为研究啮合刚度等动力学参数的波动性对齿轮传动系统固有特性影响，以四自由度扭转振动齿轮传动系统模型为例，利用区间模态分析方法对含区间动力学参数齿轮系统模态特性进行分析。通过算例给出齿轮系统固有频率波动区间，并通过上下边界相对不确定量与曲线凹凸性分析区间参数对系统固有频率影响。结果表明，参数波动导致的区间固有频率并非关于确定性模型下固有频率中心对称，而存在上下偏差，导致该偏差的主要原因为曲线凹凸性；通过上下边界相对不确定量及凹凸性可判断固有频率随系统参数的波动规律，上下边界相对不确定量间差异越大曲线凹凸性越明显。在单区间参数分析中，不同区间动力学参数对系统固有频率影响不同。当所有参数区间波动均考虑时系统区间固有频率范围最大，超过工程能接受结果，因此设计分析时参数的区间波动性不可忽略。
Abstract
The purely torsional vibration model of the geared transmission system with four degrees of freedom is developed to research the natural characteristics of the gear system with the consideration of fluctuations of tooth mesh stiffness and other dynamical parameters. The interval modal analysis method, relative uncertainties and the concavity and convexity analysis are used to investigate the modal characteristic with the interval dynamic parameters. The fluctuation intervals of natural frequencies are obtained by a numerical example. The results show that: the natural frequency under the deterministic model is not the central value of the interval natural frequency caused by parameter fluctuations. There are upper and lower deviations caused by the concavity and convexity. The fluctuating laws of natural frequency with fluctuation parameters can be identified by the relative uncertainties of the upper and lower bounds and the concavity and convexity. The greater the difference between the relative uncertainties of the upper and lower bound, the more obvious the corresponding concavity and convexity of the curve. The effects of different interval dynamic parameters to the natural frequency are different at the analysis of single interval parameter. The interval natural frequency is largest and exceeds the acceptable results of engineering when the fluctuations of all the corresponding parameters are taken into account. Therefore the analysis of the interval fluctuations of system parameters is significant.
关键词
齿轮 /
固有频率 /
模态 /
区间分析
{{custom_keyword}} /
Key words
gear /
natural frequencies /
modal /
interval analysis
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Han Q, Zhao J, Chu F. Dynamic analysis of a geared rotor system considering a slant crack on the shaft [J]. Journal of Sound and Vibration, 2012, 331(26): 5803-5823.
[2] Parker R G, Wu X. Vibration modes of planetary gears with unequally spaced planets and an elastic ring gear [J]. Journal of Sound and Vibration, 2010, 329(11): 2265-2275.
[3] 杨通强，宋轶民，张策，等. 斜齿行星齿轮系统自由振动特性分析[J]. 机械工程学报, 2005, 41(7): 50-55.
YANG Tong-qiang, SONG Yi-min, ZHANG Ce,et.al. Property analysis of free vibration of helical planetary gear trains [J]. Chinese Journal of Mechanical Engineering, 2005, 41(7): 50- 55.
[4] 李润方，王建军. 国外齿轮系统动态特性的统计分析[J]. 机械传动, 1995, 19(4): 45-47.
LI Run-fang, WANG Jian-jun. Statistical analysis of characteristics for gear system at overseas[J]. Journal of Mechanical Transmission, 1995, 19(4): 45-47.
[5] Driot N, Perret-Liaudet J. Variability of modal behavior in terms of critical speeds of a gear pair due to manufacturing errors and shaft misalignments[J]. Journal of Sound and Vibration, 2006, 292(3): 824-843.
[6] 魏永祥，陈建军，王敏娟. 随机参数齿轮-转子系统扭转振动固有频率分析[J]. 工程力学, 2011, 28(4): 172-177.
WEI Yong-xiang, CHEN Jian-jun, WANG Min-juan. Natural frequency analysis for torsional vibration of a gear-rotor system with random parameters [J]. Engineering Mechanics, 2011, 28(4): 172-177.
[7] 陈塑寰. 结构动态设计的矩阵摄动理论[M]. 北京: 科学出版社, 1999.
[8] Sim J, Qiu Z, Wang X. Modal analysis of structures with uncertain-but-bounded parameters via interval analysis[J]. Journal of Sound and Vibration, 2007, 303(1/2): 29-45.
[9] 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.
[10] Kahraman A, Ozguven H N, Houser D R, et al. Dynamic analysis of geared rotors by finite elements[R]. DTIC Document, 1990.
[11] Chen S, Qiu Z, Song D. A new method for computing the upper and lower bounds on frequencies of structures with interval parameters [J]. Mechanics Research Communications, 1994, 21(6): 583-592.
[12] 李明，孙涛，胡海岩. 齿轮传动转子-轴承系统动力学的研究进展[J]. 振动工程学报, 2002, 15(3): 5-12.
LI Ming, SUN Tao, HU Hai-yan. Review on dynamics of geared rotor-bearing systems[J]. Journal of Vibration Engineering, 2002, 15(3): 5-12.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(3023 KB)
