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Gas Lubricated Bearings Table 72
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Slocum s performance comparison of load, flow rate stiffness and tilt stiffness for typical journal bearing geometries and arrangements modified with station locations [1]
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Load capacity Stiffness Angular stiffness Flow rate Stations
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L/D = 10
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L/D = 10
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2 L/D = 05
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2 L/D = 05
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Aerostatic grinding spindle
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Aerostatic work spindle
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Fig 741: Aerostatic work and grinding spindles in action [29]
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A consideration of the manufacturing facilities available suggests that geometric errors may total to 00002 in (508 m) in relation to the diametrical clearance and holes down to 0005 in (0127 mm) diameter can be drilled The machine design limits the bearing diameter to 2 in (508 mm) but does
Precision Engineering not restrict the bearing length Ultimately, the completed design of the whole spindle is shown in Figure 743 Here the work spindle consists of both aerostatic journal and thrust bearings From Table 710, it is seen that for externally pressurized gas bearings, a thrust face must be provided to carry the axial load This is even more critical when designing the grinding spindle, as the forces will be concentrated in the axial direction Most bearings have linear operating characteristics up to an eccentricity ratio of 05 as can be seen from Figure 75 Thus, this permits an accurate estimation of the radial stiffness for values below an eccentricity of 05 In addition, higher
Fig 742: An aerostatic grinding spindle [29]
Fig 743: A typical ultra-precision aerostatic spindle and drive system [2]
Gas Lubricated Bearings
eccentricity ratios are used to provide a capacity to withstand an overload It is important to consider the geometrical error for the manufacturing process at this stage since the bearing clearance comes into picture Figure 744 indicates the actual load capacity that can be achieved by aerostatic bearings at a supply pressure of 100 lbf/in2 (689 kPa), which is common for industrial applications The figure is useful for obtaining a rough idea of the load capacity for a given dimension For other values of the supply pressure, the load capacity can be corrected by multiplying with
( Po Pa )
where (Po Pa) is expressed in lbf/in For example, the information in Figure 744 is valid for e = 05 and a supply pressure gauge of 100 lbf/in2 A diameter of 2 in is given with a load capacity of 100 lbf From the figure, a length of 3 in which will give a load value (145 lbf, on interpolation of curve 100 lbf and 150 lbf) that is higher than the load capacity at the intersection of the length and accordingly the diameter is chosen For a supply pressure gauge of less than 100 lbf/in2, a correction factor is required (as indicated before) Therefore, for the available supply pressure gauge that is 75 lbf/in2, the corrected load capacity is
75 485 N = 109 lbf 100 Figure 744 shows the performance of bearings when the diametrical clearance, 2ho = 0001 in (25 m) The airflow is proportional to the cube of the bearing clearance so that a reduction in clearance provides a significant reduction in the demand for the compressor power as well as an increase in the radial stiffness The value of the airflow is read on the curve (023 cfm) at the point of intersection of the length (3 in) and diameter (2 in) For a supply pressure gauge of less than 100 lbf/in2, a correction factor is required (indicated at the bottom of Figure 744) This final value of the air flow would be less than the airflow that is available for our design At a supply pressure of 75 lbf/in2, the airflow needed is 023 065 = 015 scfm 00042 m3/min This value is within the capability of the air supply system that is available In addition, the clearance that is chosen is also five times greater than the available manufacturing error In fact, it is possible for us to design a bearing that has a clearance, which is better than the chosen value However, it is always a good idea to design something that is in the middle range and not at the extreme ends Next, it is necessary to verify that the clearance chosen will gives an adequate radial stiffness The stiffness of the bearing is inversely proportional to the clearance where the reduction in radial clearance will increase the radial stiffness This reduction in radial clearance is limited by the cost and the difficulty in manufacturing From Figure 75, it can be seen that the stiffness of an aerostatic journal bearing is constant up to an eccentricity ratio of 05 The aerostatic stiffness, K, can then be defined as
145
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