## 5 Verification of Comprehensive Evaluation Model for Honing Processing Quality  
### Determining the Weight of Influencing Factors of Honing Machining Quality  
According to the gear honing quality evaluation hierarchy shown in Figure 2, the questionnaire was designed to hire five experts of equal status with relevant industry backgrounds to score the factors affecting machining quality. After consistency adjustment and testing, an improved trapezoidal fuzzy number assignment calculation method was applied. It determines the quality of the internal gear honing wheel's CBN coating, the effectiveness of abrasive grains, and the micro-edge honing processing quality. The hierarchical structure of the factors under the relative evaluation index and the corresponding Tra-FAHP weights are shown in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Evaluation Objective** & **Factor of Evaluation** & **Tra-FAHP Weight** \\ \hline \multirow{3}{*}{Analysis of Honing Characteristics A} & Honing accuracy B1 & (0.278, 0.373, 0.712, 0.964) \\  & Processing efficiency B2 & (0.097, 0.136, 0.254, 0.341) \\  & Surface quality B3 & (0.166, 0.222, 0.403, 0.542) \\ \hline \multirow{3}{*}{Honing accuracy B1} & Tooth pitch error C1 & (0.250, 0.331, 0.577, 0.774) \\  & Tooth profile error C2 & (0.181, 0.237, 0.398, 0.518) \\  & Helix error C3 & (0.151, 0.198, 0.331, 0.426) \\ \hline \multirow{3}{*}{Processing efficiency B2} & Material removal amount C4 & (0.188, 0.241, 0.395, 0.515) \\  & Processing time C5 & (0.164, 0.212, 0.350, 0.452) \\ \hline \multirow{7}{*}{Tooth pitch error C1} & Abrasive grain abrasion D1 & (0.032, 0.047, 0.098, 0.140) \\  & Abrasive grain fracture D2 & (0.043, 0.064, 0.137, 0.202) \\  & Abrasive grain detachment D3 & (0.064, 0.096, 0.217, 0.348) \\  & Grinding cutting angle D4 & (0.024, 0.037, 0.077, 0.111) \\  & Shape of abrasive grain D5 & (0.031, 0.046, 0.098, 0.147) \\  & Abrasive grain size D6 & (0.036, 0.053, 0.110, 0.159) \\  & Effective number of abrasive grain D7 & (0.044, 0.066, 0.143, 0.219) \\  & Clearance between abrasive grains D8 & (0.028, 0.041, 0.081, 0.112) \\  & Honing speed D9 & (0.026, 0.040, 0.087, 0.125) \\  & Honing depth D10 & (0.049, 0.073, 0.158, 0.241) \\  & Honing speed D11 & (0.026, 0.039, 0.080, 0.114) \\  & Cross axis angle D12 & (0.054, 0.082, 0.180, 0.280) \\ \hline \multirow{7}{*}{Tooth profile error C2} & Abrasive grain abrasion D1 & (0.031, 0.046, 0.095, 0.136) \\  & Abrasive grain fracture D2 & (0.048, 0.070, 0.145, 0.214) \\  & Abrasive grain detachment D3 & (0.062, 0.093, 0.210, 0.331) \\  & Grinding cutting angle D4 & (0.031, 0.045, 0.090, 0.126) \\  & Shape of abrasive grain D5 & (0.024, 0.035, 0.070, 0.097) \\  & Abrasive grain size D6 & (0.036, 0.053, 0.109, 0.156) \\  & Effective number of abrasive grain D7 & (0.033, 0.049, 0.101, 0.145) \\  & Clearance between abrasive grains D8 & (0.031, 0.045, 0.092, 0.131) \\  & Honing speed D9 & (0.046, 0.067, 0.141, 0.211) \\  & Honing depth D10 & (0.047, 0.068, 0.139, 0.204) \\  & Honing speed D11 & (0.034, 0.050, 0.101, 0.143) \\  & Cross axis angle D12 & (0.049, 0.072, 0.150, 0.223) \\ \hline \multirow{7}{*}{Helix error C3} & Abrasive grain abrasion D1 & (0.032, 0.046, 0.090, 0.126) \\  & Abrasive grain fracture D2 & (0.043, 0.064, 0.136, 0.201) \\  & Abrasive grain detachment D3 & (0.059, 0.089, 0.205, 0.326) \\  & Grinding cutting angle D4 & (0.027, 0.039, 0.079, 0.110) \\  & Shape of abrasive grain D5 & (0.025, 0.034, 0.069, 0.097) \\  & Abrasive grain size D6 & (0.034, 0.049, 0.100, 0.142) \\  & Effective number of abrasive grain D7 & (0.033, 0.049, 0.100, 0.146) \\  & Clearance between abrasive grains D8 & (0.025, 0.037, 0.074, 0.104) \\  & Honing speed D9 & (0.046, 0.068, 0.147, 0.223) \\  & Honing depth D10 & (0.045, 0.067, 0.141, 0.211) \\  & Honing speed D11 & (0.044, 0.065, 0.137, 0.203) \\  & Cross axis angle D12 & (0.054, 0.080, 0.173, 0.262) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The Tra-FAHP weights of the relative evaluation indicators of factors.