Optimization of the straightness measurements on rough surfaces by Monte Carlo simulation

The straightness error of a coordinate measuring machine (CMM) is determined by measuring a rule standard. Thanks to a reversal technique, the straightness uncertainty of the CMM is theoretically dissociated from the straightness uncertainty of the rule. However, stochastic variations of the whole measurement system involve uncertainties of the CMM straightness error. To quantify these uncertainties, different sources of stochastic variations are listed with their associated probability density functions. Then Monte Carlo methods are performed first to quantify error and secondly to optimize measurement protocol. It is shown that a 5-measurement distance from 0.1 mm to each measurement coordinate allows a double reduction of uncertainties, principally due to the rule roughness amplitude (R(a) = 0.35 µm) and because this optimal distance of 0.1 mm is equal to the autocorrelation length of the rule roughness. With this optimal configuration, the final uncertainly on the straightness error of the CMM studied is less than 1 µm on the whole evaluated length of the rule (1 m). An algorithm, including Probe Tip Radius of the CMM and surface roughness of the piece, is finally proposed to increase CMM reliability by minimizing error measurements due to surface roughness of the measured piece.