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In machining, specific cutting forces and temperature fields are of primary interest. These quantities depend on many machining parameters, such as the cutting speed, rake angle, tool-tip radius, and uncut chip thickness. The finite element method (FEM) is commonly used to study the effect of these parameters on the forces and temperatures. However, the simulations are computationally intensive and thus, it is impractical to conduct a simulation-based parametric study for a wide range of parameters. The purpose of this work is to present, as a proof-of-concept, a hybrid methodology that combines the finite element method (FE method) and machine learning (ML) to predict specific cutting forces and maximum tool temperatures for a given set of machining conditions. The finite element method was used to generate the training and test data consisting of machining parameter values and the corresponding specific cutting forces and maximum tool temperatures. The data was then used to build a predictive model based on artificial neural networks. The FE models consist of an orthogonal plane-strain machining model with the workpiece being made of the Aluminum alloy Al 2024-T351. The finite element package Abaqus/Explicit was used for the simulations. Specific cutting forces and maximum tool temperatures were calculated for several different combinations of uncut chip thickness, cutting speed and the rake angle. For the machine learning-based predictive models, artificial neural networks were selected. The neural network modeling was performed using Python with Adam as the training algorithm. Both shallow neural networks (SNN) and deep neural networks (DNN) were built and tested with various activation functions (ReLU, ELU, tanh, sigmoid, linear) to predict specific cutting forces and maximum tool temperatures. The optimal neural network architecture along with the activation function that produced the least error in prediction was identified. By comparing the neural network predictions with the experimental data available in the literature, the neural network model is shown to be capable of accurately predicting specific cutting forces and temperatures.

Stability properties of micro-milling operations are characterized by the Stability Lobe Diagram (SLD). The material removal rates during micro-milling operations depend on the optimal values chosen for the depth of cut and also spindle speed. Theoretically, the stability boundary is calculated having the structural dynamics and the cutting parameters. However, some discrepancies are usually observed between the empirical results and the expected results that the theory supports. The driver of such a gap is that the dynamics is affected during machining operation by parameters such as the spindle speed, cutting loads, thermal changes, feed rate, etc whereas the theory is based on the structural dynamics parameters in the idle state of the machine (zero speed). Consequently, the selection of chatter-free values for cutting depth and spindle speed based on SLD in the idle state of the machine is not reliable. In addition, measuring structural dynamics parameters under cutting conditions is difficult. In this study, a novel approach is introduced to determine in-process structural dynamics parameters based on a multivariate Newton-Raphson method. Having the empirical SLD characterized by experimental data, our method tries to find the structural parameters under which the theory can support the given empirical SLD. Note that the theoretical SLD is usually characterized as a function of the cutting and structural dynamics parameters. Here our method follows the inverse flow and utilizes the empirical SLD to return the underlying parameters. The parameters returned by our method are those supported by the physics-based theories. Therefore, our approach is a hybrid method where the physics-based model is combined with the experimental results. For any given empirical SLD, with the cutting parameters fixed, the in-process structural dynamics parameters are determined using the proposed inverse approach. We use a multivariate Newton-Raphson method approach where through the iterations, an initial guess selected for the set of the parameters is adjusted step-by-step until the final set of the parameters can justify the empirical SLD based upon physics-based models.

In this paper, we present a deep energy method for functionally graded beams based on both Euler–Bernoulli and Timoshenko beam theory to study their mechanical and thermal properties. We consider the effect of temperature as well as porosity under saturated and unsaturated conditions. The objective function is related to the total potential energy (and boundary conditions) and minimized through neural network training. The results are validated by comparison with benchmark problems available in the literature.