针对含间隙锥齿轮系统动力学特性转迁及其控制问题，提出了基于胞元映射理论的参数解域结构和基于径向基函数神经网络的控制方法。采用集中质量法建立了7自由度弧齿锥齿轮动力学模型，基于胞元映射理论构建了频率和负载参数平面，采用伪不动点延续追踪算法求解了系统的分岔、齿面冲击、脱啮、齿背接触和动载特性转迁规律，分析发现频率和齿面冲击是影响周期分岔的主要因素，随负载增大其脱啮、冲击减弱，动载系数增大。针对平面中系统混沌现象，设计了参数反馈控制器、基于Poincaré截面欧氏距离构造适应度函数，用自适应引力搜索算法对控制器参数进行优化，从而实现了系统混沌、拟周期和周期运动向周期轨道有效控制。
Abstract
A parametric solution domain structure based on cell mapping theory and a control method based on radial basis function neural network are proposed to solve the dynamic characteristic transition and control problem of bevel gear system with backlash. The dynamics model of 7-degree-of-freedom spiral bevel gear was established by using the concentrated mass method. Then, the frequency and load parameter plane is constructed based on cell mapping theory, and the pseudo-fixed point continuous tracking algorithm is used to solve the transition rule of bifurcation, tooth surface impact, tooth no-meshing, tooth back contact and dynamic load characteristics of the straight bevel gear system. It is found that frequency and tooth impact are the main factors affecting the periodic bifurcation. With the increase of load, the tooth no-meshing and impact weaken, and the dynamic load coefficient increases. For the chaotic phenomena of the system in the plane, a parametric feedback controller is designed, and the fitness function is constructed based on Poincaré cross section Euclidean distance. The adaptive gravity search algorithm is used to optimize the controller parameters, so as to realize the effective control of chaos, quasi-period and periodic motions to periodic orbit.
关键词
非线性振动 /
弧齿锥齿轮传动系统 /
分岔 /
齿面冲击 /
RBF神经网络
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Key words
nonlinear vibration /
spiral bevel gear system /
bifurcation /
tooth impact /
RBF neural network
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参考文献
[1] 王三民，沈允文，董海军. 含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究[J]. 机械工程学报，2003, 39(2): 28-32.
Wang San-min, Shen Yun-wen, Dong Hai-jun. Nonlinear dynamical characteristics of a spiral bevel gear system with backlash and time-varying stiffness [J]. Chinese Journal of Mechanical Engineering, 2003, 39(2): 28-32.
[2] Wang Z Z, Pu W, Pei X, et al. Nonlinear dynamical behaviors of spiral bevel gears in transient mixed lubrication [J]. Tribology International, 2021, 160:107022.
[3] Hua X, Chen Z G. Effect of roller bearing elasticity on spiral bevel gear dynamics [J]. Advances in Mechanical Engineering, 2020, 12(7):1-9.
[4] Cao W , He T, Pu W, et al. Dynamics of lubricated spiral bevel gears under different contact paths [J]. Friction, 2022, 10(2): 247-267.
[5] FARSHIDIANFAR A, SAGHAFI Ａ. Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis [J]. Physics Letters A, 2014, 378(46): 3457-3463.
[6] 田亚平，徐璐，宋佩颉，等. 基于OGY的含间隙单级齿轮系统混沌运动控制 [J]. 振动与冲击，2020, 39(14): 17-21+35.
Tian Ya-ping, Xu Lu, Song Pei-jie, et al. 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+35.
[7] 林何，王三民，RATSCH Matthias, 等. 齿轮-轴承系统非线性混沌控制参数摄动与轨道偏差分析[J]. 振动与冲击，2020, 39(15): 250-256+265.
Lin He, Wang San-min, Ratsch Mattias, et al. Nonlinear chaos control paramteric perturbation and orbital deviation of a gear-bearing system [J]. Journal of Vibration and Shock, 2020, 39(15): 250-256+265.
[8] Keshtegar B，Sadeghian P, Ggolampour A, et al. Nonlinear modeling of ultimate strength and strain of FRP-confined concrete using chaos control method [J]. Composite Structures, 2017, 163: 423-431.
[9] Dehghan M, Mohannadi V. A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kuatta method [J]. Computer Physics Communications, 2017, 217: 23-24.
[10] Rashredi E, Nezamabadi-Pour H, Saryazdi S. GSA: a gravitational search algorithm [J]. Information Sciences, 2009, 179(13): 2232-2248.
[11] 卫晓娟，李宁洲，张惠，等. 一类含间隙碰撞系统混沌运动的RBF神经网络控制[J]. 振动工程学报，2018, 31(2)： 336-342.
Wei Xiao-juan, Li Ning-zhou, Zhang Hui, et al. Chaos control of a vibro-impact system with clearance based on RBF Neural network [J]. Journal of Vibration Engineering, 2018, 31(2): 336-342.
[12] 王世剑，孙洪江，王佳伟，等. 含间隙转台伺服系统的RBF神经网络反步控制[J]. 现代制造工程，2021, (5): 39-46+13.
Wang Shi-jian, Sun Hong-jiang, Wang Jia-wei, et al. RBF neural network backstepping control of turntable servo system with backlash [J]. Modern Manufacturing Engineering, 2021, (5): 39-46+13.
[13] 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[J]. 振动工程学报， 2018, 31(2): 219-225.
Tian Ya-ping, Chu Yan-dong, Rao Xiao-bo. Dynamic characteristic analysis of a single-stage spur gear system in two-parameter plane [J]. Journal of Vibration Engineering, 2018, 31(2): 219-225.
[14] Wei X J, Li N Z, Ding W C, et al. Model-free chaos control based on AHGSA for a vibro- impact system [J]. Nonlinear Dynamics, 2018, 94: 845-855.
[15] 许文俊，王锡淮，肖健梅，等. 基于改进自适应黑洞机制的引力搜索算法[J]. 计算机应用研究，2022，39(10): 10-20.
Xu Wen-jun, Wang Xi-huai, Xiao Jian-mei, et al. Gravity search algorithm based on improved adaptive black hole mechanism [J]. Application Research of Computers, 2022, 39(10): 10-20.
[16] Zhu G P, Kwong S. Gbest-guided artifical bee colony algorithm for numerical function optimization [J]. Applied Mathematics and computation, 2010, 217(7): 3166-3173.
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