Prediction of profile error in aspheric grinding of spherical fused silica by ensemble learning regression methods

Abstract

Given the low thermal expansion coefficient and excellent optical properties of fused silica in UV regions, it is widely used in lenses and other optical components. A precision grinding machine equipped with a cup grinding wheel has been employed for the aspheric grinding of spherical fused silica elements. This study aims to achieve two main objectives: firstly, to identify the contributions of feed speed and rotational speed ratio (RSR) on the profile and waviness errors of the workpieces and, secondly, to improve the prediction of profile errors by developing a high-fidelity data-driven machine learning framework. Accurate prediction of profile errors of the workpieces can be used to correct manufacturing errors. Furthermore, assessing the impact of input parameters on surface waviness errors is a viable approach to optimize the manufacturing process. Full-factorial experiments were designed for three levels of feed speed and RSR to find the sensitivity of modeling and predictions to these pertinent design variables. The trigonometric Fourier series model was used to fit form errors onto profile errors. The form errors evaluation revealed that RSR and the interaction between feed speed and RSR significantly affected the workpiece's form error. Reducing the feed speed led to a decrease in profile and waviness errors. The minimum waviness and profile errors were attained at an RSR of 50.25, regardless of the feed speed. The ensemble learning regression framework was subsequently trained using three sets of experimental datasets encompassing diverse combinations of RSR and feed speed values to model profile errors. While the profile model underwent validation on previously unseen segments of the datasets the network had been exposed to during training, the final tests were carried out using six datasets featuring entirely different profile errors that the networks had not seen before. The ensemble learning regression framework's performance tests were assessed using mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and R-squared metrics. The framework demonstrated considerable predictive efficacy for the six left profile errors (unseen data), as evidenced by the calculated R-squared values from 0.767 to 0.965, signifying the lower and upper bounds of precision, respectively.