Knowledge of the accuracies of air bearing spindles in the sub-micrometre to nanometrerange is required for the design, commissioning and operation of ultra-precise machinetools, measurement systems and other machines employing high precision rotationalmotion.In order to verify the dynamic performance of a spindle, measurement is required of itserror motions in the unwanted five degrees of freedom (one axial, two tilts and two radialmotions). Presentation of these error motions (eg in the form of polar charts) can then beused to provide critical spindle metrology data including total, asynchronous and averageerror motion rosette profiles and their average and peak values.This thesis describes a metrology system based on optical interferometry for measuringsuch unwanted error motions in three degrees of freedom involving motion along thespindle axis (axial rectilinear displacement and tilts about orthogonal axes), incurred withrotation of a precision air spindle over its specified speed-range. The system is notsensitive to orthoaxial translations which may be measured using alternative methods.Possible alternative techniques for measuring any of the degrees of freedom include anarray of proximity sensors, (one for each translational degree of freedom and a further onefor each of the other rotational degrees of freedom), to measure the run-out of an artefact.Proximity sensors based upon capacitive or optical fibre back-scatter techniques eachoffer the required single degree-of-freedom non-contacting capability and bandwidth.In the current work, a Fizeau interferometer is used to monitor the motion of the spindleof a vertical axis ultra-precision facing machine using a test-artefact. This is a mirror withless than one fringe departure from planarity from which interferogram. fringe-patterns arecaptured, digitised and analysed synchronously as the spindle rotates. The issue of theprediction of the dynamic form and motions of the observed interferograrn arises and theearlier theory is extended to optimise the set-up, including provision of automatic servo-alignment of the optical axis with the axis of the spindle.Measurement interferograrn data is sampled at selected angular incremental positions ofspindle-rotation and image processing techniques used to filter the fringe pattern,enabling measurement of spindle tilt and axial displacement. Issues of sampling withrespect to the anticipated spatial angular frequency of the spindle run-out are consideredwith respect to the speed/frequency capability of data-acquisition and processingarrangements. Essentially, with a spindle rotating at typical machining speeds of 300-3000 rev/min, for consistent error motions, the resolution of an error plot is principally afunction of observational time. It is foreseen that the system will be applicable in researchand production-support in ultra-precision machining production processes and inrotational metrology.
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