多辊轧机板形控制理论及实验研究
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摘要
在板带材生产中，板形控制理论对于改进带钢生产工艺，提升带钢质量至关重要。辊系弹性变形理论是板形控制理论的核心模型之一。辊系变形主要包括轧辊弯曲变形和辊间压扁变形。以影响函数法为基础的轧辊弯曲模型计算精度较高，且已得到广泛应用；而目前的辊间压扁模型仍存在理论缺陷，精度较低，这大大制约了板带材质量的提高。为了提高辊系变形计算精度，完善板形控制理论，本文提出了一种新型的辊间压扁解析模型。
该辊间压扁模型基于边界积分方程法推导而来，将轧辊视为有限长度的半无限体，对该半无限体的两侧面位移场进行有限元模拟，并建立侧面位移分布函数。最后通过求解边界积分方程，得到辊间压扁分布值。通过与有限元法、半无限体模型、费普尔公式进行对比，验证了新型辊间压扁模型的准确性。为了该模型的实际应用，本文对模型进行了离散化处理；为了提高该模型的计算效率，文中采用数学多项式对模型中的数值积分项进行了数值拟合。通过将半无限体模型与新型辊间压扁模型对比，文中给出了半无限体模型的计算误差以及适用范围。
为了进一步研究新型辊间压扁模型的影响效果，将其分别应用到四、六辊轧机辊系变形计算中，通过耦合辊间压扁变形与轧辊轴线弯曲变形、轧辊与带钢之间压扁变形得到综合的辊系弹性变形。所得结果与有限元法、半无限体模型、费普尔公式等不同方法所得结果进行对比验证。而后分析不同窜辊量、弯辊力、压下量、板带宽度等工艺条件下，辊间压力、辊间压扁、工作辊出口辊缝等分布值的变化规律。而后，针对在极薄带钢轧制过程中极易出现的上下工作辊端压靠现象，应用有限长半无限体压扁理论，推导了全新的工作辊辊端压靠模型，以四辊轧机为例，采用本文推导的基于有限长半无限体压扁理论的辊系变形模型，耦合基于变分法的金属塑性变形模型，得到了全新的四辊轧机板形控制模型。最后，应用该耦合模型分别就考虑压靠与否、工作辊直径、板宽、弯辊力、压下量等因素对轧制力、压靠力、辊间压力、前张力、出口厚度分布的影响规律进行了深入研究。
以极薄带钢轧机的常用机型二十辊轧机为研究对象，针对二十辊轧机辊系塔形布置、辊间接触复杂、压扁位置众多等特点，建立全新的二十辊轧机的板形控制模型。将新型辊间压扁模型考虑应用其中，并考虑了外层轧辊分段支撑的影响。以二十辊实验室精密轧机为例，分析了第一中间辊窜辊、锥段长度、工作辊直径及辊凸度、第二中间非传动辊直径及辊凸度、ASU调节量、张力大小等因素对带钢出口厚度、轧制力分布、辊间压力分布等的影响规律。
最后，在二十辊实验室精密轧机上开展轧制过程实验研究。针对二十辊轧机轧制力难以测量的问题，提出了一种采用机架贴应变片，间接标定轧制力的测量方法。基于该轧制力测量方法，以厚度为0.4mm的薄钢带为原料，改变板宽、第一中间辊锥度参数、张力、压下量等因素进行二十辊轧机板带轧制实验，研究带钢出口板形的变化规律，并与本文理论模型计算板形状况进行对比验证，所得实验结果和计算结果较为吻合。以厚度为0.04mm的普碳钢极薄带为原料，开展极薄带钢轧制实验研究，改变压下量、第一中间辊锥度、锥长等条件，探索极薄带轧制过程相关因素的影响规律，并采用本文所推导的计算模型进行理论分析，得出了一套较为合理的极薄带轧制工艺及方法。
In the strip rolling process, the plate shape control technology plays a veryimportant role in improving the product quality. Roll deformation theory is the core partof shape control theories, which includes roll flattening and roll bending deformation.The roll bending model based on influence function method and with high accuracy hasbeen widely used. However, the current roll flattening model has a low accuracy becauseof its defect theory, which restricts the strip production development. In order to improvethe calculation accuracy of the roll deformation, a new and more accurate roll flatteningmodel is proposed.
Based on boundary integral equation method, an analytical model for solving afinite length semi-infinite body is established. The lateral surface displacement field ofthe finite length semi-infinite body is simulated by finite element method (FEM) andlateral surface displacement decay functions are established. Based on the boundaryintegral equation method, the numerical solution of the finite length semi-infinite bodyunder the distributed force is obtained and an accurate roll flattening model is established.Different from the traditional semi-infinite body model, the matrix form of the new rollflattening model is established through the mathematical derivation. Compared withsemi-infinite body model and Foppl formula, the result from the new model is moreconsistent with that by FEM especially near the edges. In order to improve the efficiencyof the new model, the numerical integration in the model is fitted by mathematicalpolynomial. By comparison between the semi-infinite model and the new model,quantitative relationship and the scope of semi-infinite body model are obtained.
In order to analyze the influence of the new roll flattening model, the model isapplied in roll deformation calculation of4and6Hi mill, where the roll flattening, rollbending, the flattening between work roll and strip are coupled together, and the accuracyis verified by FEM. And then, the new model is compared with Foppl formula and semi-infinite body model in different strip width, roll shifting value and bending force, theinfluence laws are obtained. For the work roll edge contact in thin strip rolling process, based on the new model (finite length semi-infinite body flattening theory) in this paper,a new work roll edge contact deformation model is established. Based on the new rolldeformation model and coupled with the variational method (metal plastic deformationmodel), a new4Hi mill plate shape control model is established. At last, based on thecoupled model, the distribution law of rolling force and tension are analyzed by changingwork roll edge contact condition, work roll diameter, plate width, bending force, andreduction.
The20Hi mill is applied widely in thin strip rolling process. But the rolls of20Himill are arranged as cluster, contact position and roll flattening are complex, the currentroll flattening model can not obtain accurate result for20Hi mill. For the reason above,based on the finite length semi-infinite body flattening theory, a new plate shape controlmodel of20Hi mill is established, which includes roll deformation model and metalplastic deformation model. And segmented roll contact are considered in the new model.Taking a20Hi mill in laboratory as an example, the effects of the first intermediate rollshifting and taper, ASU, tension, work roll crown and the second intermediate non-driveroll crown are analyzed.
Rolling experimental study is carried out at the20Hi mill in laboratory. Because thatthe rolling force of20Hi mill is hard to measure, a new measurement method is proposed.Based on the rolling force measure method,0.4mm thickness strip as the raw material, arolling experiment is carried out by changing plate width, the first intermediate rolls andtaper, tension and reduction, the influence law of plate shape is obtain. The test resultsare analyzed by the new plate shape control model of20Hi mill, and the accuracy of thenew model is certified. Taking0.04mm thickness strip as the raw material, a rollingexperiment is carried out. By changing the first intermediate rolls and taper, reduction,the influence law of particularly thin strip shape is explored. Based on the new plateshape control model of20Hi mill, the influence factors are studied. As the result, areasonable method for particularly thin strip rolling process is obtained.
该辊间压扁模型基于边界积分方程法推导而来，将轧辊视为有限长度的半无限体，对该半无限体的两侧面位移场进行有限元模拟，并建立侧面位移分布函数。最后通过求解边界积分方程，得到辊间压扁分布值。通过与有限元法、半无限体模型、费普尔公式进行对比，验证了新型辊间压扁模型的准确性。为了该模型的实际应用，本文对模型进行了离散化处理；为了提高该模型的计算效率，文中采用数学多项式对模型中的数值积分项进行了数值拟合。通过将半无限体模型与新型辊间压扁模型对比，文中给出了半无限体模型的计算误差以及适用范围。
为了进一步研究新型辊间压扁模型的影响效果，将其分别应用到四、六辊轧机辊系变形计算中，通过耦合辊间压扁变形与轧辊轴线弯曲变形、轧辊与带钢之间压扁变形得到综合的辊系弹性变形。所得结果与有限元法、半无限体模型、费普尔公式等不同方法所得结果进行对比验证。而后分析不同窜辊量、弯辊力、压下量、板带宽度等工艺条件下，辊间压力、辊间压扁、工作辊出口辊缝等分布值的变化规律。而后，针对在极薄带钢轧制过程中极易出现的上下工作辊端压靠现象，应用有限长半无限体压扁理论，推导了全新的工作辊辊端压靠模型，以四辊轧机为例，采用本文推导的基于有限长半无限体压扁理论的辊系变形模型，耦合基于变分法的金属塑性变形模型，得到了全新的四辊轧机板形控制模型。最后，应用该耦合模型分别就考虑压靠与否、工作辊直径、板宽、弯辊力、压下量等因素对轧制力、压靠力、辊间压力、前张力、出口厚度分布的影响规律进行了深入研究。
以极薄带钢轧机的常用机型二十辊轧机为研究对象，针对二十辊轧机辊系塔形布置、辊间接触复杂、压扁位置众多等特点，建立全新的二十辊轧机的板形控制模型。将新型辊间压扁模型考虑应用其中，并考虑了外层轧辊分段支撑的影响。以二十辊实验室精密轧机为例，分析了第一中间辊窜辊、锥段长度、工作辊直径及辊凸度、第二中间非传动辊直径及辊凸度、ASU调节量、张力大小等因素对带钢出口厚度、轧制力分布、辊间压力分布等的影响规律。
最后，在二十辊实验室精密轧机上开展轧制过程实验研究。针对二十辊轧机轧制力难以测量的问题，提出了一种采用机架贴应变片，间接标定轧制力的测量方法。基于该轧制力测量方法，以厚度为0.4mm的薄钢带为原料，改变板宽、第一中间辊锥度参数、张力、压下量等因素进行二十辊轧机板带轧制实验，研究带钢出口板形的变化规律，并与本文理论模型计算板形状况进行对比验证，所得实验结果和计算结果较为吻合。以厚度为0.04mm的普碳钢极薄带为原料，开展极薄带钢轧制实验研究，改变压下量、第一中间辊锥度、锥长等条件，探索极薄带轧制过程相关因素的影响规律，并采用本文所推导的计算模型进行理论分析，得出了一套较为合理的极薄带轧制工艺及方法。
In the strip rolling process, the plate shape control technology plays a veryimportant role in improving the product quality. Roll deformation theory is the core partof shape control theories, which includes roll flattening and roll bending deformation.The roll bending model based on influence function method and with high accuracy hasbeen widely used. However, the current roll flattening model has a low accuracy becauseof its defect theory, which restricts the strip production development. In order to improvethe calculation accuracy of the roll deformation, a new and more accurate roll flatteningmodel is proposed.
Based on boundary integral equation method, an analytical model for solving afinite length semi-infinite body is established. The lateral surface displacement field ofthe finite length semi-infinite body is simulated by finite element method (FEM) andlateral surface displacement decay functions are established. Based on the boundaryintegral equation method, the numerical solution of the finite length semi-infinite bodyunder the distributed force is obtained and an accurate roll flattening model is established.Different from the traditional semi-infinite body model, the matrix form of the new rollflattening model is established through the mathematical derivation. Compared withsemi-infinite body model and Foppl formula, the result from the new model is moreconsistent with that by FEM especially near the edges. In order to improve the efficiencyof the new model, the numerical integration in the model is fitted by mathematicalpolynomial. By comparison between the semi-infinite model and the new model,quantitative relationship and the scope of semi-infinite body model are obtained.
In order to analyze the influence of the new roll flattening model, the model isapplied in roll deformation calculation of4and6Hi mill, where the roll flattening, rollbending, the flattening between work roll and strip are coupled together, and the accuracyis verified by FEM. And then, the new model is compared with Foppl formula and semi-infinite body model in different strip width, roll shifting value and bending force, theinfluence laws are obtained. For the work roll edge contact in thin strip rolling process, based on the new model (finite length semi-infinite body flattening theory) in this paper,a new work roll edge contact deformation model is established. Based on the new rolldeformation model and coupled with the variational method (metal plastic deformationmodel), a new4Hi mill plate shape control model is established. At last, based on thecoupled model, the distribution law of rolling force and tension are analyzed by changingwork roll edge contact condition, work roll diameter, plate width, bending force, andreduction.
The20Hi mill is applied widely in thin strip rolling process. But the rolls of20Himill are arranged as cluster, contact position and roll flattening are complex, the currentroll flattening model can not obtain accurate result for20Hi mill. For the reason above,based on the finite length semi-infinite body flattening theory, a new plate shape controlmodel of20Hi mill is established, which includes roll deformation model and metalplastic deformation model. And segmented roll contact are considered in the new model.Taking a20Hi mill in laboratory as an example, the effects of the first intermediate rollshifting and taper, ASU, tension, work roll crown and the second intermediate non-driveroll crown are analyzed.
Rolling experimental study is carried out at the20Hi mill in laboratory. Because thatthe rolling force of20Hi mill is hard to measure, a new measurement method is proposed.Based on the rolling force measure method,0.4mm thickness strip as the raw material, arolling experiment is carried out by changing plate width, the first intermediate rolls andtaper, tension and reduction, the influence law of plate shape is obtain. The test resultsare analyzed by the new plate shape control model of20Hi mill, and the accuracy of thenew model is certified. Taking0.04mm thickness strip as the raw material, a rollingexperiment is carried out. By changing the first intermediate rolls and taper, reduction,the influence law of particularly thin strip shape is explored. Based on the new plateshape control model of20Hi mill, the influence factors are studied. As the result, areasonable method for particularly thin strip rolling process is obtained.
引文
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