Withdrawal resistance, in the range where the value of fullness ρ exceeds 1, may well be assumed that it is the sum of the following two components;
a, Withdrawal resistance generated at the point where the fullness of the hole is equal to 1. (
F1)
b, Resistance caused by the additional side force acts on the test piece to compress it and make it possible to pass through the hole. (
Fc)
On the above assumption, and by applying the well known relation between the thickness of fabrics and the measuring pressure,
t=
a+
b/(
p+
c), the authors derived a theoretical expression to give the withdrawal resistance in the range where the fullness of the hole exceeds 1, as a function of the fullness ρ, coeficient of friction between the fabric and the ring-hole surface, comperssibility of the fabric, dimentional values of the ring-hole, etc. But the expression was too complex and inpractical to their purpose, so we boldly abbreviation it into the form: where
Fc: withdrawal resistance caused by the compression of the specimen in a. range of ρ exceeds one
Aθ: inner surface area of the ring-hole μ: coeficient of friction
R: radius of the narrowest part of the hole
r: radius of the curvature of the inner surface of the ring
n:
R/
r tθcalculated thickness of the test piece under zero pressure
K2′,
l,
m,
a,
b,
c: constants, their value vepends upon the character of the respective test piece.
This simplified expression has shown the results that practically coincided with the experimental results obtained from their various kinds of fabrics.
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