Study Of Leveling Theory Based On Curvature Integration Method For Plates

Plates are widely used in the national economic areas including automobiles,shipbuilding, bridges construction, aerospace, et al. The required quality of plates hasbeen increasing with the development of the market economy and the progress ofscientific technologies. Although advanced rolling equipments and rolling technologiescan improve the quality of plates in some degree, it could be possible to appear someplate defects such as bending, middle wave, and edge wave due to the of the differenceof the temperature, nonuniformity of the thickness of plates. In addition, flat platesmight be still instable and form a new defect during the secondary manufacturing, heattreatments and transport process if there are great enough residual stresses in plates. Themore serious situation is the appearance of some microscopic crack on the surface ofplates. Therefore, bending plates should be leveled and the residual stress should befurther removed by the leveling process in the actual production for the high qualityproduction purpose of plates.The essence of the leveling process for plates is a continuous elastic-plasticitybending and reverse bending deformation process by staggered roller gaps so that thebending shape and residual stress can be removed finally. The quality of plates afterleveling is determined by the advantage of levelers and reasonability of the levelingtechnology which depend largely on the advanced leveling theory. Current levelingtheory is too simple to describe the leveling process which is not enough to satisfy thepractical application. Although some steel industries at home have proposed their newgeneration levelers with high stiffness characteristic and hydraulic system, they still donot understand the basic design principle fully. It means they are still at analogy-baseddesign level and rely on the major company aboard about the leveling process module.Therefore, the study of the leveling theory and research of the leveling technologyoptimization have important theoretical meaning and wide application foreground forimproving the equipment design and leveling technology level and enhancing the corecompetitiveness for steel companies at home.This paper built an analytical model related the roller gap, bending curvature andresidual stress horizontally based on the curvature integration method. This model wassolved numerically by an effective algorithm and the result was verified byexperimental data. The curvature, stress, plastic ratio, trajectory and mechanical parameters distribution during leveling process for the plate were discussed. A methodof designing the structure parameters of the roller system was proposed based on thecurvature integration method and linearly decreasing roller gap schedule. The mainfactors which influenced the leveling quality were analyzed. The relationship betweenthe factors and the reasonable roller gap was summarized. The database of roll bendingcurves was built for the third generation hydraulic leveler. The curves of levelingcapacity border matched well with field data were drawn based on the curvatureintegration method. A nonlinear and implicit technology optimization model withequality and inequality constraints was built. The roller gaps were selected as designvariables and the target was to minimize the total leveling force or the final flatness inthis model. It was solved by a numerical optimization algorithm. There was aconsistency between the optimization results and field data.The achievement of this paper could be listed as follow:①The curvature integration model was proposed. This model could describe therelationship of contact angles between the plate and adjacent rollers, the roller gap andthe curvature distribution as well. An optimization method was used for the first time tosolve the nonlinear system of equations deduced by the curvature integration model.This method could avoid the disadvantage of poor convergence and precision of theiterative algorithm. The residual stress horizontally was analyzed based on this method.The influence of the roller gap on the residual stress after leveling was discussed.②The maximum leveling force and torque of the single roller were calculatedaccurately considering the linearly decreasing roller gap schedule based on theintegration method. The lower roller spacing was determined by the strength theory. Theupper roller spacing was calculated according to the limited stroke of rollers. Theminimum roller number was selected in the condition of leveling quality of plates. Themaximum value among all the lower roller spacing of the plates was chosen as the finalroller spacing. This method changed the traditional idea on how to design the rollerspacing because the traditional idea calculated the maximum roller force and torque byan assumption of the plastic limit state. It means the proposed method is innovative fordesigning the structure parameters.③A model constrained by expected plastic ratio and maximum mechanicalparameters was built to disseminate the leveling border quickly. The rough levelingcapacity curves were drawn approximately and the constitutive principle of final curvewas discussed. The maximum yield stress value was searched for each thickness considering the linearly decreasing roller gap schedule and the curvature integrationmethod. The precision leveling capacity curves closer enough to the actual curves werefound. The curves of the leveling capacity border could be used to judge whether theincoming plate could be leveled, the maximum yield stress of a specific thickness andthe maximum thickness of a specific yield stress.④The influence of the thickness, yield stress, elasticity modulus of the incomingplate, roller gap and bending value of rollers on the leveling quality were discussed. Therelationship between these single variables and the reasonable roller gap wassummarized in the condition of good leveling quality for plates. This relation and thedatabase of the bending roller curves could provide evidences on how to set roller gapsand reasonable bending forces.⑤A large scale nonlinear and implicit technology optimization model was built.The total leveling force and final flatness was selected as the target. The roller gap waschosen as the design variables. The final quality and the condition of safety operationfor the leveler were viewed as some inequality boundary conditions. The otherinequality boundary conditions were the maximum value of the roller gap related withthe leveling capacity border. The equality boundary condition was the relationshipbetween the roller gap and the bending curvature based on the curvature integrationmethod. This model was solved by an effective algorithm. The optimum results couldmatch hundreds of field data well which verify the reliability of the proposed model.This model could provide an theoretical foundation about setting reasonable roller gaps.This paper studied the basic leveling theory for plates systematically based on theachievements of former researchers. The innovative achievements could provide somestrong technical support for the cooperative enterprise.