Nonlinear Vibration Bifurcation Characteristics of Multi-Clearance 2-Stage Gear Systems

WANG Shu-guo; ZHANG Yan-bo; LIU Wen-liang; GUO Li-feng; LIAO Peng-tai; QI Li-mei

doi:10.3879/j.issn.1000-0887.2016.02.006

Volume 37 Issue 2

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2016 > 37(2): 173-183

WANG Shu-guo, ZHANG Yan-bo, LIU Wen-liang, GUO Li-feng, LIAO Peng-tai, QI Li-mei. Nonlinear Vibration Bifurcation Characteristics of Multi-Clearance 2-Stage Gear Systems[J]. Applied Mathematics and Mechanics, 2016, 37(2): 173-183. doi: 10.3879/j.issn.1000-0887.2016.02.006

Citation:

PDF( 1828 KB)

Nonlinear Vibration Bifurcation Characteristics of Multi-Clearance 2-Stage Gear Systems

doi: 10.3879/j.issn.1000-0887.2016.02.006

¹College of Information Engineering, Tarim University, Aral, Xinjiang 843300, P.R.China;²College of Mechanical and Electronic Engineering, Tarim University, Aral, Xinjiang 843300, P.R.China

Received Date: 2015-09-16
Rev Recd Date: 2015-11-02
Publish Date: 2016-02-15

Abstract

Abstract

A 5-DOF nonlinear vibration model for multi-clearance 2-stage gear systems was established with the lumped-mass method. In view of transmission errors, time-varying meshing stiffness and multiple gear clearances, the dimensionless dynamic equations for the system were derived. By means of the Poincaré maps and bifurcation diagrams, the bifurcation properties of the system were discussed under the effects of the rotation rate and the damping ratio. Given the various nonlinear factors, the 2-stage gear system exhibits rich and complex bifurcation characteristics. With the changes of the related parameters, the system will be in short-period motion, or long-period motion, or quasi-periodic motion or chaotic motion. For different damping ratios, with the decrease of the rotation rate, the system state changes from stable period-1 motion into stable period-2 motion through period-doubling bifurcation; then the system state changes into quasi-periodic motion through the Hopf bifurcation, in turn changes into stable period-1 motion after a catastrophe; finally the system enters into chaos through the Hopf bifurcation-phase locking. Moreover, with the increase of the rotation rate, the system damping ratio range corresponding to chaotic motions reduces, and the system will be in stable period-1 motion, or long-period motion or quasi-periodic motion, while the damping ratio range corresponding to long-period motion and quasi-periodic motion shortens and that corresponding to period-1 motion lengthens.
- nonlinear vibration,
- Hopf bifurcation,
- multi-clearance,
- gear

FullText(HTML)

References(16)

References

[1]	李润方, 王建军. 齿轮系统动力学——振动、冲击、噪声[M]. 北京: 科学技术出版社, 1997.(LI Run-fang, WANG Jian-jun.Gear System Dynamics—Vibration Impact Noise [M]. Beijing: Science Press, 1997.(in Chinese))
[2]	姚文席, 魏任之. 渐开线直齿轮的啮合冲击研究[J]. 振动与冲击, 1990,9(4): 25, 57-61.(YAO Wen-xi, WEI Ren-zhi. The study of damping vibration in compound automobile plates[J].Journal of Vibration and Shock,1990,9(4): 25, 57-61.(in Chinese))
[3]	鄂中凯, 蔡春源, 刘鹄然. 轮系振动基本方程[J]. 振动与冲击, 1990,9(1): 43-44.(E Zhong-kai, CAI Chun-yuan, LIU Hu-ran. Basic equation of gear train vibration[J].Journal of Vibration and Shock,1990,9(1): 43-44.(in Chinese))
[4]	唐增宝, 钟毅芳, 刘伟忠. 多级齿轮传动系统的动态仿真[J]. 机械传动, 1993,17(1): 37-41.(TANG Zeng-bao, ZHONG Yi-fang, LIU Wei-zhong. Multistage dynamic simulation of gear transmission system[J].Journal of Mechanical Transmission,1993,17(1): 37-41.(in Chinese))
[5]	唐进元, 陈思雨, 钟掘. 一种改进的齿轮非线性动力学模型[J]. 工程力学, 2008,25(1): 217-223.(TANG Jin-yuan,CHEN Si-yu, ZHONG Jue. A improved nonlinear model for a spur gear pair system[J].Engineering Mechanics,2008,25(1): 217-223.(in Chinese))
[6]	圣国梁. 基于MATLAB的齿轮间隙非线性动力学仿真研究[J]. 电子机械工程, 2008,24(5): 58-60.(SHENG Guo-liang. Simulated study on the gear gap non-linear dynamics based on MATLAB[J].Electro-Mechanical Engineering,2008,24(5): 58-60.(in Chinese))
[7]	罗冠炜, 谢建华. 一类冲击振动系统在强共振条件下的亚谐分叉与Hopf分叉[J]. 爆炸与冲击, 2003,23(1): 67-73.(LUO Guan-wei, XIE Jian-hua. Subharmonic and Hopf bifurcation of a vibra-impact system in a strong resonance case[J].Explosion and Shock Waves,2003,23(1): 67-73.(in Chinese))
[8]	盛冬平, 朱如鹏, 陆凤霞, 靳广虎. 多间隙弯扭耦合齿轮非线性振动的分岔特性研究[J]. 振动与冲击, 2014,33(19): 116-122.(SHENG Dong-ping, ZHU Ru-peng, LU Feng-xia, JIN Guang-hu. Bifurcation characteristics of bending-torsional coupled gear nonlinear vibration with multi-clearance[J].Journal of Vibration and Shock,2014,33(19): 116-122.(in Chinese))
[9]	孙智民, 沈允文, 王三民, 李华. 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-ming, SHEN Yun-wen, WANG San-ming, LI Hua. Bifurcations and chaos of star gear system[J].Chinese Journal of Mechanical Engineering,2001,37(12): 11-15.(in Chinese))
[10]	王三民, 沈允文, 董海军. 含摩擦和间隙直齿轮副的混沌与分叉研究[J]. 机械工程学报, 2002,38(9): 8-11.(WANG San-min, SHEN Yun-wen, DONG Hai-jun. Chaos and bifurcation analysis of a spur gear pair with combine friction and clearance[J].Chinese Journal of Mechanical Engineering,2002,38(9): 8-11.(in Chinese))
[11]	罗红, 梁波, 吴志华, 史石荣. 半车车辆-道路耦合动力分析模型的研究与应用[J]. 应用数学和力学, 2014,35(7): 737-749.(LUO Hong, LIANG Bo, WU Zhi-hua, SHI Shi-rong. Study and application of a 4-DOF 1/2 vehicle-road coupling dynamic model[J].Applied Mathematics and Mechanics,2014,35(7): 737-749.(in Chinese))
[12]	李倩, 刘俊卿, 陈诚诚. 随机激励下四自由度车辆-道路耦合系统动力分析[J]. 应用数学和力学, 2015,36(5): 460-473.(LI Qian, LIU Jun-qing, CHEN Cheng-cheng. Dynamic analysis of the 4-DOF vehicle-road coupling system under random excitation[J].Applied Mathematics and Mechanics,2015,36(5): 460-473.(in Chinese))
[13]	李军, 陈予恕. 低压-发电机转子系统弯扭耦合情况下的组合共振研究[J]. 应用数学和力学, 2011,32(8): 895-911.(LI Jun, CHEN Yu-shu. Study on combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling[J].Applied Mathematics and Mechanics,2011,32(8): 895-911.(in Chinese))
[14]	Lin J, Parker R G. Mesh stiffness variation instabilities in two-stage gear systems[J].Journal of Vibration and Acoustics,2002,124: 68-76.
[15]	杨富春, 周晓军, 胡宏伟. 两级齿轮减速器非线性振动特性研究[J]. 浙江大学学报(工学版), 2009,43(7): 1243-1248.(YANG Fu-chun, ZHOU Xiao-jun, HU Hong-wei. Nonlinear vibration characteristics of two-stage gear reducer[J].Journal of Zhejiang University(Engineering Science),2009,43(7): 1243-1248.(in Chinese))
[16]	陈思雨, 唐进元. 间隙对含摩擦和时变刚度的齿轮系统动力学响应的影响[J]. 机械工程学报, 2009,45(8): 119-124.(CHEN Si-yu, TANG Jin-yuan. Effect of backlash on dynamics of spur gear pair system with friction and time-varying stiffness[J].Journal of Mechanical Engineering,2009,45(8): 119-124.(in Chinese))