Bifurcation of periodic motion of rigid rotor system supported by angular contact ball bearings

Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.     

转子叶轮-定子触碰故障的分析与辨识

基于航空涡轮发动机和工业透平机中的转子叶轮定子间触碰故障背景 ,以力学建模为指导搭建了两类简支型的转子定子触碰故障实验台架 ,考察了转子定子间正常无触碰、早期尖锐型轻微触碰、中期半尖锐型触碰、晚期平钝型触碰 4种状态时转子振动位移的时域轨迹 ,观测到了早期尖锐型轻微触碰时伴生的混沌现象 .采用FFT方法对上述 4种状态试验数据的频率结构作了分析 ,结果表明当出现三分频以下 (包括三分频 )的分频特征时可以初步判断叶片发生了早期触碰 ,而当转子振动位移的频谱图中仅存有两分频分量甚至轴频分量时 ,叶片 -转子间的触碰故障已相当严重了 .     

Research on a Rigid Rotor—Sliding Bearing System with a Squeeze Film Damper

In this paper,a dynamic model on a rigid rotor-sliding bearing system with a SFD is established.The stability and bifurcation behaviors of the system are studied,on The basis of the differential equations of fluid momentum and mass continuity,the distribution pressure function is derived by taking oil film inertia force into consideration.Damping force, clearance excitation force,interference force of different frequencies and static load are also considered in the model,Finally,the governing equations of the stability and bifurcation behaviors of the system are solved by Floquet theory,Simulation of dynamic model shows that the rigid rotor-sliding bearing system can maintain stability and exhibit a Hopt bifurcation phenomenon in a certain range.     

非解析径向轴承支承转子系统非线性动力特性分析

Nomenclaturex,y,x ·, y·-displacement and velocity of rotor-x,-y,x-·,-y·-displacement and velocity of rotor , di mension less¨x,¨y-acceleration of rotor¨-x,¨-y-acceleration of rotor ,di mensionlessω-rotating speed of rotor-ω-rotating speed of rotor ,di mensionlessx,y,z-Cartesian coordinates-x,-y,-z-Cartesian coordinates ,di mensionless2m-mass of rotorg-acceleration of gravityG-weight of rotor ,di mensionlesse=e2x e2y-mass eccentricity of rotorex,ey-mass eccentricity of rotor in thexan…     

Effectof Film Force Nonlinearity on Unbalance Responseof a Jeffcot RotorJournal Bearing System

Ｎｏｍａｎｃｌａｔｕｒｅ　ｂｉｊ,Ｂｉｊ（ｉ,ｊ＝ｘ,ｙ）　ｂｅａｒｉｎｇｄａｍｐｉｎｇａｎｄｎｏｎｄｉｍｅｎｓｉｏｎａｌｄａｍｐｉｎｇｃｏｅｆｆｉｃｉｅｎｔｓ,Ｂｉｊ＝ｂｉｊΨ３ｍｉｎ／（２ｌμ）　ｃｍｉｎｍｉｎｉｍｕｍｒａｄｉａｌｃｌｅａｒａｎｃｅｏｆｂｅａｒｉｎｇｄｄｉａｍｅｔｅｒｏｆｂｅａｒｉｎｇｅｕ,Ｅｕｅｃｃｅｎｔｒｉｃｉｔｙａｎｄｒｅｌａｔｉｖｅｅｃｃｅｎｔｒｉｃｉｔｙｏｆｍａｓｓｃｅｎｔｅｒｏｆｒｏｔｏｒ,ｒｅｓｐｅｃｔｉｖｅｌｙ,Ｅｕ＝ｅｕ／ｃｍｉｎＦｓｔａｔｉｃｌｏａｄｏｎｂ…     

Nonlinear dynamic analysis of a rotor/bearing/seal system

In this study a new dynamic model of a rotor system is established based on the Hamilton principle and the finite element method (FEM). We analyze the dynamic behavior of the rotor system with the coupled effects of the nonlinear oil film force, the nonlinear seal force, and the mass eccentricity of the disk. The equations of the motion are solved effectively using the fourth order Runge-Kutta method in MATLAB. The dynamic behavior of the system is illustrated by bifurcation diagrams, largest Lyapunov exponents, phase trajectory diagrams, and Poincaré maps. The numerical results show that the rotational speed of the rotor, the pressure drop in the seal, the seal length, the seal clearance, and the mass eccentricity of the disk are the key parameters that significantly affect the dynamic characteristics of the rotor system. The motion of the rotor system exhibits complex types of periodic, quasi-periodic, double-periodic, multi-periodic, and chaotic vibrations. This analysis can be used to guide the design of seal parameters and to diagnose the vibration of rotor/bearing/seal systems.     

Application of the Non—Stationary Oil Film Force Database

The technique of non-stationary oll film force database for hydrodynamic bearing is introduced and its potential applications in nonlinear rotor-dynamics are demonstrated.Through simulations of the locus of the shaft center aided by the database technique,nonlinear stability analysis can be performed and the natural frequency can be obtained as well.The easiness of “assembling” the individual bush forces from the database to form the bearing force.makes it very convenient to evaluate the stability of various types of journal bearings,Examples are demonstrated to show how the database technique makes it possible to get technically abundant simulation results at the expense of very short calculation time.     

Investigation of high-speed rubbing behavior of labyrinth-honeycomb seal for turbine engine application

The labyrinth-honeycomb seal has been widely used in gas turbine engines as an abradable gas path seal to protect the rotor from wear and damage in rubbing interaction. It usually works with a stepped labyrinth because the knife-edged tips could produce a special dynamic sealing system, and then the minimum clearance is possible between the rotor and stationary component. To investigate the high-speed rubbing behavior between a Hastelloy-X honeycomb material and a GH4169 double stepped labyrinth, nine rubbing tests were conducted using a high-speed abrasion test rig while the blade tip speed varied from 150 to 450 m/s, and the incursion rate from 120 to 360 µm/s. The abradability of honeycomb made from Hastelloy-X was fully verified by analyzing the visual rubbing observations, rubbing forces, and impact acceleration. It is shown that compression deformation happens to the honeycomb material during the rubbing process with the labyrinth blade except for a simple cutting mechanism, which is mainly affected by the parameter of incursion rate. Thermal ablation and oxidation were the main damage occurring on the labyrinth tip and appeared more obviously at a higher blade tip speed. Rubbing forces and impact acceleration were obtained from a piezoelectric dynamometer and acceleration sensor during the rubbing process. At a blade tip speed of 300 m/s and incursion rate of 360 µm/s, radial and tangential forces show their maximum values of 716 N and 871 N, respectively. The peak value of acceleration presents 341g with the highest blade tip speed of 450 m/s and the highest incursion rate of 360 µm/s. All testing results provide a great deal of effective information on high-speed rubbing behavior for the abradablility evaluation of a honeycomb.     

A new method for studying the 3D transient flow of misaligned journal bearings in flexible rotor-bearing systems

The effects of journal misalignment on the transient flow of a finite grooved journal bearing are presented in this study. A new 3D computational fluid dynamics (CFD) analysis method is applied. Also, the quasi-coupling calculation of transient fluid dynamics of oil film in journal bearing and rotor dynamics is considered in the analysis. Based on the structured mesh, a new approach for mesh movement is proposed to update the mesh volume when the journal moves during the fluid dynamics simulation of an oil film. Existing dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. The movement of the journal is obtained by solving the moving equations of the rotor-bearing system with the calculated film pressure as the boundary condition of the load. The data exchange between fluid dynamics and rotor dynamics is realized by data files. Results obtained from the CFD model were consistent with previous experimental results on misaligned journal bearings. Film pressure, oil film force, friction torque, misalignment moment and attitude angle were calculated and compared for misaligned and aligned journal bearings. The results indicate that bearing performances are greatly affected by misalignment which is caused by unbalanced excitation, and the CFD method based on the fluid-structure interaction (FSI) technique can effectively predict the transient flow field of a misaligned journal bearing in a rotor-bearing system.     

基于Hamilton原理的双跨转子系统建模和转子动态特性分析

研究目的：研究双盘双跨转子/轴承/汽封系统在非线性油膜力和非线性汽封力共同作用下的动力学特性,分析了转子转速、密封力、油膜力和联轴器刚度等因素对转子稳定性的影响。创新要点：采用Hamilton原理和有限元方法建立双盘双跨转子/轴承/汽封系统模型,使得双跨多节点的转子系统数值求解更加容易。研究分析转子转速、非线性密封力、非线性油膜力和联轴器刚度等因素对转子稳定性的影响,为大型转子系统的设计提供理论基础。研究方法：采用Hamilton原理和有限元方法建立双盘双跨转子/轴承/汽封系统模型（图1和2）。应用四阶Runge-Kutta法进行数值求解,并采用轴承处、圆盘处的分岔图、时程图、庞加莱映射图、频率图和相轨迹图等来分析转子系统的动态特性。重要结论：1.通过数值计算分析,转子的转速、非线性汽封力、非线性油膜力和联轴器的刚度对双跨转子的稳定性有重要的影响作用。2.随着转速的上升,双跨转子系统从最初的稳定运动,到三倍周期运动,到准周期运动和多倍周期运动交替出现,运动特性相比单跨转子系统要更为复杂。     

无轴承电机悬浮控制系统的设计

无轴承电机是利用磁悬浮轴承和交流电机结构的相似性,将产生磁悬浮力的磁悬浮轴承绕组置入电机定子,省去了专门的磁悬浮轴承．通过对转矩绕组和悬浮力绕组的解耦控制,使电机的转子同时具有产生转矩和自悬浮的功能．无轴承电机能够实现高速、无摩擦等优良性能,是当前研究的热点之一,无轴承电机悬浮控制系统设计是该研究的关键．本文介绍了无轴承电机悬浮控制的基本原理,设计了基于转矩绕组转子磁场定向的悬浮控制系统．     

Magnetic Field Analysis of Interior Composite-Rotor Controllable-Flux Permanent Magnet Synchronous Machine

* A conventional permanent magnet synchronousmachine (PMSM) is built to prevent demagnetizationeven under the extreme operatingconditions in the de-signing phase of rotor magnetic circuit and dimensionof permanent magnets (PMs). The magnet thicknessis large enough to keep the counter magnetic motiveforce (MMF) of armature less than coercive force inhigh temperatures[1]. If a conventional PMSMoperates in a wide speedrange, vector control strategy is always adopted. Bycontrollingd-axis dema…     

交流圆弧磁悬浮感应电机机制研究

磁悬浮（无轴承）电机利用磁场力使转子悬浮并驱动其实现高速或超高速旋转．基于传统电机技术提出一种交流圆弧电机原理,并按电磁轴承悬浮技术,水平方向对称于转子布置2个圆弧电机,垂直方向对称于转子布置2个圆弧电机,构成交流磁悬浮感应电机;建立电机在干扰作用下转子与定子间的间隙（气隙长度）变化规律,基于电磁理论建立了气隙磁感应强度的分布规律,利用虚位移原理建立电机电磁悬浮力和电磁转矩数学模型;通过有限元分析对磁感应强度、电磁悬浮力和电磁转矩等分布特性进行了仿真研究．     

推力轴承的力学特性

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｓｉｎｃｅ 1990 ,ａｎｉｍｐｏｒｔａｎｔｄｉｓｃｏｖｅｒｙｉｎｒｏｔｏｒ ｈｙｄｒｏ ｄｙｎａｍｉｃｂｅａｒｉｎｇｓｙｓｔｅｍｄｙｎａｍｉｃｓｉｓｔｈｅｃｏｕｐｌｅｄａｃ ｔｉｏｎｏｆｔｈｒｕｓｔｂｅａｒｉｎｇｕｐｏｎｔｈｅｌａｔｅｒａｌｖｉｂｒａｔｉｏｎｉｎａｒｏｔｏｒｓｙｓｔｅｍ .Ｉｎｔｈｅ ｐｉｏｎｅｅｒｉｎｇｒｅｓｅａｒｃｈｏｆＭｉｔｔｗｏｌｌｅｎｅｔａｌ .( 1990 ) [1] ,ａｓｅｒｉｅｓｏｆｒｏｔｏｒ ｄｙｎａｍ ｉｃｃｏｅｆｆｉｃｉｅｎｔｓｏｆｔｈｒｕｓｔｍａｇｎｅ…     

Analysis on Dynamic Performance for Active Magnetic Bearing—Rotor System

In the application of active magnetic bearings(AMB),one of the key problems to be solved is the safety and stabiltiy in the sense of rotor dynamics,The project related to the present paper deals with the method for analyzing bearing rotor systems with high rotation speed and specially supported by active magnetic bearings,and studies its rotor dynamics performance,including calculation of the natural frequencies with their distribution characteristics,and the critical speeds of the system.one of the targets of this project is to formulate a theory and method valid for the analysis of the dynamic performance of the active magntic bearing-rotor systemby combining the traditional theory and method of rotor dynamics with the analytical theory and design method based on modern control theory of the AMB system.     

Dynamic characteristics analysis of a misaligned rotor-bearing system with squeeze film dampers

In this paper, a dynamic model is established for a two-stage rotor system connected by a gear coupling and supported on ball bearings with squeeze film dampers (SFDs). The nonlinear dynamic behavior of the rotor system is studied under misalignment fault condition. The meshing force of the gear coupling is calculated considering the deformation of the tooth caused by torque transmission and dynamic vibration. The contact force between the ball and race is computed based on the Hertzian elastic contact deformation theory and the elastohydrodynamic lubrication theory. The supported force of SFD is simulated by integrating the pressure distribution derived from Reynolds’s equation. The equations of motion are rewritten in non-dimensional differential form, and the fourth-order Runge-Kutta method is employed to solve the nonlinear dynamic equilibrium equations iteratively. To verify the validity of the dynamic model and the correctness of the numerical solution method, the experimental power spectra of the rotor system under various misalignment degrees are compared with the analytical results. The effects of several important parameters, such as the lubrication of the ball bearing, the centralizing spring stiffness, the radial clearance of SFD, and the misalignment of gear coupling, on the dynamic characteristics of the rotor system are investigated and discussed mainly focusing on the system stability. The response spectra, bifurcation diagrams, and Pointcaré maps are analyzed accordingly. These parametric analyses are very helpful in the development of a high-speed rotor system and provide a theoretical reference for the vibration control and optimal design of rotating machinery.     

Rotor broken bar fault diagnosis for induction motors based on double PQ transformation

A new rotor broken bar fault diagnosis method for induction motors based on the double PQ transformation is pre-sented. By distinguishing the different patterns of the PQ components in the PQ plane,the rotor broken bar fault can be detected. The magnitude of power component directly resulted from rotor fault is used as the fault indicator and the distance between the point of no-load condition and the center of the ellipse as its normalization value. Based on these,the fault severity factor which is completely independent of the inertia and load level is defined. Moreover,a method to reliably discriminate between rotor faults and periodic load fluctuation is presented. Experimental results from a 4 kW induction motor demonstrated the validity of the proposed method.     

双向简谐波荷载作用下群桩力学性状分析及其受力性能

为研究双向简谐波荷载作用下群桩的力学性状及其受力性能,采用PLAXIS有限元软件建立相应的数值模型,分析了群桩基础在双向简谐波荷载作用下内力、位移响应情况,探究了桩周土体的动应力应变关系,进而对其在循坏水平荷载作用下的受力性能进行探讨。研究结果表明,与水平静载作用相比,桩基在循坏水平荷载作用下的承载能力有所降低;桩顶荷载-位移曲线出现“滞回圈”,基桩产生“疲劳效应”;桩周土抗力的变化使得各排桩内力分配不均匀;桩周土体的动应力应变关系呈现滞后性、非线性及累积性。     

利用影响线计算力偶作用时梁的内力和反力

将力偶分解为等值、反向、平行的两个力,当荷载(集中荷载、分布荷载和力偶)位置已知时,利用影响线计算梁的内力和反力,并与截面法计算结果作一比较。     

基于ADAMS的巨型卸胎机动力学仿真分析

卸胎机夹取的巨型轮胎质量可达6 t,存在较大的惯性力,在工作过程中会因为碰撞及运动引起系统强烈振动,容易造成轴承等零件失效。 文章基于ADAMS 动力学仿真方法对卸胎机动态特性展开研究。 研究表明,导轨轮轴与定环回转约束部位在卸胎机夹紧轮胎的过程中因夹板与轮胎发生碰撞,产生较大的冲击载荷,导轨轮轴固定部位合力最大可达260 kN,定环回转约束部位反力约为设备自重。 摇臂轴轴承与定环连接的螺栓固定部位在工作过程中支反力变化趋于一致,在翻转过程中,二者合力保分别可达40 、75 kN,且存在较大冲击。 研究结果可为轴承选型、螺栓校核及定环结构的强度刚度提供载荷边界,同时为卸胎机结构的动态优化设计提供技术支撑。