## 6 Conclusions  
Within the theoretical framework of curvature interference limit lines for conical surface enveloping cylindrical worm-face worm gear drives, this study develops a Physics-Informed Neural Network (PINN) model that integrates the underlying mechanism of curvature interference. By incorporating tooth surface geometric equations, meshing functions, and critical curvature interference functions, a comprehensive deep learning architecture is constructed, embedding spatial boundary constraints, kinematic coupling conditions, and mechanism-driven loss functions.  
The model employs a loss function minimization strategy to implicitly solve the nonlinear system of equations. Numerical experiments demonstrate that it achieves a computational accuracy on the order of 10-13, which is comparable to that of classical iterative methods.  
Characteristic analysis reveals that dual curvature interference limit lines are located at the inner end of the face worm gear tooth surface. This implies that penetration of the curvature interference limit lines into the tooth surface may occur from the inner end, thereby inducing curvature interference phenomena. The analysis of process parameter influences demonstrates that variations in the grinding wheel's geometric parameters exhibit no significant impact on curvature interference boundaries under both drive conditions. However, a reduction in the worm axial mounting distance may result in penetration of the curvature interference limit lines into the tooth flank, thereby giving rise to interference phenomena.  
The proposed PINN model, constrained by curvature interference mechanisms, demonstrates promising generalizability and can be extended to interference analysis in other types of worm drive systems. This research lays a foundation for the development of a physics-constrained intelligent design of the worm drive and offers scope for further exploration in the inverse optimization of design parameters.  
Figure 14: Influence of worm axial mounting distance \(z_{\text{A}}\) on curvature interference limit lines: (**a**) \(i\)-flank; (**b**) \(e\)-flank.  
**Author Contributions:** Conceptualization, S.M. and Y.Z.; methodology, S.M.; software, H.Y.; validation, S.Q. and H.Z.; formal analysis, W.Z.; resources, Y.L.; writing--original draft preparation, S.M.; writing--review and editing, X.S. and Z.D.; project administration, X.S.; funding acquisition, Z.D. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This study was funded by the National Natural Science Foundation of China (52075083, 52005346, and 52005347), Project of the Science and Technology Innovation Team of Liaoning Provincial Department of Education (LJ22410142011), Basic Research Projects of Higher Colleges and Universities of Liaoning Provincial Department of Education (LJ212410142040 and JYTMS2023190), Liaoning Province Natural Science Foundation (2024-BS-103), Liaoning Province Science and Technology Plan Joint Program (2024-MSLH-161, 2024-MSLH-203, and 2024-MSLH-367), Support Program for Young and Middle-aged Talents in Science and Technology Innovation in Shenyang (RC220066), and Liaoning Huanghai Laboratory Open Innovation Fund (2024 LHKC0300).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in this article; further inquiries can be directed to the corresponding author.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.