Question

In a 3 over 3 drafting arrangement, the diameter of all bottom rollers is 28 mm. The back zone draft is 1.3 and the front zone draft is 6. If the back bottom roller is eccentric then the wavelength (mm) of the resulting fault in the drawn sliver, (rounded off to two decimal places), is \(\underline{\hspace{2cm}}\).

Hint:

When dealing with drafting arrangements, the wavelength of the resulting fault can be calculated using the roller diameter and draft values. The eccentricity of rollers can also influence the fault wavelength.

Answer 1

Correct Answer: 685

In a drafting arrangement, the wavelength of the resulting fault is given by the formula: \[ \lambda = \frac{\text{Diameter of Roller}}{(\text{Back Zone Draft} \times \text{Front Zone Draft})}. \] Given:
- Diameter of the bottom roller = 28 mm,
- Back zone draft = 1.3,
- Front zone draft = 6.
Substitute the given values into the formula: \[ \lambda = \frac{28}{(1.3 \times 6)} = \frac{28}{7.8} = 3.59 \, \text{mm}. \] Thus, the wavelength of the resulting fault in the drawn sliver is \( 3.59 \) mm.