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给出了一个基于冷轧过程的扩展模型,主要研究了在辊缝咬合接触区中的带钢表面粗糙度和摩擦因数的变化过程。建立此模型的基础是假设带钢表面粗糙度在纵向及横向上存在周期性分布的重复结构(如三角形结构),同时,模型综合运用了Sutcliffe’s[1]、Wilson和Sheu[2]等提出的、在理想状态假设下(单纯的横向或单纯的纵向粗糙度分布结构)得出的研究成果,预测了在轧制方向及带钢宽度方向上,轧制接触区内各种特性的变化过程。润滑剂的压力分布是由流体力学机理所决定的,同时,也会受到表面粗糙度几何结构上的长宽比的影响。模型建立时即对接触区表面进行三维建模,且认为在带钢长度方向和宽度方向上的接触区表面有着不同的几何特性。模型还考虑了轧制接触区内的“局部摩擦因数”分布。局部摩擦因数是将主要由润滑剂造成的摩擦因数以及边界接触层的摩擦因数按照其各自所占面积比重组合而来,并由此最终计算出接触区整体平均摩擦因数。同时,在带钢塑性变形、润滑油膜中的剪切及压缩作用和边界接触区的剪应力效应的共同作用下,润滑剂的温度会逐渐升高,因此,在建模时给出了一个传热学子模型,以考虑对润滑剂性质的影响。提出的模型在建立时精准地定义了模型各独立模块之间的交互接口,并基于此选择运用模块化和分层化的建模策略,对将来进一步修改各个子模型的工作带来了很多便利。为了求解模型的隐式耦合微分代数方程组(DAE系统),引入了无因次变量,以确保计算处于良态计算之中。模型通过对轧制接触弧进行空间离散化处理,将研究问题转换还原为一系列高度非线性化的耦合代数方程组,而这些方程组可以利用著名的Newton Raphson算法的一个改进算法联立求解出来。
An extended model based on cold rolling process is given. The variation of surface roughness and friction coefficient of the strip in the nip contact area of the roll gap is mainly studied. The model is based on the assumption that the surface roughness of the strip has a periodic distribution of the repeated structure (such as the triangular structure) in the longitudinal and transverse directions. Simultaneously, the model uses Sutcliffe’s [1], Wilson and Sheu [2] , The research results obtained under ideal conditions (simple horizontal or simple longitudinal roughness distribution) predict the variation of various characteristics in the rolling contact zone in the rolling direction and strip width direction. The pressure distribution of a lubricant is determined by the hydrodynamic mechanism and is also affected by the aspect ratio of the surface roughness geometry. When the model is established, the contact surface is three-dimensionally modeled, and it is considered that there are different geometrical characteristics of the contact surface in the length and width direction of the strip. The model also considers the “local friction factor” distribution within the rolling contact area. The local friction factor is the combination of the friction factor mainly caused by the lubricant and the friction factor of the boundary contact layer according to their respective area proportions, and finally the average friction coefficient of the contact zone is calculated. At the same time, the temperature of the lubricant gradually increases due to the plastic deformation of the strip, the shearing and compressing action in the lubricant film, and the shearing effect of the boundary contact zone. Therefore, Thermal sub-model to consider the impact of the lubricant properties. The proposed model precisely defines the interactive interfaces between the independent modules of the model at the time of establishment, and based on this, the modular and hierarchical modeling strategies are chosen to facilitate the further modification of each sub-model in the future . In order to solve the model of implicit coupling differential algebraic equations (DAE system), dimensionless variables are introduced to ensure that the calculations are in good state. The model discretizes the contact arc of the rolling mill to reduce the conversion of the research problem into a series of highly algebraic coupled algebraic equations that can be solved jointly by an improved algorithm of the famous Newton Raphson algorithm .