Question

A circular knitting machine of 26 inch diameter and 20 gauge with 120 feeders is running at 30 rpm to produce a plain knitted fabric using 30 tex yarn. If the loop length is 3 mm, find the rate of production (kg/h), rounded off to 1 decimal place.

Hint:

For circular knitting production: \(\text{kg/h} = \dfrac{n \times F \times (\pi D G) \times l \times \text{tex}}{1000} \times 60\), with \(D\) in inches (only inside \(\pi D G\)), \(l\) in meters, tex in g/km.

Answer 1

Step 1: Needles in the cylinder. The total number of needles is circumference \(\times\) gauge:
\(N = \pi \times D \times G = \pi \times 26 \times 20 \approx 1633.6\) needles.
Step 2: Yarn length consumed per minute.
Each revolution and each feeder knit one loop on every needle, so length/rev/feeder \(= N \times l\). With \(F=120\) feeders, \(n=30\) rpm, and loop length \(l=3~\text{mm}=0.003~\text{m}\):
\(\text{Length per min} = n F N l = 30 \times 120 \times 1633.6 \times 0.003 \approx 1.7643 \times 10^4~\text{m/min}\).
Step 3: Convert length to mass flow.
30 tex \(= 30~\text{g/km} = 0.03~\text{g/m}\). Hence,
\(\text{Mass per min} = 1.7643 \times 10^4 \times 0.03 \approx 529.3~\text{g/min}\).
Per hour: \(529.3 \times 60 \approx 31\,758~\text{g/h} = 31.8~\text{kg/h}\) (to 1 decimal).
Final Answer: 31.8 kg/h