Modeling and optimization for a 20-h cold rolling millQUALITY and its reproducibility are dominant criteria for cold rolled products.In particular,high strip surface quality can be achieved with special mill arrangements such as the 20-h mill.This type of mill uses small work rolls in contact with the strip,that are kept in place with a variety of intermediate and backup rolls.The use of different actuators which,in part,only act indirectly to affect the roll bite geometry,makes the presetting of the mill with regard to strip thickness and flatness a complex task.This article describes a model the objective of which is optimizing the entire rolling process in a 20-h mill.Results obtained from several on-line applications are discussed.A closed sendzimirmill arrangement,shown in Fig.1,illustrates the main actuators that affect roll bite geometry with regard to strip thickness and glatness.Side eccentrics located at the backup rolls are used to adjust the overall position of the corresponding roll axis over a wide range which,indirectly,adjusts the roll gap geometry with regard to the millpassline and strip thickness.Side eccentrics may be mechanically or electrically coupled.Crown eccentrics are available at several locations over the barrel length.Those,typically on upper backup rolls,are capable of providing special roll gap contours.They match the gap to the profile of the strip entering the mill.Crown eccentrics are the major actuators for achieving strip flatness.Shiftable,first intermediate rolls are also shape actuators;they mainly serve for modifications in the strip edge area using a tapered roll profile.Measurement of mill geometry is available only indirectly through the rotation of the side and crown eccentrics and through the position of the first intermediate rolls.Consideration of mill spring and elastic deformation effects in the stack leads to the roll gap geometry.Accounting for mill spring and elastic deformation requires knowledge of the roll separating force which,in a closed 20-h mill,is measured indirectly through the adjustment pressure needed for the main side eccentrics.Apart from hysteresis effects,the effects of the variable geometry make this indirect measurement critical.Besides roll gap geometry,the task of presetting the mill also includes the design of pass schedules tailored to meet requirements of a product and the current mill condition.While optimal utilization of the mill is a major objective,the pass schedule must achieve the required produce quality.Generation of pass schedules to cover the statistical average and storing them in databases related to steel grade,surface and coil geometry is state of the art technology,In particular,mill parameters such as roll geometry or the thermal condition of the work rolls require dynamic correction of the pass schedules to obtain a reproducible final product.The same applies to variations in the material characteristics of the coils rolled.Because of the complexity of 20-hmills,achieving reproducibility of the final product quality and the optimum use of available mill resources to increase productivity represents an extremely difficult task.This task can be accomplished with a comprehensive model approach that takes all relevant mill and process parameters into account.To optimize the porcess,various mathematical models are needed to describe the elastic stand behavior and the elastic/plastic characteristics of the material to the rolled because neither direct geometrical information nor accurate roll force measurements exist.1、Force,torque and powerThe roll force,roll torque and drive power necessary to form the material are some of the most important items of process information.While power requirements affect the design of a pass schedule for optimal use of the available mill resources,roll force is mandatory for presetting the geometrical actuators.Both force and torque,on the other hand,need to be known for mill presetting so that mechanical or practical limits are not exceeded.The approach selected to describe the effects in the roll gap with regard to power,torque and force,is based on a strip fiber model using the basic theory developed by Karmanand Siebel.The roll gap model provides both vertical and tangential stress components acting on the work roll.The roll separating force results from the integration of the vertical pressure components.Torque and drive power are derived from the tangential stress.The roll gap model simultaneously provides accurate information about the vertical and tangential stress components acting on the roll and,thus,the drive power and roll force.The ability to evaluate the rolling process,based on accurate calculation of the roll separating force and main drive power,enhances,in particular,the material yield stress evaluation.This is beneficial since the roll force measurement is affected,to a large extent,by measurement hysteresis present in a closed 20-h mil