Lubricants and Lubrication

List of Contributors

Thorsten Bartels

Dr.-Ing., Weisenheim am. Sand, Germany

Evonik Resource Efficiency GmbH

Director Performance Testing

Wolfgang Bock

Dipl.-Ing., Weinheim, Germany

Fuchs Schmierstoffe GmbH

International Product Management Industrial Oils

Jürgen Braun

Dr. rer. nat., Speyer, Germany

Fuchs Schmierstoffe GmbH

Head of R&D for Industrial Oils

Christian Busch

Prof. Dr. Ing., Zwickau, Germany

Westsächsische Hochschule Zwickau

Vice President

Wilfried Dresel

Dr. rer. nat., Mannheim, Germany

Fuchs Petrolub SE

R&D for Lubricating Greases (International)

Carmen Freiler

Dipl.-Ing., Hüttenfeld, Germany

Fuchs Schmierstoffe GmbH

Head of R&D and Product Management for Metal Cutting Fluids

Apu Gosalia

Dipl.-Kfm/MBA, Mannheim Germany

Fuchs Petrolub SE

Vice President Sustainability & Global Competitive Intelligence

Manfred Harperscheid

Dr. rer. nat., Römerberg, Germany

Fuchs Schmierstoffe GmbH

Head of R&D for Engine Oils

Rolf-Peter Heckler

Dipl.-Ing., Rimbach, Germany

Fuchs Petrolub SE

International Product Management for Lubricating Greases

Dietrich Hörner

Dr. rer. nat., Hassloch, Germany

Fuchs Petrolub SE

International Product Management for Metal working Fluids and Quenching Oils

Franz Kubicki

Dipl.-Ing., Hockenheim, Germany

Fuchs Petrolub SE

International Product Management for Corrosion Preventives and Sheet Metal forming

Georg Lingg

Dr.-Ing., Mannheim, Germany

Fuchs Petrolub SE

Member of the Executive Board, (until 2013)

Achim Losch

Dr. rer. nat., Westhofen, Germany

Fuchs Schmierstoffe GmbH

Head of R&D for Corrosion Preventives, Metal forming and Cleaners

Rolf Luther

Dipl.-Phys., Speyer, Germany

Fuchs Schmierstoffe GmbH

Head of Advanced Development

Theo Mang

Prof. Dr.-Ing., Weinheim, Germany

Fuchs Petrolub SE

Group's Executive Board, Technology, Group Purchasing, Human Resources (retired)

Roman Müller

Chem. Eng., Mannheim, Germany

Fuchs Petrolub SE

Vice President Know How Transfer/Group Laboratory

Christian Puhl

Dipl.-Ing., Grünstadt, Germany

Fuchs Schmierstoffe GmbH

Product Management for Compressor and Turbine Oils

Nael Zaki

Ph.D., Shawnee, Kansas, USA

Fuchs Lubricants Co.

Lubricating Grease R&D Manager

A Word of Thanks

We thank the Vogel-Verlag for permission to use texts and illustrations from the book titled Schmierstoffe in der Metallbearbeitung written by Prof. Dr. Mang, published in Würzburg in 1983.

The authors thank the following persons for their specialist and linguistic contributions:

Prof. Dr. Dieter Schmoeckel and Dirk Hortig, Institut für Produktions- und Umformtechnik, Darmstadt, Germany; Prof. Will Scott, Tribology Research Group, Queensland University of Technology, Australia; Dr. Anand Kakar, FUCHS LUBRICANTS Co., Emlenton, PA; Paul Wilson, FUCHS LUBRICANTS CO., Harvey, IL; Ted McClure, FUCHS LUBRICANTS CO., Harvey, IL; Albert Mascaro, FUCHS LUBRICANTES, Castellbisbal, Spain; Cliff Lea, FUCHS LUBRICANTS (UK), Stoke-on-Trent, UK; Paul Littley, FUCHS LUBRICANTS (UK), Stoke-on-Trent, UK; Heinz-Gerhard Theis, FUCHS, Mannheim, Germany; Mercedes Kowallik FUCHS, Mannheim, Germany; Dr. Helmut Seidel, FUCHS LUBRITECH GmbH, Weilerbach, Gisela Dressler, FUCHS PETROLUB AG, Mannheim, Germany; Ursula Zelter, FUCHS PETROLUB AG, Mannheim, Germany and Jochen Held, Bolanden-Weierhof, Germany.

Roman Müller would extend his special thanks to his former Supervisor and mentor, Siegfried Noll of FUCHS PETROLUB AG, Mannheim, who drew up the initial version of Chapter 18 in the 1st edition of Lubricants and Lubrication.

Dr. Thortsen Bartels, Evonik Resource Efficiency GmbH, Darmstadt, the test laboratory engineers Daniel Debus, Lucas Voigt, test assistants Ludwig Herdel, Marcus Stephan and Robert Cybert for collecting and preparing descriptions, making literature searches, providing valuable information and for preparing figures used in Chapter 19. The author also thanks Wolfgang Bock and Dr. Manfred Harperscheid for the good cooperation, and for providing detailed information and their permission to use their data and figures in Chapter 10.

Prof. Dr. Theo Mang thanks SKF Lubrication Systems Germany AG, formerly Willy Vogel AG, to use the internal papers of the Company in Chapter 20. He thanks especially Frank Bechtloff, Jan Ruiter, Götz Mehr, Alexander Tietz and Hans Gaca. He also thanks Dr. Hermann-J. Gummert, Viersen, Germany, Dr. Kai F. Karhausen, Hydro Aluminium Rolled Products GmbH, Bonn Germany as well as Dr. Hartmut Pavelski, SMS Siemag AG, Erhard Schloemann, Düsseldorf, Germany, for important Information in the area of drawing and rolling (Chapter 15).

Preface to the 3rd Edition

Nine years after the publication of the second edition of Lubricants and Lubrication, its high acceptance motivated the publisher and the editors to realize a third edition. The result is this largely revised and extended version in two volumes.

The use of lubricants is as old as the history of mankind but the scientific analysis of lubrication, friction and wear as an aspect of tribology is relatively new. The reduction of friction along with the reduction or even avoidance of wear by the use of lubricants and lubrication technologies results in energy savings, the protection of resources and also fewer emissions. These benefits describe the economic and ecological importance of this field of work.

This third edition spent more attention to environmental facts, to new energies, test methods for lubricants and modern applications of lubricants with centralized lubrication systems and the removal of lubricants in two additional chapters.

Only recently have lubricants begun to be viewed as functional elements in engineering and this group of substances are also attracting increasing attention from engineers.

This book offers chemists and engineers a clear interdisciplinary introduction and orientation to all major lubricant applications. The book focuses not just on the various products but also on specific application engineering criteria.

The authors are internationally recognized experts. All can draw on many years of experience in lubricant development and application.

This book offers the following readers a quick introduction to this field of work: the laboratory technician who has to monitor and evaluate lubricants; plant maintenance people for whom lubricants are an element in process technology; research and development people who have to deal with friction and wear; engineers who view lubricants as functional elements and as media which influence service life and increasingly safety and environmental protection officers who are responsible for workplace safety, an acceptable use of resources along with the reduction or avoidance of emissions and wastes.

Theo Mang

October 2016 Wilfried Dresel

Abbreviations

1

Lubricants and Their Market

Theo Mang and Apu Gosalia

1.1 Introduction

The main task and most important function of lubricants are to reduce friction by lubricants and offer wear protection, which extends machine runtimes and thereby protects raw materials. In some cases, the relative movement of two bearing surfaces is possible only if a lubricant is present. At present times when sustainability has become a driving force in the industry, saving energy and resources as well as cutting emissions have become central environmental matters. Therefore, the scarcity of resources and the responsibility towards future generations are also a particular focus of corporate action. Lubricants are increasingly attracting public awareness, because they support sustainability targets in economic, ecological and social areas. Lubricants make a contribution to the sparing use of resources and thereby to sustainability. Their task of reducing friction reduces the amount of energy input required and in this way saves emissions. Their task of wear protection extends the service life of equipment and saves resources. Scientific research has shown that up to 1% of gross domestic product could be saved in terms of energy in Western industrialized countries if current tribological knowledge, that is the science of friction, wear and lubrication, was just applied to lubricated processes.

Apart from important applications in internal combustion engines, vehicle and industrial gearboxes, compressors, turbines or hydraulic systems, there are a vast number of other applications which mostly require specifically tailored lubricants. This is illustrated by the numerous types of greases or the different lubricants for chip-forming and chip-free metalworking operations which are available. About 5000–10 000 different lubricant formulations are necessary to satisfy more than 90% of all lubricant applications.

If one thinks of lubricants today, the first type that comes to mind is mineral oil-based lubricant. Mineral oil continue to constitute quantitatively most important component of lubricants. Petrochemical components and increasing derivatives of natural, harvestable raw materials from the oleo-chemical industry are finding increasing acceptance because of their environmental compatibility and some technical advantages.

On average, lubricants consist of about 90% base oils and 10% chemical additives and other components on a volume basis, while on a value base the respective ratio is estimated to be around 80:20.

The development of lubricants is closely linked to the specific applications and application methods. As a simple description of materials in this field makes little sense, the following sections will consider both lubricants and their application.

1.2 Lubricants Demand

Lubricants today are classified into five product groups: automotive oils, industrial oils, greases, metalworking fluids (including corrosion preventatives) and process oils. Process oils are included as raw materials in processes, but above all as plasticizers for the rubber industry. Their only link with lubricants is that they are mineral oil products resulting from the refining of base oils, but they often distort lubricant consumption figures. Therefore, they will not be covered in this book.

Interestingly, the breakdown by product groups in the past 15 years only slightly changed. 56% of all lubricants still go into automotive oils (e.g. engine oils, gear oils and transmission fluids), which continue to be the prevailing product group and largely dictate what will be available (or not) for making other products. Only 26% are industrial oils, with the rest comprising process oils, lubricating greases, metalworking fluids and corrosion preventatives.

The global lube market volume (without marine oils) was at around 36 million tonnes at the turn of the millennium and more or less quite stable until 2008. Then lubricants demand on a worldwide basis plunged by more than 10% year-on-year to just around 32 million metric tonnes in 2009. Since 2010 the worldwide market consumption showed a partial recovery in light of the partly unexpected rapid economic growth, to nearly reach the 36 million tonnes level again in 2015. Thus, one could think that not much happened market volume-wise between 2000 and 2015 (Chart 1.1).

Chart 1.1 Development global lubricants demand [1–6].

However, the underlying regional lube market dynamics of the past 15 years were enormous in terms of quantity and quality. The Asia-Pacific region together with Africa and the Middle East accounted for a little more than one-third of global volume in 2000 and now makes more than half of it, as a result of growing industrialization and motorization and consequently higher consumption. The mature markets of Western Europe and North America experienced a continuous move to more quality lubricants, which resulted in extended oil change intervals and consequently lower demand per year. Asia-Pacific today consumes twice the lubricants amount per year than North America (Chart 1.2).

Chart 1.2 Development regional lubricants breakdown [1–6].

Since 1975, quantitative lubricant demand has significantly detached itself from gross national product and also from the number of registered vehicles. This quantitative view, which at first glance shows a continuous decline in lubricant volumes, gives an inadequate impression of the significance of the lubricants business today. In almost all areas, products now have a longer life and offer greater performance, that is specific lubricant consumption has declined but specific revenues have increased noticeably. This is also confirmed by the volumetrically very important group of engine oils: The doubling of requirements with extended oil change intervals in recent years has quadrupled the cost of such oils. The efforts to increase the life of lubricants are not based on the wish to reduce lubricant costs. Much more important is the reduction of service and maintenance costs which result from periodic oil changing or regreasing.

As about 50% of the lubricants sold worldwide end in and thus pollute the environment, every effort is made to minimize spillages and evaporation. An example is diesel engine particulate emissions, about a third of which are caused by engine oil evaporation. These high lubricant losses into the environment were behind the development of environment-friendly lubricants which are thoroughly covered in this book.

A further incentive to reduce specific consumption is the ever-increasing cost of disposal or recycling of used lubricants. But this again creates new demands on lubricants because reduced leakage losses means less topping-up and less refreshing of the used oil. The new oils must therefore display good ageing stability.

Another consequence of the aforementioned developments was that global per capita consumption decreased from around 9 to 5 kg per year between 1970 and 2015, that is the increase in lubricant demand (+7%) did not keep up with the worldwide growth in population (+90%) during this period; in other words, the compounded annual growth rate (CAGR) of world population between 1970 and 2015 was 1.6% and 10 times higher than the CAGR of global lubricants demand, which amounted to just 0.16% in this time frame (Chart 1.3).

Chart 1.3 Regional per capita lubricants demand [3,4,6].

Bearing in mind the growth potential in Asia where per capita consumption in some areas is still extremely low (2015: India 1 kg) and a continuing reduction in volumes or stagnation in Western industrialized countries, overall a modest global growth is forecast. The growth in value will be more pronounced because the rapid globalization of technologies will promote high-value products even in the developing and emerging lubricant markets such as India and the machines and plants used in these countries will be similar or identical to those used in the developed industrialized countries.

1.3 Lubricants Competitor Landscape

The structure of the global lubricants industry changed significantly between the mid-1990s and 2005. Towards the end of the 1990s, the petroleum industry was affected by a wave of mergers and acquisitions (M&A). These created new and larger lubricant structures at the merged companies. The principal reasons for these mergers were economic factors in crude oil extraction and refining which resulted in lower refining margins.

The number of manufacturers (with lubricants production over 1000 tonnes per year) decreased by close to 60% or in nominal terms by around 1000 players from around 1700 to just above 700 market participants at the end of 2005.

On the one hand, there are vertically integrated petroleum companies whose main business objective is the discovery, extraction and refining of crude oil (Majors). Lubricants account for only a very small part of their oil business. In 2005, there were about 130 such national and multinational oil companies engaged in manufacturing lubricants, with the focus on high-volume lubricants such as engine, gear and hydraulic oils.

The consolidation and concentration proceeded much stronger on the level of the small-sized and independent lube manufacturers (Independents), with technological, safety-at-work and ecological considerations along with the globalization of lubricant consumers playing an important role and critical mass becoming increasingly important in company strategies. Their number halved between 2000 and 2005 to around 600 players, down from around 1200 at the beginning of the millennium. These 590 independent lubricant companies view lubricants as their core business, focusing on specialties and niches, where apart from some tailor-made lubricants, comprehensive and expert customer service is part of the package. They mainly concentrate on the manufacturing and marketing of lubricants. The independent lubricant manufacturers also generally purchase raw materials on the open market from the chemical and oleo-chemical industry and their mineral base oils from the large petroleum companies and they rarely operate base oil refineries (Chart 1.4).

Chart 1.4 Structure global lubricants industry [1,3,4,6].

Consolidation nowadays proceeds rather slowly. In case there are deals, then they are mostly on a high-value basis. However, there are other driving forces in the competitive landscape of the industry today: The vertically integrated mineral oil companies of the ‘old world’ concentrate on big volume business and retract from niches. New and growing market participants enter the scene. Large oil companies restructure their lube businesses as stand-alone subsidiaries. National Oil Companies in China, South Korea and Russia, for example, go global. Companies, so far mostly known as raw material suppliers to the lubricants industry, go for vertical/forward or lateral diversification steps and Private Equity comes into play (Chart 1.5).

Chart 1.5 Driving forces global lubricants industry.

The aforementioned merger and acquisition activities changed the ranking of the top 15 lubricant manufacturers in the past 15 years:

EXXON and SHELL switched leading positions, after Shell acquired PENNZOIL

FUCHS gained 3 positions in the top 15 ranking and made it into the top 10 as number 9

GULF OIL, PERTAMINA and PETRONAS newly came into the top 15 ranking, while INDIAN OIL, AGIP and REPSOL had to leave it.

At the end of 2015, the top 15 manufacturers share two-thirds of the worldwide lube market, while the rest of more than 700 manufacturers share the other half.

The production of simple lubricants normally involves blending processes but specialties often require the use of chemical processes such as saponification (in the case of greases), esterification (when manufacturing ester base oils or additives) or amidation (when manufacturing components for metalworking lubricants). Further manufacturing processes include drying, filtration, homogenizing, dispersion or distillation. Depending on their field of activity, lubricant manufacturers invest between 1 and 5% of their sales in research and development (Chart 1.6).

Chart 1.6 Global ranking top 15 lubricants manufacturers [1,3,4,6].

1.4 Lubricant Systems

Apart from the most common lube oils, the many thousands of lubricant applications necessitate a diverse number of systems which is seldom equalled in other product groups.

The group next to oils are emulsions, which as oil-in-water emulsions are central to water-miscible cutting fluids (Chapter 14), rolling emulsions and fire-resistant HFA hydraulic fluids (Chapter 11). In these cases, the lubricant manufacturer normally supplies a concentrate which is mixed with water locally to form an emulsion. The concentration of these emulsions with water is generally between 1 and 10%. The annual consumption of such emulsions in industrialized countries is about the same as all other lubricants together. From this point of view, the volumetric proportion of these products (as concentrates) is significantly underrated in lubricant statistics with regard to the application engineering problems they create and their economic significance.

The next group of lubricant systems are water-in-oil emulsions. Their most important application is in metal forming. These products are supplied ready-to-use or as dilutable concentrates. Fire-resistant HFB fluids are designed as water-in-oil emulsions too (invert emulsions).

In some special cases, oil-in-oil emulsions are developed as lubricants and these are primarily used in the field of metalworking.

Water-based solutions in the form of non-dispersed systems are sometimes used in chip-forming metalworking operations.

Greases (Chapter 16) are complex systems consisting of base oils and thickeners based on soaps or other organic or inorganic substances. They are available in semiliquid form (semifluid greases) through to solid blocks (block greases). Special equipment is required for their production (grease-making plants). A group of products closely related to greases are pastes.

Solid lubricant suspensions normally contain solid lubricants in stable suspension in a fluid such as water or oil. These products are often used in forging and extrusion as well as other metalworking processes. Solid lubricant films can also be applied as suspensions in a carrier fluid which evaporates before the lubricant has to function.

Solid lubricant powders can be applied directly to specially prepared surfaces.

In the case of dry-film lubricants (Chapter 17), solid lubricants are dispersed in resin matrices. Dry-film lubricants are formed when the solvent (principally water or hydrocarbons) evaporates.

Molten salts or glass powder are used for hot forming processes such as extrusion. These are normally supplied as dry powders and develop lubricity when they melt on the hot surface of the metal.

Polymer films are used when special surface protection is required in addition to lubricity (e.g. the pressing of stainless steel panels). Together with greases, these products are also used to some extent in the construction industry.

An intermediary field between materials and lubrication technology is the wide area of surface treatment to reduce friction and wear. While the previously mentioned dry-film lubricants are an accepted activity of the lubricants industry, chemical coatings are somewhat controversial. These coatings are chemically bonded to the surface of the metal. They include oxalation and phosphating (zinc, iron and manganese). In cases when such coatings adopt the carrier function of an organic lubricant, the entire system could be supplied by the lubricant manufacturer. If the chemical coating is not designed to be supplemented with an additional lubricant coating (e.g. dry film on phosphatized gear), it will probably be supplied by a company which specializes in surface degreasing and cleaning.

Even more different from traditional lubricants are metallic or ceramic coatings which are applied with CVD (chemical vapour deposition) or PVD (physical vapour deposition) processes. They also sometimes replace the EP functions of the lubricants (Chapter 6). Such coatings are increasingly being used together with lubricants to guarantee improved wear protection in extreme conditions and over long periods of time.

References

1 Fuchs, M. (2002) The world lubricants market: year 2001 and outlook, 13th International Colloquium Tribology on Lubricants, Materials, and Lubrication Engineering, Technische Akademie Esslingen (TAE), Esslingen.

2 Lindemann, L. (2013) Lubricant development against the background of new raw materials, OilDoc Conference, Rosenheim.

3 Gosalia, A. (2013) The Lubricants Industry & FUCHS: A Journey along the Process & Value Chain, FUCHS Bankeninformationsveranstaltung, Mannheim.

4 Gosalia, A. (2013) Sustainability & Intelligence @ FUCHS, Mannheim Business School & Tongji Executive MBA Module, Competition & Industry, Mannheim.

5 Gosalia, A. (2012) The sustainability of the European lubricants industry, The Annual Congress of the European Lubricants Industry, Lisbon.

6 Gosalia, A. (2012) Sustainability and the global lubricants industry, The 16th ICIS World Base Oils & Lubricants Conference, London.

2

Lubricants in the Tribological System

Theo Mang and Christian Busch

The development of lubricants has become an integral part of the development of machinery and its corresponding technologies. It is irrevocably and interdisciplinarily linked to numerous fields of expertise; without this interdisciplinary aspect, lubricant developments and applications would fail to achieve success.

2.1 Lubricants as Part of Tribological Research

Tribology (derived from the Greek tribein, or tribos meaning rubbing) is the science of friction, wear and lubrication. Although the use of lubricants is as old as mankind, scientific focus on lubricants and lubrication technology is relatively new. The term tribology was first introduced in 1966 and has been used globally to describe this far-reaching field of activity since 1985. Even though efforts had been made since the sixteenth century to describe the whole phenomenon of friction scientifically (Leonardo da Vinci, Amontons, Coulomb), the work always concentrated on single aspects and lubricants were not even considered. Some research work performed up to the early 1970s totally ignored the chemical processes which take place in lubricated friction processes.

Tribology, with all its facets, is only sporadically researched. Fundamental scientific tribological research takes place at universities which have engineering or materials testing departments. Naturally, lubricant manufacturers also perform research. The advantage of tribological research by engineering departments is the dominant focus on application engineering. The most common disadvantage is the lack of interdisciplinary links to other fields of expertise. Joint research projects which combine the disciplines of engineering, materials, chemistry, health and safety, and the work conducted by lubricant manufacturers themselves therefore offer the best prospects of practical results.

2.2 The Tribological System

The tribological system (commonly referred to as the tribosystem) (Figure 2.1) consists of four elements: the contacting partner, the opposing contacting partner (material pair), the interface between the two and the medium in the interface and the environment [1]. In lubricated bearings, the lubricant is located in this gap. In plain bearings, the material pair are the shaft and the bearing shells; in combustion engines, they are the piston rings and the cylinder wall or the camshaft lobes and the tappets; in metalworking, the tool and the workpiece.

Figure 2.1 Structure of the tribosystem according to Czichos [1]. 1 and 2: material pair; 3: interface and medium in the interface (lubricant); 4: environment.

The variables are the type of movement, the forces involved, temperature, speed and duration of the stress. Tribometric parameters – such as friction, wear and temperature data – can be gathered from the stress area. Tribological stress is the result of numerous criteria of surface and contact geometry, surface loading or lubricant thickness. Tribological processes can occur in the contact area between two friction partners – which can be physical, physical–chemical (e.g. adsorption, desorption) or chemical in nature (tribochemistry).

2.3 Friction

The description of friction as the cause of wear and energy losses has always posed significant problems because of the complexity of the tribological systems. There is also no internationally recognized nomenclature. In this discussion, friction is described according to its type, and by the combination of friction and lubrication conditions, in line with the view taken by most experts [2,3].

2.3.1 Types of Friction

Friction is the mechanical force which resists movement (dynamic or kinetic friction) or hinders movement (static friction) between sliding or rolling surfaces. These types of friction are also called external friction.

Internal friction results from the friction between lubricant molecules; this is described as viscosity (Chapter 3).

The cause of external friction is, above all, the microscopic contact points between two sliding surfaces; these cause adhesion, material deformation and grooving. Energy which is lost as friction can be measured as heat and/or mechanical vibration. Lubricants should reduce or avoid the microcontact which causes external friction.

2.3.1.1 Sliding Friction

This is friction in a pure sliding motion with no rolling and no spin (Figure 2.2).

Figure 2.2 Sliding and rolling.

Figure 2.3a defines the coefficient of friction as the dimensionless ratio of the friction force F and the normal force N. The proportionality between normal force and frictional force is often given under dry and boundary friction conditions but not in fluid-film lubrication Figure 2.3b.

Figure 2.3 (a) Coefficient of friction. (b) The coefficient of friction in a tribological system as a result of four energy dissipation processes in the contact area.

2.3.1.2 Rolling Friction

This is the friction generated by rolling contact (Figure 2.4). In roller bearings, rolling friction mainly occurs between the rolling elements and the raceways, whereas sliding friction occurs between the rolling elements and the cage. The main cause of friction in roller bearings is sliding in the contact zones between the rolling elements and the raceways. It is also influenced by the geometry of the contacting surfaces and the deformation of the contacting elements. In addition, sliding also occurs between the cage pockets and the rolling elements.

Figure 2.4 ‘Wälzreibung’, mixing of rolling and sliding motions. (a) Rolling in metal forming; υ1, initial speed of the sheet metal; υ2, final speed of the sheet metal; υ3, speed of the roller; υr, speed difference in the roll gap (sliding part); N, neutral point (non-slip point, pure rolling). (b) Engagement of gear teeth, 1, 2, 4; high sliding/rolling ratio; 3: pitch circle (pure rolling, no slip).

If rolling motion and sliding motion combine to any significant extent, as for gear tooth meshing, special terminology has been created. The word ‘Wälzreibung’ which is derived from ‘Wälzen’ (rolling, e.g. steel rolling) is used in Germany. Situations in which a high sliding/rolling ratio occurs require totally different lubrication than does pure sliding. Figure 2.4 shows this ‘rolling friction’ during rolling and during gear meshing.

2.3.1.3 Static Friction

The static coefficient of friction is defined as the coefficient of friction corresponding to the maximum force that must be overcome to initiate macroscopic motion between two bodies (ASTM).

2.3.1.4 Kinetic Friction

Different from static friction, kinetic friction occurs under conditions of relative motion. ASTM defines the kinetic coefficient of friction as the coefficient under conditions of macroscopic relative motion of two bodies. The kinetic coefficient of friction sometimes called dynamic coefficient of friction is usually somewhat smaller than the static coefficient of friction.

2.3.1.5 Stick–Slip

Stick–slip is a special form of friction which often results from very slow sliding movements when the friction partners are connected to a system which can vibrate. The process is influenced by the dependence of the coefficient of sliding friction on speed. This generally occurs when the static coefficient of friction (fstat) is larger than the dynamic coefficient of friction (fdyn). Stick–slip is normally encountered with machine tools which operate with slow feeds. Stick–slip can cause chatter marks on components (Figure 2.5).

Figure 2.5 Stick–slip. (a) Test equipment for stick–slip. (b) Results of stick–slip behaviour of two oils. 1: oil with bad stick–slip behaviour; 2: oil with good stick–slip behaviour; fk: relative kinematic coefficient of friction; fs: relative static coefficient of friction.

2.3.2 Friction and Lubrication Conditions

In tribological systems, different forms of contact can exist between contacting partners.

2.3.2.1 Solid Friction (Dry Friction)

This occurs when two solids have direct contact with each other without a separating non-solid layer. If conventional materials are involved, the coefficients of friction and wear rates are high. Lubrication technology attempts to eliminate this condition.

2.3.2.2 Boundary Friction

The contacting surfaces are covered with a molecular layer of a substance whose specific properties can significantly influence the friction and wear characteristics. One of the most important objectives of lubricant development is the creation of such boundary friction layers in a variety of dynamic, geometric and thermal conditions. Such layers are of great importance in practical applications when thick, long-lasting lubricant films to separate two surfaces are technically impossible. Boundary lubricating films are created from surface-active substances and their chemically reaction products. Adsorption, chemisorption and tribochemical reactions also play significant roles.

Although boundary friction is often allocated to solid friction, the difference is of great significance to lubricant development and the understanding of lubrication and wear processes, especially when the boundary friction layers are formed by the lubricants.

2.3.2.3 Fluid Friction

In this form of friction, both surfaces are fully separated by a fluid lubricant film (full-film lubrication). This film is either formed hydrostatically or, more commonly, hydrodynamically. From a lubricants point of view, this is known as hydrodynamic or hydrostatic lubrication (Figure 2.6). Liquid or fluid friction is caused by the frictional resistance because of the rheological properties of fluids.

Figure 2.6 Hydrostatic lubrication as a form of fluid friction.

If both surfaces are separated by a gas film, this is known as gas lubrication.

2.3.2.4 Mixed Friction

This occurs when boundary friction combines with fluid friction. From a lubricants technology standpoint, this form of friction requires sufficient load-bearing boundary layers to form. Machine elements which are normally hydrodynamically lubricated experience mixed friction when starting and stopping.

For roller bearings, one of the most important machine elements, it has been shown that the reference viscosity either of lubricating oils or of the base oils of greases is not sufficient to ensure the formation of protecting lubricant layers and the required minimum lifetime. Under mixed friction conditions, it is important to choose the appropriate lubricant, that is that which enables the formation of tribolayers by antiwear and extreme pressure additives [4].

In 2004, Wiersch and Schwarze described a means of calculating mixed lubrication contacts over a wide range of operating conditions and applications. The performance of the mixed friction model was demonstrated using the example of a cam tappet contact [5,6].

2.3.2.5 Solid Lubricant Friction

This special form of friction occurs when solid lubricants are used (Chapter 17). It cannot be allocated to the previously mentioned forms of friction because particle shape, size, mobility and, in particular, crystallographic characteristics of the particles justify a separate classification.

2.3.2.6 Stribeck Diagram

The friction or lubrication conditions between boundary and fluid friction are graphically illustrated by use of Stribeck diagram (Figure 2.7) [7]. These are based on the starting-up of a plain bearing whose shaft and bearing shells are, when stationary, separated only by a molecular lubricant layer. As the speed of revolution of the shaft increases (peripheral speed), a thicker hydrodynamic lubricant film is created that initially causes sporadic mixed friction but which, nevertheless, significantly reduces the coefficient of friction. As the speed continues to increase, a full, uninterrupted film is formed over the entire bearing faces; this sharply reduces the coefficient of friction. As speed increases, internal friction in the lubricating film adds to external friction. The curve passes a minimum coefficient of friction value and then increases, solely as a result of internal friction.

Figure 2.7 Stribeck graph according to Ref. [7].

The lubricant film thickness shown in Figure 2.7 depends on the friction and lubrication conditions, including the surface roughness R.

2.3.2.7 Hydrodynamic Lubrication

Figure 2.8 demonstrates the formation of a hydrodynamic liquid film. The lubricant is pulled into the conical converging clearance by the rotation of the shaft. The created dynamic pressure carries the shaft.

Figure 2.8 Formation of a hydrodynamic liquid lubricant film. (a) Rolling, development of pressure in the hydrodynamic film. (b) Sliding, preferred geometry.

On the basis of the Navier–Stokes theory of fluid mechanics, Reynolds created the basic formula for hydrodynamic lubrication in 1886. Several criteria remained excluded, however, especially the influence of pressure and temperature on viscosity. The application of the Reynolds' formula led to theoretical calculations on plain bearings. The only lubricant value was viscosity.

2.3.2.8 Elastohydrodynamic Lubrication (EHD Regime)

Hydrodynamic calculation on lubricant films was extended to include the elastic deformation of contact faces (Hertzian contacts, Hertz's equations of elastic deformation) and the influence of pressure on viscosity (Chapter 3). This enables application of these elastohydrodynamic calculations to contact geometries other than that of plain bearings, for example those of roller bearings and gear teeth. Compared with the 25 µm films found in hydrodynamic bearings, films of generally less than 2 µm characterize EHD lubrication. The geometry of EHD is classified by Figures 2.9 and 2.10 indicating that the contact area between the mating elements is counterformal or slightly conformal.

Figure 2.9 Improvement of hydrodynamic lubrication clearance between two rollers by Hertzian deformation (elastohydrodynamic (EHD) contact), pressure distribution in the Hertzian contact.

Figure 2.10 Hertzian contacts for different pairs with non-converging lubricant clearance [8]. 1: roller bearing; 2: gear wheels; 3: chain wheels; 4: roller on flat path; 5: cam lifter.

Figure 2.9 shows the elastic deformation of the ball and raceway of a ball bearing and Figure 2.10 shows an example of Hertzian contacts for various pairs with non-converging lubricant clearance.

2.3.2.9 Thermo-Elasto-Hydrodynamic Lubrication (TEHD)

TEHD lubrication theory solves the Reynolds equation, including the energy equation of the lubricant film. Calculation of the energy takes into consideration heat convection in all directions, heat conduction in the radial direction, compression and heating caused by viscous and asperity friction.

TEHD lubrication theory has been applied, for example in important areas of automotive engines, using a model including shear rate-dependent viscosity (Chapter 3) and simulation of the lubrication conditions for the main crankshaft bearing of commercial automotive engines [9].

2.4 Wear

According to the German DIN standard 50320, wear is defined as the progressive loss of material from the surface of a contacting body as a result of mechanical causes, that is the contact and relative movement of a contacting solid, liquid or gas to the body.

2.4.1 Wear Mechanisms

Wear is created by the processes of abrasion, adhesion, erosion, tribochemical reactions and metal fatigue which are important to lubrication technology.

2.4.1.1 Abrasion

Abrasive wear or ploughing wear occurs principally when one body is penetrated by harder surface features of a mating body (two-body abrasion) or by third bodies which can be debris (three-body abrasion). Three-body abrasion can also occur by the contamination of lubricants with abrasive media (such as sharp quartz particles). Abrasion causes the surface peaks to break-off or it gouges further abrasive particles from the surface. This form of wear can combine with other wear mechanisms. Abrasive wear is demonstrated in Figure 2.11.

Figure 2.11 Abrasive wear. (a) Plowing: material is displaced to the side but not necessarily removed. (b) Plowing: material is displaced to the side and to the end of the groove tribological system: AlSi9Cu3 – 100Cr6.

2.4.1.2 Adhesion

This is the most complex of wear mechanisms. The basic theory of adhesive wear follows logically from the adhesive theory of friction which was first developed by Bowden and Tabor. Adhesion is one of the two main factors that contribute to friction between dry contacting surfaces in impending or sliding motion. The other factor is deformation. A simplified version of the theory says that contact between two rough surfaces is initially only made with some local asperity tips. Under normal load, some of the asperity tips on the softer material start to deform elastically and finally the plastic contacting asperities are cold-welded onto those on the harder surface, forming strong adhesive bonds. To break these bonds, either at the contact interface or within the softer asperities, a tangential force is needed which becomes the source of the adhesive component of friction. The tangential force causes a shear stress in the junction area. Shearing will take place at that interface, with the resulting wear. Molecular and atomic forces between the two friction partners can tear material particles out of the surfaces. The volume of worn material is proportional to the load and the sliding distance and is inversely proportional to the softer material hardness. The fragments being plucked out will be either carried away attached to the harder material or become detached as debris.

Adhesive wear is shown in Figure 2.12.

Figure 2.12 Adhesive wear. Tribological system: TiAl6V4 – 100Cr6.

2.4.1.3 Tribochemical Reactions

The chemical reactions which occur under tribological conditions are referred to as tribochemistry. It is sometimes wrongly assumed that these reactions are governed by some special laws. Nevertheless, for better understanding of the specific reaction conditions, the laws applying to tribological contact should be observed. This applies in particular to thermal effects (flash temperatures) which are not readily macroscopically recognizable and to frictional effects which lead to chemically reactive surfaces where the valences of the metal's structural matrices play a role in wear and deformation. The removal of chemically reacted surface layers thus formed constitutes tribochemical wear (Figure 2.13).

Figure 2.13 Tribochemical wear. Tribological system: GJS-600 – 100Cr6.

2.4.1.4 Surface Fatigue

Surface fatigue is the result of periodic loads in the contact zones. Frequent spot loading leads to surface fatigue which is a result of material fatigue. Micro-pits are one visible sign of this type of wear. A thick, separating lubricant film either minimizes or eliminates this problem. Machine elements which are subject to periodically severe loads in the contact zone are particularly prone to this type of damage. Figure 2.14 demonstrates wear by tribochemical reactions.

Figure 2.14 Tribochemical reaction layer. Formation of a tribochemical reaction layer system materials: AlSi12CuNi – 100Cr8.

2.4.1.5 Erosion

Erosive wear which is a loss of material from a solid surface occurs during the impingement on a surface by a fluid containing solid particles.

2.4.1.6 Fretting

Fretting is fatigue wear between two nominally static contacting surfaces. It is caused by cyclic relative tangential motion of very small amplitude. Most of the previously mentioned types of wear are included in fretting wear and this explains why fretting wear is seen as a separate form. Besides mechanical components, tribochemical reactions play an important role. Oxidation creates layers and fretting wear is sometimes known as fretting corrosion. Fretting corrosion creates trapped wear debris between the contact faces. Fretting wear can be avoided if suitable surface-active additives are added to lubricants (especially as pastes for threaded fasteners).

2.4.1.7 Cavitation

Materials can be damaged by imploding gas and vapour bubbles entrained in lubricating oils or hydraulic fluids. In systems which carry lubricants, the elimination of dragged-in air, low boiling point substances or the use of surface active components scales down the gas bubbles and thus reduces cavitation.

The condition of surfaces effected by cavitation can be further damaged by corrosion. This process can be controlled by the use of specific inhibitors.

2.4.1.8 Corrosive Wear

Corrosive wear is the removal of chemically reacted surface layers by friction processes. Air is the most common corrosive medium. A corrosive environment can be dangerous especially for steel structures. The best solution to avoid corrosive wear is by applying the correct type and amount of lubricant including speciality additives.

2.4.2 Types of Wear

There are several criteria which could be used to classify the different types of wear, for example according to the types of (kinematic) friction which lead to wear (sliding wear, rolling wear, fretting wear), wear mechanisms (adhesive wear, abrasive wear, tribochemical wear) or the shape of the wear particle.

There is also highly specialized wear terminology for different lubricant applications; this is oriented to the geometry of the various bearing faces (e.g. clearance and crater wear in the field of chip-forming tools).

2.4.3 The Wear Process

Wear can be measured gravimetrically, volumetrically or in terms of area over a period of time or against increasing load. Uniformly decreasing wear which stabilizes at a very low level can be described as running-in wear. This can be controlled by the tribochemical reactions of the additives in the lubricants. Wear can occur at relatively constant speed and ultimately lead to the functional failure of the bearing. Wear at an increasing wear rate can lead to progressive wear. In time, the material damage caused by wear will also lead to the failure of a component. To facilitate projection of possible functionality, the concept of failure analysis was introduced.

Analysis of machine element failure as a result of wear and lubrication can be performed by use of practically oriented tests. Determination of the effect of different greases on the projected failure of roller bearings has become increasingly important.

2.4.4 Tribomutation

Gervé [10] introduced this term to describe the processes of friction and wear from the tribosystem. His aim, in particular, was to separate the interpretation of wear from the confusing association with material characteristics and to highlight much more complex processes in the tribosystem in which lubricants are also included. Accordingly, friction and wear are purely system-related values. Gervé created the basis for his friction and wear concepts by conducting numerous sensitive wear measurements in the nanometre range using the established radionuclide wear measurement technique [11,12] and by successful ion implantation such as that used in metal-cutting tools and wear parts in combustion engines. He described the two most important tribological properties Tpi (once for wear and once for friction) in the equation:

where r are running conditions, for example speed, load, temperature and others, P are parameters such as M materials, G micro and macrogeometry and L the lubricant and the lubrication conditions, e are environmental conditions such as humidity, dust and temperature and τ is the life of the tribosystem.

Figure 2.15 demonstrates the system dependence of wear rate for changing running conditions for two parameters. For the running conditions r1, the wear rate for parameter p1 is significantly lower than that for parameter p2; this is reversed for r1.

Figure 2.15 Tribomutation. System dependence of wear rate for changing running conditions for two sets of parameters. (According to Ref. [10].)

Figure 2.16 shows the alteration of the material caused by tribomutation. The materials M1 and M2 at differing running times (t1 and t2) show wear occurring in the reverse order. Tribomutated materials have changed their tribological characteristics.

Figure 2.16 Tribomutation. Wear of tribosystem under constant running conditions with different materials. (According to Ref. [10].)

Changes to the material caused by tribomutation, which often occur under the surface of the material down to a depth of 150 nm, and which are reinforced by surface wear, can be quantified by sensitive methods of analysis of material composition. Gervé explained the material change caused by tribomutation by the part of the friction energy which is not consumed by heat generation and the binding energy of the wear particles.

Tribological system analysis and the associated tribomutation question the practical application of a series of friction and wear tests. Apart from what happens during running-in, other friction and wear phenomenon can be explained while the metalworking process along with the cutting fluid must be seen as an important influence on the tribological properties of a component.

Figure 2.17 shows the possible changes under tribologically stressed surfaces.

Figure 2.17 Lubrication conditions and possible changes by tribomutation.

Friction and wear development is highly influenced by the changed conditions created by tribomutation.

2.4.5 Nanotribology

The preceding chapter on tribomutation and Figure 2.17 reveal that deeper knowledge of frictional and wear processes on the micro- and nanoscale can enable explanation of different tribological phenomena. This implies the need for novel measurement methods or adaptation of current measurement procedures to the new tasks, the development and application of which constitute an essential part of nanotechnology in general and of nanotribology in particular. This enables visualization and measurement of different criteria up to the molecular scale. In the last 10 years, public interest in nanotechnology and nanotribology has grown substantially, because they are expected not only to enable theoretical explanation of different phenomena but also to improve economical realization [13]. Gervé [14] assigns three functions to micro- and nanotribology:

Analysis of the movement of single atomic groups in relation to the basic material and measurement of unequally distributed friction forces with nanometre resolution. In addition, the new definition of topographical roughness is relevant to understanding of the interrelationship between roughness and friction. This also includes experimental and theoretical analysis of frictional interactions at the atomic level, excitation of lattice oscillations and related reduction of the bond strength of the lattice elements, finally leading to wear.

Nano- and microtribology imply measurement and calculation of classical and tribological characteristics.

Examination of the effects of frictional phenomena on macroscopic tribosystems in the millimetre and micrometre range. This includes tribomutation. A recently started interesting project detected the effects of tribomutation on the piston–liner system of automotive vehicles. It was proved that production-related material changes (different cutting, grinding and honing processes, special metalworking fluids, dry cutting) had an effect on the friction and wear properties of engine components [15].

One of the most important aspects of nanotribology is the rapid development of microscale and nanoscale test equipment [15–18], for example the microtribometer for detection of forces in the micronewton range on springs, interferometer-based tribometers or fibre-optics-based microtribometers, microanalysis for hardness measurement and scratch testing and nanoscale probe techniques, in which the atomic force microscope (AFM, RKM) has become extremely important. This enables nanoscale scanning of surfaces with a tip passing over the surface with an accuracy of 10− m, corresponding to the diameter of an atom. In combination with the aforementioned spring and optical or capacitive instruments, this creates an image of the surface. The instrument also enables friction force measurement (FFM) on the nanoscale [19].

Also of interest are biological, micro- and nanotribology [20], the objective of which is to gather information about friction, adhesion and wear of biological systems and to apply this new knowledge to the design of micro-electromechanical systems and the development of new types of monolayer lubrication and other technology [20]. Nanotribology is the study of nanomaterials used as friction and wear-reducing lubricant additives. Carbon nanotubes and fullerene-like materials have entered lubricant research laboratories [21]. Submicrometre graphite particles, on the other hand, have been used as lubricant additives for many years.

2.4.6 Tribosystems of Tomorrow

To develop tribosystems and, especially, lubricants for tomorrow, collaborative research centres must be formed to integrate all the necessary competence. This could be done by organizing mutual research of the lubricant industry with universities and with the companies which use lubricants. Creation of a collaborative research centre at the university level must involve all those institutes which can contribute to the complex area of lubrication, wear, friction materials and environmental and toxicological problems. The most fascinating project in this field, ‘Environmentally Friendly Tribosystems for the Machine Tool by Use of Suitable Coatings and Fluids’, was started in the mid-1990s in Germany at the Technical University of Aachen (RWTH Aachen). The institutes involved are as follows:

A technical chemistry institute for development of appropriate lubricants

An institute for characterizing the environmental and ecotoxicological behaviour of the new lubricants

A surface engineering institute for developing the appropriate coatings (low-temperature PVD coatings for gears, bearings and pistons of hydrostatic units, high-temperature PVD coatings for tools used in metal cutting and forming);

A manufacturing technology institute

An institute for machine tools and production engineering

An institute for fluid power

An institute for machine elements and machine design [22].

References

1 Czichos, H. (1992) Basic Tribological Parameters, Friction, Lubrication and Wear Technology, ASTM Handbook, vol. 18, p. 474.

2 Bowden, F.P. and Tabor, D. (1954) The Friction and Lubrication of Solids: Part 1, Clarendon Press, Alderly, Gloucestershire, UK.

3 Archard, J.F. (1953) Contact and rubbing of flat surfaces. J. Appl. Phys., 24 (8), 981–988.

4 Karbacher, R. (2006) Mixed film lubrications of rolling bearings, 15th International Colloquium Tribology, Automotive and Industrial Lubrication (17–19 January), Technische Akademie Esslingen.

5 Wiersch, P. and Schwarze, H. (2006) EHL simulation under mixed friction conditions using the example of a cam tappet contact, 15th International Colloquium Tribology, Automotive and Industrial Lubrication, Technische Akademie Esslingen.

6 Wiersch, Petra. (2004) Berechnung thermoelastohydrodynamischer Kontakte bei Mischreibung. Dissertation, TU Clausthal.

7 Czichos, H. and Habig, K.-H. (1992) Tribologie Handbuch, Vieweg, Wiesbaden.

8 Klamann, D. (1984) Lubricants and Related Products, Wiley-VCH Verlag GmbH, Weinheim.

9 Bukovnik, S. et al. (2006) Thermo-elasto- hydrodynamic lubrication model for journal bearing including shear rate dependent viscosity. 15th International Colloquium Tribology, Automotive and Industrial Lubrication, Technische Akademie Esslingen.

10 Gervé, A. (1993) Improvement of tribological properties by ion implantation. Surf. Coat. Technol., 60, 521–524.

11 Gerve, A. (1971) Radioisotopes in mechanical engineering, Fourth United Nations International Conference on the Peaceful Uses of Atomic Energy, Geneva, Switzerland (6 September), Technical Report, AEC Conference 71-100-55.

12 Gerve, A., Kehrwald, B., Wiesner, L., Conlon, T.W. and Dearnaly, G. (1985) Continuous determination of the wear-reducing effect of ion implantation on gears by double labelling radionuclide technique. Mater. Sci. Eng., 69, 221–225.

13 Bhusan, B. (1997) Micro/Nanotribology and Its Application, Kluwer Academie Publishers.

14 Gerve, A. (2000) Mikro- und Nanotribologie, eine neue Sicht der Tribologie. 12th International Colloquium Tribology 2000-Plus, Esslingen (January 11–13).

15 Santner, E. and Stegemann, B. (2006) Tribological measurements at the nanoscale. 15th International Colloquium Tribology, Automotive and Industrial Lubrication, Technische Akademie Esslingen.

16 Gerbig, Y.B. (2006) Influence of the nanoscale topography on the microfriction of hydrophobic and hydrophilic surfaces. 15th International Colloquium Tribology, Automotive and Industrial Lubrication, Technische Akademie Esslingen (17–19 January).

17 Gold, P.W., Wolf, Th., Loos, J., Reichelt, M., Weirich, Th., Richter, S. and Mayer, J. (2006) Nanomechanical and analytical investigations on the influence of lubricant variation on tribological layers in slow running roller bearings, 15th International Colloquium Tribology, Automotive and Industrial Lubrication, Technische Akademie Esslingen (17–19 January).

18 Myshkin, N.K. and Grigoriev, A.Y. (2006) Measurement of tribological characteristics in the nano range, 15th International Colloquium Tribology, Automotive and Industrial Lubrication, Technische Akademie Esslingen (17–19 January).

19 Luther, R. and Seyfert, C. (2003) Können Motoren langer leben? Einfluss von Fertigungsmethoden auf die Motorenlebensdauer, Jahrestagung der Gesellschaft für Tribologie (GfT), Gottingen.

20 Scherge, M. and Gorb, S.N. (2001) Biological Micro- and Nanotribology, Springer, Berlin.

21 Mieno, T. and Ohmae, N. (2006) Carbon nanotubes as lubricant additives. 15th International Colloquium Tribology, Automotive and Industrial Lubrication, Technische Akademie Esslingen (17–19 January).

22 Murrenhoff, H. (2006) Introduction into the Collaborative Research Center 442: environmentally friendly tribosystems by suitable coatings and fluids with respect to the machine tool. 15th International Colloquium Tribology, Automotive and Industrial Lubrication, Technische Akademie Esslingen (17–19 January)

3

Rheology of Lubricants

Theo Mang

Consistency, flow properties or viscosity in the case of oils, are key parameters to create lubrication efficiency and the application of lubricants. These are terms which appear in nearly all lubricant specifications. Viscosity is also the only lubricant value which is adopted into the design process for hydrodynamic and elastohydrodynamic (EHD) lubrication.

3.1 Viscosity

Friction generated by a fluid surrounding contacting partners, that is without contact of the partners, is the internal friction of the fluid. In the right-hand branch of the Stribeck graph (Figure 2.7), internal friction increases with bearing speed. The measure of internal friction in a fluid is viscosity. Viscosity and its dimensions are best explained with a model of parallel layers of fluid which could be viewed molecularly (Figure 3.1). If this packet of fluid layers is sheared (τ), the individual fluid layers are displaced in the direction of the shearing force. The upper layers move more rapidly than the lower layers because molecular forces act to resist movement between the layers. These forces create resistance to shearing and this resistance is given the term dynamic viscosity. The difference in velocity between two given fluid layers, related to their linear displacement, is referred to as shear rate S. This velocity gradient is proportional to the shear stress (τ). The proportionality constant η is called dynamic viscosity and has the units Pa·s. Analysis of the dimensions uses the following equations:

(3.1) equation

(3.2)

Figure 3.1 Explanation of viscosity.

The laboratory determination of viscosity in run-out or capillary tubes is influenced by the weight of the fluid. The relationship between dynamic viscosity and specific gravity is referred to as kinematic viscosity ν. The following unit analysis applies:

(3.3)

Fluids which display the above proportionality constant between shear stress and shear rate are referred to as Newtonian fluids, that is the viscosity of Newtonian fluids is independent of shear rate (Figure 3.2). Deviations