Abstract

Currently, driven by the increasing demand for precision in optical and mechanical components, complex surfaces are now required to maintain profile errors within micrometric tolerances. The development of profile error prediction models is, therefore, not merely a technical solution but a vital instrument for optimizing product quality, enhancing cost-effectiveness, minimizing scrap rates, and streamlining machining lead times. This study presents a predictive model for the form error of spherical surface (SS) on Al6061 aluminum alloy during ultra-precision turning (UPT) using a single-crystal diamond tool. The prediction model was developed based on a back-propagation (BP) neural network (NN) structure. The dataset for establishing the prediction model was collected from 30 precision machining experiments on spherical surfaces. To ensure the objectivity and reliability of the data, the fixturing and alignment procedures as well as the measurement method for profile error were standardized and thoroughly modeled. The cutting parameters, including spindle speed (n – rev/min), feed rate (F - mm/min), and depth of cut (ap - µm), were identified as independent variables to establish the relationship with the profile error. The determination of the appropriate neuron ratio between layers was investigated through six specific network structures. The criteria for evaluating the prediction quality of the neural network included the coefficient of determination (R²), mean squared error (MSE), and mean absolute percentage error (MAPE). Accordingly, the artificial neural network ANN structure 3:5:20:1 delivered the best prediction performance, achieving an R² value of 1, MSE of 26.9, RMSE of 5.19, and MAPE of 0.2%. The results not only confirm the effectiveness of the proposed method but also provide a reliable scientific foundation for the development of profile error prediction models. At the same time, this study demonstrates the potential for extending the application to other complex surfaces such as aspheric surfaces, diffractive surfaces, or on different substrate materials.