Improved Method for Numerical Solutions of the General Incompressible Fluid Film Lubrication Problem

1967 ◽  
Vol 89 (2) ◽  
pp. 211-218 ◽  
Author(s):  
V. Castelli ◽  
W. Shapiro
Keyword(s):  
Numerical Analysis ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Incompressible Fluids ◽  
Supply System ◽  
The Other ◽  
Improved Method ◽  
Lubrication Equation ◽  
Film Lubrication ◽  
Fluid Film Lubrication

A numerical analysis for determining performance characteristics of hydrodynamic, hydrostatic, or hybrid bearings with arbitrary clearance distribution is presented. Solution of the Reynolds lubrication equation for incompressible fluids is achieved by formation of coefficient matrices that act upon column vectors of the pressures progressively from one boundary to the other without requiring an iterative scheme. Multiple recesses are handled by component solutions. The external supply system is included and solved for an arbitrary type of individual recess compensation and supply circuit network. Sample results are indicated.

A Mass-Conserving Complementarity Formulation to Study Fluid Film Lubrication in the Presence of Cavitation for Non-Newtonian and Compressible Fluids

2012 ◽  
Author(s):  
Luca Bertocchi ◽  
Matteo Giacopini ◽  
Antonio Strozzi ◽  
Mark T. Fowell ◽  
Daniele Dini
Keyword(s):  
Reynolds Equation ◽  
Incompressible Fluids ◽  
Compressible Fluids ◽  
Contact Pressure Distribution ◽  
One Dimensional ◽  
The Stability ◽  
Mathematical Derivation ◽  
Dimensional Domain ◽  
Film Lubrication ◽  
Fluid Film Lubrication

A mass-conserving formulation of the Reynolds equation has been recently developed using the concept of complementarity [1]. The mathematical derivation of the Linear Complementarity Problem (LCP) implemented in the solver favoured in [1] overcomes the drawbacks previously associated with the use of such complementarity formulations for the solution of cavitation problems in which reformation of the liquid film occurs. In the present paper, the proposed methodology, already successfully applied to solve textured bearing and squeeze problems in the presence of cavitation in a one dimensional domain and for incompressible fluids [1], has been extend to a two dimensional domain and the fluid compressibility has been included in the formulation. The evolution of the cavitated region and the contact pressure distribution are studied for a number of different configurations. Some of the results obtained with the proposed scheme are critically analysed and compared with the predictions obtained using alternative formulations (including full CFD calculations). The stability of the proposed algorithm and its flexibility in terms of the implementation of different compressibility laws is highlighted.

Two-Dimensional Elastohydrodynamic Lubrication Part 2: Solution of the Line Contact Problem

1988 ◽  
Vol 202 (5) ◽  
pp. 354-360 ◽  
Author(s):  
R W Hall ◽  
M D Savage
Keyword(s):  
Contact Problem ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Elastohydrodynamic Lubrication ◽  
Parameter Range ◽  
Line Contact ◽  
Two Dimensional ◽  
Lubrication Equation ◽  
Lubricated Contact

Following Part 1, this paper describes a method for solving the line contact problem in elastohydrodynamic lubrication. Using results derived in Part 1 together with the Reynolds lubrication equation and boundary conditions, an iterative scheme is designed so as to yield pressures, displacements and film thicknesses within a parabolic, lubricated contact. Converged numerical solutions are readily obtained over a parameter range which includes both isoviscous and weakly piezoviscous contacts.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

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