A new derivation for journal bearing stiffness and damping coefficients in polar coordinates

2006 ◽  
Vol 290 (1-2) ◽  
pp. 500-507 ◽  
Author(s):  
J.K. Wang ◽  
M.M. Khonsari
Keyword(s):  
Journal Bearing ◽  
Polar Coordinates ◽  
Damping Coefficients ◽  
Bearing Stiffness ◽  
Stiffness And Damping

Tilting Pad Journal Bearings: A Discussion on Stability Calculation, Frequency Dependence, and Pad and Pivot Flexibility

2012 ◽  
Author(s):  
Jason C. Wilkes ◽  
Dara W. Childs
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Operating Temperature ◽  
Excitation Frequency ◽  
Full Model ◽  
Stability Calculation ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

For several years, researchers have presented predictions showing that using a full tilting-pad journal bearing (TPJB) model (retaining all of the pad degrees of freedom) is necessary to accurately perform stability calculations for a shaft operating on TPJBs. This paper will discuss this issue, discuss the importance of pad and pivot flexibility in predicting impedance coefficients for the tilting-pad journal bearing, present measured changes in bearing clearance with operating temperature, and summarize the differences between measured and predicted frequency dependence of dynamic impedance coefficients. The current work presents recent test data for a 100 mm (4 in) five-pad TPJB tested in load on pad (LOP) configuration. Measured results include bearing clearance as a function of operating temperature, pad clearance and radial displacement of the loaded pad (the pad having the static load vector directed through its pivot), and frequency dependent stiffness and damping. Measured hot bearing clearances are approximately 30% smaller than measured cold bearing clearances and are inversely proportional to pad surface temperature; predicting bearing impedances with a rigid pad and pivot model using these reduced clearances results in overpredicted stiffness and damping coefficients that are several times larger than previous comparisons. The effect of employing a full bearing model versus a reduced bearing model (where only journal degrees of freedom are retained) in a stability calculation for a realistic rotor-bearing system is assessed. For the bearing tested, the bearing coefficients reduced at the frequency of the unstable eigenvalue (subsynchronously reduced) predicted a destabilizing cross-coupled stiffness coefficient at the onset of instability within 1% of the full model, while synchronously reduced coefficients for the lightly loaded bearing required 25% more destabilizing cross-coupled stiffness than the full model to cause system instability. The same stability calculation was performed using measured stiffness and damping coefficients at synchronous and subsynchronous frequencies. These predictions showed that both the synchronously measured stiffness and damping and predictions using the full bearing model were more conservative than the model using subsynchronously measured stiffness and damping, an outcome that is completely opposite from conclusions reached by comparing different prediction models. This contrasting outcome results from a predicted increase in damping with increasing excitation frequency at all speeds and loads; however, this increase in damping with increasing excitation frequency was only measured at the most heavily loaded conditions.

An Analytical Complete Model of Tilting-Pad Journal Bearing Considering Pivot Stiffness and Damping

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Zhiyong Yan ◽  
Yi Lu ◽  
Tiesheng Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Local Coordinate System ◽  
Dynamical Behavior ◽  
Complete Model ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Generalized Force ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model, as well as mathematical method, which contains 2n+2 degrees of freedom, is presented for calculating the dynamical characteristics of tilting-pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement, and the generalized force vector are chosen. The concise transformation of generalized displacement, generalized force, and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using the Newton–Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration. Numerical results show that the reduced damping coefficients and the threshold speed can be effectively enhanced by giving suitable pad pivot stiffness and damping simultaneously, and this analytical method can be applied to analyze dynamical behavior of the tilting-pad journal bearing rotor system.

Three-Dimensional Thermo-Elasto-Hydrodynamic Computational Fluid Dynamics Model of a Tilting Pad Journal Bearing—Part II: Dynamic Response

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Jongin Yang ◽  
Alan Palazzolo
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Dynamic Response ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Static Response ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearing

Part II presents a novel approach for predicting dynamic coefficients for a tilting pad journal bearing (TPJB) using computational fluid dynamics (CFD) and finite element method (FEM), including fully coupled elastic deflection, heat transfer, and fluid dynamics. Part I presented a similarly novel, high fidelity approach for TPJB static response prediction which is a prerequisite for the dynamic characteristic determination. The static response establishes the equilibrium operating point values for eccentricity, attitude angle, deflections, temperatures, pressures, etc. The stiffness and damping coefficients are obtained by perturbing the pad and journal motions about this operating point to determine changes in forces and moments. The stiffness and damping coefficients are presented in “synchronously reduced form” as required by American Petroleum Institute (API) vibration standards. Similar to Part I, an advanced three-dimensional thermal—Reynolds equation code validates the CFD code for the special case when flow Between Pad (BP) regions is ignored, and the CFD and Reynolds pad boundary conditions are made identical. The results show excellent agreement for this validation case. Similar to the static response case, the dynamic characteristics from the Reynolds model show large discrepancies compared with the CFD results, depending on the Reynolds mixing coefficient (MC). The discrepancies are a concern given the key role that stiffness and damping coefficients serve instability and response predictions in rotordynamics software. The uncertainty of the MC and its significant influence on static and dynamic response predictions emphasizes a need to utilize the CFD approach for TPJB simulation in critical machines.

Influence of Wear on the Performance of Multirecess Hydrostatic Journal Bearing Operating With Micropolar Lubricant

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
E. Rajasekhar Nicodemus ◽  
Satish C. Sharma
Keyword(s):  
Journal Bearing ◽  
Dynamic Performance ◽  
Flow Equation ◽  
Performance Characteristics ◽  
Wear Depth ◽  
Damping Coefficients ◽  
Load Line ◽  
Wide Range ◽  
Load Arrangement ◽  
Stiffness And Damping

The objective of the present work is to study theoretically the influence of wear on the performance of four-pocket capillary-compensated hydrostatic journal bearing operating with micropolar lubricant. In the present study, the lubricant containing additives and contaminants is modeled as micropolar fluid. The modified Reynolds equation for micropolar lubricant is solved using finite element method along with capillary restrictor flow equation as a constraint together with appropriate boundary conditions. The performance characteristics of a capillary-compensated four-pocket worn hydrostatic journal bearing operating with micropolar lubricant have been presented for a wide range of values of nondimensional external load, wear depth parameter, and micropolar parameters. The simulated results have also been presented for two different loading arrangements. In arrangement I, the load line acts through centers of the pockets, whereas in arrangement II, the load line bisects the land between two pockets. The simulated results suggest that a bearing lubricated with lubricant having higher micropolar effect has better static and dynamic performance characteristics as compared with Newtonian lubricant but the bearing lubricated with lubricant having higher micropolar effect is predominantly affected by the wear vis a vis static characteristics parameters as compared with Newtonian lubricant for both loading arrangements. However, in the case of stiffness and damping coefficients, loading arrangement II shows a significant higher enhancement in the value of direct stiffness and damping coefficients in z-direction due to micropolar effect as compared with load arrangement I. And also, the effect of wear on stiffness and damping coefficients in z-direction for bearing operating with micropolar lubricant is of same order as Newtonian lubricant for the loading arrangement II. A similar behavior is observed for the case of stiffness and damping coefficients in x-direction for loading arrangement I.

Steady-State and Dynamic Behaviour of Multi-Recess Hybrid Oil Journal Bearings

1979 ◽  
Vol 21 (5) ◽  
pp. 345-351 ◽  
Author(s):  
M. K. Ghosh ◽  
B. C. Majumdar ◽  
J. S. Rao
Keyword(s):  
Perturbation Theory ◽  
Steady State ◽  
Theoretical Analysis ◽  
Dynamic Behaviour ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Time Dependent ◽  
Damping Coefficients ◽  
Stiffness And Damping

A theoretical analysis of the steady-state and dynamic characteristics of multi-recess hybrid oil journal bearings is presented. A perturbation theory for small vibrations is used to solve an incompressible, finite journal bearing with a time-dependent term. Load capacity, attitude angle, friction parameter, stiffness and damping coefficients are evaluated for a capillary-compensated bearing.

Helical-Grooved Journal Bearing Operated in Turbulent Regime

1970 ◽  
Vol 92 (2) ◽  
pp. 346-357 ◽  
Author(s):  
C. Y. Chow ◽  
J. H. Vohr
Keyword(s):  
Steady State ◽  
Journal Bearing ◽  
Critical Mass ◽  
Reynolds Numbers ◽  
Turbulent Regime ◽  
Damping Coefficients ◽  
Radial Stiffness ◽  
Performance Curves ◽  
Stiffness And Damping ◽  
Laminar And Turbulent Regimes

An analysis for helical bearings operated in turbulent regime, with negligible inertia in an incompressible fluid film, was performed [10, 11]. The analysis is based on the linearised lubrication theory developed by Ng and Pan [4]. The outlines for this analysis and, in particular, the bearing performance data for various helical groovings are given in this paper. The data presented include the bearing performance at the steady state, the stiffness and damping coefficients, and the critical mass of journal in both laminar and turbulent regimes. To facilitate designs, these data are computed for optimal geometries of helical grooved bearings to provide maximum radial stiffness at various Reynolds numbers. In addition, the effect of external pressurized supply of lubricant are shown in the performance curves.

Numerical Analysis on Dynamic Characteristics of Cryogenic Hydrostatic Journal Bearing

1999 ◽  
Vol 121 (4) ◽  
pp. 879-885 ◽  
Author(s):  
Hiroyuki Yoshikawa ◽  
Terukazu Ota ◽  
Kazuyuki Higashino ◽  
Shunichiro Nakai
Keyword(s):  
Numerical Analysis ◽  
Dynamic Characteristics ◽  
Rotational Speed ◽  
Frequency Ratio ◽  
Journal Bearing ◽  
Liquid Hydrogen ◽  
Transport Systems ◽  
Rocket Engines ◽  
Damping Coefficients ◽  
Stiffness And Damping

Dynamic characteristics of a two row staggered recess cryogenic hydrostatic journal bearing used in the liquid hydrogen turbopump of rocket engines for space transport systems are numerically analyzed. Effects of the rotational speed and the shaft eccentricity are studied in the analysis. Their effects on the stiffness and damping coefficients and the whirl frequency ratio are clarified. Moreover, effects of the orifice parameter, the distance between two recess rows, and the number of recesses on these dynamic characteristics are investigated.

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