Gas Thermohydrodynamic Lubrication and Seals

By Bai Shaoxian and Wen Shizhu

Gas Thermohydrodynamic Lubrication and Seals provides contemporary theory and methods for thermo-hydrodynamic lubrication analysis in the design of gas bearings and seals. The title includes information on gas state equations and gas property, derivation of gas thermohydrodynamic lubrication equations, the theory of isothermal gas lubrication, thermal gas lubrication of rigid surfaces, gas thermoelastic hydrodynamic lubrication of face seals, vapor-condensed gas lubrication of face seals, experimental methods, and the design of gas face seals. Readers will find state-of-the-art, practical knowledge based on fifty years of research and application.

• Describes thermohydrodynamic lubrication analysis for the design of gas bearings and seals
• Considers the increased operational speed, pressure and temperature of mechanical equipment in relation to gas bearings and seals
• Describes multi-field coupled gas lubrication theory and analytical methods
• Provides a model and detailed data on the lubricating properties of typical gas bearings and seals
• Gives comprehensive coverage of the field based on a half-century of research and application

• Language: English
• Publisher: Academic Press
• Release date: Jul 10, 2019
• ISBN: 9780128172919

Bai Shaoxian

Bai Shaoxian is a professor at Zhejiang University of Technology in China. He received a PhD in mechanical engineering from South China University of Technology, and has over 10 years’ experience in fluid lubrication and sealing technology, particularly the theory of gas thermohydrodynamic lubrication. His research focusses on thermohydrodynamic lubrication, and the design of mechanical seals.

Book preview

Preface

Bai Shaoxian, Hangzhou

Gas lubrication is a form of fluid lubrication, which uses air or working medium gas as a lubricant to separate two friction pairs moving in relation to each other. It has the advantages of low friction resistance, high working accuracy, and a wide range of applicable temperatures, and is widely used in the design of gaseous static pressure bearings, high-speed thrust bearings, foil bearings, mechanical seals, and other mechanical parts and equipment under extreme conditions such as extremely high or low temperatures, ultra-high or -low speeds, and ultra-precision.

In 1854, Hirm came up with the idea of using gas as a lubricant. In 1886, Reynolds deduced the Reynold’s equation describing the pressure distribution of fluid lubrication film, which raised people’s understanding of the principle of fluid lubrication to a theoretical height. In the 1950s, research on gas lubrication theory based on bearing design requirements developed rapidly. In 1959, Elrod and Burgdorfer theoretically explained that the temperature rise effect inside the lubrication gas film could be ignored under general working conditions, and the isothermal hypothesis was generally accepted in gas lubrication analysis. After the 1980s, the development of magnetic storage technology pushed the film thickness of gas bearings from microns to nanometers, and microscopic effects such as the gas thinning effect and surface roughness were widely studied, which promoted the development of gas thin film lubrication theory.

With an increase of rotation speed in mechanical equipment and the appearance of new bearing structures, the problem of gas thermodynamic lubrication became increasingly prominent. For example, in a gas hydrostatic bearing under the conditions of a film thickness of 20 μm, pressure of 0.7 MPa, and rotation speed of 20,000 rpm, shear heat can cause the gas film lubrication temperature to rise above 30°C. The increase of rotor temperature rise and gas viscosity can improve the stiffness and damping coefficient of the bearing, but in the absence of sufficient cooling, the bearing is prone to thermal instability, which is particularly prominent in a high-speed bearing design.

Compared with bearing gas lubrication dominated by shear flow, there is also pressure flow caused by seal pressure in the gas seal lubrication area. In the process of gas leakage flow from the high-pressure side to the low-pressure side, gas film temperature decreases because of rapid volume expansion, resulting in thermal distortion and other gas thermohydrodynamic lubrication problems.

In 1968, the John Crane Company first developed the circular arc surface spiral groove gas-lubricated seal and introduced plane spiral groove gas-lubricated seal products. With the development of gas sealing technology to high-temperature, high-pressure, high-speed, and other high parameters; the diversification of sealing media; and the continuous expansion of application fields, the surface thermal distortion, supersonic flow, media phase change, and other gas thermohydrodynamic lubrication problems are increasing.

Based on the research methods and results of elastohydrodynamic lubrication theory of Prof. Wen Shizhu, this book summarizes the research results of the authors in recent years. Grounded in the application background of lubrication design of high-speed gas bearings and high-pressure gas seals, theory and analysis methods of gas thermohydrodynamic lubrication are systematically expounded. In this book, theoretical model and lubrication characteristics of gas lubrication are discussed for typical bearings and seals.

The book is divided into 10 chapters.

In Chapter 1, Properties of gases, properties of gases are introduced. Based on the principle of energy equipartition, the ideal gas state equation is decomposed into two independent gas equations.

In Chapter 2, Gas lubrication equations, the derivation of the Reynolds equation, energy equation, heat conduction equation, interface equation, and other basic lubrication equations are explained. The lubrication analysis of force balance and flow conservation problems are also discussed.

In Chapter 3, Isothermal gas lubrication, we introduce the modeling method and basic lubrication characteristics of isothermal gas lubrication of typical structures such as the slider bearing, radial bearing, thrust bearing, and face seal.

In Chapter 4, Gas thermohydrodynamic lubrication of rigid surfaces, the gas thermodynamic lubrication law of gas-lubricated bearings and low-pressure gas seals under high-speed working conditions are analyzed without consideration of surface distortions.

Chapter 5, Gas thermoelastichydrodynamic lubrication of face seals, discusses the high-pressure gas face seal, the modeling method of TEHL, and fundamental characteristics of choked flow effect, thermoelastic distortion of seal faces, and the temperature distribution of gas film.

In Chapter 6, Transient thermoelastichydrodynamic gas lubrication of face seals, targets the gas face seal, dynamic load characteristics of the seal gas film under the conditions of isothermal lubrication, rigid surface thermal lubrication, and TEHL, exploring these in detail.

Chapter 7, Vapor-condensed gas lubrication of face seals, explores the face seal of high-pressure gas, the law of condensation and precipitation of water vapor in the seal gas film, and the movement of liquid drops in the seal gap under TEHL conditions.

Chapter 8, Cryogenic gas lubrication of face seals, uses the inclined ellipse dimpled gas face seal as an example and natural gas as the sealing medium to introduce the modeling method of cryogenic gas lubrication and the fundamental characteristics of phase change in seal film and thermoelastic distortion of seal faces.

In Chapter 9, Surface grooves of gas face seals and testing technology, typical seal grooves and their laser processing methods and experimental measurement methods are presented. Opening characteristics, hydrodynamic characteristics, and friction characteristics of gas face seals are discussed by taking the micro-dimpled face seal as an example.

In Chapter 10, Design of gas face seals, an internal flow single-face spiral groove gas seal is used as an example to introduce the basic method and design process of gas face seals.

In the process of compiling this book, Prof. Huang Ping has given great support and help. Here I would like to express my sincere gratitude. At the same time, I would like to express my heartfelt thanks to my colleagues and graduate students who have given me warm support and help in the preparation of this book.

Chapter 1

Properties of gases

Abstract

Viscosity and other fluid properties are the material preconditions for fluid lubrication. Because of the compressibility and the strong coupling between density and temperature and pressure, lubrication gases show different viscosity–pressure and viscosity–temperature relationships compared to liquids. In addition, water held in gas often leads to a condensing problem in high-pressure gas seals, which also makes characteristics of gas lubrication different from those of liquid lubrication. Essentially, it depends on the physical properties of the gas.

This chapter introduces a basic knowledge of gases related to lubrication calculation, including equations of the gas state, the relationship between viscosity, and pressure and temperature and the relationship between humidity and pressure and temperature.

Keywords

Viscosity; gas equation; relationship; pressure; humidity; temperature

Viscosity and other fluid properties are the material preconditions for fluid lubrication. Because of the compressibility and the strong coupling between density and temperature and pressure, lubrication gases show different viscosity–pressure and viscosity–temperature relationships compared to liquids. In addition, water held in gas often leads to a condensing problem in high-pressure gas seals, which also makes characteristics of gas lubrication different from those of liquid lubrication. Essentially, it depends on the physical properties of the gas.

This chapter introduces a basic knowledge of gases related to lubrication calculation, including equations of the gas state; the relationship between viscosity, and pressure and temperature; and the relationship between humidity and pressure and temperature.

1.1 Gas equations

In gas lubrication, the flow of gas is also the process of changing the state of gas. Generally, the gas lubrication Reynolds equation describes the macroscopic motion of the gas under external forces such as velocity shear and extrusion, and the energy equation presents the relationship between gas and external heat exchange and the transformation of macroscopic mechanical energy and gas. The description of the state of the gas microthermal motion is described by the three parameters of pressure p, density ρ, and temperature T. For an ideal gas, the relationship between pressure, density, and temperature satisfies the ideal gas state equation,

(1.1)

where the ideal gas constant Ru=8.314472 m³ Pa/(mol K).

For a general thermal process when the pressure, density, and temperature change at the same time, a single use of the ideal gas state equation cannot give change values of the pressure, seal, and temperature because there are three variables in the equation. So, we need to build another gas equation.

The Brownian motion, discovered in 1827 by British botanist Gordn Brown, is a state of movement of microscopic particles in gases or liquids, and was discovered in 1827 by British botanist Gordon Brown. In 1907, Einstein proposed the energy equipartition principle. This basic theory of statistical mechanics holds that the kinetic energy of a microscopic particle depends only on its temperature, regardless of its size or mass. However, it had been unable to directly prove the equipartition theorem for Brownian particles because the high-speed collision between the particles in Brownian motion led to constant direction and speed change, making the instantaneous velocity of a particle in Brownian motion difficult to measure. In 2010, Li et al.’s experimental work [1] proved that the energy equipartition principle is correct for air. This provides a new way to discuss gas thermal effect in gas lubrication.

We discussed and analyzed the characterization of gas pressure and temperature based on the energy equipartition principle, and established the independent equation of pressure and temperature for an ideal gas, which makes it possible to calculate the gas temperature field for any thermal process [2]. The gas equations based on the energy equipartition principle are introduced in this section.

1.1.1 Ideal gas equations

Generally, ideal gas molecule movement can be dealt with using the rigid sphere model. Fig. 1.1 illustrates freedom of an ideal gas molecular motion. As shown in Fig. 1.1, an ideal gas molecular motion includes translation and rotation motions in the x, y, and z directions. When temperature is high, there are additional vibration motions for gas molecular movement. Motion in each of these directions is counted as one degree of freedom. According to the energy equipartition principle, the energy per degree of freedom for these kinds of motions is equal to Em. So, gas molecular energy can be expressed as