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.     

高速转子-轴承系统的复杂动力学行为研究

在高速旋转机械的故障诊断研究中,实际转子系统具有复杂的非线性动力学特性,为此,基于非线性转子动力学理论建立高速泵转子系统动力学有限元模型,研究了非线性油膜力作用下的轴承阻尼扣刚度确定方法,分析了陀螺力矩和滑动轴承油膜力作用等因素对转子系统动力学特性的影响,研究了转速、偏心距和轴段直径等因素对转子系统不平衡响应的影响,为工程实际应用中的转子轴承系统的优化设计、故障诊断、振动控制等提供了理论依据.     

Application of Hopf bifurcation theory to rotor-bearing systems with consideration of turbulent effects

This paper shows that the steady state and the dynamic characteristics of a rotor-bearing system with turbulent effects can be conveniently evaluated by applying the Hopf bifurcation theory to the equations of motion of a rigid rotor symmetrically supported by two identical fluid-film journal bearings. Results are presented for stiffness and damping coefficients and stability characteristics of a journal bearing, which take turbulence into consideration.     

Simulations and experimental investigation on motion stability of a flexible rotor-bearing system with a transverse crack

In the classical process for stability studies on the rotor-bearing system with crack faults, the simple discrete model is adopted for research on such problems, which neglect some needful dynamical influence factor, such as the material damping, shearing effect and gyroscopic effects, etc. Therefore, it is necessary to find a precise calculation model for simulation of the rotor-bearing system with cracks faults. In this paper, instead of the traditional simple discrete model, finite element （FE） model is adopted to investigate the motion stability of a nonlinear rotor system with crack fault. According to finite element theory, the FE model of the cracked rotor system is established firstly. It should be pointed out that the element where the crack occurs is modeled by a particular crack element and the supports at both ends are simulated by two nonlinear loads. Then, based on dimensionless and dimensionality reduction, the Newmark-[3 method and the shooting method are employed to study the effect of eccentricity and the depth of crack on instability speed and bifurcation feature. Furthermore, the simulation results are verified by some corresponding experiments. The simulation and experimental results show that instability speed does not change monotonically, but decreases firstly and then increases when the amount of eccentricity increases. Moreover, as the type of instability changes, the instability speed jumps concomitantly. Additionally, the presence of crack fault can disturb the oil whirl, as a result, instability speed tends to increase slightly, but it does not affect the type of instability and jumping phenomenon. This research presents an effective and convenient method which uses the finite element method （FEM） to research the motion stability of the nonlinear rotor-bearing system with cracked faults and other nonlinear force, and the proposed method can provide a theoretical reference for stability analysis and vibration control in more complex relevant rotor-bearing system.     

Chaos of rub-impact rotor supported by bearings with nonlinear suspension

The nonlinear dynamic analysis of the rotor-bearing system is studied in this paper and is supported by oil-film short bearings with nonlinear suspension. An observation of a nonlinearly supported model and the rub-impact between rotor and stator is needed. Therefore for more precise analysis of rotor-bearing systems, the rub-impact between rotor and stator is also proposed in this paper. The displacements in the horizontal and the vertical directions charactering the theoretical model of the system are considered with non-dimensional speed ratio. Inclusive of the analysis methods of the dynamic trajectory, the power spectrum, the Poincaré maps and the bifurcation diagrams are used to analyze the behavior of the rotor centre and bearing centre in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent analysis is also used in this study to identify the chaotic motion. It is concluded that the trajectory of rotor centre and bearing centre have undesirable vibrations. Especially at s=5.6, the rotor centre is at chaotic motion but the bearing centre is still at quasi-periodic motion. With the analysis of the dynamic behavior of these operating conditions, the theoretical and practical idea for controlling rotor-bearing systems and optimizing their operation can be more precise.     

Optimum design of rotor-bearing system stability performance comparing an evolutionary algorithm versus a conventional method

The main intent of this paper is to formulate, demonstrate, and validate a practical means of implementing an evolutionary optimization technique in a rotor-bearing system. The optimum design of a flexible rotor supported on three-lobe bearings is studied for the optimal performance considering system stability along with other design criteria such as fluid film thickness, power loss, film temperature, and film pressure using the genetic algorithm and the method of feasible directions. The results for different operating speed values obtained and presented in this study are to provide a comparison of these two methods, and to show the potential of the genetic algorithm in optimization of rotor-bearing systems. The genetic algorithm obtained reasonably good results for the objective function and comparable to the method of feasible directions. Thus, the genetic algorithm provides the designer an alternative design optimization approach for rotor-bearing systems.     

Effects of design parameters on the noise of rotor-bearing systems

The purpose of the present paper is to investigate the effects of design parameters on the noise produced by rotor-bearing systems supported by oil lubricated journal bearings. To do this, the effects of radial clearance and the width of the bearing, lubricant viscosity, and mass eccentricity of the rotor on the noise of the bearing are investigated, and the numerical results are presented through the graph of the A-weighted sound pressure level of the bearing for various rotational speeds of the rotor. The results show that the A-weighted sound pressure level of the bearing is markedly influenced by the mass eccentricity of the rotor and the radial clearance and the width of the bearing. High viscosity of the lubricant slightly decreases the noise of the bearing, but its effect is relatively low at high speed. The results of the paper could aid in the design of low-noise rotor-bearing systems supported by oil lubricated journal bearings.     

膜片联轴器耦合的不对中转子-轴承系统的不平衡响应分析

转子系统的不平衡是旋转机械最为常见的故障之一,它影响转子系统的振动品质。考虑了转子系统不平衡力的作用,建立了膜片联轴器耦合的转子-轴承系统的运动微分方程;并以膜片联轴器耦合的双跨转子-轴承系统为研究对象,分析了不对中状态下转子系统的不平衡稳态响应,重点讨论了两跨转子各结点之间的振幅差异,结果表明膜片联轴器具有显著的隔振效果。     

裂纹-碰摩转子-轴承系统周期运动稳定性

建立了含有裂纹-碰摩耦合故障转子轴承系统的动力学模型,利用求解非线性非自治系统周期解的延拓打靶法和F loquet理论,研究了系统周期运动的稳定性。发现碰摩转子-轴承系统在不同的转速下会发生鞍结分岔、倍周期分岔和Hopf分岔等现象,裂纹-碰摩耦合故障转子-轴承系统具有不同于单一故障的独特的动力学特性。研究结果为转子-轴承系统故障诊断和安全运行提供了一定的参考。     

Investigation on the stability of periodic motions of a flexible rotor-bearing system with two unbalanced disks

The stability of periodic motion of a rotor-bearing system with two unbalanced disks is analyzed based on a multi-degree of freedom (M-DOF) finite element model. Nonlinear effects of supporting oil-film and inertia distributions as well as shearing effect are taken into account. Focusing on the more realistic FE method to study the stability of nonlinear rotor-bearing system with the influence of the eccentricity phase, the stability calculation of the M-DOF FE model is done by using the combination of Shooting method and Newmark method. Experiments with a rotor-bearing test rig (two disks on a shaft with two bearings) are then performed and results are presented. It is found that typical instability characteristic is successfully produced. Through comparisons between calculated results and measurements, it is shown that the combination of Shooting method and Newmark method in studying the M-DOF rotor-bearing system is useful, especially for the complex rotor-bearing system. In addition, altering eccentricity phase of the two disks can significantly influence instability type and speed. When the two disks are out of phase, the occurring of oil whip is restrained effectively. It is suggested that a careful examination should be made in modeling more complex non-linear rotor-bearing system. Some response curves are shown to compare the beam motions at different load velocities.     

Stability and response analysis of symmetrical single-disk flexible rotor-bearing system

The motion equations have been established for symmetrical single-disk flexible rotor-bearing system, and non-linear oil-film forces of finite journal bearings are calculated. The rotor's stiffness and damping are considered. The motions of journal and disk have been simulated with fourth-rank Runge-kutta method. The threshold speed of the system based on linear oil-film forces has been derived. Non-linear transient simulation and unbalanced responses are investigated. Moreover, linear oil-film forces are used for computing unbalanced responses, and the feasibility is discussed.     

基于运动微分方程特征值的转子-轴承系统失稳可靠性分析

从转子-轴承系统的运动微分方程入手,应用零部件可靠性分析方法,以运动方程特征值为稳定裕度评估量选定系统的状态方程,对动压润滑的向心滑动轴承进行了可靠性分析。通过数值仿真分析对建立的可靠性模型进行了验证,为工程实际中动压润滑向心滑动轴承的选用和轴系的设计提供一定的理论依据。     

预测铣削稳定性的隐式Adams方法

针对铣削加工过程中产生的振动现象,提出了一种隐式Adams方法（Implicit Adams method,IAM）来预测铣削加工过程的稳定性。考虑再生颤振的铣削加工动力学方程可以表示为时滞线性微分方程,将刀齿周期可分为自由振动阶段和强迫振动阶段,对强迫振动阶段进行离散,运用IAM方法构建状态传递矩阵,利用Floquet理论,判定系统的稳定性,获得系统的稳定性叶瓣图。Matlab软件仿真结果表明,IAM方法是预测铣削稳定性的一种有效方法。随着离散数的增加,IAM方法的收敛速度要快于一阶半离散法（First-order semi-discretization method,1st-SDM）和二阶全离散法（Second-order full-discretization method,2nd-FDM）,离散数较少的IAM方法能达到离散数较多的1st-SDM方法和2nd-FDM方法的局部离散误差。此外,在单自由度和双自由度动力学模型下,三种方法的稳定性叶瓣图显示,IAM方法预测铣削稳定性的预测精度均好于1st-SDM方法和2nd-FDM方法,计算效率远远高于1st-SDM方法,稍高于2nd-FDM方法。切削试验和仿真结果表明,IAM方法的预测精度和可靠度均好于1st-SDM方法和2nd-FDM方法。     

裂纹故障对齿轮传动系统动力特性的影响

建立了正常与故障齿轮传动系统的动力学模型,并对其进行了动力学分析,研究了齿轮出现裂纹故障后齿轮啮合刚度的变化以及对整个齿轮传动系统动力特性的影响,通过对正常系统和故障系统动力特性的对比分析以及对正常和故障齿轮系统进行试验,表明理论分析的准确性和可靠性,这对齿轮机械系统的设计和对故障齿轮系统进行诊断有重要的价值,并对齿轮系统进行实时监测有着重要意义。     

碰摩微转子系统稳定性与分岔行为分析

微型旋转机械是MEMS中的重要动力源之一,微转子作为系统的主要驱动部件,其动力学特性直接影响到整个系统的稳定性和可靠性。本文以Jeffcott微转子系统为研究对象,建立微转子系统的碰摩力模型和系动微分方程,应用微分方程稳定性和分岔理论,分析微转子碰摩解的稳定性与分岔特性及系统参数对稳定域的影响。结果表明:微转子转动角频率、偏心量、静子径向刚度、阻尼系数及摩擦系数等系统参数是影响MEMS微转子系统稳定性的主要因素。     

非线性弹性碰摩转子周期运动稳定性分析

在同时考虑轴承油膜力、转轴非线性弹性力和碰摩发生时转静件间的相对速度对非线性摩擦力的影响基础上,构造了具有碰摩故障转子-轴承系统的动力学模型。利用求解非线性非自治系统周期解的延拓打靶法和Floquet理论,研究了系统周期运动的稳定性,分析了非线性摩擦力对系统动力学特性的影响。     

An ensemble local means decomposition method and its application to local rub-impact fault diagnosis of the rotor systems

Targeting the shock characteristics of the vibration signal of a rotor system with local rub-impact fault, a local rub-impact fault diagnosis method of rotor system based on ELMD (ensemble local means decomposition) is proposed in this paper. The local mean decomposition (LMD) is a newly self-adaptive time-frequency analysis method, by which any complicated multi-component signal could be decomposed into a set of product functions (PFs) whose instantaneous frequencies in theory have physical significance. Unfortunately, mode mixing phenomenon which makes the decomposition results devoid of physical meaning is common when LMD is performed in practice. Targeting this shortcoming, the filter bank structure of white noise by LMD is obtained by numerical experiments, and then an improved method based upon noise-assisted analysis, ensemble local mean decomposition, is put forward. In ELMD, firstly, different white noise is added to the targeted signal; secondly, LMD is used to decompose the noise-added signal into product functions (PFs); finally, the ensemble means of corresponding PF components derived from LMD is regarded as the final decomposition result. The analytical results from simulation signal and experimental rotor local rub-impact signal demonstrate that the ELMD approach can be used to overcome the mode mixing of the original LMD method effectively.     

Creep-fatigue crack growth behavior of a structure with crack like defects at the welds

A study on a creep-fatigue crack growth behavior has been carried out for a cylindrical structure with weldments by using a structural test and an evaluation according to the assessment procedures. The creep-fatigue crack growth behavior following the creep-fatigue crack initiation has been assessed by using the French A16 procedure and the conservatism for the present structural test has been examined. The structural specimen is a welded cylindrical shell made of 316 L stainless steel (SS) for one half of the cylinder and 304 SS for the other half. In the creep-fatigue test, the hold time under a tensile load which produces the primary nominal stress of 45 MPa was one hour at 600°C and creep-fatigue loads of 600 cycles were applied. The evaluation results for the creep-fatigue crack propagation were compared with those of the observed images from the structural test. The assessment results for the creep-fatigue crack behavior according to the French A16 procedure showed that the A16 is overly conservative for the creep-fatigue crack propagation in the present case with a short hold time of one hour.     

混凝土结构裂缝宽度波前编码测量系统的设计

混凝土结构裂缝宽度测量对监测建筑结构的健康状态、避免混凝土结构损坏性缺陷具有十分重要的意义。为了克服基于传统光学成像技术设计的手持式混凝土裂缝宽度测量系统焦深小准确调焦困难,以及由于存在像差和混凝土表面凹凸过大致使视场内图像无法完全清晰等缺陷,采用波前编码技术重新进行缝宽检测系统的设计,以便有效地拓展景深（焦深）。首先,讨论了波前编码立方型相位板规一化参数及其与实际系统相位板设计参数之间的关系,接着利用CODE V光学设计软件,完成了手持式裂缝宽度波前编码测量系统的设计,然后加工制作了立方型相位板并进行了初步实验。实验表明,采用基于单透镜的波前编码系统设计,在满足50mm分辨率、F数为6的前提下,可将景深拓展为15mm,达到传统光学系统相同F数时景深理论值的4.5倍。该系统能够满足混凝土结构裂缝宽度测量中扩大景深和成像的基本要求。     

松动对碰摩转子-轴承系统非线性特性的影响研究

在同时考虑轴承油膜力和碰摩发生时转子与定子之间的相对滑动速度对非线性摩擦力的影响基础上,构造了含有松动和碰摩故障转子系统的动力学模型,对转子 轴承系统由松动和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,发现该类系统在运行过程中存在周期运动、拟周期运动和混沌运动等丰富的非线性现象,研究结果为转子 轴承系统故障诊断、动态设计和安全运行提供了理论参考。