Finite Element Solution of the Steady-State Compressible Lubrication Problem

1970 ◽  
Vol 92 (3) ◽  
pp. 495-502 ◽  
Author(s):  
M. M. Reddi ◽  
T. Y. Chu
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Reynolds Equation ◽  
Finite Element Solution ◽  
Element Solution ◽  
Variational Formulations

Direct and incremental variational formulations for the steady-state compressible Reynolds’ equation are given. Finite element equations for these are derived and sample solutions are presented.

A Hybrid Mobility Solution Method for Dynamically Loaded Misaligned Journal Bearings

2012 ◽  
Author(s):  
S. Boedo
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Solution Method ◽  
Hybrid Approach ◽  
Journal Bearings ◽  
Finite Element Solution ◽  
Computational Time ◽  
Element Solution ◽  
Dynamically Loaded ◽  
Mobility Solution

This paper presents a hybrid mobility solution approach to the analysis of dynamically loaded misaligned journal bearings. Mobility data obtained for misaligned bearings (calculated from a finite element representation of the Reynolds equation) are compared with existing curve-fitted mobility maps representative of a perfectly aligned bearing. A relative error analysis of mobility magnitude and direction provides a set of misaligned journal bearing configurations (midplane eccentricity ratio and normalized misalignment angle) where existing curve-fitted mobility map components based on aligned bearings can be used to calculate the resulting journal motion. For bearing configurations where these mobility maps are not applicable, the numerical simulation process proceeds using a complete finite element solution of the Reynolds equation. A set of numerical examples representing misaligned main and connecting rod bearings in a four-stroke automotive engine illustrate the hybrid solution method. Substantial savings in computational time are obtained using the hybrid approach over the complete finite element solution method without loss of computational accuracy.

A Hybrid Mobility Solution Approach for Dynamically Loaded Misaligned Journal Bearings

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
S. Boedo
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Solution Method ◽  
Journal Bearings ◽  
Finite Element Solution ◽  
Computational Time ◽  
Element Solution ◽  
Solution Approach ◽  
Dynamically Loaded ◽  
Mobility Solution

This paper presents a hybrid mobility solution approach to the analysis of dynamically loaded misaligned journal bearings. Mobility data obtained for misaligned bearings (calculated from a finite element representation of the Reynolds equation) are compared with existing curve-fitted mobility maps representative of a perfectly aligned bearing. A relative error analysis of mobility magnitude and direction provides a set of misaligned journal bearing configurations (midplane eccentricity ratio and normalized misalignment angle), where existing curve-fitted mobility map components based on aligned bearings can be used to calculate the resulting journal motion. For bearing configurations where these mobility maps are not applicable, the numerical simulation process proceeds using a complete finite element solution of the Reynolds equation. A numerical example representing a misaligned main bearing in a four-stroke automotive engine illustrates the hybrid solution method. Substantial savings in computational time are obtained using the hybrid approach over the complete finite element solution method without loss of computational accuracy.

Transient and Steady-State Dynamic Finite Element Modeling of Belt-Drives

2002 ◽  
Vol 124 (4) ◽  
pp. 575-581 ◽  
Author(s):  
Michael J. Leamy ◽  
Tamer M. Wasfy
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Angular Velocity ◽  
Frictional Contact ◽  
Finite Element Solution ◽  
Belt Drive ◽  
Element Solution ◽  
Dynamic Finite Element ◽  
Time Accuracy ◽  
Transient And Steady State

In this study, a dynamic finite element model is developed for pulley belt-drive systems and is employed to determine the transient and steady-state response of a prototypical belt-drive. The belt is modeled using standard truss elements, while the pulleys are modeled using rotating circular constraints, for which the driver pulley’s angular velocity is prescribed. Frictional contact between the pulleys and the belt is modeled using a penalty formulation with frictional contact governed by a Coulomb-like tri-linear friction law. One-way clutch elements are modeled using a proportional torque law supporting torque transmission in a single direction. The dynamic response of the drive is then studied by incorporating the model into an explicit finite element code, which can maintain time-accuracy for large rotations and for long simulation times. The finite element solution is validated through comparison to an exact analytical solution of a steadily-rotating, two-pulley drive. Several response quantities are compared, including the normal and tangential (friction) force distributions between the pulleys and the belt, the driven pulley angular velocity, and the belt span tensions. Excellent agreement is found. Transient response results for a second belt-drive example involving a one-way clutch are used to demonstrate the utility and flexibility of the finite element solution approach.

A General Model for Liquid and Gas Lubrication, Including Cavitation

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Noël Brunetière
Keyword(s):  
Finite Element ◽  
General Model ◽  
Reynolds Equation ◽  
Previous Literature ◽  
Finite Element Solution ◽  
Element Solution ◽  
Gas Lubrication ◽  
Continuous Description

This paper presents a general formulation of the Reynolds equation for gas and liquid lubricants, including cavitation. A finite element solution of this equation is also given. The model is compared to those obtained in the previous literature on liquid and gas lubrication. One of the advantages of the model is the continuous description of cavitation in liquid lubrication. It is possible to deal with all lubricants by adjusting the amount of gas in the fluid.

scholarly journals Finite Element Solution of the Steady-State Smoluchowski Equation for Rate Constant Calculations

2004 ◽  
Vol 86 (4) ◽  
pp. 2017-2029 ◽  
Author(s):  
Yuhua Song ◽  
Yongjie Zhang ◽  
Tongye Shen ◽  
Chandrajit L. Bajaj ◽  
J. Andrew McCammon ◽  
...  
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Rate Constant ◽  
Smoluchowski Equation ◽  
Finite Element Solution ◽  
Element Solution
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