Step 1: Understanding pilling resistance.
Pilling resistance refers to the ability of a yarn or fabric to resist the formation of pills on the surface due to abrasion during use. Yarns with better fibre binding and fewer protruding fibres show higher pilling resistance.
Step 2: Characteristics of different yarns.
Air vortex yarn: Fibres are tightly wrapped around a straight core, resulting in minimal hairiness and excellent fibre binding. This provides the highest resistance to pilling.
Open end yarn: Has wrapper fibres and moderate hairiness, offering better pilling resistance than ring yarn but lower than air vortex yarn.
Ring yarn: Has higher fibre hairiness due to twisting, which increases the tendency of fibres to protrude and form pills.
Step 3: Comparing pilling resistance.
Based on fibre structure and hairiness:
\[
\text{Air vortex yarn}>\text{Open end yarn}>\text{Ring yarn}
\]
Step 4: Conclusion.
Thus, the correct order of pilling resistance is Air vortex yarn > Open end yarn > Ring yarn.