Process parameter optimization for thin-walled tube push-bending using response surface methodology

Abstract

In this paper, the response surface methodology (RSM) and finite element (FE) simulation were applied to optimize the push-bending process parameters of the thin-walled tube with polyurethane mandrel. The objective of the present work is to predict the optimal set of process parameters including the length to diameter ratio of the mandrel (L/D), the friction coefficient between die and tube ( $${\mu }_{1}$$ ), the friction coefficient between polyurethane and tube ( $${\mu }_{2}$$ ), and Poisson’s ratio of polyurethane ( $$\upsilon$$ ) to obtain qualified bent tubes. Three empirical models were developed to describe the relationship between process parameters and quality parameters of the bent tubes. In addition, the significant factors affecting the forming quality were analyzed using analysis of variance (ANOVA) of each model. Response surfaces were constructed to study the effect of each process parameter on the quality of the bent tubes. Finally, the process optimization window with the maximum thinning rate ( $$\varphi$$ ) less than 20%, the maximum thickening rate ( $$\psi$$ ) less than 17%, and the maximum cross-section ovality ( $$\xi$$ ) less than 5% of the bent tube was established. Qualified bent tubes with diameter of 144 mm, wall thickness of 2 mm, and bending radius of 280 mm were formed experimentally by following the established process window.