Knowledge of the accuracies of air bearing spindles in the sub-micrometre to nanometre range is required for the design, commissioning and operation of ultra-precise machine tools, measurement systems and other machines employing high precision rotational motion. In order to verify the dynamic performance of a spindle, measurement is required of its error motions in the unwanted five degrees of freedom (one axial, two tilts and two radial motions). Presentation of these error motions (eg in the form of polar charts) can then be used to provide critical spindle metrology data including total, asynchronous and average error motion rosette profiles and their average and peak values. This thesis describes a metrology system based on optical interferometry for measuring such unwanted error motions in three degrees of freedom involving motion along the spindle axis (axial rectilinear displacement and tilts about orthogonal axes), incurred with rotation of a precision air spindle over its specified speed-range. The system is not sensitive to orthoaxial translations which may be measured using alternative methods. Possible alternative techniques for measuring any of the degrees of freedom include an array of proximity sensors, (one for each translational degree of freedom and a further one for 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 each offer 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 spindle of a vertical axis ultra-precision facing machine using a test-artefact. This is a mirror with less than one fringe departure from planarity from which interferogram. fringe-patterns are captured, digitised and analysed synchronously as the spindle rotates. The issue of the prediction of the dynamic form and motions of the observed interferograrn arises and the earlier 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 of spindle-rotation and image processing techniques used to filter the fringe pattern, enabling measurement of spindle tilt and axial displacement. Issues of sampling with respect to the anticipated spatial angular frequency of the spindle run-out are considered with respect to the speed/frequency capability of data-acquisition and processing arrangements. 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 a function of observational time. It is foreseen that the system will be applicable in research and production-support in ultra-precision machining production processes and in rotational metrology
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