转轴上裂纹开闭模型的研究

本文提出了一种新的描述转轴裂纹开闭状态的数学模型,此模型描述了裂纹开、闭及过渡状态的持续过程,它将开裂纹、方波和余弦模型统一于同一模型中,它的使用不受动、静挠度关系的限制.用这个模型算得的裂纹轴刚度变化曲线与实验结果吻合程度比余弦和方波模型好.文中还以Jeffcott裂纹转子为例,对各模型进行了理论探讨.结果表明:当研究非同步运动时,本文模型与方波和余弦模型所得的解差别较大,且轴心位移矢量的方向角在静平衡位置处的波动,影响到所得响应的特性.而对同步运动,这种差别及影响都很小.     

A non-linear study of a cracked rotor

The influence of the presence of transverse cracks in a rotating shaft is analyzed. The paper addresses the influence of crack opening and closing on dynamic response during operation. The evolution of the orbit of the cracked rotor near half and one-third of the first critical speed is investigated. The dynamic response of the rotor with a breathing crack is evaluated by expanding the changing stiffness of the crack as a truncated Fourier series and then using the Harmonic Balance Method. This method is applied to compute various parametric studies including the effects of the crack depth and location on the dynamic of a crack rotor. The evolution of the first critical speed, associated amplitudes at the critical speed and half of the critical speed, and the resulting orbits during transient operation are presented and some distinguishing features of a cracked rotor are examined.     

Multiple crack propagation along the interface of a non-homogeneous composite subjected to anti-plane shear loading

The present work concerns with the multiple crack propagation along the interface of two bonded dissimilar strips. The crack faces are subjected to anti-plane shear traction. Galilean transformation is employed to reduce the problem to a quasi-static one. Then, using Fourier transforms and asymptotic analysis, the quasi-static problem is reduced to a pair of singular integral equations. That are solved numerically, using Gauss-Chebyshev integration formulae. The values of the dynamic stress intensity factors are obtained and compared with the previous similar works. Further, a parametric study is introduced to investigate the effect of crack growth rate, geometric and elastic characteristics of the composite on the values of dynamic stress intensity factors.     

随机变刚度电磁支撑-转子-轴承系统不定动力参数实验识别

识别出随机变刚度电磁支撑-转子-轴承系统的不定动力参数是实验研究随机支撑刚度参数转子动力学问题的前提。为此,基于Riccati传递矩阵法的相关理论和计算程序,结合电磁支撑-转子-轴承系统各种工况下的一阶固有频率实测值,对转子系统的不定动力参数进行了识别,给出转轴轴套、联轴器等附件对转子刚度加强作用的具体数值,以及滑动轴承的支撑刚度和扭转刚度参数值。将这些数据代入到转子动力学理论模型中,得到相同工况下两测点振型幅值比值的理论值,并与实验值进行了比较。结果表明:各测点振型幅值比值的理论值和实验值之间的偏差小于5%,说明转子系统不定动力参数识别结果的精度和准确度完全满足实验研究的要求。     

含裂纹梁非线性静动力特性及简化动力学建模Static and dynamic behaviour of cracked beam and simplified dynamic model

主要研究裂纹对梁结构动力特性的影响规律,进而为含裂纹梁结构状态监测提供理论依据。首先,对裂纹影响区域进行分析,建立含裂纹梁二维接触非线性有限元模型,阐明含裂纹梁具有拉压不同刚度的静力特性;其次,通过对机理模型的分析,指出拉压不同刚度会引起轴向与弯曲的耦合振动;然后,通过非线性动力学分析方法研究其动力特性,观察到含裂纹梁在冲击荷载下会产生轴向与弯曲的耦合振动现象,并指出这种轴向与弯曲耦合振动的一个重要特征是轴向振动频谱图中含有弯曲振动基频的两倍频成分;最后,通过引入非线性弹簧建立一种新颖的含裂纹梁简化动力学模型,通过与精细有限元分析对比,验证了模型的合理性。该简化动力学模型将接触非线性问题转换为材料非线性问题,避免了费时的接触非线性动力学求解过程。     

Dynamic characteristics of a rub-impact rotor-bearing system for hydraulic generating set under unbalanced magnetic pull

Electromagnetic and mechanical forces are main reasons resulting in vibrations in hydraulic generating set. The non-symmetric air-gap between the rotor and stator creates an attraction force called unbalanced magnetic pull (UMP). The UMP can produce large oscillations which will be dangerous to the machines. In this paper, the nonlinear dynamic characteristics of a rotor-bearing system with rub-impact for hydraulic generating set under the UMP are studied. The rubbing model is established based on the classic impact theory. Through the numerical calculation, the excitation current, mass eccentricity, stiffness of shaft and radial stiffness of stator are used as control parameters to investigate their effect on the system, by means of bifurcation diagrams, Poincaré maps, trajectories and frequency spectrums. Various nonlinear phenomena including periodic, quasi-periodic and chaotic motions are observed. The results reveal that the UMP has significant influence in the response of the rotor system that the continuous increase in the excitation current induces the alternation of quasi-periodic and chaotic motions, the co-occurrence of oil whip and rub in a wide excitation range aggravates the vibration and leads to the instability of the system. In addition, the large eccentricity and radial stiffness of stator, as well as the small stiffness of shaft may lead to the occurrence of full annular rubbing while increasing the stiffness of the shaft can play an important role of suppressing the chaotic motion, reducing the vibration and improving stability of the system.     

考虑密封的悬臂转子系统的裂纹故障分析

以双盘悬臂立式转子-轴承系统为研究对象，建立了系统运动微分方程，并用数值方法分析了在非线性密封力和非线性油膜力作用下的裂纹转子的动力学特性。分析表明，在一定深度裂纹下，转子系统响应随不同角频率比表现出复杂的非线性现象，出现了周期k运动、拟周期运动和混沌运动等多种运动形式。在一定角速度时，工作在远离临界角速度区的转子系统对裂纹非常敏感，而工作在近临界角速度区的转子系统对裂纹不是特别敏感，但是裂纹对它的运动状态影响较大。该研究结果为该类转子-轴承系统的安全运行与故障诊断提供了一定的理论参考。     

A novel method for slant crack detection in rotors based on turning in two directions

This paper presents a novel way to detect fatigue slant cracks in rotors based on theoretical discussion. Hence, the dynamic behaviour of a Jeffcott rotor system with a mid-span slant crack under arbitrary crack orientations is studied. First, using concepts of fracture mechanics, the flexibility matrix and subsequently the system’s stiffness matrix are calculated. A symmetric relation for a global stiffness matrix is presented and proved. Next, the motion equations of the system that are obtained in four directions, two transverse, one torsional and one longitudinal, are solved using the Runge–Kutta numerical method. The characteristics of crack orientations for angles greater than 90° (transverse crack) are investigated in detail and their influence on the elements of the crack compliance matrix is presented. Also, slant crack characteristics with complementary angles are compared to each other. It is shown that the difference between cracked systems with complementary angles is only in 3rd row (3rd column) of the crack compliance matrix, and also it is shown that due to the presence of a slant crack, the system responses in forward and backward motion are different. Using the frequency responses of the shaft obtained, a technique to detect the existence of slant cracks on the shaft was proposed. This novel method is a simple way that can be used for slant crack detection in rotors.     

滑动轴承-转子系统非线性裂纹故障特征及其实验研究

由于材料缺陷以及疲劳运转等多种因素，轴承-转子系统常出现轴上裂纹故障，进一步发展会产生断轴巨大事故。本文考虑滑动轴承支承的单盘转子系统，分析轴上裂纹对系统振动特性的影响，并采用谐波小波变换技术分析实验结果，结果表明在充分考虑支承条件的基础上，裂纹的存在不仅在频域上出现了亚频、超频的频率分量，在时域上也有明显的奇异现象。说明谐波小波变换作为时域分析的有力工具，可以用于滑动轴承-转子系统裂纹故障的早期诊断。     

Effects of flexible support stiffness on the nonlinear dynamic characteristics and stability of a turbopump rotor system

Using a flexible support is an efficient approach to solving the subsynchronous problems in a turbopump. In this paper, nonlinear rotordynamic analysis of a liquid fuel turbopump with a flexible support is presented using a dynamic modeling including two key destabilizing factors, nonlinear hydrodynamic forces induced by seals and internal rotor damping. The methodology of the partitioned direct integration method (PDIM) is described for reducing the computational efforts efficiently. Combining the PDIM and the shooting method, a nonlinear stability analysis of the rotor system is performed effectively. The numerical results, which are in good agreement with test data, indicate that the effects of flexible support stiffness k on the dynamic characteristics and stability of the rotor system are significant. The first critical speed of the rotor system rises as a nonlinear function of k markedly. The second critical speed varies slightly and approximates a linear variation as k increases. The onset speed of instability of the rotor system rises initially and then reduces as k increases. The effect of seal nonlinearities at low k is contrary to that at high k and the effect of seal length on the system stability is more significant than that of seal radius. The results explain the nature of the subsynchronous motion of a turbopump rotor system with flexible support and can be used in the design and operation of a liquid fuel turbopump rotor system to eliminate its rotordynamic problem.     

Bifurcation and chaotic response of a cracked rotor system with viscoelastic supports

Cracks appearing in the shaft of a rotary system are one of the main causes of accidents for large rotary machine systems. This research focuses on investigating the bifurcation and chaotic behavior of a rotating system with considerations of various crack depth and rotating speed of the system’s shaft. An equivalent linear-spring model is utilized to describe the cracks on the shaft. The breathing of the cracks due to the rotation of the shaft is represented with a series truncated time-varying cosine series. The geometric nonlinearity of the shaft, the masses of the shaft and a disc mounted on the shaft, and the viscoelasticity of the supports are taken into account in modeling the nonlinear dynamic rotor system. Numerical simulations are performed to study the bifurcation and chaos of the system. Effects of the shaft’s rotational speed, various crack depths and viscosity coefficients on the nonlinear dynamic properties of the system are investigated in detail. The system shows the existence of rich bifurcation and chaos characteristics with various system parameters. The results of this research may provide guidance for rotary machine design, machining on rotary machines, and monitoring or diagnosing of rotor system cracks.     

非线性碰摩力对碰摩转子分叉与混沌行为的影响

研究了具有非线性碰摩力的转子局部碰摩的分叉与混沌运动,利用计算机仿真对某发动机转子的碰摩故障进行了数值模拟,讨论了转子系统参数的变化对转子混池运动状态的影响,并与碰摩实验结果进行了比较,发现了具有非线性碰摩力的转子局部碰摩转子系统的各种多周期运动和混沌运动及其演变过程。     

螺桨转子颤振涡动的一种算法

介绍螺桨转子系统颤振涡动的一种算法。本算法考察桨叶的振动变形，桨轴－支承系统的振动特性，以及螺转子的不平衡力。利用本算法对一模型螺桨转子和一实际螺桨转子进行了分析计算，对螺桨转子轴头动刚度、浆叶弹性变形、桨盘不平衡度等因素对螺桨转子系统颤振涡动的影响进行了分析，表明螺桨转子轴头动刚度下降时，螺浆发生颤振涡动的极限飞行速度下降。模型螺桨转子的计算结果与风洞试验结果相当吻合，证明本算法是正确的。     

非稳态非线性油膜力作用下柔性轴裂纹转子的动力特性分析

分析了在动载轴承非稳态非线性油膜力作用下，具有横向裂纹柔性轴Jeffcott转子在非线性涡动影响下的动力特性。通过数值计算表明，在油膜失稳转速前，随着裂纹轴刚度变化比的增大，系统在低转速区域内具有丰富的非线性动力行为，出现倍周期分叉及混沌现象，涡动振幅随转速升高而减小，直到非稳态非线性油膜失稳，在无裂纹转子油膜临界失稳点处发现了类Hopf分叉现象，系统运动由平衡变为拟周期运动；裂纹转子在油膜临界失稳时的系统运动亦为拟周期运动，裂纹转子轴刚度变化对油膜失稳点及油膜失稳之后转子的运动影响不大，转子系统作拟周期运动。     

Rubbing analysis of a nonlinear rotor system with surface coatings

Taking into account surface coatings painted on disc and casing, a nonlinear rotor system is established for simulating unbalance-rubbing coupled fault. During the modeling process of shaft, the nonlinear geometric relation between displacement and strain is considered. According to the Hamilton's principle, the restoring force between disc and shaft is described by the equivalent spring and the equivalent damper, and then the equivalent dynamic model is further set up. For contact analysis, the novel contact force model is employed to describe the impact force between disc and casing. Meanwhile, the Coulomb model is used to simulate the frictional force. The motion equations of the equivalent dynamic model are solved numerically and the corresponding dynamic behaviors are analyzed by bifurcation diagram, whirl orbit and Poincaré map. The relationship between equivalent linear/nonlinear stiffness and structural parameters is analyzed in detail. Moreover, the effects of eccentricity of disc, surface coatings and radius of shaft on the dynamic characteristic of the equivalent model are discussed.     

Parametric instability of a Jeffcott rotor with rotationally asymmetric inertia and transverse crack

Both the rotationally asymmetric inertia and transverse crack frequently appear in the rotor system. The parametric excitations induced by this two features cause instability and severe vibration under certain operating conditions. Thus, the parametric instability of a Jeffcott rotor with asymmetric disk and open transverse crack is studied analytically. The vibration equations of four degrees-of-freedom of the system are established, and the stiffness coefficients of cracked rotor shaft are derived based upon the compliance method and strain energy release rate method. Then, utilizing the harmonic balance method and Taylor expansion technique, the unstable widths of simple and combination instability regions (SIR and CIR) are solved approximately. For a practical rotor system, the approximate unstable widths are verified by the Floquet numerical analysis. The effects of crack depth and position upon the unstable widths are discussed, and the conditions for zero unstable points (ZUPs) are given: Besides the asymmetric angle should be π/2 (for SIR) or 0 (for CIR), the relationships between the inertia asymmetry and crack parameters (depth and position) are also presented analytically. These results would be useful for crack detection and instability control of the asymmetric rotor-bearing system.     

Nonlinear dynamic force transmissibility of a flywheel rotor supported by angular contact ball bearings

The dynamic force transmissibility (DFT) of aerospace flywheel rotor system (FRS) supported by angular contact ball bearings (ACBBs) is examined in this paper. The influence of combined loads and contact angle variation is considered in the Sjovall formula to accurately solve the load distribution and nonlinear stiffness of ACBB. Subsequently, the lateral vibration model of FRS is established by considering the nonlinear stiffness characteristics of ACBB. The DFT of the system is solved via harmonic balance method and arc length continuation, and the stability of the results is determined. Numerical integration and dynamic tests are utilized to verify the accuracy of harmonic balance results. Based on the proposed model, the effects of rotor unbalance excitation, axial preload, and rotor damping on the DFT of the system are discussed. The soft-stiff transition phenomenon is observed in terms of the varying supporting stiffness of ACBB wherein deformation is measured under axial preload. The value of rotor unbalanced mass determines the nonlinear characteristics of FRS. The results provide an important reference for dynamic performance evaluation and vibration isolation device design of aerospace FRS.

     

转子裂纹识别仿真研究中的小波时频分析方法

谐波共振是识别转子裂纹的重要依据，但由于转子裂纹的弱激励、非线性、非平称稳等特性，导致利用传统信号处理方法不能准确有效地获取系统的谐波共振特性，从而难于识别出裂纹；小波时频分析方法是处理非线性、非平稳信号的强有力工具，将小波时频分析方法引入到裂纹识别的仿真研究中，基于建立的裂纹转子动力学模型，分析了利用小波时频分析方法识别裂纹的可行性。偏心激励转子裂纹故障识别的仿真研究表明了该方法的有效性。     

On stretching of a bar capable of undergoing phase transitions

The dynamic processes in an elastic bar composed of a material, which is capable of undergoing phase transitions, are under consideration. We use a model of an elastic body with non-convex strain energy potential. The bar with variable cross-sectional area is considered. Propagation of the phase boundary along the bar loaded with time-dependent tensile forces is investigated. It is assumed that the phase boundary moves at a variable speed. The problem is solved analytically by using two approaches, namely, the full dynamic approach and the quasi-static (kinetic) approach. The results obtained by means of these two methods are compared.     

Nonlinear dynamics of a spur gear pair with force-dependent mesh stiffness

Time-varying mesh stiffness is one of the main excitation sources of a gear system, and it is also considered as an important factor for the vibration and noise of gears. Thus, this excitation is usually taken as an input into the gear dynamic model to obtain the system dynamic responses. However, the mesh stiffness of a gear pair is actually nonlinear with respect to the dynamic mesh force (DMF) that fluctuates during the operation of gears. Therefore, the dynamic model of gears with the quasi-static mesh stiffness calculated under a constant load is not accurate sufficiently. In this paper, a dynamic model of spur gear is established with considering the effect of the force-dependent time-varying mesh stiffness, backlash and profile deviation. Due to the nonlinear relationship between the mesh stiffness and the load for each tooth pair, it needs first to determine the load sharing among tooth pairs and then calculate the overall mesh stiffness of the gear pair. As the mesh stiffness and DMF are related, the mesh stiffness is no longer directly taken into the gear dynamic model as an input, but is jointly solved with the numerical integration process using the gear dynamic model. Finally, the dynamic responses predicted from the established gear dynamic model are compared with the experimental results for validation and compared with the traditional models to reveal their differences. The results indicate that the established dynamic model of spur gear transmission has a wider application range than the traditional models.