椭圆齿轮传动系统非线性动态特性分析

doi:10.13229/j.cnki.jdxbgxb20181080

摘要/Abstract

摘要：

为获得椭圆齿轮副工作时的振动规律，以实现其稳定、高效传动，在分析椭圆齿轮固有特性的基础上对椭圆齿轮非线性动力学特性进行了研究。以齿轮动力学理论为基础，建立考虑时变啮合刚度、齿侧间隙、静态传递误差、粘弹性阻尼的椭圆齿轮非线性动力学模型，利用四阶变步长Runge-Kutta 数值方法对椭圆齿轮传动系统非线性动力学方程进行求解，绘制了系统的位移响应，相轨迹以及Poincaré映射，得到激励频率、阻尼比、时变啮合刚度、以及内部激励4个控制参数对传动系统动态响应的影响。椭圆齿轮副动力学模型的建立、求解和参数影响分析可以为后续的动态设计、不同参数下的振动响应趋势预测以及降噪提供一定的理论依据。

关键词: 机械制造自动化, 椭圆齿轮, 动态特性, 非线性响应

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

中图分类号:

TH132.424

董长斌,刘永平,魏永峭,邓海青,许杰. 椭圆齿轮传动系统非线性动态特性分析[J]. 吉林大学学报(工学版), 2020, 50(2): 483-493.

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.

图/表 8

图1

表1

椭圆齿轮参数"

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	$r = 64.667 1 ± 0.3287 c o s φ$

表1

图2

图3

图4

图5

图6

图7

参考文献 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.

相关文章 15

[1]	赵云伟,耿德旭,刘晓敏,刘齐. 气动柔性六足机器人定半径转弯实现方法与稳定性[J]. 吉林大学学报(工学版), 2020, 50(2): 472-482.
[2]	杨成,赵永胜,刘志峰,蔡力钢. 基于多尺度理论的栓接结合部动力学建模[J]. 吉林大学学报(工学版), 2019, 49(4): 1212-1220.
[3]	王涛, 伞晓刚, 高世杰, 王惠先, 王晶, 倪迎雪. 光电跟踪转台垂直轴系动态特性[J]. 吉林大学学报(工学版), 2018, 48(4): 1099-1105.
[4]	李静, 丁明慧, 李立刚, 陈立军. 基于活塞形状的空气弹簧动特性分析与参数优化[J]. 吉林大学学报(工学版), 2018, 48(2): 355-363.
[5]	杨越东, 陈吉清, 兰凤崇, 周云郊. 基于焊点参数识别的白车身动态特性[J]. 吉林大学学报(工学版), 2017, 47(5): 1379-1386.
[6]	刘晓为, 李海, 翁睿, 张海峰, 赵军. 应用静电力矩改善新型转子式陀螺的动态特性[J]. 吉林大学学报(工学版), 2017, 47(3): 850-854.
[7]	曲兴田, 赵永兵, 刘海忠, 王昕, 杨旭, 陈行德. 串并混联机床几何误差建模与实验[J]. 吉林大学学报(工学版), 2017, 47(1): 137-144.
[8]	何光, 张铭, 袁双石. 微机电系统后坐保险机构温度相关动态特性[J]. 吉林大学学报(工学版), 2017, 47(1): 145-150.
[9]	任书楠, 杨向东, 王国磊, 刘志, 陈恳. 大部件喷涂中的移动机械臂站位规划[J]. 吉林大学学报(工学版), 2016, 46(6): 1995-2002.
[10]	沈志煌, 姚斌, 陆如升, 冯伟, 张祥雷, 王萌萌. 精密螺杆转子齿廓成形磨削的误差分析[J]. 吉林大学学报(工学版), 2016, 46(3): 831-838.
[11]	王延忠，侯良威，吕庆军，赵兴福，吴灿辉. 基于总线控制的面齿轮复杂曲面加工技术[J]. 吉林大学学报(工学版), 2015, 45(6): 1836-1843.
[12]	刘昕晖，李倩雯，陈晋市,，张鹏，牛平杰. 负荷传感优先阀建模及仿真分析[J]. 吉林大学学报(工学版), 2015, 45(6): 1817-1824.
[13]	陈健，葛连正，李瑞峰. 考虑摩擦特性的机器人柔性关节鲁棒控制器设计[J]. 吉林大学学报(工学版), 2015, 45(6): 1906-1912.
[14]	郭黎滨, 张彬, 崔海, 张志航. 微细电火花线切割表面三维粗糙度的结构性参数[J]. 吉林大学学报(工学版), 2015, 45(3): 851-856.
[15]	王继利, 杨兆军, 李国发, 朱晓翠. EM算法的多重威布尔可靠性建模[J]. 吉林大学学报(工学版), 2014, 44(4): 1010-1015.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed