A continuous straightening formulation based on minimum curvature variation

A continuous straightening formulation is proposed in order to smooth the transition between the curved and straight sectors in a continuous caster of metals. This is accomplished by minimising the curvature variation in the straightening sector, taking into account boundary conditions usually found when designing or modifying continuous casting machines. A differential equation is obtained for the bar trajectory which is numerically solved after discretisation. The obtained algorithm is used to compare different casting configurations whose smoothness is quantified in terms of the strain and strain rate along the bar. The continuous straightening configurations developed by this formulation were found to be smoother than typical setups with 1 or 2 straightening points. It was also found that the longer the straightening length, the smoother the transition.