App-Rotary Tables Accuracy vs Radial Runout

When rotary table turns in its bearings, it typically results in a radial run-out; essentially the roundness of the rotor rotation.  For air bearings  this can be as little as 1 micron T.I.R.; for some rolling contact bearings, it can be as high as 25 microns and more.  This run-out is a linear translation along a plane which is perpendicular to the axis' centerline.

Consider this geometry:

Where A is the theoretical center of the rotary table, and B is the run-out error.  This run-out results in an offset error of ±S.  If B is small relative to the part's tolerance band, it can be ignored.  However, if B is large this error must be considered because the rotary table index position is generated about A; whereas, the part's index angle is generated from its own center, which is located on B.  A part can not be centered better than the radial run-out value.  If a table has a 10 microns run-out, the part can not be centered better than 10 microns.  The smaller the radius L, the greater will be the resulting difference between Θ and Θ', and the greater the rotary table index error.

The following formula allows to calculate the effective angular error, based on the run-out error of the rotary table bering, and the diameter of the part or feature:

where Θ_e is in arc seconds, B is the run-out and D is the diameter, with both being expressed in either inches or millimeters