弹性转子-滑动轴承系统稳定性分析

对一人考虑不平衡力和非线性油膜力的弹性转子 -轴承系统 ,用数值方法研究其稳定性和油膜失稳运动 (自激振动 )特性 ;推导出转子受冲击的运动模型 ,并分析了冲击对系统稳定性的影响规律。     

碰摩裂纹转子轴承系统的周期运动稳定性及实验研究

根据碰摩裂纹耦合故障转子轴承系统的非线性动力学方程，利用求解非线性非自治系统周期解的延拓打靶法，研究了系统周期运动的稳定性。研究发现，小偏心量下系统周期运动发生Hopf分岔，大偏心量下系统周期运动发生倍周期分岔，偏心量的加大使周期解的稳定性明显降低；系统碰摩间隙变小，碰摩影响了油膜涡动的形成，使失稳转速有所提高；裂纹深度的加大降低了系统周期运动的稳定性。本文的研究为转子轴承系统的安全稳定运行提供了理论参考。     

Dynamics of a balanced rotor under the action of an elastic force with a hysteresis characteristic

Recently, the constructions of rotors rotating on passive-type magnetic bearings designed with the use of high-temperature superconductors have been developed [1, 2]. One still open problem in the stability analysis of rotors on such bearings is the problem on the influence of the bearing rigidity characteristic on the system dynamics. The stability of a steady-state motion of a rotor with arbitrary eccentricity is studied in [3]. The present paper deals with the dynamics of a steady-state motion of a balanced rotor rotated by an infinite-power motor; in this case, the elastic force acting on the rotor has a hysteresis characteristic [4]. The equations of motion are described by a nonautonomous system of differential equations which is reduced with prescribed accuracy to an autonomous system, and the latter is then analyzed [5].     

充液或部分充液转子的动力稳定性

本文讨论了具有内外阻尼的高速充液转子的动力稳定性。首先通过对旋转流体的平面流场的求解，导出充液转子作简谐运动时流体对转子的动压力，由此导出转子的运动方程；讨论了充液转子的动力稳定性，给出了稳定性解析判据和稳定性边界。结果表明，存在转速门槛值，低于该转速时，充液转子可存在稳定区；当高于该转速时，系统永远失稳，这一结论复盖了已有文献的结果。     

碰摩转子系统的非光滑分析

通过建立转子系统碰摩的Ｐｏｉｎｃａｒｅ映射,将对非光滑碰摩系统的研究转化为对Ｐｏｉｎｃａｒｅ映射的分析,文中主要对转子碰摩当中一类特殊的运动形式－单点碰摩下的擦边现象者了详细研究。从序列的极限理论出发分析了该映射的周期不动点的稳定性及其吸引域,得到了转子系统在接近擦边运动时解随系统参数变化的分岔情形。     

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。     

Effects of flexible support stiffness on the nonlinear dynamic characteristics and stability of a turbopump rotor system

Using a flexible support is an efficient approach to solving the subsynchronous problems in a turbopump. In this paper, nonlinear rotordynamic analysis of a liquid fuel turbopump with a flexible support is presented using a dynamic modeling including two key destabilizing factors, nonlinear hydrodynamic forces induced by seals and internal rotor damping. The methodology of the partitioned direct integration method (PDIM) is described for reducing the computational efforts efficiently. Combining the PDIM and the shooting method, a nonlinear stability analysis of the rotor system is performed effectively. The numerical results, which are in good agreement with test data, indicate that the effects of flexible support stiffness k on the dynamic characteristics and stability of the rotor system are significant. The first critical speed of the rotor system rises as a nonlinear function of k markedly. The second critical speed varies slightly and approximates a linear variation as k increases. The onset speed of instability of the rotor system rises initially and then reduces as k increases. The effect of seal nonlinearities at low k is contrary to that at high k and the effect of seal length on the system stability is more significant than that of seal radius. The results explain the nature of the subsynchronous motion of a turbopump rotor system with flexible support and can be used in the design and operation of a liquid fuel turbopump rotor system to eliminate its rotordynamic problem.     

万有引力场中陀螺体的混沌运动

研究万有引力场中沿圆轨道运行的非对称陀螺体的姿态运动,引入Ｄｅｐｒｉｔ正则变量建立系统的Ｈａｍｉｌｔｏｎ结构,利用Ｍｅｌｎｉｋｏｖ方法证明在万有引力短作用的昆体产生混沌运动的可能性。对Ｐｏｉｎｃａｒｅ截面的数值计算表明提高陀螺体的转子转速可对混沌起抑制作用。     

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.     

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.     

Effect of elasticity on the dynamics of a superconducting rotor rotating in a magnetic field

A spherical shape of the outer surface of rotors of some types of noncontact gyroscopes gives rise to conditions, where the force field ensures the stability of the center of mass relative to the base and has an insignificant effect on the angular motion of the rotor. However, there are some effects (for instance, the Barnett—London effect), which lead to emergence of moments of mechanical forces even for spherical bodies. The effect of rotor elasticity on the motion of a superconducting deformable spherical solid body in a magnetic field is studies. It is shown that the moment of mechanical forces acting on the body in the magnetic field is proportional in the first approximation to the angular velocity squared. The effect of this moment on the dynamics of angular motion of the rotor is studied.     

Bifurcation analysis for a modified Jeffcott rotor with bearing clearances

A HB (Harmonic Balance)/AFT (Alternating Frequency/Time) technique is developed to obtain synchronous and subsynchronous whirling motions of a horizontal Jeffcott rotor with bearing clearances. The method utilizes an explicit Jacobian form for the iterative process which guarantees convergence at all parameter values. The method is shown to constitute a robust and accurate numerical scheme for the analysis of two dimensional nonlinear rotor problems. The stability analysis of the steady-state motions is obtained using perturbed equations about the periodic motions. The Floquet multipliers of the associated Monodromy matrix are determined using a new discrete HB/AFT method. Flip bifurcation boundaries were obtained which facilitated detection of possible rotor chaotic (irregular) motion as parameters of the system are changed. Quasi-periodic motion is also shown to occur as a result of a secondary Hopf bifurcation due to increase of the destabilizing cross-coupling stiffness coefficients in the rotor model.     

Stability analysis of the whirl motion of a breathing cracked rotor with asymmetric rotational damping

The stability of the whirl motion of a breathing cracked rotor with the distinction of stationary damping and the asymmetric rotational damping is studied. By Lagrange’s principal, the motion equations are formed in rotational frame such that the multi-asymmetric system, i.e., asymmetric rotational damping and asymmetric time-periodic varying stiffness, is simplified to be a system with anisotropic damping and anisotropic time-periodical varying stiffness in rotational operation. Based on the multiple scales solution of the simplified whirling equation in moving frame, root locus method for stability analysis is proposed. Different from the former stability estimation method, the corresponding Campbell diagram, decay rate plot, and root locus plot of the fifth-order approach are derived to prove the effects of both crack depth and damping effects. The numerical results of the instabilizing effects of the crack depth are well agreeing with the previous studies. In addition, the destabilizing influence of the rotational damping on the breathing cracked rotor is presented for the first time.     

非稳态非线性油膜力作用下柔性轴裂纹转子的动力特性分析

分析了在动载轴承非稳态非线性油膜力作用下，具有横向裂纹柔性轴Jeffcott转子在非线性涡动影响下的动力特性。通过数值计算表明，在油膜失稳转速前，随着裂纹轴刚度变化比的增大，系统在低转速区域内具有丰富的非线性动力行为，出现倍周期分叉及混沌现象，涡动振幅随转速升高而减小，直到非稳态非线性油膜失稳，在无裂纹转子油膜临界失稳点处发现了类Hopf分叉现象，系统运动由平衡变为拟周期运动；裂纹转子在油膜临界失稳时的系统运动亦为拟周期运动，裂纹转子轴刚度变化对油膜失稳点及油膜失稳之后转子的运动影响不大，转子系统作拟周期运动。     

非线性呼吸行为对带横向裂纹Jeffcott转子稳定性的影响

在分析现有力学模型局限性的基础上,考虑转子在失稳转速附近复杂的涡动状态,构建了不依赖于重力占优假设的含横向裂纹的Jeffcott转子的通用运动方程和一种拟合的裂纹呼吸模型。根据Floquet稳定性理论,用打靶法分析了该裂纹转子模型运动的稳定性。结果表明,刚度相对变化量、系统阻尼、裂纹相位角等系统参数对模型的运动稳定性都有较大影响,特别是裂纹相位角对稳定性的影响很复杂;在临界转速附近,裂纹的非线性呼吸行为可以提高转子的稳定性,且改变了失稳发散的行为;在亚临界转速附近,裂纹的非线性呼吸行为会降低转子的稳定性,使周期运动发生结构失稳。     

非线性轴承转子系统稳定性准则的研究

目前对于非线性轴承转子系统，仍普遍采用其线性化系统的对数衰减率作为系统的稳定性判据，这造成了理论和实验结果相差较大。本文对［１］中提出的ＰＣＭ法作了改进，通过对无限长滑动轴承支承对称刚性单盘转子系统的非线性稳定性规律进行的分析，揭示了上述现象的非线性本质，为建立更适用于非线性轴承转子系统的稳定性准则提供参考。     

具有封严蓖齿转子系统的动力稳定性分析

封严蓖齿的气弹力对转子系统的稳定性起重要作用，本文建立了具有封严蓖齿的转子系统动力稳定性的分析方法，该方法利用传递矩阵法建立系统的主导方程，将封严蓖齿的气弹力以等效刚度及等效阻尼系数的方式引入转子系统的主导方程，用数值积分法解主导方程，求得系统的动力特性，根据扰动解判断系统的稳定性。本文所建立的分析软件，也可计算转子系统的不平衡响应、临界转速、突加不平衡响应等。文中对一模型转子进行了算例分析。     

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.     

On the dynamics of the fluid balancer

This paper is concerned with the dynamics of a so-called fluid balancer; a hula hoop ring-like structure containing a small amount of liquid which, during rotation, is spun out to form a thin liquid layer on the outermost inner surface of the ring. The liquid is able to counteract unbalanced mass in an elastically mounted rotor. The paper derives the equations of motion for the coupled fluid–structure system, with the fluid equations based on shallow water theory. An approximate analytical solution is obtained via the method of multiple scales. For a rotor with an unbalance mass, and without fluid, it is well known that the unbalance mass is in the direction of the rotor deflection at sub-critical rotation speeds, and opposite to the direction of the rotor deflection at super-critical rotation speeds (when seen from a rotating coordinate system, attached to the rotor). The perturbation analysis of the problem involving fluid shows that the mass center of the fluid layer is in the direction of the rotor deflection for any rotation speed. In this way a surface wave on the fluid layer can counterbalance an unbalanced mass.     

Equations of Electrical Machines with a Rotating Permanent Magnet Playing the Role of the Stator and Their Nonlocal Analysis

A complete mathematical model is developed for the motion of a current loop powered from a constant voltage source and placed in the field of a permanent magnet rotating with a constant angular velocity. Local analysis of this model shows that it is unstable in the absence of external load, which contradicts the practice of motor operation. Therefore, the motor rotor model considered is incorrect although it is frequently used. The detected contradiction is eliminated by introducing an additional loop, which is orthogonal to the initial one and has the same parameters but is shortcircuited. The complete mathematical model of such a system is unstable in the absence of external load. For the case of an induction motor, the conditions of dichotomy, global asymptotic stability, and instability are formulated.