冷轧机辊缝位置压力双闭环控制方法

摘要

本发明涉及冷轧带钢轧制领域冷轧机辊缝位置压力双闭环控制方法，适用于冷轧机主压上为轧制力控制模式。该方法包括的内容是：轧机附加倾斜后双侧非对称轧制力计算；根据卡氏能量定理推导了适于非对称轧制计算的支撑辊、工作辊简支梁形式的弹性弯曲影响函数；辊系变形理论和金属横向流动理论的有效整合；对传统辊系变形理论中的变形协调方程进行了有效的改进；考虑到理论计算的误差，对理论计算模型进行实时在线自适应修正。本技术的应用能够有效抑制因倾斜调整过量而导致的断带事故的发生，同时对单边浪的控制具有显著的效果。

主权项

1.冷轧机辊缝位置压力双闭环控制方法，其特征在于，轧机附加倾斜后双侧非对称轧制力计算；根据卡氏能量定理推导了适于非对称轧制计算的支撑辊、工作辊简支梁形式的弹性弯曲影响函数；辊系变形理论和金属横向流动理论的有效整合；对传统辊系变形理论中的变形协调方程进行了有效的改进；考虑到理论计算的误差，对理论计算模型进行实时在线自适应修正；轧机支撑辊附加倾斜后轧制变形区已不再是传统意义上的以轧制中心线为中心左右对称，而是非对称的，进行非对称计算时，左右两侧的轧制力是未知数；进行计算时单元划分为沿辊全身自左向右排列，推导支撑辊弯曲影响函数为：$g_b(i,j)=\frac{1}{{3E}_b{I}_{b1}}\frac{l_b-x_i}{l_b}\frac{l_b-x_j}{l_b}{l}_O^3+\frac{1}{{3E}_b{I}_{b2}}\frac{l_b-x_i}{l_b}\frac{l_b-x_j}{l_b}(x_j^3-l_O^3)$$+\frac{1}{E_b{I}_{b2}}\frac{l_b-x_i}{l_b}\{-\frac{x_j}{l_b}\frac{1}{3}[x_i^3-x_j^3]+\frac{1}{2}{x}_j[x_i^2-x_j^2\left]\right\}$$+\frac{1}{E_b{I}_{b2}}\left\{\frac{x_i{x}_j}{l_b^2}\frac{1}{3}\right[l_D^3-x_i^3]-\frac{x_i{x}_j}{l_b}[l_D^2-x_i^2]+x_i{x}_j[l_D-x_i\left]\right\}$$\begin{array}{cc}+\frac{1}{E_b{I}_{b1}}\left\{\frac{x_i{x}_j}{l_b^2}\frac{1}{3}\right[l_b^3-l_D^3]-\frac{x_i{x}_j}{l_b}[l_b^2-l_D^2]+x_i{x}_j[l_b-l_D\left]\right\}& \left(x_i{>x}_j\right)\end{array}$$+\frac{\Phi }{{\mathrm{GA}}_{b1}}\frac{l_b-x_j}{l_b}\frac{l_b-x_i}{l_b}{l}_O+\frac{\Phi }{{\mathrm{GA}}_{b2}}\frac{l_b-x_j}{l_b}\frac{l_b-x_i}{l_b}(x_j-l_O)$$+\frac{\Phi }{{\mathrm{GA}}_{b2}}(-\frac{x_j}{l_b})\frac{l_b-x_i}{l_b}(x_i-x_j)+\frac{\Phi }{{\mathrm{GA}}_{b2}}(-\frac{x_j}{l_b})\frac{l_b-x_i}{l_b}(l_D-x_i)$$+\frac{\Phi }{{\mathrm{GA}}_{b1}}\left(\frac{x_j{x}_i}{l_b^2}\right)(l_b-l_D)$$g_b(i,j)=\frac{1}{{3E}_b{I}_{b1}}\frac{l_b-x_i}{l_b}\frac{l_b-x_j}{l_b}{l}_O^3+\frac{1}{{3E}_b{I}_{b2}}\frac{l_b-x_i}{l_b}\frac{l_b-x_j}{l_b}(x_j^3-l_O^3)$$+\frac{1}{E_b{I}_{b2}}\frac{l_b-x_j}{l_b}[\frac{x_i}{2}(x_j^2-x_i^2)-\frac{x_i}{{3l}_b}(x_j^3-x_i^3)]$$+\frac{1}{E_b{I}_{b2}}[\frac{x_i{x}_j}{l_b^2}\frac{1}{3}(l_D^3-x_j^3)-\frac{x_i{x}_j}{l_b}(l_D^2-x_j^2)+x_i{x}_j(l_D-x_j)]$$\begin{array}{cc}+\frac{1}{E_b{I}_{b1}}[\frac{x_i{x}_j}{l_b^2}\frac{1}{3}(l_b^3-l_D^3)-\frac{x_i{x}_j}{l_b}(l_b^2-l_D^2)+x_i{x}_j(l_b-l_D)]& (x_i<x_j)\end{array}$$+\frac{\Phi }{{\mathrm{GA}}_{b1}}\frac{l_b-x_j}{l_b}\frac{l_b-x_i}{l_b}{l}_O+\frac{\Phi }{{\mathrm{GA}}_{b2}}\frac{l_b-x_j}{l_b}\frac{l_b-x_i}{l_b}(x_j-l_O)$$+\frac{\Phi }{{\mathrm{GA}}_{b2}}\frac{l_b-x_j}{l_b}(-\frac{x_i}{l_b})(x_j-x_i)+\frac{\Phi }{{\mathrm{GA}}_{b2}}\left(\frac{x_j{x}_i}{l_b^2}\right)(l_D-x_j)$$+\frac{\Phi }{{\mathrm{GA}}_{b1}}\left(\frac{x_j{x}_i}{l_b^2}\right)(l_b-l_D)$工作辊弯曲影响函数为：$g_w(i,j)=\frac{1}{{3E}_w{I}_{w1}}\frac{l_w-x_i}{l_w}\frac{l_w-x_j}{l_w}{l}_{\mathrm{OW}}^3+\frac{1}{{3E}_w{I}_{w2}}\frac{l_w-x_i}{l_w}\frac{l_w-x_j}{l_w}(x_j^3-l_{\mathrm{OW}}^3)$$+\frac{1}{E_w{I}_{w2}}\frac{l_w-x_i}{l_w}\{-\frac{x_j}{l_w}\frac{1}{3}[x_i^3-x_j^3]+\frac{1}{2}{x}_j[x_i^2-x_j^2\left]\right\}$$+\frac{1}{E_w{I}_{w2}}\left\{\frac{x_i{x}_j}{l_w^2}\frac{1}{3}\right[l_{\mathrm{DW}}^3-x_i^3]-\frac{x_i{x}_j}{l_w}[l_{\mathrm{DW}}^2-x_i^2]+x_i{x}_j[l_{\mathrm{DW}}-x_i\left]\right\}$$\begin{array}{cc}+\frac{1}{E_w{I}_{w1}}\left\{\frac{x_i{x}_j}{l_w^2}\frac{1}{3}\right[l_w^3-l_{\mathrm{DW}}^3]-\frac{x_i{x}_j}{l_w}[l_w^2-l_{\mathrm{DW}}^2]+x_i{x}_j[l_w-l_{\mathrm{DW}}\left]\right\}& \left(x_i{>x}_j\right)\end{array}$$+\frac{\Phi }{{\mathrm{GA}}_{w1}}\frac{l_w-x_j}{l_w}\frac{l_w-x_i}{l_w}{l}_{\mathrm{OW}}+\frac{\Phi }{{\mathrm{GA}}_{w2}}\frac{l_w-x_j}{l_w}\frac{l_w-x_i}{l_w}(x_j-l_{\mathrm{OW}})$$+\frac{\Phi }{{\mathrm{GA}}_{w2}}(-\frac{x_j}{l_w})\frac{l_w-x_i}{l_w}(x_i-x_j)+\frac{\Phi }{{\mathrm{GA}}_{w2}}(-\frac{x_j}{l_w})\frac{l_w-x_i}{l_w}(l_{\mathrm{DW}}-x_i)$$+\frac{\Phi }{{\mathrm{GA}}_{w1}}\left(\frac{x_j{x}_i}{l_w^2}\right)(l_w-l_{\mathrm{DW}})$$g_w(i,j)=\frac{1}{{3E}_w{I}_{w1}}\frac{l_w-x_i}{l_w}\frac{l_w-x_j}{l_w}{l}_{\mathrm{OW}}^3+\frac{1}{{3E}_w{I}_{w2}}\frac{l_w-x_i}{l_w}\frac{l_w-x_j}{l_w}(x_j^3-l_{\mathrm{OW}}^3)$$+\frac{1}{E_w{I}_{w2}}\frac{l_w-x_i}{l_w}\{-\frac{x_j}{l_w}\frac{1}{3}[x_i^3-x_j^3]+\frac{1}{2}{x}_j[x_i^2-x_j^2\left]\right\}$$+\frac{1}{E_w{I}_{w2}}\left\{\frac{x_i{x}_j}{l_w^2}\frac{1}{3}\right[l_{\mathrm{DW}}^3-x_i^3]-\frac{x_i{x}_j}{l_w}[l_{\mathrm{DW}}^2-x_i^2]+x_i{x}_j[l_{\mathrm{DW}}-x_i\left]\right\}$$\begin{array}{cc}+\frac{1}{E_w{I}_{w1}}\left\{\frac{x_i{x}_j}{l_w^2}\frac{1}{3}\right[l_w^3-l_{\mathrm{DW}}^3]-\frac{x_i{x}_j}{l_w}[l_w^2-l_{\mathrm{DW}}^2]+x_i{x}_j[l_w-l_{\mathrm{DW}}\left]\right\}& \left(x_i{>x}_j\right)\end{array}$$+\frac{\Phi }{{\mathrm{GA}}_{w1}}\frac{l_w-x_j}{l_w}\frac{l_w-x_i}{l_w}{l}_{\mathrm{OW}}+\frac{\Phi }{{\mathrm{GA}}_{w2}}\frac{l_w-x_j}{l_w}\frac{l_w-x_i}{l_w}(x_j-l_{\mathrm{OW}})$$+\frac{\Phi }{{\mathrm{GA}}_{w2}}(-\frac{x_j}{l_w})\frac{l_w-x_i}{l_w}(x_i-x_j)+\frac{\Phi }{{\mathrm{GA}}_{w2}}(-\frac{x_j}{l_w})\frac{l_w-x_i}{l_w}(l_{\mathrm{DW}}-x_i)$$+\frac{\Phi }{{\mathrm{GA}}_{w1}}\left(\frac{x_j{x}_i}{l_w^2}\right)(l_w-l_{\mathrm{DW}})$工作辊和支撑辊间的变形协调方程为：式中$\stackrel{r}{T}={\left[\begin{array}{cccc}t\left(1\right)& t\left(2\right)& L& t\left(\mathrm{NB}\right)\end{array}\right]}^T$为支撑辊的倾斜向量；${\stackrel{r}{Y}}_{\mathrm{wb}}={\left[\begin{array}{cccc}{y}_{\mathrm{wb}}\left(1\right)& y_{\mathrm{wb}}\left(2\right)& L& y_{\mathrm{wb}}\left(n\right)\end{array}\right]}^T$为辊间压扁向量，${\stackrel{r}{Y}}_{\mathrm{wb}0}={\left[\begin{array}{cccc}{y}_{\mathrm{wb}0}\left(0\right)& y_{\mathrm{wb}0}\left(0\right)& L& y_{\mathrm{wb}0}\left(0\right)\end{array}\right]}^T$是常向量，即辊面中心处的压扁量；${\stackrel{r}{M}}_b={\left[\begin{array}{cccc}{m}_b\left(1\right)& m_b\left(2\right)& L& m_b\left(n\right)\end{array}\right]}^T$是支撑辊凸度向量；${\stackrel{r}{M}}_w={\left[\begin{array}{cccc}{m}_w\left(1\right)& m_w\left(2\right)& L& m_w\left(n\right)\end{array}\right]}^T$是工作辊凸度向量。