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where CLo is the load coefficient based on the axial flow model and CL is the load coefficient corrected for non-axial flow [3] For the purpose of designing, long bearings are often avoided because of the inefficiency associated with the load capacity due to the increase in the non-axial flow effect The analysis method in thrust bearings is mostly similar The assumption of incompressible flow underestimates the actual performance of thrust bearings, which can be 10% better This flaw actually allows for the incorporation of a safety margin For similar operating conditions, the simple thrust bearing with a central feed consumes four times less air than does the annular thrust bearing A common practice is to use annular thrust bearings only when the shaft projects beyond the bearing assembly It also provides a better tilting resistance [3] For a journal bearing with a slot arrangement, the gas is supplied through narrow slots in the bearing sleeve into the clearance space as shown in Figure 740
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Fig 740: A journal bearing with circumferential inlet slots
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The designing of bearings with circumferential slots involves matching the slot dimensions with the bearing clearance dimensions With reference to Figure 740, the critical design parameter, which is the ratio of dimension, a, is given as
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h y a = o for two rings of slots z l 3 h 2y a = o for one ring of slots z l where ho is the radial clearance at zero eccentricity, z the width of the inlet slot, y the radial length of the inlet slot and l is the distance of the slot from the end of the bearing The optimum value for a is 8 for an eccentricity ratio of 05, which is very unlikely due to manufacturing constraints Smaller values of a are often preferred to maintain z at a larger value to simplify the manufacturing process
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With reference to Figure 740, the expressions for flow from Po to Pd in the feed slot and Pd to Pa in the bearing slot are given as
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Po2 Pd2 = Pd2 Pa2 = 24 RTmy n D z3
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24 RTml n D h3 where y is the length of the feed slot (usually the thickness of the bearing sleeve), z the thickness of the feed slot and D n is the number of feed slots giving the width of the slot as
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A further expansion of the preceding equations by assuming a parabolic pressure distribution from the slot to the end of the bearing and the presence of a constant pressure between two adjacent slots allows for the calculation of the load on the shaft as illustrated in Figure 755 for short bearings The strength of the inlet slot design lies in the introduction of air to the clearance around the circumference of the bearing that eliminates problems due to dispersion effect On the other hand, the effect of a non-axial flow reduces the load capacity
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7310 Design of Aerostatic Journal Bearings
The design of an aerostatic bearing involves matching the various load and stiffness requirements with bearing clearance, orifice design, air supply pressure and flow rate Table 72 provides some guidelines for the design of aerostatic journal bearings Relative values are given for each parameter It is found that two air bearings with feeding at the quarter station give the best performance in terms of load capacity, stiffness and angular stiffness However, the air flow rate is comparatively much higher Figure 741 shows the operation of work and grinding spindles in the Moore ultra-precision machine [29] Most of the air bearings in the work spindle from various manufacturers are almost similar in terms of performance and dimension The same can be said about the grinding spindle which is shown in Figure 742 It is found that there are different approaches to design the aerostatic journal bearing in either the work or the grinding spindle However, Powell s approach seems to be accurate and comprehensive Therefore, the design of an aerostatic journal bearing similar to those used in ultra-precision machines will be explained based on an example adapted from Design of Aerostatic Bearings by JW Powell [3] Example: Design of an Aerostatic Journal Bearing An air-lubricated journal bearing must be designed to carry a load of 100 lbf (445 N) at an eccentricity ratio of 05 Its radial stiffness should exceed 400,000 lbf/in (70,000 N/mm) A workshop airline is available at a 75 lbf/in2 (51675 kPa) gauge The airflow should not exceed 050 scfm (00142 m3/min)
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