可倾瓦径向滑动轴承支承的转子系统瞬态响应计算

研究了可倾瓦径向滑动轴承支承的转子系统瞬态响应的计算方法,提出了可倾瓦径向滑动轴承非线性滑膜力计算的数据库方法,将可倾瓦与轴颈的结构和运动参数归结到三个参数中,建立了起可倾瓦的非线性油膜力数据库,通过精确插值到每一运动参数组合下轴承提代的油力和轴瓦上所受的油膜力矩。     

Evolutive and nonlinear vibrations of rotor on aerodynamic bearings

The use of air as a lubricant in aerodynamic bearings is advantageous, particularly in the food industry. Aerodynamic bearings with tilting pads have complicated stiffness and damping properties and need a very detailed theoretical and experimental research. Response curves of rigid rotor supported on aerodynamic bearings are presented for a linear but evolutive mathematical model. Due to non-monotone properties of stiffness and damping matrices at variable revolutions, a new resonance appears. The mathematical model of rotor vibrations in the whole area of bearing clearance is also developed in the consideration of strongly nonlinear properties of aerodynamic bearing.     

Dynamics and stability of turbocharger rotors

The paper discusses the bifurcation and stability behavior of (automotive) turbochargers with full-floating ring bearings. Turbocharger rotors exhibit a highly nonlinear behavior due to the nonlinearities introduced by the floating ring bearings. A flexible multibody model of the rotor/bearing system is presented. Numerical run-up simulations are compared with corresponding test rig measurements. The nonlinear oscillation effects are thoroughly investigated by means of simulated and measured rotor vibrations. The influence of various system parameters on the bifurcation behavior of the rotor/bearing system is analyzed. The article examines rotors supported in full-floating ring bearings with plain circular bearing geometry in the inner and outer oil gap. By recapitulating the well-known oil whirl and oil whip phenomena for single and double oil film bearings, the paper gives an overview on the fundamental dynamic effects occurring in turbocharger systems.     

四瓦可倾瓦径向滑动轴承动力特性的实验研究

采用在线分析方法考察了300MW汽轮发电机可倾瓦轴承的静、动力特性,探讨了载荷、轴颈转速以及动态激振力频率等参数变化对可倾瓦轴承的静、动态性能的影响,比较试验结果与理论计算结果发现,在不同频率激振力作用下,理论计算所得到的可倾瓦轴承动特性参数与试验结果有较大的差异。     

Directional frequency response applied to wear identification in hydrodynamic bearings

This work analyzes the influence of the wear in hydrodynamic bearings in the directional frequency response of a rotating system. Previous works presented a numerical approach to identify the bearing wear parameters using the unbalance response of the system in different rotational speeds. In continuity, this paper analyzes the directional frequency response function (dFRF) to identify the wear model, prompting a feasible application of the method, taken into account that it is not possible to operate the rotor near the critical speeds. The results show that the dFRF matrix is sensitive to the wear parameters and more suitable for bearing wear identification, based on the cross-coupled terms of the dFRF matrix, which present a higher sensitivity to the bearing wear.     

Modeling of hydrodynamic bearing wear in rotor-bearing systems

Hydrodynamic bearings are widely used in industry mainly due to their simplicity, efficiency and low cost. However, these components also represent one of the main critical factors with respect to stability and failure analysis of the system. During the operation of rotating machines, these bearings are subjected to a progressive wear process, which can be accentuated in starts and stops or during the passage through the critical speed of the rotor. To prevent catastrophic failure of the rotating system, it is necessary to precisely detect wear, and purpose, it is necessary to accurately model the wear in this kind of bearing. Within this context, the main objective of this paper is to present a numerical model that characterizes both the hydrodynamic bearing as well as the wear present in its wall, and then, to analyze the influence of the wear on the dynamic response of the rotor-bearing system in frequency domain, taking into account the rising of the backward component due to the increase of the bearing anisotropy.     

Subharmonic resonance of a symmetric ball bearing–rotor system

The performance of a ball bearing–rotor system is often limited by the occurrence of subharmonic resonance with considerable vibration and noise. In order to comprehend the inherent mechanism and the feature of the subharmonic resonance, a symmetrical rotor system supported by ball bearings is studied with numerical analysis and experiment in this paper. A 6DOF rotordynamic model which includes the non-linearity of ball bearings, Hertzian contact forces and bearing internal clearance, and the bending vibration of rotor is presented and an experimental rig is offered for the research of the subharmonic resonance of the ball bearing–rotor system. The dynamic response is investigated with the aid of orbit and amplitude spectrum, and the non-linear system stability is analyzed using the Floquet theory. All of the predicted results coincide well with the experimental data to validate the proposed model. Numerical and experimental results show that the resonance frequency is provoked when the speed is in the vicinity of twice synchroresonance frequency, while the rotor system loses stability through a period-doubling bifurcation and a period-2 motion i.e. subharmonic resonance occurs. It is found that the occurrence of subharmonic resonance is due to the together influence of the non-linear factors, Hertzian contact forces and internal clearance of ball bearings. The effect of unbalance load on subharmonic resonance of the rotor system is minor, which is different from that of the sliding bearing–rotor system. However, the moment of couple has an impact influence on the subharmonic resonances of the ball bearing–rotor system. The numerical and experimental results indicate that the subharmonic resonance caused by ball bearings is a noticeable issue in the optimum design and failure diagnosis of a high-speed rotary machinery.     

Improvement of rotor performance under rubbing conditions through active auxiliary bearings

This paper develops a new concept to enhance the adaptive capability of rotating machinery to the rubbing conditions through active auxiliary bearings. To demonstrate the feasibility of this idea, a model with a Jeffcott rotor and an active auxiliary bearing, which accounts for both the dynamics of the auxiliary bearing and the deformation on the contact surface, is investigated. The dynamics and the stability of the non-linear piecewise-smooth passive rotor/stator (auxiliary bearing) system are first studied. Then, two control approaches are proposed with the aim to reduce the rubbing severity during the rotor/stator rubbing. It is shown that by using an optimal controller, the harmful heavy rubbing between the rotor and the stator can be well stabilized to the mild light rub through the active auxiliary bearing, and the already established rotor-to-stator rubbing can even be released by using PD-controllers.     

High-speed electrospindle running on air bearings: design and experimental verification

In high-speed machining there are a number of applications in which the spindle is supported by air bearings. This type of bearings has very low friction and wear, resulting in virtually unlimited life. If the system is designed correctly the radial stiffness on the tool is comparable to that of ceramic ball bearings. A mathematical model of rotor-air bearing system and experimental work on high-speed spindle for machining applications are presented. The model is numerically solved paying special attention to boundary condition of supply ports. The discharge coefficient c _d is considered on the basis of experimental findings. The influence of clearance and supply port diameter is discussed for radial bearings and axial thrust bearings. The aim is to find an optimum solution representing the compromise between high stiffness, supply flow and stability. The prototype of a high-speed electrospindle running on air bearings is described. The rotor, 50 mm in dia. and weighing 7 kg, is designed for 100 krpm. The spindle is driven by a high frequency asynchronous motor featuring closed loop speed control. Experimental stiffness curves are shown at different supply pressure ratings.     

滑动轴承非线性油膜力的神经网络模型

在已有的滑动轴承非线性油膜力数据库基础上 ,将轴承的位置和速度参数加以综合 ,利用变量状态空间变换将分段的油膜力数据转换成连续的数据空间 ,建立非线性油膜力连续型数据库和相应的网络模型 .以圆轴承 -转子系统为例 ,分别采用有限差分法、数据库法和 BP网络模型计算了轴承系统的非线性油膜力和轴心轨迹 .结果表明 ,网络模型计算结果与基于数值方法的结果较为吻合 ,可以显著地提高轴承系统的计算效率     

Nonlinear Dynamics of a Rigid Unbalanced Rotor in Journal Bearings. Part I: Theoretical Analysis

The dynamic behaviour of a rigid rotor supported on plain journal bearings was studied, focusing particular attention on its nonlinear aspects. Under the hypothesis that the motion of the rotor mass center is plane, the rotor has five Lagrangian co-ordinates which are represented by the co-ordinates of the mass center and the three angular co-ordinates needed to express the rotor's rotation with respect to its center of mass. In such conditions, the system is characterised not only by the nonlinearity of the bearings but also by the nonlinearity due to the trigonometric functions of the three assigned angular co-ordinates. However, if two angular co-ordinates have values that are generally quite small because of the small radial clearances in the bearings, the system is de facto linear in these angular co-ordinates. Moreover, if the third angular co-ordinate is assumed to be cyclic [18], the number of degrees of freedom in the system is reduced to four and nonlinearity depends solely on the presence of the journal bearings, whose reactions were predicted with the -film, short bearing model. After writing the equations of motion in this way and determining a numerical routine for a Runge–Kutta integration the most significant aspects of the dynamics of a symmetrical rotor were studied, in the presence of either pure static or pure couple unbalance and also when both types of unbalance were present. Two categories of rotors, whose motion is prevailingly a cylindrical whirl or a conical whirl, were put under investigation.     

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.     

航空高速涡轮制冷机用气体轴承的研制

本文介绍了高参数航空涡轮制冷机用高速气体轴承研制中的部分工作。在论述工作环境条件苛刻的这类制冷机中用气体轴承替代滚动轴承的必要性、可行性和特殊性的基础上,叙述了研制这类气体轴承时在设计、选材、加工和调试等方面完成的多项特殊试验以及气体轴承改装产品的航空环境适应性试验和应用概况。     

Dynamics of Slider-Crank Mechanisms with Flexible Supports and Non-Ideal Forcing

Transient and steady state dynamic response of a class of slider-crank mechanisms is investigated. Specifically, the class of mechanisms examined involves rigid members but compliant supporting bearings. Moreover, the mechanisms are subjected to non-ideal forcing. Namely, both the driving and the resisting loads are expressed as a function of the angular coordinate describing the crank rotation. First, an appropriate set of equations of motion is derived by applying Lagrange's equations. These equations are strongly nonlinear due to the large rigid body rotation of the crank and the connecting rod, as well as due to the nonlinearities associated with the bearing action and the form of the driving and the resisting loads. Consequently, the dynamics of the resulting dynamical system is examined by solving the equations of motion numerically. More specifically, transient response is captured by direct integration, while determination of complete branches of steady state response is achieved by applying appropriate numerical methodologies. Initially, mechanisms whose crankshaft is supported by bearings with rolling elements and linear stiffness characteristics are examined. Then, numerical results are presented for rolling element bearings with nonlinear stiffness characteristics. Finally, the study is focused on mechanisms supported by hydrodynamic bearings. In all cases, the attention is focused on investigating the influence of the system parameters on its dynamics. Moreover, models with constant crank angular velocity are first analysed, since they provide valuable insight into some aspects of the system dynamics. Eventually, the emphasis is shifted to the general case of non-ideal forcing, originating from the dependence of the driving and the resisting moments on the crankshaft motion.     

Bifurcation of limit cycles in fluid film bearings

Rotors supported by journal bearings may become unstable due to self-excited vibrations when a critical rotor speed is exceeded. Linearised analysis is usually used to determine the stability boundaries. Non-linear bifurcation theory or numerical integration is required to predict stable or unstable periodic oscillations close to the critical speed. In this paper, a dynamic model of a short journal bearing is used to analyse the bifurcation of the steady state equilibrium point of the journal centre. Numerical continuation is applied to determine stable or unstable limit cycles bifurcating from the equilibrium point at the critical speed. Under certain working conditions, limit cycles themselves are shown to disappear beyond a certain rotor speed and to exhibit a fold bifurcation giving birth to unstable limit cycles surrounding the stable supercritical limit cycles. Numerical integration of the system of equations is used to support the results obtained by numerical continuation. Numerical simulation permitted a partial validation of the analytical investigation.     

Analytical bifurcation analysis of a rotor supported by floating ring bearings

Like with other types of fluid bearings, rotors supported by floating ring bearings may become unstable with increasing speed of rotation due to self-excited vibrations. In order to study the effects of the nonlinear bearing forces, within this contribution a perfectly balanced symmetric rotor is considered which is supported by two identical floating ring bearings. Here, the bearing forces are modeled by applying the short bearing theory for both fluid films. A linear stability analysis about the static equilibrium position of the rotor shows that for a critical revolution speed the real part of an eigenvalue pair changes its sign. By means of a center manifold reduction it is shown that this destabilization of the steady state is due to a Hopf-bifurcation. Furthermore, the type of this bifurcation is determined as well as the existence and stability of limit-cycles. Notably it is found that depending on the parameters of the floating ring bearing subcritical as well as supercritical bifurcations may occur. Additionally, the analytical results obtained from the center manifold reduction are compared to numerical results by a continuation method. In conclusion, the influences of bearing design parameters on the stability and on the limit-cycles are discussed.     

Influence of detailed ball-and-socket modelling on tilting pad journal bearings dynamics

Nonlinear Dynamics - The paper focuses on local phenomena modelling in the ball-and-socket pivot of tilting pad journal bearings. It provides an in-depth analysis of the influence of nonlinear...     

Reduction of subsynchronous vibrations in a single-disk rotor using an active magnetic damper

Rotor instabilities in turbomachinery often manifest themselves as a re-excitation of the first rotor critical speed resulting in lateral rotor vibrations at a frequency below the rotor operating frequency. Considerable work exists in the literature involving the analysis of destabilizing mechanisms and passive solutions for reducing subsynchronous vibrations. The authors propose here a novel active control solution utilizing active magnetic bearing (AMB) technology in conjunction with conventional support bearings. The AMB is utilized as an active magnetic damper (AMD) at rotor locations inboard of conventional support bearings. Presented here are initial proof-of-concept experimental results using an AMD for vibration control of subsynchronous rotor vibrations in a high-speed single-disk laboratory rotor. The study shows that subsynchronous vibrations are reducible with an AMD and up to a 93% reduction in the amplitude of subsynchronous vibrations is demonstrated. The study also shows that the AMD can significantly increase synchronous vibration response (up to 218% in one case) by increasing system stiffness and pushing a critical speed closer to an operating speed. The overall results from this work demonstrate that reduction in subsynchronous response is feasible and that full rotor dynamic analysis and design is critical for the successful application of this approach.     

Rotordynamic model for electromagnetic excitation caused by an eccentric and angular rotor core in an induction motor

The paper shows a rotordynamic model for electromagnetic excitation caused by an eccentric and angular rotor core in an induction motor. It is shown that an eccentric rotor core leads to an electromagnetic force and an angular rotor core to an electromagnetic moment, which both force the rotor to vibrate. For these two kinds of magnetic unbalance, a rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness—radial and angular electromagnetic stiffness—the mass moment of inertia and the gyroscopic effect of the rotor. With this model, the absolute orbits of the shaft centre, the shaft journals and the bearing housings can be calculated, as well as the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be computed. In addition to the mathematical derivation of the model, also a numerical example is shown for clarification. The aim of the paper is, on the one hand, to show the mathematical coherences—based on an analytical model—between rotordynamics and the electromagnetics for an induction motor with an eccentric and angular rotor core and, on the other hand, to derive a calculation method for evaluating the vibration sensitivity regarding these two different kinds of magnetic unbalance.     

瓦块弹性对大型水轮发电机组径向可倾瓦轴承润滑性能的影响

用有限元素法和有限差分法建立了可倾瓦轴承瓦块三维弹为形及热效应的计算模型。分析了由瓦面油膜压力引起的三维瓦块弹性变形对采用小包角径向可倾瓦及瓦块支点非均匀密集布置方式下滑动轴承热动力润滑性能的影响。结果表明：在大型低速重载条件下,瓦块三维弹性变形及热效应对小包角瓦块非均匀布置的径向可倾轴承后静态特性和动力特性均有较大影响。