Stability of Rotor-Bearing Systems With Generalized Support Flexibility and Damping and Aerodynamic Cross-Coupling

1975 ◽  
Vol 97 (3) ◽  
pp. 461-469 ◽  
Author(s):  
R. E. Warner ◽  
A. I. Soler

This paper examines stability of the flexible single mass rotor, acted on by motion induced forces due to aero-dynamic cross-coupling and supported most generally by oil film tilting pad bearings which are in turn mounted on flexible, damped supports. Plotted results include the frequency dependent spring and damping coefficients for the 4-pad tilting pad bearing, damping coefficients for the 360-deg squeeze bearing and stability plots of rotor-bearing systems including aerodynamic cross-coupling, the 4-pad tilting pad bearing and the 150-deg partial arc bearing with various support arrangements.

1978 ◽  
Vol 100 (1) ◽  
pp. 165-172 ◽  
Author(s):  
E. A. Bulanowski

A simplified stability analysis for flexible rotors in tilting pad bearings is developed which provides a convenient and practical approach for the consideration of nonsynchronous vibrations during the design phase of rotor bearing systems. It is known that the synchronous unbalance response of a single mass Jeffcott rotor in linear isotropic bearings is identical in form to the response of a simple spring-mass-damper system excited by a rotating unbalance. This paper demonstrates that the free vibrations, and hence the system damping factor, of a distributed mass flexible rotor in tilting pad bearings may be analyzed using a single mass, two tier spring-damper model. The relationship between the system damping factor and rotor stability is discussed. Non-synchronous tilting pad bearing characteristics are incorporated into the expression for the damping factor, and nondimensional curves are presented which establish values of the damping factor as a function of operating speed, critical speed, bearing clearance and Sommerfeld number. The subject curves provide a quick method for establishing stability guidelines during rotor design and for comparing existing rotor bearing systems.


2000 ◽  
Vol 6 (5) ◽  
pp. 345-353 ◽  
Author(s):  
Li-Feng Ma ◽  
Xin-Zhi Zhang

A new numerical method is proposed for predicting the nonlinearity of tilting-pad guide bearing oilfilm force in the rotor-bearing system in a large hydro-unit. Nonlinear displacement and velocity of the journal center, as well as nonlinear tilting angles and angular velocities of the pads in non-stationary Reynolds equation are taken into account. This method is also suited for other small rotor-bearing system. As an example, the response due to a momentarily created unbalance is Calculated. The nonlinear motion patterns of the pad and journal whirling orbit are obtained. Finally, the nonlinear orbit is compared to the linear one that could be calculated from linear stiffness and damping coefficients. It is shown that there are important differences between those two orbits and that the nonlinear simulation is more accurate.


1995 ◽  
Vol 117 (3) ◽  
pp. 593-599 ◽  
Author(s):  
P. Arumugam ◽  
S. Swarnamani ◽  
B. S. Prabhu

The dynamic behavior of the rotating machinery supported by the hydrodynamic journal bearings is significantly influenced by the dynamic characteristics of the oil film. In the present work an efficient identification method is used to identify the stiffness and damping coefficients of the tilting pad and cylindrical journal bearings of a flexible rotor-bearing system. The method uses FRFs (Frequency Response Functions) obtained by the measurements and the finite element method. The accuracy and feasibility of the method were tested and demonstrated by theoretical simulation. The possible effects of oil-film inertia is also verified by the theoretical simulation. The method can be further extended to identify twelve linearized oil-film coefficients.


2004 ◽  
Vol 126 (4) ◽  
pp. 848-854 ◽  
Author(s):  
Ilmar F. Santos ◽  
Rodrigo Nicoletti ◽  
Alexandre Scalabrin

In this paper the complete set of modified Reynolds’ equations for the active lubrication is presented. The solution of such a set of equations allows the determination of stiffness and damping coefficients of actively lubricated bearings. These coefficients are not just dependent on Sommerfeld number, as it would be the case of conventional hydrodynamic bearings, but they are also dependent on the excitation frequencies and gains of the control loop. Stiffness as well as damping coefficients can be strongly influenced by the choice of the control strategy, servo valve dynamics and geometry of the orifices distributed over the sliding surface. The dynamic coefficients of tilting-pad bearings with and without active lubrication and their influence on an industrial compressor of 391 Kg, which operates with a maximum speed of 10,200 rpm, are analyzed. In the original compressor design, the bearing housings are mounted on squeeze-film dampers in order to ensure reasonable stability margins during full load condition (high maximum continuous speed). Instead of having a combination of tilting-pad bearings and squeeze-film dampers, another design solution is proposed and theoretically investigated in the present paper, i.e., using actively lubricated bearings. By choosing a suitable set of control gains, it is possible not only to increase the stability of the rotor-bearing system, but also enlarge its operational frequency range.


Author(s):  
Jason C. Wilkes

Many researchers have compared predicted stiffness and damping coefficients for tilting-pad journal bearings (TPJBs) to measurements. Most have found that direct damping is consistently overpredicted. Continuing to test TBJBs in the same fashion is not likely to produce an explanation for the discrepancies between measured and predicted damping. Most analytical models for TPJBs are based on the assumption that explicit dependence on pad motion can be eliminated by assuming a solution for rotor motion such that the amplitude and phase of pad motions are predicted by rotor-pad transfer functions. Direct measurements of pad motion during test excitation are needed to produce measured transfer functions between rotor and pad motion, and a comparison between these measurements and predictions is needed to identify model discrepancies. A test setup was designed to fulfill these objectives. Motion probes were added to the loaded pad to obtain accurate measurement of pad radial and tangential motion, as well as tilt, yaw and pitch. For the remainder of this work, the loaded pad refers to the pad whose pivot sits on the static load line. Testing was performed primarily at low speeds and high loads, since this is the operating region for which predictions are most erroneous. Single frequency excitations were performed ranging from 10–350 Hz, producing rotor and pad motion, acceleration, and force vectors. This motion was used to determine frequency-dependent bearing impedances and rotor-pad transfer functions. A new pad perturbation model is proposed including the effects of pad angular, radial, and circumferential pad motion. This model was implemented in a Reynolds-based TPJB code to predict the frequency-dependent bearing impedances and rotor-pad transfer functions. These predictions are compared with measurements and discussed. Good agreement was found between the amplitude of the measured and predicted transfer functions concerning tilt and radial motions for low to moderate loads, but deviated in accuracy at the highest loaded case. Circumferential (sliding) pad motion was predicted and observed; however, the effect of this degree of freedom on dynamic bearing coefficients has not been quantitatively assessed. For the bearing investigated, radial motion accounted for more than 67% of total motion of the fluid-film height at the leading and trailing edges of the pad when operating at 4400 rpm under heavily loaded conditions. The measurements show that predicting TPJB stiffness and damping coefficients without accounting for pad pivot deformation will not produce satisfactory outcomes.


2011 ◽  
Vol 338 ◽  
pp. 611-617
Author(s):  
Zhen Shan Zhang ◽  
Xu Dong Dai

Considering the coupling moving of shaft and pads, a theoretical model for calculating the complete dynamic coefficients of tilting-pad bearing is described in this paper. The model includes the influence of turbulence. Based on this model, the effect of turbulence on journal equilibrium position, pads inclinations, and complete dynamic coefficients is investigated for given load cases. The numerical results indicate that the effect of turbulence is not neglected for higher Reynolds number.


Author(s):  
Luis San Andrés ◽  
Oscar De Santiago

Measurements of the imbalance responses of a massive 45 kg rotor supported on series (flexure pivot) tilting pad bearings and integral squeeze film dampers (SFDs) are presented. The rotor-bearing configuration is of interest in compressor applications where often oil lubricated dampers are introduced in series with fluid film bearings to relocate critical speeds, enhance the overall system damping, and reduce the risks of rotordynamic instabilities due to seals and impellers, for example. Coast-down experiments from 9,000 rpm are conducted for increasing levels of rotor imbalance, and equivalent system damping coefficients identified from the peak amplitude of rotor response while traversing cylindrical mode critical speeds. The tests performed with locked (inactive) and active SFDs demonstrate the effectiveness of the flexible damped support in reducing the system critical speed and improving the overall rotor response with reduced transmitted forces to ground. The SFDs allow safe rotor operation with values of imbalance twice as large as the maximum sustained by the rotor supported on tilting pad bearings alone. The experiments reveal a linear relationship between the peak amplitude of vibration at the critical speeds and the imbalance displacement, even for rotor motions larger than 50% of the tilting pad bearing and damper clearances. The tests also show little cross-coupling effects with the shaft centerline moving along a nearly vertical path. The rotor-bearing system remained stable in the entire range of operation and without the appearance of subsynchronous vibration or non-linear damper jump response.


2003 ◽  
Vol 125 (4) ◽  
pp. 1026-1032 ◽  
Author(s):  
L. San Andre´s ◽  
O. De Santiago

Measurements of the imbalance responses of a massive 45 kg rotor supported on series (flexure pivot) tilting pad bearings and integral squeeze film dampers (SFDs) are presented. The rotor-bearing configuration is of interest in compressor applications where often oil lubricated dampers are introduced in series with fluid film bearings to relocate critical speeds, enhance the overall system damping, and reduce the risks of rotordynamic instabilities due to seals and impellers, for example. Coast-down experiments from 9000 rpm are conducted for increasing levels of rotor imbalance, and equivalent system damping coefficients identified from the peak amplitude of rotor response while traversing cylindrical mode critical speeds. The tests performed with locked (inactive) and active SFDs demonstrate the effectiveness of the flexible damped support in reducing the system critical speed and improving the overall rotor response with reduced transmitted forces to ground. The SFDs allow safe rotor operation with values of imbalance twice as large as the maximum sustained by the rotor supported on tilting pad bearings alone. The experiments reveal a linear relationship between the peak amplitude of vibration at the critical speeds and the imbalance displacement, even for rotor motions larger than 50% of the tilting pad bearing and damper clearances. The tests also show little cross-coupling effects with the shaft centerline moving along a nearly vertical path. The rotor-bearing system remained stable in the entire range of operation and without the appearance of subsynchronous vibration or nonlinear damper jump response.


Author(s):  
C. F. Kettleborough

Abstract The starting of large thrust bearings in turbines is one of the most critical points in their operation as a pressure carrying oil film must be generated from initial conditions of load and zero relative velocity between the two surfaces. A force equal and opposite to the applied load must be produced before the surfaces separate. It is the purpose of this paper to discuss the origin and formation of this force. The results show that lapped and ground surfaces have inefficient lifting characteristics as compared with surfaces having irregularities on the surface of 1/20 mil and greater. In general, surface oil pockets have an important influence on the starting behavior of tilting pad bearings; without these oil pockets it is doubtful if the two bearing surfaces would part.


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