Simplified analytical models of chip formation mechanics (e.g. the well-known Merchant’s model) are widely used to compute the machining forces in orthogonal cutting operations. The accuracy of analytical models, however, diminishes when the cutting edge has a rounded shape, known as edge (or hone) radius, which is common for most cutting tools. Finite element (FE) simulation can be used to obtain more accurate predictions of the forces in the presence of edge radius, but FE is computationally expensive because it should numerically solve a thermo-mechanical contact problem with nonlinear material properties to model the plastic deformation and damage of the workpiece. The high computational cost of FE simulations indeed becomes crucial when the force model is used for process optimization or for online simulations in the digital twin of the machining process. In this research, we present a computationally efficient data-driven model with acceptable accuracy when compared to the FE simulation.

The presented model combines the predictions of FE simulations (i.e., high-fidelity dataset) and the predictions of the analytical model (i.e., low-fidelity dataset) and generates a new regression multi-fidelity model. The high-fidelity dataset is generated by an FE simulation in Abaqus and using Johnson-Cook constitutive equation to model the plastic deformation and damage of an aluminum workpiece during chip formation. The low-fidelity dataset is generated by Merchant’s analytical model. In both datasets, the inputs are the tool rake angle and uncut chip thickness, and the outputs are the cutting and feed forces. In total, 440 data points (40 high-fidelity points and 400 low-fidelity points) are generated. Based on this dataset, a multi-fidelity model is trained and tested through the emulator-embedded neural network (E2NN) method. The Root Mean Squared Error (RMSE) is then computed between the predictions of the trained model and the predictions from the FE simulation to quantify the performance of the presented multi-fidelity model.

The results show a close agreement between the predictions of the high-fidelity and the multi-fidelity models. The computed RMSE was less than 8.5%. Yet, the accuracy would gradually improve by increasing the high-fidelity samples. Moreover, note that the computational time of a FE simulation is typically a few (~5) minutes while it is less than a second for the presented multi-fidelity model. The presented modelling approach therefore can efficiently replace high-cost FE simulations in process optimization or online simulations.