Modeling and optimization for a 20-h cold rolling mill QUALITY 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 power The 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 mill. 2、 Material yield stress adaption Material yield stress adaption is required in any case where there is the need to roll a wide range of steel grades.Also,the demand for self-learning model algorithms forces the use of adaptive methods with regard to the yield stress. The yield stress of the material is initially evaluated in off-line tests using torsion bar samples.While off-line tests provide good initial information,each process and product has its own personality.This may result from the annealing practices or variations in the chemical composition of the steel grades. The yield stress adaption is broken down into a short-term adaption to rapidly adjust the yield stress curve,and a long-term adaption,where complex relationships between strain,strain rate and temperature are evaluated and represented. Statistical yield stress information is available by grade and also on an individual coil basis if needed,which improves quality assurance. 3、 Friction representation Besides obtaining a representation of the material yield stress,it isalso mandatory to describe the friction in the roll gap.In a variety of applications,the friction coefficient is adjusted so that during long-term analysis the most appropriate friction coefficient；ie,the coefficient that provides the best match between calculation and measurement,is applied. Another approach is to carry out rolling tests and analyze the results.While rolling tests affect production, the analysis method is time-consuming and may often have the disadvantage that not all relevant factors affecting friction are adequately considered.The approach selected in the current study is based on an artificial neural network. The entry layer of the neural network receives all relevant information as it has been gathered and may affect friction.This information is processed through the multilayer perceptron feed forward network in an off-line investigation using the back propagation method for training that,finally,leads to the friction coefficient.With a representative work,even physical relationships between the friction coefficient and process information can be evaluated. The results derived from the neural network have been used as the basis for an analytical model,which was implemented on-line. The accuracy of the representation has been evaluated in several on-line rolling tests in industrial facilities.Since mill speed is one of the main variables affecting friction,one pass was made during the commissioning phase of the model with different mill speeds.Both the measured and calculated roll force were recorded. Apart from the friction coefficient,both the temperature of the strip approaching the roll bite and the strain varied in the test. 4、 Elastic mill stand behavior In addition to roll force,power and torque,the elastic behavior of the mill stand must also be described to allow propagation from the measured eccentric adjustments to the roll bite contour,which is the target for further optimization steps. One requirement in the elastic mill stand model was its ability to cover a variety of different mill configurations,roll profiles and roll materials.These variables were also specified with respect to each individual roll in the stack to cover situations where unusual roll combinations are selected and to allow the model to be used during design phases. To provide maximum flexibility,the description of the elastic mill stand behavior is based on a numerical solution approach for the roll stack.The different effects,such as flattening between the rolls,flattening between the strip and the work rolls,and deflection of the several rolls,are derived from multiple iterations. The elastic mill stand model for the 20-h cold rolling mill can,generally,be divided into two parts.The initial phase involves a rapid determination of the load share in the second phase.The initial load share derived is then taken,in the second phase,as basis for the iterative determination of the interaction between load distribution,flattening and deflection. The deflection of each roll is derived from the load distribution determined in each iteration step.The geometrical differences between neighboring rolls are interpreted as flattening of the rolls for which a certain load distribution must be present.This leads to a new load along the contact area of the various rolls.This new load distribution leads,again,to a new deflection. The total effect of elastic deformation between the rolls produces a new load at the saddle segments of the backup rolls.Thus,the mill spring appears to be different,and a new iteration needs to be performed.The iteration is carried out until a solution has been reached,where the entire load,the deflection and flattening match. 5、 Summary The accuracy of force measurement in a closed sendzimir mill is inadequate for high-precision process control.To solve this problem,special model for determination of roll force and roll torque has been developed.The tangential and vertical stress components acting on the work rolls are described to permit the calculation for yield stress adaptions based on the power consumption of the main drive. A model has been developed that describes the elastic mill stand behavior and considers the interaction of roll deflection with load distribution and roll flattening.The model represents a multiple iterative solution approach. 20-h 冷軋機(jī)的模型化和優(yōu)化 質(zhì)量和其再現(xiàn)性是冷軋產(chǎn)品的主要標(biāo)準(zhǔn)。尤其像 20-h 軋機(jī)，通過特殊的軋機(jī)布置，可以達(dá)到高標(biāo)準(zhǔn)的鋼板表面質(zhì)量。這種類型的軋機(jī)利用小工作輥來軋制鋼板，而小工作輥又是通過多個中間輥和后備輥來保持其位置。各種調(diào)節(jié)器的使用實(shí)際上僅僅 間接影響輥?zhàn)拥膸缀我耄鵀榱诉_(dá)到鋼板的厚度和平 直 度要求預(yù)先對軋機(jī)進(jìn)行調(diào)整卻是一項(xiàng)復(fù)雜的工作。 本文描述了在 20-h 軋機(jī)中優(yōu)化整個軋制過程的模型，討論了一些在聯(lián)機(jī)應(yīng)用中可能獲得的結(jié)果。 一臺封閉式的森吉米爾軋機(jī)舉例說明了在鋼板厚度和平 直 度方面對軋輥幾何咬入產(chǎn)生影響的主調(diào)節(jié)器是如何布置的。位于后備輥旁的偏心邊是用來在一個較大的范圍內(nèi)調(diào)整其相應(yīng)的輥軸的位置，并且還可以間接調(diào)整能夠影響軋 制 線和鋼板厚度的軋輥開度。偏心邊可以是機(jī)械連接或是電器連接的。偏心頂可以在一些位置上調(diào)整輥身長度。那些一般位于后備輥上的偏心頂還 能夠調(diào)整特殊的軋輥開度輪廓。他們與被軋制鋼板的側(cè)面間隙相匹配。偏心頂是實(shí)現(xiàn)板帶平 直 度的主要調(diào)節(jié)器。第一中間輥也是形狀調(diào)節(jié)器；他們主要是利用細(xì)小的輥側(cè)對鋼板邊緣部分進(jìn)行修正。 軋機(jī)幾何形狀的測量可以通過旋轉(zhuǎn)邊和偏心頂，以及第一中間輥的位置來間接獲得。 軋機(jī)的彈塑性變形會影響軋輥的間隙。解釋軋機(jī)的彈塑性變形需要軋輥間分開的力，在封閉的 20-h 軋機(jī)中，這些力可以通過調(diào)整作用在主偏心邊上壓力來間接測量獲得。除了滯后的影響外，各種各樣的幾何影響是間接測量的關(guān)鍵。 除了軋輥開度外，軋機(jī)預(yù)設(shè)置的任務(wù)還包括為了滿足產(chǎn)品和當(dāng) 前 軋機(jī)條件要求需要的軋制表的設(shè)計(jì)。軋機(jī)應(yīng)用的主要目標(biāo)就是利用軋制表制造出所需要的產(chǎn)品。有關(guān)軋制表的最新生產(chǎn)技術(shù)是統(tǒng)計(jì)軋制過程中一些數(shù)值的平均值并將這些數(shù)值存儲在數(shù)據(jù)庫中，數(shù)據(jù)庫中包含鋼的等級，表面質(zhì)量，鋼卷數(shù)量等等。此外，軋機(jī)參數(shù)還包括諸如軋輥幾何參數(shù)或者在最終產(chǎn)品中獲得的隨時間變化的工作輥溫度變化情況。軋制表同樣還可以應(yīng)用在卷曲軋制的材料中。 由于 20-h 軋機(jī)的復(fù)雜性，要實(shí)現(xiàn)最終產(chǎn)品的質(zhì)量再現(xiàn)性和最大化的利用軋機(jī)資源來增加產(chǎn)量成了一項(xiàng)極端困難的任務(wù)。這個任務(wù)可以利用一個接近于軋機(jī)和生產(chǎn)過程參數(shù)的模型來綜合 研究分析。 為了對過程進(jìn)行優(yōu)化，同時又因?yàn)樵谲堉七^程中沒有可以直接測量軋制力的方法， 所以可以利用各種各樣的數(shù)學(xué)模型來研究材料在軋制時產(chǎn)生的彈性變形和其彈塑性變形的特點(diǎn)。 1、 軋制強(qiáng)度，扭轉(zhuǎn)力矩和動力矩 軋制強(qiáng)度，扭轉(zhuǎn)力矩和驅(qū)動力矩是材料在軋制過程中最重要的參數(shù)。當(dāng)設(shè)計(jì)一份需要最佳化利用可使用的軋機(jī)資源的軋制表時，對于強(qiáng)度的要求是調(diào)節(jié)器預(yù)先強(qiáng)迫施加軋制強(qiáng)度。換一方面講，在軋機(jī)預(yù)置時施加軋制強(qiáng)度和扭轉(zhuǎn)力矩，在實(shí)際軋制時就不會因?yàn)閺?qiáng)度過大或力矩過大而形成失效。 在卡爾曼和西貝爾所創(chuàng)造的一種鋼板纖維模型理論中描述 了與軋輥開度之間的動力矩，扭轉(zhuǎn)力矩和軋制強(qiáng)度所接近的結(jié)果。軋輥開度模型展示了作用于工作輥間的垂直應(yīng)力和切線應(yīng)力，切軋制力與垂直應(yīng)力是分開研究的，而扭轉(zhuǎn)力矩和驅(qū)動力矩則是由切線應(yīng)力產(chǎn)生。 軋輥開度模型同時相對準(zhǔn)確地提供了作用于工作輥垂直應(yīng)力，切線應(yīng)力以及驅(qū)動力矩和軋制強(qiáng)度信息。 對于軋制過程能力的評價，尤其是提高金屬材料壓力的評價，主要是基于對軋制力和驅(qū)動力矩的準(zhǔn)確計(jì)算。在封閉的 20-h 軋機(jī)中，軋制強(qiáng)度的測量在很大程度上受到要延遲作用的影響，但這并沒有多大壞處。 2、 材料屈服強(qiáng)度自適應(yīng) 材料的屈服強(qiáng)度自適應(yīng)在 各種等級的鋼材軋制時都需要用到。同時，關(guān)于屈服強(qiáng)度的自學(xué)習(xí)模型要求使用自適應(yīng)方法來計(jì)算。 材料屈服強(qiáng)度初期是在脫機(jī)測試中利用扭轉(zhuǎn)杠桿抽樣的方法來測量，如果想要脫機(jī)測試?yán)锏玫胶玫臏y試結(jié)果，那么每個步驟和每個產(chǎn)品都要分別進(jìn)行測試，不同等級的鋼的化學(xué)成分不同，退火時產(chǎn)生不同的變形體，所以測試的結(jié)果也不同。 屈服強(qiáng)度在短期自適應(yīng)中下降，在