, Volume 25, Issue 5, pp 875-881
Date: 20 Sep 2012

Monte carlo method for the uncertainty evaluation of spatial straightness error based on new generation geometrical product specification

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Abstract

Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product specification(GPS) requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on “The Guide to the Expression of Uncertainty in Measurement(GUM)”. In order to compute spatial straightness error(SSE) accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization(QPSO) is proposed to solve the minimum zone SSE and Monte Carlo Method(MCM) is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function(PDF) for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine(CMM) is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.

This project is supported by National Natural Science Foundation of China (Grant No. 51075198), Jiangsu Provincial Natural Science Foundation of China (Grant No. BK2010479), Innovation Research of Nanjing Institute of Technology, China (Grant No. CKJ 20100008), Jiangsu Provincial Foundation of 333 Talents Engineering of China, and Jiangsu Provincial Foundation of Six Talented Peak of China
WEN Xiulan, born in 1966, is currently a professor at Nanjing Institute of Technology, China. She received her PhD degree from Southeast University, China, in 2004. Her research interests include precision measurement, intelligent computation, and new generation geometrical product specification.
XU Youxiong, born in 1982, is currently a lecture at Nanjing Institute of Technology, China. XU Youxiong, born in 1982, is currently a lecture at Nanjing Institute of Technology, China. He received his PhD degree from Nanjing University of Science and Technology, China, in 2010. Nanjing University of Science and Technology, China, in 2010.
LI Hongsheng, born in 1966, is currently a professor at Nanjing Institute of Technology, China. He received his PhD degree from Southeast University, China, in 2005.
WANG Fenglin, born in 1978, is currently a lecture at Nanjing Institute of Technology, China. She received her PhD degree from Southeast University, China, in 2005.
SHENG Danghong, born in 1965, is currently a professor at Nanjing Institute of Technology, China. She received her PhD degree from Nanjing University of Science and Technology, China, in 2009.