# Distribution and Prediction of Incremental Cutter Flank Wear in High-Efficiency Milling
## 6 Wear Prediction of Flank Face of Cutter Tooth
### Validation of the Predictive Model for Flank Wear  
When considering the generalization ability of the BPNN, this research chooses the 5-1-1 structure for the neural network. There are six main factors affecting the wear of the cutter tooth: contact stiffness \(k\), flank feature point co-ordinates (\(u_{c}\), \(v_{c}\), \(w_{c}\)), milling cutter rotation angle \(\varphi\), and vibration displacement \(l_{a}\), as shown in Equation (32). Therefore, the number of input layer nodes is 6, the number of output layers is 1, and \(P_{k}\) is set as the input layer set of the neuron network. The correct selection of the number of neurons and activation functions in the hidden layer significantly affects the effectiveness of predicting tool wear. If the number of neurons is too large, the training time of the model will be extremely long and the error will be large. Conversely, if the number of neurons is extremely small, the generalization ability and fault tolerance of the model will be reduced. \[P_{k}=\{k,u_{c},v_{c},w_{c},\varphi,l_{a}\} \tag{32}\]  
The training parameters of the neural network flank-wear-prediction model are set as follows: the maximum number of training events is 1000, the learning efficiency is 0.01, and the target mean square error (MSE) is 1 \(\times\) 10\({}^{-5}\). After a lot of training, the unoptimized BPNN repeatedly falls into the local optimal solution and stops training when the number of training times or the target MSE is reached. After determining the parameters of the BPNN, 600 sets of test data obtained from the tool wear test were used as network training and verification samples. In the MATLAB software (version 2022a), we used the rand function to randomly select 500 sets of data from the 600 sets in the table as the network training samples. Before network training, we used the maximum mapping function in the MATLAB toolbox to normalize the test data. This process can reduce the errors caused (by different orders of magnitude and dimensions), avoid neuron saturation, and improve the convergence speed of the neural network [41]. The MATLAB neural network toolbox is used, as shown in Figure 12. The BPNN can achieve the target MSE. When the test data is in the 67 th iteration, the accuracy of the algorithm meets the optimal requirement of setting error. The instantaneous contact stiffness \(k\), the flank feature point co-ordinates (\(u_{c}\), \(v_{c}\), \(w_{c}\)) of the cutter tooth co-ordinate system, the instantaneous rotation angle \(\varphi\) of the cutter tooth, and the vibration displacement \(l_{a}\) are taken as a group of inputs, and the instantaneous incremental wear is taken as a group of outputs. Among the 600 groups of signals, 500 groups were randomly selected as the training set for BPNN flank-wear-prediction training, and the remaining 100 groups of signals were used as the test set and verification set for BPNN flank-wear prediction. The prediction results are as follows:  
Figure 12: MATLAB neural network toolbox. In order to train the proposed BPNN neuron learning model and verify its effectiveness, all the schemes were verified, and the curves of the BPNN flank-wear prediction training set and test set were obtained. As shown in Figures 13 and 14, the abscissa is the training sample number, and the ordinate is the instantaneous amount of wear. As shown in Figures 13 and 14, the instantaneous incremental wear of 100 test points is basically consistent with the actual incremental wear. Overall, the deviations between the predicted values of the instantaneous wear at the 100 test points and the measured values are all within 1 \(\times\) 10\({}^{-8}\) mm. The results show that the method has good prediction accuracy regarding incremental wear. Figure 14: BPNN wear training set test error. Figure 13: BPNN flank wear test set.