Batch Roundness Characterization and Evaluation

A new concept referred to as the batch roundness is presented in this paper. This concept is derived to illustrate the worst possible form error for a batch of circular features machined under the same conditions. It is to be used as a statistical quality measure for such a batch of circular features and evaluated by analyzing their systematic and random form error components. The definition of batch roundness is introduced first and the associated evaluation algorithm is then presented. The evaluation algorithm starts by characterizing the deterministic profile for the batch of circular features. When the deterministic profile is obtained, the residuals, which are regarded as the random form error component, are available. The batch roundness can then be evaluated and the corresponding confidence level of the batch roundness zone determined. Case studies using both the simulated and experimental data sets have successfully demonstrated that the batch roundness can be reliably estimated from the inspection data of only one circular feature in the batch. This unique feature of the presented algorithm will hold as long as the measurement data size is adequate and the relative magnitude of the random form error component with respect to the batch roundness is not too large.