Co-Kriging Method for Form Error Estimation Incorporating Condition Variable Measurements

Abstract

The form error estimation under various machining conditions is an essential step in the assessment of product surface quality generated in machining processes. Coordinate measuring machines (CMMs) are widely used to measure complicated surface form error. However, considering measurement cost, only a few measurement points are collected offline by a CMM for a part surface. Therefore, spatial statistics is adopted to interpolate more points for more accurate form error estimation. It is of great significance to decrease the deviation between the interpolated height value and the real one. Compared to univariate spatial statistics, only concerning spatial correlation of height value, this paper presents a method based on multivariate spatial statistics, co-Kriging (CK), to estimate surface form error not only concerning spatial correlation but also concerning the influence of machining conditions. This method can reconstruct a more accurate part surface and make the estimation deviation smaller. It characterizes the spatial correlation of machining errors by variogram and cross-variogram, and it is implemented on one of the common features: flatness error. Simulated datasets as well as actual CMM data are applied to demonstrate the improvement achieved by the proposed multivariate spatial statistics method over the univariate method and other interpolation methods.

Case study of surface micro-waves in ultra-precision raster fly cutting

“…They found that chip serration causes microwaves on machined surfaces, which increases machined surface roughness. In addition, Du and Fei conducted a series of studies on surface topography classification and measurement in conventional milling [14][15][16][17]. However, there has been no relevant research involving UPRFC.…”

Calibration and uncertainty estimation of non-contact coordinate measurement systems based on Kriging models

“…The literature on spatial statistics-based calibration methods is sparse. A method based on Co-Kriging models to estimate the errors of the surface form not only concerning spatial correlation but also concerning the influence of machining conditions is developed in [46]. A spatial statistical method to design adaptive inspection plans for the geometric control of mechanical parts with CMSs is presented in [47].…”

Spatial Interpolation for Periodic Surfaces in Manufacturing Using a Bessel Additive Variogram Model

“…Spatial interpolation is one possible solution to acquiring high-resolution surface data with relatively low cost [1,7,8]. When using this type of technique, the value of properties, e.g., surface heights and pixel RGB values, at unobserved locations is estimated with measurement data from its vicinal sampled locations based on spatial models.…”