# Performance of the Compliant Foil Gas Seal with Surface Micro-Textured Top Foil+
## 6 Conclusions  
In this paper, considering the specific structure of the compliant foil gas seal, as well as the stiffness and damping of the bump foil, the micro-scale dynamic lubrication equations of the synchronous circular motion of gas and the rotor in the cylindrical coordinate system are obtained. Then, the finite difference method and the iterative method are used to solve the thickness and deformation equations simultaneously, following which, the static and dynamic sealing characteristics corresponding to different micro-texture shapes are obtained. The analysis results are as follows:  
1. Micro-textures machined on the surface of flat foil create local pressure rise regions within a stable flow field. Owing to the difference in the texture shape characteristics and directionality, the gas film thickness and pressure distribution of different compliant foil gas seals are different.
2. As the rotational speed increases, the force and the viscous friction force increase and the attitude angle decreases; however, the effect of the rotational speed on the mass leakage rate is negligible. Thus, the compliant foil gas seal shows good usability under low pressure and high-speed conditions.
3. Stiffness coefficients \(k_{xy}\) and \(k_{yx}\) and cross damping coefficients \(c_{xy}\) and \(c_{yx}\) are symmetrical. This reflects the circularity and quasi-symmetry of the flow field distribution as well as conform to the structural law of the compliant foil gas seal. Moreover, according to the dynamic parameters, the texture depth can be selected within the range of less than 9 \(\upmu\)m to ensure stability.
4. Among the six typical texture shapes, the elliptical texture has the smallest gas film force and the largest mass leakage rate, which is the most unfavorable to the static sealing performance. The gas film force of the triangle and the inverted triangle are basically the same, but the inverted triangular texture can control the mass leakage rate and improve stability, thus showing the best comprehensive sealing performance.  
This article selects the optimal shape and depth of micro-textures for compliant foil gas seals, and the results can guide the experimental testings and application of sealing surface modification. Furthermore, the image recognition technology used in this study provides implications for the complex interface design of friction pairs.  
Conceptualization, S.Y. and X.D.; methodology, J.X.; software, J.X.; validation, J.X. and LL.; formal analysis, X.D.; investigation, H.J. and L.L.; resources, X.D.; data curation, J.X. and H.J.; writing--original draft preparation, J.X.; writing--review and editing, J.X.; visualization, H.J.; supervision, S.Y.; project administration, S.Y. and J.X.; funding acquisition, S.Y. and J.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Outstanding Postgraduate \"Innovation Star\" Project of Gansu Provincial Department of Education (grant no. 2021 CXZX-459) and Major Scientific Research and Technological Innovation Project 2025, Ningbo (grant no. 2020Z112).  
Not applicable.  
The current research has been supported by Outstanding Postgraduate \"Innovation Star\" Project of Gansu Provincial Department of Education (grant no. 2021 CXZX-459) and Major Scientific Research and Technological Innovation Project 2025, Ningbo (grant no. 2020Z112).  
The authors declare no conflict of interest.