Technical Briefs

Analytical Solution to the Hydrodynamic Lubrication of Fan-Shaped Thrust Step Bearings

[+] Author and Article Information
Shuangbiao Liu

Product Development Center of Excellence, TCE854 Caterpillar Inc., Peoria, IL 61656-1875liu_jordan@cat.com

W. Wayne Chen

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208

Diann Y. Hua

Product Development Center of Excellence, TCE854 Caterpillar Inc., Peoria, IL 61656-1875

J. Tribol 132(2), 024504 (Apr 06, 2010) (8 pages) doi:10.1115/1.4001013 History: Received May 22, 2009; Revised January 11, 2010; Published April 06, 2010; Online April 06, 2010

Step bearings are frequently used in industries for better load capacities. Analytical solutions to the Rayleigh step bearing and a rectangular slider with a finite width are available in literature, but none for a fan-shaped thrust step bearing. This study starts with a known solution to the Laplace equation in a cylindrical coordinate system, which is in the form of an infinite summation. A set of analytical solutions to pressure, load capacity, flow rate, and torque loss is derived in this paper for hydrodynamic lubrication problems encountered in the fan-shaped step bearing. These analytical solutions are compared with those for the rectangular slider and the Rayleigh step bearing to reveal relationships among them. When the inner radius becomes smaller, the load capacity increases, almost linearly in a certain region. The effects of inner radius, step height, and step location on pressure distribution and load capacity are studied in general and under a specific set of bearing geometry as an example. The presented solutions can be useful for designers to maximize bearing performance as well as for researchers to benchmark numerical lubrication models.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 4

Effect of the inner radius on load and maximum pressure

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Figure 5

Effect of the inner radius on the number of terms

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Figure 6

Effect of the step height on load and maximum pressure

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Figure 7

Influence of step location, ns

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Figure 8

Optimal step location to achieve maximum load capacity

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Figure 1

Schematics of a thrust step bearing

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Figure 2

3D pressure distribution for case 2

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Figure 3

2D cross section of the pressure distribution



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