Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System with Radial Clearances and Waviness Considered

A rotor system supported by roller beatings displays very complicated nonlinear behaviors due to nonlinear Hertzian contact forces, radial clearances and bearing waviness. This paper presents nonlinear bearing forces of a roller bearing under four-dimensional loads and establishes 4-DOF dynamics equations of a rotor roller bearing system. The methods of Newmark-β and of Newton-Laphson are used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through the bifurcation, the Poincar è maps, the spectrum diagrams and the axis orbit of responses of the system. The results show that the system is liable to undergo instability caused by the quasi-periodic bifurcation, the periodic-doubling bifurcation and chaos routes as the rotational speed increases. Clearances, outer race waviness, inner race waviness, roller waviness, damping, radial forces and unbalanced forces-all these bring a significant influence to bear on the system stability. As the clearance increases, the dynamics behaviors become complicated with the number and the scale of instable regions becoming larger. The vibration frequencies induced by the roller bearing waviness and the orders of the waviness might cause severe vibrations. The system is able to eliminate non-periodic vibration by reasonable choice and optimization of the parameters.

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 the dynamic stiffness characteristics of a squirrel cage,which is a common support structure for aero-engine.Moreover,the static stiffness experiment is also performed for comparison.Finally,a rotor system model considering the dynamic stiffness of the support structure is presented.The presented rotor model is used to validate the results of the theoretical analysis.The results illustrate that the dynamic stiffness reduces the critical speed of the rotor system and may lead to a new resonance.

Emerging structures and dynamic mechanisms ofγ-secretase for Alzheimer’s disease

γ-Secretase,called“the proteasome of the membrane,”is a membrane-embedded protease complex that cleaves 150+peptide substrates with central roles in biology and medicine,including amyloid precursor protein and the Notch family of cell-surface receptors.Mutations inγ-secretase and amyloid precursor protein lead to early-onset familial Alzheimer’s disease.γ-Secretase has thus served as a critical drug target for treating familial Alzheimer’s disease and the more common late-onset Alzheimer’s disease as well.However,critical gaps remain in understanding the mechanisms of processive proteolysis of substrates,the effects of familial Alzheimer’s disease mutations,and allosteric modulation of substrate cleavage byγ-secretase.In this review,we focus on recent studies of structural dynamic mechanisms ofγ-secretase.Different mechanisms,including the“Fit-Stay-Trim,”“Sliding-Unwinding,”and“Tilting-Unwinding,”have been proposed for substrate proteolysis of amyloid precursor protein byγ-secretase based on all-atom molecular dynamics simulations.While an incorrect registry of the Notch1 substrate was identified in the cryo-electron microscopy structure of Notch1-boundγ-secretase,molecular dynamics simulations on a resolved model of Notch1-boundγ-secretase that was reconstructed using the amyloid precursor protein-boundγ-secretase as a template successfully capturedγ-secretase activation for proper cleavages of both wildtype and mutant Notch,being consistent with biochemical experimental findings.The approach could be potentially applied to decipher the processing mechanisms of various substrates byγ-secretase.In addition,controversy over the effects of familial Alzheimer’s disease mutations,particularly the issue of whether they stabilize or destabilizeγ-secretase-substrate complexes,is discussed.Finally,an outlook is provided for future studies ofγ-secretase,including pathways of substrate binding and product release,effects of modulators on familial Alzheimer’s disease mutations of theγ-secretase-substrate complexes.Comprehensive understanding of the functional mechanisms ofγ-secretase will greatly facilitate the rational design of effective drug molecules for treating familial Alzheimer’s disease and perhaps Alzheimer’s disease in general.

Quantum Mechanics: Harmonic Wave-Packets, Localized by Resonant Response in Dispersion Dynamics

From a combination of Maxwell’s electromagnetism with Planck’s law and the de Broglie hypothesis, we arrive at quantized photonic wave groups whose constant phase velocity is equal to the speed of light c = ω/k and to their group velocity dω/dk. When we include special relativity expressed in simplest units, we find that, for particulate matter, the square of rest mass , i.e., angular frequency squared minus wave vector squared. This equation separates into a conservative part and a uniform responsive part. A wave function is derived in manifold rank 4, and from it are derived uncertainties and internal motion. The function solves four anomalies in quantum physics: the point particle with prescribed uncertainties;spooky action at a distance;time dependence that is consistent with the uncertainties;and resonant reduction of the wave packet by localization during measurement. A comparison between contradictory mathematical and physical theories leads to similar empirical conclusions because probability amplitudes express hidden variables. The comparison supplies orthodox postulates that are compared to physical principles that formalize the difference. The method is verified by dual harmonics found in quantized quasi-Bloch waves, where the quantum is physical;not axiomatic.

Analysis of Flight Dynamics Characteristics of Tilt Quad Rotor with Partial Tilt-Wing

The aerodynamic model of propeller,wing,fuselage and vertical tail are established for the tilt quad rotor(TQR)with partial tilt-wing,and then the flight dynamic model is established.Based on the six-degree-of-freedom equation and the small disturbance linearization assumption,the trimming and stability of the tilt quad rotor with partial tilt-wing and the tilt quad rotor without tilt-wing are analyzed.The results show that in the hovering state,due to the existence of tilt-wing,the propeller wake reduces the downwash on the wing,thereby reducing the vertical weight gain of the aircraft.It is beneficial to increase the endurance time and improve the endurance performance.The transition corridor of the TQR with tilt-wing is narrower than that of the TQR without tilt-wing,but the transition corridor of TQR with tilt-wing still has a large space for design.Furthermore,the stability analysis shows that the Dutch roll damping ratio is larger,and in other modes the aircraft has a certain stability.The manipulation response analysis shows that in the transition mode the lateral-directional coupling is strong.

Dynamics Modeling and Numerical Analysis of Rotor with Elastic Support/Dry Friction Dampers

The elastic support/dry friction damper is a type of damper which is used for active vibration control in a rotor system.To establish the analytical model of this type of damper,a two-dimensional friction model-ball/plate model was proposed.By using this ball/plate model,a dynamics model of rotor with elastic support/dry friction dampers was established and experimentally verified.Moreover,the damping performance of the elastic support/dry friction damper was studied numerically with respect to some variable parameters.The numerical study shows that the damping performance of the elastic support/dry friction damper is closely related to the stiffness distribution of the rotor-support system,the damper location,the pressing force between the moving and stationary disk,the friction coefficient,the tangential contact stiffness of the contact interface,and the stiffness of the stationary disk.In general,the damper should be located on an elastic support which has a large vibration amplitude in order to achieve a better damping performance,and the more vibration energy in this elastic support concentrates,the better performance of the damper will be.The larger the tangential contact stiffness of the contact interface,and the stiffness of the stationary disk are,the better performance of the damper will be.There will be an optimal value of the friction force at which the damper performs best.

Dynamics of Rotor Drop on New Type Catcher Bearing

In an active magnetic bearing(AMB)system,the catcher bearings(CBs)are indispensable to protect the rotor and stator in case the magnetic bearings fail or overload.A new CB structure composed of two ball bearings is introduced.Detailed simulation models containing contact model between rotor and inner race,double-decker catcher bearing(DDCB)model as well as single-decker catcher bearing(SDCB)model are established using multibody dynamics simulation software MSC.ADAMS.Then,using those established models,the rotor orbits and the contact forces between rotor and inner race are simulated respectively after rotor drop on DDCBs and SDCBs.The simulation result shows that the rotor vibration range using DDCBs is significantly smaller than that using SDCBs;the maximum contact forces drop about 15%—27% compared with the contact forces using SDCBs.Finally,the test bench for the rotor drop experiments is built and the rotor drop experiments for different types of CBs are carried out.Labview data acquisition system is utilized to collect the displacement of rotor and the rotating frequencies of both inner race and intermediate races after rotor drop.The experimental results are comparatively analyzed,and the conclusion that DDCB can help to reduce vibration amplitude and collision force is obtained.The studies can provide certain theoretical and experimental references for the application of DDCBs in AMB system.

Dynamics in large generators due to oval rotor and triangular stator shape

Earlier measurements in large synchronous generators indicate the existence of complex whirling motion, and also deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator,called unbalanced magnetic pull（UMP）.The target of this paper is to analyse responses due to certain deviations of shape in the rotor and the stator.In particular,the perturbation on the rotor is considered to be of oval character,and the perturbations of the stator are considered triangular.By numerical and analytical methods it is concluded for which generator parameters harmful conditions,such as complicated whirling motion and high amplitudes,will occur.During maintenance of hydro power generators the shapes of the rotor and stator are frequently measured.The results from this paper can be used to evaluate such measurements and to explain the existence of complex whirling motion.

Computational Fluid Dynamics Analysis of Multi-Bladed Horizontal Axis Wind Turbine Rotor

The principal objective of this work was to investigate the 3D flow field around a multi-bladed horizontal axis wind turbine (HAWT) rotor and to investigate its performance characteristics. The aerodynamic performance of this novel rotor design was evaluated by means of a Computational Fluid Dynamics commercial package. The Reynolds Averaged Navier-Stokes (RANS) equations were selected to model the physics of the incompressible Newtonian fluid around the blades. The Shear Stress Transport (SST) k-ω turbulence model was chosen for the assessment of the 3D flow behavior as it had widely used in other HAWT studies. The pressure-based simulation was done on a model representing one-ninth of the rotor using a 40-degree periodicity in a single moving reference frame system. Analyzing the wake flow behavior over a wide range of wind speeds provided a clear vision of this novel rotor configuration. From the analysis, it was determined that the flow becomes accelerated in outer wake region downstream of the rotor and by placing a multi-bladed rotor with a larger diameter behind the forward rotor resulted in an acceleration of this wake flow which resulted in an increase the overall power output of the wind machine.

Seasonal Dynamics of Energy Return Through Litterfall of A Mixed Forest of Chinese Fir and T. odorum

Based on the measurement of monthly litterfall and their gross calor ic values, the seasonal dynamics of energy return through litterfall were determ ined in a pure and a mixed T. odorum (Tsoongiodendron odorum Chun) forests with Ch inese fir (Cunninghamia lanceolata (Lamb.) Hook.) in Sanming, Fujian Provinc e. Annual ene rgy return through litterfall was estimated as 12.648×10 6J·m -2 for the mixed fo rest, being 4 2% higher than that of the pure forest, and a large proportion of the energy return comprised leaf litter. The conversion efficiency of solar rad i ation energy into litterfall was 0 56% for mixed forest and 0 54% for pure for es t, respectively. The monthly energy flux in litterfall of Chinese fir showed a t hree-apex curve, peaked in March, August and December, respectively, which was s imilar to that in various fractions of leaf, twig, flower and fruit litter. The consistency in monthly patterns among different litter fractions of Chinese fir was attributed to their solid connections all the while. The monthly energy flux in litterfall of T. odorum culminated in January, May and August, the same was true for its leaf and twig litter. However, energy flux in flower litter only oc curred during March to May and that in fruit litter appeared in January and Marc h. The monthly dynamics of energy flux through litterfall of the two forests wer e both determined by their respective litterfall pattern of Chinese fir. Seasona l energy flux in litterfall for both mixed and pure forests followed the sequenc e of spring>winter>summer>autumn, but fluctuations in the former were less disti nct than those in the latter.

基于数值模拟的高速公路S型曲线积水规律分析

S型曲线由于特殊的线型几何特征形成了易积水的路面区域,对于积水规律的掌握有利于在设计和建造阶段提前预防和处理积水路段的危害。该文基于计算流体力学软件Fluent,结合计算流体力学分析中基于欧拉-拉格朗日方法的欧拉液膜模型EWF(Eulerian Wall Film),针对精细化处理的典型S型曲线双向多车道道路模型进行模拟计算。模拟包含了几何特征与降雨量等不同变量因素,得出了积水的水膜厚度以及流速分布规律。模拟结果表明:在降雨阶段,S型曲线横坡坡度0%~1%路段为积水路段,横坡坡度1%~2%路段为易积水路段,横坡坡度大于2%的路段积水情况受到降雨强度影响;在排水阶段,S型曲线横坡坡度0%~1%路段为排水困难路段,横坡坡度1%~2%路段为排水不畅路段,横坡坡度大于2%的路段排水顺畅,在排水时间结束时,路面在不同的几何条件和降雨条件下均能将积水排除至水膜厚度小于2 cm,横坡的大小与渐变影响了积水的横向分布与纵向分布,横向呈现中间高两边低、横断面上标高大的位置水膜厚度小和标高小的位置水膜厚度大的水膜厚度分布规律,总体呈现S型的分布规律;水膜流速在积水阶段呈现纵向上中间低两边高、水膜厚度大则水膜流速大的水膜厚度分布规律,在排水阶段则为纵向上中间高两边低的水膜流速分布规律。道路宽度影响了降雨落到路面的积水总量,进而对积水水膜厚度产生了影响;超高缓和率则主要使得积水路段、易积水路段增长,从而影响了积水分布的范围。

基于数据流的K-S变化检测的动态多目标规划算法

为了更加准确地判断环境是否发生变化并快速追踪动态多目标规划问题(dynamicmulti-objectiveoptimization problem,DMOP)当前时刻的Pareto前沿,提出了一种基于数据流的Kolmogorov-Smirnov(K-S)变化检测的动态多目标规划(DSK-SDMOP)算法。该算法以NSGA-Ⅱ为基础,通过数据流建立2个时刻的检验窗口,再利用K-S检验基于数据流的Pareto最优前沿是否发生变化,检测2个窗口的数据是否服从同一分布来判断环境是否发生变化,并就环境变化的剧烈程度实行相应的应答机制,以提高对环境的适应程度。利用基于数据流的K-S检测方法,对环境变化不会过于敏感,而且不用提前假设对应目标值的分布,易于操作。通过5个动态多目标规划标准测试函数对该算法进行测试,并和现有的2种算法进行对比分析,结果表明该算法处理动态多目标规划问题具有良好的性能。

基于加权D-S证据理论的旋翼故障诊断

旋翼作为直升机的升力面和操作面,其健康状态对直升机的安全至关重要。旋翼故障诊断技术仍是直升机健康与使用监测系统(Health and usage monitoring system, HUMS)领域的薄弱环节,开发旋翼故障诊断技术具有重要价值。基于信息融合技术,首先分析了旋翼故障的诊断机理,建立了旋翼故障模型,通过流固耦合仿真获取了不同故障下桨叶、轮毂和机身的故障特征信息,生成数据集进行网络训练和验证。然后,利用遗传算法反向传播(Genetic algorithm-backpropagation, GA-BP)优化神经网络诊断3种类型的直升机旋翼故障,即后缘调整片误调、变距拉杆误调和桨叶质量不平衡。3个逐级神经网络分别对旋翼故障类型、故障位置和故障程度进行了诊断识别。最后采用加权的Dempster-Shafer(D-S)证据理论对旋翼故障进行诊断和分析。结果证明基于改进D-S证据理论的旋翼故障诊断方法能够成功应用到旋翼故障诊断中,并具有良好的识别效果。

DYNAMIC BEHAVIOR OF A CRACKED FLEXIBLE ROTOR SUPPORTED ON JOURNAL BEARINGS

The dynamic behavior of a cracked flexible rotor supported on three kinds ofjournal bearings is presented. Numerical experiments show that nonsynchronous responseswill happen due to the rotor crack, and the amplitudes of the nonsynchronous componentsbecome larger with the increase of crack. On the other hand, the fluid forces of journalbearings can suppress the nonsynchronous response. The (1/2) × or (3/2) × harmoniccomponent rarely appears for small crack near the rotating speed ratio Ω = 2Ωc or Ω =(2/3)Ωc. In the case of supercritical rotating speed, the additional 0× harmonic component is increased as the crack increases. The bearing parameters affect greatly the occur-rence of the nonsynchronous responses by means of exerting innuence on the critical spedand the stabi1ity of the system.

Dynamic Responses of Rotor Drops onto Double-decker Catcher Bearing

In an active magnetic bearing （AMB） system, the catcher bearings （CBs） are indispensable to protect the rotor and stator in case the magnetic bearings fail. Most of the former researches associated with CBs are mainly focused on the dynamic responses of the rotor drops onto traditional single-decker catcher bearings （SDCBs）. But because of the lower limited speed of SDCB, it cannot withstand the ultra high speed rotation after rotor drop. In this paper, based on the analysis of the disadvantages of SDCBs, a new type of double-decker catcher bearings （DDCBs） is proposed to enhance the CB work performance in AMB system. In order to obtain thc accurate rotor movements before AMB failure, the dynamic characteristics of AMB are theoretically derived. Detailed simulation models containing rigid rotor model, contact model between rotor and inner race, DDCB force model as well as heating model after rotor drop are established. Then, using those established models the dynamic responses of rotor drops onto DDCBs and SDCBs are respectively simulated. The rotor orbits, contact forces, spin speeds of various parts and heat energies after AMB failure are mainly analyzed. The simulation results show that DDCBs can effectively improve the CBs limit rotational speed and reduce the following vibrations, impacts and heating. Finally, rotor drop experiments choosing different types of CBs are carried out on the established AMB test bench. Rotor orbits, inner race temperatures as well as the rotating speeds of both inner race and intermediate races after rotor drop are synchronously measured. The experiment results verify the advantages of DDCB and the correctness of theoretical analysis. The studies provide certain theoretical and experimental references for the application of DDCBs in AMB system.

Manufacturing Error Effects on Mechanical Properties and Dynamic Characteristics of Rotor Parts under High Acceleration

Stress, strain and vibration characteristics of rotor parts should be changed significantly under high acceleration, manufacturing error is one of the most important reason. However, current research on this prob- lem has not been carried out. A rotor with an acceleration of 150,000 g is considered as the objective, the effects of manufacturing errors on rotor mechanical properties and dynamic characteristics are executed by the selection of the key affecting factors. Through the force balance equation of the rotor infinitesimal unit establishment, a theoretical model of stress calculation based on slice method is pro- posed and established, a formula for the rotor stress at any point derives. A finite element model （FEM） of rotor with holes is established with manufacturing errors. The chan- ges of the stresses and strains of a rotor in parallelism and symmetry errors are analyzed, which verify the validity of the theoretical model. The pre-stressing modal analysis is performed based on the aforementioned static analysis. The key dynamic characteristics are analyzed. The results demonstrated that, as the parallelism and symmetry errors increase, the equivalent stresses and strains of the rotor slowly increase linearly, the highest growth rate does not exceed 4%, the maximum change rate of natural frequency is 0.1%. The rotor vibration mode is not significantlyaffected. The FEM construction method of the rotor with manufacturing errors can be utilized for the quantitative research on rotor characteristics, which will assist in the active control of rotor component reliability under high acceleration.

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 stability 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 magnetic bearing rotor system by 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.

Effects of Tightening Torque on Dynamic Characteristics of Low Pressure Rotors Connected by a Spline Coupling

A rotor dynamic model is built up for investigating the effects of tightening torque on dynamic characteristics of low pressure rotors connected by a spline coupling.The experimental rotor system is established using a fluted disk and a speed sensor which is applied in an actual aero engine for speed measurement.Through simulating calculation and experiments,the effects of tightening torque on the dynamic characteristics of the rotor system connected by a spline coupling including critical speeds,vibration modes and unbalance responses are analyzed.The results show that when increasing the tightening torque,the first two critical speeds and the amplitudes of unbalance response gradually increase in varying degrees while the vibration modes are essentially unchanged.In addition,changing axial and circumferential positions of the mass unbalance can lead to various amplitudes of unbalance response and even the rates of change.

Dynamic Characteristics of Rotor System with a Slant Crack Based on Fractional Damping

The traditional modeling method of rotor system with a slant crack considers only integer-order calculus.However,the model of rotor system based on integer-order calculus can merely describe local characteristics,not historical dependent process.The occur of fractional order calculus just makes up for the deficiency in integer-order calculus.Therefore,a new dynamic model with a slant crack based on fractional damping is proposed.Here,the stiffness of rotor system with a slant crack is solved by zero stress intensity factor method.The proposed model is simulated by Runge-Kutta method and continued fraction Euler method.The influence of the fractional order,rotating speed,and crack depth on the dynamic characteristics of rotor system is discussed.The simulation results show that the amplitude of torsional excitation frequency increases significantly with the increase of the fractional order.With the increase of the rotating speed,the amplitude of first harmonic component becomes gradually larger,the amplitude of the second harmonic becomes smaller,while the amplitude of the other frequency components is almost invariant.The shaft orbit changes gradually from an internal 8-type shape to an ellipse-type shape without overlapping.With the increase of the slant crack depth,the amplitude of the transverse response frequency in the rotor system with a slant crack increases,and the amplitude in the second harmonic component also increases significantly.In addition,the torsional excitation frequency and other coupling frequency components also occur.The proposed model is further verified by the experiment.The valuable conclusion can provide an important guideline for the fault diagnosis of rotor system with a slant crack.

Dynamic Analysis Model of Embedded Fluid Elastomeric Damper for Bearingless Rotor

According to the structural characteristics of embedded fluid elastomeric damper and dynamic modeling method of bearingless rotor(BR)system,a time-domain dynamic model based on multilayer elastomeric theory and fluid dynamic equations is developed.The parameters contained in the analysis model are identified by dynamic experiment data of embedded fluid elastomeric damper.The dynamic characteristics curves calculated through dynamic model are compared with those derived from experimental data.The consistent results illustrate that the model can describe the nonlinear relationship between stress and strain of embedded fluid elastomeric damper under different displacement amplitude and frequency.Due to the validity and reliability of the dynamic analysis model,it can be used in aeroelastic characteristics calculation of BR with embedded fluid elastomeric damper for helicopters.