Two key parameters which govern the market value of strip metal are profile and flatness. Profile is defined as the variation of thickness across strip width. Flatness is determined by the residual stresses locked into the strip after rolling. Control of these properties during rolling is made difficult by thermal expansion of work rolls, roll deformation, spreading at strip edges, strip thermal crown and non-uniform properties at entry to the process.
The design of control systems for cross-directional properties is explored through an orthogonal basis function expansion of error signals and actuator responses. Actuators are analysed to show how much power they have within the “spectrum” of this basis function expansion. Sensors are analysed to show their filtering effect within the spectrum. The consequent theory is used to develop a rationale to future actuator design and a benchmark for the assessment of control performance with existing actuators.
The design and implementation of such control systems is facilitated by models of the strip rolling process – which must allow prediction of the effect of roll stack actuators on strip profile and residual stress distributions. Two broad approaches to this modelling problem have developed in the literature – an approximate approach based on simple infinite width models of rolling and an ‘exact’ approach usually using finite element solutions. The approximate approach has wide application in cold rolling, but is inaccurate at strip edges and cannot describe hot rolling. The ‘exact’ approach typically requires a very fine mesh and is generally only used for infinite width models. Furthermore, in hot rolling, the ‘exact’ approach requires solution of a steady-state elasto-viscoplastic model, which is known to cause convergence problems in finite element solvers.
A 2.5 dimensional model of rolling is presented which solves the required model using a first order finite difference technique which gives stable convergence. The model provides sufficient accuracy to allow prediction of profile and flatness in both hot and cold rolling. The results of the model are used to demonstrate the design of future cross-directional control systems.