Effects of unbalance location on dynamic characteristics of high-speed gasoline engine turbocharger with floating ring bearings

For the high-speed gasoline engine turbocharger rotor, due to the heterogeneity of multiple parts material, manufacturing and assembly errors, running wear in impeller and uneven carbon of turbine, the random unbalance usually can be developed which will induce excessive rotor vibration, and even lead to nonlinear vibration accidents. However, the investigation of unbalance location on the nonlinear high-speed turbocharger rotordynamic characteristics is less. In order to discuss the rotor unbalance location effects of turbocharger with nonlinear floating ring bearings(FRBs), the realistic turbocharger of gasoline engine is taken as a research object. The rotordynamic equations of motion under the condition of unbalance are derived by applied unbalance force and nonlinear oil film force of FRBs. The FE model of turbocharger rotor-bearing system is modeled which includes the unbalance excitation and nonlinear FRBs. Under the conditions of four different applied locations of unbalance, the nonlinear transient analyses are performed based on the rotor FEM. The differences of dynamic behavior are obvious to the turbocharger rotor systems for four conditions, and the bifurcation phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different from the different unbalance locations, and the non-synchronous vibration does not occur in the turbocharger and the amplitude is relative stable and minimum under the condition 4. The turbocharger vibration and non-synchronous components could be reduced or suppressed by controlling the applied location of unbalance, which is helpful for the dynamic design, fault diagnosis and vibration control of the high-speed gasoline engine turbochargers.     

Investigation of Induced Unbalance Magnitude on Dynamic Characteristics of High-speed Turbocharger with Floating Ring Bearings

Due to operational wear and uneven carbon absorption in compressor and turbine wheels, the unbalance(me) vibration is induced and could lead to sub?synchronous vibration accidents for high?speed turbocharger(TC). There are very few research works that focus on the magnitude e ects on such induced unbalance vibration. In this paper, a finite element model(FEM) is developed to characterize a realistic automotive TC rotor with floating ring bearings(FRBs). The nonlinear dynamic responses of the TC rotor system with di erent levels of induced unbalance magni?tude in compressor and turbine wheels are calculated. From the results of waterfall and response spectral intensity plots, the bifurcation and instability phenomena depend on unbalance magnitude during the startup of TC. The sub?synchronous component 0.12× caused rotor unstable is the dominant frequency for small induced unbalance. The nonlinear e ects of induced unbalance in the turbine wheel is obvious stronger than the compressor wheel. As the unbalance magnitude increases from 0.05 gbration 1·mm to 0.2 g·mm, the vibration component changes from mainly 0.12× to synchronous vi×. When unbalance increases continuously, the rotor vibration response amplitude is rapidly growing and the 1× caused by the large unbalance excitation becomes the dominant frequency. A suitable un?balance magnitude of turbine wheel and compressor wheel for the high?speed TC rotor with FRBs is proposed: the value of induced un?balance magnitude should be kept around 0.2 g·mm.     

航空发动机高速滚珠轴承振动特性研究（英文）

Ball bearing is widely used as rotor supporting.It is a non-negligible source of vibration in aero-engines.The vibration characteristics of the highspeed ball bearing are studied in this paper.Bearing kinematics theory is applied to discuss the basic characteristics of ball bearings.The vibration factors caused by ball bearings are analyzed,and then the vibration model of ball bearings is set up.The effect of the unbalance,the ball passage vibration,the radial clearance and the surface waviness ...     

CONTROL SYSTEM OF MAGNETIC BEARINGS BASED ON LINEAR QUADRATIC METHOD OF OPTIMAL CONTROL STRATEGY

A state equation for radical 4-degree-of-freedom active magnetic bearings is built, and the approach on how to use linear quadratic method of optical control theory to design a centralized and decentralized parameters control system is introduced, and also Matlab language is used to simulate and analyze. The simulation results have proved that the differences are small between centralized parameters and decentralized parameters control system. The conclusions of experiments have shown that decentralized controllers designed from optimal state feedback theory meet the requirements of active magnetic bearing system. The vibration amplitude of the rotor is about 20 μm when the speed of the rotor runs between 0 to 60 000 r/min. This method may be used in the study and design of controllers of magnetic bearings.     

Dynamic Control of a Flexible Shaft Mounted in Adaptive or Active Bearing

The dynamic behavior of rotors is highly influenced by bearing characteristics. In previous works, the authors have shown that it may be beneficial to adapt the bearing behavior to the shaft behavior. Several adaptive and active components will be developed in this paper in order to control the shaft dynamical amplitude. Different models of hydrodynamic bearings behavior are described. The Reynolds equation resolution may be done by numerical or analytical solutions. A physical analysis of the equation of thin films will identify the most sensitive parameters. The shaft flexibility is taking into account by a modal approach. The fluid-structure coupling process is a simulation, step by step, of the rotor behavior. At each step, the nonlinear fluid force is numerically calculated to obtain the unbalanced shaft response. The results, presented in this paper, concern the dynamic response of unbalanced shaft mounted in adaptive or active bearings： bearings with variable clearance, variable viscosity or variable housing speed. It is shown that the fluid bearing parameters must be adapted to the rotor speed （in particular near or far a critical speed）. Then, the paper presents a new kind of active bearing. It works with a mechanical control of the housing position. Several parameters are tested and compared. The robustness of the dynamic control parameters is presented. In conclusion, the bearing adaptation could be very useful to control the shaft dynamic. This limits the effect of the critical speed, in particular by diminishing the shaft amplitude and the dynamic forces transmitted to the housing.     

UNBALANCE RESPONSE AND TOUCH-RUBBING THRESHOLD SPEED OF ROTOR SUBJECTED TO NONLINEAR MAGNETIC FORCES

Because of the effect of unbalance excitation and nonlinear magnetic force, the large vibration of the rotor supported by active magnetic bearing（AMB） will go beyond the radial gap of the bearing, even causing mechanical touch-rubbing when the system works at an operational speed closer to the critical speed. In order to investigate this problem, the linear model and nonlinear model of the single mass symmetric rigid rotor system supported by AMB are established respectively and the corresponding transfer functions of close-loop system are given. To pass through the numerical calculation by using MATLAB/Simulink, the effect of both the unbalance response and threshold speed of touch-rubbing of the system subjected to nonlinear magnetic forces and nonlinear output current of power amplifier are studied. Furthermore, threshold speed of touch-rubbing of the rotor-bearing system is defined and the results of numerical simulation are presented. Finally, based on above studies, two methods of increasing the touch-rubbing threshold speed are discussed.     

Time-dependent vibration frequency reliability analysis of blade vibration of compressor wheel of turbocharger for vehicle application

Blade vibration failure is one of the main failure modes of compressor wheel of turbocharger for vehicle application. The existing models for evaluating the reliability of blade vibration of compressor wheel are static, and can not reflect the relationship between the reliability of compressor wheel with blade vibration failure mode and the life parameter. For the blade vibration failure mode of compressor wheel of turbocharger, the reliability evaluation method is studied. Taking a compressor wheel of turbocharger for vehicle application as an example, the blade vibration characteristics and how they change with the operating parameters of turbocharger are analyzed. The failure criterion for blade vibration mode of compressor wheel is built with the Campbell diagram, and taking the effect of the dispersity of blade natural vibration frequency and randomness of turbocharger operating speed into account, time-dependent reliability models of compressor wheel with blade vibration failure mode are derived, which embody the parameters of blade natural vibration frequency, turbocharger operating speed, the blade number of compressor wheel, life index and minimum number of resonance, etc. Finally, the rule governing the reliability and failure rate of compressor wheel and the method for determining the reliable life of compressor with blade vibration is presented. A method is proposed to evaluate the reliability of compressor wheel with blade vibration failure mode time-dependently.     

ANALYSIS ON MOTION STABILITY OF A HIGH-SPEED ROTOR-BEARING SYSTEM

A non-linear dynamic model of one type of high-speed rotor system with gas supporting system is set up. The laws between the capacity force and the parameters of bearing, the static equilibrium position and rotating speed are studied on the basis of above model. Then, the failure rotating speed is given in the working state, and the relation between the minimum failure rotating speed and clearance of bearing is also studied. At last, the stability and failure condition are discussed in different working conditions.     

DESIGN AND ANALYSIS OF NOVEL ACTIVE ACTUATOR TO CONTROL LOW FREQUENCY VIBRATIONS OF SHAFT SYSTEM

Aiming at providing with high-load capability in active vibration control of large-scale rotor system, a new type of active actuator to simultaneously reduce the dangers of low frequency flexural and torsional vibrations is designed. The actuator employs electro-hydraulic system and can provide a high and circumferential load. To initialize new research, the characteristics of various kinds of active actuators to control rotor shaft vibration are briefly introduced. The purpose of this paper is to introduce the preliminary results via presenting the structure, functions and operating principles, in particular, the working process of the electro-hydraulic system of the new actuator which includes a set of high speed electromagnetic valves and a series of sloping cone-shaped openings, and presenting the transmission relationships among the control parameters from control signals into the valves to active load onto shaft. The course of the work is dynamic, and a series of spatial forces and moments are put on the shaft to get an external resultant force to reduce excitations that induce vibration of shafts. By checking states of vibration, the actuator can control the impulse width and the interval of injection time for applying different control force to a vibration shaft in two circumference directions through the regulating action of a set of combination directional control valves. The results from simulating analysis and experiment show evidence of that this design can satisfy the case of active process of decreasing of flexural and torsional vibrations.     

RESEARCH ON MODELING AND CHARACTERISTICS OF THE SPINDLE DYNAMIC COUPLING ABSORBERING SYSTEM OF A SUPER－PRECISION SURFACE GRINDING MACHINE

The bearing is described by constrain matrix, and the spindle system of a NC surface grinding machine is simplified as elastic-coupling beam, then modal synthesis method is used to establish the dynamic model of beam. Moreover, the response of the end of rotor is analyzed, and the natural frequency, principle mode and other dynamic characteristics of the coupling system are studied, the law of bearing stiffness to coupling frequency and amplitude of rotor is also found. Finally, according to the actual condition, a dynamic absorber is designed. The simulation and experimental results show that the amplitude of spindle can be declined effectively when the dynamic absorber is attached.     

Effects of Floating Ring Bearing Manufacturing Tolerance Clearances on the Dynamic Characteristics for Turbocharger

The inner and outer oil film dynamic characteristic coefficients of floating ring bearings(FRBs) change due to the manufacturing tolerance of the floating ring, journal and intermediate, which leads to...     

长周期变转速下入口油温对高速轻载涡轮增压器转子振动特性影响

高速轻载涡轮增压器转子系统的入口油温在长周期变转速运行条件下会产生动态变化,从而改变转子系统振动特性甚至导致非线性振动事故。以某型汽油机用高速轻载涡轮增压器转子为研究对象,分析浮环轴承内油膜最小厚度与偏心率随入口油温参数的变化规律,构建涡轮增压器转子-浮环轴承系统动力学有限元模型,采用Newmark积分法分析转子系统的非线性瞬态响应,结合涡轮增压器升速实验,得到不同入口油温下转子系统三维振动瀑布图与Colormap频谱图,探究入口油温对转子系统振动响应特性的影响。结果表明:随着入口油温从50℃增至130℃时,内油膜最小厚度会减少,环速比与偏心率会增加,内油膜振荡幅值逐渐降低,但出现内油膜振荡与外油膜涡动的轴颈转速点会提前约30%,且外油膜涡动幅值会逐步增加。综合内外油膜涡动与振动幅值,入口油温约为90℃时转子振动情况较好。结论可为设计具有智能抗振性能的高速轻载涡轮增压器转子系统的运行参数提供理论参考。     

浮环轴向长度对高速轻载涡轮增压器转子系统振动特性影响研究

浮环轴承内外轴向长度结构参数会影响油膜压力分布与偏心率,产生显著分频振动而引发高速轻载涡轮增压器转子非线性振动故障。基于流体润滑理论和浮环力矩平衡方程,推导了含浮环轴承的涡轮增压器转子系统动力学方程,揭示浮环轴承轴向长度与转子系统振动响应之间的关系。以某型汽油机用涡轮增压器转子系统为例,分析浮环内、外轴向长度对轴承油膜压力、偏心率等动力特性的影响,构建转子系统动力学有限元模型,通过三维振动瀑布图研究不同浮环轴向长度下转子系统频域瞬态振动响应,结果表明：浮环内轴向长度从2.6增加到4.6 mm,导致浮环转速升高,最大内油膜压力减小,轴颈偏心率降低,分频幅值增加且出现分频的轴颈转速由142 kr/min降至76 kr/min,更易产生明显的非线性涡动现象;浮环外轴向长度从3.6增加到6.15 mm,使浮环转速降低,最大外油膜压力变小,浮环偏心率及轴颈相对浮环的偏心率减小,低转速下分频幅值减少且出现分频的轴颈转速由10 kr/min升至22 kr/min,可抑制转子系统过早发生非线性涡动,为浮环轴承结构参数设计与试验提供理论支撑。     

Nonlinear Numerical Prediction of a Rotor–Bearing System Using Damped Flexure Pivot Tilting Pad Gas Bearings

Flexure pivot tilting pad gas bearings with pad radial compliance (FPTPGB-Cs) and metal mesh dampers (MMDs) in parallel (FPTPGB-C-MMDs) have been considered for application to high-speed and high-performance turbomachinery because of their advantages of high effective damping level and adequate compliance with variations in rotor geometry or misalignment. Although the dynamic coefficients of FPTPGB-C-MMDs have been predicted using the linear method, a nonlinear study is urgently needed for their high nonlinear behavior. A nonlinear numerical investigation on the rotor–bearing system supported by FPTPGB-C-MMDs is presented in this study by using the time domain orbit simulation method that couples rotor motion equations, the unsteady Reynolds equation, and pad motion (considering MMDs) equations. The nonlinear predictions are verified by the prediction and experimental results of a published paper.FPTPGB-C-MMDs can effectively suppress the subsynchronous vibrations compared with the rotor system supported by FPTPGB-Cs. The prediction results show that a high damper mesh density has a more positive effect on improving the stability of the rotor system by reducing the subsynchronous vibrations. Investigation shows that MMDs can improve the ability of the rotor system to sustain the effect of destabilizing forces. A high damper mesh density can sustain large destabilizing forces. The simulation results also indicate that low pad radial stiffness or preload leads to high amplitudes of subsynchronous vibrations. A small clearance results in an increase in critical speed and its synchronous amplitude. Moreover, large clearance results in a wide speed range that leads to the occurrence of subsynchronous vibrations with large amplitudes.     

Characteristics analysis of aero-engine whole vibration response with rolling bearing radial clearance

For the influence of rolling bearing radial clearance on the whole vibration in the aero-engine whole system, a real engine rotorbearing- casing whole model is established. The rotor and casing systems are modeled by means of FEM; the support systems are modeled by lumped-mass model; rolling bearing radial clearance and strong-nonlinearity of Hertz contact force at four different supports are considered. The coupled system response is obtained by the numerical integral method. The characteristics of the whole vibration response are analyzed. For rolling bearing at a typical support, the rotor, outer ring of rolling bearing and casing response characteristics at different rotating speeds are analyzed. The changing law of contact forces for each ball and the global contact forces at different speeds are analyzed. The influence of the radical clearance on the contact forces on the whole vibration is analyzed. The results show that the contact forces will be larger and the acceleration amplitude jumps obviously when the radial clearance is increased, and due to the variable stiffness of the rolling bearing, the natural frequency will appear when the stiffness changes fiercely, that is frequency-locked phenomenon. When the radical clearance is larger and the rotating speed is between two critical speeds, the rotor squeezes the outer ring now and then. Reducing the radical clearance can reduce the whole vibration and increase the rotor’s stability.     

无油涡轮增压器的设计及其试验研究

对采用空气箔片轴承支承的无油涡轮增压器进行了设计和试验性研究。详细阐述了无油涡轮增压器以及所采用的空气箔片轴承的设计过程。通过静态加载试验预估了空气箔片轴承的名义间隙,采用Link-Spring模型预测了空气箔片轴承支承结构的刚度,结合Link-Spring模型和雷诺方程,采用扰动法对轴承的动态刚度和阻尼系数进行了有效预测。线性转子动力学分析表明设计的无油涡轮增压器转子的前两阶刚体模态临界转速均在所用空气箔片轴承的起飞转速之下,转子的正常运行转速在一阶弯曲模态临界转速之下并具有足够的安全裕度。对整个转子系统进行了转子动力学分析与计算之后,在此基础上搭建了无油涡轮增压器试验台,初步的升降速试验结果表明：转子在20 kr/min~60 kr/min出现较大的次同步振动,但是转子在68 kr/min时次同步振动显著减小,转子在68 kr/min稳速时的轨迹以及FFT分析表明转子在该转速下的主要振动来自同步振动,这表明增压器可以在68 kr/min稳定运行。同时,实时测量了推力轴承和径向轴承的温度,在68 kr/min稳速期间,推力轴承和径向轴承温度分别在52℃和32℃处小幅波动,说明了该转子-轴承系统的相对稳定性。     

转子对高压涡轮叶尖间隙变化规律的影响

基于涡轮叶尖间隙主动控制的需要,初步分析了涡轮叶尖间隙的变化机理,建立了机匣、叶片和转子的简化模型。在此基础上,分别仿真计算转速变化和发动机起动过程瞬态温度下转子的径向变化,讨论了转子在飞行器机动飞行情况下的振动幅值对叶尖间隙的影响。结果表明,转子振动幅值和径向位移对叶尖间隙变化有重要作用。     

考虑螺栓联接结构的轴承-转子系统振动特性分析

针对含螺栓联接结构的轴承-转子系统,建立考虑陀螺力矩及因螺栓预紧力不均匀产生的初始变形量的非线性转子系统动力学模型。采用法求解转子系统运动方程,通过分岔图、时域曲线、频谱及Poincaré映射图研究存在轴承游隙时转子系统的混沌路径,并分析不同初始变形量及轴承游隙对转子系统非线性振动特性的影响,通过试验验证所得结论的准确性。研究表明,当存在轴承游隙时,预紧力不均匀产生的初始变形量增加会抑制低转速下盘的混沌运动,拟周期运动进入混沌运动状态的转速升高,临界转速附近的振动幅值增加,系统混沌路径发生变化;存在初始变形量时,随着轴承径向游隙增大,系统在低转速工作状态下即进入混沌运动运动状态,拟周期运动进入混沌运动状态的转速降低。研究结果可为含螺栓联接结构的轴承-转子系统设计提供理论参考。     

Numerical analysis of the dynamic behavior of a rotor-bearing-brush seal system with bristle interference

To minimize leakage and maintain the efficiency of turbomachinery, brush seal can be installed with zero clearance or interference as the flexibility. This leads to contact between the rotor and bristle pack, and may cause self-excited vibration, even instability. In this study, to establishment a mathematical model of the rotor system, a seal force model with bristle interference is proposed and the nonlinear oil-film force is applied in view of short bearing assumption. The influences of main factors containing rotor rotational speed, installing interval, disc mass, and disk eccentricity on the nonlinear characteristics of the rotor-bearing-brush seal system are conducted by adopting bifurcation diagram, spectrum cascade, axis orbit, and Poincaré map. The results indicate that the vibration amplitude of the system with bristle interference is a bit larger than that without interference. The system stability is enhanced with smaller disk mass at a higher rotational speed. The proposed model could provide valuable reference for the design of a rotor-bearing-seal system.