Dynamic characteristics of multi-degrees of freedom system rotor-bearing system with coupling faults of rub-impact and crack

Extensive studies on rotor systems with single or coupled multiple faults have been carried out. However these studies are limited to single-span rotor systems. A finite element model for a complex rotor-bearing system with coupled faults is presented. The dynamic responses of the rotor-bearing system are obtained by using the rotor dynamics theory and the modern nonlinear dynamics theory in connection with the continuation-shooting algorithm（commonly used for obtaining a periodic solution for a nonlinear system） for a range of rub-impact clearances and crack depths. The stability and Hopf instability of the periodic motion of the rotor-bearing system with coupled faults are analyzed by using the procedure described. The results indicate that the finite element method is an effective way for determining the dynamic responses of such complex rotor-bearing systems. Further for a rotor system with rub-impact and crack faults, the influences of the clearances are significantly different for different rub-impact stiffness. On the contrary, the influence of crack depths is rather small. The instability speeds of the rotor-bearing system increase due to the presence of the crack fault. The results obtained using the new finite element model, presented for computation and analysis of dynamic responses of the rotor-bearing systems with coupled faults, are in accordance with measurements in experiment. The formulations given can be used for diagnosis of faults, vibration control, and safe and stable operations of real rotor-bearing systems.     

Investigation on the stability of periodic motions of a flexible rotor-bearing system with two unbalanced disks

The stability of periodic motion of a rotor-bearing system with two unbalanced disks is analyzed based on a multi-degree of freedom (M-DOF) finite element model. Nonlinear effects of supporting oil-film and inertia distributions as well as shearing effect are taken into account. Focusing on the more realistic FE method to study the stability of nonlinear rotor-bearing system with the influence of the eccentricity phase, the stability calculation of the M-DOF FE model is done by using the combination of Shooting method and Newmark method. Experiments with a rotor-bearing test rig (two disks on a shaft with two bearings) are then performed and results are presented. It is found that typical instability characteristic is successfully produced. Through comparisons between calculated results and measurements, it is shown that the combination of Shooting method and Newmark method in studying the M-DOF rotor-bearing system is useful, especially for the complex rotor-bearing system. In addition, altering eccentricity phase of the two disks can significantly influence instability type and speed. When the two disks are out of phase, the occurring of oil whip is restrained effectively. It is suggested that a careful examination should be made in modeling more complex non-linear rotor-bearing system. Some response curves are shown to compare the beam motions at different load velocities.     

Stability of periodic motion on the rotor-bearing system with coupling faults of crack and rub-impact

A dynamic model was set up for the rotor-bearing system with coupling faults of crack and rub-impact. Using the continuation-shooting algorithm for periodic solution of nonlinear non-autonomous system, the stability of the system periodic motion was studied by the Floquet theory. The saddle-node bifurcation, periodic-doubling bifurcation and the Hopf bifurcation were found. There are peculiar dynamic characteristics of the rotor-bearing system with coupling faults of crack and rub-impact that differs from single fault. The conclusions provide theoretic basis reference for the failure diagnosis of the rotor-bearing system with coupling faults of crack and rub-impact fault.     

高速转子-轴承系统的复杂动力学行为研究

在高速旋转机械的故障诊断研究中,实际转子系统具有复杂的非线性动力学特性,为此,基于非线性转子动力学理论建立高速泵转子系统动力学有限元模型,研究了非线性油膜力作用下的轴承阻尼扣刚度确定方法,分析了陀螺力矩和滑动轴承油膜力作用等因素对转子系统动力学特性的影响,研究了转速、偏心距和轴段直径等因素对转子系统不平衡响应的影响,为工程实际应用中的转子轴承系统的优化设计、故障诊断、振动控制等提供了理论依据.     

某核电站主泵转子-轴承系统碰摩故障分析

为了使核电站的主泵安全、长期、稳定地运行，利用非线性有限元方法、现代非线性理论与转子动力学理论，建立了某核电站主泵转子-轴承系统有限元模型，研究了主泵的碰摩故障问题，分析了碰摩刚度、不平衡质量偏心量与碰摩间隙对转子的影响。研究结果对核电站主泵等相似旋转机械的碰摩故障的诊断具有一定的参考价值。     

裂纹-碰摩转子-轴承系统周期运动稳定性

建立了含有裂纹-碰摩耦合故障转子轴承系统的动力学模型,利用求解非线性非自治系统周期解的延拓打靶法和F loquet理论,研究了系统周期运动的稳定性。发现碰摩转子-轴承系统在不同的转速下会发生鞍结分岔、倍周期分岔和Hopf分岔等现象,裂纹-碰摩耦合故障转子-轴承系统具有不同于单一故障的独特的动力学特性。研究结果为转子-轴承系统故障诊断和安全运行提供了一定的参考。     

松动-碰摩耦合故障转子系统振动特性分析

针对动态油膜力下带有支座松动 碰摩耦合故障的转子 轴承系统的非线性动力学模型,采用数值模拟等方 法,考察其随转速比变化及改变最大松动间隙值时发生松动和碰摩故障的分岔与混沌特性,并分别与相同参数条件 下带有支座松动故障的转子系统和碰摩故障转子系统进行比较,得到如下结论:该耦合故障系统中碰摩与松动故障 主要发生在主共振区、油膜振荡区及转速比大于3.4的转速范围内,发生碰摩故障时系统运动多为混沌运动;随着 松动最大间隙值的减小,碰摩的转速范围越来越大,而发生松动的转速范围越来越小;两种故障的产生相对独立。     

基于轴心轨迹形态的转子裂纹故障分析与诊断

基于转子系统轴心轨迹的形态分析,提出一种对多故障中的裂纹故障进行初步诊断的简便方法。通过对转子系统1/2临界转速附近的轴心轨迹形态分析,表明在1/2临界转速附近,裂纹-碰摩双故障转子系统轴心轨迹的内环形状随着转速的变化而改变,内环的偏置方向也随转速旋转一定角度。在碰摩转子系统中,其1/2临界转速附近的轴心轨迹形态与裂纹-碰摩双故障转子有明显区别。多故障系统轴心轨迹的形态分析为对其中的裂纹故障进行初步诊断提供了新方法,使转子故障诊断效率得到提高。同时结合分岔图及频谱图对不同转子系统的动力学响应进行了分析,利用Bently转子实验台对裂纹转子系统的轴心轨迹进行了实验验证。     

Crack identification in a rotor with an open crack

A finite element (FE) model, which is based on a transfer matrix analysis and local flexibility theorem, is introduced for crack identification of a static (non-rotating) rotor with an open crack. Through numerical simulation, the effects of crack location and crack depth on the mode shapes and the changes in the eigenfrequencies of the cracked rotor are investigated. A crack identification algorithm that makes use of the translations of the first mode at two symmetric points and the contour diagram of crack location versus crack depth for the first two given normalized eigenfrequencies is proposed to estimate the crack location and depth in the rotor. Two illustrative examples are demonstrated and compared for availability and validity of the proposed algorithm.     

不对称润滑工况下碰摩转子-轴承系统的动力学分析

在考虑非线性油膜力的基础上，建立了具有碰摩故障的转子一轴承系统的动力学模型。研究了具有碰摩故障的转子在两支承轴承使用相同和不同粘度润滑剂时的动力学行为，发现随着一端轴承润滑油粘度的降低，转子的混沌区域和拟周期区域扩大了。该结果为采用不同粘度润滑剂的转子一轴承系统的故障诊断提供了依据。     

Second Generation Wavelet Finite Element and Rotor Cracks Quantitative Identification Method

The presence of cracks in the rotor is one of the most dangerous and critical defects for rotating machinery. Defect of fatigue cracks may lead to long out-of-service periods, heavy damages of machines and severe economic consequences. With the method of finite element, vibration behavior of cracked rotors and crack detection was received considerable attention in the academic and engineering field. Various researchers studied the response of a cracked rotor and most of them are focused on the crack detection based on vibration behavior of cracked rotors. But it is often difficult to identify the crack parameters quantitatively. Second generation wavelets (SGW) finite element has good ability in modal analysis for singularity problems like a cracked rotor. Based on the fact that the feature of SGW could be designed depending on applications, a multiresolution finite element method is presented. The new model of SGW beam element is constructed. The first three natural frequencies of the rotor with different crack location and size were solved with SGW beam elements, and the database for crack diagnosis is obtained. The first three metrical natural frequencies are employed as inputs of the database and the intersection of the three frequencies contour lines predicted the normalized crack location and size. With the Bently RK4 rotor test rig, rotors with different crack location and size are tested and diagnosed. The experimental results denote the cracks quantitative identification method has higher identification precision. With SGW finite element method, a novel method is presented that has higher precision and faster computing speed to identify the crack location and size.     

Model-based identification of two cracks in a rotor system

The dynamics and diagnostics of cracked rotor have been gaining importance in recent years. Relatively few authors have addressed the problem of multi crack assessment for rotors. In the present study a model-based method is proposed for the on-line identification of two cracks in a rotor. The fault-induced change of the rotor system is taken into account by equivalent loads in the mathematical model. The equivalent loads are virtual forces and moments acting on the linear undamaged system to generate a dynamic behaviour identical to the measured one of the damaged system. The rotor has been modelled using finite element method, while the cracks are considered through local flexibility changes. The cracks have been identified for their depths and locations on the shaft. The nature and symptoms of the fault, that is crack, are ascertained using the FFT.     

转子-滑动轴承系统不对中-碰摩耦合故障分析

针对滑动轴承支撑下的转子系统发生不对中故障进而引起不对中-碰摩耦合故障的诊断问题,基于非线性有限元法,应用短轴承油膜力、等效不对中力矩及Hertz接触理论建立双盘不对中-碰摩耦合故障转子系统动力学模型,并通过增广的拉格朗日方法来处理接触约束条件,以保证转盘和机匣相互接触时满足边界渗透深度在规定的容差范围内。同时,结合试验研究分析了在不同转速条件时,滑动轴承支撑下的耦合故障转子系统的相关动力学特性。研究表明碰摩故障在耦合故障中处于主导地位,不对中故障主要会激发高倍频谱处于从属地位;并且随着转速的提高,系统频率成分以高倍频为主,逐步由拟周期运动进入混沌运动状态,同时由于不对中力矩与碰摩力的作用,油膜失稳现象局部被抑制,一、二阶油膜振荡现象均滞后显现。研究结果可为滑动轴承支撑下耦合故障转子系统故障诊断提供依据。     

松动-裂纹耦合故障转子系统的非线性响应

基于现代非线性动力学和转子动力学理论,采用Newmark-β法和Poincaré映射对裂纹和一端支座松动耦合故障转子系统进行了数值模拟研究,给出了系统响应随转速比、松动质量和裂纹深度变化的分岔图,分析了一些主要参数变化的影响以及典型的Poincaré截面图。研究发现,系统存在拟周期环面破裂、阵发性分岔和多倍T周期运动失稳进入混沌三条混沌道路。这些结论为旋转机械的故障诊断提供了理论基础和参考。     

非线性转子-轴承系统的动力学特性及稳定性

研究非线性转子—轴承系统的动力学特性及稳定性。采用改进的自由界面模态综合技术给出一种自由度降阶方法，该方法将非线性油膜力及非线性自由度保留在物理空间，以增加非线性分析的精度，使降阶系统仍具有局部非线性特征。基于打靶法及将延续算法和打靶法相结合的轨迹预测追踪算法，研究系统非线性不平衡响应，结合Floquet理论分析非线性轴承—转子系统T周期运动的局部稳定性和分岔行为。     

Effects of cracks on rotor system instability

The stability threshold of a rotor-bearing system having a transverse crack has been studied by using FEM and considering the various crack parameters and shaft internal damping (viscous and hysteretic damping) and geometric parameters. It has been observed that the instability speed has reduced considerably with increase in crack depth and influenced more with hysteretic damping compared to viscous damping. The stability of the rotor system including shaft with two open cracks has also been carried out and observed the influence of one crack over the other for threshold speed limits.     

双盘转子轴承系统不对中-碰摩耦合故障分析

针对由于轴承不对中而引起不对中-碰摩耦合故障的转子-轴承系统,建立了考虑电机联轴器影响的双盘不对中-碰摩耦合故障转子系统力学模型和有限元模型。基于非线性有限元方法,使用等效不对中力矩及接触理论研究了碰摩刚度和不对中角度两个重要参数对系统动力学特性的影响。通过对在不同碰摩刚度及不对中角度时系统动力学特性的研究分析,发现不对中-碰摩耦合故障常常以碰摩故障特征为主,并且二倍频出现较早及其峰值会急速增大,这一特性可以作为诊断不对中-碰摩耦合故障的一个依据。     

不对称润滑对碰摩转子-轴承系统的动力学影响

在考虑非线性油膜力的基础上,建立了具有碰摩故障的转子-轴承系统的动力学模型。用数值方法研究了在非线性油膜力作用下具有碰摩故障的转子系统的动力学特性,并研究了当改变其中一个支承轴承润滑油的粘度时,转子系统的动力学特性。研究发现,随着一轴承润滑油粘度的降低,转子系统亚临界角速度区的混沌区域和拟周期区域扩大了。该结果为采用不同粘度润滑剂的转子-轴承系统的优化设计、安全运行和故障诊断等提供了一定的理论参考     

基于改进EMD的旋转机械耦合故障诊断方法研究

提出一种基于改进EMD的旋转机械耦合故障诊断方法。该方法结合相似极值延拓和加余弦窗函数运算的优点,解决了延拓部分不精确和加窗函数后使原信号发生改变的问题,提高了EMD方法的运算精度。应用该方法对存在裂纹碰摩故障的转子－轴承系统振动信号进行了特征提取,并进行了故障诊断,与单一故障特性相比,诊断出的振动信号既有裂纹引起的高频成分,也有碰摩引起的低频成分,得到的耦合故障特征证明了该方法的有效性。     

Dynamics analysis of a cracked dual-disk over-hung rotor-bearing system

A dynamic model of a dual-disk vertical over-hung rotor-bearing system is developed, taking into account nonlinear oil-film force. Its dynamic behaviors are investigated by numerical Runge-Kutta method. Its bifurcation and chaos characteristics are analyzed with crack fault and without crack fault. By analyzing the bifurcation plot, Poincare section plots and amplitude spectra, we found that the crack greatly influences the dynamic characteristics of the rotor-bearing system. Because of the strong effect of the nonlinear oil-film force and crack to the system, 1/2 times, 1/3 times frequency components appear in the response spectrum map. The results may bring up theoretical references for fault diagnosis of rotor-bearing systems. __________ Translated from Journal of Vibration Engineering, 2005, 18(1) (in Chinese)