The application of grey theory to the prediction of measurement points forcircularity geometric tolerance

The objective of this study is to improve the efficiency of achieving accur ate and speedy inspection when a coordinate measuring machine (CMM) is used to measure circularity geometric tolerance. Grey prediction ruing grey the ory was applied in developing tire heuristic algorithm for predicting the n umber of measuring points required for measuring circularity geometric tole rance. The heuristic algorithm was used to plan the number of measuring poi nts of the next workpiece and to predict the circularity geometric toleranc e dimensions. This step provides a better foundation for on-line inspection to determine tire number of measuring points required for measurement insp ection of tire nest workpiece. It can also predict,whether the circularity geometric tolerance of the next workpiece will conform with the circularity geometric tolerance dimension on the design drawing. This heuristic algori thm could also be used to determine whether the manufacturing process requi res modification, in order to save human and material resources and reduce failure rate. In this paper, a circularity heuristic algorithm for deciding the number of measuring points for the circularity geometric dimension is proposed to re duce the angle between measuring points. In this heuristic algorithm, the a ddition of measuring points is determined by whether the predicted circular ity value exceeded the scope of the grey interval. When more points are to be inspected equiangular inspection is again performed. Once the predicted circularity value exceeds the limitation of the design drawing circularity geometric dimensions, the manufacturing process is examined immediately. Th e concept of adding measuring points for on-line inspection is combined wit h the grey prediction and the standard deviation concept to establish the c ircularity heuristic algorithm for deciding the number of the measuring poi nts. Experimental data are also introduced to verify the measuring point algorit hm for the circularity geometric dimension of a workpiece. The objective is to reach a balance between the smallest number of measuring points require d for inspection an inspection accuracy. Consequently, it is possible to av oid using too many measuring points, which increases the inspection time, w hile achieving the required measurement accuracy.