【作者】 于明；

【导师】 刘相华； 王君；

【作者基本信息】 东北大学 ， 材料加工工程， 2009， 博士

【摘要】 中厚板轧后冷却过程自动控制是控冷技术得到有效、稳定、精确实施的重要保障,其中冷却过程温度模型是提高温度控制精度的核心和关键。随着计算机技术的快速发展,数值解法得到了广泛的应用,目前温度场有限差分计算模型已成功实现了在线应用,温度控制精度有了明显提高。温度场解析解法由于只能用于求解比较简单的问题,对于实际冷却过程的复杂情况无能为力,因而在工程实际中极少应用。但是解析解具有不可替代的理论价值,在认识问题本质,分析不同变量之间的物理关系,以及作为标准解用于检验和发展数值解法等方面都起到至关重要的作用。为此,本文以中厚板轧后冷却过程为研究对象,从简化条件下的温度场解析解研究入手,对解析解描述的温度分布规律进行了深入研究,结合实际重点探讨表面温度、心层温度与平均温度之间的对应关系,并基于此,对在线温度模型及离线模拟优化模型提出了改进方案。主要研究进展如下:(1)针对中厚板轧后冷却过程的特点,详细研究冷却过程温度场各种解法,包括:一维、二维、三维解析解法和一维显式、隐式、C-N格式,二维显式、ADI格式以及三维显式格式的有限差分解法。调试开发这些解法的计算程序,在统一计算条件下,解析与差分程序的计算结果具有很好的一致性。在此基础上,以解析解为基准,研究不同差分格式的稳定性和计算误差,并进一步通过程序运行时间的分析,探讨适于在线应用的差分格式及步长。研究结果对于在线温度模型差分方法的选定以及模型精度与实时性的分析有重要的参考价值。(2)研究非稳态热传导过程正规阶段的温度分布规律,提出正规解概念。正规解的温度分布、心表温差及平均温度由表面温度和Bi数综合确定,在正规阶段,可通过正规解法来求解温度分布。给出正规阶段的判定方法:当正规解的计算偏差减小到工程误差允许范围以内时,标志导热过程进入正规阶段,并定义相应的无量纲时间Fo_m作为非正规阶段和正规阶段的分界点。分析表明,Fo_m并不是某一定值,具体根据偏差要求、正规解计算偏差初值和Bi值共同确定。(3)针对边界条件和物性条件变化的实际情况,提出近似正规阶段概念。同样通过分析正规解计算偏差确定Fo_m值来判定近似正规阶段,在近似正规阶段,可应用正规解近似描述钢板的温度分布。经分析证实,钢板在水冷阶段前后的空冷过程中存在近似正规阶段,并且该阶段里的正规解温度分布是每一时刻实际温度分布的可能下限。特别得出,返红结束时刻可代替Fo_m值作为判定到达近似正规阶段的标志。(4)结合解析解描述的温度分布规律,研究钢板水冷后返红过程发生机理,模拟计算出不同钢种规格钢板在不同冷却条件下的返红结束位置,为终冷温度控制及测温仪位置确定提供参考依据;同时得出较厚钢板需在矫直之前停留时间的参考值。进一步针对实际的返红过程,研究钢板内部温度值等于平均温度的位置变化情况,得出返红发生的明显区域为温度值等于平均温度的稳定位置至表面,即无量纲位置X=0.57～1部分,这一结果为分析返红过程温度回复对钢板组织性能的影响提供了参考数据。此外,研究钢板在水冷及之后返红过程心表温差和均表温差的变化规律,为合理制定冷却策略以及返红结束后心表温差和均表温差的估算提供理论指导。(5)提出改进中厚板轧后冷却过程控制系统的思路和方法。确定返红结束后就近测温仪的实测表面温度作为终冷温度控制依据;将正规解计算嵌入到在线模型中,为模型设定计算和自学习计算提供较可信的温度分布和平均温度,可提高模型预报精度;离线模型扩展三个新的功能:返红过程分析、心表温差和均表温差分析以及正规解偏差分析,为在线模型控制精度提高起到促进作用。本文基于温度场解析解所做的研究工作,对于中厚板轧后冷却过程温度模型精度的提高有重要的理论指导意义。其中定义的正规解为实时深入了解物体内部的温度分布提供了可靠的计算方法,具有实用价值。在中厚板生产过程中,中间坯在粗轧、精轧之间待温过程,钢板在冷床上的空冷过程等,都具备条件应用正规解法计算温度分布。钢板越厚,采用正规解法计算温度分布的意义越大。更多还原

【Abstract】 Automation control system for accelerated cooling process of plate is essential for controlled cooling technology to put into practice effectively, stably and accurately. Specifically, accuracy of temperature control for cooling process is subject to mathematical models. With the development of computer technology, numerical solutions have been applied widely. At present, the model based on finite difference method has been used on line to calculate temperature evolution, which increased accuracy of temperature control significantly. Due to the complexity of actual accelerated cooling process, analytical solution can be exactly solved only by simplifying conditions of the problem, which has limited its application in industrial practice. However, analytical solutions have irreplaceable theoretical value. They play very important roles in understanding essence of the problems, analyzing physical relation between different variables and acting as standard solutions to verify and develop numerical solutions. Therefore, concentrating on accelerated cooling process of plate, and commencing on the study of analytical solution for temperature field under the simplified conditions, the regularities of temperature distribution is researched in detail. In combination with the practical cooling process, the relation of surface, center and average temperatures is discussed. Based on the researches in this dissertation, improved projects for on-line temperature calculation model and off-line simulation model are put forward. The main progresses are as follows:(1) To obtain the temperature field for accelerated cooling process of plate, the solving methods consisting of one, two and three dimensional analytical solutions, as well as finite difference solutions including one-dimensional explicit, implicit and C-N (Crank-Nicolson) scheme, two-dimensional explicit and ADI (Alternating Direction Implicit) scheme, and three-dimensional explicit scheme are researched in detail. Computer programs of all these solutions are developed, and the results of them are good agreement under identical computational conditions. Then, compared with analytical solution, the computational stability and truncation error of different finite difference schemes with various step-sizes are investigated. The scheme of finite difference method adequate for on-line calculation with appropriate spacing and time step is discussed. The conclusion provides significant reference for analyzing the accuracy and real-time performance of on-line temperature model based on finite difference method.(2) Through analyzing the characteristic of temperature field in regular regime of unsteady heat conduction process, the concept of regular solution is defined. Regular solution depends on surface temperature and Bi number, and it is analytical solution in regular regime. Regular regime will be indicated by the calculation deviation of regular solution within the accepted tolerances. And Fo_m number, namely, the dimensionless time is defined as the dividing point between initial regime and regular regime. It is obtained that Fo_m is not a fixed value corresponding to same calculation deviation but depends on Bi number and the initial value of calculation deviation of regular solution.(3) In consideration of the actual variations of boundary conditions and thermophysical properties, the concept of approximate regular regime is defined. Approximate regular regime will also be indicated by the calculation deviation of regular solution within the accepted tolerances or by Fo_m. In approximate regular regime, regular solution is approximate to actual temperature field. It is proved that approximate regular regime exists in two air cooling processes which before and after water cooling process. And the regular solution of air-cooling in this regime is lower limit of the actual temperature field. In particular, it is drawn that the time of surface temperature recovery finishing after water-cooling can be considered as the sign of arriving in approximate regular regime instead of Fo_m .(4) Combined with the regularities of temperature distribution described by analytical solution, the mechanism of temperature recovery after water-cooling is introduced. The position of surface temperature recovery finishing is obtained by simulated calculation given different thickness, steel grade and cooling conditions, which provides reference for the control of finish cooling temperature and the location of pyrometers. And the reference values of stay time for thicker plates before leveling are presented. Furthermore, the position where the value of temperature equals to average temperature is analyzed according to temperature recovery process after water-cooling. It shows that the region of X = 0.57～1 is the distinct area of temperature recovery which will provide reference data to discuss the influence of temperature recovery on the structure and performance of plate. In addition, the difference between center and surface temperatures and that between average and surface temperatures in the water-cooling process and temperature recovery process after that are researched. The conclusion will provide theoretical direction to establish cooling strategies and estimate the difference between center and surface temperatures and that between average and surface temperatures after temperature recovery finishing.(5) The improved projects of process control system for accelerated cooling of plate are presented. Surface temperature measured by the pyrometer which close to the position of temperature recovery finishing will be the basis of finishing cooling temperature control. The regular solution is applied into on-line model, and provides reliable temperature distribution and average temperature to the preset model and self-learning model to increase the preset accuracy essentially. Three new functions can be extended into off-line model to promote the control accuracy of on-line model, which involve analysis of temperature recovery process after water-cooling, estimate of the difference between center and surface temperatures and that between average and surface temperatures, as well as research on the calculation deviation of regular solution.The researches on analytical solution for temperature field are of great theoretical significance to improve accuracy of temperature control in accelerated cooling of plate. The regular solution defined in this dissertation creates a reliable calculation method for real-time acquiring temperature distribution of things, which exhibiting significant utility value. In plate mills, holding process of inter-slab between rough rolling and finish rolling and cooling process of plate on cooling bed, etc., both meet conditions to apply regular solution to calculate temperature distribution. Application of the regular solution is more meaningful for thicker plate.更多还原