Question

A monofilament gets extruded at a speed of 10 m/min from a spinneret of 0.2 mm diameter. In order to ensure a spin draw ratio of 11, the first godet roller with a diameter of 70 cm has to rotate with an angular velocity (rpm) of (rounded off to nearest integer) ______________.

Hint:

The spin draw ratio is the ratio of the speeds of the godet roller and the extrusion system, and angular velocity is related to linear velocity by the radius of the roller.

Answer 1

Correct Answer: 49

The spin draw ratio is defined as the ratio of the velocity of the godet roller to the extrusion speed:
\[ \text{Spin Draw Ratio} = \frac{V_{\text{godet}}}{V_{\text{extrusion}}} \] We are given that the extrusion speed \( V_{\text{extrusion}} = 10 \, \text{m/min} \) and the spin draw ratio is 11. Therefore, the velocity of the godet roller is:
\[ V_{\text{godet}} = 11 \times 10 = 110 \, \text{m/min} \] Now, we calculate the angular velocity of the godet roller. The relationship between linear velocity and angular velocity is given by:
\[ V_{\text{godet}} = \omega R \] where \( R = \frac{D_{\text{godet}}}{2} = \frac{70}{2} = 35 \, \text{cm} = 0.35 \, \text{m} \), and \( \omega \) is the angular velocity in radians per second. Substituting the known values:
\[ 110 = \omega \times 0.35 \] \[ \omega = \frac{110}{0.35} = 314.2857 \, \text{radians/second} \] Finally, converting from radians per second to revolutions per minute (rpm):
\[ \omega \, \text{(rpm)} = \frac{314.2857 \times 60}{2\pi} = 3000 \, \text{rpm} \] Final Answer: 3000