Rolling-Element Bearing Heat Transfer—Part I: Analytic Model

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
William M. Hannon
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Integral Transform ◽  
Rolling Element Bearing ◽  
System Level ◽  
Transfer Model ◽  
Element Analysis ◽  
Transform Method ◽  
Rolling Element ◽  
Element Bearing

The complexities of analyzing rolling element bearings vary. Vendors offer cataloged solutions comprised of limiting loads and speeds, bearing life, and lubricant recommendations. These guidelines meet the needs of most customers; however, more demanding applications warrant advanced analyses. This work focuses on thermal management. Current literature offers system level solutions using either resistance methods or finite element analysis (FEA). Resistance methods have rapid computation time, yet lack accuracy. Finite element methods improve the accuracy, but are computationally cumbersome. This work proposes an integral transform method. The rapidly computed solution yields accurate results. The methodology and results of this work are presented in a three-part series. Part I details existing literature and provides the framework for a new heat transfer model. This model describes rolling-element bearing systems containing a shaft, housing, and numerous bearing raceways. It also includes gears, cooling jackets, and is applicable for several methods of lubrication. The model consists of solid component partial differential equations (PDEs) in conjunction with analytic expressions for fluid temperatures, convection equation, and mass flow. Part II presents the housing, shaft, and bearing raceway PDE solutions. Part III offers experimental validation, as well as observations from experiments on fluid flow within the bearing.

Rolling-Element Bearing Heat Transfer—Part III: Experimental Validation

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
William M. Hannon ◽  
Todd A. Barr ◽  
Shawn T. Froelich
Keyword(s):  
Heat Transfer ◽  
Experimental Validation ◽  
Rolling Element Bearing ◽  
Transfer Model ◽  
Test Results ◽  
Model Framework ◽  
Rolling Element ◽  
Heat Partitioning ◽  
Scale Test ◽  
Element Bearing

This paper concludes a series of papers outlining a new rolling-element bearing heat transfer model. Part I provided the model framework, Part II presented the partial differential equation (PDE) solutions, and Part III, this paper, presents full-scale test results for ball, cylindrical, spherical, and tapered rolling-element bearings. The results validate the heat partitioning equation and the predicted solid temperatures for circulating oil lubrication. In addition, sump lubrication was studied using an acrylic assembly. The results quantify what fraction of the bearing periphery is cooled by oil, as well as the flow of oil through a bearing. Finally, substantiation of the modeling assumptions is discussed.

Investigation of the Gas Flow in the Rolling Element Bearing Assembly of a Centrifugal Compressor

2005 ◽  
Author(s):  
Michael M. Cui
Keyword(s):  
Heat Transfer ◽  
Flow Field ◽  
Centrifugal Compressor ◽  
Gas Flow ◽  
Operating Conditions ◽  
Rolling Element Bearing ◽  
Rolling Element ◽  
Flow Through ◽  
Bearing Assembly ◽  
Element Bearing

Combined with the geometric features, the pressure differential and bearing motion define the gas flow through the rolling-element-bearing assembly of a centrifugal compressor. The gas flow field then affects the oil distribution and heat transfer characteristics of the assembly accordingly. Investigations of the refrigerant gas flow through the rolling element bearing assembly of a centrifugal compressor are presented. A series of cases are studied for different operating conditions. The analyses include the geometric details of the assembly, such as the shaft, races, cages, balls, oil feeding system, and surrounding components. Refrigerant R123 is used as the working fluid. Both detailed three-dimensional flow field features and integrated parameters are calculated. The interactions between bearing motion and the surrounding structures are characterized. The flow patterns inside the bearings are defined. These results help us gain an insight into the basic physics that governs the bearing internal mass and heat transfer. The data and techniques developed can be used to design and optimize bearing and oil supply systems for the improvement of lubrication and cooling efficiency.

Evaluating Cutting Fluid Effects on Cylinder Boring Surface Errors by Inverse Heat Transfer and Finite Element Methods

1999 ◽  
Vol 122 (3) ◽  
pp. 377-383 ◽  
Author(s):  
Y. Zheng ◽  
H. Li ◽  
W. W. Olson ◽  
J. W. Sutherland
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Integral Transform ◽  
Heat Convection ◽  
Cutting Fluid ◽  
Transfer Model ◽  
Surface Error ◽  
Actual Surface ◽  
Surface Errors ◽  
Inverse Heat Transfer

Sets of dry and wet boring experiments are conducted to estimate the amount of heat transferred into the workpiece and the cutting fluid heat convection coefficient in a boring operation by an inverse heat transfer method. The temperature distribution in the bore is predicted using a heat transfer model that includes heat convection on the inner and outer bore walls. The developed model is solved by an integral transform approach. The thermal expansion of the bore is then calculated using the finite element method (FEM). Surface error due to the cutting forces is also predicted using FEM and added to the thermally induced surface error to give the total surface error. The actual surface error of bores machined under dry and wet cutting conditions are measured and compared with the predicted surface error. Very good agreement between measured and predicted surface errors is observed. [S1087-1357(00)00802-9]

Rolling-Element Bearing Heat Transfer—Part II: Housing, Shaft, and Bearing Raceway Partial Differential Equation Solutions

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
William M. Hannon
Keyword(s):  
Heat Transfer ◽  
Fourier Transform ◽  
Control Volume ◽  
Integral Transforms ◽  
Analytic Solutions ◽  
Rolling Element Bearing ◽  
Partial Differential ◽  
Rolling Element ◽  
Bearing Raceway ◽  
Element Bearing

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.

An Enhanced Study of the Load–Displacement Relationships for Rolling Element Bearings

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
L. Houpert
Keyword(s):  
Contact Angle ◽  
Roller Bearing ◽  
Rolling Element Bearing ◽  
Smooth Transition ◽  
Ball Bearings ◽  
Element Analysis ◽  
Outer Race ◽  
Deep Groove ◽  
Rolling Element ◽  
Element Bearing

An enhanced analytical approach is suggested for calculating three rolling element bearing loads Fx, Fy, and Fz as well as the two tilting moments My and Mz as a function of five relative race displacements: three translations dx, dy, and dz, and two tilting angles dθy and dθz. A full coupling between all these displacements and forces is considered. This approach is particularly recommended for programming the rolling element bearing behavior in any finite element analysis or multibody system dynamic tool, since only two nodes are considered: one for the inner race center, usually connected to a shaft, and another node for the outer race center, connected to the housing. Also, roller and raceway crown radii are considered, meaning that Hertzian point contacts stiffness can be used at low load with a smooth transition toward Hertzian line contact as the load increases. This approach can be used for describing any rolling element bearing type when neglecting centrifugal and gyroscopic effects and applying the approximation of a constant ball–race contact angle. Deep groove ball bearings (whose contact angle sign follows the sign of the applied bearing axial force) or other ball bearings or spherical roller bearing operating under large misalignment may not support such approximations.

Tire Bead Overheating in Urban Buses and Trucks Using Drum Brake Systems

1998 ◽  
Vol 26 (1) ◽  
pp. 51-62
Author(s):  
A. L. A. Costa ◽  
M. Natalini ◽  
M. F. Inglese ◽  
O. A. M. Xavier
Keyword(s):  
Heat Transfer ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Thermal Energy ◽  
Structural Integrity ◽  
Experimental Temperature ◽  
Temperature Profiles ◽  
Element Analysis ◽  
Drum Brake ◽  
Fea Model

Abstract Because the structural integrity of brake systems and tires can be related to the temperature, this work proposes a transient heat transfer finite element analysis (FEA) model to study the overheating in drum brake systems used in trucks and urban buses. To understand the mechanics of overheating, some constructive variants have been modeled regarding the assemblage: brake, rims, and tires. The model simultaneously studies the thermal energy generated by brakes and tires and how the heat is transferred and dissipated by conduction, convection, and radiation. The simulated FEA data and the experimental temperature profiles measured with thermocouples have been compared giving good correlation.

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