Introduction

The satisfactory operation of both hydrostatic and hydrodynamic bearings requires that the solid surfaces which constitute the bearing faces are completely separated by the intervening fluid film. Since the bearing surfaces are then not physically touching, the resistance to their tangential motion, that is, the force of friction, is directly attributable to viscous losses in the lubricant. If the lubricant (whether liquid or gas) exhibits Newtonian rheological behaviour with constant viscosity then the value of this frictional force, and the associated coefficient of friction, will increase with the value of the tangential sliding velocity. We have seen (eqn (7.27)) that the coefficient of friction within a hydrodynamically lubricated bearing is generally dependent on the square root of the group ULη/W where U is the relative sliding speed of the surfaces, W/L the normal load supported per unit length, and η the Newtonian viscosity. A reduction in speed, or an increase in the specific load on the bearing, leads to a fall in the friction coefficient. However, there is a limit to this process: when the specific load is very high, or the relative sliding speed small, it is difficult to build up a sufficiently thick film to entirely separate the bearing faces, and so there will be some mechanical interaction between opposing surface asperities. This is inevitable, even allowing for the large increase in effective lubricant viscosity and the elastic flattening of the surface profiles that can occur in the elasto-hydrodynamic regime.

Introduction

The definition and measurement of wear

Wear is the progressive damage, involving material loss, which occurs on the surface of a component as a result of its motion relative to the adjacent working parts; it is the almost inevitable companion of friction. Most tribological pairs are supplied with a lubricant as much to avoid the excessive wear and damage which would be present if the two surfaces were allowed to rub together dry as it is to reduce their frictional resistance to motion. The economic consequences of wear are widespread and pervasive; they involve not only the costs of replacement parts, but also the expenses involved in machine downtime, lost production, and the consequent loss of business opportunites. A further significant factor can be the decreased efficiency of worn plant and equipment which can lead to both inferior performance and increased energy consumption.

The wear rate w of a rolling or sliding contact is conventionally defined as the volume lost from the wearing surface per unit sliding distance; its dimensions are thus those of [length]. For a particular dry or unlubricated sliding situation the wear rate depends on the normal load, the relative sliding speed, the initial temperature, and the thermal, mechanical, and chemical properties of the materials in contact. There are many physical mechanisms that can contribute to wear and certainly no simple and universal model is applicable to all situations.

Tribology

The word tribology was coined only just over twenty years ago and appears in only the most up to date of dictionaries; however, the topics with which tribologists are concerned have been of vital interest to scientists, engineers, and those who design or operate machinery, for as long as mechanical devices have existed. Formally, tribology is defined as the science and technology of interacting surfaces in relative motion and of related subjects and practices; it deals with every aspect of friction, lubrication, and wear. The word is derived from the Greek τριβοσ (TRIBOS) meaning rubbing, although the subject embraces a great deal more than just the study of rubbing surfaces.

Perhaps as much as one third of our global energy consumption is consumed wastefully in friction: at a time when energy resources are at a premium the contribution that can be made to their efficient utilization, as well as to the reduction of pollution, by making use of the best tribological practices is obvious. In addition to this primary saving of energy there are very significant additional economies to be made by reductions in the cost involved in the manufacture and replacement of prematurely worn components. An important landmark in the development of the subject was the publication in 1966 in Great Britain of the report of the government committee, chaired by Mr Peter Jost, which had been formed to report on the position of industrial lubrication in the United Kingdom: it was asked specifically to identify those areas of industrial practice where significant improvements could be made.

Introduction

Not all sliding tribological pairs are designed to operate in the presence of a generous supply of lubricant. The nature of the working environment may make it impossible, or impracticable, to arrange for the contact to be lubricated by a full hydrostatic or hydrodynamic fluid film, for example, in deep space or satellite applications where any liquid lubricant would be lost or degraded by evaporation, or in food processing or chemical plant where contamination of either the product or the environment by any escape of a lubricating fluid would be unacceptable. In other, simpler applications the design constraint may simply be the cost of the lubricants supply and handling equipment. Generally, the aim in the design of machinery is to minimize friction; however, in some devices (clutches, brakes, friction drives, and so on) friction is beneficial, indeed essential, and often components of this sort are operated unlubricated. In this chapter, as well as the tribology of dry sliding (taking as examples both brakes and clutches as well as dry rubbing bearings) we shall also consider the tribological aspects of some ‘marginally’ lubricated contacts. These are only intermittently lubricated by a less than complete fluid film and so rely for their success on a combination of hydrodynamic, elasto-hydrodynamic, and boundary lubrication. Bearings and bushes designed to run completely dry are often manufactured as monolithic solid components and involve at least one nonmetallic material, while marginally lubricated bearings often make use of porous, sintered metals (usually bronze) impregnated by an appropriate mineral oil, grease, or solid boundary lubricant.

Introduction

When two engineering surfaces are loaded together there will always be some distortion of each of them. These deformations may be purely elastic or may involve some additional plastic, and so permanent, changes in shape. Such deflections and modifications in the surface profiles of the components can be viewed at two different scales. For example, consider the contact between a heavily loaded roller and the inner and outer races in a rolling-element bearing. In examining the degree of flattening of the roller we could choose to express the deflections as a proportion of their radii, that is, to view the distortions on a relatively macroscopic scale. On the other hand, as we have seen in Chapter 2, at the microscale no real surface, such as those of the roller or the race, can be truly smooth, and so it follows that when these two solid bodies are pushed into contact they will touch initially at a discrete number of points or asperities. The sum of the areas of all these contact spots, the ‘true’ area of contact, will be a relatively small proportion of the ‘nominal’ or geometric contact area–perhaps as little as only a few per cent of it. Some deformation of the material occurs on a very small scale at, or very close to, these areas of true contact. It is within these regions that the stresses are generated whose total effect is just to balance the applied load.

Introduction

A hydrostatic bearing is one in which the loaded surfaces are separated by a fluid film which is forced between them by an externally generated pressure. Formation of the film, and so successful operation of the bearing, requires the supply pump to operate continuously, but it does not depend on the relative motion of the surfaces (hence the term ‘hydrostatic’). Such bearings have a great attraction to engineers; machine elements supported in this way move with incomparable smoothness and the only restriction to motion arises from the small viscous losses in the fluid. A mass supported on a hydrostatic bearing will glide silently down the slightest incline.

The essential features of a typical hydrostatic single-pad thrust bearing are shown in Fig. 6.1 (a). The bearing is supplied with fluid under pressure ps which, before entering the central pocket or recess, passes through some form of restrictor or compensator in which its pressure is dropped to some lower value pr. The fluid then passes out of the bearing through the narrow gap, shown of thickness h, between the bearing land and the opposing bearing surface or slider which is also often known as the bearing runner. The depth of the pocket is very much greater than the gap h. The restrictor is an essential feature of the bearing since it allows the pocket pressure pr to be different from the supply pressure; this difference, between pr and ps, depends on the load applied W.

Introduction

In many internal flows there are only limited regions in which the velocity can be considered irrotational; i.e. in which the motion is such that particles travel without local rotation. In an irrotational, or potential, flow the velocity can be expressed as the gradient of a scalar function. This condition allows great simplification and, where it can be employed, is of enormous utility. Although we have given examples of its use, potential flow theory has a narrower scope in internal flow than in external flow and the description and analysis of non-potential, or rotational, motions plays a larger role in the former than in the latter. One reason for this difference is the greater presence of bounding solid surfaces and the accompanying greater opportunity for viscous shear forces to act. Even in those internal flow configurations in which the flow can be considered inviscid, however, different streamtubes can receive different amounts of energy (from fluid machinery, for example), resulting in velocity distributions which do not generally correspond to potential flows. Because of this, we now examine two key fluid dynamic concepts associated with rotational flows: vorticity, which has to do with the local rate of rotation of a fluid particle, and circulation, a related, but more global, quantity.

Before formally introducing these concepts, it is appropriate to give some discussion concerning the motivation for working with them, rather than velocity and pressure fields only. The equations of motion for a fluid contain expressions of forces and acceleration, derived from Newton's laws.

Introduction

In this chapter we address three-dimensional flows in which streamwise vorticity is a prominent feature. Three main topics are discussed. The first, and principal, subject falls under the general label of secondary flows, cross-flow plane (secondary) circulations which occur in flows that were parallel at some upstream station. The second is the enhancement of mixing by embedded streamwise vorticity and the accompanying motions normal to the bulk flow direction (see for example Bushnell (1992)). The third is the connection between vorticity generation and fluid impulse.

The different topics are linked in at least three ways. First, the class of fluid motions described are truly three-dimensional. Second, focus on the vortex structure in these flows is a way to increase physical insight. The perspective of the chapter is that the flows of interest are rotational and three-dimensional, and the appropriate tools for capturing their quantitative behavior are three-dimensional numerical simulations (e.g. Launder (1995)). Results from such computations, as well as from experiments, are used to illustrate the overall features. To complement detailed simulations and experiments, however, it is often helpful to have a simplified description of the motion which can guide the interrogation and scope of the computations, enable understanding of why different effects are seen, and suggest scaling for different mechanisms. The ideas about vorticity evolution and vortex structure, introduced in Chapter 3, provide a skeleton for this type of description.