THERMAL CAMBER MODEL FOR HOT AND COLD-ROLLING

The MDS profile and flatness control system is based on many physical part models. The thermal camber model is the only one of these part mo dels which, apart from the spatial dimensions, inherently depends on t he time dimension as opposed to part models like roll bending or even roll wear. This means that work roll temperature and shape keep changi ng even ii boundary conditions like water distribution or strip contac t stay constant. The exact mathematical solution of the resulting dyna mic equations is a very time consuming task usually not suitable for o n-line purposes. Here a new mathematical approach is presented, which solves the 2-dimensional Fourier heat conduction equation with 3-dimen sional boundary conditions at a speed suitable for on-line application s. Furthermore an approximate solution of the Hooke stress strain rela tions is derived, which translates the temperature distribution of the roll into an expansion distribution. This thermal camber model has be en implemented in several hot and cold rolling mills. Data collected t here show good agreement with the model.