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.

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.

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.

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.

Contact characteristic and vibration mechanism of rolling element bearing in the process of fault evolution

2021 ◽  
Vol 235 (1) ◽  
pp. 19-36 ◽  
Author(s):  
Wenbing Tu ◽  
Jinwen Yang ◽  
Wennian Yu ◽  
Ya Luo
Keyword(s):  
Fault Diagnosis ◽  
Vibration Response ◽  
Rolling Element Bearing ◽  
Bearing Fault Diagnosis ◽  
Rolling Element ◽  
Vibration Mechanism ◽  
Contact Characteristic ◽  
Element Bearing ◽  
Bearing Vibration ◽  
Fault Evolution

The vibration response of rolling element bearing has a close relation with its fault. An accurate evaluation of the bearing vibration response is essential to the bearing fault diagnosis. At present, most bearing dynamics models are built based on rigid assumptions, which may not faithfully reveal the dynamic characteristics of bearing in the presence of fault. Moreover, previous similar works mainly focus on the fault with a specified size without considering the varying contact characteristics as the fault evolves. This paper developed an explicit dynamics finite element model for the bearing with three types of raceway faults considering the flexibility of each bearing component in order to accurately study the contact characteristic and vibration mechanism of defective bearings in the process of fault evolution. The developed model is validated by comparing its simulation results with both analytical and experimental results. The dynamic contact patterns between the rolling elements and the fault, the additional displacement due to the fault and the faulty characteristics within the bearing vibration signal during the fault evolution process are investigated. The analysis results from this work can provide practitioners an in-depth understanding towards the internal contact characteristics with the existence of raceway fault and theoretical basis for rolling bearing fault diagnosis.

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