Needle Loom Punch Density Calculation

This solution explains how to calculate the punch density for a needle-punched nonwoven fabric based on the machine's operating parameters.

Key Machine Parameters

• Needle linear density: $N_L = 2000$ needles/m
• Stroke frequency: $F_S = 2000$ strokes/min
• Fabric production speed: $V_F = 5$ m/min

Calculating Punch Density

Punch density is defined as the total number of punches applied per unit area of the fabric. We can calculate it using the given parameters.

The formula for punch density can be derived as follows:

Let's consider a time interval of 1 minute:

• Total Punches per Minute: This is the product of the number of needles acting on the fabric and the frequency at which each needle punches. Assuming the needle linear density ($N_L$) applies across the fabric width, and let the fabric width be $W$ meters, the total number of needles is $N_L \times W$. $ \text{Total Punches/min} = (N_L \times W) \times F_S $ $ \text{Total Punches/min} = (2000 \text{ needles/m} \times W \text{ m}) \times (2000 \text{ strokes/min}) $ $ \text{Total Punches/min} = 4,000,000 W \text{ punches/min} $
• Area Processed per Minute: This is the product of the fabric width ($W$) and the fabric speed ($V_F$). $ \text{Area/min} = W \times V_F $ $ \text{Area/min} = W \text{ m} \times 5 \text{ m/min} $ $ \text{Area/min} = 5W \text{ m}^2/\text{min} $

Punch Density in Punches per Square Meter ($m^2$)

Now, we calculate the punch density in punches per square meter ($m^2$):

Notice that the fabric width ($W$) cancels out:

Convert to Punches per Square Centimeter ($cm^2$)

To express the punch density in punches per square centimeter ($cm^2$), we use the conversion factor $1 \text{ m}^2 = 10,000 \text{ cm}^2$:

Conclusion

The calculated punch density is 80 punches/$cm^2$. This value falls within the specified range of 79 to 81.