Calibration Of Measurement Error And Analysis Of Product Form Error Based On Kriging Method

The product form error estimation for machined parts is an essential step in the assessment of product quality surface inspection and control. In the quality inspection process, Coordinate Measuring Machine(CMM) is widely used to measure complicated surface form error due to its high measurement flexibility and rigorous measurement accuracy. With continuous improvement of the quality requirements for the mechanical parts, the exigency of CMM measuring efficiency and accuracy becomes higher. However, measurement error caused by the measurement process greatly influences the part surface form error estimation. What's more, considering measurement cost and efficiency, it is still unable to meet the requirement of whole space measurement on the mechanical part surface. Limited measurement samples affect the accuracy estimation of the form error. On the other hand, in the machining process of mechanical part surface, the processing conditions, such as feed rate, cutting force and vibration of the tool cutting, have significant impacts on the form error. Moreover, with strict monitoring for machining process, the processing conditions are achieved through online monitoring equipment.Therefore, this thesis does the research from three aspects: firstly it aims at improving the accuracy of measurement by CMM, and a measurement error calibration procedure based on Kriging method is developed. It calculates the measurement error through the CMM measuring data on the datum plane. Then it establishes the spatial model of correlation and variability for the measurement error. And the measurement error calibration model is characterized based on the Kriging method to realize the compensation for the new measurement at any site in the space. Secondly, 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 Kriging method is derived to predict the height value of unmeasured points. Ultimately the form error estimation model is established on the measured points and estimated points. Thirdly, compared to traditional univariate spatial statistics only concerning spatial correlation of height value measurements, this thesis presents a method of multivariate spatial statistics, Co-Kriging, to estimate surface form error not only concerning spatial correlation but also concerning the influence of machining conditions, which are online obtained. This method can reconstruct more accurate part surface and make the estimation deviation smaller. It characterizes the spatial correlation of manufacturing errors by variogram and cross-variogram.Case studies show that the measurement error calibration model based on Kriging method enables to compensate the measurement error in the whole space around of the part surface. While the cross-validation methods conclude that spherical variogram model is the best model to characterize the measurement error correlation in this case. And ordinary Kriging method achieves the most accurate calibration compensation. Through analyzing the case of form error estimation based on univariate method, it concludes that the form error estimation model based on Universal Kriging method could improve the accuracy of form error estimation over traditional direct method up to 5-10%. For the form error estimation model based on multivariate spatial interpolation method considering processing machining conditions, it demonstrates that the improvement achieved by the proposed multivariate spatial statistics method over the traditional univariate method to 3-5%.