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TABLE 19.2 Physical Properties of Journal Bearing Materials
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19.9 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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JOURNAL BEARINGS 19.10
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BEARINGS AND LUBRICATION
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TABLE 19.3 Bearing Alloy Material Applications
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bearing operates in a clean, moderate-temperature environment and is not part of an electric machine. After the list of criteria has been established, each component criterion is compared with all other criteria, and a graduation mark is allocated from 0, if there is no difference in the criterion, to 3, if there are large differences. For example, compressive strength (A1 in Table 19.6) might receive a 0 when compared with fatigue strength (A2) but receive a 3 when compared to thermal conductivity (B1), and so forth. When all component criteria have been compared with one another and graduation marks assigned, the graduation marks of each criterion are totaled and the sum of all these totals is divided into each amount, to obtain the component criteria weighting factors. The sum of all the weighting factors obviously is unity.
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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TABLE 19.4 Performance Ratings from 5 (High) to 1 (Low) for Bearing Alloy Materials
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19.11 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
JOURNAL BEARINGS
TABLE 19.5 General Information on Self-Lubricating Bearing Materials
19.12 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
JOURNAL BEARINGS 19.13
JOURNAL BEARINGS
TABLE 19.6 Journal Bearing Material Selection Criteria
Next the candidate materials are given quality marks for the various component criteria. These marks range from 5 (excellent, or high) to 1 (poor, or low). For instance, tin-based babbitts are known to have only fair (2) fatigue strength, whereas they have excellent (5) resistance to corrosion. The final ranking of the candidate materials is obtained by comparing the sums of the products of all component criteria weighting factors and quality marks.
19.4 PRESSURE EQUATION FOR A LUBRICATING FILM
19.4.1 Reynolds Equation The differential equation which governs the pressure in a lubricating film is called the Reynolds equation. Bearing performance can be evaluated once the solution of this equation is in hand. To develop the Reynolds equation, consider a portion of the fluid film of a journal bearing (Fig. 19.1). In general, there are three velocity components in the film: u, v, and w. There are three equations of motion (momentum equations), one for each coordinate direction. The collection is known as the Navier-Stokes equations, and each equation may be written in the following form: Inertial forces = pressure forces + body forces + viscous forces (19.1)
The Navier-Stokes equations in their complete form are too involved for analytical solution.They can, however, be reduced, and subsequently solved, by making several simplifying yet plausible assumptions:
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JOURNAL BEARINGS 19.14
BEARINGS AND LUBRICATION
1. The flow is laminar. 2. The inertial and body forces are small compared to the pressure and viscous forces. 3. The curvature of the film is negligible; the bearing surfaces are, therefore, nearly parallel. 4. The variation of pressure across the film P/ y is negligibly small. 5. The transverse velocity component across the film, v, is small compared to the other velocity components. 6. The velocity gradients across the film dominate over all other velocity gradients. Application of these assumptions to mathematical versions of Eq. (19.1), and to an integrated version of the conservation of mass (the continuity equation), yields the Reynolds equation for a liquid-lubricated bearing: (Ub + Uj) h3 p h3 p h h + = 6(Ub + Uj) + 6h + 12 x x x z z x t (19.2)
The first grouping on the right-hand side of Eq. (19.2) is called the wedge term and must be negative to generate positive pressures. The third term on the right is called the squeeze term, and it will generate positive pressures when h/ t < 0. The squeeze term vanishes for a steadily loaded bearing. Both the wedge and the squeeze terms vanish for a purely hydrostatic case. If the bearing surface is fixed (Ub = 0), if the shaft is rotating with a speed (that is, Uj = U = R ), and if the viscosity of the lubricant is constant, then Eq. (19.2) may be written as p p h U h h3 + h3 = 6 R + 6 h + 12 x z x z x x t (19.3)
For comparative purposes, it is useful to cast the steady version of Eq. (19.3) into nondimensional form. This can be accomplished by defining the following nondimensional variables: x R z L/2
p Also, since = 2 N,
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