Fabric pilling is the formation of small, fuzzy balls on the surface of a fabric. It detracts from the appearance of the fabric, making it look old and worn, and it is often difficult to restore a garment with fabric pilling to its original condition. Certain types of fibers and weaves are more prone to fabric pilling than others, but it is often a normal part of wear and tear.

Short or loose fibers on the surface of a fabric tend to tangle together, leading to fabric pilling. Fuzzier fabrics, like angora, are particularly prone to fabric pilling, since they are characterized by plentiful loose fibers. In other textiles, fabric pilling occurs either due to the natural tendency of fibers to migrate to the surface of a woven fabric or as a result of friction on the fabric surface, which loosens fibers and tangles them. This friction may be a result of wear and tear, or of improper laundering techniques. Fabric pilling is more likely to occur in areas of the clothing that experience more friction, such as under the arms and on the sides of a sweater.

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Note added at 20 mins (2008-09-04 11:44:11 GMT)
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Кстати, пилингуемость это образование катышков на поверхности ткани (а не стойкость к образованию на поверхности ткани катышков): http://shop.8marta.ru/zametka/#piling

ПИЛИНГУЕМОСТЬ - Это образование катышков на поверхности ткани. Обязательным условием качественной мебельной ткани является отсутствие пилингуемости. Определение стойкости к пилингообразованию определяют в процессе испытания ткани на стойкость к истиранию. Если на материале после 500 циклов катышков не появилось, ткань считается непилингующейся.

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Note added at 23 mins (2008-09-04 11:46:50 GMT) Post-grading
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отсутствие пилингуемости/стойкость к истиранию - (fabric) pilling resistance) http://www.freepatentsonline.com/3802954.html