Regression Analysis and Neural Network Model of Working Diameter of Ball-end Mill

Abstract

In ball-end milling, a clear distinction exists between the nominal and the working (or effective) diameters, particularly when machining free-form surfaces. The working diameter is not constant; instead, it changes dynamically based on several factors, including the surface inclination (A_N2), tool diameter (D), depth of cut (a_p), and feed direction (A_f). Accurately predicting the working diameter is essential for improving surface quality and dimensional accuracy. Three primary approaches are commonly used for this purpose: the geometric model, which analytically describes the geometric relationships between machining parameters and the working diameter; regression analysis, which builds mathematical models from empirical data; and artificial neural network (ANN) models, which are capable of modeling complex, non-linear interactions between multiple input variables and the working diameter. In this study, one geometric model, two types of regression models, and two ANN models were developed and evaluated. Their performance was assessed using a set of statistical measures, including the standard deviation of the prediction error, the coefficient of determination (R²), the root mean square error (RMSE), and the mean absolute percentage error (MAPE). These metrics provided a comprehensive basis for comparing the accuracy and reliability of each approach. The results highlight the strengths and limitations of each method in capturing the variability of the working diameter during ball-end milling of free-form surfaces.