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BEARINGS AND LUBRICATION
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pared from a comprehensive series of papers on hydrostatic bearing design by Rippel [19.15]. In addition to flow-load control, the resistor affects the stiffness of the bearing. Bearing stiffness is related to the ability of the bearing to tolerate any changes in the applied load. 19.8.2 Design Parameters For hydrostatic journal bearings at low rotational speeds, the primary design parameters are maximum load, lubricant flow rate, and stiffness. Of secondary importance are considerations of frictional horsepower and lubricant temperature rise. The load-carrying capacity of a hydrostatic journal bearing is generally written as W = af Ap pr (19.19)
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where af = pad load coefficient, Ap = projected bearing area, and pr = recess pressure. The pad load coefficient is dimensionless and physically represents the ratio of the average lubricant pressure in the pad to the lubricant pressure supplied to the pad. O Donoghue and Rowe [19.16] give equations for af for both multirecess and multipad bearings. The lubricant flow rate may be determined from Q = qf h3pr (19.20)
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where qf = flow factor for a single pad. The flow factor depends on the geometry and land widths of the bearing. Journal bearing stiffness expresses the ability of the bearing to accommodate any changes in the applied load. Stiffness is proportional to the slope of the bearing load versus film thickness curve, or s= dW dh (19.21)
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Stiffness will depend on the method of flow control (capillary tube, etc.) and the amount of circumferential flow. O Donoghue and Rowe [19.16] provide a detailed derivation of the journal bearing stiffness and have developed equations for both multipad and multirecess bearings. 19.8.3 Design Procedures A variety of design procedures are available for hydrostatic bearings. Some are based on experimental findings, whereas others are based on numerical solutions of the Reynolds equation. Many existing methods incorporate numerous charts and tables which clearly place a limit on the methods; in order to use these procedures, the appropriate reference must be consulted. Alternatively, O Donoghue and Rowe [19.16] have developed a general approximate method of design that does not require the use of various design charts. The method is strictly valid for thin land bearings, and many of the parameters are conservatively estimated. The following is a condensation of this design procedure for a multirecess bearing:
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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 19.22 Comparison of Three Types of Flow Resistors
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19.55 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 19.56
BEARINGS AND LUBRICATION
Design Specification 1. Set the maximum load W. 2. Select the number of recesses n (typically n = 4, but n = 6 for high-precision bearings). 3. Select a pressure ratio pr /ps (a design value of 0.5 is recommended).
Bearing Dimensions 1. Calculate the bearing diameter D = W/50 in. 2. Set width L = D. 3. Calculate the axial-flow land width a (refer to Fig. 19.28; recommended value: a = L/4).
FIGURE 19.28 Hydrostatic pad geometry.
4. Calculate the circumferential land width b [refer to Fig. 19.28; recommended value: b = D/(4n)]. 5. Calculate the projected pad area Ap = D(L a). 6. Calculate the recess area for one pad only: Ar = ( D nb)(L a)/n. 7. Calculate the effective frictional area: Af = ( DL/n) 0.75Af. Miscellaneous Coefficients and Parameters 1. Establish a design value of film thickness hd (recommended value: 50 to 10 times larger than the machinery tolerance on h). 2. Calculate the circumferential flow factor = na(L a)/( Db); for recommended values of D, L, a, and b: = 3 4(n/ )2. 3. Compute the design dimensionless stiffness parameter s from Table 19.23 depending on the method of flow control selected. 4. Calculate the flow factor qf = D/(6an). Performance Parameters 1. Calculate the minimum supply pressure ps,min = 2W/(afAp) [recommended: af = s (capillary tube at design Table 19.23)].
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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