Research on the Complete Dynamical Model of Tilting-Pad Bearings Considering the Coupling Moving of Shaft and Pads with Turbulent Oil Film

2011 ◽  
Vol 338 ◽  
pp. 611-617
Author(s):  
Zhen Shan Zhang ◽  
Xu Dong Dai
Keyword(s):  
Reynolds Number ◽  
Theoretical Model ◽  
Equilibrium Position ◽  
Numerical Results ◽  
Dynamical Model ◽  
Oil Film ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Tilting Pad Bearings

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.

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
Keyword(s):  
Cross Coupling ◽  
Frequency Dependent ◽  
Oil Film ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Rotor Bearing ◽  
Single Mass ◽  
Tilting Pad Bearings

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.

Frequency Response Analysis of an Actively Lubricated Rotor/Tilting-Pad Bearing System

2004 ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Ilmar Ferreira Santos
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Response Analysis ◽  
Oil Film ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Body Dynamics ◽  
Vibration Problems ◽  
Proportional Controller ◽  
Operational Range

In the present paper, the dynamic response of a rotor supported by an active lubricated tilting-pad bearing is investigated in the frequency domain. The theoretical part of the investigation is based on a mathematical model obtained by means of rigid body dynamics. The oil film forces are inserted into the model by using two different approaches: (a) linearized active oil film forces and the assumption that the hydrodynamic forces and the active hydraulic forces can be decoupled; (b) equivalent dynamic coefficients of the active oil film and the solution of the modified Reynolds equation for the active lubrication. The second approach based on the equivalent dynamic coefficients leads to more accurate results since it includes the frequency dependence of the active hydraulic forces. Theoretical and experimental results reveal the feasibility of reducing resonance peaks by using the active lubricated tilting-pad bearing. By applying a simple proportional controller, it is possible to reach 30% reduction of the resonance peak associated with the first rigid body mode shape of the system. One of the most important consequences of such a vibration reduction in rotating machines is the feasibility of increasing their operational range by attenuating resonance peaks and reducing vibration problems.

scholarly journals Tilting-Pad Journal Bearings With Active Lubrication Applied as Calibrated Shakers: Theory and Experiment

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Alejandro Cerda Varela ◽  
Ilmar Ferreira Santos
Keyword(s):  
Theoretical Model ◽  
Research Effort ◽  
Control Signal ◽  
Calibration Function ◽  
Oil Film ◽  
Machine Element ◽  
Lumped Parameter ◽  
Tilting Pad ◽  
Specific Frequency ◽  
Tilting Pad Journal Bearing

In recent years, a continuous research effort has transformed the conventional tilting-pad journal bearing (TPJB) into a mechatronic machine element. The addition of electromechanical elements provides the possibility of generating controllable forces over the rotor as a function of a suitable control signal. Such forces can be applied in order to perform parameter identification procedures “in situ,” which enables evaluation of the mechanical condition of the machine in a noninvasive way. The usage of a controllable bearing as a calibrated shaker requires obtaining the bearing specific frequency dependent calibration function, i.e., the transfer function between control signal and force over the rotor. This work presents a theoretical model of the calibration function for a TPJB with active lubrication. The bearing generates controllable forces by injecting pressurized oil directly into the bearing clearance. The injected flow is controlled by means of a servovalve. The theoretical model includes the dynamics of the hydraulic system using a lumped parameter approach, which is coupled with the bearing oil film using a modified form of the Reynolds equation. The oil film model is formulated considering an elastothermohydrodynamic lubrication regime. New contributions to the mathematical modeling are presented, such as the inclusion of the dynamics of the hydraulic pipelines and the obtention of the bearing calibration function by means of harmonic analysis of a linearized form of the controllable bearing constitutive equations. The mathematical model is used to study the relevance and effects of different parameters on the calibration function, aiming at providing general guidelines for the active bearing design. Finally, experimental results regarding the calibration function and the usage of the studied bearing as a calibrated shaker provide insight into the possibilities of application of this technology.

Design of Tilting-Pad Journal Bearings Considering Bearing Clearance Uncertainty and Reliability Analysis

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Heitor Antonio Pereira da Silva ◽  
Rodrigo Nicoletti
Keyword(s):  
Reliability Analysis ◽  
Dynamic Characteristics ◽  
Stochastic Analysis ◽  
Design Procedure ◽  
Journal Bearings ◽  
Dynamic Coefficients ◽  
Bearing Clearance ◽  
Tilting Pad ◽  
Tilting Pad Bearings ◽  
Tilting Pad Journal Bearings

The dynamic characteristics of tilting-pad journal bearings (TPJBs) are strongly related to their geometric parameters, most importantly the bearing clearance. In turn, the bearing clearance in TPJBs is strongly dependent on the machining tolerances of the bearing parts and their assembling. Considering that, the machining tolerances of the pads can be of the same magnitude order of the oil film thickness in the bearing, it is uncertain that the TPJB will have the originally designed geometry after assembling. Therefore, the resultant dynamic characteristics of the TPJB also become uncertain. In this work, we present an investigation of tilting-pad bearings and their equivalent dynamic coefficients when subjected to dimensional variability. First, we perform a stochastic analysis of the system using a thermo-hydrodynamic (THD) model of the tilting-pad bearing and considering the bearing clearance in each pad as an independent random variable (varying between minimum and maximum values). We show that the scattering of the results of the dynamic coefficients is limited by the values obtained from TPJBs with all pads with maximum or minimum possible clearances. Second, we apply the concepts of reliability analysis to develop a design procedure for tilting-pad bearings. This design methodology considers the results obtained in the stochastic analysis and it allows the Engineer to appropriately design the bearing for a given probability of success or, inversely, a given probability of failure. Such approach assures a level of reliability to the dynamic coefficients of designed TPJBs in face of their dimensional variability.

Starting Phenomena of Tilting Pad Bearings

2001 ◽  
Author(s):  
C. F. Kettleborough
Keyword(s):  
Critical Points ◽  
Relative Velocity ◽  
Applied Load ◽  
Initial Conditions ◽  
Important Influence ◽  
Oil Film ◽  
Thrust Bearings ◽  
Tilting Pad ◽  
Oil Pockets ◽  
Tilting Pad Bearings

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.

On the Effect of Pad Clearance and Preload Manufacturing Tolerances on Tilting Pad Bearings Rotordynamic Coefficients

2013 ◽  
Author(s):  
Jose L. Gomez ◽  
Saira Pineda ◽  
Sergio E. Diaz
Keyword(s):  
High Speed ◽  
Numerical Study ◽  
Numerical Code ◽  
Perturbation Approach ◽  
The Finite Element Method ◽  
Rotordynamic Coefficients ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Manufacturing Tolerances ◽  
Tilting Pad Bearings

Tilting pad bearings (TPB) are commonly used in high-speed and high-power turbomachines, due to its contributions in avoiding rotor instabilities. Studies related to the estimation of dynamic coefficients have been carried out considering a uniform value of the geometric parameters (clearance, pre-load) for all bearing pads. These assumptions give a reasonable agreement on the direct coefficients prediction while, recently, some discrepancies have been found on the cross-coupled coefficients. In this work, a numerical study is devised to analyze the influence of the pre-load and clearance variations from pad to pad, due to manufacturing tolerances, on the dynamic coefficients prediction. The numerical code for the estimation of the dynamic coefficients uses the finite element method to integrate the Reynolds’s equation through a perturbation approach. Variations on the pre-load and clearance for each bearing’s pad were performed, producing plots quantifying the sensitivity of the tilting pad bearing cross coupled coefficients to manufacturing tolerances.

Calculation of Equilibrium Position and Dynamic Coefficients of a Journal Bearing Using Free Boundary Theory

1999 ◽  
Vol 122 (3) ◽  
pp. 616-621 ◽  
Author(s):  
Tiesheng Zheng ◽  
Norio Hasebe
Keyword(s):  
Finite Element ◽  
Equilibrium Position ◽  
Static Load ◽  
Journal Bearing ◽  
Computing Time ◽  
Oil Film ◽  
Dynamic Coefficients ◽  
Newton Raphson ◽  
Raphson Method ◽  
Oil Film Pressure

A finite element method, which is based on the variational inequality approach, is introduced to calculate the oil film pressure distribution of a journal bearing. The cavitation zone is found by solving a linear complementary problem. By means of this approach a perturbation can be performed directly on the finite element equation and, consequently, the Jacobian matrices of the oil film forces are obtained concisely. The equilibrium position of the bearing at a given static load is found by the Newton-Raphson method and, as byproducts, dynamic coefficients are obtained simultaneously without any extra computing time. Numerical examples show that the method works satisfactorily. [S0742-4787(00)02302-X]

Frequency Response Analysis of an Actively Lubricated Rotor/Tilting-Pad Bearing System

2005 ◽  
Vol 127 (3) ◽  
pp. 638-645 ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Ilmar Ferreira Santos
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Response Analysis ◽  
Oil Film ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Body Dynamics ◽  
Vibration Problems ◽  
Proportional Controller ◽  
Operational Range

In the present paper, the dynamic response of a rotor supported by an active lubricated tilting-pad bearing is investigated in the frequency domain. The theoretical part of the investigation is based on a mathematical model obtained by means of rigid body dynamics. The oil film forces are inserted into the model by using two different approaches: (a) linearized active oil film forces and the assumption that the hydrodynamic forces and the active hydraulic forces can be decoupled, and (b) equivalent dynamic coefficients of the active oil film and the solution of the modified Reynolds equation for the active lubrication. The second approach, based on the equivalent dynamic coefficients, leads to more accurate results because it includes the frequency dependence of the active hydraulic forces. Theoretical and experimental results reveal the feasibility of reducing resonance peaks by using the active lubricated tilting-pad bearing. By applying a simple proportional controller, it is possible to reach 30% reduction of the resonance peak associated with the first rigid body mode shape of the system. One of the most important consequences of such a vibration reduction in rotating machines is the feasibility of increasing their operational range by attenuating resonance peaks and reducing vibration problems.

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