Abstract
The current researches mainly adopt “Guide to the expression of uncertainty in measurement (GUM)” to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not appropriate to calculate the uncertainty of profile error because the mathematical model of profile error is strongly non-linear. An improved second-order GUM method (GUMM) is proposed to calculate the uncertainty. At the same time, the uncertainties in different coordinate axes directions are calculated as the measuring points uncertainties. In addition, the correlations between variables could not be ignored while calculating the uncertainty. A k-factor conversion method is proposed to calculate the converge factor due to the unknown and asymmetrical distribution of the output quantity. Subsequently, the adaptive Monte Carlo method (AMCM) is used to evaluate whether the second-order GUMM is better. Two practical examples are listed and the conclusion is drawn by comparing and discussing the second-order GUMM and AMCM. The results show that the difference between the improved second-order GUM and the AMCM is smaller than the difference between the standard GUM and the AMCM. The improved second-order GUMM is more precise in consideration of the nonlinear mathematical model of profile error.
Highlights
Profile error is an important feature to evaluate the machining quality of sculptured surfaces
Profile error could be obtained by non-uniform rational B-splines (NURBS) surface fitting according to the data points
The uncertainties are calculated in the first-order and the second-order GUM method (GUMM)
Summary
Profile error is an important feature to evaluate the machining quality of sculptured surfaces. Profile error could be obtained by non-uniform rational B-splines (NURBS) surface fitting according to the data points. The method of calculating the profile error could not get the corresponding uncertainty. GUMM is a method to estimate the uncertainty by calculating the first-order Taylor series expansion of profile error. GUM S1 [12] used the Monte Carlo method (MCM) to analyze the uncertainty without considering the distribution of the output variable and the format of the mathematical model. AMCM is not suitable to calculate the uncertainty It can still be used as a suitable method to evaluate the GUMM. The second-order GUMM was proposed to estimate the uncertainty considering the difficulty of the prior information
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