(6B-3) MULTI-VARIABLE SHAPE ACTUATION CAPABILITIES ENVELOPES OF 6-HIGH MILLS WITH APPLICATIONS TO MILL SET-UP AND SCHEDULING OPTIMIZATION

摘要

Traditional methods of characterizing shape actuator behavior in 6-high cold mills involve describing the range of actuated roll gap profiles within a 2-dimensional space that spans the quadratic curvature and a composite collection of even, higher order terms. This approach is satisfactory for general evaluations, but not suited for considering the actuators’ adjustments to the transverse stress distributions involved in assessing shape target reachability. Recent developments in describing shape actuation capabilities of highly coupled 20-high cluster mills offer an extension of the roll gap profile characterization of 6-high mill shape actuation in terms of the differential, transverse stress distribution. This approach combines the spatial influence functions of the 6-high mill’s multiple shape actuators and maps-out their combined capabilities, over the entire range of constrained actuation. Orthogonal polynomial decomposition is employed, whose results are plotted within a multi-dimensional spatial curvature basis, from which the achievable shape adjustment curvatures form a closed region (envelope). These results span odd and even orders of curvature, typically up to the 8th order. This paper examines the 6-high mill’s shape actuation capabilities envelopes as functions of material geometry, work hardening, mill set-up and operating conditions, with a focus on their use in mill set-up and scheduling.