Compared to traditional design methods, finite element analysis (FEA) offers a more accurate simulation of real-world conditions for components, enabling engineers to obtain detailed solutions to complex problems. This approach provides a stronger foundation for both product design and quality assurance. In this paper, we adopt FEA based on several key considerations: first, conventional design typically only evaluates the inner side of the spring's working ring, while neglecting other critical areas. In contrast, FEA allows for data collection from any location on the model. Second, during testing, strain gauges have size limitations and may not provide precise stress values—only averages are recorded. Third, experimental measurements often rely on personal judgment, focusing only on selected points and potentially missing important areas. Finally, some locations are inaccessible for direct measurement, making it difficult to gather extensive data. Therefore, FEA serves as an essential complement to physical testing.
The finite element model was constructed with point A located approximately 100 mm from the end on the inner side of the spring support ring, while points B and C were placed in the middle of the inner side of the spring’s working ring. The middle working ring was modeled using SOLID45 elements with 10,656 brick-shaped elements and 12,054 nodes. The support ring was represented by SOLID92 tetrahedral elements, consisting of 6,680 units and 1,952 nodes. Altogether, the model contained 17,336 elements and 14,008 nodes. To validate the accuracy of the FEA model, experimental stress measurements were conducted on the springs. Although FEA has significant advantages, its reliability must be confirmed through testing. To identify the maximum local stress on the ST spring under axial loading, the main fatigue-sensitive areas—the inner side of the spring support ring and the inner side of the working ring—were analyzed. Additional measurements were taken on the outer side of the working ring for comparison. The applied loads were 40, 50, 60, and 88 kN, respectively. A right-angle three-directional strain rosette was used for the test. By comparing the experimental results with the FEA predictions, it was found that the maximum stress occurred at point B on the inner side of the working ring, consistent with classical theory. Additionally, point A on the inner side of the support ring showed relatively high stress, matching both the experiment and FEA. However, the results for points B and C showed minor differences compared to the FEA. The relative deviation D was calculated using the formula: D = |ReY - ReS| / ReS. For points B and C, the maximum deviation occurred at 50 kN for point B, reaching 4178%. For point A, the deviation was significantly higher, peaking at 60 kN (or 88 kN), with a value of 26154%. The experimental data for point A was lower than the FEA results, primarily due to the limitations of the testing equipment. The strain gauges used in the test could not capture high-stress gradients accurately, especially at the inner edge of the support ring. As a result, the maximum stress value from the FEA was observed there. The stress values at points B and C increased almost linearly with the load, whereas the stress at point A showed a sharp increase between 40–50 kN, followed by a reduction after 50–60 kN, and then stabilized between 60–88 kN. According to the FEA results, when the axial load reached 56 kN, the stress on the inner side of the support ring changed minimally. During the test, it was observed that the spring support ring came into contact with the working ring. The specified clearance between the spring support ring and the working ring was 216.714 mm, and the FEA model assumed a gap of 5 mm. The actual measured gap in the test specimen was also approximately 5 mm. However, due to machining tolerances, the actual gap could not be maintained precisely. When the gap was larger, the support ring made contact later, leading to increased stress within the support ring.
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