为了减小直齿圆柱齿轮系统由于外载荷波动和时变啮合刚度引起的振动，建立了直齿圆柱齿轮的时滞反馈减振动力学模型，并利用多尺度法对时滞反馈齿轮传动系统进行求解，获得了齿轮系统主共振频率响应方程，通过分析比较载荷波动、啮合刚度波动和时滞反馈控制参数对主共振的影响，可以得出：齿轮系统存在的载荷波动和啮合刚度波动都会导致齿轮系统主共振不稳定；合理匹配的时滞控制参数能够使主共振快速收敛到稳定解，反之可能导致系统振动加剧，使系统稳定性变差。
Abstract
In order to reduce vibration of a spur gear system caused by external load fluctuation and time-varying meshing stiffness one, its dynamical model with time delay feedback control was established.The multi-scale method was applied to solve this system, and obtain its primary resonance frequency equation.Effects of load fluctuation, mesh stiffness one and time delay feedback control parameters on the system’s primary resonance were analyzed contrastively.The results showed that the load fluctuation and gear meshing stiffness one can cause the system main resonance unstable; time delay control parameters should be matched reasonably to make the primary resonance quickly converge to the stable solution, otherwise, the system vibration may be intensified to cause the system’s stability worse.
关键词
时滞反馈 /
直齿圆柱齿轮 /
多尺度法 /
主共振 /
稳定性.
{{custom_keyword}} /
Key words
Time delay feedback /
Spur gear /
Method of multiple scales /
Primary resonance /
Stability.
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Moradi Hamed; Salarieh Hassan. Analysis of nonlinear oscillations in spur gear pairs with approximated modelling of backlash nonlinearity [J]. Mechanism and Machine Theory, 2012, 51: 14-31.
[2] Jian-Wei Lu; Hao Chen; Fan-Ling Zeng et al. Bergman. Influence of system parameters on dynamic behavior of gear pair with stochastic backlash [J]. Meccanica, 2014, 49(2):429-440.
[3] Song He; Rajendra Singh. Dynamic Transmission Error Prediction of Helical Gear Pair Under Sliding Friction Using Floquet Theory [J]. Journal of Mechanical Design, ASME, 2008, 130(5): 052603-052611.
[4] 张微, 丁千. 直齿圆柱齿轮啮合耦合振动系统参数振动研究[J]. 工程力学, 2015, 32 (5): 213-220.
ZHANG Wei; DING Qian. Research on properties for parametric vibration of a spur gear meshing and coupling system [J]. Engineering Mechanics, 2015, 32 (5): 213-220.
[5] 魏莎, 韩勤锴, 褚福磊. 考虑不确定参数的齿轮副非线性动态特性分析 [J]. 振动与冲击, 2016, 35 (10): 44-48, 59.
WEI Sha; HAN Qin-kai; CHU Fu-lei. Nonlinear dynamic analysis of gear-pair systems with uncertainties [J]. Journal of Vibration and Shock, 2016, 35(10): 44-48, 59.
[6] Chen M.H.; Brennan M.J.. Active control of gear vibration using specially configured sensors and actuators [J]. Smart Materials and Structures, 2000, 9:342-350.
[7] MF Li; TC Lim; WS Shepard. Modeling active vibration control of a geared rotor system [J]. Smart Materials and Structures, 2004, Vol.13:449-458.
[8] MF Li; TC Lim; WSS Jr et al. Experimental active vibration control of gear mesh harmonics in a power recirculation gearbox system using a piezoelectric stack actuator [J]. Smart Materials and Structures, 2005, 14 (5): 917-927.
[9] 李以农, 张锋, 丁庆中等. 齿轮啮合振动的主动控制方法与实验研究 [J]. 振动工程学报, 2014, 27(2): 215-221.
LI Yi-nong; ZHANG Feng; DING Qing-zhong et al. Method and experiment study for active vibration control of gear meshing [J]. Journal of Vibration Engineering, 2014, 27(2): 215-221.
[10] S He; R Gunda; R Singh. Inclusion of Sliding Friction in Contact Dynamics Model for Helical Gears [J]. Journal of Mechanical Design, ASME, 2007, 129 (129): 48-57.
[11] Jingyue Wanga ; Haotian Wangb; Lixin Guoc. Analysis of effect of random perturbation on dynamic response of gear transmission system [J]. Chaos, Solitons and Fractals, 2014, 68:78-88.
[12] A. Farshidianfar; A. Saghafi. Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis [J]. Physics Letters. A, 2014, 378(46):3457-3463.
[13] Jian Peng; Lianhua Wang; Yueyu Zhao et al. Bifurcation analysis in active control system with time delay feedback [J]. Applied Mathematics and Computation, 2013, 219 (19):10073-10081.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(1517 KB)
