The harmonic fitting method for the assessment of the substitute geometry estimate error. Part II: statistical approach, machining process analysis and inspection plan optimisation

The Harmonic Fitting Method (HFM), presented in the first part of this work, is here used to describe the estimate error in statistical terms. In fact, the estimate error can be considered as a random variable that depends on three different random processes: the machining, the part positioning, and the measurement processes. With the HFM it is possible to determine the moments of the estimate error (systematic value and covariance matrix) as a function of the inspection plan. It will be demonstrated that the systematic part of the estimate error derives from the systematic part of the machined surface deviations, and that the random part derives from the variability of the machining and measurement processes. In particular, the causes of the machining process variability will be analysed in terms of harmonics, thus establishing a direct relationship between the machining process and the substitute geometry estimate error. Moreover, the possibility of obtaining the probability density function of the estimate error from the HFM will be analysed, together with the problem of the inspection plan optimisation. The HFM will be used to design the optimal inspection plan for a circular geometric feature, and it will be demonstrated that, when the part positioning is subjected to a rotation uncertainty, the estimate errors of the diameter and of the eccentricity are likely to follow a Gaussian and a Rayleigh distribution, respectively. A real case of turned shafts will be considered, and the HFM optimisation of the inspection plan will be discussed.