An Improved Measurement Uncertainty Calculation Method of Profile Error for Sculptured Surfaces

• Published in: Chinese journal of mechanical engineering Vol. 32; no. 1; pp. 1 - 10
• Main Authors: Liu, Chenhui, Song, Zhanjie, Sang, Yicun, He, Gaiyun
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01.12.2019; Springer Nature B.V; SpringerOpen
• Edition: English ed.
• Subjects: Adaptive Monte Carlo method; Computer simulation; Converge factor; Electrical Machines and Networks; Electronics and Microelectronics; Engineering; Engineering Thermodynamics; Heat and Mass Transfer; Instrumentation; Intelligent Manufacturing Technology; Machines; Manufacturing; Mathematical models; Mechanical Engineering; Monte Carlo simulation; Original Article; Power Electronics; Processes; Second-order GUMM; Skewed distributions; Theoretical and Applied Mechanics; Uncertainty; Uncertainty; Second-order GUMM; Adaptive Monte Carlo method; Converge factor
• ISSN: 1000-9345; 2192-8258
• DOI: 10.1186/s10033-019-0404-0

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.