Question

A needlepunching machine has two needle boards which operate sequentially at the same frequency to produce nonwoven with 200 punches/cm\(^2\). Each needle board has 40000 needles per meter width. If the delivery speed of the machine is 80 m/min, then the frequency (strokes/min) of each needle board is:

Hint:

To determine the punching frequency of a needlepunching machine, consider both the punch density and the delivery speed, and divide by the number of needle boards.

Answer 1

Step 1: Calculate the total area produced per minute
Given:

Delivery speed = 80 m/min
Machine width = 1 m (since needle count is per meter width)

Area per minute = Length × Width = 80 m × 1 m = 80 m² = 800000 cm²
Step 2: Compute total punches per minute
Given punch density = 200 punches/cm²

Total punches per minute = 200 × 800000 = 160000000 punches/min
Step 3: Relate punches to needle board strokes
Each needle board has 40000 needles. Each stroke contributes:

Punches per stroke = 40000 punches

With two boards operating at frequency \( f \):

Total punches per minute = 2 × f × 40000 = 80000 × f

Step 4: Solve for frequency \( f \)

80000 × f = 160000000

\( f = \frac{160000000}{80000} = \boxed{2000} \) strokes/min
Final Answer:
The frequency of each needle board is 2000 strokes/min.