Numerical Calculation of Lubrication

Methods and Programs

Ping Huang

• Publisher: Wiley
• Year: 2013
• Print ISBN: 9781118451199
• eBook ISBN: 9781118451229
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

Focusing on basic lubrication problems this book offers specific engineering applications. The book introduces methods and programs for the most important lubrication problems and their solutions. It is divided into four parts. The first part is about the general solving methods of the Reynolds equation, including solutions of Reynolds equations with different conditions and their discrete forms, such as a steady-state incompressible slider, journal bearing, dynamic bearing, gas bearing and grease lubrication. The second part gives the 'energy equation solution'. The third part introduces methods and programs for elasto-hydrodynamic lurbication, which links the Reynolds equation with the elastic deformation equation. The final part presents application lubrication programs used in engineering.

• Provides numerical solution methodologies including appropriate software for the hydrodynamic and elasto-hydrodynamic lubrication of bearings
• Offers a clear introduction and orientation to all major engineering lubrication problems and their solutions
• Presents numerical programs for specific applications in engineering, with special topics including grease-lubricated bearings and gas bearings
• Equips those working in tribology and those new to the topic with the fundamental tools of calculation
• Downloadable programs are available at the companion website

With an emphasis on clear explanations, the text offers a thorough understanding of the numerical calculation of lubrication for graduate students on tribology and engineering mechanics courses, with more detailed materials suitable for engineers. This is an accessible reference for senior undergraduate students of tribology and researchers in thin-film fluid mechanics.

Part One

Numerical Method for Reynolds Equation

1

Reynolds Equation and its Discrete Form

1.1 General Reynolds Equation and Its Boundary Conditions

1.1.1 Reynolds Equation

The general form of the Reynolds equation is

(1.1)

where U = U ₀–U _h; V = V ₀–V _h. If we assume that the fluid density does not change with time, we have

.

1.1.2 Definite Condition

The definite conditions of the Reynolds equation usually include the boundary conditions, the initial conditions and the connection conditions.

1.1.2.1 Boundary Condition

In order to solve the Reynolds equation, the pressure boundary conditions should be used to determine the integration constants. There are commonly two forms of pressure boundary conditions, namely

where s is the boundary of the solution domain; and n is the normal direction of the border.

Usually, the inlet and outlet pressure boundaries for an oil film can be easily determined according to its geometry and the situation of the oil supply. However, such as a journal bearing which has both a convergence clearance and a divergence clearance, the position of the outlet cannot be determined in advance. Therefore, it can be assumed that both pressure and pressure derivative are equal to zero at the same time to determine the location of the outlet. Such a boundary condition is known as the Reynolds boundary condition, which is in this form

Here are two examples of boundary conditions.

One-dimensional boundary conditions in the region of 0 ≤ x ≤ l

If the boundaries are known, we have

and

.

If the outlet is unknown, we have

,

and

, where x ′ is the outlet boundary to be determined.

Two-dimensional boundary conditions in the rectangular area of (0 ≤ x ≤ l, −b /2 ≤ y ≤ b /2)

If the boundaries are known, we have

and

If the outlet is unknown, we have

,

,

and

.

1.1.2.2 Initial Condition

For the nonsteady-state lubrication problem in which the velocity and/or the load change with time, such as the fluid hydrodynamic lubrication of a crankshaft bearing in the internal combustion engine, the Reynolds equation contains the squeeze term at the right end of Equation 1.1. The lubrication film thickness changes with time, so we need to give some initial conditions for solving the Reynolds equation. The general forms of the initial condition are as follows.

Initial film thickness:

Initial pressure:

If the lubricant viscosity and density also vary with time, their initial conditions should also be given.

1.1.2.3 Connection Condition

If the film thickness varies abruptly in several ...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Part One: Numerical Method for Reynolds Equation
• Part Two: Numerical Method for Energy Equation
• Part Three: Numerical Method for Elastic Deformation and Thermal Elastohydrodynamic Lubrication
• Part Four: Calculation Programs for Lubrication Analysis in Engineering
• References
• Index