Influence of Interaction Between Torsion and Bending on Long-Term Nonlinear Rotor Dynamics

1999 ◽  
Author(s):  
Jiazhong Zhang ◽  
Bram de Kraker ◽  
Dick H. van Campen
Keyword(s):  
Critical Speed ◽  
Floquet Theory ◽  
Rotor Dynamics ◽  
Steady State Response ◽  
Bending Vibrations ◽  
Bending Vibration ◽  
State Response ◽  
Stability And Bifurcation ◽  
The Stability

Abstract An elementary system with gears and excited by unbalance mass has been constructed for analyzing the interaction between torsion and bending vibration in rotor dynamics. For this system, only the interaction caused primarily by unbalance mass has been investigated. The stability and bifurcation characteristics of the system have been studied by numerical computation based on Hopf bifurcation and Floquet theory. The results show that the interaction between torsion and bending vibrations can affect the stability and bifurcation of the unbalance response, in particular the onset speed of instability. In addition to the above, the interaction also affects the steady-state response. To investigate the influence of unbalance mass, the periodic solution and its stability have been studied near the first bending critical speed of the decoupled system. All the results show that the coupling of torsion and bending vibrations can have a significant influence on the nonlinear dynamics of the whole system.

A Numerical Study of the Stable Dynamic Behavior of Radial Face Seals With Grooved Faces

1997 ◽  
Vol 119 (3) ◽  
pp. 507-513 ◽  
Author(s):  
V. Person ◽  
B. Tournerie ◽  
J. Freˆne
Keyword(s):  
Dynamic Behavior ◽  
Numerical Study ◽  
Steady State Response ◽  
Kinematic Parameters ◽  
State Response ◽  
Dynamic Tracking ◽  
Principal Effect ◽  
Face Seals ◽  
The Stability ◽  
Hydrodynamic Effects

This paper presents a simple numerical method for modeling the dynamic tracking modes of a grooved face seal. The stability is verified using a method derived from that developed for smooth face seals. The method, enabling the calculation of the kinematic parameters which describe the steady-state response of the grooved seal, is of interest in designing this type of seal. A parametric study is presented for the case of a rotor face with eight semicircular grooves. The principal effect of the grooves is to increase the hydrostatic component of the load. In turn, this makes the seal less sensitive to fluctuations of the hydrodynamic phenomena. Sinusoidal waviness is used to simulate the periodic distortions induced by the grooves and affects the dynamic behavior only in the presence of cavitation. This occurs for very small values of the film thickness and, consequently, for very small leakage flow. In this case, the dynamic response of the seal is then strongly dependent upon the hydrodynamic effects.

scholarly journals Steady-State Deflection of a Circular Plate Rotating Near Its Critical Speed

1999 ◽  
Vol 66 (4) ◽  
pp. 1015-1017 ◽  
Author(s):  
Jen-San Chen
Keyword(s):  
Steady State ◽  
Circular Plate ◽  
Critical Speed ◽  
Applied Load ◽  
Fixed Time ◽  
Steady State Response ◽  
Plate Model ◽  
State Response ◽  
Nonlinear Plate ◽  
Time Invariant

The steady-state response of a disk spinning near its critical speed and under space-fixed time-invariant load is analyzed by using von Karman’s nonlinear plate model. It is found that as the disk rotates beyond a modified critical speed there exist three steady-state deflections, among which only one is in the same direction as the applied load and is stable in the presence of space-fixed damping.

Parametric Vibrations in a Magneto-Thermo-Elastic Layer of Finite Thickness

1995 ◽  
Author(s):  
Jörg Wauer
Keyword(s):  
Magnetic Field ◽  
Finite Thickness ◽  
Elastic Field ◽  
Steady State Response ◽  
Bias Magnetic Field ◽  
Parametric Vibrations ◽  
State Response ◽  
Parametric Resonances ◽  
The Stability ◽  
The Magnetic Field

Abstract The dynamic behavior of a magneto-thermo-elastic planar layer subjected to a bias magnetic field is examined. The magnetic field acts parallel to the layer surfaces and is composed of a constant and a harmonically oscillating part. In particular, the small coupled magneto-thermo-elastic vibrations superimposed on the basic steady state response due to the stationary magnetic excitation are analyzed. Attention is focused on the influence of the pulsating part of the bias magnetic field on the governing variational equations to prove the stability of the basic state. In general, the stability equations describing the perturbations of the magnetic, thermal and elastic field properties are coupled in a special form and also the parametric excitation acts in a non-classical manner. Hence the variety of possible parametric resonances seems to be limited.

Stability Analysis and Complex Dynamics of a Gear-Pair System Supported by a Squeeze Film Damper

1997 ◽  
Vol 119 (1) ◽  
pp. 85-88 ◽  
Author(s):  
Chin-Shong Chen ◽  
S. Natsiavas ◽  
H. D. Nelson
Keyword(s):  
Steady State ◽  
Periodic Solutions ◽  
Squeeze Film ◽  
Time Behavior ◽  
Steady State Response ◽  
Squeeze Film Damper ◽  
State Response ◽  
Mass Unbalance ◽  
Periodic Steady State ◽  
The Stability

The stability properties of periodic steady state response of a nonlinear geared rotordynamic system are investigated. The nonlinearity arises because one support of the system includes a cavitated squeeze film damper, while the excitation is caused by mass unbalance. The dynamical model and the procedure which leads to periodic steady state response of the system examined have been developed in an earlier paper. Here, the emphasis is placed on analyzing the stability characteristics of located periodic solutions. Also, within ranges of the excitation frequency where no stable periodic solutions are detected, the long time behavior of the system is investigated by direct integration of the equations of motion. It is shown that large order subharmonic, quasiperiodic and chaotic motions may coexist with unstable periodic response in these frequency ranges. Finally, attention is focused on practical consequences of these motions.

Dynamic Response of Eccentric Face Seals to Synchronous Shaft Whirl

2004 ◽  
Vol 126 (2) ◽  
pp. 301-309 ◽  
Author(s):  
J. Wileman
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Solution Technique ◽  
Steady State Response ◽  
Analytical Technique ◽  
State Response ◽  
Flexible Supports ◽  
Simple Matrix ◽  
The Stability ◽  
Degenerate Cases

This work provides an analytical technique for computing the seal face misalignment which results from synchronous whirl of the shaft. The eccentric dynamic response is obtained for seals in which both mating faces are mounted on flexible supports. Responses for seals with a single flexibly mounted stator or rotor are also obtained as degenerate cases of the more general result. Synchronous shaft whirl is shown to have a significant effect on the steady-state response of all these seals, while not affecting the stability threshold. The steady-state response is obtained by solution of a simple matrix equation for the general case, and can be obtained in closed form for the degenerate cases of the flexibly mounted stator or flexibly mounted rotor. A numerical example of the solution technique is presented, and the influence of speed is examined. Extension of the method to shaft motions other than synchronous whirl is briefly discussed.

Dynamic Analysis of a Geared Rotor-Bearing System With Viscoelastic Supports Under the Bow Effect

2007 ◽  
Author(s):  
T. N. Shiau ◽  
E. K. Lee ◽  
T. H. Young ◽  
W. C. Hsu
Keyword(s):  
Steady State ◽  
Dynamic Analysis ◽  
Loss Factor ◽  
Critical Speed ◽  
Transmission Error ◽  
Steady State Response ◽  
Critical Speeds ◽  
State Response ◽  
Rotor Bearing ◽  
Bearing System

This paper investigates the dynamic behaviors of a geared rotor-bearing system mounted on viscoelastic supports under considerations of the gear eccentricity, excitation of the gear’s transmission error and the residual shaft bow. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The coupling effect of lateral and torsional motions is considered in the system dynamic analysis. The investigated dynamic characteristics include system natural frequencies and steady-state response. The results show that the mass, the stiffness and the loss factor of the viscoelastic support will significantly affect system critical speeds and steady-state response. Larger loss factor and more rigid stiffness of the viscoelastic supports will suppress the systematic amplitude of resonance. Parameters, which include magnitude of the residual bow and phase angle, are also considered in the investigation of their effects on system critical speeds and steady-state response. Results show that they have tremendous influence on first critical speed when the geared system mounted on stiff viscoelastic supports. The transmission error of the gear mesh is assumed to be sinusoidal with tooth passing frequency and it will induce multiple low resonant frequencies in the system response. It is observed that the excited critical speed equals to the original critical speed divided by gear tooth number.

The Steady-State Response of a Two-Degree-of-Freedom Bilinear Hysteretic System

1965 ◽  
Vol 32 (1) ◽  
pp. 151-156 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Degree Of Freedom ◽  
Finite Limit ◽  
Steady State Response ◽  
Varying Parameters ◽  
Hysteretic System ◽  
State Response ◽  
The Stability ◽  
Two Degree Of Freedom

The method of slowly varying parameters is used to obtain an approximate solution for the steady-state response of a two-degree-of-freedom bilinear hysteretic system. The stability of the system is investigated and it is shown that such a system exhibits unbounded amplitude resonance when the level of excitation is increased beyond a certain finite limit.

On Internal Resonance of Nonlinear Nonuniform Beams

2009 ◽  
Author(s):  
Dumitru I. Caruntu
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Partial Differential Equation ◽  
Equation Of Motion ◽  
Steady State Response ◽  
Amplitude Equations ◽  
Bending Vibrations ◽  
State Response ◽  
Phase Amplitude

This paper reports the case of internal resonance three-to-one with frequency of excitation near natural frequency in the case of bending vibrations of nonuniform cantilever with small damping. The case of nonlinear curvature, moderately large amplitudes, is considered. The method of multiple scales is applied directly to the nonlinear partial-differential equation of motion and boundary conditions. The phase-amplitude equations are analytically determined. Steady-state response is reported.

Vibration Behavior of Flexible Rotor System Mounted on MR Squeeze Film Damper With Thermal Growth Effect

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Hamed Ghaednia ◽  
Abdolreza Ohadi
Keyword(s):  
Temperature Rise ◽  
Critical Speed ◽  
Electrical Current ◽  
Squeeze Film ◽  
Steady State Response ◽  
Flexible Rotor ◽  
Mr Fluid ◽  
Squeeze Film Damper ◽  
State Response ◽  
Thermal Growth

Semiactive vibration reduction devices using magnetorheological fluid (MR fluid) have proven to be effective in different engineering applications. MR squeeze film damper (MR-SFD) is one type of such devices that can be used to reduce unwanted vibration in rotary machinery. The behavior of these devices is a function of electric current, which controls the magnetic field in the lubricant and therefore causes the viscosity of MR fluid to be changed. In spite of all researches have been carried out in behavior analysis of different sorts of MR-SFDs, investigations over thermal growth effects on the efficiency of these actuators, in vibration reduction applications, are rare. In this paper, a Magnetorheological squeeze film damper (MR-SFD) has been modeled using two governing equations. First, considering the Bingham model for MR fluid (MRF), a hydrodynamic model has been presented. Second, a thermal model for the system has been modeled and used to calculate the temperature rise in the squeeze film and different damper’s components. Temperature rise in MR-SFD has been considered in this paper as a novel study. Time and frequency domain analysis using Newmark method has been performed over a finite element model of the system consisting of an unbalanced flexible rotor mounted on a pair of MR-SFDs. Obtained results show that the amplitude of rotor’s vibration is not a simple function of electrical current such that, increase in the current cannot guarantee decrease in the value of amplitude. Two major phenomena have been observed during studies; rigid dampers, and generation of new critical speed. The behavior of the rotor is deeply affected by these phenomena. The steady state response of rotor versus rotation velocity is presented for different values of electrical current, which show the effects of temperature and current on the steady state response of rotor. Generally, temperature rise results in inefficiency of MR-SFDs to suppress the vibration of the rotor, especially for rotational velocities near critical speed. Due to temperature rise, appearance of the second critical speed occurs at higher values of electrical current. In addition, it delays the “rigid damper” phenomenon causing rotor response to decrease.

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