CN117696636A - 一种轧制钢卷数叠加下轧辊温度场与热辊型的预报方法 - Google Patents
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Abstract
本发明涉及一种轧制钢卷数叠加下轧辊温度场与热辊型的预报方法，属于热连轧机组技术领域。本发明的技术方案是：收集轧制过程中的相关参数，然后通过计算分析得到工作辊和支撑辊的辊形,从而合理的调整轧制工艺参数,输出支撑辊与工作辊的温度场T(x)与热辊型M(x)热辊型曲线。本发明的有益效果是：能够充分考虑到冷却水以及轧制钢卷数叠加状态下的影响，对热连轧轧辊的温度场与热辊型进行计算，可以实现对板凸度和板形的良好控制，过分析得到工作辊、支撑辊的辊形，合理的调整轧制工艺参数，提高热连轧生产过程中板形的控制精度与质量，进而提高现场带钢生产的经济效益。
Description
技术领域
本发明涉及一种轧制钢卷数叠加下轧辊温度场与热辊型的预报方法，属于热连轧机组技术领域。
背景技术
随着科学技术的不断发展,我国的机械制造业也有了长足的发展,顾客对汽车,家具等的需求不断增长,这就对带钢的板形以及性能有了更高的要求,在此要求下中厚板轧机也得到了长足的进步,在需求急剧增加的当下,保证板形的精度,并提高带钢的生产效率,是企业保持核心竞争力的关键。通过对现有的相关文献进行分析，其研究内容主要是针对轧辊温度场或者热辊型的研究，通过预报工作辊的热辊型情况预测出口板形；或者是针对冷制进行轧辊温度场的研究，并没有考虑冷却水以及轧制钢卷叠加状态对的影响，使预报的板形出现一定的偏差。温度是热轧带钢生产过程中极其重要的参数之一,精确预报出轧辊温度场以及热辊型是保证带钢板形、厚度以及宽度良好的关键，对热连轧轧辊的温度场与热辊型进行计算，从而实现对板凸度和板形的控制，提高带钢质量，为生产现场带来经济效益。
发明内容
本发明目的是提供一种轧制钢卷数叠加下轧辊温度场与热辊型的预报方法，能够充分考虑到冷却水以及轧制钢卷数叠加状态下的影响，对热连轧轧辊的温度场与热辊型进行计算，可以实现对板凸度和板形的良好控制，过分析得到工作辊、支撑辊的辊形，合理的调整轧制工艺参数，提高热连轧生产过程中板形的控制精度与质量，进而提高现场带钢生产的经济效益，解决背景技术中存在的上述问题。
本发明的技术方案是：
一种轧制钢卷数叠加下轧辊温度场与热辊型的预报方法，收集轧制过程中的相关参数，利用有限差分法对热传导方程进行差分；建立工作辊温度场边界条件方程；判断当前轧制钢卷数工作辊温度场是否已经求出；求解轧辊温度场以及热凸度；求解当前钢卷数支撑辊温度场边界条件；求出支撑辊温度场与热凸度分布；判断当前轧制钢卷数是否达到目标轧制钢卷数N；输出支撑辊与工作辊的温度场T(x)与热辊型M(x)热辊型曲线。
包含以下步骤：
(A):收集轧制过程中相关参数；主要为特定机架工作辊辊身长度lw、工作辊直径dw、辊颈长度lw2、辊颈直径dw2、圆柱体的比热Cp、支撑辊直径Db、支撑辊辊身长度lb、支撑辊辊颈长度lb2、支撑辊辊颈直径Db2、热导率λt、轧辊密度ρ、带材宽度B、轧件温度TA、环境温度TC、冷却水温度TB、轴承温度TD、工作辊辊身轧制部分的热交换系数αA、工作辊辊身非轧制部分的热交换系数αB、支撑辊辊身与工作辊接触部分的热交换系数αf、辊颈部分的热交换系数αD、辊肩部分的热交换系数αC；
(B):利用有限差分法对热传导方程进行差分；根据温度场的波动仅发生在极薄的辊面层中，且任意垂直于轴的截面内的圆周方向几乎无温度波动的情况；因此，可以将轧辊的温度场简化为二维问题,工作辊的热传导方程简化为：
其中：T为轧辊温度，℃；t为时间，s；c为轧辊的比热，J/(kg·℃)；ρ为轧辊的密度，kg/m3；λ为轧辊的热传导率，J/(m·s·℃)；r为轧辊的径向坐标值，m；z为轧辊的轴向坐标值，m；
通过运用有限差分法将轧辊划分为若等个网格，其中r(j)为径向坐标，z(i)为轴向坐标，原点位于轧辊的重心上，由于轧辊温度相对于轴线和辊身中部呈对称分布，因此通过轧辊轴线所作剖面的四分之一作为研究对象，建立起整个网格系统温度分布的差分格式：
对于工作辊辊身轧制部分，轧辊外部节点由牛顿冷却定律代替，而对于轧辊内部的热传导，其热流量则用傅里叶定律表示；同理，根据能量守恒关系，可以分别写出工作辊非轧制部分边界格点、辊肩部分边界格点、辊颈部分边界格点、辊端部分边界格点、辊身非轧制部分与辊肩部分联结的角节点、辊颈部分与辊端部分联结的角节点对应的差分方程；所有格点以及角节点的差分方程联立，构成求解工作辊温度场的线性方程组，通过每经过一段时间Δt，求解一次此方程组从而得到工作辊的瞬态温度场；
(C):建立工作辊温度场边界条件方程；在轧制过程中，工作辊与周围介质：高温轧件、空气、冷却水以及支撑辊不断交替接触，因此工作辊与周围介质之间存在热流输入与热流输出，对于热轧来说，工作辊的热量输入流主要为工作辊与轧件间的接触热传导、轧件和工作辊间的摩擦热、轧件的塑性变形热，而从工作辊带走的热量主要为冷却水与轧辊表面的对流换热占主要部分；
为了确定工作辊热传导方程的边界条件，现研究工作辊与周围介质的关系，建立工作辊温度场边界条件方程如下所示：
(D):判断当前轧制钢卷数工作辊温度场是否已经求出；若没有求出，则执行E步骤，若已求出则执行G步骤；
(E):求解轧辊温度场以及热凸度；根据轧辊温度场边界条件，求解出轧辊的温度场进而对轧辊热辊型的分析，假设轧辊为无限长圆柱体，其温度相对于轧辊轴线对称分布，设轧辊的初始温度为T0(r,z)，则轧辊由于热膨胀形成的热辊型为
式中：βt为热膨胀系数；ν为轧辊材料的泊松比；T为差分法得到的温度分布；
在分析热辊型的基础上加入冷却水对轧辊热凸度的影响，在工作辊辊身边界处，冷却水与辊身通过对流换热形式进行表面热交换，而对于流体换热系数的影响因素是多样的，比如流体的流速、动力粘度、比热容等，因此建立在相似理论的基础上，通过实验建立影响冷却水热交换的影响函数
式中：k为冷却水对流换热系数,W/(m2·℃)；v为冷却水流速，m/s；λ为冷却水的导热系数，W/(m·k)；d为冷却水槽的当量直径，m；Cp为冷却水的比热容，J/(kg·k)；μ为冷却水的动力粘度，m2/s；α、β、a、b为水冷系数；
对于上述建立的冷却水对流换热系数数学模型，在温度场与热辊型计算程序中特别建立了冷却水分段冷却控制系统，通过对公式中冷却水流速v建立数组v[i]，控制轧辊辊身每一段冷却水的流速，并将冷却水温度与冷却水流速作为双变量调节，实现对轧辊轧制时单元辊身温度的精准调控；
(F):求解当前钢卷数支撑辊温度场边界条件，将此时工作辊辊身温度传递到支撑辊的温度作为支撑辊辊身边界条件，返回步骤A直到步骤D满足要求，执行步骤G；
(G)求出支撑辊温度场与热凸度分布；支撑辊与工作辊求解思路相同，只是在支撑辊的与工作辊接触部分的差分方程中，此处的边界条件由工作辊辊身温度代替了高温轧件温度。支撑辊热凸度求解方法与工作辊热凸度求解方法相同，如步骤C与步骤E；
(H)判断当前轧制钢卷数是否达到目标轧制钢卷数N，如达到则输出支撑辊与工作辊的温度场与热辊型曲线，若当前轧制钢卷n<N,则令n＝n+1返回到步骤(A)，再次执行该循环，直到当前轧制钢卷数达到目标轧制钢卷数；
(I)输出支撑辊与工作辊的温度场T(x)与热辊型M(x)热辊型曲线。
本发明的有益效果是：能够充分考虑到冷却水以及轧制钢卷数叠加状态下的影响，对热连轧轧辊的温度场与热辊型进行计算，可以实现对板凸度和板形的良好控制，过分析得到工作辊、支撑辊的辊形，合理的调整轧制工艺参数，提高热连轧生产过程中板形的控制精度与质量，进而提高现场带钢生产的经济效益。
附图说明
附图1为本发明的流程图；
附图2为本发明实施例1中支撑辊的温度场与热辊型曲线图；
附图3为本发明实施例1中工作辊的温度场与热辊型曲线图；
附图4为本发明实施例2中支撑辊的温度场与热辊型曲线图；
附图5为本发明实施例2中工作辊的温度场与热辊型曲线图。
具体实施方式
为了使发明实施案例的目的、技术方案和优点更加清楚，下面将结合实施案例中的附图，对本发明实施案例中的技术方案进行清晰的、完整的描述，显然，所表述的实施案例是本发明一小部分实施案例，而不是全部的实施案例，基于本发明中的实施案例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施案例，都属于本发明保护范围。
实施例1：
以钢种为510L,规格为1580mm×43.05mm(宽度×厚度)的产品为例,对本发明所述一种考虑冷却水以及轧制钢卷叠加状态下轧辊温度场与热辊型的预报方法进行实例说明。
收集轧制过程中相关参数主要为特定机架工作辊辊身长度lw＝2350mm、工作辊直径dw＝850mm、辊颈长度lw2＝950mm、辊颈直径dw2＝510mm、圆柱体的比热Cp＝460J/(kg℃)、支撑辊直径Db＝1600mm、支撑辊辊身长度lb＝2050mm、支撑辊辊颈长度lb2＝1150mm、支撑辊辊颈直径Db2＝1000mm、热导率λt＝20W/(mK)、轧辊密度ρ＝7.8g/mm3、带材宽度B＝1580mm、轧件温度TA＝900℃、环境温度TC＝25℃、冷却水温度TB＝30℃、轴承温度TD＝60℃、工作辊辊身轧制部分的热交换系数αA＝0.0015、工作辊辊身非轧制部分的热交换系数αB＝0.01163、支撑辊辊身与工作辊接触部分的热交换系数αf＝0.00125、辊颈部分的热交换系数αD＝0.0021、辊肩部分的热交换系数αC＝0.0023。根据以上的执行步骤,分别记录轧制钢卷数为1、5、10卷时,工作辊与支撑辊温度场与热辊型在不同轧制带钢卷数变化数据:
当轧制钢卷数为1时工作辊温度场Tw为
＝[28.79655837,28.66976171,29.93721552,32.29983873,35.48407129,39.24187414,43.35072918,47.61363933,51.85912849,55.94124156,59.73954442,63.15912393,66.13058797,68.61006539,70.57920603,72.04518072,73.0406813,73.62392058,73.87863237,73.91407146,73.86501363,73.89175568,74.18011536,73.89175568,73.86501363,73.91407146,73.87863237,73.62392058,73.0406813,72.04518072,70.57920603,68.61006539,66.13058797,63.15912393,59.73954442,55.94124156,51.85912849,47.61363933,43.35072918,39.24187414,35.48407129,32.29983873,29.93721552,28.66976171,28.79655837],支撑辊温度场
Tb＝[24.99999,25.00001,25.12157,25.33839,25.62649,25.96409,26.33168,26.71199,27.08999,27.4529,27.79019,28.09356,28.35699,28.57665,28.75102,28.88076,28.96884,29.02042,29.04294,29.04607,29.04173,29.0441,29.06957,29.0441,29.04173,29.04607,29.04294,29.02042,28.96884,28.88076,28.75102,28.57665,28.35699,28.09356,27.79019,27.4529,27.08999,26.71199,26.33168,25.96409,25.62649,25.33839,25.12157,25.00001,24.99999],当轧制钢卷数为5时,工作辊温度场
Tw＝[29.78461316,29.62819731,30.85040265,33.15602302,36.27502726,39.96255919,43.99893765,48.18965643,52.36538435,56.38196519,60.12041775,63.48693579,66.41288808,68.85481837,70.79444543,72.23866298,73.21953975,73.79431947,74.04542084,74.08043758,74.03213836,74.05846688,74.34254181,74.05846688,74.03213836,74.08043758,74.04542084,73.79431947,73.21953975,72.23866298,70.79444543,68.85481837,66.41288808,63.48693579,60.12041775,56.38196519,52.36538435,48.18965643,43.99893765,39.96255919,36.27502726,33.15602302,30.85040265,29.62819731,29.78461316],支撑辊温度场
Tb＝[24.9999791,25.00002582,25.23497701,25.65409359,26.2109758,26.86356323,27.5741348,28.30930874,29.04004262,29.74163334,30.39371712,30.98026953,31.48960544,31.91437907,32.25158398,32.50255301,32.67295839,32.77281164,32.81646361,32.8226045,32.81426383,32.81881044,32.8679525,32.81881044,32.81426383,32.8226045,32.81646361,32.77281164,32.67295839,32.50255301,32.25158398,31.91437907,31.48960544,30.98026953,30.39371712,29.74163334,29.04004262,28.30930874,27.5741348,26.86356323,26.2109758,25.65409359,25.23497701,25.00002582,24.9999791],当轧制钢卷数为10时工作辊温度场
Tw＝[28.79655837,28.66976171,29.93721552,32.29983873,35.48407129,39.24187414,43.35072918,47.61363933,51.85912849,55.94124156,59.73954442,63.15912393,66.13058797,68.61006539,70.57920603,72.04518072,73.0406813,73.62392058,73.87863237,73.91407146,73.86501363,73.89175568,74.18011536,73.89175568,73.86501363,73.91407146,73.87863237,73.62392058,73.0406813,72.04518072,70.57920603,68.61006539,66.13058797,63.15912393,59.73954442,55.94124156,51.85912849,47.61363933,43.35072918,39.24187414,35.48407129,32.29983873,29.93721552,28.66976171,28.79655837],支撑辊温度场
Tb＝[24.99998913,25.00001342,25.12156596,25.33839366,25.96408972,26.33167936,26.71198677,27.08998632,27.45289786,27.79018675,28.09356384,28.35698546,28.57665343,28.75101506,28.88076316,28.96883603,29.02041744,29.04293668,29.0460685,29.04173317,29.04409641,29.06956948,29.04409641,29.04173317,29.0460685,29.04293668,29.02041744,28.96883603,28.88076316,28.75101506,28.57665343,28.35698546,28.09356384,27.79018675,27.45289786,27.08998632,26.71198677,26.33167936,25.96408972,25.62648895,25.33839366,25.12156596,25.00001342,24.99998913]
当轧制钢卷数为1卷时,工作辊热辊型
Mw＝[0.078070961,0.106290506,0.134355004,0.161642974,0.187619773,0.211837599,0.233935493,0.253639332,0.270761837,0.285202567,0.296947924,0.306071148,0.31273232,0.317178361,0.319743035,0.320846943,0.320997529,0.320789075,0.320902706,0.322106385,0.322106385,0.322106385,0.320902706,0.320789075,0.320997529,0.320846943,0.319743035,0.317178361,0.31273232,0.306071148,0.296947924,0.285202567,0.270761837,0.253639332,0.233935493,0.211837599,0.187619773,0.161642974,0.134355004,0.106290506,0.078070961],支撑辊热辊型
Mb＝[0.002221114,0.004112085,0.006327996,0.008740744,0.011236968,0.013718043,0.016100086,0.018313949,0.020305225,0.022034245,0.02347608,0.024620538,0.025472165,0.026050249,0.026388814,0.026536623,0.02655718,0.026528724,0.026544236,0.026711433,0.026711433,0.026711433,0.026544236,0.026528724,0.02655718,0.026536623,0.026388814,0.026050249,0.025472165,0.024620538,0.02347608,0.022034245,0.020305225,0.018313949,0.016100086,0.013718043,0.011236968,0.008740744,0.006327996,0.004112085,0.002221114],当轧制钢卷数为5卷时,工作辊热辊型
Mw＝[0.091538794,0.121234956,0.149722883,0.176618072,0.201599592,0.224410091,0.244855792,0.26280649,0.278195558,0.291019944,0.301340171,0.309280337,0.315028115,0.318834754,0.321015079,0.321947487,0.322073954,0.321900029,0.321994838,0.32299108,0.32299108,0.32299108,0.321994838,0.321900029,0.322073954,0.321947487,0.321015079,0.318834754,0.315028115,0.309280337,0.301340171,0.291019944,0.278195558,0.26280649,0.244855792,0.224410091,0.201599592,0.176618072,0.149722883,0.121234956,0.091538794],支撑辊热辊型
Mb＝[0.004293274,0.007948482,0.01223187,0.016895849,0.02172131,0.026517628,0.031122659,0.035402741,0.039252695,0.042595823,0.04538391,0.047597222,0.049244507,0.050362997,0.051018404,0.051304922,0.051345229,0.051290483,0.051320326,0.05164288,0.05164288,0.05164288,0.051320326,0.051290483,0.051345229,0.051304922,0.051018404,0.050362997,0.049244507,0.047597222,0.04538391,0.042595823,0.039252695,0.035402741,0.031122659,0.026517628,0.02172131,0.016895849,0.01223187,0.007948482,0.004293274],当轧制钢卷数为10卷时,工作辊热辊型
Mw＝[0.092215858,0.121982848,0.150487623,0.177357936,0.202283909,0.225018029,0.245375155,0.263232509,0.278529686,0.291268643,0.301513708,0.309391576,0.31509131,0.31886434,0.321024464,0.321947847,0.322073023,0.321900892,0.321994722,0.322980151,0.322980151,0.322980151,0.321994722,0.321900892,0.322073023,0.321947847,0.321024464,0.31886434,0.31509131,0.309391576,0.301513708,0.291268643,0.278529686,0.263232509,0.245375155,0.225018029,0.202283909,0.177357936,0.150487623,0.121982848,0.092215858],支撑辊热辊型
Mb＝[0.005088281,0.009420568,0.014497622,0.020026067,0.025746263,0.031432306,0.03689203,0.041967004,0.046532534,0.050497663,0.053805171,0.056431572,0.058387119,0.059715802,0.060495346,0.060837212,0.0608866,0.060822444,0.060857416,0.061237925,0.061237925,0.061237925,0.060857416,0.060822444,0.0608866,0.060837212,0.060495346,0.059715802,0.058387119,0.056431572,0.053805171,0.050497663,0.046532534,0.041967004,0.03689203,0.031432306,0.025746263,0.020026067,0.014497622,0.009420568,0.005088281]。
实施例2：
以钢种为510L,规格为1580mm×15.66mm(宽度×厚度)的产品为例,对本发明所述一种考虑冷却水以及轧制钢卷叠加状态下轧辊温度场与热辊型的预报方法进行实例说明。
收集轧制过程中相关参数主要为特定机架工作辊辊身长度lw＝2350mm、工作辊直径dw＝850mm、辊颈长度lw2＝950mm、辊颈直径dw2＝510mm、圆柱体的比热Cp＝460J/(kg℃)、支撑辊直径Db＝1600mm、支撑辊辊身长度lb＝2050mm、支撑辊辊颈长度lb2＝1150mm、支撑辊辊颈直径Db2＝1000mm、热导率λt＝20W/(mK)、轧辊密度ρ＝7.8g/mm3、带材宽度B＝1580mm、轧件温度TA＝900℃、环境温度TC＝25℃、冷却水温度TB＝30℃、轴承温度TD＝60℃、工作辊辊身轧制部分的热交换系数αA＝0.0015、工作辊辊身非轧制部分的热交换系数αB＝0.01163、支撑辊辊身与工作辊接触部分的热交换系数αf＝0.00125、辊颈部分的热交换系数αD＝0.0021、辊肩部分的热交换系数αC＝0.0023。根据以上的执行步骤,分别记录轧制钢卷数为1、5、10卷时,工作辊与支撑辊温度场与热辊型在不同轧制带钢卷数变化数据:
当轧制钢卷数为1时工作辊温度场
Tw＝[28.79656484,28.66975372,29.86481249,32.09829607,35.110943,38.66767542,42.55759906,46.59400329,50.61436107,54.48032896,58.07774714,61.31663939,64.1312131,66.47985926,68.34515248,69.73385097,70.67689655,71.22941464,71.47071427,71.50428809,71.45781234,71.48314686,71.75633513,71.48314686,71.45781234,71.50428809,71.47071427,71.22941464,70.67689655,69.73385097,68.34515248,66.47985926,64.1312131,61.31663939,58.07774714,54.48032896,50.61436107,46.59400329,42.55759906,38.66767542,35.110943,32.09829607,29.86481249,28.66975372,28.79656484],支撑辊温度场
Tb＝[24.99998943,25.00001305,25.11822579,25.32909589,25.60927541,25.93760019,26.2950898,26.66494788,27.03256143,27.38550154,27.71352301,28.00856445,28.26474824,28.47838057,28.64795141,28.77413452,28.85978748,28.90995164,28.93185213,28.9348979,28.93068168,28.93298,28.95775316,28.93298,28.93068168,28.9348979,28.93185213,28.90995164,28.85978748,28.77413452,28.64795141,28.47838057,28.26474824,28.00856445,27.71352301,27.38550154,27.03256143,26.66494788,26.29508987,25.93760019,25.60927541,25.32909589,25.11822579,25.00001305,24.99998943],当轧制钢卷数为5时工作辊温度场
Tw＝[29.78461964,29.6281893,30.77775612,32.95380216,35.90064263,39.38642592,43.2031336,47.16658039,51.11641421,54.91611613,58.45300039,61.63821443,64.40673882,66.71738734,68.55280692,69.91947766,70.84771284,71.39165891,71.6292955,71.66243539,71.61672454,71.64164211,71.91050038,71.64164211,71.61672454,71.66243539,71.6292955,71.39165891,70.84771284,69.91947766,68.55280692,66.71738734,64.40673882,61.63821443,58.45300039,54.91611613,51.11641421,47.16658039,43.2031336,39.38642592,35.90064263,32.95380216,30.77775612,29.6281893,29.78461964],支撑辊温度场
Tb＝[24.99997967,25.00002512,25.22851256,25.63609865,26.17766,26.81229322,27.50331488,28.21826154,28.92888973,29.61117595,30.2453167,30.81572843,31.3110476,31.7241306,32.05205385,32.29611372,32.46182654,32.55892866,32.60137638,32.60734597,32.5992337,32.6036558,32.65144849,32.6036558,32.5992337,32.60734597,32.60137638,32.55892866,32.46182654,32.29611372,32.05205385,31.7241306,31.3110476,30.81572843,30.2453167,29.61117595,28.92888973,28.21826154,27.50331488,26.81229322,26.17766,25.63609865,25.22851256,25.00002512,24.99997967],当轧制钢卷数为10时工作辊温度场
Tw＝[29.86690233,29.67669918,30.80041473,32.95738093,35.8908453,39.36797091,43.17983637,47.14143587,51.09167911,54.89339138,58.4333135,61.62210186,64.39432838,66.70848055,68.5469614,69.91608951,70.84609903,71.39113965,71.6292766,71.66249069,71.61667825,71.6416512,71.91113697,71.6416512,71.61667825,71.66249069,71.6292766,71.39113965,70.84609903,69.91608951,68.5469614,66.70848055,64.39432838,61.62210186,58.4333135,54.89339138,51.09167911,47.14143587,43.17983637,39.36797091,35.8908453,32.95738093,30.80041473,29.67669918,29.86690233],支撑辊温度场
Tb＝[24.99997617,25.00002944,25.27082537,25.7538998,26.39578723,27.14802081,27.96713236,28.81465234,29.65710987,30.46603273,31.21794736,31.89437884,32.4818509,32.97188596,33.36100506,33.65072792,33.84757288,33.96305698,34.01369589,34.02100394,34.01149411,34.01667804,34.07306603,34.01667804,34.01149411,34.02100394,34.01369589,33.96305698,33.84757288,33.65072792,33.36100506,32.97188596,32.4818509,31.89437884,31.21794736,30.46603273,29.65710987,28.81465234,27.96713236,27.14802081,26.39578723,25.7538998,25.27082537,25.00002944,24.99997617]
当轧制钢卷数为1卷时,工作辊热辊型Mw＝[0.076748095,0.103841403,0.130586136,0.156437106,0.180927188,0.203667319,0.224346501,0.242731793,0.258668321,0.272079271,0.28296589,0.29140749,0.297561444,0.301663187,0.304026216,0.305042091,0.305180434,0.304988928,0.305093321,0.306197419,0.306197419,0.306197419,0.305093321,0.304988928,0.305180434,0.305042091,0.304026216,0.301663187,0.297561444,0.29140749,0.28296589,0.272079271,0.258668321,0.242731793,0.224346501,0.203667319,0.180927188,0.156437106,0.130586136,0.103841403,0.076748095],支撑辊热辊型Mb＝[0.002160087,0.003999101,0.006154126,0.008500581,0.010928218,0.013341123,0.015657716,0.017810751,0.019747314,0.021428828,0.022831047,0.023944059,0.024772287,0.025334487,0.02566375,0.025807498,0.025827489,0.025799815,0.025814901,0.025977504,0.025977504,0.025977504,0.025814901,0.025799815,0.025827489,0.025807498,0.02566375,0.025334487,0.024772287,0.023944059,0.022831047,0.021428828,0.019747314,0.017810751,0.015657716,0.013341123,0.010928218,0.008500581,0.006154126,0.003999101,0.002160087],当轧制钢卷数为5卷时,工作辊热辊型Mw＝[0.090211477,0.118777608,0.145941317,0.171394652,0.194884428,0.216212226,0.235234398,0.251862062,0.266061105,0.277852182,0.287310715,0.294566894,0.299805678,0.303266794,0.305244736,0.306088765,0.306202913,0.306045978,0.306131525,0.30702789,0.30702789,0.30702789,0.306131525,0.306045978,0.306202913,0.306088765,0.305244736,0.303266794,0.299805678,0.294566894,0.287310715,0.277852182,0.266061105,0.251862062,0.235234398,0.216212226,0.194884428,0.171394652,0.145941317,0.118777608,0.090211477],支撑辊热辊型Mb＝[0.004175161,0.007729807,0.011895349,0.016431008,0.021123703,0.025788054,0.030266376,0.034428685,0.038172697,0.041423823,0.044135176,0.046287566,0.047889502,0.048977191,0.04961454,0.049893154,0.049932337,0.04987909,0.049908116,0.050221812,0.050221812,0.050221812,0.049908116,0.04987909,0.0499323370.049893154,0.04961454,0.048977191,0.047889502,0.046287566,0.044135176,0.041423823,0.038172697,0.034428685,0.030266376,0.025788054,0.021123703,0.016431008,0.011895349,0.007729807,0.004175161],当轧制钢卷数为10卷时,工作辊热辊型Mw＝[0.090888539,0.119525498,0.146706054,0.172134513,0.195568739,0.216820158,0.235753754,0.252288075,0.266395226,0.278100874,0.287484246,0.294678128,0.299868869,0.303296376,0.305254118,0.306089124,0.306201981,0.306046839,0.306131409,0.307016959,0.307016959,0.307016959,0.306131409,0.306046839,0.306201981,0.306089124,0.305254118,0.303296376,0.299868869,0.294678128,0.287484246,0.278100874,0.266395226,0.252288075,0.235753754,0.216820158,0.195568739,0.172134513,0.146706054,0.119525498,0.090888539],支撑辊热辊型Mb＝[0.004948372,0.009161529,0.014098964,0.019475367,0.025038234,0.030567872,0.035877399,0.040812741,0.045252634,0.049108625,0.052325068,0.054879129,0.056780783,0.058072814,0.058830817,0.059163196,0.059211164,0.059148744,0.05918277,0.059552883,0.059552883,0.059552883,0.05918277,0.059148744,0.059211164,0.059163196,0.058830817,0.058072814,0.056780783,0.054879129,0.052325068,0.049108625,0.045252634,0.040812741,0.035877399,0.030567872,0.025038234,0.019475367,0.014098964,0.009161529,0.004948372]。
Claims (2)
1.一种轧制钢卷数叠加下轧辊温度场与热辊型的预报方法，其特征在于：收集轧制过程中的相关参数，利用有限差分法对热传导方程进行差分；建立工作辊温度场边界条件方程；判断当前轧制钢卷数工作辊温度场是否已经求出；求解轧辊温度场以及热凸度；求解当前钢卷数支撑辊温度场边界条件；求出支撑辊温度场与热凸度分布；判断当前轧制钢卷数是否达到目标轧制钢卷数N；输出支撑辊与工作辊的温度场T(x)与热辊型M(x)热辊型曲线。
2.根据权利要求1所述的一种轧制钢卷数叠加下轧辊温度场与热辊型的预报方法，其特征在于包含以下步骤：
(A):收集轧制过程中相关参数；包括特定机架工作辊辊身长度lw、工作辊直径dw、辊颈长度lw2、辊颈直径dw2、圆柱体的比热Cp、支撑辊直径Db、支撑辊辊身长度lb、支撑辊辊颈长度lb2、支撑辊辊颈直径Db2、热导率λt、轧辊密度ρ、带材宽度B、轧件温度TA、环境温度TC、冷却水温度TB、轴承温度TD、工作辊辊身轧制部分的热交换系数αA、工作辊辊身非轧制部分的热交换系数αB、支撑辊辊身与工作辊接触部分的热交换系数αf、辊颈部分的热交换系数αD和辊肩部分的热交换系数αC；
(B):利用有限差分法对热传导方程进行差分；将轧辊的温度场简化为二维问题，工作辊的热传导方程简化为：
其中：T为轧辊温度，℃；t为时间，s；c为轧辊的比热，J/(kg·℃)；ρ为轧辊的密度，kg/m3；λ为轧辊的热传导率，J/(m·s·℃)；r为轧辊的径向坐标值，m；z为轧辊的轴向坐标值，m；
通过运用有限差分法将轧辊划分为若等个网格，其中r(j)为径向坐标，z(i)为轴向坐标，原点位于轧辊的重心上，由于轧辊温度相对于轴线和辊身中部呈对称分布，因此通过轧辊轴线所作剖面的四分之一作为研究对象，建立起整个网格系统温度分布的差分格式：
对于工作辊辊身轧制部分，轧辊外部节点由牛顿冷却定律代替，而对于轧辊内部的热传导，其热流量则用傅里叶定律表示；同理，根据能量守恒关系，可以分别写出工作辊非轧制部分边界格点、辊肩部分边界格点、辊颈部分边界格点、辊端部分边界格点、辊身非轧制部分与辊肩部分联结的角节点、辊颈部分与辊端部分联结的角节点对应的差分方程；所有格点以及角节点的差分方程联立，构成求解工作辊温度场的线性方程组，通过每经过一段时间Δt，求解一次此方程组从而得到工作辊的瞬态温度场；
(C):建立工作辊温度场边界条件方程；建立工作辊温度场边界条件方程如下所示：
(D):判断当前轧制钢卷数工作辊温度场是否已经求出；若没有求出，则执行E步骤，若已求出则执行G步骤；
(E):求解轧辊温度场以及热凸度；根据轧辊温度场边界条件，求解出轧辊的温度场进而对轧辊热辊型的分析，假设轧辊为无限长圆柱体，其温度相对于轧辊轴线对称分布，设轧辊的初始温度为T0(r,z)，则轧辊由于热膨胀形成的热辊型为
式中：βt为热膨胀系数；ν为轧辊材料的泊松比；T为差分法得到的温度分布；
建立在相似理论的基础上，通过实验建立影响冷却水热交换的影响函数
式中：k为冷却水对流换热系数,W/(m2·℃)；v为冷却水流速，m/s；λ为冷却水的导热系数，W/(m·k)；d为冷却水槽的当量直径，m；Cp为冷却水的比热容，J/(kg·k)；μ为冷却水的动力粘度，m2/s；α、β、a、b为水冷系数；
对于上述建立的冷却水对流换热系数数学模型，在温度场与热辊型计算程序中特别建立了冷却水分段冷却控制系统，通过对公式中冷却水流速v建立数组v[i]，控制轧辊辊身每一段冷却水的流速，并将冷却水温度与冷却水流速作为双变量调节，实现对轧辊轧制时单元辊身温度的精准调控；
(F):求解当前钢卷数支撑辊温度场边界条件，将此时工作辊辊身温度传递到支撑辊的温度作为支撑辊辊身边界条件，返回步骤A直到步骤D满足要求，执行步骤G；
(G)：求出支撑辊温度场与热凸度分布；支撑辊与工作辊求解思路相同，只是在支撑辊的与工作辊接触部分的差分方程中，此处的边界条件由工作辊辊身温度代替了高温轧件温度；支撑辊热凸度求解方法与工作辊热凸度求解方法相同，如步骤C与步骤E；
(H)：判断当前轧制钢卷数是否达到目标轧制钢卷数N，如达到则输出支撑辊与工作辊的温度场与热辊型曲线，若当前轧制钢卷n<N,则令n＝n+1返回到步骤(A)，再次执行该循环，直到当前轧制钢卷数达到目标轧制钢卷数；
(I)：输出支撑辊与工作辊的温度场T(x)与热辊型M(x)热辊型曲线。
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