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目前常用的冷连轧张力微分方程dt=E/L(ν_b(i+1)-ν_(fi))dτ是假设机架间的带钢具有均匀的断面,引用等断面直杆虎克定律导出的,故为等断面张力微分方程。但在模拟连轧机受阶跃外扰和进行动态变规格、咬钢抛钢等连轧过程的计算时,机架间带钢的断面是不均匀的,从而建立了变断面张力微分方程: dt_(ji)=E/(hi(l_1/h_i)/(l_2/H_(i+1)) (ν_b(i+1)-νfi)dτ并以此方程为主体,提出对带钢断面阶跃变化点进行跟踪计算的动态数字模拟数学模型。经数字计算机实例模拟计算表明:当机架间带钢断面有阶跃变化时,仍采用等断面张力微分方程计算张力有较大误差,而采用变断面张力微分方程能正确地反映上述动态过程。
The commonly used cold rolling tension differential equation dt = E / L (ν_b (i + 1) -ν_ (fi)) dτ is assumed that the strip between the rack has a uniform cross-section, Therefore, it is the tension equation of equal section. But in the simulation of continuous rolling mill by step disturbance and the dynamic change specifications, bite steel and other continuous rolling process calculation, the cross-section of the strip between the racks is not uniform, and thus established a variable section tension equation: dt_ (1) () () () () () () () () () () () () () () () () () () () () Point dynamic simulation mathematical model.An example of digital computer simulation shows that when there is a step change in the cross-section of the strip between the racks, there is still a large error in the calculation of the tension by the equation of equal section tension, Tensile differential equations can correctly reflect the above dynamic process.