Multi-response design optimisation of convolution stresses of metal bellows using integrated PCA-GRA approach

This paper presents the parametric design optimisation of the bellows multi-response convolution stresses using multiple attribute decision making (MADM) technique. Grey Relational Analysis (GRA) in conjunction with Principal Components Analysis (PCA) has been employed to find a single response grade (PCA-GRG). Experimental stress analysis was carried out using L25 Taguchi orthogonal array (OA) by considering the design parameters, namely, ply thickness (tp), convolution height (H),convolution pitch (q), and bellows pitch diameter (dp). Analysis of variance (ANOVA) has been implemented to identify the most influenced significant design parameters and optimal design level settings using PCA-GRG. Confirmation test was conducted which proves the improvement in GRG by 0.042 (25.30%) over the initial setting of the factors. Further, multiple regression mathematical models were developed to find the best alternate optimal solutions and verified it by comparing with experimental GRG and Taguchi predictions. Alternate optimal solution signifies the improvement in PCA-GRG over the initial parameter setting from 13.04% to 32.6%, which directs the extensive reduction in the stresses. This verification proves the potential of the integrated PCA-GRG approach for the multi-response parametric optimisation of the convolution stresses.