Showing papers on "Critical speed published in 1998"

Vibration- and friction-induced instability in disks

Abstract: The simple shape and common occurrence of disks as machine elements belies a complexity of behavior that can be an important factor in the improvement of modern machine performance. The purpose of this paper is to give a thorough account of the understanding gained from recent research investigations into the dynamics of disks. Friction-induced vibration and parametric resonance phenomena are areas of research activity that have received considerable attention. The approach taken here is to build up to the discussion of complex topics such as these by first establishing the basic principles of critical speed instability, forward and backward traveling waves, and destabilization by a transverse elastic system.

Condition monitoring of cracked rotors through transient response

Abstract: In the present study a simple Laval rotor with a transverse crack is considered. The analysis assumes that the vibrations remain small in comparison to the sag of the rotor under its own weight. If a cracked shaft rotates slowly under the load of its own weight, then the crack will open and close once per revolution. i.e. it breathes. Considering a simple hinge model which is a very good model for small cracks with the breathing action of crack, the transient vibration response of a cracked rotor passing through its critical speed is analysed. as an attempt for crack detection and monitoring. Effects of different factors such as crack depth. unbalance eccentricity with phase and acceleration influencing vibration are investigated.

Hopf Bifurcation and Hunting Behavior in a Rail Wheelset with Flange Contact

Abstract: An analytical investigation of Hopf bifurcation and hunting behavior of a rail wheelset with nonlinear primary yaw dampers and wheel-rail contact forces is presented. This study is intended to complement earlier studies by True et al., where they investigated the nonlinearities stemming from creep-creep force saturation and nonlinear contacts between a realistic wheel and rail profile. The results indicate that the nonlinearities in the primary suspension and flange contact contribute significantly to the hunting behavior. Both the critical speed and the nature of bifurcation are affected by the nonlinear elements. Further, the results show that in some cases, the critical hunting speed from the nonlinear analysis is less than the critical speed from a linear analysis. This indicates that a linear analysis could predict operational speeds that in actuality include hunting.

Effect of System Nonlinearities on Locomotive Bogie Hunting Stability

Abstract: SUMMARY This paper presents the effect of system parameters on hunting of a rail vehicle with nonlinear yaw dampers and wheel-rail interface. This study is intended to complement earlier studies by True et al. where they investigated the effect of nonlinearities stemming from creep-creep force saturation and wheel/rail contact forces. The rail vehicle is represented by a two-axle truck (bogie) that includes the dynamics of the wheelsets and the truck frame. The numerical simulation results show that yaw damping can have a mixed effect on the hunting critical speed. In some ranges, increasing damping can actually lower the critical speed, unlike the results commonly obtained from a linear model. Flange contact nonlinearities can also have a significant effect on the hunting behavior. Large lateral stiffness of the rail can increase lateral force to vertical force (L/V) ratio during hunting. Increasing the gauge clearance, however, can have an opposite effect. The effect of a variety of other parameters, su...

Free Vibration and Stability Analysis of Internally Damped Rotating Shafts With General Boundary Conditions

Abstract: Vibration analysis of an internally damped rotating shaft, modeled using Timoshenko beam theory, with general boundary conditions is performed analytically. The equations of motion including the effects of internal viscous and hysteretic damping are derived. Exact solutions for the complex natural frequencies and complex normal modes are provided for each of the six classical boundary conditions. Numerical simulations show the effect of the internal damping on the stability of the rotor system.

On the Eigenvalues and Critical Speed Stability of Gyroscopic Continua

Abstract: In order to provide analytical eigenvalue estimates for general continuous gyroscopic systems, this paper presents a perturbation analysis to determine approximate eigenvalue loci and stability conclusions in the vicinity of critical speeds and zero speed. The perturbation analysis relies on a formulation of the general continuous gyroscopic system eigenvalue problem in terms of matrix differential operators and vector eigenfunctions. The eigenvalue λ appears only as λ 2 in the formulation, and the smoothness of λ 2 at the critical speeds and zero speed is the essential feature. First-order eigenvalue perturbations are determined at the critical speeds and zero speed. The derived eigenvalue perturbations are simple expressions in terms of the original mass, gyroscopic, and stillness operators and the critical-speed/zero-speed eigenfunctions. Prediction of whether an eigenvalue passes to or from a region of divergence instability at the critical speed is determined by the sign of the eigenvalue perturbation. Additionally, eigenvalue perturbation at the critical speeds and zero speed yields approximations for the eigenvalue loci over a range of speeds. The results are limited to systems having one independent eigenfunction associated with each critical speed and each stationary system eigenvalue. Examples are presented for an axially moving tensioned beam, an axially moving string on an elastic foundation, and a rotating rigid body. The eigenvalue perturbations agree identically with exact solutions for the moving string and rotating rigid body.

Critical Speed for Floppy Disks

Abstract: This paper uses Lyapunov's method to determine the critical speed of a flexible spinning disk enclosed in a housing that hydrodynamically couples the transverse motion of the disk to the motion of the thin films of air surrounding the disk. Depending on the clamping ratio, this critical speed is three to ten times higher than the critical speed in the absence of hydrodynamic coupling and does not depend on the strength of the hydrodynamic coupling. Despite the nonlinearity of the underlying model, the critical speed problem is linear and tractable. The linearized free-vibration problem is also computed to verify the stability prediction and to examine linearized damping and stiffness as possible design criteria. The results are relevant to the design of both conventional computer floppy disks and the emerging generation of 100+ MB floppies.

Vibration Suppression of Rotating Shafts Passing Through Resonances by Switching Shaft Stiffness

Abstract: A method suggested in the past to suppress the vibrations of flexible rotor systems passing through critical speeds is reconsidered. An appropriate switching of the system stiffness (by using shape memory alloys, for instance) is utilized. To model the nonstationary system behavior more realistically, the rotor is driven by a limited power supply. A special feature is the inclusion of unequal bending stiffnesses of the shaft. The stationary and transient behavior of the motor and system characteristic and the deformation amplitudes and phase angles, are examined. Attention is focussed on the strategy for switching the stiffness to yield small resonance deflections.

Reducing Lateral Vibrations of a Rotor Passing Through Critical Speeds by Acceleration Scheduling

Abstract: A method is presented for reducing the lateral response of an imbalanced rotor accelerating or decelerating through its first lateral bending critical speed by using a variable acceleration rate. A lumped parameter model along with a numerical integration scheme is used to simulate the response of a simply supported, single disk rotor during fast acceleration and deceleration through critical speed. The results indicate that the maximum response and/or the total vibrational energy ofa rotor passing through the critical speed can be reduced significantly by using a variable acceleration schedule. That is, reducing the acceleration rate after the nominal critical speed is passed. These predictions were verified experimentally for a single disk rotor.

Nonstationary oscillations of a nonlinear rotor during acceleration through the major critical speed: Influence of internal resonance

Abstract: The Jeffcott rotor is the most widely used theoretical model in the analysis of rotor systems.This model satisfies the condition of 1:(-1)internal resonance, and we clarified the effect of this internal resonance on nonlinear steady-state oscillations at the major, twice the major and three times the major critical speeds in previous papers.In this study, we investigated nonstationary oscillations during acceleration through the major critical speed in the Jeffcott rotor and other rotor systems which almost but not exactly satisfy the 1:(-1)internal resonance relation, and investigated the influence of internal resonance.The following are clarified theoretically and experimentally.(a)Nonstationary oscillations of the Jeffcott rotor and other rotor systems whose natural frequencies almost satisfy the 1:(-1)relation are influenced by the internal resonance.(b)It is easier to pass the major critical speed of a rotor system with internal resonance than that of a rotor system with no internal resonance.(c)When the system has slight discrepancies among critical speeds, that is, almost satisfies the relation of internal resonance, the rotor can pass the major critical speed very easily with small amplitude even if the acceleration is small.

Effect of Material Properties in Certain Thermoelastic Contact Problems

Abstract: When two conforming bodies slide against each other, frictional heating and thermoelastic distortion generally causes the contacting surfaces to become convex and hence leads to a reduction in the size of the contact area. It is shown that, under such circumstances, the contact area is independent of the applied contact loads and the thermal and mechanical fields are linearly proportional to these loads. For two-dimensional problems involving a plane boundary, it is shown that there is a reduced dependence on material properties and in the case of a single material, the solution depends only on a single parameter which can be interpreted as a dimensionless sliding speed. These results extend to both steady-state and transient problems and therefore also characterize the critical sliding speed above which the system is unstable.

Influence of Axial Thrust Bearing Defects on the Dynamic Behavior of an Elastic Shaft

Abstract: In this work, the non-linear dynamic behavior of a flexible shaft is presented. The shaft is mounted in two bearings and axial load is supported by a hydrodynamic thrust bearing, at one end. The coupling between the axial thrust bearing behavior and the bending vibrations of the shaft is especially studied. The shaft is modeled by typical beam finite element including effects such as gyroscopic. A modal reduction allows reducing the number of degrees of freedom. The dynamic behavior of the bearings is considered as non-linear. The dynamic behavior is analysed with an unsteady time integration procedure. The thrust bearing provides an additional stiffness on the flexible shaft. A defect on the thrust-bearing rotor excites a critical speed.

Rotor Vibration Due to Collision With Annular Guard During Passage Through Critical Speed

Abstract: This paper deals with a nonstationary vibration of a rotor due to its collision with a guard during passage through a critical speed. An unbalanced rigid rotor supported by springs and dampers is accelerated at a constant angular acceleration and collides with an annular guard supported by springs and dampers. This dynamic process is calculated by the Runge-Kutta method, and effects of system-parameters on the process are discussed. The collision phenomenon is analyzed through two different theories. In the collision theory, the law of conservation of momentum and the coefficient of restitution are used in order to obtain rotor and guard velocities after collision. The impulse of the force induced by collision is assumed to be equal to the momentum change before and after collision. In the contact force theory, the contact force is assumed to be proportional to the overlapped displacement of the two bodies. Few differences are observed between the calculated responses based on the two theories. In some cases, the rotor executes a diverging backward whirl due to the friction force that occurs during collision with the guard and can not pass through the critical speed. The criteria maps for nonoccurrence of the backward whirl are shown.

Determination of Buckling Speed for Rotating Orthotropic Disk Restrained at Outer Edge

Abstract: The critical angular speed of rotating polar orthotropic circular plates whose outer boundary is constrained from deforming radially is obtained as a function of ply orientation angle. Because the expressions obtained for radial compressive stresses formed due to centrifugal forces were complicated, attaining a closed-form solution of the governing differential equation was not possible. Galerkin formulation of the finite element method has been resorted to, and the results are presented for a full plate and for a plate fixed at its center to a rigid shaft. Increasing the angle of ply orientation up to a certain value decreased the critical speed. In the case of a concentric shaft, increasing the shaft radius increased the critical speed, contributing to the stability of the plate.

Method for balancing a rotating body

Abstract: The method for balancing the drum (3) of a washing machine (1) involves accelerating the drum to a first speed at which a stationary imbalance is created. The position of the imbalance is registered and the drum (3) is subsequently accelerated further to a second rotational speed. This speed is above the critical speed of the drum or its bearing system and takes the drum out of a position in which the imbalance is located opposite the centre of gravity of the weights of the balancing installation. Also claimed is a device for carrying out the above method.

Lateral Dynamics and Stability of Two Full Vehicles in Tandem

Abstract: The lateral dynamics and stability of two full vehicles in tandem are investigated. The nonlinear differential equations of motion of this four-axle articulated vehicle system are presented in matrix form and then linearized. The critical forward velocity of the steady state for oversteering conditions is derived in a closed form, and the criteria for understeer, neutral steer, or oversteer are given. Uncertainty of the critical forward velocity and its sensitivity to errors in the system parameters are evaluated using the root mean square method. Conditions for nonoscillatory and oscillatory instabilities of the linearized vehicle system are given. Effects of the critical system parameters (mainly the mass distribution) on the stability are investigated.

Stability of a flexible wheelset for high speed rail vehicles with constant and varying parameters

Abstract: The stability of an elastic wheelset coupled with torsional spring and damper is studied in this paper. With flexible elements between two wheels, the advantages of both rigid and independently rotating wheel systems may be obtained. Previous investigations indicated that axle flexibility will affect the vehicle dynamic behavior and an optimal design may improve the system performance. Those studies were limited to constant wheel/rail geometry as the wheelset rolls along the track. In this paper, it is intended to determine the critical speed regions for both constant and time-varying models. The variation in conicity is assumed to be periodic thus the Floquet stability concept may be employed. The computation of the state-transition matrix is based on a Runge-Kutta algorithm.

Finite Width Effects on the Critical Speed of Axially Moving Materials

Abstract: An exact solution is provided to determine the effects of the free end boundary conditions and the slenderness ratios on the critical speed of two dimensional, axially moving materials. The axially moving beam theory and the mathematical, two-dimensional model with all edges simply supported are also considered for comparison.

Homopolar reluctance motor

Abstract: PROBLEM TO BE SOLVED: To rotate a rotating shaft in a levitating condition for high-speed rotation by magnetic levitation by positioning a magnetomotive force generating means which excites a salient pole, outside a stator provided with a torque generation drive coil which generates torque at a rotator. SOLUTION: This homopolar reluctance motor 1 is disposed, so that a field coil 5 may surround the outsides of two stators 4A, 4B, and therefore, two stators 2A, 2B, and the two stators 4A, 4B can be kept respectively in proximity to each other as much as possible. In this homopolar type reluctance motor 1, a rotating shaft 7. can be shortened, thus it is possible to increase the rigidity of the shortened rotating shaft 7. Even if the rotating shaft 7 is rotated at a high speed, therefore, no deflection is generated at both ends of the rotating shaft 7 Thus it is possible to increase critical speed, and rotate the rotating shaft 7 in a levitating condition at a high speed by means of magnetic levitation.

Speed change transition control apparatus for an automatic transmission

Abstract: Disclosed herein is a speed change transition control apparatus for an automatic transmission. The speed change transition control apparatus comprises rotational speed detection unit for detecting an input shaft rotation speed of the speed change mechanism, and a feedback control unit for controlling engagement pressure through a fluid pressure control element in such a manner that the input shaft rotation speed during a speed change follows a target rotation slope with an actual input shaft rotation speed detected at an actual inertia phase start point by the rotational speed detection unit as its starting point.