## 5 Conclusions  
This paper investigated the stress distribution, movement characteristics, and stress optimization potential of diaphragms in a dual-stage diaphragm compressor. Firstly, a finite element method (FEM) model and a theoretical stress analysis model were developed and validated through experimental comparisons. Subsequently, by integrating experimental pressure and gas mass flowrate data with the fluid pressure model, the variations in oil and gas pressures within the dual-stage diaphragm compressor were calculated. Furthermore, building upon these foundations, the diaphragm movement characteristics and stress distributions were systematically analyzed through the diaphragm motion and stress models. Finally, a novel double arc cavity profile was proposed, and the optimization comparison was conducted on various diaphragm cavity profile configurations. Key findings were summarized as follows:  
1. The DSDC experimental results indicated that under operating conditions of 1.6 MPa suction pressure, 8 MPa second-stage discharge pressure, and 200 rpm rotational speed, the volumetric efficiencies reached 74.02% and 87.63% for the first-stage and second-stage diaphragm compressors, respectively. Figure 21: Optimization results. (**a**) First-stage cavity profiles. (**b**) First-stage diaphragm’s characteristics. (**c**) Second-stage cavity profiles. (**d**) Second-stage diaphragm’s characteristics. 2. The theoretical stress analysis results indicated that for the DSDC test rig, the driving pressure differences at the TDC position reached 85.58 kPa for the first-stage diaphragm and 75.49 kPa for the second-stage diaphragm. 3. The diaphragm movement analysis results indicated that under operating conditions of 1.6 MPa suction pressure, 8 MPa second-stage discharge pressure, and 200 rpm rotational speed, the first-stage and second-stage diaphragms reached the maximum center deflections of 4.14 mm and 2.53 mm, respectively, at the BDC position. 4. The optimized first-stage SEP, DEP, and DAP diaphragm cavity profiles reached cavity volumes of 1.005, 1.015, and 1.017 times that of the experimental SEP profile, respectively, while the maximum principal stresses were reduced to 0.999, 0.993, and 0.965 times the baseline value. The optimized second-stage SEP, DEP, and DAP diaphragm cavity profiles reached cavity volumes of 1.104, 1.111, and 1.171 times the experimental SEP baseline, accompanied by maximum principal stress reductions to 0.947, 0.944, and 0.930 times the baseline value. The diaphragm movement analysis and stress optimization results investigated in this paper will provide valuable references for the diaphragm compressor's design optimization. However, factors including the fatigue life of diaphragms in novel diaphragm cavity profiles, the nonlinear deformation, and the friction or sliding effects between diaphragms were not considered in the model. In future work, the influence of oil holes and gas valve ports on diaphragm stress distributions within optimized diaphragm cavities will be experimentally investigated. Moreover, the high-cycle fatigue life of diaphragms in novel diaphragm cavity structures and the experimental performance of dual-stage diaphragm compressors will be further investigated. The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app15158353/s1](https://www.mdpi.com/article/10.3390/app15158353/s1)]([https://www.mdpi.com/article/10.3390/app15158353/s1](https://www.mdpi.com/article/10.3390/app15158353/s1)), Figure S1: Radial relative elongation; Figure S2: ANN-fitting architecture of the Matlab; Figure S3: Variation of maximum surface stress with the Young's modulus; Table S1: Detailed parameters of DSDC system; Table S2: Diaphrag material; Table S3: Preset experimental conditions; Table S4: Measurements and instrument accuracies. Conceptualization, C.S. ; Methodology, C.S. ; Software, C.S., X.C., J.T., M.Y. and X.K. ; Validation, C.S. ; Formal analysis, C.S. ; Investigation, C.S. ; Data curation, C.S. and X.C. ; Writing--original draft, C.S.