平稳随机激励下随机参数齿轮副的动力可靠性分析
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摘要
将一对啮合齿轮等效为单自由度随机振动系统,研究随机参数齿轮副在平稳随机激励下的动力可靠度的求解方法。从其平稳随机响应的表达式出发,同时考虑齿轮物理参数、几何尺寸的随机性,利用求解随机变量数字特征的矩法和代数综合法,导出随机参数齿轮副在平稳随机激励下位移及其导数响应的数字特征,再由动力可靠度的公式导出随机参数齿轮副动力可靠度的均值和方差的计算公式。通过与MonteCarlo方法结果的比较,验证文中方法的可行性和有效性。
A method of calculating dynamic reliability of gear with stochastic parameters stationary random excitation is discussed under the condition of single degree random vibration. Considering the randomness of the structural physical parameters and the geometric dimensions parameters and utilizing the random variable's functional moment method and the algebra synthesis method, the mean value and the variance of the mean square value of the structural displacement and stationary random excitation are computed firstly from the expressions of system stationary response in frequency domain. And then the expressions of the mean value and the variance of stochastic gear dynamic reliability are educed from the Poisson formula of calculating dynamic reliability. Finally, the influence of the randomness of system physical and geometric dimensions parameters on the system dynamic reliability is analyzed through comparing with the Monte Carlo method, validating the feasibility of this method.
A method of calculating dynamic reliability of gear with stochastic parameters stationary random excitation is discussed under the condition of single degree random vibration. Considering the randomness of the structural physical parameters and the geometric dimensions parameters and utilizing the random variable's functional moment method and the algebra synthesis method, the mean value and the variance of the mean square value of the structural displacement and stationary random excitation are computed firstly from the expressions of system stationary response in frequency domain. And then the expressions of the mean value and the variance of stochastic gear dynamic reliability are educed from the Poisson formula of calculating dynamic reliability. Finally, the influence of the randomness of system physical and geometric dimensions parameters on the system dynamic reliability is analyzed through comparing with the Monte Carlo method, validating the feasibility of this method.
引文
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[9]张锁怀,沈允文,董海军,刘梦军.齿轮拍击系统的动力响应[J].振动工程学报,2003,16(1):62-66.ZHANGSuoHuai,SHENYunWen,DONG HaiJun,LIU MengJun.Dy-namic response of a gear rattling system[J].Journal of Vibration Engi-neering,2003,16(1):62-66(In Chinese).
[10]Parey A,Badaoui MEl,Guillet F,Tandon N.Dynamic modelling of spur gear pair and applicationof empirical mode decomposition-basedsta-tistical analysis for early detection of localizedtooth defect[J].Journal of Sound and Vibration,2006,294(3):547-561.
[11]Chen J J,Che J W,Sun HA,et al.Probabilistic dynamic analysis of truss structures[J].Structural Engineering&Mechanics,2002,13(2):231-239.
[12]高伟,陈建军,程怡,马娟.随机刚架结构在平稳随机激励下的动力响应分析[J].振动与冲击,2004,23(2):88-91.GAO Wei,CHENJianJun,CHENG Yi,MAJuan.Dynamic response analysis of stochastic rigid structures under stationary randomexcitation[J].Journal of Vibration and Shock,2004,23(2):88-91(In Chi-nese).
[2]李桂青,曹宏.动力可靠性述评[J].地震工程与工程震动,1983,3(3):42-61.LI GuiQing,CAO Hong.Reviewon the dynamic reliability of structures[J].Earthquake Engineering an Engineering Vibration,1983,3(3):42-61(In Chinese).
[3]Crandall S H.First-crossing probabilities of the linear oscillator[J].Journal of Sound and Vibration,1970,12(3):285-299.
[4]李桂青,曹宏,李秋胜,等.结构动力可靠性理论及其应用[M].北京:地震出版社,1993:152-159.LI GuiQing,CAO Hong,LI QiuSheng,et al.Structural dynamic reli-abilitytheory and application[M].Beijing:Earthquake Press,1993:152-159(In Chinese).
[5]胡太彬,陈建军,王小兵.随机参数刚架结构的平稳随机位移响应动力可靠性分析[J].机械强度,2005,27(5):590-593.HUTaiBin,CHENJianJun,WANG XiaoBing.Displacement dynamic reliability analysis of stochastic rigidframes under stationaryrandomexci-tation[J].Journal of Mechanical Strength,2005,27(5):590-593(In Chinese).
[6]Abhijit Chaudhuri,Subrata Charkraborty.Reliability of linear structures with parameter uncertainty under non-stationaryearthquake[J].Structural Safety,2006,28(3):231-246.
[7]乔红威,吕震宙.非平稳随机激励下随机结构的动力可靠性分析[J].固体力学学报,2008,29(1):36-40.QIAO HongWei,LUZhenZhou.Dynamic reliability analysis of stochastic structures under non-stationary randomexcitation[J].Chinese Journal of Solid Mechanics,2008,29(1):36-40(In Chinese).
[8]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,1997:1-247.LI RunFang,WANGJianJun.Dynamics of gear system-vibration,shock,noise[M].Beijing:Science Press,1997:1-247(In Chinese).
[9]张锁怀,沈允文,董海军,刘梦军.齿轮拍击系统的动力响应[J].振动工程学报,2003,16(1):62-66.ZHANGSuoHuai,SHENYunWen,DONG HaiJun,LIU MengJun.Dy-namic response of a gear rattling system[J].Journal of Vibration Engi-neering,2003,16(1):62-66(In Chinese).
[10]Parey A,Badaoui MEl,Guillet F,Tandon N.Dynamic modelling of spur gear pair and applicationof empirical mode decomposition-basedsta-tistical analysis for early detection of localizedtooth defect[J].Journal of Sound and Vibration,2006,294(3):547-561.
[11]Chen J J,Che J W,Sun HA,et al.Probabilistic dynamic analysis of truss structures[J].Structural Engineering&Mechanics,2002,13(2):231-239.
[12]高伟,陈建军,程怡,马娟.随机刚架结构在平稳随机激励下的动力响应分析[J].振动与冲击,2004,23(2):88-91.GAO Wei,CHENJianJun,CHENG Yi,MAJuan.Dynamic response analysis of stochastic rigid structures under stationary randomexcitation[J].Journal of Vibration and Shock,2004,23(2):88-91(In Chi-nese).
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