Small-sample linear profile error uncertainty assessment based on grey system

Abstract

The uncertainty assessment of the profile error of the cam profile, as defined in the national standard method, is difficult to carry out under conditions of small sample size and absence of probability distribution assumptions. This paper proposes a small-sample assessment model for the uncertainty of the profile error based on grey system. Firstly, the coordinate transformation is conducted using Vector Alignment Method to reduce systematic errors, and the non-uniform rational B-splines curve interpolation is utilized to fit the cam profile curve and perform error assessment. Subsequently, based on the error assessment results, Grey Information Measurement Model (GIMM) for the uncertainty of the profile error in small samples is established. This model employs Grey Relational Analysis to eliminate outliers and evaluates the uncertainty of the profile error by solving grey correlation coefficients. Maximum-Minimum Information Measure Method is used to assess the optimal sample size. Finally, numerical experiments and experimental tests were conducted on the uncertainty of camshaft profile error in automobiles. A total of 15 sets of profile data were compared with Guide to the Representation of Uncertainty in Measurement (GUM) and Monte Carlo Method (MCM) under different sample sizes. The results showed that GIMM achieved evaluation with only 8 sets of data samples under small sample and poor information conditions, with an uncertainty of 0.6338 μm, compared to 0.6346 μm for GUM and 0.6391 μm for MCM. The acceptance rate of GIMM reached 95.2%. This model outperforms other methods, providing a simplified and reliable assessment of cam profile error uncertainty.