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.     

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。     

Simulations and experimental investigation on motion stability of a flexible rotor-bearing system with a transverse crack

In the classical process for stability studies on the rotor-bearing system with crack faults, the simple discrete model is adopted for research on such problems, which neglect some needful dynamical influence factor, such as the material damping, shearing effect and gyroscopic effects, etc. Therefore, it is necessary to find a precise calculation model for simulation of the rotor-bearing system with cracks faults. In this paper, instead of the traditional simple discrete model, finite element （FE） model is adopted to investigate the motion stability of a nonlinear rotor system with crack fault. According to finite element theory, the FE model of the cracked rotor system is established firstly. It should be pointed out that the element where the crack occurs is modeled by a particular crack element and the supports at both ends are simulated by two nonlinear loads. Then, based on dimensionless and dimensionality reduction, the Newmark-[3 method and the shooting method are employed to study the effect of eccentricity and the depth of crack on instability speed and bifurcation feature. Furthermore, the simulation results are verified by some corresponding experiments. The simulation and experimental results show that instability speed does not change monotonically, but decreases firstly and then increases when the amount of eccentricity increases. Moreover, as the type of instability changes, the instability speed jumps concomitantly. Additionally, the presence of crack fault can disturb the oil whirl, as a result, instability speed tends to increase slightly, but it does not affect the type of instability and jumping phenomenon. This research presents an effective and convenient method which uses the finite element method （FEM） to research the motion stability of the nonlinear rotor-bearing system with cracked faults and other nonlinear force, and the proposed method can provide a theoretical reference for stability analysis and vibration control in more complex relevant rotor-bearing system.     

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     

不同轴承支撑下碰摩转子系统的动力学特性

研究了不同类型轴承支撑下的转子碰摩故障振动特征。首先,采用了计及回转效应、剪切效应及横向扭转的梁单元建立了实验装置转子的有限元分析模型;然后,通过二维计算流体力学方法得到不同类型轴承的动力学参数;最后,在此基础上,结合非线性动力学理论,分析比较了转子在圆柱轴承、可倾瓦轴承等5种轴承支撑下的碰摩非线性动力学行为。研究结果表明：在椭圆轴承、五瓦轴承和四瓦可倾瓦轴承支撑下,系统主要表现为同频周期运动;而对于圆柱轴承和四油叶轴承支撑,系统会出现较复杂的运动。本研究工作是对之前转子碰摩非线性动力学研究的扩展,所得计算结果可为大型高速旋转机械系统动态设计制造和碰摩故障的诊断和控制提供理论参考。     

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。     

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。     

松动—碰摩耦合故障转子系统动力学特性分析

基于有限元法,建立考虑松动、碰摩及松动—碰摩耦合故障的转子—轴承系统的动力学模型,其中松动故障采用分段线性刚度和阻尼模型,转定子碰摩采用点—点接触模型。通过增广的拉格朗日方法来处理接触约束条件,修订的库仑摩擦模型来模拟转定子之间摩擦。考虑不同转速对松动、碰摩及松动—碰摩转子系统动力学特性的影响,并对比三者之间的异同点。研究表明,碰摩在耦合故障中处于主导地位,而松动主要影响松动端局部振动处于从属地位;松动—碰摩耦合故障响应在低转速和高转速与单一碰摩故障类似,在中间转速存在一些差别,但总体运动趋势基本一致;与单一松动故障相比发现,碰摩能够减小松动引起的低频振动,主要激发高频振动。研究结果可为转子系统耦合碰摩故障诊断提供依据。     

双盘悬臂转子轴承系统松动碰摩耦合故障分析

针对考虑松动-碰摩耦合故障的双盘悬臂立式转子-轴承系统，建立了该系统的力学模型和有限元模型，并基于非线性有限元方法和接触理论研究了松动刚度和碰摩间隙两个重要参数对系统动力学特性的影响。通过对在不同松动刚度和不同碰摩间隙时系统动力学特性的研究分析，发现转静件碰摩能够减小松动引起的低频振动，支座松动产生的碰摩具有明显的方向性，从而得出转子系统中诊断松动-碰摩耦合故障的依据。     

Chaos of rub-impact rotor supported by bearings with nonlinear suspension

The nonlinear dynamic analysis of the rotor-bearing system is studied in this paper and is supported by oil-film short bearings with nonlinear suspension. An observation of a nonlinearly supported model and the rub-impact between rotor and stator is needed. Therefore for more precise analysis of rotor-bearing systems, the rub-impact between rotor and stator is also proposed in this paper. The displacements in the horizontal and the vertical directions charactering the theoretical model of the system are considered with non-dimensional speed ratio. Inclusive of the analysis methods of the dynamic trajectory, the power spectrum, the Poincaré maps and the bifurcation diagrams are used to analyze the behavior of the rotor centre and bearing centre in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent analysis is also used in this study to identify the chaotic motion. It is concluded that the trajectory of rotor centre and bearing centre have undesirable vibrations. Especially at s=5.6, the rotor centre is at chaotic motion but the bearing centre is still at quasi-periodic motion. With the analysis of the dynamic behavior of these operating conditions, the theoretical and practical idea for controlling rotor-bearing systems and optimizing their operation can be more precise.     

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。     

非线性弹性碰摩转子周期运动稳定性分析

在同时考虑轴承油膜力、转轴非线性弹性力和碰摩发生时转静件间的相对速度对非线性摩擦力的影响基础上,构造了具有碰摩故障转子-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Floquet理论,研究了系统周期运动的稳定性,分析了非线性摩擦力对系统动力学特性的影响。     

Nonlinear dynamic analysis of a relatively short spherical gas journal bearing system

This paper studies the nonlinear dynamic behavior and bifurcation of a rigid rotor supported by two relatively short spherical gas journal bearings. The modified Reynolds equation is solved by a hybrid numerical method combining the differential transformation method (DTM) and the finite difference method (FDM). The analytical results reveal a complex dynamic behavior comprising periodic, subharmonic and quasi-periodic responses as the rotor mass and bearing number are increased. The results obtained using the hybrid DTM&FDM scheme are found to be in good agreement with those of a hybrid scheme comprising the successive over relaxation (SOR) method and the FDM scheme. Therefore, the DTM&FDM method provides an effective means of gaining insights into the nonlinear dynamics of relatively short spherical gas rotor-bearing systems.     

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。     

Coupled bending and torsional vibration of a rotor system with nonlinear friction

Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating machinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincaré maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose selfexcited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.     

Nonlinear Dynamic Analysis of a Rigid Rotor Supported By a Spiral-Grooved Opposed-Hemisphere Gas Bearing

The nonlinear dynamic behavior of a rigid rotor supported by a spiral-grooved opposed-hemisphere gas bearing is investigated in this article, focusing particular attention on its whirl motion. The finite element method combined with the finite difference method is employed to solve the time-dependent Reynolds equation that is coupled with the rotor motion considering five degrees of freedom. The rotor responses to the initial disturbance and synchronous and nonsynchronous excitations are investigated. To analyze the complicated dynamic behavior of the rotor–bearing system, the trajectories of the rotor centerline, time responses, phase portraits, power spectra, Poincare maps, and bifurcation diagrams are obtained from the numerical procedure. The results show that the conical whirl instability appears earlier than the cylindrical whirl instability with increasing rotational speed for the rotor–bearing system with no unbalance mass. Moreover, it reveals that the complex dynamic behavior of the system excited by unbalance mass varies with rotational speed and rotor mass. In addition, bifurcation diagrams employing the rotating speed and rotor mass as bifurcation parameters are obtained. Finally, the nonsynchronous excitation responses are presented, which behave in a different way than the synchronous excitation responses. The results of this study offer a further understanding of the nonlinear characteristics of spiral-grooved opposed-hemisphere gas bearings.     

非稳态油膜力作用下非线性刚度转子系统的碰摩故障分析

研究了在非稳态油膜力作用下非线性刚度转子系统发生碰摩时的振动问题。建立了非稳态油膜力作用的非线性刚度转子一轴承系统碰摩模型，应用数值分析的方法对其进行研究。通过Poincare截面图、轴心轨迹图、波形图和频谱图，直观地显示了系统在某些参数域中的运动状态。发现了由于油膜力作用出现油膜涡动和反向涡动现象以及倍周期分岔、概周期和混沌等复杂的动力学行为。数值分析结果为该类转子一轴承系统的设计和运行状态控制提供了理论参考。     

时频分析在油膜失稳与局部碰摩耦合故障中的应用

通过建立转子模型实验台, 模拟油膜失稳和局部碰摩耦合故障,把实验采集到的发生故障的振动信号,利用三维谱振图对转子升降速过程进行粗略分析.在频率成分较复杂的地方,利用小波尺度图和再分配小波尺度图进行细化分析.结果表明,再分配小波尺度图具有高的时频分辨率,可以清楚地识别出频率成分接近的低频分量;油膜失稳引起的转定子碰摩故障,会产生一些低频成分,油膜振荡会产生半频成分; 非线性油膜力是对系统起决定作用的重要因素,一般程度的碰摩对系统影响不大.     

吴消元法在转子动力学研究中的应用

以转子一轴承系统中短轴承的转子涡动，具有非线性支撑的柔性Jeffcott转子模型的周期响应为研究对象，对吴消元法在转子动力学研究中的应用作了初步探索。将吴消元法的特征列思想和Maple软件的符号计算机功能相结合，实现了对短轴承涡动参数的解析计算及对柔性Jeffcott转子模型周期响应的解析分析，在此基础上对Jeffcott转子的动态特性作了进一步的分析。     

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。