Abstract: The flatness error estimation under given machining conditions is an essential step in the assessment of product surface quality generated in machining processes. Coordinate measuring machine (CMM) is widely used to measure complicated surface flatness error. However, considering measurement cost, only a few measurement points are collected by CMM for a part surface. Therefore, spatial statistics method is adopted to achieve more interpolated points for more accurate form error estimation. The spatial correlation on part surface is characterized by appropriate variogram. By taking the spatial correlation into consideration, the universal Kriging (UK) method is derived to predict the height value of unmeasured points. Ultimately flatness error estimation model is established by the least square method. Through analyzing the case, it concludes that spherical variogram can effectively describe the spatial correlation on part surface and the Universal Kriging method could improve the accuracy of flatness error estimation 5%-10%over traditional method.

Key words: universal Kriging;variogram;flatness error;spatial correlation, Aesthetic measure, Maximum Flux Principle, Self-Organizing feature Mapping, Synthetic evaluation, Product form