Compared to traditional design methods, finite element analysis offers a more accurate simulation of real-world conditions for parts, allowing engineers to obtain precise solutions and ensuring reliable results for product design and inspection. This paper explores the use of finite element analysis based on several key considerations: (1) Traditional design methods only focus on the inner side of the spring's working ring, neglecting other critical areas. In contrast, finite element models can provide data from any location on the structure. (2) During testing, strain gauges have size limitations and adhesive quality issues, resulting in only average stress values at measured points rather than exact measurements. (3) Experimental tests may rely on personal experience, leading to limited data collection at only selected points, potentially missing important areas. (4) Some locations are simply inaccessible for direct measurement, making it necessary to rely on finite element analysis to supplement the data.
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 brick elements with 10,656 units and 12,054 nodes, while the support ring used SOLID92 tetrahedral elements with 6,680 units and 1,952 nodes. The total number of elements and nodes in the model was 17,336 and 14,008, respectively. To validate the model, experimental stress measurements were conducted on the springs. Although finite element analysis has clear advantages, its accuracy must be verified through physical 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, with measurements taken on the outer side of the working ring as a reference.
For specific testing, the applied loads were 40, 50, 60, and 88 kN. A right-angle three-directional strain rosette was used for the test. When comparing the finite element results with the experimental data, the maximum stress was found 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, aligning with the simulation results. However, the stress values at points B and C showed some deviation from the finite element predictions. 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, reaching 4178% at point B. At point A, the deviation was even larger, with a maximum value of 26154% at 60 kN (and 88 kN). The experimental data at point A was consistently lower than the finite element results, primarily due to the limitations of the strain gauge size and placement, which made it difficult to capture high-stress gradients. As a result, the maximum stress predicted by the finite element model appeared at the inner edge of the support ring, where the strain gauge could not accurately measure the actual stress.
The stress at points B and C increased linearly with the applied load, while the stress at point A showed a more complex behavior. At 40–50 kN, there was a significant change, but the variation between 50–60 kN dropped by about half. From 60–88 kN, the stress changes became minimal. According to the finite element analysis, when the axial load reached 56 kN, the stress on the inner side of the support ring changed very little. Observations during the test revealed that the spring support ring came into contact with the working ring. The drawing specified a clearance of 2.16714 mm between the support ring end and the working ring, and the finite element model used a 5 mm gap. The actual test piece also had a similar gap of around 5 mm. However, during machining, the gap could not be precisely maintained. A larger gap caused the support ring to make contact later, increasing the internal stress in the support ring. These findings highlight the importance of both numerical modeling and experimental validation in understanding the real behavior of mechanical components under load.
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