多轴系耦合作用下齿轮系统转子裂纹故障的振动特性研究
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摘要
为了探究多轴系耦合齿轮系统中的转子裂纹故障与单轴系转子裂纹故障振动响应特性的异同点,基于Jones轴承建模理论,建立滚动轴承的拟静力学模型;利用Timoshenko梁单元建立传动轴的有限元模型;考虑时变啮合刚度、齿轮传递误差、陀螺效应等因素,利用集中参数法建立齿轮副的动力学模型。将轴承、传动轴与齿轮副模型进行集成,建立齿轮系统非线性动力学模型;利用能量释放率理论与应力强度因子为零法分析裂纹转子单元的呼吸效应,利用Newmark-β数值积分法对转子裂纹故障进行动力学仿真,研究转子裂纹故障的振动响应特征。结果表明:与单轴转子系统转子裂纹的振动响应特征不同,当齿轮系统发生转子裂纹故障时,由于齿轮啮合的引起的耦合效应及转子裂纹引起的呼吸效应,时域响应表现出明显的幅值调制现象,频域中转频及其2倍频幅值增加明显,在啮合频率处伴有明显的边频带。研究结果可为齿轮系统转子裂纹故障的监测与诊断提供理论基础。
The objective of this article is to explore the differences of vibration response characteristics between the single-axis rotor and the multi-axis coupled gear system with rotor crack faults. A quasi static model of rolling bearings is established based on Jones bearing modeling theory. Timoshenko beam elements are used to establish the finite element model of the transmission shaft. Considering the time-varying meshing stiffness, gear transmission error, gyroscopic effect etc., the dynamic model of the gear pair is established by using lumped parameter method. The bearings, drive shaft and gear pair model are integrated to build the nonlinear dynamic model of the gear system. The energy release rate theory is used to analyze the breathing effect of the cracked rotor. The vibration response characteristics of the rotor crack faults are simulated by Newmark-β numerical integral method. The results show that when the rotor crack faults occur, the time-domain response shows obvious amplitude modulation phnomenon due to the coupling effect induced by gear meshing and the breathing effect induced by rotor crack faults. The amplitudes of the rotational frequency and the octave rotational frequency increase significantly. There are obvious sidebands at the meshing frequency. The research results provide a theoretical basis for the monitoring and diagnosis of gear transmission system with rotor crack faults.
The objective of this article is to explore the differences of vibration response characteristics between the single-axis rotor and the multi-axis coupled gear system with rotor crack faults. A quasi static model of rolling bearings is established based on Jones bearing modeling theory. Timoshenko beam elements are used to establish the finite element model of the transmission shaft. Considering the time-varying meshing stiffness, gear transmission error, gyroscopic effect etc., the dynamic model of the gear pair is established by using lumped parameter method. The bearings, drive shaft and gear pair model are integrated to build the nonlinear dynamic model of the gear system. The energy release rate theory is used to analyze the breathing effect of the cracked rotor. The vibration response characteristics of the rotor crack faults are simulated by Newmark-β numerical integral method. The results show that when the rotor crack faults occur, the time-domain response shows obvious amplitude modulation phnomenon due to the coupling effect induced by gear meshing and the breathing effect induced by rotor crack faults. The amplitudes of the rotational frequency and the octave rotational frequency increase significantly. There are obvious sidebands at the meshing frequency. The research results provide a theoretical basis for the monitoring and diagnosis of gear transmission system with rotor crack faults.
引文
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[8]颜逸飞,荆建平.行星齿轮减速器故障动力学模拟和特征提取[J].噪声与振动控制,2016,36(2):65-68.
[9]丁闯,张兵志,冯辅周,等.行星轮系动力学仿真分析与故障诊断[J].噪声与振动控制,2017,37(4):144-149.
[10] LIANG XIHUI, ZUO MING J, FENG ZHIPENG.Dynamic modeling of gearbox faults:A review[J].Mechanical Systems and Signal Processing, 2018, 98:852-876.
[11] DIMAROGONAS AD. Vibration of cracked structures:A state of the art review[J]. Engineering Fracture Mechanics, 1996, 55(5):831-857.
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[13] PAPADOPOULOS CA. The strain energy release approach for modeling cracks in rotors:A state of the art review[J]. Mechanical Systems and Signal Processing,2008, 22(4):763-789.
[14]王帅,訾艳阳,何正嘉.含裂纹离心压缩机叶轮结构的振动局部化[J].振动与冲击,2017,36(6):108-113.
[15]曹宏瑞,李亚敏,成玮,等.局部损伤滚动轴承建模与转子系统振动仿真[J].振振动动、测试与诊断,2014,34(3):549-552.
[16]曹宏瑞.高速机床主轴数字建模理论及其应用研究[D].西安:西安交通大学,2010.
[17] Darpe AK. Dynamics of a Jeffcott rotor with slant crack[J]. Journal of Sound And Vibration, 2007, 303(1-2):1-28.
[18]林言丽,禇福磊.裂纹转子的刚度模型[J].机械工程学报,2008,44(1):114-120.
[2] ENDO H, RANDALL RB, GOSSELIN C. Differential diagnosis of spall vs. cracks in the gear tooth fillet region:Experimental validation[J]. Mechanical Systems and Signal Processing, 2009, 23(3):636-651.
[3] CHEN Z, SHAO Y. Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth[J]. Engineering Failure Analysis, 2011, 18(8):2149-2164.
[4] MA R, CHEN Y, CAO Q. Research on dynamics and fault mechanism of spur gear pair with spalling defect[J].Journal of Sound and Vibration, 2012, 331(9):2097-2109.
[5]韩振南,孙文婷,高建新.含轮齿剥落的齿轮系统动力学故障模拟[J].振振动动、测试与诊断,2012,32(1):101-104+165.
[6] WAN ZHIGUO, CAO HONGRUI, ZI YANYANG. 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.
[7]雷亚国,罗希,刘宗尧,等.行星轮系动力学新模型及其故障响应特性研究[J].机械工程学报,2016,52(13):111-122.
[8]颜逸飞,荆建平.行星齿轮减速器故障动力学模拟和特征提取[J].噪声与振动控制,2016,36(2):65-68.
[9]丁闯,张兵志,冯辅周,等.行星轮系动力学仿真分析与故障诊断[J].噪声与振动控制,2017,37(4):144-149.
[10] LIANG XIHUI, ZUO MING J, FENG ZHIPENG.Dynamic modeling of gearbox faults:A review[J].Mechanical Systems and Signal Processing, 2018, 98:852-876.
[11] DIMAROGONAS AD. Vibration of cracked structures:A state of the art review[J]. Engineering Fracture Mechanics, 1996, 55(5):831-857.
[12] SABNAVIS G KRG, QUINN D. Cracked shaft detection and diagnosis:a literaute review[J]. The Shock and Vibration Digest, 2004, 36:287-296.
[13] PAPADOPOULOS CA. The strain energy release approach for modeling cracks in rotors:A state of the art review[J]. Mechanical Systems and Signal Processing,2008, 22(4):763-789.
[14]王帅,訾艳阳,何正嘉.含裂纹离心压缩机叶轮结构的振动局部化[J].振动与冲击,2017,36(6):108-113.
[15]曹宏瑞,李亚敏,成玮,等.局部损伤滚动轴承建模与转子系统振动仿真[J].振振动动、测试与诊断,2014,34(3):549-552.
[16]曹宏瑞.高速机床主轴数字建模理论及其应用研究[D].西安:西安交通大学,2010.
[17] Darpe AK. Dynamics of a Jeffcott rotor with slant crack[J]. Journal of Sound And Vibration, 2007, 303(1-2):1-28.
[18]林言丽,禇福磊.裂纹转子的刚度模型[J].机械工程学报,2008,44(1):114-120.