張力微分方程研究-閱讀頁
2025-07-08 03:06本頁面
【正文】 research, as figure 2 shown. Meanwhile do the assumptions:(1) The strip tension under the action of deformation is elastic deformation, obey hooke39。L139。 L1 , L2 strip length after elastic deformation which is before and after FGC point。, L2 39。e1, e2 the absolute elongation of strip which is before and after FGC point。2 變形微分方程Deformation differential equation在圖2所示的張力作用下，變規(guī)格點(diǎn)前后帶鋼的絕對(duì)伸長(zhǎng)量為：Under the influence of the tension shown in figure 2, before and after FGC point the absolute stretching quantity of strip is: (1)相對(duì)伸長(zhǎng)為Relative elongation is (2)上式可變化為The above formula can be changed into (3)于是帶鋼絕對(duì)總伸長(zhǎng)可用相對(duì)伸長(zhǎng)表示為Then strip of absolute total elongation can be expressed in relative elongation (4)將絕對(duì)總伸長(zhǎng)e對(duì)時(shí)間t取導(dǎo)數(shù)，得到用相對(duì)伸長(zhǎng)表示的帶鋼拉伸速度：Will absolutely total elongation e of time take time t derivative, the strip pulling speeds are relative elongation: （5）另一方面，帶鋼拉伸速度又可用速度差來表示。其出入口的位移差u－U即為帶鋼的絕對(duì)伸長(zhǎng)e，即：e= u－U。為彈性模量，由虎克定律，式(7)可簡(jiǎn)化為We can know from the hypothesis: and, and are all small, so the subsequent two items in (7) are highorder small, which can be neglected. is modulus of elasticity, formula (7) can be simplified by hooke39。該式表明，動(dòng)態(tài)變規(guī)格過程張力的變化不僅與前后機(jī)架的出入口速度差有關(guān)，而且與前后卷帶鋼的寬度、厚度等規(guī)格有關(guān)，還與變規(guī)格點(diǎn)在機(jī)架間所處的位置有關(guān)。Formula (11) is the simplified tension differential equations when strip rolling FGC. This formula shows that the tension changes in dynamic FGC process not only related to the velocity difference in front and rear frame with entrance and inlet, but also related to the strip width and thickness in front and rear frame of such specifications, at the same time related to the location of the FGC point between frames. This is the difference between dynamic FGC rolling and tension differential equation in steadystate rolling time. 當(dāng)或=0時(shí)，式(11)就變成穩(wěn)態(tài)軋制時(shí)常用的張力微分方程[12]。So, the steadystate tension differential equation is the special form of FGC tension of differential equation.5 結(jié)論conclusion變規(guī)格軋制時(shí)的張力微分方程，不同于穩(wěn)定軋制時(shí)的張力微分方程，需要重新建立。動(dòng)態(tài)變規(guī)格過程中，機(jī)架間張力變化不僅與速度差有關(guān)，還與前后卷帶鋼規(guī)格及變規(guī)格點(diǎn)所處機(jī)架間的位置有關(guān)。 flying gauge change。 differential equation 。 speed differ
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