Unpredictable and uncertain failure of the bellows needs the attention of the designer toward maximum meridional deflection stresses generated on the U-shaped convolutions. Evaluation of these maximum stress points on the flexible convolutions is multifaceted. This paper deals with the identification of these stresses induced on the bellows convolutions by analytical and experimental methods. Further, the influence of the pivotal design parameters on meridional deflection stresses is studied mainly in two aspects: (1) effect of number of convolutions (N) and pitch diameter (d p) on the meridional deflection stresses and (2) the determination of the optimized design parameters to reduce the stress levels using effective multi-response gray relational grade (GRG) optimization technique. Three bellows of stainless steel material (Grade SS321) are used for the experimentation with a different number of convolutions (N) and pitch diameters (d p). The optimal design parameter setting is found by using GRG analysis through ANOVA and regression mathematical model. The effect of design factors on GRG is analyzed. Besides, using GRG, the regression model enhances to give alternative optimal solutions; in turn, it increases the designer's choice for the selection of the parametric levels. In the confirmation test, it is seen that the average improvement in GRG for all selected Taguchi orthogonal runs is 23%.

Metal expansion bellows are a mechanical device for absorbing energy or displacement in structures. It is widely used to deal with vibrations, thermal expansion, and the angular, radial, and axial displacements of components. The main objective of this paper is to perform numerical analysis to find various characteristics of stresses in U-shaped metal expansion bellows as per the requirement of vendor and ASME standards. In this paper, extensive analytical and numerical study is carried out to calculate the different characteristics of stresses due to internal pressure varying from 1 MPa to 2 MPa in U-shaped bellows. Finite element analysis by using Ansys14 is performed to find the characteristics of U-shaped metal expansion bellows. Finally, the results of analytical analysis and finite element method (FEM) show a very good agreement. The results of this research work could be used as a basis for designing a new type of the metal bellows.

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