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In order to investigate the thermal effect of a servo axis' positioning error on the accuracy of machine tools, an empirical modeling method was proposed, which considers both the geometric and thermal positioning error. Through the analysis of the characteristics of the positioning error curves, the initial geometric positioning error was modeled with polynomial fitting, while the thermal positioning error was built with an empirical modeling method. Empirical modeling maps the relationship between the temperature points and thermal error directly, where the multi-collinearity among the temperature variables exists. Therefore, fuzzy clustering combined with principal component regression (PCR) is applied to the thermal error modeling. The PCR model can preserve information from raw variables and eliminate the effect of multi-collinearity on the error model to a certain degree. The advantages of this modeling method are its high-precision and strong robustness. Experiments were conducted on a three-axis machine tool. A criterion was also proposed to select the temperature-sensitivity points. The fitting accuracy of the comprehensive error modeling could reach about 89%, and the prediction accuracy could reach about 86%. The proposed modeling method was proven to be effective and accurate enough to predict the positioning error at any time during the machine tool operation. [ABSTRACT FROM AUTHOR]

Optical interferometry plays an important role in the topographical surface measurement and characterization in precision/ultra-precision manufacturing. An appropriate surface reconstruction algorithm is essential in obtaining accurate topography information from the digitized interferograms. However, the performance of a surface reconstruction algorithm in interferometric measurements is influenced by environmental disturbances and system noise. This paper presents a comparative analysis of three algorithms commonly used for coherence envelope detection in vertical scanning interferometry, including the centroid method, fast Fourier transform (FFT), and Hilbert transform (HT). Numerical analysis and experimental studies were carried out to evaluate the performance of different envelope detection algorithms in terms of measurement accuracy, speed, and noise resistance. Step height standards were measured using a developed interferometer and the step profiles were reconstructed by different algorithms. The results show that the centroid method has a higher measurement speed than the FFT and HT methods, but it can only provide acceptable measurement accuracy at a low noise level. The FFT and HT methods outperform the centroid method in terms of noise immunity and measurement accuracy. Even if the FFT and HT methods provide similar measurement accuracy, the HT method has a superior measurement speed compared to the FFT method. [ABSTRACT FROM AUTHOR]