Improved Geometrical Product Specification (GPS) Uncertainty Theory And Application

The improved GPS system is an information system of standard and metrology, which adapts to the economic globalization and faces the digital designing, manufacturing and measuring. The uncertainty theory is an important component of the improved GPS system, which not only is destined for measurement uncertainty, but also includes such new concepts as total uncertainty, correlation uncertainty, compliance uncertainty, specification uncertainty, method uncertainty and implementation uncertainty. The study of the improved GPS uncertainty theory starts just now, and there are no relative international standards and guides for application. This theory and its application techniques are researched systematically in this paper. The more rational decision rules for conformance comparison of workpieces and the calculation method for uncertainty propagation of GPS standard-chain are supplied. Furthermore, the study will help China to attend the establishment of relative international standards. The main researches and creative points are as follows:After discussing the shortages of the decision rules based on measurement uncertainty given by ISO 14253-1, the decision rules based on improved GPS uncertainty are put forward, which include the decision rules based on compliance uncertainty for a given GPS specification and the decision rules based on total uncertainty for a given workpiece. In the decision rules presented in this paper, specification uncertainty and correlation uncertainty are taken into account besides measurement uncertainty. Therefore, the decision rules based on improved GPS uncertainty are more rational than the decision rules based on measurement uncertainty because they are accordant with the basic principle of the improved GPS system.The calculation framework for compliance uncertainty of GPS standard-chain is proposed. Based on the modeling of GPS standard-chain, the calculation flow for compliance uncertainty of GPS standard-chain is given respectively either in a default state or in a special state. In the default state, the compliance uncertainty should be calculated by the propagation of implementation uncertainty and specification uncertainty though the specification operator. However, in the special state, the compliance uncertainty should be obtained by the propagation of implementation uncertainty, specification uncertainty and method uncertainty though the verification operator.Aiming at the filtration operation, the calculation method for uncertainty propagation of linear profile filter is put forward. According to the filter equation of linear profile filter, the covariance matrix of filtered profile can be derived from the covariance matrix of unfiltered profile, so the uncertainty of filtered profile can be deduced from the unfiltered profile by the algorithm. Furthermore, two measurement examples of Gaussian filter are given, and the experimental results indicate that the uncertainty is variational after filtration operation. The variation of uncertainty is very important to the calculation of compliance uncertainty.Aiming at the association operation, the calculation method for the uncertainty of flatness and spatial straightness least-square verification is proposed. According to the basic principle of flatness and spatial straightness least-square verification, the calculation equation for the uncertainty of flatness and spatial straightness in three-dimensional measurement is deduced. The experimental results indicate that the method not only assures the integrity of the verification result, but also improves the veracity of verification by providing the index of uncertainty.