The use of three-dimensional (3D) data in the industrial measurement field is becoming increasingly popular because of the rapid development of laser scanning techniques based on the time-of-flight principle. However, the accuracy and uncertainty of these types of measurement methods are seldom investigated. In this study, a mathematical uncertainty evaluation model for the diameter measurement of standard cylindroid components has been proposed and applied to a 3D laser radar measurement system (LRMS). First, a single-point error ellipsoid analysis for the LRMS was established. An error ellipsoid model and algorithm for diameter measurement of cylindroid components was then proposed based on the single-point error ellipsoid. Finally, four experiments were conducted using the LRMS to measure the diameter of a standard cylinder in the laboratory. The experimental results of the uncertainty evaluation consistently matched well with the predictions. The proposed uncertainty evaluation model for cylindrical diameters can provide a reliable method for actual measurements and support further accuracy improvement of the LRMS.

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The uncertainty determination of the geometrical feature measurement for coordinate measuring machines (CMMs) is an essential part in the reliable quality control process. However, the most commonly-used methods for uncertainty assessment are difficult and require not only a large number of repeated measurements but also rich operation experience. Based on the error ellipse theory and the Monte Carlo simulation method, an uncertainty evaluation method for CMM measurements is presented. For circular features, the uncertainty evaluation model was established and extended into the use of an application of two holes’ central distance measurement through Monte Carlo Simulation. The verification experiment of the new method was conducted and results were compared with the traditional ones and they fit reasonably well, which proved the validity of the proposed method.

For high-precision machining, a convenient and accurate detection of motion error for machine tools is significant. Among common detection methods such as the ball-bar method, the laser tracker approach has received much more attention. As a high-accuracy measurement device, laser tracker is capable of long-distance and dynamic measurement, which increases much flexibility during the measurement process. However, existing methods are not so satisfactory in measurement cost, operability or applicability. Currently, a plausible method is called the single-station and time-sharing method, but it needs a large working area all around the machine tool thus leaving itself not suitable for the machine tools surrounded by a protective cover. In this paper, a novel and convenient positioning error measurement approach by utilizing a single laser tracker is proposed followed by two corresponding mathematical models including a laser tracker base point coordinate model and a target mirror coordinates model. Also, an auxiliary apparatus for target mirrors to be placed on is designed, for which sensitivity analysis and Monte-Carlo simulation are conducted to optimize the dimension. Based on the method proposed, a real experiment using single API TRACKER 3 assisted by the auxiliary apparatus is carried out and a verification experiment using a traditional RENISHAW XL-80 interferometer is conducted under the same condition for comparison. Both results demonstrate a great increase in the Y-axis positioning error of machine tool. Theoretical and experimental studies together verify the feasibility of this method which has a more convenient operation and wider application in various kinds of machine tools.