## 6 Conclusions  
1. Based on Tra-FAHP and SPA, a comprehensive evaluation model for CBN micro-edge honing quality is established, which eliminates the subjective influence of AHP and ensures that the evaluation results are more reasonable and objective. The established evaluation model can quantitatively and effectively identify and evaluate the quality of the honing process with certainty and uncertainty factors, guiding the honing process of high-performance hardened gears.
2. With increasing grain size, the mean value of total helix deviation sequentially decreases. The distribution of tooth pitch deviation gradually approaches the zero line; the correction ability of the change of the length of the common normal line increases; the average value of the total profile deviation decreases, making the accuracy of the honed workpiece gradually improve. However, affected by the phenomenon of error reenactment, the maximum error reduction of the helix of the tooth surface after honing with large-sized abrasive grain is not obvious. Increasing the number of honing operations and reducing the error reflection coefficient can effectively reduce the maximum error of the workpiece tooth surface helix and improve the honing machining accuracy.
3. With abrasive grain size decreasing, the average spacing of abrasive grain decreases, resulting in decreased maximum valley height H\({}_{\text{v}}\), which makes the surface roughness value Ra smaller. Improvement of surface quality after honing.
4. With the increase of abrasive grain size, the cutting performance improves, and the honing machining efficiency obviously improves, which is applied to rough honing machining.  
The article evaluates the effect of abrasive grain size on the quality of the honing process. The established comprehensive evaluation model can also be applied to the evaluation of other 11 key factors on the quality of the honing process. The study provides a theoretical basis for the comprehensive evaluation of honing quality and the optimization of process parameters. In the future, we will focus on studying the influence of key factors, such as abrasive grain and process parameters, on honing quality by improving the comprehensive evaluation model of honing characteristics and proposing a more scientific control strategy to guide the development of honing wheels and the honing process. of the manuscript.  
Conceptualization, J.S. and Y.L.; methodology, J.Z., Y.G., J.S. and F.W.; software, J.S.; validation, Y.Y. and J.Z.; formal analysis, Y.G.; investigation, Y.Y., J.Z. and J.S.; resources, Y.G.; data curation, J.S.; writing--original draft preparation, J.S. and Y.Y.; writing--review and editing, Y.G., F.W. and L.L.; visualization, F.W., L.L. and Y.G.; supervision, Y.Y.; project administration, Y.G.; funding acquisition, Y.L. and Y.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by [the Young Talent Cultivation Programme of North Minzu University] grant number [No. 2023 QNYP13], [the Ningxia Natural Science Foundation] grant number [No. 2023 AAC02047], [the Ningxia Engineering Research Center for Hybrid Manufacturing System Foundation] grant number [No. 2023 GCJS008], and [Key research and development projects of North Minzu University] grant number [No. FHZL20240731].  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.