Deformation mode selection and orthonormalization for an efficient simulation of the rolling contact problem

The dynamic simulation of contact in rolling processes is very time-consuming. This is mainly based on the fine resolution of the surface domain of each roll, which, however, is essential in order to capture the effect of concentrated contact forces. Existing model order reduction techniques cannot be readily applied due to the nonlinear nature of the contact dynamics. In order to improve the speed of contact analysis, the present paper proposes a sophisticated combination of so-called characteristic static correction modes and vibration normal modes for describing the deformation of each roll. While the characteristic static correction modes are required to capture the concentrated nonlinear contact forces, the vibration normal modes describe the global deformation behavior of the rolls. For the computation of the characteristic static correction modes, first attachment modes are computed for a longitudinal sub-area of each roll. Then an eigenanalysis is performed on the component mode synthesis mass and stiffness matrices that correspond to the attachment modes. The resultant eigenvectors have been truncated and applied to the entire surface domain of the rolls. In order to obtain well-conditioned equations, all modes are finally orthonormalized. An example from the metal forming industry is used to demonstrate the results.