椭圆齿轮传动系统非线性动态特性分析

doi:10.13229/j.cnki.jdxbgxb20181080

Abstract

Abstract:

In order to obtain the vibration law of elliptic gear pair and realize its stable and efficient transmission, the nonlinear dynamic characteristics of elliptic gear were studied based on the analysis of the inherent characteristics of elliptic gear. Based on the theory of gear dynamics, a nonlinear dynamic model of elliptic gear with time-varying meshing stiffness, backlash, static transmission error and viscoelastic damping is established. The nonlinear dynamic equation of elliptic gear transmission system is solved by the fourth-order variable step Runge-Kutta numerical method, and the displacement response, phase trajectory and Poincaré mapping of the system are plotted. The effects of excitation frequency, damping ratio, time-varying mesh stiffness, and internal excitation parameters on the dynamic response of the transmission system are obtained. The establishment, solution and parameter analysis of dynamic model of elliptic gear pair can provide a theoretical basis for subsequent dynamic design, vibration response trend prediction and noise reduction under different parameters.

Key words: machinery manufacturing automation, elliptic gear, dynamic characteristics, nonlinear response

CLC Number:

TH132.424

Chang-bin DONG,Yong-ping LIU,Yong-qiao WEI,Hai-qing DENG,Jie Xu. Analysis of nonlinear dynamic characteristic of elliptic gear transmission system[J].Journal of Jilin University(Engineering and Technology Edition), 2020, 50(2): 483-493.

Figures/Tables 8

Fig.1

Table 1

Elliptic gear design parameters"

参数	数值
模数m	3
齿数Z	47
中心距a/mm	150
齿顶高系数h_a^*	1
顶隙系数C^*	0.25
齿宽B/mm	30
偏心率e	0.3287
节曲线方程r	$r = 64.667 1 ± 0.3287 c o s φ$

Table 1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

References 22

1	魏爽, 李殿起, 刘光辉. 非圆行星齿轮液压马达的动力学研究[J]. 机械传动, 2017, 41(9): 18-24.
	Wei Shuang, Li Dian-qi, Liu Guang-hui. Study on the dynamics of non-circular planetary gear hydraulic motor[J]. Journal of Mechanical Transmission, 2017, 41(9): 18-24.
2	刘振皓, 巫世晶, 王晓笋, 等. 基于增量谐波平衡法的复合行星齿轮传动系统非线性动力学[J]. 振动与冲击, 2012, 31(3): 117-122.
	Liu Zhen-hao, Wu Shi-jing, Wang Xiao-sun, et al. Nonlinear dynamics of compound planetary gear sets based on incremental harmonic balance method[J]. Journal of Vibration and Shock, 2012, 31(3): 117-122.
3	李应刚, 陈天宁, 王小鹏, 等. 外部动态激励作用下齿轮系统非线性动力学特性[J]. 西安交通大学学报, 2014, 48(1): 101-105.
	Li Ying-gang, Chen Tian-ning, Wang Xiao-peng, et al. Non-linear dynamics of spur gear pair under external periodic excitation[J]. Journal of Xi'an Jiaotong University, 2014, 48(1): 101-105.
4	Kim W, Lee J Y, Chung J. Dynamic analysis for a planetary gear with time-varying pressure angles and contact ratios[J]. Journal of Sound & Vibration, 2012, 331(4): 883-901.
5	Saghafi A, Farshidianfar A. An analytical study of controlling chaotic dynamics in a spur gear system[J]. Mechanism & Machine Theory, 2016, 96: 179-191.
6	Farshidianfar A, Saghafi A. Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems[J]. Nonlinear Dynamics, 2014, 75(4): 783-806.
7	Xiang L, Gao N, Hu A. Dynamic analysis of a planetary gear system with multiple nonlinear parameters[J]. Journal of Computational & Applied Mathematics, 2018, 327: 325-340.
8	Li S, Wu Q, Zhang Z. Bifurcation and chaos analysis of multistage planetary gear train[J]. Nonlinear Dynamics, 2014, 75(1/2): 217-233.
9	巫世晶, 刘振皓, 潜波, 等. 复合行星齿轮传动系统分岔与混沌特性研究[J]. 华中科技大学学报: 自然科学版, 2012, 40(2): 9-13.
	Wu Shi-jing, Liu Zhen-hao, Qian Bo, et al. Bifurcation and chaotic characteristics of compound planetary gear train sets[J]. Journal Huazhong University of Science and Technology (Natural Science Edition), 2012, 40(2): 9-13.
10	孙智民, 沈允文, 王三民, 等. 星形齿轮传动系统分岔与混沌的研究[J]. 机械工程学报, 2001, 37(12): 11-15.
	Sun Zhi-min, Shen Yun-wen, Wang San-min, et al. Bifurcations and chaos of star gear system[J]. Journal of Mechanical Engineering, 2001, 37(12): 11-15.
11	冉小虎. 非圆齿轮传动特性与实验研究[D]. 重庆：重庆大学机械工程学院, 2007.
	Ran Xiao-hu. Study on characters and experiment of noncircular gear transmission[D]. Chongqing: College of Mechanical Engineering， Chongqing University, 2007.
12	王艾伦, 马强, 刘琳琳. 椭圆齿轮动态特性仿真研究[J]. 机械传动, 2006, 30(4): 7-10.
	Wang Ai-lun, Ma Qiang, Li Lin-lin. Modeling and simulation of ellipse gears[J]. Journal of Mechanical Transmission, 2006, 30(4): 7-10.
13	杨红普, 李宪奎, 郑学然. 椭圆齿轮驱动的结晶器非正弦振动系统动力学分析[J]. 机械设计, 2007, 24(5): 30-33, 36.
	Yang Hong-pu, Li Xian-kui, Zheng Xue-ran. Dynamics analysis on non-sinusoidal vibration system of crystallization utensil driven by elliptical gears[J]. Journal of Machine Design, 2007, 24(5): 30-33, 36.
14	张爱梅, 蒋佳, 魏丽君, 等. 非圆齿轮的动力学特性研究[J]. 机械传动, 2009, 33(5): 20-23.
	Zhang Ai-mei, Jiang Jia, Wei Li-jun, et al. Study on dynamic characteristics of non-circular gear[J]. Journal of Mechanical Transmission, 2009, 33(5): 20-23.
15	Liu X, Nagamura K, Ikejo K. Analysis of the dynamic characteristics of elliptic gears[J]. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 2012, 6(4): 484-497.
16	Liu X, Nagamura K, Ikejo K. Simulation on the vibration characteristics of elliptic gears[J]. Proceedings of Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2013, 227(4): 819-830.
17	刘大伟, 任廷志, 金昕. 非圆齿轮传动系统的动力学模型及其应用[J]. 机械设计, 2016, 33(1): 35-39.
	Liu Da-wei, Ren Ting-zhi, Jin Xin. Dynamic model and its application of transmission system in noncircular gears[J]. Journal of Machine Design, 2016, 33(1): 35-39.
18	刘大伟, 任廷志, 巴延博, 等. 基于弹性转角分离的非圆齿轮扭振模型及其动态特性[J]. 振动与冲击, 2016, 35(23): 228-233.
	Liu Da-wei, Ren Ting-zhi, Ba Yan-bo, et al. Torsional vibration model and its dynamic characteristics for a noncircular gear based on separation of elastic rotating angle[J]. Journal of Vibration and Shock, 2016, 35(23): 228-233.
19	刘永平, 董长斌, 安建民, 等. 新型抽油机换向装置结构设计及运动仿真分析[J]. 机械传动, 2017, 41(9): 115-118, 134.
	Liu Yong-ping, Dong Chang-bin, An Jian-min. et al. Analysis of motion simulation and structure design of the reversing device of new pumping unit[J]. Journal of Mechanical Transmission, 2017, 41(9): 115-118, 134.
20	陈忠敏, 侯力, 段阳, 等. 新型摆线针轮行星减速器传动系统的振动特性[J]. 吉林大学学报: 工学版, 2018, 48(1): 174-185.
	Chen Zhong-min, Hou Li, Duan Yang, et al. Viboration analysis of a new pin-cycloid speed reducer[J]. Journal of Jilin University (Engineering and Technology Edition), 2018, 48(1): 174-185.
21	李润方, 王建军. 齿轮系统动力学——振动、冲击、噪声[M]. 北京: 科学出版社, 1997.
22	李瑰贤, 于广滨, 温建民, 等. 求解齿轮系统非线性动力学微分方程的多尺度方法[J]. 吉林大学学报: 工学版, 2008, 38(1): 75-79.
	Li Gui-xian, Yu Guang-bin, Wen Jian-min, et al. Method of multiple scales in solving nonlinear dynamic differential equations of gear systems[J]. Journal of Jilin University (Engineering and Technology Edition), 2008, 38(1): 75-79.

Related Articles 15

[1]	Xing-jun HU,Zheng HUI,Peng GUO,Yang-hui ZHANG,Jing-long ZHANG,Jing-yu WANG,Fei LIU. Characteristics of aerodynamics for an automobile by fluid-structure coupled method [J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(5): 1414-1419.
[2]	WANG Yan, GAO Qing, WANG Guo-hua, ZHANG Tian-shi, YUAN Meng. Simulation of mixed inner air-flow integrated thermal management with temperature uniformity of Li-ion battery [J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(5): 1339-1348.
[3]	WANG Tao, SAN Xiao-gang, GAO Shi-jie, WANG Hui-xian, WANG Jing, NI Ying-xue. Dynamic characteristics of vertical shaft system of photoelectric turntable [J]. 吉林大学学报(工学版), 2018, 48(4): 1099-1105.
[4]	LI Jing, DING Ming-hui, LI Li-gang, CHEN Li-jun. Dynamic characteristics analysis and optimization of air spring based on the piston shape [J]. 吉林大学学报(工学版), 2018, 48(2): 355-363.
[5]	WEI Zhi-gang, SHI Cheng-lin, LIU Han-bing, ZHANG Yun-long. Dynamic characteristics of steel-concrete composite simply supported beam under vehicles [J]. 吉林大学学报(工学版), 2017, 47(6): 1744-1752.
[6]	YANG Yue-dong, CHEN Ji-qing, LAN Feng-chong, ZHOU Yun-jiao. BIW dynamic characteristics based on spot-welding parameter identification [J]. 吉林大学学报(工学版), 2017, 47(5): 1379-1386.
[7]	LI Xian-sheng, MENG Xiang-yu, ZHENG Xue-lian, CHENG Zhu-qing, REN Yuan-yuan. Dynamic characteristics of liquid sloshing in partially-filled tank [J]. 吉林大学学报(工学版), 2017, 47(3): 737-743.
[8]	LIU Xiao-wei, LI Hai, WENG Rui, ZHANG Hai-feng, ZHAO Jun. Application of electrostatic torque to improve dynamic characteristics of novel rotational gyroscope [J]. 吉林大学学报(工学版), 2017, 47(3): 850-854.
[9]	HE Guang, ZHANG Ming, YUAN Shuang-shi. Temperature-related dynamic characteristics of MEMS setback arming device [J]. 吉林大学学报(工学版), 2017, 47(1): 145-150.
[10]	WANG Yan-zhong, HOU Liang-wei, LYU Qing-jun, ZHAO Xing-fu, WU Can-hui. Processing technology of face gear complex surface based on bus control [J]. 吉林大学学报(工学版), 2015, 45(6): 1836-1843.
[11]	LIU Han-bing, SHI Cheng-lin, TAN Guo-jin, WANG Hua, HUANG Bin. Calculation method of the dynamic characteristics of continuous beam bridge with variable cross-section based on staging concept [J]. 吉林大学学报(工学版), 2015, 45(6): 1779-1783.
[12]	WANG Jing-yu, WANG Ze-wei, GU Qing-tong, HU Xing-jun, WANG Bao-yu. Numerical simulation of transient aerodynamic characteristics of turning vehicle [J]. 吉林大学学报(工学版), 2015, 45(1): 44-48.
[13]	LIU Shun-an, HE Xing-zhu, CHEN Yan-li,YANG Lu-hong,LI Wan-lin. Aerodynamic characteristics of a ducted tail rotor with asymmetric layout [J]. 吉林大学学报(工学版), 2014, 44(5): 1353-1359.
[14]	on improved EM algorithm. Reliability modeling of finite Weibull distribution based [J]. 吉林大学学报(工学版), 2014, 44(4): 1010-1015.
[15]	YANG Zhao-jun,WANG Ji-li,LI Guo-fa,ZHANG Xin-ge. Reliability growth prediction based on fuzzy analytical hierarchy process for punching machines [J]. 吉林大学学报(工学版), 2014, 44(3): 686-691.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 0

No Suggested Reading articles found!

Analysis of nonlinear dynamic characteristic of elliptic gear transmission system

RICH HTML

PDF (PC)