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1、<p>  Modeling and optimization for a 20-h cold rolling mill</p><p>  QUALITY and its reproducibility are dominant criteria for cold rolled products.In particular,high strip surface quality can be achie

2、ved 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 actua

3、tors 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</p><p>  This article describes a model the objective of w

4、hich is optimizing the entire rolling process in a 20-h mill.Results obtained from several on-line applications are discussed.</p><p>  A closed sendzimirmill arrangement,shown in Fig.1,illustrates the main

5、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 wh

6、ich,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 </p>

7、<p>  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.</p><p>  Consideration of

8、 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 m

9、easured 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.</p><p>  Bes

10、ides 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

11、 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

12、 of the art technology,In particular,mill parameters such</p><p>  Because of the complexity of 20-hmills,achieving reproducibility of the final product quality and the optimum use of available mill resource

13、s 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.</p><p>  

14、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 n

15、or accurate roll force measurements exist.</p><p>  1、Force,torque and power</p><p>  The roll force,roll torque and drive power necessary to form the material are some of the most important ite

16、ms 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 torq

17、ue,on the other hand,need to be known for mill presetting so that mechanical or practical limits are not exceeded.</p><p>  The approach selected to describe the effects in the roll gap with regard to power,

18、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

19、 force results from the integration of the vertical pressure components.Torque and drive power are derived from the tangential stress.</p><p>  The roll gap model simultaneously provides accurate information

20、 about the vertical and tangential stress components acting on the roll and,thus,the drive power and roll force.</p><p>  The ability to evaluate the rolling process,based on accurate calculation of the roll

21、 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

22、closed 20-h mill.</p><p>  2、Material yield stress adaption</p><p>  Material yield stress adaption is required in any case where there is the need to roll a wide range of steel grades.Also,the

23、demand for self-learning model algorithms forces the use of adaptive methods with regard to the yield stress.</p><p>  The yield stress of the material is initially evaluated in off-line tests using torsion

24、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 grade

25、s.</p><p>  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 te

26、mperature 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.</p><p>  3、Friction repres

27、entation</p><p>  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 adjuste

28、d 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.</p><p>  Another approach is to

29、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 adequa

30、tely considered.The approach selected in the current study is based on an artificial neural network.</p><p>  The entry layer of the neural network receives all relevant information as it has been gathered a

31、nd 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 c

32、oefficient.With a representative work,even physical relationships between the friction coefficient and process information can be evaluated.</p><p>  The results derived from the neural network have been use

33、d as the basis for an analytical model,which was implemented on-line.</p><p>  The accuracy of the representation has been evaluated in several on-line rolling tests in industrial facilities.Since mill speed

34、 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.</p><p>  A

35、part from the friction coefficient,both the temperature of the strip approaching the roll bite and the strain varied in the test.</p><p>  4、Elastic mill stand behavior</p><p>  In addition to r

36、oll 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

37、steps.</p><p>  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 r

38、espect 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.</p><p>  To provide maximum flexibility,th

39、e 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

40、 deflection of the several rolls,are derived from multiple iterations.</p><p>  The elastic mill stand model for the 20-h cold rolling mill can,generally,be divided into two parts.The initial phase involves

41、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,flattenin

42、g and deflection.</p><p>  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 flatten

43、ing 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.</p><p>

44、  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 iterat

45、ion is carried out until a solution has been reached,where the entire load,the deflection and flattening match.</p><p><b>  5、Summary</b></p><p>  The accuracy of force measurement i

46、n 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 compone

47、nts acting on the work rolls are described to permit the calculation for yield stress adaptions based on the power consumption of the main drive.</p><p>  A model has been developed that describes the elasti

48、c mill stand behavior and considers the interaction of roll deflection with load distribution and roll flattening.The model represents a multiple iterative solution approach.</p><p>  20-h冷軋機的模型化和優化</p>

49、;<p>  質量和其再現性是冷軋產品的主要標準。尤其像20-h軋機,通過特殊的軋機布置,可以達到高標準的鋼板表面質量。這種類型的軋機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。各種調節器的使用實際上僅僅間接影響輥子的幾何咬入,而為了達到鋼板的厚度和平直度要求預先對軋機進行調整卻是一項復雜的工作。</p><p>  本文描述了在20-h軋機中優化整個軋制過程的模型,討

50、論了一些在聯機應用中可能獲得的結果。</p><p>  一臺封閉式的森吉米爾軋機舉例說明了在鋼板厚度和平直度方面對軋輥幾何咬入產生影響的主調節器是如何布置的。位于后備輥旁的偏心邊是用來在一個較大的范圍內調整其相應的輥軸的位置,并且還可以間接調整能夠影響軋制線和鋼板厚度的軋輥開度。偏心邊可以是機械連接或是電器連接的。偏心頂可以在一些位置上調整輥身長度。那些一般位于后備輥上的偏心頂還能夠調整特殊的軋輥開度輪廓。他們

51、與被軋制鋼板的側面間隙相匹配。偏心頂是實現板帶平直度的主要調節器。第一中間輥也是形狀調節器;他們主要是利用細小的輥側對鋼板邊緣部分進行修正。</p><p>  軋機幾何形狀的測量可以通過旋轉邊和偏心頂,以及第一中間輥的位置來間接獲得。</p><p>  軋機的彈塑性變形會影響軋輥的間隙。解釋軋機的彈塑性變形需要軋輥間分開的力,在封閉的20-h軋機中,這些力可以通過調整作用在主偏心邊上壓

52、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鍵。</p><p>  除了軋輥開度外,軋機預設置的任務還包括為了滿足產品和當前軋機條件要求需要的軋制表的設計。軋機應用的主要目標就是利用軋制表制造出所需要的產品。有關軋制表的最新生產技術是統計軋制過程中一些數值的平均值并將這些數值存儲在數據庫中,數據庫中包含鋼的等級,表面質量,鋼卷數量等等。此外,軋機參數還包括諸如軋輥幾何參數或者在最終產品中

53、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用在卷曲軋制的材料中。</p><p>  由于20-h軋機的復雜性,要實現最終產品的質量再現性和最大化的利用軋機資源來增加產量成了一項極端困難的任務。這個任務可以利用一個接近于軋機和生產過程參數的模型來綜合研究分析。</p><p>  為了對過程進行優化,同時又因為在軋制過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

54、數學模型來研究材料在軋制時產生的彈性變形和其彈塑性變形的特點。</p><p>  1、軋制強度,扭轉力矩和動力矩</p><p>  軋制強度,扭轉力矩和驅動力矩是材料在軋制過程中最重要的參數。當設計一份需要最佳化利用可使用的軋機資源的軋制表時,對于強度的要求是調節器預先強迫施加軋制強度。換一方面講,在軋機預置時施加軋制強度和扭轉力矩,在實際軋制時就不會因為強度過大或力矩過大而形成失效。

55、</p><p>  在卡爾曼和西貝爾所創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,扭轉力矩和軋制強度所接近的結果。軋輥開度模型展示了作用于工作輥間的垂直應力和切線應力,切軋制力與垂直應力是分開研究的,而扭轉力矩和驅動力矩則是由切線應力產生。</p><p>  軋輥開度模型同時相對準確地提供了作用于工作輥垂直應力,切線應力以及驅動力矩和軋制強度信息。</p>

56、<p>  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動力矩的準確計算。在封閉的20-h軋機中,軋制強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。</p><p>  2、材料屈服強度自適應</p><p>  材料的屈服強度自適應在各種等級的鋼材軋制時都需要用到。同時,關于屈服強度的自學習模型要求使用自適應方法來計算。<

57、/p><p>  材料屈服強度初期是在脫機測試中利用扭轉杠桿抽樣的方法來測量,如果想要脫機測試里得到好的測試結果,那么每個步驟和每個產品都要分別進行測試,不同等級的鋼的化學成分不同,退火時產生不同的變形體,所以測試的結果也不同。</p><p>  屈服強度在短期自適應中下降,在長期自適應中被快速調整上升,這期間的主要代表因素有變形,變形率和溫度。屈服強度數值的統計是基于鋼材的等級,并且如果有

58、需要提高或保證質量的需要,可以從一個單獨的帶卷中測試得到。</p><p><b>  3、摩擦表示</b></p><p>  軋輥開度間除了要表示材料的屈服強度外,還要將摩擦的情況表示出來。在各種應用里,為了在長期的分析計算中得到最優化的摩擦系數,摩擦系數需要經常修正;可以說,為了計算和測量的準確性,總要利用到摩擦系數。</p><p> 

59、 還有一個比較接近的方法就是進行軋制測試并且分析其結果。當軋制測試關系最終生產時,分析結果的方法經常消耗大量時間并且會由于各種影響到摩擦的因素沒有被充分考慮而對最后的結果產生不利的影響。目前關于摩擦的研究都是在一個人工中樞網絡進行的。</p><p>  當周圍的信息被收集起來并且可能因摩擦時,這個中樞網絡的進入層會收到所有有關的信息。獲得有關摩擦的信息的方法是在脫機測試中使用聯合視感控制器來處理前方網絡的情況,

60、然后利用后臺傳送的方法將摩擦系數的信息分析計算出來。有了這個分析工作,摩擦系數體現出來的物理關系和過程信息都可能表示出來。</p><p>  中樞網絡計算得出結果可以作為用來聯機計算分析模型的基礎。</p><p>  在工業設備中有些聯機測試的表示方法的準確性已經被認同。軋機的軋制速度是摩擦系數的主要影響因數,軋制期間不同的速度會產生不同的摩擦系數,同時測量和計算的軋制強度也被紀錄下來

61、。</p><p>  除了摩擦系數,鋼板被軋輥咬入時的溫度和變形也在測試范圍內。</p><p><b>  4、機座彈性變形</b></p><p>  除了軋制強度,力矩和扭轉力矩外,為了進一步的優化工作,在軋輥咬入角的偏心調整測量中,需要將軋機機座的彈性變形表示出來。</p><p>  在機座彈性變形模型中需要

62、的前提條件是各種軋機的配置情況,鋼卷的輪廓和鋼卷材料。在設計階段,每個單獨的軋輥與指定的軋輥之間結合的情況中產生的各種變量也被明確說明。</p><p>  為了提供最大的撓度,對機座彈性變形的表示是基于鋼卷的數字解決方案。多重的反復性工作造成了不同的結果,例如不同軋輥間的矯直,鋼板和工作輥之間的矯直,和一些軋輥的偏轉等。</p><p>  20-h冷軋機的機座彈性變形模型一般分為兩部分

63、。第一階段包括了對第二階段所承受負荷的快速分析,然后這個快速分析的結果在第二階段被用來作為負荷的分配,矯正,偏轉間相互作用的基礎。</p><p>  每個軋輥的偏轉量都取決于這兩個階段中確定的負荷分配量,相鄰的軋輥間存在的差異是因為要得到一定的負荷分配量而必須對軋輥進行矯直造成的,這就導致在不同的軋輥間產生了一個新的負荷,而這個新的負荷被再次分配,又引起了一個新的偏轉。</p><p>

64、  軋輥間的彈性變形所引起的所有效果是在后備輥的托架部分產生一個新的負荷,要是軋機的彈性變形看起來不對,就需要重新計算負荷,直到計算出來的一個負荷可以使其分配,偏轉,矯正相互平衡。</p><p><b>  5、總結</b></p><p>  一臺封閉式的森吉米爾軋機的強度測試的準確性對于一個高精度的控制過程是不夠的,為了解決這個問題,開發了測定軋制強度和軋制扭轉

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