Verification of a Reduced-Order Extension Spring Model

Abstract

Springs play important roles in many mechanisms, including critical safety components employed by Sandia National Laboratories. Due to the nature of these safety component applications, serious concerns arise if their springs become damaged or unhook from their posts. Finite element analysis (FEA) is one technique employed to ensure such adverse scenarios do not occur. Ideally, a very fine spring mesh would be used to make the simulation as accurate as possible with respect to mesh convergence. While this method does yield the best results, it is also the most time consuming and therefore most computationally expensive process. In some situations, reduced order models (ROMs) can be adopted to lower this cost at the expense of some accuracy. This study quantifies the error present between a fine, solid element mesh and a reduced order spring beam model, with the aim of finding the best balance of a low computational cost and high accuracy analysis. Two types of analyses were performed, a quasi-static displacement-controlled pull and a haversine shock. The first used implicit methods to examine basic properties as the elastic limit of the spring material was reached. This analysis was also used to study the convergence and residual tolerance of the models. The second used explicit dynamics methods to investigate spring dynamics and stress/strain properties, as well as examine the impact of the chosen friction coefficient. Both the implicit displacement-controlled pull test and explicit haversine shock test showed good similarities between the hexahedral and beam meshes. The results were especially favorable when comparing reaction force and stress trends and maximums. However, the EQPS results were not quite as favorable. This could be due to differences in how the shear stress is calculated in both models, and future studies will need to investigate the exact causes. The data indicates that the beam model may be less likely to correctly predict spring failure, defined as inappropriate application of tension and/or compressive forces to a larger assembly. Additionally, this study was able to quantify the computational cost advantage of using a reduced order model beam mesh. In the transverse haversine shock case, the hexahedral mesh took over three days with 228 processors to solve, compared to under 10 hours for the ROM using just a single processor. Depending on the required use case for the results, using the beam mesh will significantly improve the speed of work flows, especially when integrated into larger safety component models. However, appropriate use of the ROM should carefully balance these optimized run times with its reduction in accuracy, especially when examining spring failure and outputting variables such as equivalent plastic strain. Current investigations are broadening the scope of this work to include a validation study comparing the beam ROM to physical testing data.