Simplified roll-temperature model: convective cooling

A simple model is derived of the cyclic temperature variations set up within a work roll during the hot-rolling process. The equations have been normalized so that they can be used easily for different roll dimensions, strip temperatures, roll-cooling coefficients, and roll speeds. The model is sufficiently simple for it to be programmed (for example, on a modern calculator), and provides solutions typically within 5% of results obtained from more precise equations which can be solved only by using powerful computing facilities. The model is ideally suited for ‘real-time’ calculations or as part of a hot-mill simulation, providing a rapid solution to equations which implicitly relate strip and roll temperatures in a train of roughers or a finishing mill. The model is derived entirely from physical approximations and arguments which incidentally provide considerable engineering insight into roll-heating phenomena. The model can be used to calculate internal roll-temperature distributions, and hence to estimate the cyclic stresses which occur within the roll.