Combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling

A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.

Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system

Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.

ZERO MODE NATURAL FREQUENCY AND NONLINEAR VIBRATION OF COUPLED LATERAL AND TORSION OF A LARGE TURBINE GENERATOR

Zero mode natural frequency (ZMNF) is found during experiments. The ZMNF andvibrations resulted by it are studied. First, calculating method of the ZMNF excited byelectromagnetic in vibrational system of coupled mechanics and electrics are given from the view ofmagnetic energy. Laws that the ZMNF varies with active power and exciting current are obtained andare verified by experiments. Then, coupled lateral and torsional vibration of rotor shaft system isstudied by considering rest eccentricity, rotating eccentricity and swing eccentricity. UsingLargrange-Maxwell equation when three phases are asymmetric derives differential equation of thecoupled vibration. With energy method of nonlinear vibration, amplitude-frequency characteristics ofresonance are studied when rotating speed of rotor equals to ZMNF. The results show that ZMNF willoccur in turbine generators by the action of electromagnetic. Because ZMNF varies withelectromagnetic parameters, resonance can occur when exciting frequency of the rotor speed is fixedwhereas exciting current change. And also find that a generator is in the state of large amplitudein rated exciting current.

Nonlinear Dynamic Analysis of Coupled Gear-Rotor-Bearing System with the Effect of Internal and External Excitations

Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom（8-DOF） nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system（SGRBS） is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.

转子偏心效应下大范围转动弹性梁外激励非线性动力学行为与振动机制

为实现大范围转动弹性梁类柔性机械的高速、安全、平稳运行,综合应用Galerkin模态截断法和Hamilton原理建立弹性梁刚-柔耦合动力学模型,并建立转子偏心运动微分方程;基于行波叠加原理,应用高阶Runge-Kutta法完成非线性动力学解耦;应用时、频域分析法解析转子偏心效应下弹性梁的振动机制以及外激励下的频谱响应特性。研究结果表明:外激励响应在转子偏心效应下会衍生新的低频谐波分量,转速和激励幅值的增加会导致频域内多个低频谐波分量高于主振,易引发不同程度的间歇性振动;外激励频率提高会引起频域谱峰后移,数值仿真5~35 Hz频段的外激励,当频率为25 Hz时其低频谐波分量是主振幅值的2倍,高达0.181 mm,进而呈现明显的外激励突发性激振。因此,借助时、频域分析可有效解析具有随机性的间歇性或突发性振动产生机制,可为大型旋转柔性机械的动力学优化设计提供重要的理论基础和数据支持。

动力吸振器在转子叶片系统振动抑制中的应用

设计了一种动力吸振器(DynamicVibrationAbsorber,DVA),可以抑制转子-叶片系统在一阶临界转速处的横向振动。文中介绍了DVA的结构,在建立转子-叶片-DVA耦合系统的动力学模型和方程后,采用数值法分析了该DVA装置的抑振效果。最终实验结果表明在给定参数下DVA可以分别抑制转子-叶片系统中转子和叶片的一阶共振,而且效果非常好。

Investigation on nonlinear lateral-torsional coupled vibration of a rotor system with substantial unbalance

Substantial unbalance may be caused by fan blade off during the operation period of gas turbine engines,and related dynamic problems are very critical to the safety design of rotor system in aero-engine.This article aims to understand lateral-torsional coupled vibration of the rotor system with substantial unbalance.The governing equation of a modified unbalanced rotor system is established based on Lagrangian approach.Then,a mathematical analytical method is proposed in which a linear approximation is derived and the Floquet theory and Hill’s method are incorporated,from which the modal characteristics of the unbalanced rotor are obtained.The modal characteristics of the unbalanced rotor system are revealed comprehensively for the first time.Furthermore,the relation between the modes and responses of the unbalanced rotor is discussed in detail.The results show that the lateral vibration and torsional vibration of the unbalanced rotor are coupled through the inertial terms in the governing equations.Due to the coupling,veering and lock-in phenomena occur between the frequencies of the forward whirl mode and the torsional mode.Furthermore,lock-in can lead to a kind of principal instability.With regard to the response of the unbalanced rotor,both natural vibration components and enforced vibration components appear in the lateral response,while only natural vibration components appear during torsional vibration.Moreover,natural vibration components play a crucial role in the response within the principal instability region and cause divergence of the vibration amplitudes in the lateral and torsional directions.

Modeling unbalanced rotor system with continuous viscoelastic shaft by frequency-dependent shape function

A reduced-order dynamic model for an unbalanced rotor system is developed, taking the coupling between torsional and lateral vibrations into account. It is assumed that a shaft is regarded as a continuous viscoelastic shaft with unbalanced and small deformation properties. The equations of motion for the torsional and lateral vibrations are derived using Lagrange's approach with the frequency-dependent shape function. The rotor torsional vibration is coupled with the lateral vibrations by unbalance elements in a way of excitations. Simulation and experiment results show clearly that the torsional vibration has strong impact on the rotor lateral vibrations, and it causes subharmonic and superharmonic excitations through unbalance elements, which leads to the superharmonic resonances in the lateral vibrations. This model with low-order and high accuracy is suitable for rotor dynamic analysis in real time simulation as well as for active vibration control syntheses.

转子支承不对中故障建模与机理分析

针对工程实际所出现的不对中现象,建立了一个转子支承不对中故障的通用模型。将任意形式的联轴器在径向刚度和角向刚度等效的前提下简化为1个等效模型,该模型与实际的总体径向刚度和角向刚度等效,依据实际联轴器刚度计算得到等效模型参数;根据等效联轴器模型推导出转子系统由于连接对角向位置的不均匀、连接刚度的差异性和非线性等不确定性因素所产生的不对中激励力,基于此建立含转子支承不对中故障的转子-支承耦合动力学模型。通过故障仿真分析得到转子支承不对中故障激励下的振动特征,通过数值仿真验证了平行不对中和角度不对中故障的2倍频和4倍频现象,以及由于角度不对中产生的1倍频轴向振动现象。利用含套齿联轴器的3支点转子故障模拟试验器进行了特征转速下多种不对中工况的振动响应试验,通过比较仿真结果的精度达到85%以上,表明所提出的转子支承不对中故障通用模型的正确有效性。

不平衡转子系统弯扭耦合复杂故障智能诊断

弯曲振动与扭转振动耦合在旋转机械实际运行中往往不可避免。考虑不平衡转子不同复杂工况的弯扭耦合情况,利用深度学习技术的优势,构建了基于一维卷积神经网络的诊断模型,提出了一种用于处理不平衡转子发生弯曲,扭转以及弯扭耦合振动情况的智能故障诊断方法。分析了数据输入类型和L 2正则化对诊断的影响,优化了诊断模型以提高诊断精度,并进行了试验验证。研究结果表明,该方法可以实现不同转速下,发生弯扭耦合振动时单种或多种复合故障的智能诊断,获得比其他方法更好的诊断效果。

机电复合传动高线速转子-行星齿轮系统耦合振动特性

机电复合传动系统作为未来传动形式的主要发展方向,有着传递功率大,运转速度高等特点。在运行过程中转子自身由于高转速所带来的振动会与行星齿轮啮合时产生的振动相互影响,从而形成转子-行星齿轮系统耦合振动过程。建立了机电复合传动转子-行星齿轮系统耦合振动动力学模型,分析了不同转速下转子-行星齿轮系统振动特性,开展了转子-行星齿轮系统模态分析并将模态分析结果与振动特性进行了对比,通过研究转子-行星齿轮系统的振动特性,揭示了系统振动随转速升高而增大,在经过一定转速区间时振动会维持在一定水平内,随着转速继续升高,系统振动又将逐渐增大。通过研究得到了齿轮系统与驱动电机转子耦合作用下的振动特性,为机电复合传动系统高速化设计提供了理论依据。

叶片出口梯形切割对离心泵蜗壳流激噪声影响的研究

为探究叶片出口梯形切割对离心泵蜗壳流激噪声的影响,以一台比转速为66的单级单吸离心泵为对象,通过定义切割宽度系数δ与径向高度系数γ,设计了9种切割方案。基于RNG k-ε湍流模型对离心泵进行全三维非定常数值模拟,在此基础上采用边界元法(boundary element method,BEM)计算内场噪声,采用结构有限元法(finite element method,FEM)耦合声学边界元方法计算外场流激噪声;分析不同切割方案下离心泵水力特性和噪声幅射特性,经试验方法验证数值计算的准确性。研究表明:动静干涉是离心泵蜗壳流激噪声产生的主要原因,合理的叶片出口梯形切割能使离心泵水力性能基本稳定的同时有效降低动静干涉强度及蜗壳流激噪声水平;声学性能最优切割方案,叶频处的进、出口监测点声压级分别下降13%和7.5%,外场噪声监测点声压级下降2.4%。

基于耦合源误差分析的转子振动信号识别方法

转子振动信号实时监测是保障旋转机械健康运行的关键,转子圆度误差和电涡流位移传感器误差的耦合源误差在以往的研究和振动监测中很少考虑,使得转子振动信号有一定的失真,甚至会引起误判。以实际转子为例,提出了圆度误差测量表达式;测量和分析了两种常用电涡流位移传感器的误差,利用傅里叶拟合方法构建了圆度误差和电涡流位移传感器耦合源误差表达式,建立了耦合源误差与转子振动信号之间的映射关系。提出了点-点法、平均值法与最大值法3种转子振动信号识别方法,3种方法都能有效识别转子振动信号,其中点-点法最精确,识别误差占比约20%;平均值法计算简便,识别误差占比约10%;最大值法偏保守,但可有效避免误判,识别误差占比约32%。

A new vibration mechanism of balancing machine for satellite-borne spinning rotors

The centrifugal force and overturning moment generated by satellite-borne rotating payload have a significant impact on the stability of on-orbit satellite attitude, which must be controlled to the qualified range. For the satellite-borne rotors＇ low working revs and large centroidal deviation and height, and that the horizontal vibration produced by centrifugal force is not of the same magnitude as the torsional vibration by overturning moment, the balancing machine＇s measurement accuracy is low. Analysis shows that the mixture of horizontal vibration and torsional vibration of the vibrational mechanism contribute mainly to the machine＇s performance, as well as the instability of vibration center position. A vibrational mechanism was put forward, in which the horizontal and torsional vibration get separated effectively by way of fixing the vibration center. From experimental results, the separation between the weak centrifugal force signal and the strong moment signal was realized, errors caused by unstable vibration center are avoided, and the balancing machine based on this vibration structure is able to meet the requirements of dynamic balancing for the satellite＇s rotating payloads in terms of accuracy and stability.

复合故障状态下行星齿轮-转子耦合系统振动响应特性研究

目前,国内外学者对齿轮-转子耦合系统的动力学特性进行了研究,但是上述研究均没有考虑行星齿轮-转子复合故障状态。为此,以单级行星齿轮箱为例,通过构建含转子偏心和齿根裂纹故障的行星齿轮-转子耦合系统动力学模型,对复合故障状态下的行星齿轮-转子耦合系统振动响应特性进行了仿真分析和实验研究。首先,采用了集中参数法和Timoshenko梁理论,考虑了时变啮合刚度、支撑刚度、阻尼、陀螺效应、传动轴柔性等因素,建立了含转轴偏心-齿根裂纹复合故障的行星齿轮-转子耦合系统动力学模型;然后,采用了时间历程、频谱、轴心轨迹及相轨迹等方法,并根据其数值分析了不同故障对系统动态特性的影响,研究了偏心状态下裂纹扩展对系统振动响应特性的影响;最后,采用不同裂纹故障测试实验,验证了模型的准确性。研究结果表明:转轴偏心对啮合振动的影响显著,在行星轮系故障特性的分析中不可忽视;偏心-裂纹耦合影响下,系统振动响应由不平衡振动、正常啮合振动、故障冲击振动多源耦合而成,频谱中出现了转频f_( r)、啮合谐波kf _(m)以及复杂边带成分kf _(m)±f _(r)、kf _(m)±f _(r)±nf _(sc),并且随着裂纹程度的加大,调制现象更加明显。该研究结果可以为行星齿轮-转子系统复合故障诊断提供一定的理论依据。

Study on dynamic stiffness of supporting structure and its influence on vibration of rotors

The dynamic response of the rotor depends on not only itself but also the dynamical characteristics of the structures that support it. In this paper, the coupling vibration characteristics of the rotor and supporting structure are studied using one simple rotor-supports model firstly, and then the dynamic stiffness of the typical supporting structure of an aero-engine is investigated in use of both numerical and experimental methods. While, one simulation strategy is developed to include dynamic stiffness of realistic supports in the dynamical analysis of the rotor system. The simulated and tested results show that the dynamic stiffness of the supporting structure not only depends on the structural parameters but also is related to the frequency of the excitation force. The dynamic stiffness is affected by the damping and inertia effect when the excitation frequency is high and closed to the resonance frequency of the support, which may decrease the dynamic stiffness sharply.More resonance frequencies may be induced and the critical speed could be reduced or increased.While higher vibration response peak and overload of the bearing may also be caused by the varied dynamic stiffness, which needs to be avoided in the design of the rotor-supports system.

动车组牵引电机转子系统弯扭耦合振动研究

本文利用离散化的方式将连续的转子结构转化为刚性盘、弹性轴,在转子的输入端、输出端、铁芯段分别形成一个刚性圆盘,并在此基础上建立转子的力矩关系和运动学模型。以拉格朗日运动微分方程为理论基础,构建转子动能、势能及耗散能方程,设置参数,依托四阶Runge-Kutta法对方程进行求解,最后分析了转子重力、机械不平衡力、不平衡磁拉力、转子弯扭负荷及径向负荷对系统弯扭耦合振动的影响。

Nonlinear vibration analysis of a rotor supported by magnetic bearings using homotopy perturbation method

In this paper,the effects of nonlinear forces due to the electromagnetic field of bearing and the unbalancing force on nonlinear vibration behavior of a rotor is investigated.The rotor is modeled as a rigid body that is supported by two magnetic bearings with eightpolar structures.The governing dynamics equations of the system that are coupled nonlinear second order ordinary differential equations(ODEs)are derived,and for solving these equations,the homotopy perturbation method(HPM)is used.By applying HPM,the possibility of presenting a harmonic semi-analytical solution,is provided.In fact,with equality the coefficient of auxiliary parameter(p),the system of coupled nonlinear second order and non-homogenous differential equations are obtained so that consists of unbalancing effects.By considering some initial condition for displacement and velocity in the horizontal and vertical directions,free vibration analysis is done and next,the forced vibration analysis under the effect of harmonic forces also is investigated.Likewise,various parameters on the vibration behavior of rotor are studied.Changes in amplitude and response phase per excitation frequency are investigated.Results show that by increasing excitation frequency,the motion amplitude is also increases and by passing the critical speed,it decreases.Also it shows that the magnetic bearing system performance is in stable maintenance of rotor.The parameters affecting on vibration behavior,has been studied and by comparison the results with the other references,which have a good precision up to 2nd order of embedding parameter,it implies the accuracy of this method in current research.

多平行轴齿轮耦合转子系统的振动响应

以一个两对斜齿轮耦合的三平行轴转子系统膨胀机子系统为研究对象,建立了斜齿轮啮合副动力学模型和转子系统有限元模型,考虑了齿轮啮合刚度、方位角、啮合角、螺旋角以及主动轴转动方向的影响,推导出齿轮啮合刚度矩阵。基于模态叠加法,对弯-扭耦合转子系统膨胀机子系统进行了固有特性分析和瞬态方式的不平衡响应分析,得到齿轮啮合前、后系统加载处的不平衡响应变化曲线。研究表明,齿轮间的耦合使系统之间的振动强烈,系统可能会在某个非固有频率处不平衡响应进行积累叠加,出现最大振动的现象,同时识别出共振峰的产生机理。齿轮耦合对转子系统动力学特性产生了很大的影响,使系统振型表现为耦合振型,必须以耦合的方式分析系统的振动特性,为防止系统发生大的振动提供依据,对齿轮系统的设计和故障分析具有指导意义。

大型潜水轴流泵转子部件湿模态数值模拟

为了得到大型潜水轴流泵在水介质中的模态分布,并分析水介质对结构模态的影响,该文采用UDF二次开发,运用ANSYS WORKBENCH和APDL命令流耦合的方法,对特大型潜水轴流泵的轴系转动部件进行了考虑预应力情况下的湿模态数值模拟,分别计算了定常和非定常状态下预应力和不存在预应力情况下的固有频率和振型,以及转子部件在真空(干模态)和清水介质(湿模态)中的固有频率和振型,研究了预应力和清水介质对结构模态的影响。分析了不同情况下造成模态分布差异的原因,为下一步进行更加复杂的动力学分析、疲劳分析以及结构优化奠定基础。