A generalized closed-form model of cutting energy for arbitrary-helix cylindrical milling tools and its applications

The knowledge of energy consumption of different machine tool production processes leading to products is necessary for energy labeling of machined parts in the increasingly sustainability-aware world thus the need for better machining energy modeling techniques. The milling process dynamics is complicated thus numerical and averaging techniques are hitherto usually applied in the cutting energy modeling thus limiting decision-making. This work proposes a generalized force-based closed-form model for the milling process cutting energy. To the best of the author's knowledge, the model is the first closed-form cutting energy model for milling which not only applies to the conventional cylindrical milling tools with constant helix angle but also to cylindrical milling tools with any helix angle variation. The demonstrated applications of the proposed model include modeling of milling machine electrical energy consumption, modeling/optimization of milling project energy/efficiency and helix angle optimization for passive reduction of cutting energy. The proposed model is checked with experimentally-verified results in literature. For example, the model agrees with numerically computed cutting energy in literature by absolute error of 0.0320%-0.4025% and modeling of milling machine electrical energy consumption using the proposed model recorded the goodness-of-fit indices of 0.9980 R-2-value and -0.1271 mean percentage error compared to a published experimental data. A parametric plot and an optimization based on genetic algorithm showed that increase of helix angle increases cutting energy due to increased influence of edge forces, and the effect is more pronounced at higher helix angles. Various potential applications of the presented model are highlighted in the concluding section.