Profile Uncertainty Estimation for Roundness Measurements of Glass Hemisphere Using the Multistep and Phase Combination Methods

Abstract

In order to evaluate the performance of ultraprecision machining, precise and accurate roundness or form profile measurements of a glass hemisphere are required. In such measurements, the multistep method is a commonly used self-calibration method. This method allows the roundness error of the workpiece to be separated from the spindle error of the machine. Recently, the phase combination method has also been used for high-accuracy measurements. This method produces results equivalent to those obtainable using a large number of steps, by combining two sets of results for different smaller numbers of steps. However, there have been no reports describing the uncertainties associated with the estimated roundness profiles using these methods. If the required accuracy is above the specifications, it is necessary to measure of a larger number of steps, which is both time consuming and leads to wear of the workpiece. This paper describes the estimated uncertainty in the profile for roundness measurements using both the multistep and phase combination methods. Based on the estimated uncertainty, the optimum number of steps to achieve a specific level of precision can then be predicted. Furthermore, for the phase combination method, the optimum combination of step numbers is suggested.