转子与定子碰摩的非线性动力学研究

转子与定子碰摩的动力学行为及其与系统参数关系对旋转机械设计和安全运行至关重要. 转子/定子碰摩系统是一类多参数控制的高维非光滑强非线性系统, 其动力学行为非常复杂. 本文主要从动力学与控制的角度对过去半个世纪有关转子与定子碰摩的研究成果进行归纳和总结, 其目的在于帮助读者尽可能全面系统地了解该问题的研究现状, 提炼尚待解决的问题, 以求推动转子与定子碰摩研究的进一步深入, 并为解决实际问题提供帮助. 本文将首先从碰摩局部模型和碰摩系统模型两个方面对已有的转子/定子碰摩系统的建模进行了简单的划分和归类. 其次, 以典型碰摩非线性响应为主线, 分别介绍了有关同频碰摩响应、谐波周期碰摩响应、准周期局部碰摩响应、干摩擦自激反向全周涡动响应、碰摩的全局响应行为以及碰摩响应的分岔与混沌方面的研究成果. 接下来讨论了在主被动抑制碰摩振动方面取得的结果. 最后, 给出结论并提出有待进一步研究的问题.     

转子/定子碰摩响应的全局动力学特性研究

在不考虑自重的转子系统全局碰摩动力响应特性的解析分析基础上,应用数值分析方法,研究了考虑自重的转子系统的全局碰摩动力响应特性。通过大量的数值计算得到了不同参数平面内、不同碰摩响应的稳定区域图。研究表明重力引起的静变形与偏心距之比是决定转子的碰摩响应的变化大小的重要参数,比值越大,转子碰摩响应较不考虑自重的转子碰摩响应的变化越大,会出现多种复杂的响应和共存现象。本研究有助于认清系统参数相互作用对出现不同碰摩响应序列的影响。     

航空发动机整机耦合动力学模型及振动分析

面向航空发动机整机振动, 建立了航空发动机转子-滚动轴承-机匣耦合动力学模型. 该模型具有如下特点: (1)考虑转子、滚动轴承及机匣之间的耦合作用; (2)考虑了实际航空发动机的弹性支承及挤压油膜阻尼效应; (3)将转子考虑为等截面自由欧拉梁模型, 运用模态截断法进行分析; (4)考虑了滚动轴承间隙、非线性赫兹接触力以及变柔性VC(Varyingcompliance)振动; (5)考虑了转子与机匣之间的碰摩故障. 运用数值积分方法研究了航空发动机的整机振动规律, 包括: 滚动轴承VC振动分析、弹性支承刚度对耦合系统临界转速的影响、转轴模态截断阶数NM对系统响应的影响分析、挤压油膜阻尼器参数对系统响应的影响分析、突加不平衡的瞬态响应分析以及转静碰摩故障特性分析等.      

非线性碰摩力对碰摩转子分叉与混沌行为的影响

研究了具有非线性碰摩力的转子局部碰摩的分叉与混沌运动,利用计算机仿真对某发动机转子的碰摩故障进行了数值模拟,讨论了转子系统参数的变化对转子混池运动状态的影响,并与碰摩实验结果进行了比较,发现了具有非线性碰摩力的转子局部碰摩转子系统的各种多周期运动和混沌运动及其演变过程。     

Determination of the global responses characteristics of a piecewise smooth dynamical system with contact

In this paper the global response characteristics of a piecewise smooth dynamical system with contact, which is specifically used to describe the rotor/stator rubbing systems, is studied analytically. A method to derive the global response characteristics of the model is proposed by studying each piece of the equations corresponding to different phases of the rotor motion, i.e., the phase without rubbing, the phase with rubbing and the phase of self-excited backward whirl. After solving the typical responses in each phase and deriving the corresponding existence boundaries in the parameter space, an overall picture of the global response characteristics of the model is obtained. As is shown, five types of the coexistences of the different rotor responses and deep insights into the interactive effect of parameters on the dynamic behavior of the model are gained.     

异步进动转子与限位器碰摩试验

利用限位器来限制储能飞轮实验转子的大幅度低频异步进动,设计了转子与限位器碰摩试验装置,研究转子的碰摩振动。分析了转子内表面碰摩力对转子运动的影响。转子与内置式限位器发生稳定的局部碰摩时,转子低频进动幅值不再增加,转子自转速度保持不变。碰摩转子的强迫振动在时域及频域都表现出了复杂性,碰摩冲击作为宽频激励,能够激励出转子-支承系统的第二模态正向进动。     

考虑定子质量和碰摩面刚度的转子/定子系统碰摩响应的全局动力学特性研究

对考虑定子质量和碰撞面刚度的四自由度转子/定子模型的全局响应特性进行了研究。首先,通过解析方法确定了无碰摩响应的边界,然后,求解了同频全周碰摩解并进行了稳定性分析得到了同频全周碰摩响应的区域。在此基础上,利用非线性动力学分析的数值方法,确定了准周期局部碰摩与反向涡动失稳的边界,由此得出了参数平面内的不同碰摩响应的稳定区域图。进而研究了定子与转子质量比和碰撞面刚度对碰摩全局响应特性的影响,得到了不同碰摩响应共存及随系统参数变化的典型全局响应分岔图。     

Dynamic characteristics of a rub-impact rotor-bearing system for hydraulic generating set under unbalanced magnetic pull

Electromagnetic and mechanical forces are main reasons resulting in vibrations in hydraulic generating set. The non-symmetric air-gap between the rotor and stator creates an attraction force called unbalanced magnetic pull (UMP). The UMP can produce large oscillations which will be dangerous to the machines. In this paper, the nonlinear dynamic characteristics of a rotor-bearing system with rub-impact for hydraulic generating set under the UMP are studied. The rubbing model is established based on the classic impact theory. Through the numerical calculation, the excitation current, mass eccentricity, stiffness of shaft and radial stiffness of stator are used as control parameters to investigate their effect on the system, by means of bifurcation diagrams, Poincaré maps, trajectories and frequency spectrums. Various nonlinear phenomena including periodic, quasi-periodic and chaotic motions are observed. The results reveal that the UMP has significant influence in the response of the rotor system that the continuous increase in the excitation current induces the alternation of quasi-periodic and chaotic motions, the co-occurrence of oil whip and rub in a wide excitation range aggravates the vibration and leads to the instability of the system. In addition, the large eccentricity and radial stiffness of stator, as well as the small stiffness of shaft may lead to the occurrence of full annular rubbing while increasing the stiffness of the shaft can play an important role of suppressing the chaotic motion, reducing the vibration and improving stability of the system.     

油膜支承转子系统动静件碰摩特征分析

以支承在油膜轴承上的Jeffcott转子为对象，分析了油膜力对碰摩转子动力学行为的影响。通过与刚支情形对比，发现油膜力是耦合作用于碰摩转子系统，有时能够抑制振动，有时却加剧振动。因此实际转子碰摩故障诊断过程中，必须在充分考虑支承情况的基础上建立合理的非线性动力学模型，才能为实际转子系统的碰摩故障分析提供必要的理论依据。     

Contact analysis of a flexible bladed-rotor

This paper presents a model of fully flexible bladed rotor developed in the rotating frame. An energetic method is used to obtain the matrix equations of the dynamic behaviour of the system. The gyroscopic effects as well as the spin softening effects and the centrifugal stiffening effects, taken into account through a pre-stressed potential, are included in the model. In the rotating frame, the eigenvalues' imaginary parts of the latter matrix equation give the Campbell diagram of the system and its stability can be analysed through its associated eigenvalues' real parts. The turbo machine casing is also modelled by an elastic ring in the rotating frame through an energetic method. Thus, in some rotational speed ranges the contact problem between the rotor and the stator can be treated as a static problem since both structures are stationary to each other. Prior to the study of the complete problem of contact between the flexible blades of the rotor and the flexible casing, a simple model of an elastic ring having only one mode shape, excited by rotating loads is developed in the rotating frame too, in order to underline divergence instabilities and mode couplings. Then, the complete problem of frictionless sliding contact between the blades and the casing, without rubbing, is studied. The stable balanced static contact configurations of the structure are found as function of the rotational speed of the rotor. Finally, the results are compared to these of the simple model of rotating spring-masses on an elastic ring, showing good adequacy. The present model of rotor appears thus particularly adapted to the study of blades-casing contacts and highlighted an unstable phenomenon near the stator critical speed even in case of frictionless sliding.     

Bifurcation and chaos for porous squeeze film damper mounted rotor–bearing system lubricated with micropolar fluid

This study presents a dynamic analysis of a flexible rotor supported by two porous squeeze micropolar fluid-film journal bearings with nonlinear suspension. The dynamics of the rotor center and bearing center are studied. The analysis of the rotor–bearing system is investigated under the assumptions of non-Newtonian fluid and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various nondimensional speed ratios. The dynamic equations are solved using the Runge–Kutta method. The methods of analysis employed in this study are inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincaré maps, and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the dynamic system varies with the nondimensional speed ratios, the nondimensional parameter, and permeability. The modeling results obtained by using the method proposed in this paper can be employed to predict the dynamics of the rotor–bearing system, and the undesirable behavior of the rotor and bearing centers can be avoided.     

The numerical modeling of rotor–stator rubbing in rotating machinery: a comprehensive review

Nonlinear Dynamics - The rotor–stator rubbing in rotating machinery generated as a consequence of rotor imbalance, shaft misalignment, and casing deformation is a potential threat to the...     

Non-linear dynamic of rotor–stator system with non-linear bearing clearanceDynamique non-linéaire d'un ensemble rotor–stator comportant un roulement non-linéaire avec jeu

The study deals with a rotor–stator contact inducing vibration in rotating machinery. A numerical rotor–stator system, including a non-linear bearing with Hertz contact and clearance is considered. To determine the non-linear responses of this system, non-linear dynamic equations can be integrated numerically. However, this procedure is both time consuming and costly to perform. The aim of this Note is to apply the Alternate Frequency/Time Method and the ‘path following continuation’ in order to obtain the non-linear responses to this problem. Then the orbits of rotor and stator responses at various speeds are investigated. To cite this article: J.-J. Sinou, F. Thouverez, C. R. Mecanique 332 (2004).     

Modeling the rubbing contact in honeycomb seals

Metallic honeycomb labyrinth seals are commonly used as sealing systems in gas turbine engines. Because of their capability to withstand high thermo-mechanical loads and oxidation, polycrystalline nickel-based superalloys, such as Hastelloy X and Haynes 214, are used as sealing material. In addition, these materials must exhibit a tolerance against rubbing between the rotating part and the stationary seal component. The tolerance of the sealing material against rubbing preserves the integrity of the rotating part. In this article, the rubbing behavior at the rotor–stator interface is considered numerically. A simulation model is incorporated into the commercial finite element code ABAQUS/explicit and is utilized to simulate a simplified rubbing process. A user-defined interaction routine between the contact surfaces accounts for the thermal and mechanical interfacial behavior. Furthermore, an elasto-plastic constitutive material law captures the extreme temperature conditions and the damage behavior of the alloys. To validate the model, representative quantities of the rubbing process are determined and compared with experimental data from the literature. The simulation results correctly reproduce the observations made on a test rig with a reference stainless steel material (AISI 304). A parametric study using the nickel-based superalloys reveals a clear dependency of the rubbing behavior on the sliding and incursion velocity. Compared to each other, the two superalloys studied exhibit a different rubbing behavior.     

Impact phenomena of rotor-casing dynamical systems

Rubbing and impacting between a rotor and adjacent motion-constraining structures is a serious malfunction in rotating machinery. A shaver rotor-casing system with clearance and mass imbalance is modelled with two second-order ordinary differential equations and inelastic impact conditions. The dynamics is investigated analytically, as well as by numerical simulation. A Lyapunov exponent technique is developed to characterize the topologically different behavior as the parameters are varied. The dry friction coefficient and the eccentricity of the rotor imbalance were chosen to be the two variable parameters, the effect of which on the system dynamics is illustrated through phase plots, bifurcation diagrams, as well as Poincaré maps. The results demonstrate the existence of both rubbing and impacting behavior. Depending on values of the parameters, rubbing motion in both the clockwise and counter-clockwise directions may occur. Within the impact regime, the impact behavior could be periodic, quasi-periodic or chaotic, as confirmed by the calculation of Lyapunov exponents.     

密封环挠性安装形式对干气密封动态追随性的影响

基于气体润滑理论,并通过小扰动法建立了螺旋槽干气密封微扰膜压控制方程,在高速高压条件下获得了气膜动态特性系数;基于动力学相关知识,在考虑转轴轴向振动的情况下,利用气膜轴向动态刚度和阻尼系数分别求解了静环挠性安装、动环挠性安装和两环均挠性安装的干气密封挠性环运动方程.在不同轴向激励振幅、激励频率、挠性环质量、弹簧刚度和辅助密封圈阻尼下分别研究了三种典型结构干气密封动态追随性并进行了对比分析.结果表明:当轴向激励频率较高或挠性环质量较大时,静环挠性安装干气密封在刚受到外界激励时膜厚突变相对严重,动态追随性较差;在轴向激励频率较低且挠性环质量较小时,静环挠性安装干气密封相比动环挠性安装干气密封表现出更好的动态追随性;在三种密封环挠性安装形式中,两环均挠性安装干气密封动态追随性最好,且具有绝对优势.     

A numerical scheme for solving a periodically forced Reynolds equation

A modified Reynolds equation is used to model the air‐film in a high‐speed squeeze‐film bearing. The axial position of the bearing stator is prescribed as a finite amplitude periodic oscillation. A numerical approach is considered for solving the uncoupled and coupled periodic problems associated with this model. The uncoupled problem requires the computation of the squeeze‐film dynamics when the rotor is held at a fixed axial position and the coupled problem incorporates the additional air–rotor interaction since the rotor position is unknown and modelled as a spring‐mass‐damper system. The details of a Fourier spectral collocation scheme are provided for the reduction of the modified Reynolds equation to a system of non‐linear, first‐order ordinary differential equations in space. Using the Matlab boundary value problem solver bvp4c this system of equations is solved to give the periodic pressure distributions and rotor heights. The high degree of accuracy in the spectral collocation scheme is demonstrated through comparison with an appropriate analytical solution. Further analysis indicates that the direct periodic solver is at least 10 times faster than the equivalent Crank–Nicholson finite‐difference scheme. For changing values of a selected physical parameter the method of arc‐length continuation is employed to track branches of solutions computed using the spectral collocation scheme. A selection of results is presented to demonstrate the range of accessible solutions and the robust nature of the numerical scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Study on catastrophic mechanism for rotor drop transient vibration following magnetic bearing failure

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Nonlinear analysis of a rub-impact rotor-bearing system with initial permanent rotor bow

A general model of a rub-impact rotor-bearing system with initial permanent bow is set up and the corresponding governing motion equation is given. The nonlinear oil-film forces from the journal bearing are obtained under the short bearing theory. The rubbing model is assumed to consist of the radial elastic impact and the tangential Coulomb type of friction. Through numerical calculation, rotating speeds, initial permanent bow lengths and phase angles between the mass eccentricity direction and the rotor permanent bow direction are used as control parameters to investigate their effect on the rub-impact rotor-bearing system with the help of bifurcation diagrams, Lyapunov exponents, Poincaré maps, frequency spectrums and orbit maps. Complicated motions, such as periodic, quasi-periodic even chaotic vibrations, are observed. Under the influence of the initial permanent bow, different routes to chaos are found and the speed when the rub happens is changed greatly. Corresponding results can be used to diagnose the rub-impact fault in this kind of rotor systems and this study may contribute to a further understanding of the nonlinear dynamics of such a rub-impact rotor-bearing system with initial permanent bow.     

Dynamic response of a rub-impact rotor system under axial thrust

A model of a rigid rotor system under axial thrust with rotor-to-stator is developed based on the classic impact theory and is analyzed by the Lagrangian dynamics. The rubbing condition is modeled using the elastic impact-contact idealization, which consists of normal and tangential forces at the rotor-to-stator contact point. Mass eccentricity and rotating speed are used as control parameters to simulate the response of rotor system. The motions of periodic, quasi-periodic and chaotic are found in the rotor system response. Mass eccentricity plays an important role in creating chaotic phenomena.