Back tension required to cause slip in rolling

It is to be expected that in rolling a strip that if the back tension, $σ_{b}$ , is too high, the rolls will begin to slip. Derive an expression for the magnitude of back tension required to make the rolls begin to slip.

Question

Back tension required to cause slip in rolling

It is to be expected that in rolling a strip that if the back tension, [latex]σ_{b} [/latex], is too high, the rolls will begin to slip. Derive an expression for the magnitude of back tension required to make the rolls begin to slip.

Accepted Answer

Slipping of the rolls means that the neutral point has moved all the way to the exit in the roll gap. Thus, the whole contact area now becomes the entry zone, and therefore Eq. (6.34)

Entry zone :[latex]p=(Y^{′}_{f} -\sigma _{b} )\frac{h}{h_{0}}e^{\mu (H_{0}-H)} [/latex] (6.34)

is applicable. We also know that when [latex]\phi= 0 , H = 0[/latex]; hence, the pressure at the exit is given by

[latex]p_{\phi =0}=(Y^{′}_{f} -\sigma _{b} )\left\lgroup\frac{h_{f}}{h_{0}} ight group e^{\mu H_{0}} . [/latex]

However, the pressure at the exit is equal to [latex]Y^{1}_{f} [/latex]. Rearranging this equation, we have

[latex]\sigma _{b}=Y^{′}_{f}\left[1- \left\lgroup\frac{h_{0}}{h_{f}} ight group (e^{-\mu H_{0}}) ight], [/latex]

where [latex]H_{0} [/latex] is obtained from Eq. (6.29)

[latex]H=2\sqrt{\frac{R}{h_{f}} } an ^{-1} \left\lgroup\sqrt{\frac{R}{h_{f}} } \phi ight group. [/latex] (6.29)

for the condition of [latex] \phi = α[/latex] . Since all the quantities are known, the magnitude of the back tension can be calculated.

Question 6.3: Back tension required to cause slip in rolling It is to be e...

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