Comparison of the GUM and Monte Carlo methods on the flatness uncertainty estimation in coordinate measuring machine

Abstract

Abstract. In engineering industry, control of manufactured parts is usually done on a coordinate measuring machine (CMM), a sensor mounted at the end of the machine probes a set of points on the surface to be inspected. Data processing is performed subsequently using software, and the result of this measurement process either validates or not the conformity of the part. Measurement uncertainty is a crucial parameter for making the right decisions, and not taking into account this parameter can, therefore, sometimes lead to aberrant decisions. The determination of the uncertainty measurement on CMM is a complex task for the variety of influencing factors. Through this study, we aim to check if the uncertainty propagation model developed according to the guide to the expression of uncertainty in measurement (GUM) approach is valid, we present here a comparison of the GUM and Monte Carlo methods. This comparison is made to estimate a flatness deviation of a surface belonging to an industrial part and the uncertainty associated to the measurement result.

In-Process Measurement for the Process Control of the Real-Time Manufacturing of Tapered Roller Bearings

“…Simulations were programmed using the Monte Carlo method [ 24 , 25 ] to determine the contribution of each parameter to the final uncertainty. The probability density distributions (PDD) of each factor were defined based on its calibration data or the characteristics of the process.…”

“…The authors describe the model and analysis of a measurement system and the effects of its main error sources, namely the temperature and the misalignment of the devices or of the work piece and the master piece. The influence of the error sources was studied and an estimation of the uncertainty of the system was provided using simulations programmed using the Monte Carlo method [ 24 , 25 ], and finally the process improvement achieved when the measurement results were fed back into the manufacturing process is shown. A general approach for modelling the uncertainty associated with coordinate measuring systems (CMSs) is given in [ 26 ].…”

“…A general approach for modelling the uncertainty associated with coordinate measuring systems (CMSs) is given in [ 26 ]. Several authors [ 24 , 25 ] have shown a comparison between the estimation of measurement uncertainty using the law of propagation of uncertainty [ 27 ] and that using the propagation of distribution using the Monte Carlo method [ 28 ]. In this case, the method presented in [ 28 ] was the one that better fit our application, as the variables affecting the results of the measurement presented different distributions, some of them with asymmetrical effects.…”

Application of the sampling strategies in the inspection process

“…5 Meanwhile, the rise in complex part designs and the growing demands of tighter tolerances have led to the requirements of an established and an effective plan for inspection process on CMMs. According to previous studies, 6–8 there can be many factors as shown in Figure 1, which contribute to the measurement uncertainty of CMM results. These factors include sampling strategy, workpiece position and orientation, surface conditions, sensor type and configuration, and environment conditions.…”

Estimation of parallelism measurement uncertainty according to the Geometrical Product Specifications standard using coordinate measuring machine

“…Balasubramanian et al [7] estimated uncertainty in angle measurement using the GUM method taking into consideration the geometrical errors, temperature, vibrations, and probing strategy. Using a comparison between these two methods (GUM and the MCM) to validate an uncertainty measurement model, has been proven to give consistent results, it's within this framework that Jalid proposed a comparison of these two methods on the estimation of flatness uncertainty [8] based on the orthogonal distance regression (ODR) that provided the parameters of the substitute plane and their uncertainties, then studied the influence of sample size on the flatness estimation and uncertainty [9].…”