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.

Steady-State Dynamic Response of a Limited Slip System

1968 ◽  
Vol 35 (2) ◽  
pp. 322-326 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Slip System ◽  
External Load ◽  
Initial Conditions ◽  
Viscous Damping ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
System Nonlinearity

The steady-state response of a system constrained by a limited slip joint and excited by a trigonometrically varying external load is discussed. It is shown that the system may possess such features as disconnected response curves and jumps in response depending on the strength of the system nonlinearity, the level of excitation, the amount of viscous damping, and the initial conditions of the system.

The Steady State Response of Systems With Hardening Hysteresis

1978 ◽  
Vol 100 (1) ◽  
pp. 193-198 ◽  
Author(s):  
R. K. Miller
Keyword(s):  
Steady State ◽  
Degree Of Freedom ◽  
General Nature ◽  
Model Parameters ◽  
Steady State Response ◽  
Single Degree Of Freedom ◽  
Analytical Technique ◽  
State Response ◽  
Single Degree ◽  
Critical Model

A physical model for hardening hysteresis is presented. An approximate analytical technique is used to determine the steady-state response of a single-degree-of-freedom system and a multi-degree-of-freedom system incorporating this model. Certain critical model parameters which determine the general nature of the responses are identified.

Stability of a Vehicle on a Multispan Simply Supported Guideway

1978 ◽  
Vol 100 (4) ◽  
pp. 326-332 ◽  
Author(s):  
Y. I. Chung ◽  
J. Genin
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Suspension System ◽  
Performance Criteria ◽  
Inertial Effect ◽  
Steady State Response ◽  
Span Length ◽  
Simply Supported ◽  
State Response

The dynamic response of a vehicle, with a conventional suspension system, traversing a multispan simply supported guideway system is studied parametrically. The steady state response of the system and conditions for dynamic instabilities are presented for the case where the ratio of vehicle length/span length is small. Using vehicle heave acceleration and maximum guideway deflection as performance criteria, it is shown that the interactive inertial effect is significant, even at relatively low traversing speeds.

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.

Response of Cylindrical Sandwich Shells to Moving Loads

1967 ◽  
Vol 34 (1) ◽  
pp. 81-86 ◽  
Author(s):  
G. Herrmann ◽  
E. H. Baker
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Initial Stress ◽  
Axial Stress ◽  
Steady State Response ◽  
Sandwich Shell ◽  
Moving Loads ◽  
Axially Symmetric ◽  
Cylindrical Sandwich Shell ◽  
State Response

This paper presents an analysis into the dynamic response of a long cylindrical sandwich shell under a moving axially symmetric ring load. The shell is assumed to be orthotropic and subjected to an initial axial stress. The uniform velocity of the load is prescribed and only the steady-state response is considered. Numerical results indicate the effects of various relevant parameters. The behavior of orthotropic sandwich cylinders under initial stress is compared with that of homogeneous isotropic cylindrical shells free of initial stress, and differences are pointed out.

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.

Dynamic Response of Pressurized Thin Cylindrical Shells Subjected to Torsional Loads

1973 ◽  
Vol 95 (3) ◽  
pp. 797-802
Author(s):  
P. G. Kessel ◽  
N. K. Liao
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Biaxial Stress ◽  
Steady State Response ◽  
Thin Cylindrical Shell ◽  
Line Load ◽  
State Response ◽  
Dynamic Loadings ◽  
Torsional Loads ◽  
Shell Geometry

This paper presents a theoretical analysis of the transient and steady-state response of a thin cylindrical shell of finite length, simply supported at both ends, under a uniform initial biaxial stress and subjected to either a circumferentially tangential harmonic point force of a sinusoidally distributed harmonic line load acting in the circumferential direction. The analyses are based on both Flugge’s and Donnell’s theories. Numerical results of the steady-state response are presented for both theories to illustrate the effects of various relevant parameters on the dynamic deflection, and to provide a direct comparison between Donnell’s and Flugge’s theories for dynamic loadings. This paper establishes the range of shell geometry for which Donnell’s equations give satisfactory results in predicting the steady-state response. The dynamic behavior after the first resonant frequency and the effect of initial stress on the dynamic response are also pointed out.

Steady-State Analysis of Mechanical Seals With Two Flexibly Mounted Rotors

1997 ◽  
Vol 119 (1) ◽  
pp. 200-204 ◽  
Author(s):  
J. Wileman ◽  
I. Green
Keyword(s):  
Steady State ◽  
Dynamic Behavior ◽  
Reference Frames ◽  
Rapid Determination ◽  
Equations Of Motion ◽  
Steady State Response ◽  
Mechanical Seals ◽  
State Response ◽  
Forcing Functions ◽  
Flexible Supports

The dynamic behavior of a mechanical face seal with two flexibly mounted rotors is investigated. The equations of motion are derived using linearized rotor dynamic coefficients to model the dynamic behavior of the fluid film. The equations are shown to be linear in the inertial reference with harmonic forcing functions which result from the initial misalignment of the flexible supports. A method for obtaining the steady-state response in the system is derived by transforming the equations of motion into reference frames which rotate with the shafts. The resulting equations contain constant forcing functions and can be readily solved for the magnitude of the steady-state response. The method presented allows a rapid determination of the steady-state misalignment of a seal without resorting to numerical modeling.

The Steady-State Response of the Double Bilinear Hysteretic Model

1965 ◽  
Vol 32 (4) ◽  
pp. 921-925 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Steady State Solution ◽  
Degree Of Freedom ◽  
State Solution ◽  
Steady State Response ◽  
Hysteretic Model ◽  
Jump Phenomenon ◽  
State Response ◽  
The Stability

The steady-state response of a one-degree-of-freedom double bilinear hysteretic model is investigated and it is shown that this model gives rise to the jump phenomenon which is associated with certain nonlinear systems. The stability of the steady-state solution is discussed and it is shown that the model predicts an unbounded resonance for finite excitation.

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