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BEARINGS AND LUBRICATION
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FIGURE 19.16 Inlet flow variable versus Sommerfeld number for parametric values of temperature-rise variable; L/D = 1, full journal bearing. (From Connors [19.9].)
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For Qi /(RCNL) = 1, the following sets of data were obtained by performing this calculation procedure: 1.5 10 6 reyn = 3.0 10 reyn 6.0 10 6 reyn J C*(Ta Ti) = P 32 60 115 Ta =
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0.12 S = 0.24 0.48 126.8 F 150.2 F 196.2 F
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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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Using these and the lubricant versus T relation as presented in Table 19.16, we find the operating point to be Ta = 155 F = 3.2 10 6 reyn
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Hence, S = 0.256. Also from Fig.19.14 we obtain h0/C = 0.52, and so h0 = 0.00208. Further, from Fig. 19.15, (R/C)(f ) = 5, and so f = 0.01, which allows us to calculate the power loss to be 0.857 horsepower (hp). Assuming other values of Qi /(RCNL) permits Fig. 19.17 to be drawn. The Raimondi-Boyd value corresponding to Qi is also presented.
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FIGURE 19.17 Lubricant temperature rise versus lubricant input flow rate (Example 3).
In Sec. 19.5.4 it was shown that (Ta Ti)conduction = (1 )(Ta Ti)no conduction where = ratio of heat conduction to heat generation rate and is assumed to be a constant. By using this idea, a new operating point for a given Qi /(RCNL) can be determined. For example, with = 0.25 and Qi /(RCNL) = 1, we find that Ta = 147 F, h0 = 0.0023, and HP = 0.960 hp.
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JOURNAL BEARINGS 19.40
BEARINGS AND LUBRICATION
19.6.3 Optimization In designing a journal bearing, a choice must be made among several potential designs for the particular application. Thus the designer must establish an optimum design criterion for the bearing. The design criterion describes the designer s objective, and numerous criteria can be envisioned (e.g., minimizing frictional loss, minimizing the lubricant temperature rise, minimizing the lubricant supply to the bearing, and so forth). The search for an optimum bearing design is best conducted with the aid of a computer. However, optimum bearing design can also be achieved graphically. Moes and Bosma [19.10] developed a design chart for the full journal bearing which enables the designer to select optimum bearing dimensions. This chart is constructed in terms of two dimensionless groups called X and Y here. The groups include two quantities of primary importance to the bearing designer: minimum film thickness h0 and frictional torque Mj; the groups do not contain the bearing clearance. The dimensionless groups are X P h0 R 2 N
Mj P WR 2 N
(19.15)
Both X and Y can be written in terms of the Sommerfeld number. Recalling that h0 = C(1 ) and S = ( N/P)(R/C)2, we can easily show that X= 1 2 S and Y= Mj WC 1 2 S
Figure 19.18 is a plot of full journal bearing design data on the XY plane. In the diagram, two families of curves can be distinguished: curves of constant L/D ratio and curves of constant . Use of this diagram permits rather complicated optimization procedures to be performed. Example 4. Calculate the permissible range of minimum film thickness and bearing clearance that will produce minimum shaft torque for a full journal bearing operating under the following conditions: = 5 10 6 reyn N = 1800 rev/min W = 1800 lbf Solution. As a first step, we calculate the largest h0 for the given conditions. This is easily accomplished by locating the coordinates on Fig. 19.18 corresponding to the maximum X for L/D = 3 4, or X Y = 0.385 4.0 0.54 at X = Xmax D = 4 in L = 3 in
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