Vibration characteristics of a hydraulic generator unit rotor system with parallel misalignment and rub-impact

The object of this research aims at the hydraulic generator unit rotor system. According to fault problems of the generator rotor local rubbing caused by the parallel misalignment and mass eccentricity, a dynamic model for the rotor system coupled with misalignment and rub-impact is established. The dynamic behaviors of this system are investigated using numerical integral method, as the parallel misalignment, mass eccentricity and bearing stiffness vary. The nonlinear dynamic responses of the generator rotor and turbine rotor with coupling faults are analyzed by means of bifurcation diagrams, Poincaré maps, axis orbits, time histories and amplitude spectrum diagrams. Various nonlinear phenomena in the system, such as periodic, three-periodic and quasi-periodic motions, are studied with the change of the parallel misalignment. The results reveal that vibration characteristics of the rotor system with coupling faults are extremely complex and there are some low frequencies with large amplitude in the 0.3–0.4× components. As the increase in mass eccentricity, the interval of nonperiodic motions will be continuously moved forward. It suggests that the reduction in mass eccentricity or increase in bearing stiffness could preclude nonlinear vibration. These might provide some important theory references for safety operating and exact identification of the faults in rotating machinery.     

Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system

This research studies the effects of axial preload on nonlinear dynamic characteristics of a flexible rotor supported by angular contact ball bearings. A dynamic model of ball bearings is improved for modeling a five-degree-of-freedom rotor bearing system. The predicted results are in good agreement with prior experimental data, thus validating the proposed model. With or without considering unbalanced forces, the Floquet theory is employed to investigate the bifurcation and stability of system periodic solution. With the aid of Poincarè maps and frequency response, the unstable motion of system is analyzed in detail. Results show that the effects of axial preload applied to ball bearings on system dynamic characteristics are significant. The unstable periodic solution of a balanced rotor bearing system can be avoided when the applied axial preload is sufficient. The bifurcation margins of an unbalanced rotor bearing system enhance markedly as the axial preload increases and relates to system resonance speed.     

Dynamic characteristics of self-acting gas bearing–flexible rotor coupling system based on the forecasting orbit method

This paper studies the nonlinear dynamic characteristics of a flexible rotor supported by self-acting gas bearings theoretically. The multiple degree freedom model of flexible rotor is established by the finite element method and analyzed coupled with the transient gas lubricated Reynolds equation by employing the forecasting orbit method. The Reynolds equation is solved by the alternating direction implicit method and the dynamic response of the rotor is calculated by the Newmark integral method. To settle the problem that the two kinds of transient solving processes (transient Reynolds equation for bearing and transient equation of motion for rotor) cannot be solved simultaneously, which arises from the fact that they need each other??s results as their initial values, the multi-field coupling algorithm based on the forecasting method is proposed and applied in this paper. By employing the numerical method, the rotor trajectory diagram, phase diagram, frequency spectrum, power spectrum, bifurcation diagram, and vibration mode diagram were obtained. It is to note that the dynamic characteristics of self-acting gas bearing?Crotor system and whirling instability of the system could be depicted successfully. This would establish the foundation for contributing to a further understanding of the gas bearing?Cflexible rotor system.     

Bifurcation analysis of reduced rotor model based on nonlinear transient POD method

The singularity theory is applied to study the bifurcation behaviors of a reduced rotor model obtained by nonlinear transient POD method in this paper. A six degrees of freedom (DOFs) rotor model with cubically nonlinear stiffness supporting at both ends is established by the Newton's second law. The nonlinear transient POD method is used to reduce a six-DOFs model to a one-DOF one. The reduced model reserves the dynamical characteristics and occupies most POM energy of the original one. The singularity of the reduced system is analyzed, which replaces the original system. The bifurcation equation of the reduced model indicates that it is a high co-dimension bifurcation problem with co-dimension 6, and the universal unfolding (UN) is provided. The transient sets of six unfolding parameters, the bifurcation diagrams between the bifurcation parameter and the state variable are plotted. The results obtained in this paper present a new kind of method to study the UN theory of multi-DOFs rotor system.     

Combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling

A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.     

Investigation on dynamic characteristics of a rod fastening rotor-bearing coupling system with fixed-point rubbing

The aim of this paper is to gain insight into the nonlinear vibration feature of a dynamic model of a gas turbine. First, a rod fastening rotor-bearing coupling model with fixed-point rubbing is proposed, where the fractal theory and the finite element method are utilized. For contact analysis, a novel contact force model is introduced in this paper. Meanwhile, the Coulomb model is adopted to expound the friction characteristics. Second, the governing equations of motion of the rotor system are numerically solved, and the nonlinear dynamic characteristics are analyzed in terms of the bifurcation diagram, Poincaré map, and time history. Third, the potential effects provided by contact degree of joint interface, distribution position, and amount of contact layer are discussed in detail. Finally, the contrast analysis between the integral rotor and the rod fastening rotor is conducted under the condition of fixed-point rubbing.

     

The effects of unbalance on oil whirl

The nonlinear behavior of an unbalanced rotor supported in a fluid film bearing is analyzed. A simplified two dimensional model is adopted which uses the long-bearing approximation with a -film to account for cavitation. This model has been thoroughly studied by Myers [1] in the balanced case, where it is shown that the whirl instability is the result of a Hopf bifurcation. The implications of imbalance are studied in this paper. This leads to the study of a periodically perturbed Hopf bifurcation. It is shown that the dynamics in this situation can, especially under certain nonlinear resonance conditions, have an extremely complicated dependence on the system parameters and the rotor speed. Complete bifurcation diagrams are presented for a particular rotor model which demonstrate this dependence.     

弹性支承滑动轴承不平衡转子系统非线性动力稳定性和分岔的研究

研究弹性支承滑动轴承不平衡转子系统的稳定性及分岔特性。建立了弹性支承-滑动轴承-转子非线性动力系统的力学模型，在油膜力非线性的情况下，应用数值模拟，采用打靶法计算了刚性转子系统的周期解，并与龙格-库塔法计算的结果进行了对比，依据Floquet理论，分析了周期解的稳定性，再结合龙格-库塔法、Poineare映射法作出了系统运动分岔图。最后，讨论了轴的柔性对转子系统运动稳定性的影响。     

Nonlinear response and bifurcation analysis of a Duffing type rotor model under sine maneuver load

This paper focuses on the nonlinear dynamic and bifurcation characteristics of an aircraft rotor system affected by the maneuvering flight of the aircraft. The equations of motion of the system are formulated with the consideration of the nonlinear supports of Duffing type and the sine maneuver load of a proposed maneuvering flight model. By utilizing the multiple scales method to solve the motion equations analytically, the bifurcation equations are obtained. Accordingly, the response and the bifurcation characteristics of the system are analyzed respectively. Basically, the increase of the maneuver load may increase the formant frequency as well as the primary resonance frequencies. Through numerical simulations, four different types of response characteristics of the system during the maneuvering flight are found, which are compared with the theoretical results, and it shows good qualitative agreements between them. Furthermore, the maneuver load can make an apparent effect on the bifurcation. The results in this paper will provide a better understanding for the effect of aircraft maneuvering flight on the dynamics and bifurcations of the rotor system.     

Bifurcation on synchronous full annular rub of rigid-rotor elastic-support system

An aero-engine rotor system is simplified as an unsymmetrical-rigid-rotor with nonlinear-elastic-support based on its characteristics. Governing equations of the rubbing system, obtained from the Lagrange equation, are solved by the averaging method to find the bifurcation equations. Then, according to the two-dimensional constraint bifurcation theory, transition sets and bifurcation diagrams of the system with and without rubbing are given to study the influence of system eccentricity and damping on the bifurcation behaviors, respectively. Finally, according to the Lyapunov stability theory, the stability region of the steady-state rubbing solution, the boundary of static bifurcation, and the Hopf bifurcation are determined to discuss the influence of system parameters on the evolution of system motion. The results may provide some references for the designer in aero rotor systems.     

高速涡轮增压器轴承-转子系统不平衡响应及稳定性分析

汽车涡轮增压器广泛采用浮环轴承支承的小型轻质转子系统,以实现100 000~300 000 r/min的工作转速,提高发动机功率和动力性能,并降低燃油消耗和排放. 在此超高速工况下,动压油膜的强非线性作用和转子固有的不平衡效应使该系统呈现出复杂的动力学现象,其中油膜涡动、振荡、跳跃、倍周期分岔和混沌等非线性动力学行为对增压器的健康运转意义重大,因而备受关注. 本文作者从摩擦学动力学耦合的角度出发,基于流体动压轴承润滑理论和有限差分法计算非稳态油膜压力,结合达朗贝尔原理和传递矩阵法建立了转子离散化动力学方程,提出了一种由双油膜浮环支承的涡轮增压器转子系统动力学模型,并从转子轨迹、轴承偏心率、频谱响应、庞加莱映射和分岔特性等方面比较分析,描述了该非线性轴承-转子系统的不平衡效应及油膜失稳特征. 结果表明:转子一般在相对低速下作稳定的单周期不平衡振动,在高转速下其被油膜失稳引起的次同步涡动所抑制,但不平衡量的增加可阻碍转子以拟周期运动通向混沌运动的路径;适当不平衡补偿下,由于内、外油膜间交互的非线性刚度和阻尼作用,在油膜失稳区间之间的中高速区会出现适合增压器健康运转的稳定区间.      

Nonlinear dynamic behaviors of a rotor-labyrinth seal system

The nonlinear model of rotor-labyrinth seal system is established using Muszynska’s nonlinear seal forces. We deal with dynamic behaviors of the unbalanced rotor-seal system with sliding bearing based on the adopted model and Newmark integration method. The influence of the labyrinth seal one the nonlinear characteristics of the rotor system is analyzed by the bifurcation diagrams and Poincare’ maps. Various phenomena in the rotor-seal system, such as periodic motion, double-periodic motion, quasi-periodic motion and Hopf bifurcation are investigated and the stability is judged by Floquet theory and bifurcation theorem. The influence of parameters on the critical instability speed of the rotor-seal system is also included.     

迷宫密封转子系统非线性动力稳定性的研究

研究迷宫密封对转子系统动力稳定性的影响，迷宫密封的气动力采用Muszynska非线性力模型，计算了单盘Jeffcott转子非线性动力学特性。对Jacobi矩阵的分析表明，在密封力的影响下，转子达到一定转速后开始失稳，发生Hopf分岔，进入周期涡动状态，涡动幅度随转速的提高而增大，提高到一定程度，密封和转子发生碰摩，采用Runge-Kutta法数值模拟了转子的轴心轨迹。最后分析了迷宫密封的物理和结构参数对系统运动特性的影响。     

发动机叶片扭转和弯曲变形同步测量新方法

扭转和弯曲变形测量可以确定叶片弯扭变形耦合的特征,为叶片弯扭耦合分析提供可用的试验手段。本文提出了一种发动机叶片扭转和弯曲变形同步测量的新方法,其中,扭转角度测量方法能更加灵活地应用于测量叶片类形状不规则构件的扭转变形,而弯曲变形测量方法解决了叶片变形方向未知且存在弯扭耦合时的叶片变形测量问题,从而可实现对叶片截面扭转和弯曲变形的同步测量。对上述测量方法进行了专门的验证试验,结果表明:与传统方法测量结果相比,扭转角度测量偏差小于1%,挠度测量偏差小于2%,满足工程测量精度要求。     

裂纹转子在支承松动时的振动特性研究

以具有支承松动的Jeffcott裂纹转子为研究对象，分析了支承松动和轴上横向裂纹对转子系统刚度的影响，建立了转子系统振动的微分方程，并用数值方法分析了其振动特性。分析表明，转子在裂纹和支承松动这两种非线性因素的作用下，表现出复杂的非线性行为。     

多维磁浮柔性转子控制系统分岔与控制器设计

讨论了多维悬浮柔性转子控制系统局部及全局分岔问题,首先建立了该复杂系统动力学模型,应用中心流形和求规范形综合方法,得到此系统非半简双零特征值问题的规范形及其普适开折,并进一步讨论了此控制系统的分岔 行为（余维二分岔）及稳定性;给出了为实现稳定控制,控制器参数、转子系统结构参数的相互关系及稳定控制域,即给出分岔 参数条件、分岔曲线、转迁集,最后,给出此柔性转子控制系统的数值仿真结果。     

Interaction between torsional and lateral vibrations in flexible rotor systems with discontinuous friction

In this paper, we analyze the interaction between friction-induced vibrations and self-sustained lateral vibrations caused by a mass-unbalance in an experimental rotor dynamic setup. This study is performed on the level of both numerical and experimental bifurcation analyses. Numerical analyses show that two types of torsional vibrations can appear: friction-induced torsional vibrations and torsional vibrations due to the coupling between torsional and lateral dynamics in the system. Moreover, both the numerical and experimental results show that a higher level of mass-unbalance, which generally increases the lateral vibrations, can have a stabilizing effect on the torsional dynamics, i.e. friction-induced limit cycling can disappear. Both types of analysis provide insight in the fundamental mechanisms causing self-sustained oscillations in rotor systems with flexibility, mass-unbalance and discontinuous friction which support the design of such flexible rotor systems.     

多自由度转子-轴承系统周期运动分岔及稳定性研究

建立考虑诸多因素的转子-轴承系统多自由度模型,将与Newmark结合的打靶法应用到多自由度转子-轴承系统的周期稳定性分析中。着重研究了转子-轴承系统失稳转速随系统偏心量、轴承间隙、润滑油动力粘度以及轴承长径比的变化规律,研究结果表明:提高系统偏心量、减小轴承间隙、增大润滑油动力粘度以及选择适当的轴承长径比均能提高转子-轴承系统的失稳转速;对于不同的参数值,系统表现出不同的分岔规律,系统发生半速涡动时表现为倍周期分岔或拟周期分岔,发生油膜振荡时则表现为拟周期分岔。     

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。     

Response analysis of a dual-disc rotor system with multi-unbalances–multi-fixed-point rubbing faults

Rotor unbalance and rub-impact are major concerns in rotating machinery. In order to study the dynamic characteristics of these machinery faults, a dual-disc rotor system capable of describing the mechanical vibration resulting from multi-unbalances and multi-fixed-point rub-impact faults is formulated using Euler beam element. The Lankarani–Nikravesh model is used to describe the nonlinear impact forces between discs and casing convex points, and the Coulomb model is applied to simulate the frictional characteristics. To predict the moment of rub-impact happening, a linear interpolation method is carried out in the numerical simulation. The coupling equations are numerically solved using a combination of the linear interpolation method and the Runge–Kutta method. Then, the dynamic behaviours of the rotor system are analysed by the bifurcation diagram, whirl orbit, Poincaré map and spectrum plot. The effects of rotating speed, phase difference of unbalances, convex point of casing and initial clearance on the responses are investigated in detail. The numerical results reveal that a variety of motion types are found, such as periodic, multi-periodic and quasi-periodic motions. Moreover, the energy transfer between the compressor disc and the turbine disc occurs in the multi-fixed-point rubbing faults. Compared with the parameters of the turbine disc, those of the compressor disc can affect the motion of the rotor system more significantly. That is, the responses exhibit simple 1T-periodic motion in the wide range of rotating speed under the conditions of sharp convex point and larger initial clearance. These forms of dynamic characteristics can be effectively used to diagnose the fixed-point rub-impact faults.