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

Abstract

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.

Influence of the Lander Size and Shape on the Ballistic Landing Motion

“…Taking the longitude and latitude as two variables, the 95% confidence ellipse describes the concentration degree. With a given confidence coefficient, the error ellipse is determined by the mean values and the covariance matrix of the settling points’ longitudes and latitudes (Zhu et al., 2019). In the Monte Carlo simulation, the 95% error ellipse indicates that the probability that one trajectory settling position will fall in this ellipse is 95%.…”

Virtual task-specific measurement uncertainty determination for laser scanning

“…The use of digital twins to examine the task-specific uncertainty is extensively researched for conventional CMM measurements, i.e., tactile probing [11][12][13]. Furthermore, literature scrutinizes some geometrical characteristics specifically: straightness [14,15], flatness [16][17][18], roundness [19][20][21], cylindricity [22] and distance between two derived characteristics [23]. However, similar research for optical measurement systems is non-existing, due to the lack of reliable digital twins of optical systems due to the high number of error contributors [24].…”

Uncertainty analysis of two-dimensional self-calibration with hybrid position using the GUM and MCM methods

“…Published in 2008, the Propagation of Distributions Using a Monte Carlo Method, Supplement 1 to the guide, discusses the propagation of probability distributions through a mathematical measurement model [22,23]. The GUM method and Monte Carlo method (MCM) have been widely used in numerous fields to evaluate measurement uncertainties [24][25][26][27][28][29][30][31].…”