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.     

The dynamic behavior of a rotor system with a slant crack on the shaft

For a Jeffcott rotor system with a 45° slant crack on the shaft, the motion equations are established with four directions, i.e. two transversal directions, one torsional direction and one longitudinal direction. It can be seen from the deducing process of the stiffness with the strain energy release approach that there are coupling stiffnesses of bending–torsion, bending–tension and torsion–tension for the slant-cracked shaft and only bending–tension for the transverse-cracked one. The paper shows that besides the coupling stiffnesses, there is bending–torsion coupling caused by the eccentricity. All these couplings affect the responses of the slant-cracked shaft and the transverse-cracked one. Comparing responses of a cracked shaft with an open crack model and those with a breathing crack model finds that there are the same prominent characteristic frequencies for these two kinds of shafts, even though the cracked shaft with a breathing crack model behaves much more non-linear than that with an open crack model. Therefore, almost all studies in this paper adopt the open crack model since it needs taking much longer time to compute responses of a breathing cracked shaft than that of an open cracked shaft. Analyses of steady responses indicate that the combined frequencies of the rotating speed and the torsional excitation in the transversal response and the frequency of the torsional excitation in the longitudinal response can be used to detect the slant crack on the shaft of the rotor system.     

单盘含裂纹转子系统的非线性响应分析与实验研究

建立含裂纹Jeffcott转子的动力学运动方程。针对裂纹深度对转子系统动态响应的影响及转子盘摆振响应的特点进行仿真计算和试验研究。数值仿真表明，对于较浅的裂纹，系统响应为周期性运动，在某些转速下会出现倍周期运动，同时还出现各种倍频分量。此时的摆振运动常包含激振频率的倍频成分。当裂纹较深时，盘的摆振运动与横向振动都会出现各种非协调响应。试验结果表明，当轴上存在裂纹时，盘的横向振动响应和摆振响应中都会出现高次谐波分量，这些分量虽然从频率成分上讲是相同的，但各分量的大小有明显差异。这些结论对于转子裂纹故障的监测与诊断具有新的意义。     

运用综合设计法的多功能转子-轴承试验平台设计及实验研究

以大型旋转机械转子系统为研究对象,利用综合设计法设计模拟试验装置。功能优化设计通过编写试验台任务书,确认系统的功能,通过二级模糊评价方法确认总体设计方案。动态优化设计完成基于ANSYS Workbench仿真分析软件对四跨转子系统进行模态分析与谐响应分析,获得前六阶固有频率及振型。研究不同支撑刚度对转子系统临界转速的影响,通过坎贝尔图观察随着转速的升高,转子系统的固有频率的变化情况,还通过谐响应分析得出在不同载荷下转子系统的振幅规律。智能优化设计完成了平行不对中与偏角不对中实验装置的设计,可以精确控制不对中量。试验研究偏角不对中做了不对中量为1°与2°两组试验研究;平行不对中做了不对中量为1 mm与2 mm两组试验研究。系统不仅会有工频还会出现二倍频,随着偏角不对中量的增加二倍频成分也更加明显,幅值会增大;轴心轨迹出现″8″字形与内凹形。出现平行不对中时系统二倍频占主要成分且出现明显的三倍频。     

The partial and full rubbing of a flywheel rotor–bearing–stop system

The forced nonlinear vibration of a rotor rubbing with motion-limiting stops is investigated by means of numerical method. In the dynamic analysis, the large vibration of the multiple-degree-of-freedom rigid rotor is excited not only by the unbalance force but also by a harmonic excitation force as the simulation of low frequency disturbance and thus causes the rubbing between the inner wall of the hollow rotor and the stop which locates in the rotor. The simple Coulomb friction model and piecewise linear spring model are used to describe the contact between the rotating rotor and the stationary stop. The rotor to stop collision and rub happens occasionally on certain conditions. The forced vibration may become chaotic like when the collision and rubbing occurs. The stable partial rubbing motion shows that the stop is able to limit the vibration amplitude of the rotor which whirls violently at low frequency. With the increase of the amplitudes of the excitation, the partial rubbing will expand to full rubbing in which the rotor keeps contact with the stop. The full rubbing is periodic or quasi-periodic. It is supposed that the stop loses effectiveness when the full rubbing happens. The full rubbing takes place earlier as the friction factor becomes larger, and consequently the disturbance scope in which the stop works effectively becomes smaller.     

单盘裂纹转子次谐波共振实验研究

采用Bently模拟转子试验台,对轴上含裂纹的单盘转子系统进行了实验研究。发现裂纹会导致响应在1/2和2/3倍临界转速附近出现次谐波共振现象,在这些转速下系统响应出现了次谐波和高次谐波分量,如1/2倍频、3/2倍频、2倍频、3倍频和4倍频分量,并导致这些转速下振幅急剧增大,影响转子的稳定运转。摆振对裂纹非常敏感,在裂纹较小时就可观察到较为明显的倍频成分,并且其幅值比无裂纹时大一倍以上,可作为转轴上裂纹识别的重要参数。     

基于有限元的呼吸裂纹转子动力学特性

采用有限单元法建立了含裂纹Jeffcott转子的有限元模型,利用应变能释放率方法得到了裂纹单元的刚度矩阵,采用应力强度因子为零法模拟了裂纹的呼吸效应.计算分析了在一个稳态旋转周期内裂纹开闭的规律,以及直斜裂纹转子振动响应的特点.计算结果表明,斜裂纹开始张开以及闭合的时间迟后于直裂纹,斜裂纹处于全闭与全开状态所经历的时间比直裂纹长.直斜裂纹转轴的1X和2X倍频响应随着裂纹深度的增加而增加,但3X倍频分量变化不大.     

Simulation on the motion of crankshaft with a slant crack in crankpin

A new model for vibration analysis of a crankshaft with a slant crack in crankpin is proposed, and the influence of crack depth on the transient response of a cracked crankshaft is investigated. A slant cracked shaft element is developed by deducing the local flexibility due to a slant crack. The frequently occurred slant crack in crankpin is studied, and a new finite element model of crankshaft including the slant crack in crankpin, which combines the slant cracked shaft element and Timoshenko beam elements, is derived. The support of engine block and the switching behaviour of the crack are considered, and the non-linear equation of motion for cracked crankshaft-bearing system is set up in a rotating coordinate system. The motion of a crankshaft of a four in-line cylinder engine with and without an initial crack is simulated. The influence of the crack depth on the transient response is investigated. The numerical simulation demonstrates that the current model is valid for simulating the motion of cracked crankshaft system. The results show that a useful foundation is laid for crack detection of crankshaft.     

转子运动激励下叶片的振动特性分析

研究了航空发动机叶片在转子运动激励下的非线性动力学特性,利用一阶活塞理论来计算气动力,考虑大变形所带来的几何非线性的影响,利用Hamilton原理建立了叶片的连续体模型,采用伽辽金法将叶片简化为单自由度模型,通过多尺度法导出了叶片在参数激励与强迫激励作用下联合共振幅频响应的一阶近似方程;分析了转子扭转角度的幅值、稳定转速、气体的来流速度以及叶片的形状参数对于叶片幅频响应特性的影响。通过解析和数值分析,表明以上的参数是促使叶片动力学行为发生变化的敏感参数。同时应用奇异性理论得到系统主参数共振-主共振稳态响应的转迁集和分岔图,并对低风速情况下的叶片进行了试验分析。     

斜向激振模式下振动轮的滞回响应特性分析

考虑物料在斜向激振模式下压实进程中的弹塑性变形,提出一种仅依据土壤特性参数的水平对称及垂直不对称滞回动力学模型。在一次近似的前提下,利用渐进法(krylov-ogoliubov mitropolsky,简称KBM)将非线性作用力线性化为等效刚度和等效阻尼,并推导出系统的频响方程及响应解。数值仿真结果表明,由于非线性滞回力作用,压实进程中系统出现"软化"趋势,振动轮波形发生畸变,稳态下水平方向上呈现只含基波和奇次倍谐波的响应谱,垂直方向上呈现含除基波外明显的各奇、偶次倍谐波的谱特征。土壤现场压实试验分析结果与仿真结果基本吻合,滞回响应特性的研究为压实工况的实时监测和提高压实性能提供了理论依据。     

含间隙和时变啮合刚度的弧齿锥齿轮传动系统非线性振动特性研究

齿面侧隙和时变啮合刚度等因素的存在,将导致弧齿锥齿轮传动系统在工作过程中呈现典型的非线性特性;置于转子上的弧齿锥齿轮传动系统被等效处理为8自由度动力学模型,借助动态相对传动误差,使两轮转动自由度合并,建立了7自由度的非线性振动方程。采用A算符算法获得了不同工况下弧齿锥齿轮系统的扭转、横向及轴向的振动位移和速度,发现随着啮合频率的变化,系统经倍周期分岔进入混沌,而随着支承刚度的变化,系统经拟周期分岔进入混沌振动,在啮合频率的变化过程中,系统存在跳跃现象。     

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。     

基于视觉位感条纹的转轴裂纹缺陷检测

裂纹缺陷是转轴系统中常见的故障形式,裂纹的呼吸效应会改变转轴的动态特性,使转轴的径向振动信号中出现倍频分量。提出一种基于单目视觉位感条纹振动测量原理的转轴裂纹缺陷检测新方法,可实现转轴振动信号的高效测量和裂纹缺陷的快速检测。分析了含裂纹转轴系统的动力学方程,并系统描述了单目相机成像条件下采用位感条纹图案实现转轴径向二维振动测量的原理,建立了成像位感条纹动态编码参数与转轴径向振动位移之间的数学模型。通过与传统基于两路电涡流传感器测量系统的试验对比分析,验证了本方法测量结果的精确性。分析转轴系统在不同转速下径向振动中的频率分量,当转速接近1/2临界转速时,2倍频信号非常明显,且其幅值接近转频幅值,可实现对于转轴系统中裂纹缺陷的有效检测。     

Coupled bending and torsional vibration of a rotor system with nonlinear friction

Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating machinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincaré maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose selfexcited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.     

基于参数化时频分析的转子全工况动平衡方法

针对现有转子动平衡方法处理非平稳数据的不足,提出了基于参数化时频分析的转子全工况动平衡方法。该方法根据转频信号频率变化函数构造匹配的旋转算子,将启车信号的时频特征进行旋转,准确提取出转频分量。通过添加试重,结合全息动平衡方法获得各个转速下的迁移矩阵,实现转子全工况的动平衡,避免了传统动平衡方法需要获取稳态数据的缺点。实验结果表明,该方法可以方便、快捷地确定出转子的失衡量和失衡方位,有效降低转子系统不平衡振动,同时减少平衡过程中的启车次数。     

大型混流式模型机组动应力及压力脉动测试研究

最近几年在若干水力工程中,由于设计及机组运行调度的不合理,一些电站的机组,尤其是转轮叶片出现了局部裂纹问题,这引起了业界的高度关注。为此,东方电机在模型机组和真机上开展了叶片表面的动应力及表面压力脉动的测试。呈现模型机组测试的结果,通过这种测试发现最大的压力脉动幅值出现在转轮进口边区域,叶片表面上的压力脉动幅值明显大于转轮与活动导叶动静干涉所在的无叶区诱发的压力脉动幅值以及尾水涡所在的尾水管区域诱发的压力脉动幅值。叶片表面的压力脉动对应的主频和动应力对应的主频一致,主要为叶片数通过频率。动应力表现为类转频、尾水涡频率和动静干涉频率的叠加。     

基于分数阶阻尼的超磁致伸缩致动器非线性动力学研究

为进一步揭示超磁致伸缩致动器(Giant magnetostrictive actuator, GMA)系统非线性运动过程中的内在机理和动力学特征,基于分数阶微积分理论,将GMA动力学系统模型拓展至分数阶,建立含有分数阶阻尼的非线性GMA系统动力学方程,基于平均法分析系统主共振,得到系统的幅频响应方程;使用幂级数方法求解系统的数值解,通过Matlab数值模拟分析不同激励幅值和阻尼阶次对GMA系统的影响机理,从定性和定量的角度研究系统的分岔和混沌运动现象。结果表明：激励幅值和阻尼阶次对系统的幅频特性有显著影响;阻尼阶次对系统的分岔和混沌行为影响较大;不同阻尼阶次下由激励幅值变化引起系统的动力学行为相似但混沌区域不同。该研究有助于更好地了解GMA系统动力学特性,对工程实践中控制GMA系统稳定运行提供新的视角。     

基于开关电容技术的信号跟踪滤波方法及其在转子动平衡中的应用

为了满足转速波动时高精度动平衡测试的需求，精确、快速地分离出不平衡响应中的同频振动分量，利用开关和电容可等效为电阻的原理，导出了开关电容跟踪滤波方法，研制了一种新的开关电容模拟窄带跟踪滤波器，并对滤波器主要性能指标进行了测试与应用验证。试验结果表明：开关电容窄带跟踪滤波器有良好的跟踪特性，其中心频率由开关控制脉冲频率确定，是一种恒品质因素和恒定幅值增益的带通滤波器，具有良好的线性度。     

船体横荡运动对转子-浮筏气囊耦合系统非线性动力学特性的影响*

为研究横荡作用下船用转子-浮筏气囊耦合系统的非线性动力学特性,基于短轴承理论建立系统的数学模型,并用数值方法分析系统的动力学行为,探究转子转速、横荡幅值和频率变化对系统非线性动力学特性的影响。结果表明：与无横荡作用时相比,系统的动力学特性更为复杂;在转子转速较低时,系统在船体横荡作用下处于拟周期运动状态,随着转子转速的增加,系统出现分岔现象然后又合为一支直至混沌;随着横荡幅值的增大,转子的振动幅值也会随之增大,然而频率比的增加会使转子的振幅变小。     

Vibration analysis of a cracked rotor using Hilbert–Huang transform

In this paper, the startup transient response of a rotor with a propagating transverse crack is investigated using Hilbert–Huang Transform (HHT)—a relative novel time-frequency analysis method. The rotor with a growth crack is modeled by finite element method (FEM) and Dimarogonas’ method. The influence of crack propagating ratio (CGR) on instantaneous response of the rotor as it passes through the critical speed and sub-harmonic resonances is analyzed. The 1X (one times rotating frequency), 2X (two times rotating frequency) and 3X (three times rotating frequency) vibration components are studied when they appear, reach its peak and decay during startup process. Some conclusions are achieved which may be useful to detect transverse crack on the shaft. It demonstrates that the HHT is an effective tool for the analysis of non-linear, unsteady transient vibration response.