Evaluation of Pivot Stiffness for Typical Tilting-Pad Journal Bearing Designs

Kirk, R. G.; Reedy, S. W.

doi:10.1115/1.3269494

Cited by 79 publications

(40 citation statements)

References 4 publications

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“…In 1988, Kirk and Reedy [7] presented analytical contact stiffness formulas for various pivot types using Hertzian-stress models. Although this work applies to some conventional pivots, contact stiffnesses for many pivot geometries remain to be defined, especially for mostly "cylindrical" pivots having a very slight radius of curvature, or crowning in the axial direction.…”

Section: Introductionmentioning

confidence: 99%

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

Wilkes

Childs

2012

Journal of Engineering for Gas Turbines and Power

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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 fi-equency was only measured at the most heavily loaded conditions.

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Section: Introductionmentioning

confidence: 99%

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

Wilkes

Childs

2012

Journal of Engineering for Gas Turbines and Power

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“…The rotor speed ranges from 4400 rpm to 13,100 rpm, and the static specific load W/(LD) on the bearing is as high as 3.13 MPa. Recall that fluid inertia effects are usually not significant in the performance of mineral oil lubricated bearings, and hence, ignored in their analysis [2][3][4][5][6][11][12][13]. For operation at 10,200 rpm, a frequency reduction [K,C,M] model delivers predictions for the bearing static stiffness, damping and virtual mass coefficients that compare satisfactorily against test data; in particular for the damping coefficients at specific loads equaling 783 kPa and 3134 kPa.…”

Section: Introductionmentioning

confidence: 99%

The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings

Andrés

Tao

2013

Journal of Engineering for Gas Turbines and Power

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Recent comprehensive experimental data showcasing the force coefficients of commercial size tilting pad journal bearings has brought to rest the long standing issue on the adequacy of the [K,C,M] physical model to represent frequency independent bearing force coefficients, in particular viscous damping. Most experimental works test tilting pad journal bearings (TPJBs) with large preloads, operating over a large wide range of rotor speeds, and with null to beyond normal specific loads. Predictions from apparently simple fluid film bearing models stand poor against the test data which invariably signals to theory missing pivot and pad flexibility effects, and most importantly, ignoring significant differences in bearing and pad clearances due to actual operation, poor installation and test procedures, or simply errors in manufacturing and assembly. Presently, a conventional thermo hydrodynamic bulk flow model for prediction of the pressure and temperature fields in TPJBs is detailed. The model accounts for various pivot stiffness types, all load dependent and best when known empirically, and allows for dissimilar pad and bearing clearances. The algorithm, reliable even for very soft pad-pivots, predicts frequency reduced bearing impedance coefficients and over a certain frequency range delivers the bearing stiffness, damping and virtual mass force coefficients. Good correlation of predictions against a number of experimental results available in the literature bridges the gap between a theoretical model and the applications. Predicted pad reaction loads reveal large pivot deflections, in particular for a bearing with large preloaded pads, with significant differences in pivot stiffness as a function of specific load and operating speed. The question on how pivot stiffness acts to increase (or decrease) the bearing force coefficients, in particular the dynamic stiffness versus frequency, remains since the various experimental data show contradictory results. A predictive study with one of the test bearings varies its pivot stiffness from 10% of the fluid film stiffness to an almost rigid one, 100 times larger. With certainty, hearings with nearly rigid pivot stiffness show frequency independent force coefficients. However, for a range of pad pivot stiffness, 1110 to ten times the fluid film stiffness, TPJB impedances vary dramatically with frequency, in particular as the excitation frequency grows above synchronous speed. The bearing virtual mass coefficients become negative, thus stiffening the bearing for most excitation frequencies.

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“…Since it is not the intent of this article to provide a review of tilting-pad bearing literature, the reader can refer to some of the studies by Lund (1964), Nilsson (1978), Nicholas et al (1979), Allaire (1979), Rouch (1982, 1983), Lundand Pederson (1987, and Kirk and Reedy (1988).…”

Section: Figurementioning

confidence: 97%

Design Optimization of Tilting-Pad Journal Bearing Using a Genetic Algorithm

Saruhan¹,

Rouch²,

Roso³

2004

The International Journal of Rotating Machinery

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This article focuses on the use of genetic algorithms in developing an efficient optimum design method for tiltingpad bearings. The approach optimizes based on minimum film thickness, power loss, maximum film temperature, and a global objective. Results for a five tilting-pad preloaded bearing are presented to provide a comparison with more traditional optimum design methods such as the gradientbased global criterion method, and also to provide insight into the potential of genetic algorithms in the design of rotor bearings. Genetic algorithms are efficient search techniques based on the idea of natural selection and genetics. These robust methods have gained recognition as general problem solving techniques in many applications.Many numerical optimization methods have been developed and used for design optimization of journal bearings. Most of these methods are based on gradient techniques. These methods are reasonably effective for well-behaved objective functions. This is because the gradient of the function helps to guide the direction of the search. However, when the continuity and existence of derivatives of the function are not assured, gradient methods lack robustness and may trap in local optima. To overcome these problems, many different approaches exist in the literature. The development of faster computers has allowed development of more robust and efficient optimization methods. One of these robust methods is the genetic algorithm, which has gained recognition as a general problem solving technique in many applications. The genetic algorithm is a guided random search technique. It uses objective function information, instead of derivatives as in gradient-based methods.Numerical search techniques are good at exploitation but not exploration of the parameter space. They focus on the area around the current design point, using local gradient calculations to move to a better design. Since there is no exploration for all regions of parameter space, they can easily be trapped in local optima (Davis, 1991). Genetic algorithms are a class of general-purpose algorithms that can achieve a "remarkable balance between exploration and exploitation of the search space" (Mitsuo and Runwei, 1997). The genetic algorithm is new to the field of journal bearing analysis, and in current literature there is limited work in the area of rotor-bearing system using genetic algorithms. Interested readers can refer to the studies by

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Evaluation of Pivot Stiffness for Typical Tilting-Pad Journal Bearing Designs

Cited by 79 publications

References 4 publications

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

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

The Role of Pivot Stiffness on the Dynamic Force Coefficients of Tilting Pad Journal Bearings

Design Optimization of Tilting-Pad Journal Bearing Using a Genetic Algorithm

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