Use and calibration of ultraprecision axes of rotation with nanometer level metrology

A spindle calibration device is designed and built to resolve and quantify the nanometer level error motions of ultraprecision axes of rotation. The calibrator has the ability to determine all error motions (radial, axial, and tilt for fixed and rotating sensitive directions) of the spindle under test. A new and unique adaptation of the Donaldson reversal technique is implemented to achieve sub-nanometer repeatability and nanometer-level uncertainty in spindle measurements.; The calibrator uses a rotary table and reversal chuck to perform Donaldson reversal with a single displacement indicator that does not move between the normal and reversed measurements. This equipment gives the calibrator the ability to employ other error separation techniques as well as reversal. Experimentation indicates that error motion results between Donaldson reversal test and other error separation techniques agree to better than 2 nanometers (0.08 μin.). Additionally, an alternative method of separating the spindle error motions from measurements based on the general error motion case is presented which uses displacement indicators that are not oriented purely in the radial or axial direction.; The Master Axis method for measuring spindle error motions is investigated and validated with artifact-based measurement techniques to agree within the sub-nanometer repeatability of the calibrator. The details of implementing Donaldson reversal with the Master Axis are also presented; both rotor and stator of the spindle under test are required to complete the separation of error motions. Additional tests show that error motion magnitudes can vary by nearly a factor of two depending on the choice of fixed sensitive direction. Moreover, the calculated and measured results for any fixed sensitive direction agree to less than 1 nanometer (0.04 μin.), indicating that the fixed sensitive direction error motion can be completely determined from two measurements.; Finally, the results of a spindle calibration are integrated into a mathematical model of a measuring machine generated using homogeneous transformation matrices (HTMs). The model enables the orientation angles of spindles used in the machine to be chosen such that the error in measurement is minimized. Simulated measurement results indicate that a 50% reduction in error is achieved for specific choices of spindle orientations.