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20.3 LIQUID LUBRICANTS: PRINCIPLES AND REQUIREMENTS
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The most important single property of a liquid lubricant is its viscosity. Figure 20.3 shows how the viscosity of the lubricant affects the nature and quality of the lubrication. This figure is often called a Stribeck curve, although there seems to be some doubt as to whether Stribeck used the diagram in the form shown. The expression N/P is known as the Sommerfeld number, in which is the lubricant viscosity, N represents the relative speed of movement between the counterfaces of the bearing, and P is the mean pressure or specific load supported by the bearing. Of these three factors, only the viscosity is a property of the lubricant. And if N and P are held constant, the figure shows directly the relationship between the coefficient of friction and the lubricant viscosity .
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FIGURE 20.3 Effect of viscosity on lubrication.
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The graph can be conveniently divided into three zones. In zone 3, the bearing surfaces are fully separated by a thick film of the liquid lubricant. This is, therefore, the zone of thick-film or hydrodynamic lubrication, and the friction is entirely viscous friction caused by mechanical shearing of the liquid film. There is no contact between the interacting surfaces and therefore virtually no wear. As the viscosity decreases in zone 3, the thickness of the liquid film also decreases until at point C it is only just sufficient to ensure complete separation of the surfaces. Further reduction in viscosity, and therefore in film thickness, results in occasional contact between asperities on the surfaces. The relatively high friction in asperity contacts offsets the continuing reduction in viscous friction, so that at point B the friction is roughly equal to that at C. Point C is the ideal point, at which there is zero wear with almost minimum friction, but in practice the design target will be slightly to the right of C, to provide a safety margin. With further reduction in viscosity from point B, an increasing proportion of the load is carried by asperity contact, and the friction increases rapidly to point A. At this point the whole of the bearing load is being carried by asperity contact, and further viscosity reduction has only a very slight effect on friction. Zone 1, to the left of point A, is the zone of boundary lubrication. In this zone, chemical and physical properties of the lubricant other than its bulk viscosity control the quality of the lubrication; these properties are described in Sec. 20.5. Zone 2, between points A and B, is the zone of mixed lubrication, in which the load is carried partly by the film of liquid lubricant and partly by asperity interaction. The proportion carried by asperity interaction decreases from 100 percent at A to 0 percent at C. Strictly speaking, Fig. 20.3 relates to a plain journal bearing, and N usually refers to the rotational speed. Similar patterns arise with other bearing geometries in which some form of hydrodynamic oil film can occur. The relationship between viscosity and oil-film thickness is given by the Reynolds equation, which can be written as follows: P P h U h3 + h3 = 6U + 6h + 12V x z x x x z
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where h = P= x, z = U, V =
lubricant-film thickness pressure coordinates speeds in directions x and z
Fuller details of the influence of lubricant viscosity on plain journal bearings are given in Chap. 19. In nonconformal lubricated systems such as rolling bearings and gears, the relationship between lubricant viscosity and film thickness is complicated by two additional effects: the elastic deformation of the interacting surfaces and the increase in lubricant viscosity as a result of high pressure. The lubrication regime is then known as elastohydrodynamic and is described mathematically by various equations. For roller bearings, a typical equation is the Dowson-Higginson equation: hmin = 2.65( oU)0.7R0.43 0.54 E 0.03p0.13
where o = oil viscosity in entry zone R = effective radius = pressure coefficient of viscosity Here U represents the speed, p a load parameter, and E a material parameter based on modulus and Poisson s ratio. For ball bearings, an equivalent equation is the one developed by Archard and Cowking: hmin = 1.4( oU )0.74E0.074 R0.74p0.074
For such nonconformal systems, a diagram similar to Fig. 20.3 has been suggested in which zone 2 represents elastohydrodynamic lubrication. It is difficult to think of a specific system to which the relationship exactly applies, but it may be a useful concept that the lubricant-film thickness and the friction in elastohydrodynamic lubrication bridge the gap between thick-film hydrodynamic lubrication and boundary lubrication. A form of microelastohydrodynamic lubrication has been suggested as a mechanism for asperity lubrication under boundary conditions (see Sec. 20.5). If this suggestion is valid, the process would probably be present in the zone of mixed lubrication. Where full-fluid-film lubrication is considered necessary but the viscosity, load, speed, and geometry are not suitable for providing full-fluid-film separation hydrodynamically, the technique of external pressurization can be used. Quite simply, this means feeding a fluid into a bearing at high pressure, so that the applied hydrostatic pressure is sufficient to separate the interacting surfaces of the bearing. Externally pressurized bearings broaden the range of systems in which the benefits of full-fluid-film separation can be obtained and enable many liquids to be used successfully as lubricants which would otherwise be unsuitable. These include aqueous and other low-viscosity process fluids. Remember that the lubricant viscosity considered in Fig. 20.3 and in the various film-thickness equations is the viscosity under the relevant system conditions, especially the temperature. The viscosity of all liquids decreases with increase in temperature, and this and other factors affecting viscosity are considered in Sec. 20.4.
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