【正文】 cally when strip temperature gauges are available at entry and exit side (no more offline calibration necessary). 當(dāng)帶材溫度 表配備于 入口側(cè)和出口側(cè)時(shí)， 可以 自動(dòng)調(diào)整 帶材溫度模型。（沒有必要進(jìn)行離線校準(zhǔn)） Thermal Crown Model 熱凸度模型 This twodimensional transient model observes permanently the actual thermal expansion of the work roll during and between rolling. 這個(gè)二維瞬變 模型在軋制期間和軋制 等待時(shí)間內(nèi) 連續(xù) 計(jì)算工作輥的實(shí)際 熱膨脹 狀態(tài)。 The finitedifference technique is used to calculate the temperature distribution in the work roll balancing the heat flows into and out of the roll. The volume of the roll is suitably divided into small elements and the heat flow into and out of each element is described mathematically. 用 有限元微分技術(shù) 計(jì)算工作輥的溫度分布，平衡進(jìn)出軋輥的熱流 量 。 適當(dāng)?shù)匕?軋輥 體積 分為許多 小元，進(jìn)出每個(gè) 小元 的熱流由數(shù)學(xué)模型描述。 The external heat flow to the roll from the strip and from the roll to the coolant, the backup roll and the air are represented by suitable heat transfer coefficients. The spatial thermal expansion of the roll is then calculated from the resulting temperature distribution. 從帶材流向軋輥， 從 軋輥流向冷卻劑 、 支承輥 和空氣 的 熱量 分別由適當(dāng)?shù)臒醾鬏斚禂?shù)描述 。之后根據(jù)溫度分布計(jì)算軋輥的空間熱膨脹。 軋制模型設(shè)計(jì) 描述 翻譯：林秀蓮 校譯：吳燕翔 2021 年 7 月 16 The heat input rate is determined by the strip temperature model. The distribution of cooling effect along the roll is derived by the roll cooling model taking into account the spray pattern of the spray bar’s nozzles (including Hot Edge Sprays, HES) and their interactions. The heat exchange rate is calculated for all zones along the roll in axial direction with the following formula: 熱輸入率由帶材溫度模型確定。 沿 軋輥 方向 冷卻效應(yīng)的分布 由 軋輥冷卻模型 推導(dǎo)出來， 考慮了 噴射梁 油嘴的 噴射模式 （包括 熱 油 邊緣 噴射： HES） 和他們的相互作用。對(duì)軋輥軸向所有區(qū)域按下列公式計(jì)算熱交換率： dQ/dt = α * Area * (Temperature_Roll – Temperature_Coolant) dQ/dT: Heat exchange rate between roll and coolant [kW] dQ/dT:軋輥和冷卻液間的熱交換率 [kW] α : Heat transfer coefficient [W/K/m178。 ] α :傳熱系數(shù) [W/K/m178。 ] Area: Area sprayed by nozzles of one zone (=0 when off) Area:一個(gè)區(qū)域的噴嘴噴射的 面積 (關(guān)閉時(shí)面積 =0) This model will be calibrated offline by manual temperature measurements. 通過手動(dòng)溫度測(cè)量離線校準(zhǔn)模型。 Flatness Model平整 度模型 The flatness model calculates the flatness actuators of a 6high mill: Roll bending and axial roll shifting. These actuators will adjust the roll gap in such a way that the profile of the ining strip will be considered as well as the target tension distribution. 平整度模型計(jì)算 6輥軋機(jī)的平整度執(zhí)行機(jī)構(gòu)： 彎輥 和中間輥軸向竄動(dòng)。這些執(zhí)行機(jī)構(gòu)將以這樣一種方式調(diào)整輥縫，考慮來料帶材的 凸度 和目標(biāo)張力分布。 The flatness model is a finite difference model additionally taking into account: 這個(gè)平整度 是有限元微分 模型 ，附加考慮了： . roll deflection 軋輥撓度 . flattening of backup, intermediate and work rolls 支承輥，中間 輥和工作輥的 壓扁 . embedding of the strip into the work roll 帶材 在 工作輥 中 的嵌入 . roll force and tension distribution 軋制力和張力分布 . roll grindings 軋輥磨削 . thermal crown of the work roll 工作輥熱凸度 Measurements of the strip flatness in the plant will be used for short and long term adaptation of this model. 工廠 /設(shè)備 里帶材平整度 的測(cè)量將 用于這個(gè)模型 的 短期和長(zhǎng)期調(diào)整 （自適應(yīng)） 。 Profile assumption 形狀假定 The roll gap profile h(x) to be adjusted can be described by a polynom of 4th grade: 軋制模型設(shè)計(jì) 描述 翻譯：林秀蓮 校譯：吳燕翔 2021 年 7 月 17 輥縫形狀 h(x)的調(diào)整用一個(gè) 4次多項(xiàng)式描述。 where其中： x = width coordinate, x = 寬度坐標(biāo) , h0 = strip thickness, h0 =帶材厚度 The non symmetric part of the equation is not being considered ( a1,a3 = 0). 等式不對(duì)稱的部分將不考慮 ( a1,a3 = 0) The symmetric portion of the profile is described by the profile parameters c2 and c4 based on the following transformation: 形狀對(duì)稱的部分用基于下列 轉(zhuǎn)換式的形狀參數(shù) c2和 c4描述 ： c2 = (a2 + a4) and c4 = a4 / 4 Overlay of profile influences 形狀影響 的重疊： For c2 and c4 the following equations can be set up: 通過下列等式 得到 c2和 c4： 軋制模型設(shè)計(jì) 描述 翻譯：林秀蓮 校譯：吳燕翔 2021 年 7 月 18 其中： c2, c4 來料帶材的凸度參數(shù) Yi 實(shí)際值 Y i_R 參考值 ：凸度梯度 y1 CRA (中間輥凸度 ) y2 Dwr (工作輥直徑 ) y3 Dir (中間輥直徑 ) y4 Dbr (支承輥直徑 ) y5 Fr (軋制力 ) y6 Fb (工作輥彎輥力 ) y7 Fb (中間輥彎輥力 ) y8 s_Shift (中間輥竄動(dòng) ) c2_base c2當(dāng)所有影響值都為基準(zhǔn)值時(shí) c4_base c4當(dāng)所有影響值都為基準(zhǔn)值時(shí) c2_A c2的調(diào)整值 (將加到等式的右側(cè) ) c4_A c4的調(diào)整值 (將加到等式的右側(cè) ) The actuator values (bending WR, bending IR, shifting) to adjust the desired roll gap 軋制模型設(shè)計(jì) 描述 翻譯：林秀蓮 校譯：吳燕翔 2021 年 7 月 19 profile will be determined by an iterative optimization algorithm. Rolling one coil the CVC position will remain at the same position during all rolling phases. 調(diào)整 輥縫形狀以達(dá)到希望值的 執(zhí)行機(jī)構(gòu)值（工作輥 彎曲 ，中間輥 彎曲 ， 竄動(dòng) ） ，將由一個(gè) 迭代的 優(yōu)化法則進(jìn)行確定。軋制一個(gè)卷材期間， CVC位置都將在該卷材全部軋制階段內(nèi)保持相同的位置。 For calculation the bending values for threading phase are firstly set to small positive values (close to balancing forces at feeding phase). The CVC position will be found by onedimensional search adjusting the desired roll gap profile. If actuator limits are violated the bending is modified for the next iteration step. 為計(jì)算 ， 穿帶階段的 軋輥 彎曲值，首先應(yīng)設(shè)置 到稍小的正值 （接近給料階段的平衡力）。 通過一維搜索找到 CVC位置， 調(diào)整 輥縫形狀以達(dá)到希望值。如果超出執(zhí)行機(jī)構(gòu)的限制范圍，則在下一個(gè) 迭代 階段修改軋輥 彎曲值 。 7. Adaption調(diào)整 （自適應(yīng)） Overview概述 In order to improve the prediction capability of the setup model, an online model adaption for updating coefficients and parameters is performed which considers variations of material and mill behavior. 為了提高設(shè)定模型預(yù) 測(cè) 的能力，執(zhí)行更新系數(shù)和參數(shù)的在線模型調(diào)整，它考慮不同的材料和軋機(jī)性能 的 變化 。 The adaption considers process variations and disturbances like product changes (. percentage of alloy elements varies), changes of strip or roll roughness, thermal effects and systematic model errors. 調(diào)整考慮了工藝的變化和干 擾 ， 像產(chǎn)品更換（例如合金元素 百分率的 變化），帶材的更換或軋輥的粗糙 度 變化 ，熱效應(yīng)和系統(tǒng)模型誤差。 During rolling measured data is acquired in a time based cycle (see “Input Variables” in Fig.). After a plausibility check and filtering the recalculation (Box “Rolling Model” in Fig.) and adaption is started for the current coil in order to make the adaption coefficients and parameters available for the next pass to be rolled (passtopassadaption). 在軋制期間， 按周期 時(shí)間 收集 測(cè)量數(shù)據(jù)（見圖里的“輸入 變量 ”）。真實(shí)性檢查