Uncertainty evaluation of straightness in coordinate measuring machines based on error ellipse theory integrated with Monte Carlo method

According to the new generation geometrical product specification, it is necessary to provide measurement uncertainty together with measurement results in order to determine the reliability of results. The traditional methods used for the uncertainty evaluation of straightness are laborious and time-consuming owing to a large quantity of repeated measurements or a complicated computational process. Based on the error ellipse theory and the Monte Carlo method, a novel method for uncertainty evaluation is proposed. Through the error ellipse theory, in the measuring space of coordinate measuring machines, the positional uncertainty of sampling points can be more accurately considered to be represented by an ellipse. By integrating the Monte Carlo method, only with limited sets of real measured data in small experimental trials, the uncertainty propagation from a single sampling point to the whole straight line can be demonstrated clearly in the simulation without requiring large amounts of time and labour. The detailed procedures of uncertainty evaluation are given. The straightness uncertainty can then be obtained by statistical analysis of the simulation results. Real straightness measurement experiments were carried out and compared with the results from the proposed method. The difference was no more than 5%, which verified the validity of the method.