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Rolling Element, Hydrodynamic and Hydrostatic Bearings Q = 14
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Q = 430 in3/s Hf = 26 (Figure 659)
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4000 00053 196 83 10 6
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7046438 mm3/s
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F h3 P = Hf Ap
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3 4000 0005 P = 26 6 196 83 10 P = 1631 lbin/s 2
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1631 12 550 P = 0247 hp
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(b) Multi-recess circular pads Other than having a circular shape, hydrostatic pads can have shapes such as square, rectangular, annular recess circular, conical spherical, multi-recess circular, multi-recess rectangular, rectangular with radiussed recess corners and annular multi-recess Example: Multi-Recess Circular Pad Hydrostatic Bearings The design for the foregoing example is repeated for the multi-recess circular pad arrangement as shown in Figure 658 (a) The required design data are presented in Figure 658 (b) As the suggested design value for C/R is between 015 and 025, the C/R ratio for the design purpose of this problem is assumed to be 020 Therefore, from Figure 658 (b), the coefficients A and B are read as 066 and 22, respectively The bearing pad area is calculated as follows: F = A pR A p
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F APR 4000 Ap = 066 400
Ap =
Ap = 1515 in2 977515 mm2 The radius, R, can be determined from the following relation: Ap = pR2 R =
Precision Engineering
R = 220 in 5578 mm The land width, C, can be calculated from the C/R ratio
C = 020R C = 020 (220) C = 044 in 1118 mm The clearance, h, is recommended to be between 0001 and 001 in Assume h = 0005 in = 0127 mm The viscosity can be obtained from Figure 635 for a given type of lubricant and temperature In this case, it is assumed that viscosity, = 83 10 6 lbs/in2 The oil flow can be approximated as
A pQ Fh 3
C = 020 R
Q = Q =
Fh3 B Ap 4000 00053 22 1515 83 10 6
Q = 875 in3/s 143 35179 mm3/s The pumping power can be calculated as P = PRQ P = 400 875 P = 3500 lbin/s 3500 P = 12 550 P = 0530 hp 39517 W From Table 69, it can be seen that for a similar load, circular pads require less lubricant flow and pumping power However, multi-recess bearings are superior because they are able to exert a Table 69 Comparison between a circular pad and a multi-recess circular pad
Circular pad Oil flow, Q Pumping power, P 430 in3/s 0247 hp Multi-recess circular pad 875 in3/s 0530 hp
Rolling Element, Hydrodynamic and Hydrostatic Bearings
Fig 658: Multi-recess circular pad data for load and flow: (a) bearing geometry and (b) bearing coefficients
(suggested design value 015 < C/R < 025) [19]
Precision Engineering
self-aligning torque when the film is non-parallel Similarly, different pads can be tested to obtain an arrangement that is most suitable for a particular application (c) Rectangular pads The design of hydrostatic thrust bearings for worktable application is illustrated using Stansfield s [17] approach with an example to further enhance the understanding of the procedure Example: Rectangular Pad Hydrostatic Bearings Figure 659 shows an arrangement of 10 hydrostatic pads designed to meet the following specification for the worktable of a large planing machine (Figure 638 (b)) [17]
Minimum load, most lightly loaded pad Maximum load, most heavily loaded pad Nominal (design) working load per pad Maximum permissible range of deflection 1 350 lbf 10 660 lbf 6 000 lbf 0003 in SI units 6 010 N 47 400 N 26 700 N 00762 10 3 m
Fig 659: Arrangement of hydrostatic pads on a planer table [17]
The information given is listed as follows: a = 775 in b = 1200 in c = 200 in r(int) = 0828 in dR = 003345 in l = 341 in h = 0002 in
197 10 3 m 305 10 3 m 508 10 3 m 210 10 3 m 085 10 3 m 865 10 3 m 00508 10 3 m
Rolling Element, Hydrodynamic and Hydrostatic Bearings
Fig 660: Dimensions of a rectangular pad [17]
Dynamic viscosity, h = 5 10 6 lbf s in 2 0345 N s m 2 Supply pressure, Ps = 225 lbf in 2 155 106 N m 2 1 (maximum) Relative sliding velocity, n = 50 in s 127 m s 1 Number of pads, n = 10 A condition when the applied load is equal to the design load and the clearance, h, is equal to the design clearance, hd, is known as the design condition In addition, if r(int) = 0414c, the design can be greatly simplified Furthermore, the value of the resistance ratio, z, is taken as unity because this value gives the highest stiffness for any design thrust capacity Inflow Resistance, Ri capillary inflow restrictor For an inflow restrictor of a simple capillary tube of a constant and circular cross-section, assuming that the flow occurs in the capillary is purely laminar, and the drop in pressure locally at the inlet to and exit from the capillary is negligible, the inflow resistance, Ri, is given by 128l Ri = 4 dR Ri =
128 341 5 10 6
( 003345 )
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