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The best control system is one that doesn t have to do anything, where the laws of physics do all of the work automatically. For example, think about balance. You can stand a pencil on its eraser and it will stay there. Gravity is pushing straight down through the pencil and the center of gravity is over the eraser. It could stand there for a hundred years. But it is not stable. Tip the pencil just a little bit. Perhaps you bump the desk or somebody can t resist the urge to blow on the pencil, and it falls over. Figure 6-1 shows this condition, where the center of gravity gets moved away from the eraser. When that happens, gravity s acceleration pulls that center of mass down to the table. The pencil s natural behavior takes over and you can rely on the force of gravity to make the pencil fall each and every time. What if you wanted to make something that would not tip over like the pencil How could you arrange the system so that gravity would make it return to its original position instead of tipping it over The secret goes all the way back to 2. The pencil is full of potential energy, equal to the height of its center of gravity. Given any opportunity,



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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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this energy will be spent and the pencil will end up with the lowest possible energy, at on the table. We need to shape the system so that the center of gravity is below the pivot point instead of above it. That way, when we bump it, the center of gravity moves up instead of down, and gravity acts to correct the bump.

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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)

Slocum s performance comparison of load, flow rate stiffness and tilt stiffness for typical journal bearing geometries and arrangements modified with station locations [1]

Try This: Figure 6-2 shows a machine that uses gravity control to keep it stable, balanced on the tip of our previous pencil. Of course, you could also tape two pencils together in an upside-down V shape (like ) and balance that instead. When this machine tips left or right the center of gravity rises and is accelerated back down until it is directly under the pivot point.

Fig 741: Aerostatic work and grinding spindles in action [29]

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

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