# Prediction of Manufacturing Quality of Holes Based on a BP Neural Network
## 4 Training and Verification Experiment of BP Neural Network Model
### Model Verification  
The exit surface morphology was observed by ultra-depth electron microscopy (VHX-500F). The accuracy of the BP neural network in predicting drilling quality was verified by comparing the surface topography. Firstly, the edge morphology was observed when the hole was magnified 100\(\times\) and the measuring scale was 300 \(\upmu\)m. Then, the inner surface topography of the holes was observed when the hole was magnified 300\(\times\) and the measuring scale was 150 \(\upmu\)m. The results of sample No. 155 and sample No. 158 are shown in Figure 10; through a comparison, it can be found that the tearing defects at the hole exit and the delamination defect on the inner surface of the hole were obvious. The delamination generated during drilling has a certain functional relationship with the drilling thrust force. When the drilling tool approaches the plane of exit, the stiffness of the cutting delamination cannot withstand the axial thrust force. Thus, the material around the bottom plate layer drilling may be separated and removed from the junction of the internal laminates. The circular plate model for hierarchical analysis is shown in Figure 11 and the defect range of the hole surface is shown in Figure 12.  
Figure 10: Surface topography of CFRP samples: (**a**) sample No. 155; (**b**) sample No. 158. i—interior surface morphology; ii—edge morphology; iii—exit appearance. Figure 9: The comparation of predicted and expected values. As shown in Figure 11, a drill bit with a radius \(C\) applies a load to the center of the circular plate. \(F_{A}\) denotes the thrust, \(X\) denotes the displacement, \(H\) is the thickness, \(h\) is the thickness of the uncut layer under the tool, and \(a\) is the radius of the delamination range. Assuming that the composite laminate of each layer is isotropic, Equation (1) can be obtained according to the linear elastic fracture mechanics and the law of conservation of energy [19]. \[G_{IC}dA=F_{A}X-dU, \tag{1}\]  
where: \(G_{IC}\) donates critical crack propagation energy per unit area, which is constant as a function of strain rate [20], \(dA=2\pi a\cdot d_{a}\) denotes the growth area of the delamination, and \(U\) donates the stored strain energy, which can be calculated using the classical thin plate theory [21]. \[U=\frac{8\pi MX^{2}}{a^{2}}, \tag{2}\]  
where \(M\) donates the stiffness of CFRP material per unit width, and the expression is  
\[M=\frac{Elt^{3}}{12(1-v^{2})}, \tag{3}\]  
where \(E\) denotes [PERSON]'s modulus, \(v\) denotes the Poisson's ratio of CFRP material, and the displacement \(X\) is  
\[X=\frac{F_{A}\alpha^{2}}{12\pi M}. \tag{4}\]  
Figure 11: Circular plate model for drilling CFRP. Figure 12: The defect diagram of tearing. Combining the above formulas, the drilling thrust at the beginning of crack propagation [22] can be expressed as  
\[F_{A}=\pi\left[\frac{8G_{IC}El^{3}}{3(1-v^{2})}\right]^{\frac{1}{2}}, \tag{5}\]  
where \(h\) can be calculated by \(\frac{\partial F_{A}}{\partial h}=0\). As shown in Figure 12, \(D_{0}\) denotes the drill diameter (mm), \(D_{max}\) denotes the maximum diameter of the tearing range (mm), \(A_{max}\) denotes the area of the tearing defect (mm\({}^{2}\)), and \(A_{0}\) denotes the area formed by \(\Phi D_{0}\). The stratification adjustment factor \(F_{da}\) can be expressed as  
Figure 10:0  
where \(\alpha\) and are the weighting factor (\(\alpha=1-\beta\)). When the tool drilled out the surface of the composite material, the composite material was pressed by the axial force and the blade, and cracks were formed at the edge of the holes at the initial stage [23]. As the process continued, the thickness of the material to be cut became thinner, the rigidity decreased, and the cracks gradually expanded; the fiber of surface at the center of the drill bit fractured. Under the action of friction force, greater shear stress was generated at the outlet of the work piece. Finally, the crack formed a tearing range, which is the most common defect in the hole-making process.