Characterization of surface profiles using discrete measurement systems
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Form error estimation techniques based on discrete point measurements can lead to significant errors in form tolerance evaluation. By modeling surface profiles as random variables, we are able to show how sample size and fitting techniques affect form error estimation. Depending on the surface characteristics, typical sampling techniques can result in estimation errors of as much as 50%;We investigate current available interpolation procedures. Kriging is an optimal interpolation for spatial data when the model of variogram is known a priori. Due to the difficulty in identifying the correct variogram model from the limited sampled data and lack of complete computer software, there is no significant advantage to apply kriging to estimate form error in the inspection process;We apply the Shannon sampling theorem and represent the surface profiles as band-limited signals. We show that the Shannon sampling function is in fact an infinite degree B-spline interpolation function and thus a best approximation for band-limited signals. Both Shannon sampling series and universal kriging (using a priori correlation function) are applied to flatness error estimation for uniform sample points measured from five common machined surfaces. The results show both methods perform similarly. The probability of over-estimating form error increases and the probability of accepting bad parts decreases using interpolation methods versus using the points directly.