连铸过程铸坯动态轻压下压下模型的研究与应用
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摘要
连铸坯动态轻压下技术已成为改善连铸坯中心偏析和疏松最有效手段之一,是现代连铸机技术先进性的一个重要标志。本文以国家技术创新计划项目《板坯连铸机动态轻压下技术的研究、开发与应用》和《某厂大方坯连铸机动态轻压下工艺控制技术研究》为依托,进行了连铸板坯和方坯动态轻压下过程关键工艺控制模型——压下模型的研究开发,并在实际生产中进行应用研究。本文的主要研究内容和取得主要结果如下：
1.连铸坯轻压下压下率理论模型的建立。通过对轻压下过程质量流量特征分析,理论推导获得了板坯／方坯压下率模型,该模型完整描述了任意矩形铸坯断面内凝固收缩、热收缩、铸坯变形对压下率的影响,即：式中：VRG为压下率,VSZ为拉速,Xsuf为铸坯宽度,Ysuf为铸坯厚度,x为沿宽度方向的坐标,y为沿厚度方向的坐标,z为沿拉坯方向的坐标,ρL、ρS分别为钢液相、固相密度,ρ为等效密度,由ρLfL+ρS(1-fL)表示,fL为液相率。
2.连铸坯压下率理论模型的求解方法研究。结合实际轻压下过程,提出了压下率理论模型求解方法。即忽略变形对固液相断面形状的影响,单独求解由温度变化引起的固液相密度变化对压下率的影响,简化的压下率模型即：
变形对压下率的影响通过压下效率模型来计算。
3.连铸坯轻压下压下效率模型的建立。在理论分析轻压下过程铸坯的变形基础之上,经过理论推导,提出了压下效率模型的准确计算公式,该式可计算任意形状铸坯轻压下过程的压下效率,即：式中：η为压下效率,ΔAi为液芯减少面积,ΔAH为铸坯表面压下面积。
4.连铸坯压下率的数值分析研究。结合板坯／方坯的铸机条件,采用有限元数值计算方法对铸坯传热过程进行求解,得到了不同拉速、钢种、断面尺寸下压下率的取值范围与变化规律。研究结果表明：板坯／方坯的压下率和压下速率均沿拉坯方向近似线性减少；板坯／方坯的平均压下率与拉速呈线性减少关系；板坯／方坯的压下速率取值范围不随拉速的变化而变化；钢种对板坯／方坯压下率和压下速率的影响小；宽度对板坯／方坯的压下率的影响均很小；厚度对压下率影响大,厚度越大,压下率在板坯／方坯轻压下入口、出口值就越小,在压下区间内减少越平缓；宽度越大,厚度增加时方坯的平均压下率减少越快,而板坯的平均压下率减少程度不变。
5.连铸坯压下效率的数值分析研究。结合某厂板坯和方坯实际铸机条件,对铸坯轻压下过程进行三维有限元数值计算,获得了不同压下量、液芯厚度、钢种、断面尺寸下压下效率的取值范围与变化规律。结果表明：板坯的压下效率在压下量小于2.3mm时,压下效率随压下量的增加而增加,压下量大于2.3mm后,压下效率不再随压下量的增加而增加,保持某个定值；方坯的压下效率在压下量小于0.6mm时,压下效率随压下量的增加而增加,在压下量为0.6-4.7mm,压下效率随压下量的增加而减少,在压下量大于4.7mm时,压下效率不再随压下量的增加而增加,保持某个定值；板坯压下效率与液芯厚度的1次方成线性正比,方坯压下效率与液芯厚度的平方成线性正比；钢种对板坯／方坯压下效率影响小；板坯压下效率随宽度变化小,与厚度呈近似线性增加关系；方坯压下效率随宽度增加或厚度减少而线性增加。
6.模型应用。将本文研究开发的模型应用于板坯连铸轻压下,应用效果良好：各钢种中心偏析C级0.5以内比率达到100%；各钢种中心疏松0.5级比率达到98%以上；各钢种角部裂纹0.5级比率达88.2%；各钢种中间裂纹和三角区裂纹0.5级比率均达96%。
Dynamic soft reduction technology has become one of the best methods to improve center segregation and porosity of continuous casting products, and is an important indication of modern conticaster. Based on national technology innovation projects "Research, development and application of dynamic soft reduction technology for slab conticaster" and "Process control technology research of dynamic soft reduction for bloom conticaster", research of a key process control model-soft reduction model was processed. The main contents and findings are as follows:
(1) Reduction gradient model of soft reduction
Based on the analysis of quality flow in soft reduction process, a theoretical model of reduction gradient, suitable for any rectangular continuous casting products, was derived. The impact of arbitrary rectangular section, solidification contraction, thermal shrinking, deformation on reduction gradient can well be described by the formula as follows: Where:VRG is for the reduction gradient,VSZ for the speed, Xsuf for width of casting product, Ysuf for thickness of casting product, x for the direction of coordinates along width, y for the direction of coordinates along thickness, z for the direction of coordinates along casting direction,ρL andρs for steel liquid and solid phase density respectively. The equivalent densityρ, is from theρLfL+ρs(1-fL), fL is for liquid fraction.
(2) Methods for solving reduction gradient model
Based on the actual soft reduction process, a method to solve reduction gradient model was proposed. That overlooks the impact of deformation on the solid-liquid phase sectional shape, and calculates reduction gradient with the solid-liquid phase density variations. The simplified model of reduction model is described by the formula as follows:
The impact of deformation on the reduction gradient is calculated by reduction efficiency model.
(3) Model building of reduction efficiency model
Based on the theoretical analysis of the deformation process, an accurate calculation formula of reduction efficiency model was derived. That formula can calculate the reduction efficiency with arbitrary shape, namely:
Where:77 is for the reduction efficiency,ΔAi for the reduced area of liquid core,ΔAH for the reduced surface area of casting products.
(4) Numerical analysis of reduction gradient
A finite element numerical method of solving heat transfer was adapted to calculate reduction gradient, combined with different speeds, steel grades and section sizes. The results show that:
●Reduction rate and reduction gradient decrease linearly along the casting strand for continuous casting slab and bloom.
●The average reduction gradient decreases linearly as the casting speed increases linearly.
●The range of reduction rate does not change with the change of speed.
●Steel grade has little effect on reduction gradient and reduction rate for continuous casting slab and bloom. Reduction gradient has little change with different grades.
●Reduction gradient is influnced heavily by thickness. The greater thickness, the less reduction gradient at the inlet and outlet of soft reduction zone.
●Thickness has little effect on average reduction gradient of slab. And the average reduction gradient decreases as thickness increases.
(5) Numerical analysis of reduction efficiency
With actual casting conditions of a factory, the process of soft reduction was simulated by a 3D finite element numerical calculation. And reduction efficiency was calculated with different reduction amount, liquid core thickness, steel grade and section size. The results show that:
●As reduction amount is less than 2.3 mm, reduction efficiency of slab increases with the increase of reduction amount. When the reduction amount is bigger than 2.3 mm, reduction efficiency of slab keeps a certain value with the increase of reduction amount.
●Reduction efficiency of bloom with reduction amount of less than 0.6 mm, increases with increase of reduction amount. As reduction amount is between 0.6 mm and 4.7mm, reduction efficiency of bloom decreases with increase of reduction amount. When reduction amount is bigger than 4.7 mm, reduction efficiency is independent with the increase of reduction amount.
●Reduction efficiency of slab increases linearly as thickness increases linearly, and the reduction efficiency of bloom increases linearly with the linear increase of 2nd power of thickness.
●Steel grade has little effect on reduction efficiency.
●Reduction efficiency of slab is affected mainly by thickness, compared to width, and increases linearly as thickness increases linearly.
●Reduction efficiency of bloom increases linearly with the linear increase of width or linear decrease of thickness.
(6) Application model of soft reduction model
The soft reduction model was applied on a slab caster with good results. The ratios of class C of 0.5 for centre segregation, centre porosity, angle crack are 100%,98%,88.2% respectively for all testing steel grades. And the ratio of class C of 0.5 for middle crack and triangle crack is up to 96%.
1.连铸坯轻压下压下率理论模型的建立。通过对轻压下过程质量流量特征分析,理论推导获得了板坯／方坯压下率模型,该模型完整描述了任意矩形铸坯断面内凝固收缩、热收缩、铸坯变形对压下率的影响,即：式中：VRG为压下率,VSZ为拉速,Xsuf为铸坯宽度,Ysuf为铸坯厚度,x为沿宽度方向的坐标,y为沿厚度方向的坐标,z为沿拉坯方向的坐标,ρL、ρS分别为钢液相、固相密度,ρ为等效密度,由ρLfL+ρS(1-fL)表示,fL为液相率。
2.连铸坯压下率理论模型的求解方法研究。结合实际轻压下过程,提出了压下率理论模型求解方法。即忽略变形对固液相断面形状的影响,单独求解由温度变化引起的固液相密度变化对压下率的影响,简化的压下率模型即：
变形对压下率的影响通过压下效率模型来计算。
3.连铸坯轻压下压下效率模型的建立。在理论分析轻压下过程铸坯的变形基础之上,经过理论推导,提出了压下效率模型的准确计算公式,该式可计算任意形状铸坯轻压下过程的压下效率,即：式中：η为压下效率,ΔAi为液芯减少面积,ΔAH为铸坯表面压下面积。
4.连铸坯压下率的数值分析研究。结合板坯／方坯的铸机条件,采用有限元数值计算方法对铸坯传热过程进行求解,得到了不同拉速、钢种、断面尺寸下压下率的取值范围与变化规律。研究结果表明：板坯／方坯的压下率和压下速率均沿拉坯方向近似线性减少；板坯／方坯的平均压下率与拉速呈线性减少关系；板坯／方坯的压下速率取值范围不随拉速的变化而变化；钢种对板坯／方坯压下率和压下速率的影响小；宽度对板坯／方坯的压下率的影响均很小；厚度对压下率影响大,厚度越大,压下率在板坯／方坯轻压下入口、出口值就越小,在压下区间内减少越平缓；宽度越大,厚度增加时方坯的平均压下率减少越快,而板坯的平均压下率减少程度不变。
5.连铸坯压下效率的数值分析研究。结合某厂板坯和方坯实际铸机条件,对铸坯轻压下过程进行三维有限元数值计算,获得了不同压下量、液芯厚度、钢种、断面尺寸下压下效率的取值范围与变化规律。结果表明：板坯的压下效率在压下量小于2.3mm时,压下效率随压下量的增加而增加,压下量大于2.3mm后,压下效率不再随压下量的增加而增加,保持某个定值；方坯的压下效率在压下量小于0.6mm时,压下效率随压下量的增加而增加,在压下量为0.6-4.7mm,压下效率随压下量的增加而减少,在压下量大于4.7mm时,压下效率不再随压下量的增加而增加,保持某个定值；板坯压下效率与液芯厚度的1次方成线性正比,方坯压下效率与液芯厚度的平方成线性正比；钢种对板坯／方坯压下效率影响小；板坯压下效率随宽度变化小,与厚度呈近似线性增加关系；方坯压下效率随宽度增加或厚度减少而线性增加。
6.模型应用。将本文研究开发的模型应用于板坯连铸轻压下,应用效果良好：各钢种中心偏析C级0.5以内比率达到100%；各钢种中心疏松0.5级比率达到98%以上；各钢种角部裂纹0.5级比率达88.2%；各钢种中间裂纹和三角区裂纹0.5级比率均达96%。
Dynamic soft reduction technology has become one of the best methods to improve center segregation and porosity of continuous casting products, and is an important indication of modern conticaster. Based on national technology innovation projects "Research, development and application of dynamic soft reduction technology for slab conticaster" and "Process control technology research of dynamic soft reduction for bloom conticaster", research of a key process control model-soft reduction model was processed. The main contents and findings are as follows:
(1) Reduction gradient model of soft reduction
Based on the analysis of quality flow in soft reduction process, a theoretical model of reduction gradient, suitable for any rectangular continuous casting products, was derived. The impact of arbitrary rectangular section, solidification contraction, thermal shrinking, deformation on reduction gradient can well be described by the formula as follows: Where:VRG is for the reduction gradient,VSZ for the speed, Xsuf for width of casting product, Ysuf for thickness of casting product, x for the direction of coordinates along width, y for the direction of coordinates along thickness, z for the direction of coordinates along casting direction,ρL andρs for steel liquid and solid phase density respectively. The equivalent densityρ, is from theρLfL+ρs(1-fL), fL is for liquid fraction.
(2) Methods for solving reduction gradient model
Based on the actual soft reduction process, a method to solve reduction gradient model was proposed. That overlooks the impact of deformation on the solid-liquid phase sectional shape, and calculates reduction gradient with the solid-liquid phase density variations. The simplified model of reduction model is described by the formula as follows:
The impact of deformation on the reduction gradient is calculated by reduction efficiency model.
(3) Model building of reduction efficiency model
Based on the theoretical analysis of the deformation process, an accurate calculation formula of reduction efficiency model was derived. That formula can calculate the reduction efficiency with arbitrary shape, namely:
Where:77 is for the reduction efficiency,ΔAi for the reduced area of liquid core,ΔAH for the reduced surface area of casting products.
(4) Numerical analysis of reduction gradient
A finite element numerical method of solving heat transfer was adapted to calculate reduction gradient, combined with different speeds, steel grades and section sizes. The results show that:
●Reduction rate and reduction gradient decrease linearly along the casting strand for continuous casting slab and bloom.
●The average reduction gradient decreases linearly as the casting speed increases linearly.
●The range of reduction rate does not change with the change of speed.
●Steel grade has little effect on reduction gradient and reduction rate for continuous casting slab and bloom. Reduction gradient has little change with different grades.
●Reduction gradient is influnced heavily by thickness. The greater thickness, the less reduction gradient at the inlet and outlet of soft reduction zone.
●Thickness has little effect on average reduction gradient of slab. And the average reduction gradient decreases as thickness increases.
(5) Numerical analysis of reduction efficiency
With actual casting conditions of a factory, the process of soft reduction was simulated by a 3D finite element numerical calculation. And reduction efficiency was calculated with different reduction amount, liquid core thickness, steel grade and section size. The results show that:
●As reduction amount is less than 2.3 mm, reduction efficiency of slab increases with the increase of reduction amount. When the reduction amount is bigger than 2.3 mm, reduction efficiency of slab keeps a certain value with the increase of reduction amount.
●Reduction efficiency of bloom with reduction amount of less than 0.6 mm, increases with increase of reduction amount. As reduction amount is between 0.6 mm and 4.7mm, reduction efficiency of bloom decreases with increase of reduction amount. When reduction amount is bigger than 4.7 mm, reduction efficiency is independent with the increase of reduction amount.
●Reduction efficiency of slab increases linearly as thickness increases linearly, and the reduction efficiency of bloom increases linearly with the linear increase of 2nd power of thickness.
●Steel grade has little effect on reduction efficiency.
●Reduction efficiency of slab is affected mainly by thickness, compared to width, and increases linearly as thickness increases linearly.
●Reduction efficiency of bloom increases linearly with the linear increase of width or linear decrease of thickness.
(6) Application model of soft reduction model
The soft reduction model was applied on a slab caster with good results. The ratios of class C of 0.5 for centre segregation, centre porosity, angle crack are 100%,98%,88.2% respectively for all testing steel grades. And the ratio of class C of 0.5 for middle crack and triangle crack is up to 96%.
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