Rotating Shaft System Research Articles

Fault Diagnosis of Rotating Shaft Systems Based on Wavelet Entropy and GA-SVM

Fault Diagnosis of Rotating Shaft Systems Based on Wavelet Entropy and GA-SVM

Approach to rotor-shaft hysteretic whirl using Krylov–Bogoliubov techniques

The internal friction associated with the shaft hysteresis or with the possible release of some shrink-fit coupling exerts a destabilizing effect on the over-critical rotor running, but may be efficiently counteracted by other external dissipative sources or by a proper anisotropic configuration of the support stiffness. The present analysis considers a symmetric rotor-shaft system on viscous-flexible supports with different stiffness on two orthogonal planes containing the bearing axis. The internal friction of the shaft is described either by a linear hysteretic model or by a nonlinear Coulombian force contrasting the rotor motion relative to the shaft ends. The nonlinear equations of motion are solved using an averaging approach of the Krylov–Bogoliubov type, which yields the steady orbit depending on the support dissipation applied to damp the whirl motion, for various working conditions. The beneficial influence of the support stiffness anisotropy is clearly identified.

내부감쇠가 있는 축비대칭 구동축의 안정성 해석

This paper intends to provide the whirling characteristics of an asymmetric rotor-shaft system with a non-ideal DC motor. The equations of motion have been derived in terms of system parameters such as the internal/external damping, the asymmetry and the motor voltage. By imposing the conditions that the motor input power should be balanced by the dissipated power, steadystate whirling characteristics are obtained such as the whirling amplitude, the whirling frequency and the stability diagrams. Results show that the whirling stability is affected by the internal/external damping and the asymmetry as well as the motor voltage. Also, the whirling amplitude at the steadystate is increased and the motor speed is lowered as the internal damping becomes higher or the external damping is reduced. In addition, the asymmetry causes the variation of the whirling orbit, which becomes splitted into two distinct trajectories. Finally, non-ideal characteristics of the DC motor is found to reduce the whirling motion in case of steadystate whirling with high asymmetry and high internal damping.

Design of a Non-Contact Condition Monitoring System for the Fault Diagnosis of Shaft in Marine Propulsion System

The working condition of shaft determines whether the ship can continuously acquire propulsive force from diesel engine. It is hard to operate the contact measurement of shaft power and torque neither is it accurate, so the non- contact measurement that is easier and more flexible to use should be the direction to go. A novel contact-less shaft condition monitoring system based on photo-electronic technology is proposed in this paper. Two coding wheels and optoelectronic position sensors are settled to detect the torsion angle of a length of shaft, and the torsion angle of shaft can be quantified by logic circuits in field programmable gate array (FPGA) according to counter frequency and central angle of vane. And then the power and torque on shaft can be worked out in computer. To avoid the drift of optoelectronic device, a logic algorithm was studied to eliminate the bias of trigger point for position detector. The experimental result shows that this method is adequate for measuring the torsion angle of shaft, and gets rid of the redundant optical fiber which might induce danger in online monitoring of rotating shaft system. The design of this monitoring system gives an idea for monitoring and diagnosis of not only the shaft of marine propulsion system but also large rotating machines.

Torsional vibration measurements on rotating shaft system using laser doppler vibrometer

In this work, a laser torsional vibrameter was used to measure the torsion vibration of a rotating shaft system under electrical network impact. Based on the principles of laser Doppler velocimetry, the laser torsional vibrometer (LTV) are non-contact measurement of torsional oscillation of rotating shafts, offering significant advantages over conventional techniques. Furthermore, a highly complex shafting system is analyzed by a modified Riccati torsional transfer matrix. The system is modeled as a chain consisting of an elastic spring with concentrated mass points, and the multi-segments lumped mass model is established for this shafting system. By the modified Riccati torsional transfer matrix method, an accumulated calculation is effectively eliminated to obtain the natural frequencies. The electrical network impacts can activize the torsional vibration of shaft system, and the activized torsion vibration frequencies contained the natural frequencies of shaft system. The torsional vibrations of the shaft system were measured under electrical network impacts in laser Doppler torsional vibrometer. By comparisons, the natural frequencies by measurement were consistent with the values by calculation. The results verify the instrument is robust, user friendly and can be calibrated in situ. The laser torsional vibrometer represents a significant step forward in rotating machinery diagnostics.

Optimal design of a magneto-rheological brake absorber for torsional vibration control

This research presents an optimal design of a magneto-rheological (MR) brake absorber for torsional vibration control of a rotating shaft. Firstly, the configuration of an MR brake absorber for torsional vibration control of a rotating shaft system is proposed. Then, the braking torque of the MR brake is derived based on the Bingham plastic model of the MR fluid. By assuming that the behaviour of the MR brake absorber is similar to that of a dry friction torsional damper, the optimal braking torque to control the torsional vibration is determined and validated by simulation. The optimal design problem of the MR brake absorber is then developed and a procedure to solve the optimal problem is proposed. Based on the proposed optimal design procedure, the optimal design of a specific rotating shaft system is performed. Vibration control performance of the shaft system employing the optimized MR brake absorber is then investigated through simulation and discussion on the results is given.

Modal analysis of rotor-shaft system under the influence of rotor-shaft material damping and fluid film forces

The present work attempts to study the influences of internal rotor material damping and the fluid film forces (generated as a result of hydrodynamic action in journal bearings) on the modal behaviour of a flexible rotor-shaft system. This is relevant as both journal bearing and the internal material damping introduce tangential forces increasing with the rotor spin speed. Such forces considerably influence the dynamic behaviour of a rotor and tend to destabilize the rotor-shaft system as spin speed increases. Under this system of forces the modal behaviour of the rotor-shaft is studied to get better ideas about the dynamic behaviour of the system, estimated in terms of modal damping factors, stability limit speed, the frequency response functions, as well as the direction of whirl of the shaft in different modes. It is seen that correct estimation of internal friction, in general, and the journal bearing coefficients at the rotor spin-speed are essential to accurately predict the rotor dynamic behaviour. This serves as a first step to get an idea about dynamic rotor stress and, as a result, a dynamic design of rotors.

A reduced rotor model using modified SEREP approach for vibration control of rotors

For analysis and control of dynamic behaviour of continua, equations of motion are usually obtained after discretizing the continuum into finite elements. Thus discretization gives rise to a set of simultaneous differential equations, the number of which increases with the fineness of discretization. As an associated effect, increasing fineness increases the number of states, many of which are difficult to measure and feedback, due to impracticability of location of measurement or non-availability of proper sensor, in addition to the constraint on the cost of sensors and computation. Solution to the above problem calls for a suitable scheme to reduce the problem size, however, keeping the modal information unspoilt as far as possible. For a vibratory system, a reduced model is built by retaining modes with higher participation factor and also choosing conveniently within the retained modes, a number of pre-decided measurable states. Fewer state equations are thus found helpful for formulating suitable control law, applicable for improving the system dynamic performance over uncontrolled condition. This paper attempts first to obtain a reduced model for a rotor–shaft system, generally a non-self-adjoint system, and next uses the reduced model to implement active vibration control action using a single, stator-mounted electromagnetic actuator suitably located at a section along the rotor–shaft.

Robust design optimization of the vibrating rotor-shaft system subjected to selected dynamic constraints

The commonly observed nowadays tendency to weight minimization of rotor-shafts of the rotating machinery leads to a decrease of shaft bending rigidity making a risk of dangerous stress concentrations and rubbing effects more probable. Thus, a determination of the optimal balance between reducing the rotor-shaft weight and assuring its admissible bending flexibility is a major goal of this study. The random nature of residual unbalances of the rotor-shaft as well as randomness of journal-bearing stiffness have been taken into account in the framework of robust design optimization. Such a formulation of the optimization problem leads to the optimal design that combines an acceptable structural weight with the robustness with respect to uncertainties of residual unbalances – the main source of bending vibrations causing the rubbing effects. The applied robust optimization technique is based on using Latin hypercubes in scatter analysis of the vibration response. The so-called optimal Latin hypercubes are used as experimental plans for building kriging approximations of the objective and constraint functions. The proposed method has been applied for the optimization of the typical single-span rotor-shaft of the 8-stage centrifugal compressor.

Active control of coupled flexural-torsional vibration in a flexible rotor–bearing system using electromagnetic actuator

Rotor–shaft systems are subject to non-uniform spin speed during start-up, coast-down or any non-stationary situation changing the spin speed suddenly, e.g., load fluctuation or sudden mass-loss like loss of a blade or a part thereof. For a flexurally and torsionally compliant rotor-shaft, the dynamics under non-uniform spin-speed shows inertial coupling among transverse and torsional coordinates through mass-unbalance and gyroscopic effect. This results into coupled transverse-torsional vibration, where torsional response consists of significant harmonic components at bisynchronous spin frequency, torsional natural frequency of the shaft, and at combination frequencies corresponding to sum and difference of spin and transverse natural frequencies and twice the transverse natural frequency of the rotor-shaft. As a result of the coupling, transverse rotor motion also influences the torsional motion. The Method of Multiple Scales (MMS) is used in this work to carry out an analysis of a simplified system to get an idea about the dominant frequencies of excitation. Results of numerical simulation are presented next to show the effectiveness and influence of actively controlling the transverse rotor motion on its torsional motion, at the dominant frequencies, with the help of non-contact electromagnetic force from an actuator. Transverse vibration control is also observed to control the torsional oscillations due to coupled nature of the problem. The Stability Limit Speed (SLS) of the system is also increased as a result of application of the active control action. Constant axial torque is observed to diminish the influence of coupling, and protect the system against torsional instability, but control action is a must to stabilize the transverse vibration of the system above SLS.

Application of FEM Analysis to Fault Diagnosis of Cracked Rotor

Based on the simple crack model and the finite element method (FEM) theorem, the corresponding dynamic equation of the cracked rotor based on FEM analysis is modeled and the numerical simulation solutions are obtained. By analyzing the dynamic characteristics of cracked rotor in diverse conditions, the properties of the un-cracked rotor and cracked rotor are discussed. A valid fault diagnosis method of cracked rotor is purposed. The method demonstrates that the cracked rotor can be identified by estimating if the swing of disk center obviously accretion and appear wave crest when rotate speed is a half critical speed of rotor shaft system.

Bond Graph Modeling of an Internally Damped Nonideal Flexible Spinning Shaft

The rotating internal damping or nonconservative circulatory force in a rotor shaft system causes instability beyond a certain threshold rotor spinning speed. However, if the source loading of the drive is considered, then the rotor spin is entrained at the stability threshold and a stable whirl orbit is observed about the unstable equilibrium. As we move toward the use of more and more lightweight rotor dynamic components such as the shaft and the motor, overlooking this frequency entrainment phenomenon while sizing the actuator in the design stage may lead to undesirable performance. This applies to many emerging areas of strategic importance such as in vivo medical robots where flexible probes are used and space robotics applications involving rotating tools. We analyze this spin entrainment phenomenon in a distributed parameter model of a spinning shaft, which is driven by a nonideal dc motor. A drive whose dynamics is influenced by the dynamics of the driven system is called a nonideal source and the whole system is referred to as a nonideal system. In particular, we show the advantages of representing such nonideal drive-system interactions in a modular manner through bond graph modeling as compared to standard equation models where the energetic couplings between dynamic variables are not explicitly shown. The developed modular bond graph model can be extended to include rotor disks and bearings placed at different locations on the shaft. Moreover, the power conserving property of the junction structure of the bond graph model is exploited to derive the source loading expressions, which are then used to analytically derive the steady-state spinning frequency and whirl orbit amplitude as functions of the drive and the rotor system parameters. We show that the higher transverse modes may become unstable before the lower ones under certain parametric conditions. The shaft spinning speed is entrained at the lowest stability threshold among all transverse modes. The bond graph model is used for numerical simulation of the system to validate the steady-state results obtained from the theoretical study.

Simulation of Crack Dynamic Characteristics of Rotor Based on FEM Analysis

A new simulation method is proposed for dynamic characteristics of cracked rotor based on the finite element analysis, in which the stiffness model has been derived for the exact description of variation rules of cracked shafts. A non-linear dynamic equation is constituted according to stiffness characteristic of cracked-rotor change in time domain. Then the corresponding dynamic equation of the cracked rotor based on FEM analysis is modeled and the numerical simulation is carried out with solutions of high accuracy. At last, the dynamic characteristics of cracked rotor in diverse conditions are analyzed, and the simulation results are compared. It is shown that the non-linear oil film bearing force coupling with periodicity variety stiffness of cracked rotor has a great effect on dynamic behavior of the rotor and that the cracked rotor can be diagnosed effectively by the criterion that the swing of disk center obviously accretes and the wave crest appears when rotation speed is a half critical speed of rotor shaft system.

Viscoelastic modelling of rotor—shaft systems using an operator-based approach

Damping exists in every material in varying degrees, so materials in general are viscoelastic in nature. Energy storage, as well as dissipation in varying degrees, accompanies every time-varying deformation, with the effect that stress and strain in a material get out of phase. This work presents the development of equations of motion of a rotor—shaft system with a viscoelastic rotor after discretizing the system into finite elements. Subsequently, these equations are used to study the dynamics of the rotor—shaft system in terms of stability limit of spin speed and time response of a disc as a result of unbalance. The primary inspiration for a viscoelastic model arises from the need to capture the influence of broad band spectral behaviour of rotor—shaft materials, primarily polymers and polymer composites, which are principally the materials of light rotors, on the dynamics of rotor—shaft system. For this, the material constitutive relationship has been represented by a differential time operator. Use of operators enables one to consider general linear viscoelastic behaviours, represented in the time domain by multi-element (three, four, or higher elements) spring—dashpot models or internal variable models, for which, in general, instantaneous stress and its derivatives are proportional to instantaneous strain and its derivatives. Again such representation is fairly generic, in a sense that the operator may be suitably chosen according to the material model to obtain the equations of motion of a rotor—shaft system. The equations so developed may be easily used to find the stability limit speed of a rotor—shaft system as well as the time response when the rotor—shaft system is subjected to any dynamic forcing function.

Active Vibration Control of Flexible Rotors on Maneuvering Vehicles

This paper presents a simulation to actively control transverse vibration of a flexible rotor shaft system mounted on a moving vehicle (e.g., a ship or an aircraft). Discretizing the rotor continuum with beam finite elements, equations of motion are written with respect to a noninertial frame attached to the frame of the moving vehicle. Such equations are linear but contain time-varying parametric terms due to the motion of the carrier vehicle. Through numerical simulation, it is shown that the transverse response in the bending vibration of the rotor shaft relative to the supporting structure is significantly influenced by the inertia force, as well as the parametric excitations due to vehicle motion. A control strategy is proposed using an electromagnetic actuator placed at a suitable location along the span of the rotor, and it is found extremely useful in reducing the vibration of the rotor and improving its stability. Examples are given in support by studying both the uncontrolled and the controlled motion of a rotor shaft system carried by an aircraft undergoing two different kinds of maneuvers.

Active vibration control of unbalanced flexible rotor–shaft systems parametrically excited due to base motion

Rotor vibrations caused by large time-varying base motion are of considerable importance as there are a good number of rotors, e.g., the ship and aircraft turbine rotors, which are often subject to excitations, as the rotor base, i.e. the vehicle, undergoes large time varying linear and angular displacements as a result of different maneuvers. Due to such motions of the base, the equations of vibratory motion of a flexible rotor–shaft relative to the base (which forms a non-inertial reference frame) contains terms due to Coriolis effect as well as inertial excitations (generally asynchronous to rotor spin) generated by different system parameters. Such equations of motion are linear but time-varying in nature, invoking the possibility of parametric instability under certain frequency–amplitude combinations of the base motion. An investigation of active vibration control of an unbalanced rotor–shaft system on moving bases is attempted in this work with electromagnetic control force provided by an actuator consisting of four electromagnetic exciters, placed on the stator in a suitable plane around the rotor–shaft. The actuator does not levitate the rotor or facilitate any bearing action, which is provided by the conventional suspension system. The equations of motion of the rotor–shaft continuum are first written with respect to the non-inertial reference frame (the moving base in this case) including the effect of rotor internal damping. A conventional model for the electromagnetic exciter is used. Numerical simulations performed on the flexible rotor–shaft modelled using beam finite elements shows that the control action is successful in avoiding the parametric instability, postponing the instability due to internal material damping and reducing the rotor response relative to the rigid base significantly, with sufficiently low demand of control current in comparison with the bias current in the actuator coils.

Special issue on recent advances in nonlinear rotordynamics

This issue of Nonlinear Dynamics is devoted to actual problems in rotordynamics. Rotating machinery plays an important role in many disciplines of engineering. The dynamics of such machines are rich in nonlinearity so that a survey on topics concerning nonlinear phenomena in rotor dynamics is interesting for theory and practice. In organizing this issue, we did not intend to target one special topic within this field. We simply wanted to reflect its breadth of interests. The results of this informal survey are published in this issue indicating that many different problems occur. Nine contributions are collected from all over the world. Okabe and Cavalca investigate the dynamics of systems with a nonlinear model of tilting pad bearings including turbulence effects. Boyaci et al. perform an analytical bifurcation analysis of a rotor supported by floating ring bearings while Schweizer studies oil whirl, oil whip and whirl/whip synchronization occurring in such systems. Szolc et al. examine the nonlinear and parametric vibrations of rotor-shaft systems as fault identifi-

Damage identification in vibrating rotor-shaft systems by efficient sampling approach

In the paper a stochastic method for fault detection and identification in the shafts of rotating machines is proposed. This approach is based on the Monte Carlo simulations of rotor-shaft lateral–torsional–longitudinal vibrations mutually coupled by transverse cracks of various possible and randomly selected depths and locations on the shaft. For this purpose the structural hybrid model of a real faulty object is applied. This model is characterized by a high practical reliability and great computational efficiency, so important for many hundred thousand single numerical simulations necessary for a creation of the databases applied for inverse problem solution finally leading to crack identification. These databases are created with an arbitrary assumed probability densities of crack parameters which ensures appropriate spread of the dynamic responses of the considered faulty mechanical system. A sufficiently large database determined for the investigated object enable us to estimate almost immediately, i.e. within less than 1 s, the crack depth and axial position with identification errors not exceeding 9% and 5%, respectively. Thus, the proposed method seems to be a very convenient diagnostic tool for engineering applications in the industry.

Nonlinear and parametric coupled vibrations of the rotor-shaft system as fault identification symptom using stochastic methods

In the paper several stochastic methods for detection and identification of cracks in the shafts of rotating machines are proposed. All these methods are based on the Monte Carlo simulations of the rotor-shaft lateral-torsional-longitudinal vibrations mutually coupled by transverse cracks of randomly selected depths and locations on the shaft. For this purpose there is applied a structural hybrid model of a real cracked rotor-shaft. This model is characterized by a high practical reliability and great computational efficiency, so important for hundreds of thousands numerical simulations necessary to build databases used in solving the inverse problem, i.e. crack parameter identifications. In order to ensure a good identification accuracy, for creating the Monte Carlo samples of data points there are proposed special probability density functions for locations and depths of the crack. Such an approach helps in enhancing databases corresponding to the most probable faults of the rotor-shaft system of the considered rotor machine. In the presented study six different database sizes are considered to compare identification efficiency and accuracy of considered methods. A sufficiently large database enables us to estimate almost immediately (usually in less than one second) the crack parameters with precision that is in most of the cases acceptable in practice. Then, as a next stage, one of the proposed fast improvement algorithms can be applied to refine identification results in a reasonable time. The proposed methods seem to provide very convenient diagnostic tools for industrial applications.

Contoured shaft and rotor dynamics

Abstract The dynamics of shaft–rotor systems, where the shaft profiles are contoured, are considered. Shafts with diameters which are functions of the shaft length are analysed. Procedures enabling the determination of the deflection, slope, bending moment and shear force at the extremities of the shaft are employed. Resonance, critical speed or whirling frequency conditions are computed using simple harmonic response methods. The response of the system for particular shaft–rotor dimensions and rotational speeds is determined, establishing the dynamic characteristics in the vicinity of the whirling speed. A cantilevered shaft–rotor system with an exponential – sinusoidal profile is investigated for purposes of illustration. The flexibility of the approach and the general applicability of the technique proposed is emphasised.