## 5 Verification of Comprehensive Evaluation Model for Honing Processing Quality
### Analysis of Comprehensive Evaluation Result of Gear Honing Processing Quality  
The experiments mainly measured the experimental values of different abrasive grain size D6 on the five factors of sub-criterion layer indexes C1, C2, C3, C4, and C6. Based on the characteristics that the unit, order of magnitude, and trend of each index's influence on honing quality are not uniform and cannot be measured, the threshold method is adopted to conduct dimensionless processing of experimental data [33] to ensure the reliability of the evaluation.  
The greater the indicator value, the better the honing quality. The material removal rate indicator value falls into the category of \"the larger, the better\". The formula for dimensionless processing is as follows:  
Figure 10: Relationship between abrasive grain size and material removal rate with honing gear.  
\[\lambda_{ik}=\frac{x_{ik}-minx_{k}}{maxx_{k}-minx_{k}} \tag{21}\]  
If the index value of the sub-criterion layer increases, the quality of honing teeth will deteriorate. Parameters such as surface roughness, single pitch deviation, total tooth profile deviation, and total helix deviation all follow the principle of \"the smaller, the better.\" The dimensionless processing formula is as follows:  
\[\lambda_{ik}=\frac{maxx_{k}-x_{ik}}{maxx_{k}-minx_{k}} \tag{22}\]  
In this context, \(\lambda_{ik}\) represents the normalized value of the i-th factor in the k-th group of experiments, while \(x_{ik}\) denotes the honed experimental value of the i-th factor in the k-th group.  
By incorporating the aforementioned experimental values into the sub-criteria layer C, we can evaluate the quality differences of CBN grinding with varying granularity. The comprehensive evaluation model can be derived from Equation (23).  
\[M_{z}=W_{z}R_{z} \tag{23}\]  
In the equation, \(W_{z}\) represents the evaluation weight matrix of factors, with specific values obtained for the weight matrix \(W_{z}\) of sub-criteria layer C referenced in Table 6 as \(W_{z}=[0.24\ 0.18\ 0.16\ 0.25\ 0.17]\). \(R_{z}\) denotes the evaluation weight of experimental data.  
\(R_{z6}\) is a dimensionless matrix of 100\({}^{\#}\),300\({}^{\#}\), 540\({}^{\#}\), The calculation result is:  
\[R_{z6}=\begin{bmatrix}0&0.42&0.64&0.63&0.92\\ 0.12&0.68&0.76&0.85&0.45\\ 0.11&0.51&0.39&0.62&0.06\end{bmatrix}^{T}\]  
Bring the results of \(W_{z}\) and \(R_{z6}\) into Formula (23), obtained \(M_{z}=[0.49\ 0.56\ 0.35]\). The comprehensive evaluation of the honing quality corresponding to the three-grain sizes was ranked \(0.53>0.47>0.34\). This indicates that 300\({}^{\#}\) CBN grit has the best honing quality, 540\({}^{\#}\) CBN grit has the worst honing quality, and 100\({}^{\#}\) is in between. In the \(R_{z6}\) matrix, the weights of 100\({}^{\#}\) and 300\({}^{\#}\) abrasive grits are in good agreement, and the difference in the evaluation of machining efficiency between the two in the matrix is 0.23, and the difference in the evaluation of surface roughness is 0.52, which is larger than that of the evaluation of the individual tooth pitch deviation, the cumulative total deviation of the tooth profile, and the total deviation of the helix. This indicates that the abrasive grain size has a greater impact on machining efficiency and surface roughness and a smaller impact on honing accuracy. The conclusion is consistent with the conclusion of the comprehensive evaluation sensitivity in Figure 4, which verifies the correctness of the established comprehensive evaluation model of honing machining quality and can provide a decision-making basis for the manufacture of high-performance hardened gears.