直齿圆柱齿轮分度圆的裂纹损伤机理研究
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摘要
针对齿轮分度圆位置长期处于交变载荷状态容易产生疲劳裂纹的问题,综合考虑齿轮、转子和轴承之间的耦合关系,建立了十二自由度齿轮—转子—轴承弯扭耦合非线性动力学模型,并分析了分度圆裂纹对齿轮副时变啮合刚度的影响。采用Runge-kutta法求解了齿轮传动系统的运动微分方程,获得了分度圆裂纹损伤状态下系统的动态响应,研究了系统动态响应中的无量纲参数指标。研究结果表明:当分度圆处存在裂纹损伤时,齿轮系统时—频域上均呈现相应的损伤特征,振动信号序列中的峭度指标、裕度因子、峰值因子和脉冲因子均随裂纹的加深而增大;研究可为分度圆处裂纹损伤的演化机理分析和齿轮故障诊断研究提供理论基础。
Aiming at the problem of gear pitch circles are heavily affected by the alternating loads,which could easily lead to fatigue cracks,a coupling of 12-degree-of-freedom gear-rotor-bearing bending-torsion coupling was established by considering the coupling relationship between gear,rotor and bearing. The kinematic model and the effects of the pitch circle crack on the gear transmission system were reflected by the change of the integrated time-varying mesh stiffness. The Runge-kutta numerical solution was applied to formulate the differential equation of motion of spur gear transmission,and the dynamic response of the system under the circular crack with pitching was obtained,and which were applied to investigate the dimensionless parameter indicators in the dynamic response of the system. The results indicate that the corresponding damage signal appears in the time-frequency domain of the gear system when the crack occurs in the pitch circle. Meanwhile,the kurtosis pitch,margin factor,peak factor and pulse factor of the vibration signal sequence have obvious changes,and as the crack deepens,the kurtosis pitch of the vibration signal sequence also increases accordingly. This study can provide theoretical basis for the evolutionary mechanism of the crack damage in the gear pitch circles and the fault diagnosis of the gear transmission.
Aiming at the problem of gear pitch circles are heavily affected by the alternating loads,which could easily lead to fatigue cracks,a coupling of 12-degree-of-freedom gear-rotor-bearing bending-torsion coupling was established by considering the coupling relationship between gear,rotor and bearing. The kinematic model and the effects of the pitch circle crack on the gear transmission system were reflected by the change of the integrated time-varying mesh stiffness. The Runge-kutta numerical solution was applied to formulate the differential equation of motion of spur gear transmission,and the dynamic response of the system under the circular crack with pitching was obtained,and which were applied to investigate the dimensionless parameter indicators in the dynamic response of the system. The results indicate that the corresponding damage signal appears in the time-frequency domain of the gear system when the crack occurs in the pitch circle. Meanwhile,the kurtosis pitch,margin factor,peak factor and pulse factor of the vibration signal sequence have obvious changes,and as the crack deepens,the kurtosis pitch of the vibration signal sequence also increases accordingly. This study can provide theoretical basis for the evolutionary mechanism of the crack damage in the gear pitch circles and the fault diagnosis of the gear transmission.
引文
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[12]邵忍平,徐志锋,薛腾.裂纹对齿轮三维弹性体振动声辐射特性影响的研究[J].振动与冲击,2010,29(9):175-180,251.
[13]樊嘉峰,邓铁松,苏钊颐,等.分度圆裂纹齿轮副动态特性及故障诊断[J].机车电传动,2016(3):74-78.
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[15]陈忠.滚动轴承及其支承的刚度计算[J].煤矿机械,2006,27(3):387-388.
[16]苏文胜,王奉涛,张志新,等. EMD降噪和谱峭度法在滚动轴承早期故障诊断中的应用[J].振动与冲击,2010,29(3):18-21,201.
[17]彭宵微,彭翠云.基于无量纲参数分析的驱动机构运行性能研究[J].核电子学与探测技术,2015,35(10):1011-1013.
[2]王延忠,田志敏,侯良威,等.航空重载面齿轮三维裂纹分析与疲劳寿命预测[J].北京航空航天大学学报,2014,40(2):148-153.
[3]徐颖强,吕国志.航空齿轮接触疲劳裂纹萌生寿命预测方法的研究[J].西北工业大学学报,2003,21(4):473-476.
[4] WAN Zhi-guo,CAO Hong-rui,ZI Yan-yang,et al. An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack[J]. Engineering Failure Analysis,2014(42):157-177.
[5]林腾蛟,钟声,沈亮.圆柱齿轮齿根三维裂纹扩展分析及寿命预测[J].重庆大学学报,2012,35(11):1-7.
[6]蒋宇,李志雄,李力.基于双谱分析的齿轮故障诊断方法[J].机电工程,2008,25(11):83-86.
[7] Mohammed O D,Rantatalo M,AidanpaaJ O,et al. Vibration signal analysis for gear fault diagnosis with various crack progression scenarios[J]. Mechanical Systems&Signal Processing,2013,41(1-2):176-195.
[8]万志国,訾艳阳,曹宏瑞,等.时变啮合刚度算法修正与齿根裂纹动力学建模[J].机械工程学报,2013,49(11):153-160.
[9]马辉,逄旭,宋溶泽,等.基于改进能量法的直齿轮时变啮合刚度计算[J].东北大学学报:自然科学版,2014,35(6):863-866,884.
[10]王西.齿轮故障的动力学建模与轮齿裂纹刚度计算方法研究[D].重庆:重庆大学机械工程学院,2012.
[11]舒斌.含裂纹齿轮副啮合刚度与模态频率的研究[D].南昌:南昌航空大学航空制造工程学院,2018.
[12]邵忍平,徐志锋,薛腾.裂纹对齿轮三维弹性体振动声辐射特性影响的研究[J].振动与冲击,2010,29(9):175-180,251.
[13]樊嘉峰,邓铁松,苏钊颐,等.分度圆裂纹齿轮副动态特性及故障诊断[J].机车电传动,2016(3):74-78.
[14]徐斌,高跃飞,余龙. MATLAB有限元结构动力学分析与工程应用[M].北京:清华大学出版社,2009.
[15]陈忠.滚动轴承及其支承的刚度计算[J].煤矿机械,2006,27(3):387-388.
[16]苏文胜,王奉涛,张志新,等. EMD降噪和谱峭度法在滚动轴承早期故障诊断中的应用[J].振动与冲击,2010,29(3):18-21,201.
[17]彭宵微,彭翠云.基于无量纲参数分析的驱动机构运行性能研究[J].核电子学与探测技术,2015,35(10):1011-1013.