## 5 Experiments and Discussions
### Cutting Force Prediction  
The preprocessed datasets were randomly divided to train the HDL model. A total of 70% of the datasets were used for the training model, and 30% were used for the verification of the model after training. In the training process, mean square error (MSE) was used as the training loss function, and the Adam algorithm was used as the optimizer of model training. The training learning rate was 0.01 and the training epochs were 7000. The loss of the trained HDL model on the whole dataset was 0.00615, and the coefficient of determination between the estimated cutting force and the actual cutting force was 0.99685. The estimated data curve is basically the same as the training data curve when the tool is in low-frequency motion. When the tool is in high-frequency motion and subjected to low-frequency cutting force, the error of the estimation is large. It is speculated that the excessive motion frequency leads to the heating of the voice coil motor, which leads to the change of some electrical parameters. Considering that the tool motion frequency rarely reaches such a high frequency in the actual cutting situation, the method is still of high application value. To apply the trained HDL model to the actual cutting situation, the command signals and the actual signals during the machining of the groove were collected. Then the cutting forces were estimated by the HDL model with collected signal data inputting. In addition, the resulting cutting force signals were compared with those measured by the Kistler dynamometer. By comparing the cutting forces estimated by the proposed HDL model with the cutting forces measured by the Kistler dynamometer, it can be found that the cutting forces are consistent and the trend is the same. The MSE between the estimated cutting forces and the measured cutting forces is 3.3147 \(\times\) 10\({}^{-4}\). It can be seen that under different machining morphologies, the variation trend of the estimated cutting forces and the acquired cutting forces is the same. To verify the method's ability to distinguish static force, variable magnitude load was applied to the experimental system by the methods that hung weights for a while and then removed them. Through the test, the static resolution of the neural network model to estimate cutting forces was measured. In the test, weights of 1 g, 2 g, 5 g, and 10 g were used for loading, respectively. The load was then removed after a certain period of loading. The measurement results of loading based on the above method are shown in Figure 9. To verify the repeatability of the model, the above weights were still used to apply loads to the experimental system. The duration of each loading was about 5 s, and each weight loading was repeated five times. The estimated forces in the loading process were obtained, as shown in Table 6. The maximum measurement error happens at the 5 g load, which is \(-\)2.23 mN. It can be concluded that the method has high repeatability and high measurement accuracy. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **No Wear Status** & **Slight Wear Status** & **Severe Wear Status** \\ \hline Horizontal situation & 486 & 474 & 558 \\ \hline Inclined situation & 282 & 177 & 261 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Distribution of data samples. Figure 9: Applied load measurement results. For measuring the bandwidth and the dynamic frequency response range of cutting force estimated by the model, additional experiments have been carried out. A spring was added at the bottom of the tool, and the tool was subjected to an elastic force proportional to its displacement of sinusoidal motion. The elastic force emulated the sinusoidal cutting force of different frequencies suffered by the tool. Then the cutting tool was driven to carry out sinusoidal motion of different frequencies by applying a sinusoidal sweep signal.