Gyroscopic and Support Effects on the Steady-State Response of a Noncontacting Flexibly Mounted Rotor Mechanical Face Seal

1989 ◽  
Vol 111 (2) ◽  
pp. 200-206 ◽  
Author(s):  
I. Green
Keyword(s):  
Dynamic Response ◽  
Closed Form Solution ◽  
Form Solution ◽  
Steady State Response ◽  
Face Seal ◽  
State Response ◽  
High Speeds ◽  
Relative Response ◽  
Mechanical Face Seal ◽  
Stiffness And Damping

The dynamic behavior of a noncontacting rotary mechanical face seal is analyzed. A closed-form solution is presented for the response of a flexibly mounted rotor to forcing misalignments which normally exist due to manufacturing and assembly tolerances. The relative misalignment between the rotor and the stator, which is the most important seal parameter, has been found to be time dependent with a cyclically varying magnitude. The relative response is minimum when support stiffness and damping are minimum. The gyroscopic couple is shown to have a direct effect on the dynamic response. This effect is enhanced at high speeds, and depending on the ratio between the transverse and polar moments of inertia, it can either decrease or increase the dynamic response. Its effect is most beneficial to seal performance when the rotor is a “short disk.” A numerical example demonstrates that a flexibly-mounted rotor seal outperforms a flexibly mounted stator seal with regard to the total relative misalignment, the critical stator misalignment, and the critical speed.

Moving Load on a Fluid-Solid Interface: Supersonic Regime

1973 ◽  
Vol 40 (1) ◽  
pp. 137-142 ◽  
Author(s):  
T. C. Kennedy ◽  
G. Herrmann
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
Steady State Response ◽  
Entire Space ◽  
State Response ◽  
Supersonic Regime

The steady-state response of a semi-infinite solid with an overlying semi-infinite fluid subjected at the plane interface to a moving point load is determined for supersonic load velocities. The exact, closed-form solution valid for the entire space is presented. Some numerical results for the displacements at the interface are calculated and compared to the results obtained when no fluid is present.

Rotordynamics of a Mechanical Face Seal Riding on a Flexible Shaft

1994 ◽  
Vol 116 (2) ◽  
pp. 345-350 ◽  
Author(s):  
An Sung Lee ◽  
Itzhak Green
Keyword(s):  
Dynamic Analysis ◽  
High Speed ◽  
Center Of Mass ◽  
Steady State Response ◽  
Face Seal ◽  
Rotating Shaft ◽  
State Response ◽  
Flexible Shaft ◽  
Mechanical Face Seal ◽  
Rotor Center

A mechanical face seal is a triboelement intended to minimize leakage between a rotating shaft and a housing, while allowing the shaft to rotate as freely as possible. All dynamic analysis to date have concentrated on the seal itself. In reality, however, especially in high speed turbomachinery, shafts are made flexible and the dynamics of seals must be coupled with the dynamics of shafts. (Perhaps the dynamics of other triboelements, such as gears, bearings, etc., have to be included as well.) In this work the complex extended transfer matrix method is established to solve for the steady state response of a noncontacting flexibly mounted rotor mechanical face seal that rides on a flexible shaft. This method offers a complete dynamic analysis of a seal tribosystem, including effects of shaft inertia and slenderness, fluid film, secondary seal, flexibly mounted rotating element, and axial offset of the rotor center of mass. The results are then compared to those obtained from an analysis that implicitly assumed the shaft rigid. The comparison shows that shaft dynamics can greatly affect the seal performance even at relatively low speeds.

Closed-Form Steady-State Response Solution of the Twin Rotor Damper and Experimental Validation

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Richard Bäumer ◽  
Uwe Starossek
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Parameters ◽  
Control Force ◽  
Steady State Response ◽  
Active Mass ◽  
State Response ◽  
Twin Rotor

In previous research, the twin rotor damper (TRD), an active mass damper, was presented including control algorithms for monofrequent vibrations. In a preferred mode of operation, the continuous rotation mode, two eccentric masses rotate in opposite directions about two parallel axes with a mostly constant angular velocity. The resulting control force is harmonic. Within this paper, the steady-state response of a single-degree-of-freedom (SDOF) oscillator subjected to a harmonic excitation force with and without the TRD is studied. A closed-form solution is presented and validated experimentally. It is shown that the TRD provides damping to the SDOF oscillator until a certain frequency ratio is reached. The provided damping is not only dependent on the design parameters of the TRD but also depends on the steady-state vibration amplitude. The solution serves as a powerful design tool for dimensioning the TRD. The analytical closed-form solution is applicable for other active mass dampers.

Steady State Response of a Piezoelectric Power Harvesting System

Aerospace ◽  
2006 ◽  
Author(s):  
Y. C. Shu ◽  
I. C. Lien
Keyword(s):  
Steady State ◽  
Electromechanical Coupling ◽  
Damping Ratio ◽  
Closed Form Solution ◽  
Form Solution ◽  
Electromechanical Coupling Coefficient ◽  
Steady State Response ◽  
Power Normalization ◽  
Power Harvesting ◽  
State Response

We study the steady state response of a piezoelectric generator connected to an AC-DC bridge rectifying circuit plus a resistor as the basis for design analysis. In contrast with estimates obtained by various degrees of approximations in recent literature, a closed form solution is derived under the steady-state operation. We show that the average harvested power density depends on the input vibration characteristics (frequency and acceleration), the electric load, the natural frequency, the density, the mechanical damping ratio, and the overall electromechanical coupling coefficient of the system. With it an effective power normalization scheme is provided in order to compare power harvesting devices of different sizes and with different vibration inputs to estimate efficiencies. The theoretical predictions are validated and found in good agreement with our recent experiment.

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.

Nonlinear Isolator Optimization Using RMS Cost Function

2004 ◽  
Author(s):  
A. Narimani ◽  
M. F. Golnaraghi
Keyword(s):  
Closed Form Solution ◽  
Optimization Method ◽  
Relative Displacement ◽  
Form Solution ◽  
Jump Phenomenon ◽  
Nonlinear Parameters ◽  
Strongly Nonlinear ◽  
Damping Characteristics ◽  
Stiffness And Damping ◽  
Boundary Limits

In this paper using a modified averaging method the frequency response of a general nonlinear isolator is obtained. Stiffness and damping characteristics are considered cubic functions of displacement and velocity through the isolator. Analytical results are compared with those obtained by numerical integration in order to validate the closed form solution for strongly nonlinear isolator. While increasing the nonlinearity in the system improves the response of the isolator, stability and jump avoidance conditions set boundary limits for the parameters. The effects of nonlinear parameters to avoid jump phenomenon are discussed in detail. The set of parameters where the system behaves regularly are found and the nonlinear isolator is optimized based on RMS optimization method. Using this method the RMS function of absolute acceleration of the sprung mass is minimized versus the RMS function of relative displacement.

Closed-Form Representation of Beam Response to Moving Line Loads

2000 ◽  
Vol 68 (2) ◽  
pp. 348-350 ◽  
Author(s):  
Lu Sun
Keyword(s):  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Winkler Foundation ◽  
Line Load ◽  
State Response ◽  
Form Representation ◽  
Mach Numbers ◽  
Moving Line

Fourier transform is used to solve the problem of steady-state response of a beam on an elastic Winkler foundation subject to a moving constant line load. Theorem of residue is employed to evaluate the convolution in terms of Green’s function. A closed-form solution is presented with respect to distinct Mach numbers. It is found that the response of the beam goes to unbounded as the load travels with the critical velocity. The maximal displacement response appears exactly under the moving load and travels at the same speed with the moving load in the case of Mach numbers being less than unity.

Dynamic Reynolds equation for micropolar fluids and the analysis of plane inclined slider bearings with squeezing effect

2007 ◽  
Vol 221 (7) ◽  
pp. 823-829 ◽  
Author(s):  
N. B. Naduvinamani ◽  
G. B. Marali
Keyword(s):  
Reynolds Equation ◽  
Coupling Parameter ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Form Solution ◽  
Squeezing Effect ◽  
Micropolar Fluids ◽  
Slider Bearings ◽  
Damping Characteristics ◽  
Stiffness And Damping

The general dynamic Reynolds equation of sliding-squeezing surfaces with micro-polar fluids is derived for the assessment of dynamic characteristics of bearings with general film thickness. The detailed analysis is presented for the plane inclined slider bearings by using perturbation method. Two Reynolds-type equations corresponding to steady performance and perturbed characteristics are obtained. The closed form solution of these equations is obtained. The numerical computations of the results show that, the micropolar fluids provide an improved characteristics for both steady-state and the dynamic stiffness and damping characteristics. It is found that the maximum steady-load-carrying capacity is function of coupling parameter and is achieved at smaller values of profile parameter for larger values of the coupling parameter.

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