Stability and Unbalance Response of Centrally Preloaded Rotors Mounted in Journal and Squeeze Film Bearings

1979 ◽  
Vol 101 (2) ◽  
pp. 120-128 ◽  
Author(s):  
E. J. Hahn
Keyword(s):  
Steady State ◽  
Vibration Isolation ◽  
Journal Bearings ◽  
Squeeze Film ◽  
State Behavior ◽  
Unbalance Response ◽  
Radial Stiffness ◽  
Rolling Element ◽  
Orbit Eccentricity ◽  
Vertical Bearing

The unbalance response and stability of centrally preloaded symmetric rigid rotors are investigated. Steady state solutions for unbalance transmissibilities, orbit eccentricity radii, and stability are presented for rotors running in hydrodynamic journal bearings and in rolling element bearings which are supported in squeeze film bearings. The Ocvirk and Warner approximations are used to evaluate the fluid film forces, rendering the data applicable to any length/diameter ratio. Both pressurized (2π film) and unpressurized (π film) oil supply are considered. Pressurization has a far reaching influence on the steady state behavior of both journal and squeeze film bearings. For unpressurized bearings, conditions of multistable operation and for stability are depicted, with journal bearings exhibiting ‘half frequency whirl’ possibilities as well. The error involved in predicting vertical bearing behavior by assuming an equivalent unidirectional load equal to the unbalance load is demonstrated. For pressurized bearings multistable operation is eliminated but both squeeze film and journal bearings are unstable for most length/diameter ratios in the absence of external radial stiffness. The stabilizing effect of superimposed external radial stiffness on pressurized bearings is clearly demonstrated. While pressurized journal bearings can run stably, they are less suited than pressurized squeeze film bearings for vibration isolation.

Steady-State Performance of Squeeze Film Damper Supported Flexible Rotors

1977 ◽  
Vol 99 (4) ◽  
pp. 552-558 ◽  
Author(s):  
M. D. Rabinowitz ◽  
E. J. Hahn
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Rolling Element Bearing ◽  
Squeeze Film ◽  
Response Curves ◽  
Flexible Rotors ◽  
Steady State Operation ◽  
Bearing Life ◽  
Rolling Element ◽  
Single Mass

The synchronous steady-state operation of a centrally preloaded single mass flexible rotor supported in squeeze film bearing dampers is examined theoretically. Assuming the short bearing approximation and symmetric motions, frequency response curves are presented exhibiting the effect of relevant system parameters on rotor excursion amplitudes and unbalance transmissibilities for both pressurized and unpressurized lubricant supply. Hence, the influence of rotor flexibility, rotor mass distribution, rotor speed, bearing dimensions, lubricant viscosity, support flexibility can be readily determined, allowing for optimal rotor bearing system design. It is shown that with pressurized bearing mounts, the possibility of undesirable operation modes is eliminated and a smooth passage through the first pin-pin critical speed of the rotor is feasible, while absence of pressurization significantly limits the maximum safe unbalance in the vicinity of this critical speed. Significant decrease in transmissibility and rotor excursion amplitudes over those obtainable with rigid mounts are shown to be a practical possibility, with consequent decrease in the vibration level of the rotor mounts and prolongation of rolling element bearing life, while maintaining acceptable rotor vibration amplitudes. A design example is included to illustrate the use of the data.

Steady-State Dynamics of Smooth and Non-Smooth Systems With Strong Nonlinearities

2003 ◽  
Author(s):  
Xiaoai Jiang ◽  
Alexander F. Vakakis
Keyword(s):  
Steady State ◽  
Vibration Isolation ◽  
High Order ◽  
State Behavior ◽  
Energy Pumping ◽  
Nonlinear Energy Pumping ◽  
Clearance Nonlinearity ◽  
High Order Nonlinearity ◽  
Odd Nonlinearity ◽  
Nonlinear Energy

The nonlinear energy sinks (NESs) with strong essential stiffness nonlinearities have been shown to result in vibration isolation in the studied system. In comparison, we also studied the steady-state dynamic response of a system with its smooth high-order odd nonlinearity replaced with the best fitted nonsmooth “clearance nonlinearity”. The analysis was based on the complexification technique and the separation of the dynamic terms into the “slow-varying” and the “fast-varying” components. We found that the steady-state behavior of a system with the non-smooth NES resembles that of the system with the smooth high-order nonlinearity, preserving the nonlinear energy-pumping feature. This finding paves the way for constructing practical NESs and applying them to practical vibration-isolation problems.

Compressible Squeeze Films and Squeeze Bearings

1964 ◽  
Vol 86 (2) ◽  
pp. 355-364 ◽  
Author(s):  
E. O. J. Salbu
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Journal Bearings ◽  
Squeeze Film ◽  
Thrust Bearings ◽  
Finite Difference Solution ◽  
Squeeze Number ◽  
Gas Bearing ◽  
Compressibility Effects ◽  
Piezoelectric Devices

Experimental agreement with a finite-difference solution of the isothermal squeeze film equation was obtained for steady-state sinusoidal squeeze motion of parallel, coaxial disks. At low squeeze number, the film force is in phase with the velocity; at high squeeze number, with the displacement. Compressibility effects at high squeeze number introduce a superambient mean film pressure, so that it is possible to operate a gas bearing on squeeze effects alone. Thrust bearings, spherical bearings, and journal bearings have been successfully operated as squeeze bearings, using both electromagnetic and piezoelectric devices to generate the squeeze motion.

Transmissibility Study of a Flexibly Mounted Rolling Element Bearing in a Porous Bearing Squeeze-Film Damper

1977 ◽  
Vol 99 (1) ◽  
pp. 50-56 ◽  
Author(s):  
C. Cusano ◽  
P. E. Funk
Keyword(s):  
Steady State ◽  
Wall Thickness ◽  
Rolling Element Bearing ◽  
Squeeze Film ◽  
State Data ◽  
Squeeze Film Damper ◽  
Porous Bearing ◽  
Rolling Element ◽  
Element Bearing ◽  
Transient And Steady State

The purpose of this investigation is to study the transmissibility characteristics of a centrally preloaded porous bearing squeeze-film damper supporting a rolling element bearing. Using the short-bearing approximation and isothermal, incompressible lubrication, transient and steady-state data are presented which show that, for the range of parameters considered, porous bearing dampers exhibit superior transmissibility characteristics over equivalent dampers using solid bearings. The data presented are for squeeze-film porous bearings having a wall thickness-to-length ratio of 0.1 and three degrees of permeability, including the case of zero permeability which corresponds to a solid bearing.

Unbalance Response of a Jeffcott Rotor Incorporating Short Squeeze Film Dampers

1989 ◽  
Author(s):  
A. El-Shafei
Keyword(s):  
Fast Algorithm ◽  
Vibration Isolation ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Unbalance Response ◽  
Squeeze Film Dampers ◽  
Jeffcott Rotor ◽  
Second Mode ◽  
Parametric Studies ◽  
Inertia Forces

The steady state unbalance response of a Jeffcott rotor incorporating short squeeze film dampers executing circular centered whirl is obtained by a fast algorithm. Savings in execution time of the order of fifty times are gained over numerical integration. Fluid inertia forces are included in the model of the squeeze film dampers. The fast algorithm allows parametric studies to be performed. It is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor, decreases the possibility of jump resonance, and decreases the useful range of vibration isolation of the dampers. It is also shown that a squeeze film damper with no centering spring (or a very soft spring) may be advantageous with regards to the unbalance response and the vibration isolation capability of the dampers.

Unbalance Response of a Jeffcott Rotor Incorporating Short Squeeze Film Dampers

1990 ◽  
Vol 112 (4) ◽  
pp. 445-453 ◽  
Author(s):  
A. El-Shafei
Keyword(s):  
Fast Algorithm ◽  
Vibration Isolation ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Unbalance Response ◽  
Squeeze Film Dampers ◽  
Jeffcott Rotor ◽  
Second Mode ◽  
Parametric Studies ◽  
Inertia Forces

The steady-state unbalance response of a Jeffcott rotor incorporating short squeeze film dampers executing circular centered whirl is obtained by a fast algorithm. Savings in execution time of the order of fifty times are gained over numerical integration. Fluid inertia forces are included in the model of the squeeze film dampers. The fast algorithm allows parametric studies to be performed. It is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor, decreases the possibility of jump resonance, and decreases the useful range of vibration isolation of the dampers. It is also shown that a squeeze film damper with no centering spring (or a very soft spring) may be advantageous with regards to the unbalance response and the vibration isolation capability of the dampers.

The Nonlinear Response of Multimode Rotors Supported on Squeeze Film Dampers

2000 ◽  
Vol 123 (4) ◽  
pp. 839-848 ◽  
Author(s):  
R. Y. Yakoub ◽  
A. El-Shafei
Keyword(s):  
Differential Equations ◽  
Computer Time ◽  
Squeeze Film ◽  
Fast Method ◽  
State Behavior ◽  
Unbalance Response ◽  
Analysis Theory ◽  
Squeeze Film Dampers ◽  
Modal Force ◽  
Parametric Studies

This paper describes the development of an extremely fast method to obtain the unbalance response of multiple mode rotors supported on squeeze film dampers (SFDs). Planar modal analysis theory is used to model the rotor-SFD system. Undamped critical speed analysis is performed to obtain the rotor eigenvalues and eigenvectors. The SFD nonlinear forces are included in the modal force vector. The system differential equations are constructed and are uncoupled using the orthogonal properties of modal vectors. Assuming circular orbit, consistent with planar modes, the differential equations are converted into algebraic ones. A polynomial in speed is obtained through algebraic manipulations. This polynomial represents the steady-state behavior of the rotor-SFD system. The full unbalance response is directly obtained by finding the roots of the polynomial for each particular orbit. This method is extremely fast compared to numerical integration and to iterative methods. The developed method is useful in performing parametric studies and optimum design of SFDs. Twenty-five orders of magnitude computer time savings are reported. Parametric studies of an aircraft gas turbine fan rotor supported by an SFD are presented. The parametric studies show the possibility of appropriately locating the SFD, to dampen the rotor modes. In addition, parametric studies are also used to determine the effect of the SFD parameters on the AGTFR unbalance response.

scholarly journals Investigation of the Steady-State Response of a Dual-Rotor System With Inter-Shaft Squeeze Film Damper

1985 ◽  
Author(s):  
Qihan Li ◽  
Litang Yan ◽  
James F. Hamilton
Keyword(s):  
Steady State ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Rotor System ◽  
Squeeze Film ◽  
Turbine Engine ◽  
Squeeze Film Damper ◽  
State Response ◽  
Unbalance Response

This paper presents an analysis of the steady-state unbalance response of a dual-rotor gas turbine engine with a flexible intershaft squeeze film damper using a simplified transfer matrix method. The simplified transfer matrix method is convenient for the evaluation of the critical speed and response of the rotor system with various supports, shaft coupling, intershaft bearing, etc. The steady-state unbalance response of the rotor system is calculated for different shaft rotation speeds. The damping effects of an intershaft squeeze film damper with different radial clearances under various levels of rotor unbalance are investigated.

Effect of Pressurization on the Vibration Isolation Capability of Squeeze Film Bearings

1976 ◽  
Vol 98 (1) ◽  
pp. 109-117 ◽  
Author(s):  
S. Simandiri ◽  
E. J. Hahn
Keyword(s):  
Vibration Isolation ◽  
Rolling Element Bearing ◽  
Squeeze Film ◽  
Vibration Level ◽  
Design Data ◽  
Supply Pressure ◽  
Rolling Element ◽  
Approximation Constant ◽  
Unbalance Force ◽  
Lubricant Viscosity

This paper investigates theoretically the effect of pressurization on the vibration isolation capability of centrally preloaded squeeze film bearings supporting a rigid rotor which in turn is mounted in rolling element bearings. Assuming the short bearing approximation, constant lubricant properties, and that steady state conditions have been reached with the journal center describing synchronous circular orbits about the bearing center, the theory is developed for the general case of arbitrary pressurization at either end of the bearing. The design data are for bearings pressurized at one end only as in circumferentially grooved bearings and conservatively assume that the saturation vapor pressure of the lubricant is atmospheric. These design curves show the effect of the relevant system parameters on the possibility of undesirable operation modes, on the unbalance force transmissibility and on rotor vibration amplitudes. Hence, the influence of lubricant viscosity, lubricant supply pressure, bearing dimensions, rotor speed, rotor mass, rotor unbalance and support flexibility may be readily determined, allowing for optimal system design. It is shown that significant unbalance force isolation is a practical possibility with consequent decrease in the vibration level of the rotor mounts and increase in rolling element bearing life, while maintaining rotor excursion amplitudes at an acceptable level, even with relatively high unbalance loading. In particular, with increased pressurization, the likelihood of bistable operation can be considerably reduced. The data suggest that by varying the supply pressure and/or the lubricant viscosity, the rotor bearing system may be gainfully controlled to run at minimum vibration level and/or with minimum unbalance transmissibility.

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