碰摩转子弯扭摆耦合振动非线性动力学特性

为进一步提高旋转轴系的安全性,研究旋转轴系弯扭摆振动耦合振动问题.推导一般意义下,考虑陀螺力矩的单盘转子弯扭摆耦合振动非线性方程,基于该方程推出不平衡转子和碰摩转子的非线性弯扭摆耦合振动方程.应用数值方法研究碰摩转子弯扭摆耦合振动相应的复杂动力学行为,研究转子转速对碰摩转子弯扭摆耦合振动的分岔和混沌行为的影响,以及扭转振动和摆动振动对弯曲振动的影响.分析结果为转子的安全运行和弯扭摆耦合振动故障的判别提供了理论依据.     

转子弯扭耦合振动非线性动力学特性研究

对Jeffcott转子的非线性弯扭耦合振动微分方程进行了理论分析，得出了在弯扭组合共振区内弯曲振动和扭转振动的频率特征，利用数值方法对转子系统在较宽的参数域内进行分岔研究，得出了弯扭组合共振为概周期运动的结论，求出了弯扭组合共振区与不平衡量之间的关系，分析结果为转子的安全运行和弯扭组合共振故障的判别提供了理论依据。     

碰摩转子弯扭耦合振动特性分析

在给出单盘转子弯扭耦合振动的一般理论模型后 ,对碰摩转子的弯扭耦合振动动力特性进行了理论分析。在给出几个基本概念和碰摩转子弯扭耦合振动的激振力形式、刚度与阻尼的变化后 ,建立了碰摩转子的非线性弯扭耦合振动微分方程。然后对弯扭耦合振动转子的碰摩特性进行了数值分析 ,得出了若干结论 ,找出了扭转对弯曲的影响特征。     

Stability and dynamics of rotor system with 45° slant crack on shaft

Crack on a shaft is one of the common damages in a rotor system. In this paper, transverse vibrations are calculated to compare the influences of transverse crack and slant crack on the rotor system. Results show that the vibration amplitude of the rotor system with a 45° slant crack on the shaft is larger than that with a transverse crack when the two types of crack have the same depth and the rotor system runs in the same condition. Stability and dynamic characteristics of the rotor system with a 45° slant crack on the shaft under torsional excitation are analyzed by considering opening and closing of the crack. It is shown that the instability of the transverse vibration of the rotor system increases with increasing difference between the bending stiffness in two main directions, and the vibration is stable when the two bending stiffness are identical. The spectrum analysis of the steady-state response reveals that the gravity and the eccentricity produce different frequency components, and when the two bending stiffness are identical, the multiple frequency components of the torsional excitation disappear. Further investigation shows that the vibration amplitudes in combined frequencies increase rapidly in transversal, torsional, and axial vibration with increasing slant crack depth. The results are helpful for the understanding the dynamic behavior of a rotor system with a slant crack on a shaft and can be used for the detection of the slant crack on a shaft.     

一种新的转子碰摩故障诊断特征的研究

建立Jeffcott碰摩转子的弯扭耦合振动非线性微分方程，通过数值仿真手段，着重分析转子碰摩故障的扭振时频域特点及其非线性振动特性，并描述动静间隙对碰摩转子扭振非线性特性的影响。研究表明，转子碰摩激起丰富的扭振频谱信息，主要包括N/2X、N/3X等分频成分以及1X、2X等倍频成分，且分频幅值往往比倍频大许多。在一定转速范围内，周期运动与复杂的非线性运动交替出现。而动静间隙对转子扭振特性影响明显，动静间隙越小，转子动静碰摩越严重，频谱成分越丰富，运动形式更趋复杂，相应的各复杂运动区的范围也越宽。文中揭示的扭振特征为转子碰摩的状态识别与诊断提供了一种新方法。     

齿轮-转子系统的振动特性分析

根据转子动力学和齿轮啮合的基本原理,建立了考虑陀螺力矩的齿轮转子系统的动力学模型,以此求得齿轮转子啮合刚度矩阵和阻尼矩阵。探讨了啮合刚度、支承刚度对系统固有频率以及系统稳定性的影响。结果表明齿轮的啮合刚度对弯曲振动以及弯扭耦合振动固有频率的影响不大,而当啮合刚度介于2×105~2×108之间时,对弯扭耦合振动的相对稳定性却有较大的影响;另增大支承刚度,固有频率相应提高;减小跨距可以提高系统的稳定性。分析结果对工程应用具有重要的意义。     

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 and vibrations resulted by it are studied. First, calculating method of the ZMNF excited by electromagnetic in vibrational system of coupled mechanics and electrics are given from the view of magnetic energy. Laws that the ZMNF vanes with active power and exciting current are obtained and are verified by experiments. Then, coupled lateral and torsional vibration of rotor shaft system is studied by considering rest eccentricity, rotating eccentricity and swing eccentricity. Using Largrange-Maxwell equation when three phases are asymmetric derives differential equation of the coupled vibration. With energy method of nonlinear vibration, amplitude-frequency characteristics of resonance are studied when rotating speed of rotor equals to ZMNF. The results show that ZMNF will occur in turbine gen erators by the action of electromagnetic Because ZMNF varies with electromagnetic parameters, resonance can occur when exciting frequency of the     

运行工况下风电传动系统机电耦合建模及其动态特性分析

为研究风电传动系统在变速变载运行工况下的机电耦合动态特性,构建的包括齿轮系统动力学模型、永磁同步发电机有限元模型以及风机运行控制模型的风电传动系统机电耦合模型,计入了齿轮时变啮合刚度以及发电机齿槽效应、磁饱和等非线性因素.仿真分析了风电传动系统在启动、发电运行工况下的动态响应和机电耦合动态特性.研究结果表明:启动工况下...     

齿式联接不对中转子的弯扭耦合振动特性分析

以齿式联轴器的不对中故障为研究对象,推导不对中激励力表达式,并从动力学的角度,建立不对中弯扭耦合振动微分方程。基于该微分方程,文中先从理论分析角度,定性分析弯振对扭振的影响和扭振对弯振的影响,接着从变转速过程、质量偏心、不对中量以及阻尼系数对弯扭耦合特性影响几方面进行数值仿真分析。计算表明,弯振与扭振是相互耦合的,质量偏心是耦合的前提。弯振频率包含工频和二倍频成分等,不对中越严重,二倍频所占比例越大,其轴心轨迹为双环椭圆。弯扭耦合将激发各阶谐波扭振,包括工频、二倍频和三倍频,其中工频扭振占主导地位。     

热连轧机工作辊水平-垂直非线性振动特性及抑制

基于振动情况下轧制界面水平-垂直方向摩擦力模型和动态轧制力模型,考虑轧机的结构和工作辊轴承座与牌坊立柱间的摩擦力等因素的影响,建立了热连轧机工作辊水平-垂直系统的非线性振动模型。运用平均法求解得到幅频特性方程,分析外扰力和非线性参数等因素对系统幅频特性的影响,为抑制轧机工作辊水平-垂直振动提供理论指导。通过分析李雅普诺夫指数和位移分岔图,发现系统随外扰力幅值变化表现出周期、倍周期和混沌等不同运动状态。最后,通过分析工作辊轴承座与牌坊立柱间有无衬板间隙这两种情况下的幅频特性及衬板间隙对系统振动的影响规律,提出一种抑制工作辊水平振动和垂直振动的方法,仿真和实验结果均表明该方法有效。     

Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation

Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.     

Jeffcott裂纹转子弯扭耦合振动特性分析

以重力决定的开闭裂纹模型为研究对象，导出了固定坐标系下该模型的刚度扭阵，建立了裂纹转子弯扭耦合振动微分方程，并对转子裂纹的升速瞬态响应和影响因素进行了计算机仿真研究。结果表明：升速过程中，弯振存在1／3阶和1／2阶亚谐共振现象，扭振出现1／2阶亚谐共振；在弯扭左耦合区，出现弯扭耦合共振；在亚临界转速区，存在1X，2X和3X等倍频分量的弯振和扭振；影响弯扭耦合振动特性的因素很多，包括裂纹刚度、裂纹夹角、质量偏心和阻尼等。     

齿轮传动转子系统弯扭耦合振动研究

为分析齿轮传动复杂轴系的振动问题,根据有限元法和拉格朗日法,考虑陀螺效应、油膜支承等因素,得到了转子-轴承系统的弯扭耦合振动模型;在此基础上,根据齿轮副运动过程中啮合刚度和啮合阻尼的变化,得到了齿轮副系统的弯扭耦合振动模型。然后,根据齿轮副的实际排列方式,引入方位角,使得转子模型与齿轮副模型坐标统一化,并将其耦合到一起,得到了更加接近实际的齿轮转子模型,并且计算了其临界转速和振型。研究结果表明,耦合后转子的临界转速低于单转子的临界转速,齿轮传动对转子轴系振动有着明显影响。     

含柔性转子的齿轮-轴承系统动态特性分析

为了分析齿轮系统动力学中的全耦合振动,提出采用虚拟样机建模的方法,将柔性转子引入到啮合耦合系统中,考虑齿轮时变啮合刚度、齿侧间隙和轴承间隙的影响,建立齿轮-柔性转子-轴承系统虚拟样机模型,通过求解模型的动力学方程得到系统的非线性动力学响应。仿真结果表明:考虑柔性转子的耦合系统,啮合冲击峰值下降明显;转子柔性增加,齿轮低频扭转振动出现"拍"现象;高速轻载时啮合振动非线性特性增强;轴承间隙增大使啮合力振动幅值显著增大。     

液压缸非线性约束下的轧机辊系振动行为

以四辊板带轧机为例,分析液压压下缸及弯辊缸在轧机辊系振动时表现出的分段弹性力和摩擦力两种非线性约束,建立液压缸非线性约束作用下的轧机辊系振动模型,并采用平均法求得振动系统的幅频响应。通过比较两种非线性作用下辊系振动速度和振动幅值的仿真曲线,研究辊系受分段弹性力和摩擦力影响时的行为特性。取不同分段弹性力和摩擦力,仿真分析两种非线性因素分别对轧机辊系幅频特性的影响规律。结果表明,轧机辊系振动速度受分段弹性力大小影响,系统不稳定频率区域随分段弹性力增大而变宽;摩擦力较小时,对辊系振动行为影响表现为阻尼特性,较大时,摩擦力的非线性成为影响辊系振动行为的主要特性。该结论为轧机辊系振动控制提供了理论参考。     

Dynamic characteristics of multi-degrees of freedom system rotor-bearing system with coupling faults of rub-impact and crack

Extensive studies on rotor systems with single or coupled multiple faults have been carried out. However these studies are limited to single-span rotor systems. A finite element model for a complex rotor-bearing system with coupled faults is presented. The dynamic responses of the rotor-bearing system are obtained by using the rotor dynamics theory and the modern nonlinear dynamics theory in connection with the continuation-shooting algorithm（commonly used for obtaining a periodic solution for a nonlinear system） for a range of rub-impact clearances and crack depths. The stability and Hopf instability of the periodic motion of the rotor-bearing system with coupled faults are analyzed by using the procedure described. The results indicate that the finite element method is an effective way for determining the dynamic responses of such complex rotor-bearing systems. Further for a rotor system with rub-impact and crack faults, the influences of the clearances are significantly different for different rub-impact stiffness. On the contrary, the influence of crack depths is rather small. The instability speeds of the rotor-bearing system increase due to the presence of the crack fault. The results obtained using the new finite element model, presented for computation and analysis of dynamic responses of the rotor-bearing systems with coupled faults, are in accordance with measurements in experiment. The formulations given can be used for diagnosis of faults, vibration control, and safe and stable operations of real rotor-bearing systems.     

旋转机械耦合传动系统参激振动分析与控制

以一类旋转机械传动系统的扭振为研究对象,考虑轴系时变刚度变化和非线性摩擦阻尼力的影响,根据Lagrange原理建立了一类旋转机械传动系统的耦合非线性动力学方程,利用多尺度方法推导出了系统的平均方程,并根据Hopf分岔理论给出了系统发生Hopf分岔的充要条件及周期运动稳定性的判别方法,分析了参数共振和内共振条件下系统的分岔特性。为抑制传动系统因亚临界Hopf分岔引起的失稳振荡,引入非线性反馈控制,对系统的Hopf分岔点进行转移并控制周期运动的稳定性和幅值。研究结果为非线性旋转机械参激振动的分析及控制提供了有效方法。     

含轮齿剥落的齿轮系统动力学故障模拟

利用计算机对齿轮传动系统进行动态仿真,建立了考虑轮齿啮合摩擦力的直齿圆柱齿轮转子-轴承系统的动力学模型,根据不同接触位置上扭转啮合刚度的值,通过采用Matlab数值计算方法求解系统的时变非线性微分方程,模拟在扭转激励下,有剥落缺陷系统的动态响应,通过比较得到其与无缺陷系统响应的不同.仿真计算结果表明,该模拟方法能对齿轮传动系统的动力学性能做出较为全面的预测,为齿轮故障诊断提供参考.     

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。     

单跨度转子柔性碰摩振动特性研究

本文给出了单跨度转子柔性碰摩数学模型并建立起柔性碰摩实验,利用实验对比了转子在无碰摩和有柔性碰摩下的动力学特性。通过实验分析发现在有无柔性碰摩下存在着许多不同的振动特性。发现了柔性碰摩除了提高转子的临界转速外,还能有效降低转子通过临界转速时的振动幅值;有效地抑制油膜涡动的形成和油膜振荡的发生,同时出现了较为明显的高频振动现象。