## 4 Key Enablers in the HDL Model  
### The Upper-Level Machine Learning Module for Cutting Force Estimation  
When the FTS device is used for diamond cutting, there will be a variety of machining forces including Lorentz force (\(F_{driving}\)), spring force (\(F_{spring}\)), inertia force (\(F_{inertia}\)), damping force (\(F_{damping}\)), and cutting force (\(F_{cutting}\)). Lorentz force is the force generated by the voice coil motor that is used to drive the device to cut, so it can also be called the driving force. Spring forces are produced by the deformation of elastic hinges. The acceleration of the moving parts results in the presence of inertial forces. Damping forces are caused by the air and the inevitable friction within the device. Cutting force is the resistance to deformation generated during the process of material deformation and removal. Their relationship is complex. Due to the existence of the above forces, it is difficult to accurately obtain the cutting force of the interaction between the diamond tool and the workpiece surface along the axial direction of the system. The driving force, spring force, damping force, and inertia force of the device can be expressed as follows:  
\[F_{driving}=B\cdot I\cdot L\cdot n=B\cdot L\cdot n\cdot p\cdot V, \tag{1}\]  
\[F_{spring}=k\cdot x, \tag{2}\]  
\[F_{damping}=c\cdot\dot{x}, \tag{3}\]  
\[F_{inertia}=m\cdot\ddot{x}, \tag{4}\]  
where \(B\) represents the magnetic field intensity of the voice coil motor; \(I\) represents the current passing through the voice coil motor; \(L\) represents the length of one turn of the coil; \(n\) represents the number of turns of the voice coil motor; \(V\) represents the driving voltage  
Figure 2: Flow diagram of HDL-based diamond-tool prediction. signal used for the voice coil motor; \(p\) represents the proportional coefficient between the driving voltage and the output current; \(x\) represents the position of the tool; \(k\) represents the spring coefficient of the elastic hinge; \(c\) represents the sum of damping coefficients in the air and device; and \(m\) represents the mass of the moving parts. Utilizing the relationship between each machining force in the force equation, the cutting force can be calculated according to the machining signal (e.g., tool displacement signal) and control signal (e.g., drive voltage signal) in the machining process of the device, to achieve the estimation of cutting force. However, due to the uneven distribution of the magnetic field in the range of travel of the voice coil motor, the intensity of the magnetic field is related to the position of the tool, so the driving current and the driving force are not linear. The corresponding relationship between the two is a nonlinear relationship coupled with the displacement of the tool, which is shown in the following equation. \[F_{driving}=f(x)\cdot I=f(x)\cdot pV. \tag{5}\]  
This relationship hinders accurate perception and estimation of cutting forces. At the same time, it is difficult to obtain the exact values of the spring coefficient and damping coefficient. Therefore, it is still difficult to estimate cutting forces accurately by the force balance equation. According to the above analysis, the corresponding relationship between the cutting force and machining signal, and the control signal of the FTS device can be obtained. To achieve an accurate estimation of cutting force in the machining process, this paper collects the machining signal, control signal, and cutting force in the machining process to train the neural network model, and thus realize an accurate estimation of cutting force. To obtain the relationship between the extracted seven signal features and the actual cutting force (i.e., sample label), it is necessary to train the neural network to reveal the relationship. This paper uses a fully connected neural network as a machine learning model. The extracted seven features are input into the neural network through seven neurons in the input layer.