Analytical and empirical modeling of top roller position for three-roller cylindrical bending of plates and its experimental verification

Reported work proposes an analytical and empirical model to estimate the top roller position explicitly as a function of desired (final) radius of curvature for three-roller cylindrical bending of plates, considering the contact point shift at the bottom roller plate interfaces. Effect of initial strain and change of material properties during deformation is neglected. Top roller positions for loaded radius of curvature are plotted for a certain set of data for center distance between bottom rollers and bottom roller radius. Applying the method of least square and method of differential correction to the generated data, a unified correlation is developed for the top roller position, which in turn is verified with the experiments, on a pyramid type three-roller plate-bending machine. Uncertainty analysis of the empirical correlation is reported using the McClintockʹs method.