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

Correct Answer: 2000

Step 1: Calculate the total area produced per minute Given: Delivery speed = \SI{80}{m/min} Machine width = \SI{1}{m} (since needle count is per meter width) \[ {Area per minute} = {Length} \times {Width} = \SI{80}{m} \times \SI{1}{m} = \SI{80}{m^2} = \SI{800000}{cm^2} \] Step 2: Compute total punches per minute Given punch density = \SI{200}{punches/cm^2} \[ {Total punches per minute} = \num{200} \times \num{800000} = \num{160000000}\,{punches/min} \] Step 3: Relate punches to needle board strokes Each needle board has \num{40000} needles. Each stroke contributes: \[ {Punches per stroke} = \num{40000}\,{punches} \] With two boards operating at frequency \( f \): \[ {Total punches per minute} = 2 \times f \times \num{40000} = \num{80000} \times f \] \subsection*{Step 4: Solve for frequency \( f \)} \[ \num{80000} \times f = \num{160000000} \] \[ f = \frac{\num{160000000}}{\num{80000}} = \boxed{\num{2000}}\,{strokes/min} \] Final Answer The frequency of each needle board is \boxed{\SI{2000}{strokes/min}}.