Chaos control of a single-stage spur gear system with backlash based on the OGY method

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (14) : 17-21.

TIAN Yaping1，XU Lu1，SONG Peijie1，CHU Yandong2

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Abstract

For the chaotic motion of a single-stage gear system with tooth backlash and bearing clearance in some parameter region, the unstable periodic orbit of chaotic attractor was stabilized by improved OGY chaotic control principle. The OGY control for a smooth dynamic system was transformed to a non-smooth multi-dimensional dynamic system by the finite difference method instead of the Jacobi matrix under non-smooth point. And PNF method is used to search the pseudo-fixed points of unstable periodic in chaotic region. The Jacobi matrix and sensitivity column vectors in the improved OGY algorithm were solved according to the dynamic equation and variation form, the periodic orbital interval and transfer characteristics of chaotic attractor were analyzed combined with Poincaré mapping. The simulation results show that the improved OGY control method is also effective for chaos control of multi-dimensional non-smooth gear systems. When the multi-period orbit was continuously controlled, the difficulty of chaos control increases with the increase of the target periodic orbit, and the required parameter perturbation increases correspondingly.

Key words

single-stage spur gear system

/ chaotic attractors / unstable periodic orbit / OGY chaotic control method / gear backlash

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TIAN Yaping1，XU Lu1，SONG Peijie1，CHU Yandong2. Chaos control of a single-stage spur gear system with backlash based on the OGY method[J]. Journal of Vibration and Shock, 2020, 39(14): 17-21

References

[1] Kahraman A, Singh R. Non-linear dynamics of a spur gear pair [J]. Journal of Sound and Vibration, 1990, 142(1):49-75.
[2] Vinayak H, Singh R, Padmanabhan C. Linear dynamic analysis of multi-mesh transmissions containing external rigid Gears [J]. Journal of Sound and Vibration, 1995, 185(1): 1-32.
[3] 苟向锋,陈代林. 三自由度齿轮传动系统的分岔与混沌研究[J]. 机械科学与技术, 2014, 33(2): 199-203.
Gou Xiangfeng, Chen Dailin. Research on bifurcation and chaos of 3-DOF gear transmission system [J]. Mechanical Science and technology for aerospace engineering, 2014, 33(2): 199-203.
[4] 田亚平, 褚衍东, 饶晓波.单级齿轮系统的周期运动及其稳定性[J]. 机械设计，2017,34(2):45-49.
Tian Yaping, Chu Yandong, Rao Xiaobo. Periodic motion and its stability of a single-stage gear system [J]. Journal of Machine Design, 2017,34(2):45-49.
[5] 田亚平,褚衍东,饶晓波.双参平面内单级直齿圆柱齿轮系统动力特性综合分析.振动工程学报，2018,31(2):219-225.
Tian yaping, Chu Yandong, Rao Xiaobo. Dynamic characteristic analysis of a single-stage spur gear system in two-parameter plane [J]. Journal of Vibration Engineering, 2018, 31(2):219-225.
[6] 郜志英, 沈允文, 董海军,等. 齿轮系统倍周期分岔和混沌层次结构的研究[J]. 机械工程学报, 2005, 41(04):48-52.
GAO Zhi-ying, SHEN Yun-wen, DONG Hai-jun, et al. Research on period-doubling bifurcation and chaos hierarchy in gear system[J]. Chinese Journal of Mechanical Engineering, 2005, 41(04):48-52.
[7] Saghafi A, Farshidianfar A. An analytical study of controlling chaotic dynamics in a spur gear system[J]. Mechanism & Machine Theory, 2016, 96:179-191.
[8] Farshidianfar A, Saghafi A. Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems[J]. Nonlinear Dynamics, 2014, 75(4):783-806.
[9] Kengne J, Tabekoueng Z N, Fotsin H B. Coexistence of multiple attractors and crisis route to chaos in autonomous third order Duffing-Holmes type chaotic oscillators[J]. Communications in Nonlinear Science & Numerical Simulation, 2016, 36:29-44.
[10] Roozegar M, Angeles J. A two-phase control algorithm for gear-shifting in a novel multi-speed transmission for electric vehicles[J]. Mechanical Systems and Signal Processing, 2018, 104: 145-154.
[11] Boukabou A, Mansouri N. Controlling chaos in higher-order dynamical systems[J]. International Journal of Bifurcation & Chaos, 2011, 14(14): 4019-4025.
[12] ZHANG Yong-xiang. Strange nonchaotic attractors with Wada basins[J]. Physica D Nonlinear Phenomena, 2013, 259 (3):26-36.
[13] Akhmet M U, Fen M O. Chaotic period-doubling and OGY control for the forced duffing equation[J]. Communications in Nonlinear Science & Numerical Simulation, 2012, 17(4): 1929-1946.
[14] Gritli H, Belghith S. Displayed phenomena in the semi-passive torso-driven biped model under OGY-based control method: Birth of a torus bifurcation[J]. Applied Mathematical Modelling, 2016, 40(4):2946-2967.
[15] 刘晓宁，沈允文，王三民，郜志英.基于OGY方法的间隙非线性齿轮系统混沌控制[J]. 机械工程学报, 2005, 41(11):26-31.
LIU Xiaoning，SHEN Yunwen， WANG Sanmin, GAO Zhi-ying. Chaos control for a gear system with clearance nonlinearity based on the OTT-Gerbogi-Yorke method[J]. Chinese Journal of Mechanical Engineering, 2005, 41(11):26-31.