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30 = 30 10
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Gas Lubricated Bearings Table 76 Design dimensions and performance of aerostatic thrust bearings
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Annular thrust bearing Outside Diameter Inside/Pocket Diameter Design Clearance Ultimate Load Airflow 30 in 10 in 00005 in 125 lbf 0463 scfm Combined Axial Stiffness = 1 000 000 lbf / in Combined Airflow = 0926 scfm
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By referring to Figure 764, it can be seen that for a design clearance of 05 10 3 in the jet diameter is 10 10 3 in when b/a is 3 A correction is required since the figure is plotted based on 50 lbf/in2 The multiplication factor is obtained from the vertical axis at the intersection of a supply pressure of 75 lbf/in2 with the curve of Figure 765 (a) The corrected diameter is given as 12 (10 10 3) = 0012 in The influence of pressure, temperature and gas properties on the optimum jet diameter and mass flow is similar to that of the journal bearings, and the related figures can be applied for the design of thrust bearings In this case, multiple jets will be arranged, feeding into a circular groove of radius given by c2 = 10 075 = 075 c = 0866 in The number of feed holes will be determined in the limit by the smallest size that can be drilled Figure 765 (b) shows the variation in feed hole diameter with the number of feed holes The practical choice of most designers would lie between eight and 16 and possibly the best compromise between considerations of aerostatic instability and manufacturing difficulty would be to use 12 feed holes of a 72 10 3 in diameter The final drawing is as shown in Figure 766 Figure 767 and Figure 768 clearly show the use of aerostatic bearings in the work spindle and the grinding spindle, respectively Both the spindles employ aerostatic journal bearings and aerostatic thrust bearings to obtain the various advantages of ultra-precision applications
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74 HYBRID GAS BEARINGS
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Hybrid gas bearings combine the principle of aerodynamic and aerostatic bearings They also combine higher load capacities due to the external pressure of an aerostatic bearing with additional aerodynamic
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Data for air at 15 C Pa = 147 lbf/in2 Po Pa = 50 lbf/in2 Kg = 069
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40 b = 15 b= 3 a b=2 a b= b=6 a a 125 a b= a 4
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Jet diameter d * (in 10 3)
Data for simple thrust bearing with single jet a b h*
d* For annular thrust bearing of same b/a and n jets d * = 2 (Fig 47 (b)) n 05 10 15 Design clearance h * (in 10 3)
Fig 764: The jet diameter versus clearance for a simple thrust bearing [3]
forces that increase with speed (Figure 769) These bearings are also inherently more stable than self-acting bearings as the speed at which whirl occurs greatly increases, due to an increased film stiffness [34] The performance of a hybrid bearing can be approximated by superpositioning the aerostatic and aerodynamic load components The performance of the bearing is indicated by the compressibility number 2
Gas Lubricated Bearings
Fig 765: Variation of the optimum jet diameter
with the supply pressure and the number of jets in annular bearings [3]
Fig 766: An annular aerostatic thrust bearing
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W Load coefficient based on diameter CL= (P P )D 2 o a
Kgo = 04 n =8 zero speed 04
03 l = 050 L 02
01 Simple orifices with circular pockets e = 05 For e = 09 multiply C L by 165 0 0 05 10 15 20 25 30
Length-to-diameter ratio L/D
Fig 767: A work spindle assembly
a = Pa ho where is the viscosity of the gas, Pa the ambient pressure, a the radius of the shaft and ho is the radial clearance The load capacity of the aerodynamic journal bearing increases with increasing compressibility numbers as in Figure 770 The load capacity also depends on the length-to-diameter ratio of the bearing Long bearings are more efficient for load carrying than short bearings Hybrid bearings also have the advantage in the case of internal supply pressure failure Most hybrid bearings are capable of working on a pure hydrodynamic film For a thrust bearing, a Rayleigh step may be incorporated at the leading edge of each pad to combine the hydrodynamic capacity with an adequate land area for the action of hydrostatic pressure [35] This arrangement can be seen in Figure 771
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