zjujournals.com/gcsjxb/Y2022/V29/I6/713

基于接触应力优化的摆线轮修形设计

对摆线轮进行合理的修形能够极大改善RV（rotary vector，旋转矢量）减速器的传动性能和承载能力。为了进一步优化“反弓”齿廓的接触应力，在综合分析组合修形对反弓齿廓啮合力和接触应力的影响的基础上，提出了一种两段修形方法。该方法是将摆线轮齿廓分成2段，并根据需要对不同工作段的齿廓采用不同的修形量，以更灵活地设计摆线轮的齿廓。以RV-40E减速器为例，先利用MATLAB软件建立摆线轮受力分析模型，并按照两段修形方法确定新齿廓的修形量和方程；再利用ANSYS软件建立摆线轮与针齿接触的有限元模型，并对比新齿廓与反弓齿廓的接触应力。理论计算结果显示，新齿廓的最大接触应力降低了8.34%；有限元仿真结果显示，新齿廓的最大接触应力降低了4.39%，并分析了可能的误差来源。研究表明，两段修形方法可以改善摆线轮齿廓的接触应力和延长摆线轮的使用寿命，这为摆线轮的修形设计提供了一定的参考。

关键词： 摆线轮, 接触应力, 组合修形, 两段修形, 有限元分析

Fig.1 Schematic diagram of meshing force and contact stress distribution of cycloidal gear inverse arch-shaped tooth profile

Fig.2 Isometric modification quantity curve of cycloidal gear tooth profile based on two-stage modification

参数	数值
摆线轮齿数 $z c$	39
针齿数 $z p$	40
径向间隙 $Δ j /$ mm	0.225
偏心距 $a$ /mm	1.3
针齿半径 $r r p$ /mm	3
针齿中心圆半径 $r p$ /mm	64
摆线轮厚度b/mm	7.9
额定输出扭矩T/（N·m）	412

Table 1 Basic parameters of RV-40E reducer

Fig.3 Comparison of meshing force and contact stress between two tooth profiles

Fig.4 Finite element model of contact between cycloidal gear and needle tooth

网格尺寸/mm	最大接触应力 $σ H ? m a x / M P a$
网格尺寸/mm	反弓齿廓	新齿廓
0.200	584.15	500.70
0.100	1 128.90	909.68
0.050	1 661.40	1 504.10
0.020	1 892.30	1 790.10
0.010	1 995.70	1 907.70
0.007	2 049.10	1 934.70
0.005	2 081.60	1 990.30

Table 2 Maximum contact stress of two tooth profiles under different mesh sizes

Fig.5 Finite element simulation results of contact stress of cycloidal gear tooth profile

Fig.6 Comparison between finite element simulation results and theoretical calculation results of contact stress of two tooth profiles


[1]	RODRÍGUEZ-GUERRA D， SORROSAL G， CABANES I， et al. Human-robot interaction review： challenges and solutions for modern industrial environments［J］. IEEE Access， 2021， 9： 108557-108578.

[2]	PHAM A D， AHN H J. Rigid precision reducers for machining industrial robots［J］. International Journal of Precision Engineering and Manufacturing， 2021， 22（8）： 1469-1486.

[3]	LI Tian-xing， TIAN Meng， XU Hang， et al. Meshing contact analysis of cycloidal-pin gear in RV reducer considering the influence of manufacturing error［J］. Journal of the Brazilian Society of Mechanical Sciences and Engineering， 2020， 42（10）： 2-5.

[4]	WANG Ruo-yu， GAO Feng-qiang， LU Meng， et al. Meshing efficiency analysis of modified cycloidal gear used in the RV reducer［J］. Tribology Transactions， 2019， 62（3）： 337-349.

[5]	ZHANG Yue-ming， LI Lian-song， JI Shu-ting. Influence of cycloid-pin gear design parameters on bearing capacity and optimized design［J］. Journal of the Brazilian Society of Mechanical Sciences and Engineering， 2022， 44（4）： 1-10.

[6]	何卫东，单丽君.RV减速器研究现状与展望［J］. 大连交通大学学报，2016，37（5）：13-18. HE Wei-dong， SHAN Li-jun. Status and development of RV reduce［J］. Journal of Dalian Jiaotong University， 2016， 37（5）： 13-18.

[7]	陆龙生，张飞翔，唐恒，等.基于优化承载能力的RV减速器摆线齿轮齿廓的等距‒移距修形［J］.中国机械工程，2019，30（17）：2022-2029. LU Long-sheng， ZHANG Fei-xiang， TANG Heng， et al. Equidistant and radial-moving modifications of cycloidal gear tooth profiles used in RV reducer based on optimized carrying capacity［J］. China Mechanical Engineering， 2019， 30（17）： 2022-2029.

[8]	关天民. FA型摆线针轮行星传动齿形优化方法与相关理论的研究［D］.大连：大连交通大学，2005：12-38. doi：10.3969/j.issn.1001-2354.2005.03.012 GUAN Tian-min. Study on tooth-profile optimization method and correlative theory of FA cycloid drive［D］. Dalian： Dalian Jiaotong University， 2005： 12-38. doi: 10.3969/j.issn.1001-2354.2005.03.012

[9]	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. doi：10.3321/j.issn：0577-6686.2005.01.030 GUAN Tian-min， ZHANG Dong-sheng. Inverse arch-shaped teeth profile and its optimization in a cycloid drive ［J］. Journal of Mechanical Engineering， 2005， 41（1）： 151-156. doi: 10.3321/j.issn：0577-6686.2005.01.030

[10]	关天民.摆线针轮行星传动中修形所产生的回转误差计算与分析［J］.组合机床与自动化加工技术，2001（10）：17-20. doi：10.3969/j.issn.1001-2265.2001.10.005 GUAN Tian-min. Calculation and analysis on the return error resulting from cycloid-disk modification in the cycloid drive［J］. Modular Machine Tool & Automatic Manufacturing Technique， 2001（10）： 17-20. doi: 10.3969/j.issn.1001-2265.2001.10.005

[11]	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）：811-814. GUAN Tian-min. The optimum profile modification on cycloid disks in the cycloid gearing mechanism with small teeth difference［J］. China Mechanical Engineering， 2002， 13（10）： 811-814.

[12]	张飞翔.工业机器人RV减速器摆线轮齿廓修形技术研究［D］.广州：华南理工大学，2018：40-45. ZHANG Fei-xiang. The profile modification investigation of cycloidal gears for RV reducers applied in industrial robot［D］. Guangzhou： South China University of Technology， 2018： 40-45.

[13]	丁国龙，秦园，明廷伯，等.基于接触应力均化的摆线轮修形方法［J］.中国机械工程，2019，30（9）：1081-1089. doi：10.3969/j.issn.1004-132X.2019.09.010 DING Guo-long， QIN Yuan， MING Ting-bo， et al. Modifiction method of cycloidal gear based on contact stress equalization［J］. China Mechanical Engineering， 2019， 30（9）： 1081-1089. doi: 10.3969/j.issn.1004-132X.2019.09.010

[14]	邓纪辰.基于接触强度的FA传动反弓齿廓优化与有限元分析［D］.大连：大连交通大学，2008：23-53. DENG Ji-chen. "Inverse arch-shaped" teeth profile optimization and finite element analysis about FA transmission based on contact strength［D］. Dalian： Dalian Jiaotong University， 2008： 23-53.

[15]	李力行.摆线针轮行星传动的齿形修正及受力分析［J］.大连交通大学学报，1984，5（4）：29-40. LI Li-xing. The modification manner for tooth profile and the analysis of forces on the cycloid disk of a cycloid speed reducer［J］. Journal of Dalian Jiaotong University， 1984， 5（4）： 29-40.

[16]	YU Hong-liu， YI Jin-hua， HU Xin， et al. Study on teeth profile modification of cycloid reducer based on non-Hertz elastic contact analysis［J］. Mechanics Research Communications， 2013， 48： 87-92.

[17]	何芝仙，陈曦，时培成.基于动力学分析的大重合度直齿圆柱齿轮强度计算［J］.工程设计学报，2020，27（6）：729-734. doi：10.3785/j.issn.1006-754X.2020.00.092 HE Zhi-xian， CHEN Xi， SHI Pei-cheng. Strength calculation of high contact-ratio spur gear based on dynamics analysis［J］. Chinese Journal of Engineering Design， 2020， 27（6）： 729-734. doi: 10.3785/j.issn.1006-754X.2020.00.092

[1]	Chao XIE,Yunzhuang CHEN,Guangnan SHI,Leijie LAI. Design and compliance analysis of large stroke flexible ball hinge with orthogonal reeds[J]. Chin J Eng Design, 2023, 30(5): 626-633.

[2]	Tao ZHANG,Kaisong WANG,Wei TANG,Kecheng QIN,Yang LIU,Yuhao SHI,Jun ZOU. Design and analysis of flexible bending actuator driven by electrohydrodynamic pumps[J]. Chin J Eng Design, 2023, 30(4): 467-475.

[3]	Qin LI,Rui YAN,Zhiqiang HUANG,Gang LI. Research on matching design and optimization of drive motor of electric drive vibroseis[J]. Chin J Eng Design, 2023, 30(2): 172-181.

[4]	San-ping LI,Teng-jia SUN,Long-qiang YUAN,Li-guo WU. Design and experimental research of pneumatic soft picking manipulator[J]. Chin J Eng Design, 2022, 29(6): 684-694.

[5]	Zheng-feng ZHANG,Xiao-yu SONG,Xiao-lei YUAN,Wen-juan CHEN,Wei-dong ZHANG. Reliability optimization design for crashworthiness of Al/CFRP hybrid thin-walled structure[J]. Chin J Eng Design, 2022, 29(6): 720-730.

[6]	Jiang LIU,Zheng-ming XIAO,Long-long ZHANG,Wei-biao LIU. Transmission accuracy reliability analysis and parameter optimization of RV reducer considering cycloid gear wear[J]. Chin J Eng Design, 2022, 29(6): 739-747.

[7]	Guang-ming SUN,Yi-miao WANG,Qian WAN,Kun GONG,Wen-jin WANG,Jian ZHAO. Optimization design of precision machine tool bed considering assembly deformation[J]. Chin J Eng Design, 2022, 29(3): 318-326.

[8]	Fei FENG,Yu-chen FU,Wei FAN,Ju MA. Design and performance analysis of triangular hybrid two-stage lever micro-displacement amplification mechanism[J]. Chin J Eng Design, 2022, 29(2): 161-167.

[9]	CHEN Hong-yue, ZHANG Zhan-li, LU Zhang-quan. Design and performance study of cylindrical arm coil spring for linear compressor[J]. Chin J Eng Design, 2021, 28(4): 504-510.

[10]	WANG Cheng-jun, LI Shuai. Design and bending performance analysis of three-joint soft actuator[J]. Chin J Eng Design, 2021, 28(2): 227-234.

[11]	ZHOU Chao, QIN Rui-jiang, RUI Xiao-ming. Analysis of mechanical properties of V-shaped insulator string under wind load[J]. Chin J Eng Design, 2021, 28(1): 95-104.

[12]	HUANG Wei, XU Jian, LU Xin-zheng, HU Ming-yi, LIAO Wen-jie. Research on dynamic vibration absorption for power equipment and building floor[J]. Chin J Eng Design, 2021, 28(1): 25-32.

[13]	HE Zhi-xian, CHEN Xi, SHI Pei-cheng. Strength calculation of high contact-ratio spur gear based on dynamics analysis[J]. Chin J Eng Design, 2020, 27(6): 729-734.

[14]	ZHOU Chao, WANG Yang, RUI Xiao-ming. Finite element analysis and experimental study on wind-induced swing of 500 kV transmission line jumper wire[J]. Chin J Eng Design, 2020, 27(6): 713-719.

[15]	LI Cheng-bing, LEI Peng. Stress analysis and weak roof performance evaluation for 5 000 m³vertical dome storage tank[J]. Chin J Eng Design, 2020, 27(2): 182-190.

Viewed

Full text

Abstract

Cited

Shared

Discussed