Question

A ring frame is scheduled to run with the following settings:
Linear speed of traveller = 30 m/s
Front roller delivery speed = 18 m/min
Bobbin diameter = 25 mm
Spindle rpm = 15430
What ring diameter (in mm) will be appropriate for the above settings?

• A. 37.7
• B. 62.8
• C. 35.5
• D. 0.628

Hint:

In ring spinning problems, remember that traveller speed is governed mainly by ring diameter and spindle speed. Always convert rpm into per-second terms using division by 60.

Answer 1

The Correct Option is A

Step 1: Understanding the concept.
In a ring frame, the linear speed of the traveller is equal to the peripheral speed of the ring. The traveller speed depends on the ring diameter and the spindle speed. The relationship between traveller speed, ring diameter, and spindle speed is given by:
\[ V = \frac{\pi \times D \times N}{60} \] where:
$V$ = linear speed of traveller (m/s)
$D$ = ring diameter (m)
$N$ = spindle speed (rpm)
Step 2: Substituting the given values.
Given:
\[ V = 30 \text{ m/s}, \quad N = 15430 \text{ rpm} \] Rearranging the formula to find ring diameter:
\[ D = \frac{V \times 60}{\pi \times N} \] Step 3: Calculation.
\[ D = \frac{30 \times 60}{\pi \times 15430} \] \[ D = \frac{1800}{48473} \] \[ D \approx 0.0371 \text{ m} \] Step 4: Converting into millimetres.
\[ D = 0.0371 \times 1000 = 37.1 \text{ mm} \] This value is closest to 37.7 mm among the given options.
Step 5: Conclusion.
Hence, the appropriate ring diameter for the given operating conditions is approximately 37.7 mm.