Bifurcation analysis of fan casing under rotating air flow excitation

A fan casing model of cantilever circular thin shell is constructed based on the geometric characteristics of the thin-walled structure of aero-engine fan casing. According to Donnelly＇s shell theory and Hamilton＇s principle, the dynamic equations axe established. The dynamic behaviors are investigated by a multiple-scale method. The effects of casing geometric parameters and motion parameters on the natural frequency of the system are studied. The transition sets and bifurcation diagrams of the system are obtained through a singularity analysis of the bifurcation equation, showing that various modes of the system such as the bifurcation and hysteresis will appear in different parameter regions. In accordance with the multiple relationship of the fan speed and stator vibration frequency, the fan speed interval with the casing vibration sudden jump is calculated. The dynamic reasons of casing cracks are investigated. The possibility of casing cracking hysteresis interval is analyzed. The results show that cracking is more likely to appear in the hysteresis interval. The research of this paper provides a theoretical basis for fan casing design and system parameter optimization.     

TIME DOMAIN PARAMETERS IDENTIFICATION OF FOUNDATION-STRUCTURE INTERACTION SYSTEM

The time domain parameter laenuncauon memoa oi me iounuauon-structure interaction system is presented. On the basis of building the computation mode and the motion equation of the foundation-structure interaction system, the system parameter identification method was established by using the extended Kalman filter （EKF） technique and taking the unknown parameters in the system as the augment state variables. And the time parameter identification process of the foundation-structure interaction system was implemented by using the data of the layer foundation-storehouse interaction system model test on the large vibration platform. The computation result shows that the established parameter identification method can induce good parameter estimation.     

STUDY ON INFLUENCE OF BENDING-TORSION COUPLING IN AN IMPACTING-RUB ROTOR SYSTEM

A mathematical model of an impacting-rub rotor system with bending-torsion coupling was established. It was compared with the model without bending-torsion coupling through the modem nonlinear dynamic theory . It is observed that periodical, chaotic, period adding phenomena in them and the two models have a similar bifurcation process in their bifurcation figures . But the influence of bending-torsion on the dynmaic characteristics of the system is not neglected. The results have considerable meanings to analyze and improve the characteristics of an impacting- rub rotor system .     

Dynamical behavior of a mobile system with two degrees of freedom near the resonance

The design of mobile robots that can move without wheels or legs is an important engineering and technological problem.Self-propelling mechanisms consisting of a body that has contact with a rough surface and moveable internal masses are considered.Mathematical models of such systems are presented in this paper.First,a model of a vibration driven robot that moves along a rough horizontal plane with isotropic dry friction is studied.It is shown that by changing the off-resonance frequency detuning in sign,one can control the direction of motion of the system.In addition,a locomotion system which moves in an environment with anisotropic viscous friction is considered.For all models,the method of averaging to obtain an algebraic equation for the steady-state"average"velocity of the system is used. Prototypes were constructed to compare the theoretical results with experimental ones.     

PROBABILISTIC DAMAGE IDENTIFICATION OF STRUCTURES WITH UNCERTAINTY BASED ON DYNAMIC RESPONSES

The probabilistic damage identification problem with uncertainty in the FE model parameters, external-excitations and measured acceleration responses is studied. The uncertainty in the system is concerned with normally distributed random variables with zero mean value and given covariance. Based on the theoretical model and the measured acceleration responses, the probabilistic structural models in undamaged and damaged states are obtained by two-stage model updating, and then the Probabilities of Damage Existence （PDE） of each element are calculated as the damage criterion. The influences of the location of sensors on the damage identification results are also discussed, where one of the optimal sensor placement techniques, the effective independence method, is used to choose the nodes for measurement. The damage identification results by different numbers of measured nodes and different damage criterions are compared in the numerical example.     

Dynamic stiffness characteristics of aero-engine elastic support structure and its effects on rotor systems: mechanism and numerical and experimental studies

The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e., the dynamic stiffness). However, the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system. Therefore, this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system. Then,the numerical study and experimental verification are conducted on...     

FREE TRANSVERSE VIBRATIONS OF A DOUBLE-WALLED CARBON NANOTUBE：GRADIENT AND INTERNAL INERTIA EFFECTS

This is a modest contribution on higher-order continuum theory for predicting size effects in small-scale objects. It relates to a preceding article of the journal by the same authors（AMSS, 2013, 26： 9-20） which considered the longitudinal dynamical analysis of a gradient elastic fiber but, in addition to an internal length, an internal time parameter is also introduced to model delay/acceleration effects associated with the underlying microstructure. In particular, the free transverse vibration of a double-walled carbon nanotube（DWNT） is studied by employing gradient elasticity with internal inertia. The inner and outer carbon nanotubes are modeled as two individual elastic beams interacting with each other through van der Waals（vdW） forces. General explicit expressions are derived for the natural frequencies and the associated inner-to-outer tube amplitude ratios for the case of simply supported DWNTs. The effects of internal length（or scale）and internal time（or inertia） on the vibration behavior are evaluated. The results indicate that the internal length and time parameters of the adopted strain gradient-internal inertia generalized elasticity model have little influence on the lower order coaxial and noncoaxial vibration modes,but a significant one on the higher order modes.     

Magnetic field effects on the nonlinear vibration of a rotor

The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonlinearity in the inertia, the curvature, and the electromagnetic load. After discretization of the governing partial differential equations by the Galerkin method, the multiple-scale perturbation method is used to derive the approximate solutions to the equations. In the numerical results, the effects of the electromagnetic parameter load, the damping coefficient, the amplitude of the initial displacement, the mass moment of inertia, and the rotation speed on the linear and nonlinear backward and forward frequencies are investigated. The results show that the magnetic field has significant effects on the nonlinear frequency of oscillation.     

Active control and experiment study of a flexible hub-beam system

The first-order approximation coupling （FOAC） model was proposed recently for dynamics and control of flexible hub-beam systems. This model may deal with system dynamics for both low and high rotation speed, while the classical zeroth-order approximation coupling （ZOAC） model is only available for low rotation speed. This paper assumes the FOAC model to present experimental study of active positioning control of a flexible hub-beam system. Linearization and nonlinear control strategies are both considered. An experiment system based on a DSP TMS320F2812 board is introduced. The difference between linearization and nonlinear control strategies are studied both numerically and experimentally. Simulation and experimental results indicate that, linearized controller can make the system reach an expected position with suppressed vibration of flexible beam, but the time taken to position is longer than expected, whereas nonlinear controller works well with precise positioning, suppression of vibration and time control.     

New method for oblique impact dynamics research of a flexible beam with large overall motion considering impact friction force

A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is divided into a stick state and a slip state. The contact constraint model and Coulomb friction model are used respectively to deal with the two states. Based on this hybrid mod-eling method, dynamic equations of the system, which include all states (before, during, and after the collision) are obtained. Simulation results of a concrete example are compared with the results obtained from two other models: a nontangential friction model and a modified Coulomb model. Differences in the results from the three models are discussed. The tangential friction force cannot be ignored when an oblique impact occurs. In addition, the results obtained from the model proposed in this paper are more consistent with real movement.     

转子系统模态参数现场识别技术研究

基于时域振动参数识别理论,本文讨论了由转子和油膜轴承构成的转子系统的模态参数现场识别问题。本文所述方法不需要施加人工激振,仅在轴承座处测量轴承座的振动和转子的绝对振动,可以在线应用。     

磁悬浮挠性转子系统模型复合辨识方法

针对磁悬浮挠性转子的纯有限元分析模型精度低的问题,提出一种磁悬浮挠性转子系统模型复合辨识方法。该方法首先采用有限元方法把磁悬浮挠性转子划分为多个Timoshenko梁单元,建立磁悬浮挠性转子系统模型,并对其挠性临界频率、阻尼、刚度和振型等关键参数进行分析,进而得到磁悬浮挠性转子的等效降阶数学模型;然后采用鲁棒自适应方法分析磁悬浮挠性转子系统的动态特性;最后,采用变LEVY方法从动态特性分析数据中对磁悬浮挠性转子进行系统辨识,校正有限元分析得到的降阶数学模型。实验结果表明,本方法可以得到磁悬浮挠性转子较为准确的系统模型。     

The effect of tangential elasticity of the contact layer between stator and rotor in travelling wave ultrasonic motors

In travelling wave ultrasonic motors the elliptical motion of material points of the stator drives the rotor due to frictional mechanisms. The motor characteristic strongly depends on the mechanical properties of the components stator, rotor and contact layer. In order to predict the motor behaviour, a model for the contact between stator and rotor has been developed. The goal of the present paper is to point out the importance of the tangential elasticity of the contact layer which is responsible for the formation of stick zones and also for the amount of friction losses and overall efficiency. Therefore a comparison with a model with a contact layer rigid in tangential direction is given. Based on a visco-elastic foundation model for the contact layer, torque-speed curves as well as torque-efficiency curves are computed. Experimental investigations for identification of parameters, check of assumptions and model validation are carried out. Finally, the model is used to show the results of parameter variations for normal force, vibration amplitude and modulus of elasticity of the contact layer.     

推力主动磁轴承的动特性参数辨识

针对五自由度刚性非对称磁轴承 -转子系统 ,建立了系统动力学模型 ,在此基础上推导出系统动特性参数辨识公式 ,并用多频电流激励法辨识出参数 .与理论计算结果相比表明 :系统所建模型符合实际 ,辨识方法有效 ;径向轴承在 x和 y方向上的力 -刚度和力 -电流系数相同 ,与推力轴承对应系数相比稍大 ;推力轴承对转子横向振动产生的耦合效应明显影响系统的稳定性 ,在设计系统时必须加以考虑     

Model based online diagnosis of unbalance and transverse fatigue crack in rotor systems

A model based technique for online identification of malfunctions in rotor systems is discussed. Presence of fault changes the dynamic behavior of the system. This change is taken into account by equivalent loads acting on the undamaged system model. Equivalent loads are fictitious forces and moments acting on the undamaged system model, which generate a dynamic behavior identical to that of the real damaged system. The mathematical representation of equivalent loads is referred to as Fault Model. The work focuses on developing a fault model for a transverse fatigue crack in shaft and testing it through simulated studies. The basic principle of the technique is validated for unbalance identification, through numerical simulations as well as by experiments on a real rotor system.     

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。     

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.     

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(Varying compliance)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.     

转子系统非线性动力学DEM建模研究

将DEM方法引入转子系统非线性动力学的分析计算,对其建模过程和有关本构关系,作了比较详尽的介绍。该模型可用于碰摩、弯曲振动和扭转振动等转子系统的大部分动力学和运动学问题分析计算,不仅适用于单跨转子系统,也适用于多跨转子系统,尤其是在碰摩计算时,可考虑其摩擦特性随时间历程而变的特点,从而使分析计算更加接近实际情况。