三维条元法及其对热轧板带轧制过程的仿真
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摘要
板形和板凸度是板带轧制的重要质量指标，板形控制是板带轧机的关键技术。随着板形控制技术的发展，板形理论越来越受到人们的重视，并逐步得到深入的研究。板带轧制的三维变形理论是板形理论研究的重点和难点。随着冷轧带材板形控制技术的不断发展，冷轧带材板形理论的不断完善，以及对热轧板带成品质量要求的不断提高，人们逐渐将注意力转向热轧板带板形理论的研究和板形控制技术的开发。板形和板凸度已经成为热轧板带的一项主要的质量指标和决定其市场竞争力的重要因素。热轧板带的三维变形理论也己经成为当前研究的前沿和热点。
在已有流线条元法的基础上，针对热轧带材和厚板比较厚的特点，提出一种模拟板带轧制过程三维变形的新型条元法——条层法。首先沿高向将变形区均匀地划分为若干层，然后再沿着金属的流动轨迹将变形区内的每层带材划分为若干流线条元，为了方便分析与计算，又将流线条元映射为矩形条元。横向位移的纵向分布被构造为四次曲线，横向分布用三次样条插值函数表示，高向分布用抛物线拟合。根据塑性力学流动理论，分析推导了变形区三维变形和应力的数学模型。与流线条元法相比，考虑了应力与变形沿高向的不均匀分布，实现了精确的三维分析和计算。对热带钢连轧和厚板轧制的仿真实例表明，该方法和模型符合实际，为板带轧制过程的三维力学仿真提供了一个新的实用工程数值方法。
在已有流线条元法的基础上，提出模拟板带轧制过程三维变形的一种新型条元法——流面条元法。沿着金属的流动轨迹，将变形区划分为若干流面(曲面)条元，为了方便分析和计算，又将其映射为平面条元。横向位移和高向位移的纵向分布被分别构造为四次曲线和二次曲线，其横向分布均采用三次样条插值函数表示，高向分布均用二次曲线拟合。根据塑性力学流动理论，分析推导了变形区三维变形和应力的数学模型。与条层法相比，考虑了金属的高向位移及其沿高向的不均匀分布，近似和简化更少，推导更简单，是一种理论更加成熟，分析与计算更加简明的三维条元法。仿真实例表明，流面条元法更加符合实际，应用范围比较广，为板带轧制过程的三维力学仿真提供了一个新的实用工程数值方法。
在流面条元法的基础上，将接触面视为三维曲面，结合塑性力学中斜面上应力的求法，给出了带材与轧辊接触表面上的精确应力边界条件，减少了简化和假设，提高了仿真计算精度，实现了对流面条元法的完善。对热轧带钢轧制力的仿真结果表明，在轧件较厚、压下量较大的情况下，新算法的计算精度高于原算法。
将四辊轧机辊系弹性变形模型与流面条元法耦合，建立了四辊轧机板形和板凸
度的分析计算模型。对1450 mm四辊六机架热带钢连轧、1660 mm四辊七机架热带钢连轧和2050 mm四辊CVC七机架热带钢连轧的仿真实例表明，该模型的计算结果与试验结果吻合良好，证明了耦合模型具有较好的准确性。
对2050 mm四辊CVC轧机各种控制手段对板形和板凸度的控制能力进行了研究。结果表明，四辊CVC轧机对热轧带钢具有很强的板凸度控制能力和较强的板形控制能力。
Shape and profile are the important quality indexes of rolled plate and strip, and shape control is the key technology of plate and strip mills. With the development of shape control technology, shape theory is paid bigger attention day by day and studied deeply. In shape theory, the three-dimensional deformation theory of plate and strip rolling is an important and difficult study content. With the continuous development of shape control technology and shape theory of cold rolled strip, and the continuous enhancement of the demand to the product quality of hot rolled plate and strip, people transfer their attentions to shape theory research and shape control technology exploitation of hot rolled plate and strip, shape and profile have been the primary quality indexes and the important factors of deciding the market competitive power of hot rolled plate and strip, and the three-dimensional deformation theory of hot rolled plate and strip have also been the leading edge and the focus of current research and exploitation.
On the basis of the streamline strip element method, to the character that hot rolled strip and thick plate are thicker, a new strip element method ——the strip layer method is put forward to simulate the three-dimensional deformations of plate and strip rolling process. The rolling deformation zone is divided into a number of layers along the altitudinal direction of plate and strip, every layer plate (strip) is divided into a number of streamline strip elements along metal flow traces, and the streamline strip elements are mapped into the corresponding rectangle strip elements for analysis and computation. The longitudinal distribution model of metal lateral displacement is constructed to be a quartic curve, its lateral distribution is expressed as the three-power spline function, and its altitudinal distribution is fitted to be a parabolic curve. Based on the flow theory of plastic mechanics, the three-dimensional deformations and stresses of deformation zone are analyzed and formulated. Compared with the streamline strip element (SSEM), the strip layer method (SLM) consider the uneven distributions of stresses and deformations along the altitudinal direction, and realizes accurate analysis and computation. The simulating examples of hot strip rolling and thick plate rolling indicate that the method and the model are in accord with facts, and provide a new reliable engineering-computation method for a three-dimensional mechanics simulation of plate and strip rolling process.
On the basis of the SSEM, a new method—the stream surface strip element method (SSSEM) for simulating the three-dimensional deformations of plate and strip rolling process is put forward. The rolling deformation zone is divided into a number of stream surface (curved surface) strip elements along metal flow traces, and the stream surface strip elements are mapped into the corresponding plane strip elements for analysis and computation. The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal are respectively constructed to be a quartic curve and a quadratic curve, the lateral distributions of them are expressed as the third-power spline function, and the altitudinal distributions of them are fitted to be the quadratic curve. From the flow theory of plastic mechanics, the three-dimensional deformations and stresses of the deformation zone are analyzed and formulated. Compared with the SLM, the SSSEM takes into account the altitudinal displacement of metal and its uneven distributions along altitudinal direction, its approximations and simplifications are fewer, its derivation is simpler, and it is a new three-dimensional strip element method whose theory is more and whose analysis and computation are more concise. The simulation examples indicate that the SSSEM is better in accord with facts, has a wider range of application, and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.
On the SSSEM
在已有流线条元法的基础上，针对热轧带材和厚板比较厚的特点，提出一种模拟板带轧制过程三维变形的新型条元法——条层法。首先沿高向将变形区均匀地划分为若干层，然后再沿着金属的流动轨迹将变形区内的每层带材划分为若干流线条元，为了方便分析与计算，又将流线条元映射为矩形条元。横向位移的纵向分布被构造为四次曲线，横向分布用三次样条插值函数表示，高向分布用抛物线拟合。根据塑性力学流动理论，分析推导了变形区三维变形和应力的数学模型。与流线条元法相比，考虑了应力与变形沿高向的不均匀分布，实现了精确的三维分析和计算。对热带钢连轧和厚板轧制的仿真实例表明，该方法和模型符合实际，为板带轧制过程的三维力学仿真提供了一个新的实用工程数值方法。
在已有流线条元法的基础上，提出模拟板带轧制过程三维变形的一种新型条元法——流面条元法。沿着金属的流动轨迹，将变形区划分为若干流面(曲面)条元，为了方便分析和计算，又将其映射为平面条元。横向位移和高向位移的纵向分布被分别构造为四次曲线和二次曲线，其横向分布均采用三次样条插值函数表示，高向分布均用二次曲线拟合。根据塑性力学流动理论，分析推导了变形区三维变形和应力的数学模型。与条层法相比，考虑了金属的高向位移及其沿高向的不均匀分布，近似和简化更少，推导更简单，是一种理论更加成熟，分析与计算更加简明的三维条元法。仿真实例表明，流面条元法更加符合实际，应用范围比较广，为板带轧制过程的三维力学仿真提供了一个新的实用工程数值方法。
在流面条元法的基础上，将接触面视为三维曲面，结合塑性力学中斜面上应力的求法，给出了带材与轧辊接触表面上的精确应力边界条件，减少了简化和假设，提高了仿真计算精度，实现了对流面条元法的完善。对热轧带钢轧制力的仿真结果表明，在轧件较厚、压下量较大的情况下，新算法的计算精度高于原算法。
将四辊轧机辊系弹性变形模型与流面条元法耦合，建立了四辊轧机板形和板凸
度的分析计算模型。对1450 mm四辊六机架热带钢连轧、1660 mm四辊七机架热带钢连轧和2050 mm四辊CVC七机架热带钢连轧的仿真实例表明，该模型的计算结果与试验结果吻合良好，证明了耦合模型具有较好的准确性。
对2050 mm四辊CVC轧机各种控制手段对板形和板凸度的控制能力进行了研究。结果表明，四辊CVC轧机对热轧带钢具有很强的板凸度控制能力和较强的板形控制能力。
Shape and profile are the important quality indexes of rolled plate and strip, and shape control is the key technology of plate and strip mills. With the development of shape control technology, shape theory is paid bigger attention day by day and studied deeply. In shape theory, the three-dimensional deformation theory of plate and strip rolling is an important and difficult study content. With the continuous development of shape control technology and shape theory of cold rolled strip, and the continuous enhancement of the demand to the product quality of hot rolled plate and strip, people transfer their attentions to shape theory research and shape control technology exploitation of hot rolled plate and strip, shape and profile have been the primary quality indexes and the important factors of deciding the market competitive power of hot rolled plate and strip, and the three-dimensional deformation theory of hot rolled plate and strip have also been the leading edge and the focus of current research and exploitation.
On the basis of the streamline strip element method, to the character that hot rolled strip and thick plate are thicker, a new strip element method ——the strip layer method is put forward to simulate the three-dimensional deformations of plate and strip rolling process. The rolling deformation zone is divided into a number of layers along the altitudinal direction of plate and strip, every layer plate (strip) is divided into a number of streamline strip elements along metal flow traces, and the streamline strip elements are mapped into the corresponding rectangle strip elements for analysis and computation. The longitudinal distribution model of metal lateral displacement is constructed to be a quartic curve, its lateral distribution is expressed as the three-power spline function, and its altitudinal distribution is fitted to be a parabolic curve. Based on the flow theory of plastic mechanics, the three-dimensional deformations and stresses of deformation zone are analyzed and formulated. Compared with the streamline strip element (SSEM), the strip layer method (SLM) consider the uneven distributions of stresses and deformations along the altitudinal direction, and realizes accurate analysis and computation. The simulating examples of hot strip rolling and thick plate rolling indicate that the method and the model are in accord with facts, and provide a new reliable engineering-computation method for a three-dimensional mechanics simulation of plate and strip rolling process.
On the basis of the SSEM, a new method—the stream surface strip element method (SSSEM) for simulating the three-dimensional deformations of plate and strip rolling process is put forward. The rolling deformation zone is divided into a number of stream surface (curved surface) strip elements along metal flow traces, and the stream surface strip elements are mapped into the corresponding plane strip elements for analysis and computation. The longitudinal distributions of the lateral displacement and the altitudinal displacement of metal are respectively constructed to be a quartic curve and a quadratic curve, the lateral distributions of them are expressed as the third-power spline function, and the altitudinal distributions of them are fitted to be the quadratic curve. From the flow theory of plastic mechanics, the three-dimensional deformations and stresses of the deformation zone are analyzed and formulated. Compared with the SLM, the SSSEM takes into account the altitudinal displacement of metal and its uneven distributions along altitudinal direction, its approximations and simplifications are fewer, its derivation is simpler, and it is a new three-dimensional strip element method whose theory is more and whose analysis and computation are more concise. The simulation examples indicate that the SSSEM is better in accord with facts, has a wider range of application, and provide a new reliable engineering-computation method for the three-dimensional mechanics simulation of plate and strip rolling process.
On the SSSEM
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