Form Error Estimation Using Spatial Statistics

Abstract

Form error estimation is an essential step in the assessment of product geometry created through one or more manufacturing processes. We present a new method using spatial statistics to estimate form error. Using large sets of uniform sample points measured from five common machined surfaces, we compare the form error estimates using individual points and fitted surfaces obtained through spatial statistical methods. The results show that spatial statistics can provide more accurate estimates of form error under certain conditions. Disciplines Industrial Engineering | Statistics and Probability | Systems Engineering CommentsThis is an article from Transactions of the ASME 262 (2000)

Gaussian process method for form error assessment using coordinate measurements

“…We also model both systematic errors (using a spatially correlated term) and random errors (using a spatially uncorrelated term). In contrast, both Dowling et al (1993) and Yang and Jackman (2000) did not include spatially uncorrelated errors. This might not be reasonable if the considered manufacturing process produces both lowfrequency systematic errors (because of machine tool wear) and high-frequency random errors (because of machine vibration).…”

“…However, little research on the spatial-modelbased approach has been performed and the literature on this topic is sparse. In Dowling et al (1993) and Yang and Jackman (2000), the spatial models require one CMM coordinate measurement to be an explicit function of the other two coordinates. Thus, these models cannot be applied to generic geometric features, such as a circle, where one coordinate cannot be expressed as an explicit function of the other two.…”

“…Another line of approaches is to use a spatial statistical model (typically, a Gaussian process model) to represent systematic manufacturing errors (Dowling et al 1993;Yang and Jackman, 2000). The non-parametric nature of Gaussian processes offers an improved flexibility in learning general types of systematic errors over the basis-function fitting method and the Fourier analysis method.…”

“…The empirical distribution reflects the estimation uncertainty (resulting from the sampling and modeling uncertainty) Downloaded by [Florida Atlantic University] at 22:02 17 November 2014 and can help quantify the risk of a part not being accepted. Dowling et al (1993) and Yang and Jackman (2000) used one predicted surface to estimate the form error and to decide on accepting or rejecting a part. They did not provide uncertainty information about the form error assessment.…”

Prediction of porosity in metal-based additive manufacturing using spatial Gaussian process models

“…To date, fewer works use spatial models in manufacturing applications. Yang and Jackman [59] scan points on the surface of a workpiece and use a spatial model to predict and estimate form (geometry) errors. Colosimo et al [60] propose a process control method that combines control charts with spatial correlated noise, and apply this method to monitor the roundness geometrical tolerance for parts produced by turning.…”