热轧带钢板凸度和板形计算及预设定建模理论研究
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摘要
热轧带钢是重要的钢材品种，广泛应用于国民经济的各个领域，对整个钢铁工业的技术进步有着重要影响。随着轧机设备的改进和现代轧制技术的进步，市场对热轧板带产品精度的要求不断提高。板带的几何尺寸精度包括纵向厚差、横向厚差和平直度三大质量指标，其中板带纵向厚差控制技术已得到成熟应用，由于影响板形和板凸度的因素复杂多变，在基础理论、检测技术和控制技术方面都有许多问题没有得到根本解决。本文据此对板凸度和板形理论开展了更加深入和细致的研究，探索各种影响因素与板凸度及板形之间的相互关系，建立板形预测、分析和设定的高精度数学模型。
板形理论主要包括金属塑性变形和辊系弹性变形两大模块。在金属塑性变形方面，本文采用变分法求解金属在辊缝中的横向流动，进而确定前后张力的横向分布，通过对欧拉方程中定积分的取值范围进行研究，提出适用于热轧过程的计算方法，提高了横向位移的计算精度。在辊系弹性变形方面，针对传统压扁模型在轧辊端部较大的计算误差，推导了综合采用平面应变假设和平面应力假设的新模型，改善了辊间压扁计算的端部效应。本文还对轧辊热凸度和磨损进行了研究，分析了工作辊窜动对热凸度分布的影响。
在理论分析的基础上，综合采用基于变分法的金属变形模型、基于影响函数法的辊系变形模型、轧辊热凸度及磨损模型，通过迭代求解，建立了板形离线模拟的解析模型。通过对程序迭代过程的研究，从初值设定、矩阵求解等方面提出了提高迭代效率、缩短计算时间的方法和措施。通过离线模拟计算，将板形及其调控问题考虑在内，对辊系尺寸的设计和轧制规程的制定进行了分析，提出了多目标的优化方案。
为了进一步精确模拟板带轧制过程，同时校验解析模型的准确性，采用基于Lagrange乘数法的刚塑性有限元法作为金属塑性变形的分析模型，采用影响函数法分析辊系弹性变形，通过耦合迭代的方案，开发和完善了适用于多机型轧制过程的三维耦合模拟系统。针对有限元法计算时间过长的问题，将解析模型与三维有限元耦合模型相结合，优化了程序迭代过程，在保证计算精度的基础上，提出了有效提高计算效率的快速算法。
以宝钢2050热轧线若干轧制计划的在线和实测数据为基础，从不考虑热凸度和磨损，考虑热凸度和磨损两方面对板凸度进行了模拟计算；为详细对比板厚分布结果，在宝钢1780热轧线上进行了轧制测量实验，充分验证了板形离线模拟系统的准确性。
对宝钢2050热轧线板形预设定有载辊缝的计算模型进行了研究，通过大量离线模拟计算，修正了在线模型中的板凸度计算基值及各因素影响率系数，减小了预设定模型中板凸度的计算误差。针对原模型中仅采用二次曲线对轧制力横向分布进行描述的问题，本文直接采用考虑金属塑性变形的耦合模型，分析各因素对板凸度的影响，建立了新的板形预设定有载辊缝凸度模型，具有较高的计算精度。
运用Visual Basic与C++混合编程技术，开发了一套界面友好、操作方便、计算高效的板形分析软件。该软件可用于对带钢热连轧各种机型进行板凸度和平直度分析，计算辊系尺寸、轧辊凸度、弯辊力、张力、轧制力及来料凸度等对板凸度和平直度的影响系数，为板形控制机理分析、在线板形模型开发与维护提供有效平台。
Hot rolled steel strip is an important type of steel product, which is widely used invarious fields of the national economy and has an important impact on technologicalprogress for the entire steel industry. With the improvement of mill equipment andadvance of modern rolling technology, the market puts more and more attentions on theaccuracy of hot rolled strip products. The geometry accuracy of strip includinglongitudinal thickness difference, transverse thickness difference and flatness three fields.Because of the complex influence factors of plate shape and crown, many problems in thebasic theory, shape detection and control technology have not been solved. So in thispaper, the basic theory of strip shape and crown, the relationship between the variousinfluence factors and the shape are studied systemically and deeply, and mathematicalmodels of shape analysis, forecasting and setting are established precisely.
The theory of plate shape mainly includes two modules: metal plastic deformationand rolls elastic deformation. Variational method is used to solve the lateral flow of metalin the roll gap, and the lateral distribution of tension is obtained. Through the research ofthe range of the definite integral in the Euler equation, the calculation method is proposedto adapt to the hot rolling, and the accuracy of the lateral displacement is improved. Inrolls elastic deformation, for the errors of roll ends flattening calculated by traditionalflattening models, a new model is derived by using a combination of plane strainassumption and plane stress assumption, which improves the calculation accuracy of theflattening between rolls. Thermal crown and roll wear are also studied, and the impact ofthermal crown distribution caused by the work roll shifting is analyzed.
Based on the theoretical analysis, a scientific off-line analytic system of plate shapeis established by using variational method to simulate metal plastic deformation, usinginfluence function method to calculate rolls elastic deformation, considering thermalcrown and roll wear. According to the research of the program iterative process, theiterative efficiency is increased and the calculation time is reduced by the improvement ofinitial value setting and matrix solving. Then, taking good shape as an important goal, a new optimization scheme of the rolls size and rolling schedule is proposed bymulti-objective optimization.
In order to simulate the rolling process accurately, on the basis of others' research,using three dimensional rigid plastic FEM base on Lagrange multiplier to analysis theplastic deformation of the strip, influence function method to analysis the rolls deflection,a coupled simulation system is developed by virtue of iteration scheme. Because of thelow efficiency of the finite element method, a rapid algorithm is proposed bycombination of the analytic model and three-dimensional finite element coupling model,and the iterative process is optimized based on the calculation accuracy.
To verify the accuracy of the off-line computational models of plate shape, stripcrown with consideration and without consideration of thermal crown and wear arecalculated based on the experimental data of Baosteel2050hot rolling line. For detailedcomparison of thickness distribution, the rolling measurement experiment is conducted inBaosteel1780hot rolling line.
Pre-set model of plate shape in Baosteel2050hot rolling line is studied, and theinfluence coefficients are modified by offline simulation, so the calculation errors isreduced. The original model only uses the quadratic curve to describe the lateraldistribution of rolling force and this will cause some errors. So, in this paper, by using thecoupled model to calculate the rolling force distribution and analyze the influence ofdifferent factors, a new model which has high precision is established to calculate stripcrown of pre-set model.
An off-line simulation software of plate shape which has friendly interfaces andhigh-efficiency operation is developed by taking Visual Basic and C++as program tools.The software can simulate the strip crown and flatness in hot rolling, calculate theinfluence coefficient of rolls size, roll crown, bending force, tension, rolling force, stripinlet crown and so on, and offer an effective platform for mechanism analysis of shapecontrol and on-line shape model.
板形理论主要包括金属塑性变形和辊系弹性变形两大模块。在金属塑性变形方面，本文采用变分法求解金属在辊缝中的横向流动，进而确定前后张力的横向分布，通过对欧拉方程中定积分的取值范围进行研究，提出适用于热轧过程的计算方法，提高了横向位移的计算精度。在辊系弹性变形方面，针对传统压扁模型在轧辊端部较大的计算误差，推导了综合采用平面应变假设和平面应力假设的新模型，改善了辊间压扁计算的端部效应。本文还对轧辊热凸度和磨损进行了研究，分析了工作辊窜动对热凸度分布的影响。
在理论分析的基础上，综合采用基于变分法的金属变形模型、基于影响函数法的辊系变形模型、轧辊热凸度及磨损模型，通过迭代求解，建立了板形离线模拟的解析模型。通过对程序迭代过程的研究，从初值设定、矩阵求解等方面提出了提高迭代效率、缩短计算时间的方法和措施。通过离线模拟计算，将板形及其调控问题考虑在内，对辊系尺寸的设计和轧制规程的制定进行了分析，提出了多目标的优化方案。
为了进一步精确模拟板带轧制过程，同时校验解析模型的准确性，采用基于Lagrange乘数法的刚塑性有限元法作为金属塑性变形的分析模型，采用影响函数法分析辊系弹性变形，通过耦合迭代的方案，开发和完善了适用于多机型轧制过程的三维耦合模拟系统。针对有限元法计算时间过长的问题，将解析模型与三维有限元耦合模型相结合，优化了程序迭代过程，在保证计算精度的基础上，提出了有效提高计算效率的快速算法。
以宝钢2050热轧线若干轧制计划的在线和实测数据为基础，从不考虑热凸度和磨损，考虑热凸度和磨损两方面对板凸度进行了模拟计算；为详细对比板厚分布结果，在宝钢1780热轧线上进行了轧制测量实验，充分验证了板形离线模拟系统的准确性。
对宝钢2050热轧线板形预设定有载辊缝的计算模型进行了研究，通过大量离线模拟计算，修正了在线模型中的板凸度计算基值及各因素影响率系数，减小了预设定模型中板凸度的计算误差。针对原模型中仅采用二次曲线对轧制力横向分布进行描述的问题，本文直接采用考虑金属塑性变形的耦合模型，分析各因素对板凸度的影响，建立了新的板形预设定有载辊缝凸度模型，具有较高的计算精度。
运用Visual Basic与C++混合编程技术，开发了一套界面友好、操作方便、计算高效的板形分析软件。该软件可用于对带钢热连轧各种机型进行板凸度和平直度分析，计算辊系尺寸、轧辊凸度、弯辊力、张力、轧制力及来料凸度等对板凸度和平直度的影响系数，为板形控制机理分析、在线板形模型开发与维护提供有效平台。
Hot rolled steel strip is an important type of steel product, which is widely used invarious fields of the national economy and has an important impact on technologicalprogress for the entire steel industry. With the improvement of mill equipment andadvance of modern rolling technology, the market puts more and more attentions on theaccuracy of hot rolled strip products. The geometry accuracy of strip includinglongitudinal thickness difference, transverse thickness difference and flatness three fields.Because of the complex influence factors of plate shape and crown, many problems in thebasic theory, shape detection and control technology have not been solved. So in thispaper, the basic theory of strip shape and crown, the relationship between the variousinfluence factors and the shape are studied systemically and deeply, and mathematicalmodels of shape analysis, forecasting and setting are established precisely.
The theory of plate shape mainly includes two modules: metal plastic deformationand rolls elastic deformation. Variational method is used to solve the lateral flow of metalin the roll gap, and the lateral distribution of tension is obtained. Through the research ofthe range of the definite integral in the Euler equation, the calculation method is proposedto adapt to the hot rolling, and the accuracy of the lateral displacement is improved. Inrolls elastic deformation, for the errors of roll ends flattening calculated by traditionalflattening models, a new model is derived by using a combination of plane strainassumption and plane stress assumption, which improves the calculation accuracy of theflattening between rolls. Thermal crown and roll wear are also studied, and the impact ofthermal crown distribution caused by the work roll shifting is analyzed.
Based on the theoretical analysis, a scientific off-line analytic system of plate shapeis established by using variational method to simulate metal plastic deformation, usinginfluence function method to calculate rolls elastic deformation, considering thermalcrown and roll wear. According to the research of the program iterative process, theiterative efficiency is increased and the calculation time is reduced by the improvement ofinitial value setting and matrix solving. Then, taking good shape as an important goal, a new optimization scheme of the rolls size and rolling schedule is proposed bymulti-objective optimization.
In order to simulate the rolling process accurately, on the basis of others' research,using three dimensional rigid plastic FEM base on Lagrange multiplier to analysis theplastic deformation of the strip, influence function method to analysis the rolls deflection,a coupled simulation system is developed by virtue of iteration scheme. Because of thelow efficiency of the finite element method, a rapid algorithm is proposed bycombination of the analytic model and three-dimensional finite element coupling model,and the iterative process is optimized based on the calculation accuracy.
To verify the accuracy of the off-line computational models of plate shape, stripcrown with consideration and without consideration of thermal crown and wear arecalculated based on the experimental data of Baosteel2050hot rolling line. For detailedcomparison of thickness distribution, the rolling measurement experiment is conducted inBaosteel1780hot rolling line.
Pre-set model of plate shape in Baosteel2050hot rolling line is studied, and theinfluence coefficients are modified by offline simulation, so the calculation errors isreduced. The original model only uses the quadratic curve to describe the lateraldistribution of rolling force and this will cause some errors. So, in this paper, by using thecoupled model to calculate the rolling force distribution and analyze the influence ofdifferent factors, a new model which has high precision is established to calculate stripcrown of pre-set model.
An off-line simulation software of plate shape which has friendly interfaces andhigh-efficiency operation is developed by taking Visual Basic and C++as program tools.The software can simulate the strip crown and flatness in hot rolling, calculate theinfluence coefficient of rolls size, roll crown, bending force, tension, rolling force, stripinlet crown and so on, and offer an effective platform for mechanism analysis of shapecontrol and on-line shape model.
引文
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