IDENTIFICATION OF MULTIPLE FAULTS IN ROTOR SYSTEMS

Many papers are available in the literature about identification of faults in rotor systems. However, they generally deal only with a single fault, usually an unbalance. Instead, in real machines, the case of multiple faults is quite common: the simultaneous presence of a bow (due to several different causes) and an unbalance or a coupling misalignment occurs often in rotor systems. In this paper, a model-based identification method for multiple faults is presented. The method requires the definition of the models of the elements that compose the system, i.e., the rotor, the bearings and the foundation, as well as the models of the faults, which can be represented by harmonic components of equivalent force or moment systems. The identification of multiple faults is made by a least-squares fitting approach in the frequency domain, by means of the minimization of a multi-dimensional residual between the vibrations in some measuring planes on the machine and the calculated vibrations due to the acting faults. Some numerical applications are reported for two simultaneous faults and some experimental results obtained on a test-rig are used to validate the identification procedure. The accuracy and limits of the proposed procedure have been evaluated.     

Dynamic axle and wheel loads identification: laboratory studies

Two methods have been reported by Zhu and Law to identify moving loads on the top of a bridge deck. One is based on the exact solution (ESM) and the other is based on the finite element formulation (FEM). Simulation studies on the effect of different influencing factors have been reported previously. This paper comparatively studies the performances of these two methods with experimental measurements obtained from a bridge/vehicle system in the laboratory. The strains of the bridge deck are measured when a model car moves across the bridge deck along different paths. The moving loads on the bridge deck are identified from the measured strains using these two methods, and the responses are reconstructed from the identified loads for comparison with the measured responses to verify the performances of these methods. Studies on the identification accuracy due to the effect of the number of vibration mode used, the number of measuring points and eccentricities of travelling paths are performed. Results show that the ESM could identify the moving loads individually or as axle loads when they are travelling at an eccentricity with the sensors located close to the travelling path of the forces. And the accuracy of the FEM is dependent on the amount of measured information used in the identification.     

Vibration response of misaligned rotors

Misalignment is one of the common faults observed in rotors. Effect of misalignment on vibration response of coupled rotors is investigated in the present study. The coupled rotor system is modelled using Timoshenko beam elements with all six dof. An experimental approach is proposed for the first time for determination of magnitude and harmonic nature of the misalignment excitation. Misalignment effect at coupling location of rotor FE model is simulated using nodal force vector. The force vector is found using misalignment coupling stiffness matrix, derived from experimental data and applied misalignment between the two rotors. Steady-state vibration response is studied for sub-critical speeds. Effect of the types of misalignment (parallel and angular) on the vibration behaviour of the coupled rotor is examined. Along with lateral vibrations, axial and torsional vibrations are also investigated and nature of the vibration response is also examined. It has been found that the misalignment couples vibrations in bending, longitudinal and torsional modes. Some diagnostic features in the fast Fourier transform (FFT) of torsional and longitudinal response related to parallel and angular misalignment have been revealed. Full spectra and orbit plots are effectively used to reveal the unique nature of misalignment fault leading to reliable misalignment diagnostic information, not clearly brought out by earlier studies.     

Robust estimation of excitations in mechanical systems using M-estimators—Experimental applications

This second part of the study presents some experimental applications to mechanical systems in which the results of excitation estimation, obtained using traditional least squares and M-estimate, are compared.The first case presented is a single input–multiple outputs system: a simple test-rig for the study of the vibrations of a two-degrees of freedom system is employed to identify the constraint displacement that causes the measured mass vibrations in presence of heavy noise.The second case is a multiple inputs–multiple outputs system: a rotor test-rig is used to identify the positions, the amplitudes and the phases of two unbalances using the vibrations measured in the bearings. In this case, also an additional theoretical part is introduced about the basics of model-based identification in the frequency domain applied to rotor dynamics.The last case is again a single input–multiple outputs system, but in an industrial application: experimental vibrations of a 320 MW steam turbo-generator are used to identify position and amount of a known balancing mass in an on-field real case.Moreover, whilst in the numerical examples presented in the first part the knowledge of the system was perfect, in these cases some uncertainties are present also in the system model.Finally, the paper introduces the use of the M-estimate technique to evaluate the adequacy the model of the system, by means of the analysis of the weights attributed to the measures as a function of the frequency of the excitation.     

Identification of dynamic characteristics of nonlinear joint based on the optimum equivalent linear frequency response function

Identification of dynamic characteristics of local nonlinearities has been aimed in this paper. The spirit of the identification method is established on Optimum Equivalent Linear Frequency response function (OELF). Dynamic behavior of nonlinear elements in system is extracted from OELF using two different techniques. The first technique is “Direct Identification Method” (DIM) in which no pre-assumed model is considered for the nonlinearity's behavior and the second technique is “Model based Identification Method” (MIM). The second technique is introduced with two different formulations, in order to take into account the practical limits due to the inaccessibility of nonlinearity location and/or indeterminability of degree of freedom. Dynamic characteristics of common nonlinearity mechanisms like cubic stiffness, pure slip, and stick-slip have been identified using the proposed technique and it has been shown that, although the proposed identification technique is simple, it does not require any sophisticated measurement hardwares and techniques, as required by most of the identification methods proposed so far. Also, the relation of this technique to harmonic balance method is discussed.     

Piston scuffing fault and its identification in an IC engine by vibration analysis

In this paper, the effects of piston scuffing fault on engine performance and vibrations are investigated. A procedure based on vibration analysis is also presented to identify piston scuffing fault. To this end, an internal combustion (IC) engine ran under a specific test procedure. The engine parameters and vibration signals were measured during the experiments. To produce piston scuffing fault, three-body abrasive wear mechanism was employed. The experimental results showed that piston scuffing fault caused the engine performance to reduce significantly. The vibration signals were analyzed in time-domain, frequency-domain and time–frequency domain. Continuous wavelet transform (CWT) was used to obtain time–frequency representations. “dmey” wavelet was selected as the optimum wavelet type for this research among different wavelet types using the three criteria of energy, Shannon entropy and energy to Shannon entropy ratio. The results of CWT analysis by “dmey” wavelet showed that piston scuffing fault excited the frequency band of 2.4–4.7 kHz in which the frequency of 3.7 kHz was affected more. Finally, seven different features were extracted from the engine vibration signals related to the frequency band of 2.4–4.7 kHz. The results indicated that maximum, mean, RMS, skewness, kurtosis and impulse factor of the engine vibration related to the found frequency band increased significantly due to piston scuffing fault. The obtained results showed that the proposed method identified piston scuffing fault and discovered the vibration characteristics of this fault like frequency band. The results also demonstrated the possibility of using engine vibrations in piston scuffing fault identification.     

IDENTIFICATION OF MODAL PARAMETERS FROM MEASURED OUTPUT DATA USING VECTOR BACKWARD AUTOREGRESSIVE MODEL

In this paper, a modal identification system that is based on the vector backward autoregressive (VBAR) model has been developed for the identification of natural frequencies, damping ratios and mode shapes of structures from measured output data. The modal identification using forward autoregressive approach has some problems in discriminating the structure modes from spurious modes. On the contrary, the VBAR approach provides a determinate boundary for the separation of system modes from spurious modes, and an eigenvalue filter for the selection of physical modes is existent in the proposed method. For convenience of application, the backward state equation established from VBAR model is transformed into a forward state equation, which is termed as transformed VFAR model in this paper. In addition, the extraction of equivalent system matrix of state equation of motion for structures from the transformed VFAR model has been developed, and then the normal modes can be calculated from the identified equivalent system matrix. Two examples of modal identification are carried out to demonstrate the availability and effectiveness of the proposed backward approach: (1) Numerical modal identification for a three-degree-of-freedom dynamic system with noise level in 20% of r.m.s of measured output data; (2) experimental modal identification of a cantilever beam. Finally, to show the advantage of the proposed VBAR approach on the selection of physical modes, the modal identification by stochastic subspace method was performed. The results from both methods are compared.     

The use of roving discs and orthogonal natural frequencies for crack identification and location in rotors

A variety of approaches that have been developed for the identification and localisation of cracks in a rotor system, which exploit natural frequencies, require a finite element model to obtain the natural frequencies of the intact rotor as baseline data. In fact, such approaches can give erroneous results about the location and depth of a crack if an inaccurate finite element model is used to represent an uncracked model. A new approach for the identification and localisation of cracks in rotor systems, which does not require the use of the natural frequencies of an intact rotor as a baseline data, is presented in this paper. The approach, named orthogonal natural frequencies (ONFs), is based only on the natural frequencies of the non-rotating cracked rotor in the two lateral bending vibration x–z and y–z planes. The approach uses the cracked natural frequencies in the horizontal x–z plane as the reference data instead of the intact natural frequencies. Also, a roving disc is traversed along the rotor in order to enhance the dynamics of the rotor at the cracked locations. At each spatial location of the roving disc, the two ONFs of the rotor–disc system are determined from which the corresponding ONF ratio is computed. The ONF ratios are normalised by the maximum ONF ratio to obtain normalised orthogonal natural frequency curves (NONFCs). The non-rotating cracked rotor is simulated by the finite element method using the Bernoulli–Euler beam theory. The unique characteristics of the proposed approach are the sharp, notched peaks at the crack locations but rounded peaks at non-cracked locations. These features facilitate the unambiguous identification and locations of cracks in rotors. The effects of crack depth, crack location, and mass of a roving disc are investigated. The results show that the proposed method has a great potential in the identification and localisation of cracks in a non-rotating cracked rotor.     

Investigation into on-road vehicle parameter identification based on subspace methods

The randomness of road–tyre excitations can excite the low frequency ride vibrations of bounce, pitch and roll modes of an on-road vehicle. In this paper, modal parameters and mass moments of inertia of an on-road vehicle are estimated with an acceptable accuracy only by measuring accelerations of vehicle sprung mass and unsprung masses, which is based on subspace identification methods. The vehicle bounce, pitch and roll modes are characterized by their large damping (damping ratio 0.2–0.3). Two kinds of subspace identification methods, one that uses input/output data and the other that uses output data only, are compared for the highly damped modes. It is shown that, when the same data length is given, larger error of modal identification results can be clearly observed for the method using output data only; while additional use of input data will significantly reduce estimation variance. Instead of using tyre forces as inputs, which are difficult to be measured or estimated, vertical accelerations of unsprung masses are used as inputs. Theoretical analysis and Monte Carlo experiments show that, when the vehicle speed is not very high, subspace identification method using accelerations of unsprung masses as inputs can give more accurate results compared with the method using road–tyre forces as inputs. After the modal parameters are identified, and if vehicle mass and its center of gravity are pre-determined, roll and pitch moments of inertia of an on-road vehicle can be directly computed using the identified frequencies only, without requiring accurate estimation of mode shape vectors and multi-variable optimization algorithms.     

A built-in force actuator for active control of lateral rotor vibration in cage induction electrical machines

In this paper means of active control of radial rotor vibrations in electrical machines are considered. We examine a built-in force actuator for active generation of force on the machine rotor. The operation of the actuator is based on electromechanical interaction between the rotor and the stator of the machine. The actuator is given a low-order linear state-space model, which is identified by using simulation data obtained from a detailed time-stepping finite element model of the machine. Simulation results obtained by using real machine data and finite element time-stepping method are presented.     

IDENTIFICATION OF DAMPING: PART 3, SYMMETRY-PRESERVING METHODS

In two recent papers (Adhikari and Woodhouse 2001 Journal of Sound and Vibration243, 43-61; 63-88), methods were proposed to identify viscous and non-viscous damping models for vibrating systems using measured complex frequencies and mode shapes. In many cases, the identified damping matrix becomes asymmetric, a non-physical result. Methods are presented here to identify damping models which preserve symmetry of the system. Both viscous and non-viscous models are considered. The procedure is based on a constrained error minimization approach and uses only experimentally identified complex modes and complex natural frequencies together with, for the non-viscous model, the mass matrix of the system. The methods are illustrated by numerical examples.     

Selection of response measurement locations to improve inverse force determination

The forces obtained by inverse methods are prone to errors. These arise due to a combination of errors in the measurements and high condition numbers in the matrix of transfer functions to be inverted. Ill-conditioning of the frequency response function matrix causes measurement errors to be magnified significantly. When the condition numbers are small, the measurement errors simply propagate without much amplification. Due to modal behaviour of the structure, the condition numbers can vary significantly over the frequency range and with the spatial location of the response measurements. The spatial variation can be quite considerable across the structure. The potential for using this characteristic to improve force determination is explored in this paper as an alternative to matrix regularization methods. The aim is to reduce error magnification in inverse methods by an ‘optimal’ spatial distribution of response locations. A method is proposed which is based on the minimization of the average condition number across the frequency range. If many possible locations are available, however, this can involve excessive calculation. An approximate method is therefore proposed which results in consistently good location selection for use in inverse force determination but involves much less computational effort. The error reduction in reconstructed forces is found to be significant in numerical simulations on a simply supported plate and in validation experiments.     

Power law damping parameter identification

The parameter estimation of a nonlinear power damping system is studied. The parameter identification method used here assumes a priori the equation of motion describing the system dynamics. The method, which is based on the measured data (acceleration), was applied to the free and forced vibrations.The identification procedure was found to be robust on the guessed value of parameters at the numerical experimentation. The parameter values were estimated with a good accuracy for both modes of system operation (free and forced) if only the measured time history was sampled at a high enough rate for the noise level contained within. It was shown that the steady state of the harmonically excited system is not the best region for the parameter identification with this method.During the experimentation the method was applied to the free vibrations in different media (air and water). The results obtained by the parameter identification method were compared to the ones obtained by separate tests and good agreement was found. The identification procedure was found to work fine for all models under consideration and the models' responses correspond well to the measured acceleration time histories.     

基于虚拟测试仪器的诊断技术及在VMTS中应用

故障诊断是一门交叉学科,广泛应用于各个领域,在飞机维修虚拟训练系统(VMTS, Virtual Maintenance Training System)平台基础上,提出基于虚拟仪器进行测试、故障定位的仿真训练策略,构建了基于需求的虚拟测试仪器模型框架,并在VMTS系统中得到应用。通过虚拟测试仪器与推理模块协同配合的方法解决了维修虚拟训练过程中普遍存在的故障诊断类型套路化问题,并且能够完成复杂状态下的故障诊断任务,满足各种故障诊断训练要求,最后以尾桨故障诊断为例,证明该方法的可行性。     

Non-linear free torsional vibrations of thin-walled beams with bisymmetric cross-section

A finite element method for studying non-linear free torsional vibrations of thin-walled beams with bisymmetric open cross-section is presented. The non-linearity of the problem arises from axial loads generated at moderately large amplitude torsional vibrations due to immovability of end supports. The derivation of the fundamental differential equation of the problem is based on the classical assumption of a thin-walled beam with a non-deformable cross-section. The non-linear eigenvalue problem is solved iteratively by series of linear eigenvalue problems until the required accuracy is obtained. Non-linear frequencies, fundamental mode shapes and axial loads computed for various amplitude of torsional vibrations of thin-walled I beams are included.     

Convergence studies on static and dynamic analyses of plates by using the U-transformation and the finite difference method

This paper presents the exact static and dynamic analyses of simply supported rectangular plates. The analytical solutions for displacements, buckling loads, natural frequencies and dynamic responses are obtained by using the double U-transformation method and the finite difference method. After an equivalent system with cyclic periodicity in two directions is established, the difference governing equation for such an equivalent system can be uncoupled by applying the double U-transformation. Then the exact analytical finite difference solutions, the exact error expressions and the exact convergence rates are derived. These results cannot be obtained if other methods are used instead.     

A load identification method based on wavelet multi-resolution analysis

Load identification, as a kind of indirect identification method, uses system characteristic and responses to calculate loads. A method based on wavelet multi-resolution analysis is proposed in this paper. By wavelet decomposition and transform at certain resolutions, the proposed method transforms the convolution relation between responses and loads in time domain into the linear multiplicative relation between system responses and wavelet responses in the wavelet domain. Loads can be identified as long as the linear multiplicative relation is solved. Qualitative and quantitative rules are proposed for selecting parameters that affect the accuracy of the proposed method, and are illustrated via numerical investigations. The method is illustrated by a multi-input-multi-output numerical simulation. A multi-input-multi-output laboratory experiment is performed to compare the proposed method with the frequency method on the identification ability.     

基于激光二极管光反馈效应的肌肉震颤测量系统

介绍一种测量肌肉震颤频率和幅度的无损伤、非接触光学方法。分析了在直接频率调制下 ,激光二极管中的光反馈效应 ,探讨了振动微小位移和速度的理论模型。设计并研制了一套基于光反馈效应的直接频率调制激光二极管光电探测系统。利用该系统对微弱机械振动信号进行了探测 ,表明该系统能用于肌肉震颤的测量。最后介绍了人体前臂内侧屈肌群紧张收缩时 ,肌肉震颤的光学测量结果     

基于遗传算法的四旋翼无人机系统参数辨识

建立准确地系统模型是实现四旋翼无人机的自动飞行控制的基础,为此提出了一种遗传算法,并将其应用于四旋翼无人机系统参数辨识当中。首先,根据四旋翼受力分析建立了小角度下的线性系统模型;然后,将遗传算法应用于线性模型未知参数的辨识中;最后,分别对比了滚转、俯仰和偏航方向的加速度值与实际测量值。实验结果表明在悬停状态或小角度飞行状态下,该辨识方法能够建立比较精确的系统模型。     

Accurate identification of the frequency response functions for the rotor-bearing-foundation system using the modified pseudo mode shape method

In this paper, an identification technique in the dynamic analyses of rotor-bearing-foundation systems called the pseudo mode shape method (PMSM) was improved in order to enhance the accuracy of the identified dynamic characteristic matrices of its foundation models. Two procedures, namely, phase modification and numerical optimisation, were proposed in the algorithm of PMSM to effectively improve its accuracy. Generally, it is always necessary to build the whole foundation model in studying the dynamics of a rotor system through the finite element analysis method. This is either unfeasible or impractical when the foundation is too complicated. Instead, the PMSM uses the frequency response function (FRF) data of joint positions between the rotor and the foundation to establish the equivalent mass, damping, and stiffness matrices of the foundation without having to build the physical model. However, the accuracy of the obtained system's FRF is still unsatisfactory, especially at those higher modes. In order to demonstrate the effectiveness of the presented methods, a solid foundation was solved for its FRF by using both the original and modified PMSM, as well as the finite element (ANSYS) model for comparisons. The results showed that the accuracy of the obtained FRF was improved remarkably with the modified PMSM based on the results of the ANSYS. In addition, an induction motor resembling a rotor-bearing-foundation system, with its housing treated as the foundation, was taken as an example to verify the algorithm experimentally. The FRF curves at the bearing supports of the rotor (armature) were obtained through modal testing to estimate the above-mentioned equivalent matrices of the housing. The FRF of the housing, which was calculated from the equivalent matrices with the modified PMSM, showed satisfactory consistency with that from the modal testing.