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<meta property="og:description" content="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
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<meta property="og:description" content="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
<title>Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.</title>
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<title>Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu , and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.</title>
$2.8.13.$ Rolling mill rolls have radius $R$. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is $\mu$, and the gap between the rolls is $d_0$. Find the maximum thickness of the blank. The blank is not pushed.
</p>
<center>
<figure>
<img src="2.8.13.png"
loading="lazy" width="150" />
<figcaption>
For problem $2.8.13$
</figcaption>
</figure>
</center>
<p>
</p>
<h3>Solution</h3>
<p>
</p>
<center>
<figure>
<img src="2.8.13_1.png"
loading="lazy" width="280" />
<figcaption>
Forces acting on the mill rolls
</figcaption>
</figure>
</center>
<p>
As the thickness of the workpiece increases, there will come a point where the mill rolls can no longer roll the workpiece.</p><p>
It will happen until the vertical projection of friction force $\vec{F}_\text{fr}$ will exceed the vertical component of the support reaction force $\vec{N}$
$$F_\text{fr}\cos\alpha\geq N\sin\alpha$$
@@ -85,7 +85,7 @@
Considering the value of friction force $F_\text{fr} = \mu N$:
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
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<meta property="og:description" content="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
<meta property="og:description" content="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
<title>Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.</title>
<title>Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu , and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.</title>
$2.8.13.$ Rolling mill rolls have radius $R$. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is $\mu$, and the gap between the rolls is $d_0$. Find the maximum thickness of the blank. The blank is not pushed.
$2.8.13.$ Rolling mill rolls have radius $R$. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is $\mu$, and the gap between the rolls is $d_0$. Find the maximum thickness of the blank. The blank is not pushed.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="2.8.13.png"
<img src="2.8.13.png"
loading="lazy" width="150" />
loading="lazy" width="150" />
<figcaption>
<figcaption>
For problem $2.8.13$
For problem $2.8.13$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="2.8.13_1.png"
<img src="2.8.13_1.png"
loading="lazy" width="280" />
loading="lazy" width="280" />
<figcaption>
<figcaption>
Forces acting on the mill rolls
Forces acting on the mill rolls
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
As the thickness of the workpiece increases, there will come a point where the mill rolls can no longer roll the workpiece.</p><p>
As the thickness of the workpiece increases, there will come a point where the mill rolls can no longer roll the workpiece.</p><p>
It will happen until the vertical projection of friction force $\vec{F}_\text{fr}$ will exceed the vertical component of the support reaction force $\vec{N}$
It will happen until the vertical projection of friction force $\vec{F}_\text{fr}$ will exceed the vertical component of the support reaction force $\vec{N}$
$$F_\text{fr}\cos\alpha\geq N\sin\alpha$$
$$F_\text{fr}\cos\alpha\geq N\sin\alpha$$
@@ -85,7 +85,7 @@
Considering the value of friction force $F_\text{fr} = \mu N$:
Considering the value of friction force $F_\text{fr} = \mu N$:
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
