TY - JOUR

T1 - Uncertainty Calculation of Flatness in Three-Dimensional Measurements

AU - Wang, Jinxing

AU - Jiang, Xiangqian

AU - Ma, Limin

AU - Xu, Zhengao

AU - Li, Zhu

PY - 2005

Y1 - 2005

N2 - The least-square method is commonly employed to verify the flatness in actual three-dimensional measurement processes, but the uncertainty of the verification results is usually not given by the coordinate measuring machines. According to basic principles of flatness least-square verification and the uncertainty propagation formula given by ISO/TS 14253-2, a calculation method for the uncertainty of flatness least-square verification was proposed. By this method, coefficients of the plane equation were regarded as a statistical vector, so that the plane equation, the results of flatness verification and the uncertainty of the results can be obtained after the expected values and covariance matrix of vector were determined. The method assured the integrity of the verification results, and accorded with requirements of new generation of GPS standards, which can improve the veracity of verification. Experimental results indicate that in conformity to the results of flatness least-square verification and the uncertainty, the plane can be accepted or rejected quantitatively in accordance with the decision rules given by ISO 14253-1.

AB - The least-square method is commonly employed to verify the flatness in actual three-dimensional measurement processes, but the uncertainty of the verification results is usually not given by the coordinate measuring machines. According to basic principles of flatness least-square verification and the uncertainty propagation formula given by ISO/TS 14253-2, a calculation method for the uncertainty of flatness least-square verification was proposed. By this method, coefficients of the plane equation were regarded as a statistical vector, so that the plane equation, the results of flatness verification and the uncertainty of the results can be obtained after the expected values and covariance matrix of vector were determined. The method assured the integrity of the verification results, and accorded with requirements of new generation of GPS standards, which can improve the veracity of verification. Experimental results indicate that in conformity to the results of flatness least-square verification and the uncertainty, the plane can be accepted or rejected quantitatively in accordance with the decision rules given by ISO 14253-1.

KW - Flatness

KW - Geometrical product specification(GPS)

KW - Least-square verification

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=27544443834&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:27544443834

VL - 2005

SP - 1701

EP - 1703

JO - Zhongguo Jixie Gongcheng/China Mechanical Engineering

JF - Zhongguo Jixie Gongcheng/China Mechanical Engineering

SN - 1004-132X

IS - 19

ER -