Part I of this three-part series presented a heat transfer rolling-element bearing model. The model is composed of solid conduction partial differential equations (PDEs), control volume formulation for lubricant temperatures, and heat partitioning. The model applies to systems with a shaft, housing, numerous bearings, gears, and various methods of lubrication. Part II, this work, presents a solution to the thermal conduction equations. The raceways are three-dimensional (3D), the shaft and housing models are two-dimensional (2D) and lumped in the third direction. This generalized method applies to ball, cylindrical, spherical, and tapered rolling-element bearings. Semi-analytic solutions are obtained by imposing integral transforms. This approach accounts for the axial and circumferential variations in the bearing load zone and rib heating, as well as the ability to link many bearings and gears within an assembly. The housing and shaft equations are radially lumped. The lumped fluxes account for internal and external convection and radiation, as well as conduction fluxes from contiguous bearings and gears. These equations are solved using a Fourier transform. The 3D bearing raceway solution uses a Fourier transform and a modified Hankel transform. Part III of this series presents additional results and experimental validation.
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July 2015
Research-Article
Rolling-Element Bearing Heat Transfer—Part II: Housing, Shaft, and Bearing Raceway Partial Differential Equation Solutions
William M. Hannon
William M. Hannon
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William M. Hannon
Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 29, 2014; final manuscript received January 6, 2015; published online March 25, 2015. Assoc. Editor: Mihai Arghir.
J. Tribol. Jul 2015, 137(3): 031103 (11 pages)
Published Online: July 1, 2015
Article history
Received:
July 29, 2014
Revision Received:
January 6, 2015
Online:
March 25, 2015
Connected Content
This is a companion to:
Rolling-Element Bearing Heat Transfer—Part I: Analytic Model
A companion article has been published:
Rolling-Element Bearing Heat Transfer—Part III: Experimental Validation
Citation
Hannon, W. M. (July 1, 2015). "Rolling-Element Bearing Heat Transfer—Part II: Housing, Shaft, and Bearing Raceway Partial Differential Equation Solutions." ASME. J. Tribol. July 2015; 137(3): 031103. https://doi.org/10.1115/1.4029733
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