Showing papers on "Critical speed published in 2013"

Stability analysis for transverse breathing cracks in rotor systems

Abstract: Transverse breathing cracks have been considered a primary mode of damage in studies of rotordynamic systems In this paper, a Jeffcott rotor with a transverse breathing crack is examined, and stability of the system is investigated by Floquet theory considering the crack depth and rotating speed New breathing functions proposed in a recent publication are adopted to approximate the actual breathing mechanism of the crack Unlike previous studies wherein stability diagrams without detailed information about the stable and unstable regimes of the motion have been provided, in this work we perform a detailed study of the corresponding eigenvalues of the cracked rotor in the complex plane, and the effect of damping on the instability regions has been investigated Our study indicates that the unstable regions appear as the speed of the rotor approaches an integer fraction or an integer multiple of the critical speed of the rotor, whereas bifurcations are detected in certain unstable regimes The results also shows damping has significant influence on the structures of instability regions

Critical Speed and Resonance Criteria of Railway Bridge Response to Moving Trains

Abstract: The dynamic response of railway bridges to moving trains is complicated because of the involvement of the moving loads and the moving masses. Among various response characteristics, bridge resonance is of particular interest in terms of the structural effect and safety of the bridge. As far as the global bridge response is concerned, it is generally understood that when one of the apparent trainload excitation frequencies coincides with the fundamental natural frequency of the bridge, resonance could occur. However, such a general criterion is of little practical use because a typical trainload would involve numerous apparent frequencies (at equal intervals); consequently, for a given bridge (natural frequency), there could be many train speeds that satisfy the preceding resonance condition. Therefore, it is necessary to establish the relative severity of the resonance associated with each resonance scenario. This paper presents the development of a new resonance severity indicator, called Z factor, for the assessment of the resonance effect. It is found that the resonance severity is essentially governed by the ratio between the bridge and carriage lengths. When the carriage mass is significant, the same Z factor will apply; however, the underlying resonance speeds will change because of the altered natural frequency of the bridge-train system. Numerical results demonstrate that the proposed methods are effective for the determination of the resonance effects associated with the potential resonance speeds.

Improving the critical speeds of high-speed trains using magnetorheological technology

Abstract: With the rapid development of high-speed railways, vibration control for maintaining stability, passenger comfort, and safety has become an important area of research. In order to investigate the mechanism of train vibration, the critical speeds of various DOFs with respect to suspension stiffness and damping are first calculated and analyzed based on its dynamic equations. Then, the sensitivity of the critical speed is studied by analyzing the influence of different suspension parameters. On the basis of these analyses, a conclusion is drawn that secondary lateral damping is the most sensitive suspension damper. Subsequently, the secondary lateral dampers are replaced with magnetorheological fluid (MRF) dampers. Finally, a high-speed train model with MRF dampers is simulated by a combined ADAMS and MATLAB simulation and tested in a roller rig test platform to investigate the mechanism of how the MRF damper affects the train's stability and critical speed. The results show that the semi-active suspension installed with MRF dampers substantially improves the stability and critical speed of the train.

Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method

Abstract: The generalized differential quadrature method (GDQM) is employed to consider the free vibration and critical speed of moderately thick rotating laminated composite conical shells with different boundary conditions developed from the first-order shear deformation theory (FSDT). The equations of motion are obtained applying Hamilton’s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points lying on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical technique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.

Labyrinth Seal and Pocket Damper Seal High Pressure Rotordynamic Test Data

Abstract: The current centrifugal compressor design for the oil & gas market is more and more challenging, and the presence of many competitors is pushing technology towards both a casing size reduction and a rotational speed increase. The first point is leading to an increase in the number of wheels per rotor (to do the same service), and the second point is forcing to cross two or even three rotor modes (hence a higher control of rotor damping is necessary). The two points together are leading to increase the rotor “flexibility ratio” (defined as the ratio between the maximum continuous speed and the first critical speed at infinite support stiffness according to API standard, and finally the rotordynamic stability is very much challenged. The centrifugal compressor's rotordynamic stability is strongly related to the internal seals' dynamic behavior, and for this reason, the authors' company decided several years ago to develop internally a high pressure seal test rig to measure internal seals stiffness and damping. The rig is now in operation, and in a previous paper the authors described its main capabilities, the applied identification procedures, and the preliminary test results captured for a long labyrinth seal (smooth rotor, straight toothed stator) tested up to 200 bar. This paper is intended to show more data for the same long Laby with special focus on some peculiar test as negative preswirl test, single frequency versus multifrequency test, offset versus centered seal test. The negative preswirl test shows a drastic change in the effective damping (from destabilizing to stabilizing) and provides a support in favor of the selection of swirl reversal devices at seals upstream. The multifrequency excitation test approach (based on the concurrent presence of several frequencies not multiples at each other) is compared with a single frequency excitation providing similar results and thus confirming the soundness of the multiple effects linear superimposition assumption. The effect of a static offset (simulating the real position of a rotor inside an annular seal) is also investigated proving that the relevant impact is negligible within the range of eccentricity explored (10% of seal clearance). Moreover, a pocket damper seal (PDS) with the same nominal diameter, clearance, and effective length has been tested (up to 300 bar) and compared with the Laby. As expected, the PDS shows both a higher effective stiffness and damping at the same test conditions, so the promising results already collected in a previous test campaign which was performed on a smaller scale and lower pressure test rig were mostly confirmed with the only exception for the effective damping crossover frequency which was lower than expected.

Nonparametric Stochastic Modeling of Structural Uncertainty in Rotordynamics: Unbalance and Balancing Aspects

Abstract: This paper focuses on extending an earlier investigation on the systematic and rational consideration of uncertainty in reduced order models of rotordynamics systems. The current effort concentrates on the consistent introduction of uncertainty in mass properties on the modal mass and gyroscopic matrices as well as on the unbalance force vector. The uncertainty in mass is separated into uncertainty that maintains the rotor symmetry and the one which disrupts it. Both types of uncertainties lead to variations in the system modal matrices but only the latter induces an unbalance. Accordingly, the approach permits the selection of separate levels on the uncertainty on the system properties (e.g. natural frequencies) and on the unbalance.It was first found that the unbalance response is increased by considering the uncertainty in the rotor modal mass matrices. It was next noted that the approach presented not only permits the analysis of uncertain rotors but it also provides a computational framework for the assessment of various balancing strategies. To demonstrate this unique feature, a numerical experiment was conducted in which a population of rotors were balanced at low speed and their responses were predicted at their first critical speed. These response predictions were carried with the uncertainty in the system modal mass matrices but with or without the balancing weights effects on these matrices. It was found that the balancing at low speed may in fact lead to an increase in both the mean and 95th percentile of the response at critical speed.Copyright © 2013 by ASME

Evaluation of PCC Pile Method in Mitigating Embankment Vibrations from a High-Speed Train

Abstract: Dynamic response of a railway embankment to a high-speed train is simulated for two cases: the soft ground is improved by cast–in situ concrete pipe (PCC) piles, and the soft ground is not improved The obtained results are compared to evaluate the effectiveness of ground improvement in mitigating embankment vibration from a high-speed train The study shows that ground improvement significantly reduces embankment vibration at all considered train speeds (36–360 km/h) The possibility of vibrational resonance when the train speed approaches the critical speed governed by the soft soil is completely excluded However, vibrational resonance still happens when the train speed approaches the critical speed governed by the embankment material, and this suggests the following implication Even when the soft ground of a railway embankment system has already been improved, vibrational resonance can still happen at high train speeds Furthermore, for a given site, each ground improvement scheme results in

Investigation of the dynamic characteristics of a dual rotor system and its start-up simulation based on finite element method

Abstract: Recently, the finite element method (FEM) has been commonly applied in the engineering analysis of rotor dynamics. Gyroscopic moments, rotary inertia, transverse shear deformation and gravity can be included in computational models of rotor-bearing systems. In this paper, a finite element model and its solution method are presented for the calculation of the dynamics of dual rotor systems. A typical structure with two rotor shafts is discussed and the procedure for obtaining the coupling motion equations of the subsystems is illustrated. A computer program is developed to solve critical speeds and to simulate the transient motion. The influence of gyroscopic moments on co-rotation and counter-rotation is analyzed, and the effect of the speed ratio on critical speed is studied. The dynamic characteristics under different conditions of increasing speed during start-up are demonstrated by comparison with transient nodal displacements. The presented model provides a complete foundation for further investigation of the dynamics of dual rotor systems.

Development of a High Speed Induction Motor for Spindle Systems

Abstract: This paper deals with the analysis techniques of a high speed and high efficiency 10 kW, 30 000 rpm rated induction motor. The induction motor has been analyzed by the time-varying magnetic finite element method and the test results show that there is a possibility that the motor could be used in a high speed spindle system application. All performances of the prototype are successfully verified. All analysis techniques are introduced to develop a high speed and high efficiency induction motor made by copper die casting. The analysis techniques are composed of magnetic analysis, structural analysis, critical speed analysis, unbalance response analysis and computational fluid dynamics (CFD). CFD simulation results are compared with the experiment, and are within a 5% deviation.

Development of an ultra high speed permanent magnet synchronous motor

Abstract: To accomplish the research of a PM synchronous motor driven by 15 kW at a rated speed of 120 krpm. This paper represents an approach to minimize the eddy current losses that occur frequently at high speeds. Various simulation and testing techniques are applied to grasp the physical phenomena. Here, sleeve thickness is proposed parameter for analysis. Finally, this paper studies the developed model which represents a tendency for minimizing eddy current loss, von-Mises stress, unbalance vibration response and maximizing critical speed. It comes to the conclusion that sleeve thickness should be chosen after considering the function of mechanical stress, critical speed and unbalance vibration response of the rotor. The design efficiency is well suited to the efficiency test, having a maximum error of 2.7%.

Balancing of flexible rotors without trial weights based on finite element modal analysis

Abstract: With the continuous improvement of aviation engine performance, the engine rotor’s working speed is above the first critical speed, and some small engine rotor’s operating speed exceeds the second critical speed, thus most of the aircraft engine rotor is now flexible rotor. The primary goal of this research is to provide a new method without trial weights for flexible rotor balancing, which is based on the traditional modal balancing method and combines the dynamic characteristics of the rotor, such as the model shape, obtained by using finite element analysis software, the critical speed, the modal damping ratio, and so on. To demonstrate the validity and accuracy of the new method, two experiments are carried out. One is on a four-disk simply supported structure rotor experiment, which is balanced by using three balancing planes. After balancing the amplitude of the rotor through the first critical speed is reduced 80%. The other is on a turboshaft engine power turbine rotor which had been balanced quit...

Vibration and Critical Speed of Orthogonally Stiffened Rotating FG Cylindrical Shell Under Thermo-Mechanical Loads Using Differential Quadrature Method

Abstract: In this article, an approximate solution using differential quadrature method is presented to investigate the effects of thermo-mechanical loads and stiffeners on the natural frequency and critical speed of stiffened rotating functionally graded cylindrical shells. Transverse shear deformation and rotary inertia, based on first-order shear deformation shell theory (FSDT), are taken into consideration. The equations of motion are derived by the Hamilton's principle while the stiffeners are treated as discrete elements. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of the constituents. The temperature field is assumed to be varied in the thickness direction. The equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations applying the DQM. The results obtained include the relationship between frequency characteristics of different power-law index, rotati...

Bifurcation\instability forms of high speed railway vehicles

Abstract: The China high speed railway vehicles of type CRH2 and type CRH3, modeled on Japanese high speed Electric Multiple Units (EMU) E2 series and Euro high speed EMU ICE3 series possess different stability behaviors due to the different matching relations between bogie parameters and wheel profiles. It is known from the field tests and roller rig tests that, the former has a higher critical speed while large limit cycle oscillation appears if instability occurs, and the latter has lower critical speed while small limit cycle appears if instability occurs. The dynamic model of the vehicle system including a semi-carbody and a bogie is established in this paper. The bifurcation diagrams of the two types of high speed vehicles are extensively studied. By using the method of normal form of Hopf bifurcation, it is found that the subcritical and supercritical bifurcations exist in the two types of vehicle systems. The influence of parameter variation on the exported function Rec 1(0) in Hopf normal form is studied and numerical shooting method is also used for mutual verification. Furthermore, the bifurcation situation, subcritical or supercritical, is also discussed. The study shows that the sign of Re(λ) determinates the stability of linear system, and the sign of Rec 1(0) determines the property of Hopf bifurcation with Rec 1(0)>0 for supercritical and Rec 1(0)<0 for subcritical.

Non-linear dynamical analysis for an axially moving beam with finite deformation

Abstract: Non-linear dynamical analysis of a simply supported translating beam considering the interactions between beam translation and flexible deformation is presented. The extended Hamilton's principle is employed to derive the equations of the longitudinal and transverse vibration of the beam under finite deformation theory which are non-linearly coupled. Runge–Kutta method is utilized to solve the non-linear governing equations. The numerical results describe the coupling responses between the beam extension and flexible deformation where the higher the axial velocity is, the stronger the interactions will be. Furthermore, numerical analysis also demonstrates that the resulting responses are distinctly different under small deformation theory and finite deformation theory, and there exists a critical speed under small deformation theory. When the speed exceeds the critical speed, the system becomes unstable because of the divergence or flutter instability. However, under finite deformation theory the system is always stable. Further analysis reveals that, for appropriately considering the influence of axial movement on the beam deformation, a geometrically non-linear beam theory should be utilized even if the deflection is very small. Coupling responses between the transverse and longitudinal vibrations are also numerically explored.

Three-dimensional coating and rimming flow : a ring of fluid on a rotating horizontal cylinder

Abstract: The steady three-dimensional flow of a thin, slowly varying ring of Newtonian fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder is investigated. Specifically, we study “full-ring” solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all the way around the cylinder. In particular, it is found that there is a critical solution corresponding to either a critical load above which no full-ring solution exists (if the rotation speed is prescribed) or a critical rotation speed below which no full-ring solution exists (if the load is prescribed). We describe the behaviour of the critical solution and, in particular, show that the critical flux, the critical load, the critical semi-width and the critical ring profile are all increasing functions of the rotation speed. In the limit of small rotation speed, the critical flux is small and the critical ring is narrow and thin, leading to a small critical load. In the limit of large rotation speed, the critical flux is large and the critical ring is wide on the upper half of the cylinder and thick on the lower half of the cylinder, leading to a large critical load. We also describe the behaviour of the non-critical full-ring solution, and, in particular, show that the semi-width and the ring profile are increasing functions of the load but, in general, non-monotonic functions of the rotation speed. In the limit of large rotation speed, the ring approaches a limiting non-uniform shape, whereas in the limit of small load, the ring is narrow and thin with a uniform parabolic profile. Finally, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there is a region of parameter space close to the critical solution for sufficiently small rotation speed in which backflow occurs in a small region on the upward-moving side of the cylinder.

Parameters’ changing influence with different lateral stiffnesses on nonlinear analysis of hunting behavior of a bogie

Abstract: Conventionally a railway vehicle has stable motion in low speeds, when it reaches to high speeds stability changes to unstable form. The main purpose of this article is to show the authors' view of analytical investigation of bifurcation, nonlinear lateral stability and hunting behavior of rail vehicles in a tangent track. The paper includes nonlinear primary yaw dampers, and flange contact and also bogie existence. This study contains Bogoliubov method for the analysis. Linear and nonlinear critical speeds are obtained, and changing parameters' effect in differing the speeds with altered lateral stiffness in primary suspension system has been studied. General works about hunting phenomenon show that nonlinear critical speed is less than linear one.

3D analysis of high-speed trains moving on bridges with foundation settlements

Abstract: This paper investigates the derailment of trains moving on multi-span simply supported bridges with foundation settlements or rotations. Rail irregularities, train–track–bridge interactions, and wheel/rail separations were considered in the three-dimensional nonlinear finite element analysis. A moving spring-mass with separation and contact modes was used to validate the proposed finite element model. In the parametric study, finite element results indicate that foundation settlements or rotations cause sharp displacements between two simply supported girders, which generate large train derailment coefficients. The train derailment coefficients rise with increased train speed, and they greatly increase at a critical speed. The time history displacements of a train obviously contain a jump when it passes a location with foundation settlements or rotations, so a warning system can be established using this measurement.