Calculation method of contact index between loop yarn and abrasive

Loop yarn is a typical fancy yarn composed of three strands and differs significantly from conventional yarn. The loop yarn also suffers from friction and wear during use and processing. To create a unique fuzzing effect, loop yarn is usually sanded by rubbing against an abrasive. The frictional force and coefficient can only roughly reflect the frictional effect between yarn and abrasive, and it is challenging to represent the amount of contact between the two at the microscopic level. A Hertz contact model is first established to evaluate the contact between the loop yarn and the abrasive. This paper derives the calculation formula for the contact number and area between the loop yarn and the abrasive. The calculation results indicate that as the mesh of the abrasive increases, the frictional force and coefficient decrease, the contact number between the loop yarn and the abrasive gradually increases, the contact area first increases and then tends to stabilize, and the contact force and stress decrease and stabilize. The ratio of the fiber distribution force to its contact area can be used as an evaluation index for fiber wear resistance. The product of the square root of contact number, abrasive particle radius, and friction index can provide feedback on friction performance.