激励频率突变转子系统的动力学研究

根据转子动力学理论,建立了具有突变激励频率特性的Jeffcott转子力学模型及动力学方程。通过解析方法得到了激励频率突变后的转子系统振动解析表达式,并分析了激励频率突变前后稳态振幅之间的关系及激励频率突变对轴心最大位移的影响,定义了激励频率突变后的暂态过程时间,确定了碰摩参数区域。结论表明,激励频率突增的刚性转子系统及激励频率突减的柔性转子系统均会导致转子系统振动幅度增大,暂态过程时间与系统阻尼、刚度突变时的轴心位置及系统工作频率有关,碰摩参数区域随着激励频率突增幅度及质量偏心距的增大而增大。     

双转子-支承-机匣耦合系统碰摩振动响应分析及试验验证

以某型航空发动机双转子试验器为研究对象,采用Newmark-β数值积分方法求解系统的动力学响应,在考虑高低压转子中介轴承的耦合和机匣的弹性变形及其运动的基础上,建立了碰摩故障双转子-支承-机匣耦合系统动力学模型,理论分析了转速、转子偏心量和碰摩刚度对转子系统动力学特性的影响并进行了相关试验。研究结果表明：发生碰摩故障时,转子和机匣测点频谱分析图中会出现转子的倍频和组合频率,可将其作为判断系统发生局部碰摩的特征信号;随着转子偏心量和碰摩刚度的增大,碰摩幅值响应愈加明显,碰摩程度亦愈加严重;机匣测点振动量值存在衰减,后续理论建模过程中应考虑传递过程的衰减。本研究结论可为碰摩故障机理的探究和碰摩故障的诊断提供参考。     

双转子发动机转子-机匣碰摩振动特征研究

双转子发动机发生转静碰摩时,会出现高低压转子组合频率(频率和、频率差),但无法区分高、低压转子碰摩。采用简化的动力学模型,讨论双转子发动机转子与机匣碰摩的情况,认为碰摩力往往是一个旋转的力,并对碰摩的三种形式进行了理论分析和数值仿真。发现高压转子发生碰摩时,会出现高压转子的整数倍频NΩH及组合频率NΩH±ΩL的频率成分;低压转子碰摩时,则会出现低压转子的整数倍频NΩL及组合频率NΩL±ΩH的频率成分。组合频率成分在转子上反映并不显著,在机匣的振动响应中则会很突出。开展了双转子碰摩实验研究,实验结果和发动机实测结果均验证了上述结果的正确性。     

基于谐波分量的转子系统碰摩故障定量诊断方法

提出一种利用碰摩转子系统响应中的高次谐波分量进行碰摩位置和碰摩力定量诊断的新方法。基于谐波平衡理论分析碰摩故障转子系统的动力学特性,证明了碰摩故障转子系统中任意两节点之间高次谐波分量之比等于无故障转子系统频率响应矩阵的相关元素之比。根据此关系,提出转子系统碰摩故障模型诊断方法和步骤:利用正常转子系统与故障转子系统响应的任意一阶谐波分量之差,结合转子系统的动力学模型,就可以诊断出碰摩的位置;进而可以根据故障转子系统响应的各次谐波分量还原出碰摩力分量。为验证该方法的有效性,对一转子系统进行偏碰和整周碰摩时的数值仿真,并分析支撑刚度及噪声对诊断方法的影响;又在模型转子试验台上进行了试验。该方法仅利用一个转速下两个节点的振动响应即可实现碰摩故障的在线定量诊断,因此便于在实际旋转机械上实行。     

双盘转子系统不对中-碰摩故障仿真及实验研究

本文建立了通过齿式联轴器连接、滚动轴承支承的双盘转子动力学模型。该模型引入了齿式联轴器啮合力,不对中力和碰摩力。同时搭建转子实验台,并且进行了低转速下不对中-碰摩实验,研究转子在低速下的动力学特性和碰摩力特征。结果表明:低速实验下转子碰摩对于整体振动影响不大,在低转速下会产生一定的分数频率,并对倍频幅值产生一定影响;仿真结果显示,随着转速的增加,转子与静子产生碰摩,系统逐渐产生分数频率,并且系统的运动稳定性变差,碰摩力变得无规律。     

磁悬浮双转子系统的定点碰摩特性

采用Lankarani-Nikravesh模型描述了磁悬浮双转子系统定点碰摩过程中的法向冲击力,基于有限元法建立系统动力学模型,并对碰摩故障下的系统振动特性及接触过程进行了分析。研究结果表明:内外转子的转频是其转频差的整数倍时,碰摩发生时可观察到转频差的整数倍频率分量,随着碰摩程度的加剧,分数阶转频差频率分量出现;碰摩过程中的最大接触深度和法向冲击力取决于初始冲击速度;选择使系统运行角速度远离临界角速度的比例系数或较大的微分系数可显著减小系统碰摩的严重程度。     

转子系统松动与碰摩耦合故障非线性特性研究

建立了带有支座松动故障的非线性刚度转子系统局部碰摩动力学模型 ,利用数值积分和 Poincaré映射方法 ,对转子系统由于支座松动与局部碰摩耦合故障导致的非线性动力学行为进行了数值仿真研究 ,给出了系统响应随转子转动频率和偏心量变化的分岔图和一些典型的 Poincaré截面图、相平面图、轴心轨迹和幅值谱图等 ,以及非线性刚度对系统响应的影响。从中发现此类非线性振动系统具有周期、倍周期和混沌等复杂的动力学行为     

叶尖碰摩诱发的转子系统振动响应数值分析与试验研究

针对透平机械中叶尖碰摩诱发的转子系统振动问题,基于转子-叶片-定子耦合系统模型,通过对叶尖碰摩过程的数学表征,采用谐波平衡法和Newmark-β法,分别对转定子的稳态响应和瞬态响应进行数值计算,并分析了不同参数对系统振动响应的影响。通过分析发现,叶尖碰摩下的转定子稳态响应会呈现出“硬式”非线性特征;偏移量增加会导致峰值偏移提前,非线性特征更明显;接触刚度增加使得系统的振动加剧,并且离散性增加;叶片数增加后,“削峰”现象更加明显。由于定子的约束,系统的瞬态响应峰值明显被限制了,同时,在过临界转速后,系统会出现一个不稳定运动,使得系统振动出现瞬时增加。除了仿真分析,还基于转子-叶片碰摩试验台,对叶尖单侧碰摩下的转子和定子振动位移进行了测试。从测试结果可知,转轴的振动响应也会体现叶片的振动特征,而从定子的振动响应中可以看出由于转子涡动导致的频率调制现象。     

转子径向碰摩非线性流固耦合动力学特性全自由度的动态分析

基于Jeffcott转子模型,用6自由度方法研究考虑涡轮非线性流固耦合力的转子径向碰摩动力学特性.通过响应分叉图、波形图、频谱图、轨迹、Poincaré图以及频率瀑布图分析在涡轮非线性流固耦合力作用下转子径向碰摩的动力学表现.与不考虑涡轮非线性流固耦合力相比,转子的径向碰摩的稳定运动区大大减小,转子的碰摩转速门槛值也相应降低,并且碰摩一开始系统振动就出现比较复杂的运动形式;轴向振动的频谱中明显出现了密集的超谐波群,扭转振动的频谱中则明显出现了密集的亚谐波群,这种具有混沌特征的频率成分代表了系统在碰摩力和涡轮非线性流固耦合力作用下的主要运动形式;在整个转速范围内,横向振动几乎具有单一的同步频率成分,轴向振动则表现出非常丰富的超谐波频率成分,这些频率成分主要分布于三个随转速的增加分别向三个固定的频率逼近且幅值逐渐升高的密集超谐波频带,扭转振动则在1/2倍频附近表现出丰富的亚谐波频率成分,其幅值也随转速的增加而逐渐升高.上述结论对涡轮转子系统的动力学设计和故障诊断具有重要意义.     

不平衡量对转子碰摩振动的影响

建立了与限位器碰摩的转子动力学方程 ,用数值积分方法得到了碰摩非线性动力响应。分析中考虑了陀螺效应 ,采用分段线弹性和库仑摩擦模型描述碰摩力。研究双频进动、局部碰摩、拟整圈碰摩和整圈碰摩的振动特征。讨论了不平衡量和激振力幅度变化对碰摩振动形式和特征的影响 ,并给出碰摩振动试验结果 ,以验证数值分析结论。     

Dynamic analysis of three-dimensional helical geared rotor system with geometric eccentricity

A dynamic model of a multi-shaft helical geared rotor system is presented. Rotating shafts of the system are modeled as Timoshenko beams. A general three-dimensional dynamic model of helical gear pairs with geometric eccentricity is developed for the gear mesh and bearing flexibility is included in the model as well. The transmission error and gear geometric eccentricity are simulated as excitations. Eigenvalue solution and the modal summation technique are used to predict the natural frequencies and forced responses of the system. Then two geared rotor system models are presented for validation of the gear dynamic model. It is demonstrated that the gear mesh model is effective for general geared rotor systems, spur and helical gears, one-stage and multi-stage systems. Finally, forced responses of an example system are analyzed to demonstrate the influences of the helical gear geometric eccentricity and the coupling between gear geometric eccentricity and rotor mass unbalance.     

货车转向系统结构振动特性测试与优化

针对某型车开展了转向系统结构的动力学分析并进行了试验研究;采用瞬态激励测量转向系统结构的振动响应,得到加速度频响函数曲线;通过锤击法识别出转向盘、转向柱组件和汽车仪表板横梁管梁的约束模态参数。综合分析了模态振型和安装点动刚度,确定了需要优化的结构;通过对转向盘控制点的振动灵敏度测试,验证了优化方案的有效性。     

Analytical solution for dynamic behavior of multiwall carbon nanotubes subjected to mechanical shock loading

Dynamic behavior and frequency analysis of multiwall carbon nanotubes (MWCNTs) with finite length are investigated using an analytical method. By applying multiple elastic shells and a linearized model of van der Waals forces, a comprehensive continuum dynamic model of MWCNTs is developed. Also, by utilizing Laplace transform, time histories of MWCNTs subjected to shock lading are obtained. Then by using the fast Fourier transform (FFT), the time responses are transferred to the frequency domain and natural frequencies are found. The accuracy of results is verified by comparing the results of sudden loading with those obtained by numerical methods. Furthermore, an abrupt unloading after ramp loading is simulated, and the dependency of diameter and length on the axial and radial natural frequencies of MWCNTs is examined. Also, by characterizing the longitudinal displacement, the wave propagation velocities are obtained and an explicit expression is found for the axial natural frequencies of MWCNTs subjected to shock loading.     

Nonlinear Dynamic Analysis of a Rigid Rotor Supported By a Spiral-Grooved Opposed-Hemisphere Gas Bearing

The nonlinear dynamic behavior of a rigid rotor supported by a spiral-grooved opposed-hemisphere gas bearing is investigated in this article, focusing particular attention on its whirl motion. The finite element method combined with the finite difference method is employed to solve the time-dependent Reynolds equation that is coupled with the rotor motion considering five degrees of freedom. The rotor responses to the initial disturbance and synchronous and nonsynchronous excitations are investigated. To analyze the complicated dynamic behavior of the rotor–bearing system, the trajectories of the rotor centerline, time responses, phase portraits, power spectra, Poincare maps, and bifurcation diagrams are obtained from the numerical procedure. The results show that the conical whirl instability appears earlier than the cylindrical whirl instability with increasing rotational speed for the rotor–bearing system with no unbalance mass. Moreover, it reveals that the complex dynamic behavior of the system excited by unbalance mass varies with rotational speed and rotor mass. In addition, bifurcation diagrams employing the rotating speed and rotor mass as bifurcation parameters are obtained. Finally, the nonsynchronous excitation responses are presented, which behave in a different way than the synchronous excitation responses. The results of this study offer a further understanding of the nonlinear characteristics of spiral-grooved opposed-hemisphere gas bearings.     

The nonlinear and ball pass effects of a ball bearing on rotor vibration

A ball bearing is generally assumed as a linear spring in rotor dynamic analysis. In real case, the force equilibrium of the bearing is changed as the relative position, of each ball with respect to the direction of radial force. So, the stiffness of the bearing is also changed and is a function of time and position. In this study, the nonlinear characteristics of a ball bearing are considered in analyzing the vibration response of a rotating shaft due to an unbalance force. A finite element method is used to analyze the vibration characteristics of a rotor-bearing system and a direct numerical integration is performed to calculate the transient response of the rotor system. The responses are converted to the frequency domain and the effects of the parametric excitation due to a ball bearing are examined. The test rig for the investigation of the effect of a ball bearing on the rotor vibration is set up and the results are compared with those of numerical calculation. The calculation results show that the amplitudes of the nonlinear model are larger than those of the linear one. The frequencies of the calculations can be matched to the measured frequencies.     

Random displacement and acceleration responses of vehicles with uncertainty

Dynamic displacement and acceleration responses of cars with uncertain parameters under random road input excitations are investigated by using a quarter-car model. Based on the theory of random vibration, the vehicle’s random displacement and acceleration responses are developed in time domain and frequency domain. The sprung mass, unsprung mass, suspension damping, suspension and tire stiffness are considered as random variables. The mean value, standard deviation and variation coefficient of the vehicle’s natural frequencies and mode shapes are obtained by using the Monte-Carlo simulation method. The computational expressions for the numerical characteristics of the root mean square value of vehicle’s random displacement and acceleration responses in the frequency domain are developed by means of the random variable’s functional moment method and algebra synthesis method. The influences of the uncertainty of the vehicle’s parameters on the vehicle’s random responses are investigated in detail using a practical example, and some useful conclusions are obtained.     

Structural response reconstruction based on the modal superposition method in the presence of closely spaced modes

An approach for structural response reconstruction based on the modal superposition method in the presence of closely spaced modes is proposed in this paper. In this method, the entire mode-set of a structure is divided into closely spaced modes and the rest of the modes. The rest of the modal responses whose response is known will be separated into individual modal response by using the empirical mode decomposition method with intermittency criteria. Starting from the mode shapes, derived from these modal responses, the rest of the modal responses at the unavailable locations can be acquired. Furthermore, the contribution of the closely spaced modal responses at the unavailable locations can be obtained based on these responses. This proposed method is valid if there is no periodic excitation. However, in practice it is common that a structure might be excited by transient, stochastic, periodic forces or a combination thereof, i.e. hybrid excitations. A hybrid approach for solving the reconstruction problem of hybrid excitations is also developed, which is based on the proposed method and transmissibility concept in response reconstruction. Numerical studies are conducted and compared with theoretical predictions for validation. Effects of background noise level, high damping ratio and multiple forces are investigated in detail.     

基础运动对漂浮式风电机组齿轮箱传动系统附加激励的影响

风电齿轮箱传动系统是漂浮式风电机组中传递力与运动的关键传动装置,受到频繁的基础运动影响,振动特性复杂。提出一种适用于非惯性坐标系下六自由度基础运动与含公转/自转运动构件六自由度振动位移的耦合建模方法,并利用集中参数法和拉格朗日方程建立了风电齿轮箱传动系统动力学模型,分析了基础运动对构件产生的附加激励以及振动响应影响。研究结果表明：基础运动会对传动系统中构件产生时变的附加参数激励,这些附加激励的特征频率主要以系统自身特征频率与基础运动频率及其倍频的组合频率为主;作用在构件上的附加激励幅值与纵荡、纵摇基础运动幅值及其频率呈现非线性关系,纵荡、纵摇基础运动的幅值越大、频率越高,附加激励中纵荡与纵摇运动之间的耦合效应也愈明显;基础运动会增大构件的径向与轴向振动响应,使其出现与基础运动频率相关的特征频率。     

滚动轴承-转子系统非线性参数、强迫联合振动

建立考虑非线性轴承力、径向游隙、变柔度等非线性因素和不平衡力的滚动轴承-转子系统动力学方程,并用自适应Runge-Kutta-Felhberg算法对其求解,利用分岔图、Poincaré映射图和频谱图,分析参数、强迫联合激励的滚动轴承-转子系统的响应、分岔和混沌等非线性动力特性.结果表明,滚动轴承-转子系统有多种周期和混沌响应形式,其振动频率不仅有参数振动频率成分和强迫振动频率成分,而且有二者的倍频成分和组合频率成分;随着径向游隙的增大,转子系统的非线性特性增强;不平衡力较小时,系统中参数振动占主导地位,增大不平衡力有利于抑制转子系统的不稳定振动.随不平衡力的增大,强迫振动逐渐增强,大的不平衡力会诱发系统产生混沌振动;转子系统进入混沌的主要途径是倍周期分岔.     

单盘转子的瞬态不平衡动力相应分析

建立了Jeffcot转子的瞬态运动方程,采用S imu link程序进行数值仿真,得到转子系统在不同加速度下的瞬态动力响应。就不同加速度下转子系统振动的振幅、相位、进动角速度随时间和转速的变化规律分别作了较详细的讨论,得出了相应的结论。发现转子变速越过临界转速时,振幅、相位和进动角速度均与转子偏心相对于转子挠曲面的位置有关。进动角速度波动的极小值和极大值都对应着响应曲线过临界后波动的极小值。振幅、相位、进动角速度在过临界后的波动频率随转速增加而增加。该仿真结果与试验结论相吻合[4]。