High-precision coupling method for the dynamic characteristics prediction of multi-layer expansion bellows

Multi-layer expansion bellows are widely used in vibrating mechanical systems, their particular corrugated structure is susceptible to induced vibrations, making it essential to accurately predict its natural characteristics to avoid resonance. In this paper, the bellows are simplified into a homogeneous beam to establish its analytical model for axial natural frequency prediction, which considers three boundary cases. The analytical model combines the stiffness derived from testing to determine a high-precision coupling method. Modal simulations are then carried out based on finite element analysis(FEA) to validate the accuracy of the coupled method. The results show that the discrepancy is minimal and preliminarily demonstrates the accuracy of the coupled method. Furthermore, a detailed comparison study is provided between the coupling method, FEA, and EJMA standard. The comparison indicates that the coupling method reaches the lowest natural frequency, while FEA has the highest. Followed reveals an interesting conclusion: the frequency predicted by the coupled method decreases gradually with the number of layers, whereas the other two methods show the opposite trend. It is worth noting that as the mode order or layers increases, the error between the coupling method and FEA expands, while between the coupling method and EJMA standard lies only in the stiffness values error. Finally, an experimental study has been carried out, and the results align well with those from the coupled method, demonstrating that the coupled method has significant advantages in predicting the natural characteristics of multi-layer bellows. Research contents present the insights necessary for the dynamic characteristics of multi-layer expansion bellows.