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Research Papers: Gas Turbines: Structures and Dynamics

Modeling Reichardt's Formula for Eddy Viscosity in the Fluid Film of Tilting Pad Thrust Bearings

[+] Author and Article Information
Xin Deng

Rotating Machinery and Controls (ROMAC) Lab,
Mechanical and Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: xd9fw@virginia.edu

Brian Weaver

Rotating Machinery and Controls (ROMAC) Lab,
Mechanical and Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: bkw3q@virginia.edu

Cori Watson

Rotating Machinery and Controls (ROMAC) Lab,
Mechanical and Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: cw2xw@virginia.edu

Michael Branagan

Rotating Machinery and Controls (ROMAC) Lab,
Mechanical and Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: mkb2sr@virginia.edu

Houston Wood

Rotating Machinery and Controls (ROMAC) Lab,
Mechanical and Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: hgw9p@virginia.edu

Roger Fittro

Rotating Machinery and Controls (ROMAC) Lab,
Mechanical and Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: rlf9w@virginia.edu

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received November 12, 2017; final manuscript received December 5, 2017; published online April 26, 2018. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(8), 082505 (Apr 26, 2018) (9 pages) Paper No: GTP-17-1614; doi: 10.1115/1.4038857 History: Received November 12, 2017; Revised December 05, 2017

Oil-lubricated bearings are widely used in high-speed rotating machines such as those used in the aerospace and automotive industries that often require this type of lubrication. However, environmental issues and risk-adverse operations have made water-lubricated bearings increasingly popular. Due to different viscosity properties between oil and water, the low viscosity of water increases Reynolds numbers drastically and therefore makes water-lubricated bearings prone to turbulence effects. The turbulence model is affected by eddy viscosity, while eddy viscosity depends on wall shear stress. Therefore, effective wall shear stress modeling is necessary in producing an accurate turbulence model. Improving the accuracy and efficiency of methodologies of modeling eddy viscosity in the turbulence model is important, especially considering the increasingly popular application of water-lubricated bearings and also the traditional oil-lubricated bearings in high-speed machinery. This purpose of this paper is to study the sensitivity of using different methodologies of solving eddy viscosity for turbulence modeling. Eddy viscosity together with flow viscosity forms the effective viscosity, which is the coefficient of the shear stress in the film. The turbulence model and Reynolds equation are bound together to solve when hydrodynamic analysis is performed, therefore improving the accuracy of the turbulence model is also vital to improving a bearing model's ability to predict film pressure values, which will determine the velocity and velocity gradients in the film. The velocity gradients in the film are the other term determining the shear stress. In this paper, three approaches applying Reichardt's formula were used to model eddy viscosity in the fluid film. These methods are for determining where one wall's effects begin and the other wall's effects end. Trying to find a suitable model to capture the wall's effects of these bearings, with an aim to improve the accuracy of the turbulence model, would be of high value to the bearing industry. The results of this study could aid in improving future designs and models of both oil- and water-lubricated bearings.

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References

Brockett, T. S. , 1995, “ Thermoelastohydrodynamic Lubrication in Thrust Bearings,” Ph.D. dissertation, University of Virginia, Charlottesville, VA. https://libra2.lib.virginia.edu/public_view/v692t662v
He, M. , and Allaire, P. , 2003, “ Thermoelastohydrodynamic Analysis of Fluid Film Journal Bearings,” Ph.D. thesis, University of Virginia, Charlottesville, VA. https://elibrary.ru/item.asp?id=5710650
Elrod , H. G., Jr. , and Ng, C. W. , 1967, “ A Theory for Turbulent Fluid Films and Its Application to Bearings,” ASME J. Lubr. Technol., 89(3), pp. 346–362. [CrossRef]
Suganami, T. T. , and Szeri, A. Z. , 1979, “ A Thermohydrodynamic Analysis of Journal Bearings,” ASME J. Lubr. Technol., 101(1), pp. 21–27. [CrossRef]
Szeri, A. Z. , 1980, Tribology: Friction, Lubrication, and Wear, McGraw-Hill, New York.
Huebner, K. H. , 1974, “ Solution for the Pressure and Temperature in Thrust Bearings Operating in the Thermohydrodynamic Turbulent Regime,” ASME J. Lubr. Technol., 96(1), pp. 58–68. [CrossRef]
Ng, C.-W. , 1964, “ Fluid Dynamic Foundation of Turbulent Lubrication Theory,” ASLE Trans., 7(4), pp. 311–321. [CrossRef]
Ng, C. , and Pan, C. T. , 1965, “ A Linearized Turbulent Lubrication Theory,” ASME J. Basic Eng., 87(3), pp. 675–682. [CrossRef]
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Figures

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Fig. 3

Graph of method II

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Fig. 4

Graph of method III

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Fig. 5

Schematic of a thrust bearing

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Fig. 6

Structure of a thrust bearing

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Fig. 7

Schematic diagram of the test rig [13]

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Fig. 8

Photograph of the facility: 1—motor, 2—intermediate shaft, 3—journal bearings, 4—housing with test bearings, 5—flexible line for oil supply, 6—hydraulic system, 7—one of four steel disks supporting the housing, 8—load cell, and 9—oil reservoir [13]

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Fig. 9

Photograph of the instrumented bearing [13]

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Fig. 10

Schematic diagram of the monitoring point

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Fig. 11

Pad temperature of the monitoring point: 1500 rpm and 2 MPa bearing load (a) and 3000 rpm with 2 MPa bearing load (b)

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Fig. 1

Photo of a typical water-lubricated thrust bearing

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Fig. 12

Minimum film thickness using method I and III for applying Reichardt's formula, for oil lubrication

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Fig. 13

Minimum film thickness using method II and III for applying Reichardt's formula, for oil lubrication

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Fig. 14

With method I, relative difference between including and excluding methods III for oil lubrication

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Fig. 15

With method II, errors between including and excluding methods III for oil lubrication

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Fig. 16

Minimum film thickness using method I and III for applying Reichardt's formula for water lubrication

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Fig. 17

Minimum film thickness using method II and III for applying Reichardt's formula for water lubrication

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Fig. 18

Relative difference between including and excluding method III with method I for water lubrication

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Fig. 19

Relative difference between including and excluding method III with method II for water lubrication

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Fig. 20

Minimum film thickness versus Reynolds number using method I or method II with method III included or excluded for oil lubrication

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Fig. 21

Minimum film thickness versus Reynolds number using method I or method II with method III included or excluded for water lubrication

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Fig. 22

Relative difference between including and excluding method III with methods I and II versus Reynolds number for oil lubrication

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Fig. 23

Relative difference between including and excluding method III with methods I and II versus Reynolds number for water lubrication

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Fig. 24

Minimum film thickness versus Reynolds number with runner thermal deformation included and excluded for oil lubrication

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Fig. 25

Relative difference between including and excluding runner thermal deformation versus Reynolds number for oil lubrication

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Fig. 26

Minimum film thickness versus Reynolds number with runner thermal deformation included and excluded for water lubrication

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Fig. 27

Relative difference between including and excluding runner thermal deformation versus Reynolds number for water lubrication

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