Effect of Bending Rigidity on the Capstan Equation

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JUNG, JAE HO; KANG, TAE JIN; Youn, Jae Ryoun
Issue Date
SAGE Publications
Textile Res. J. 74(12), 1085-1096
A tensioned fiber or yam in contact with a circular body is analyzed. In the model, a
fiber is considered as a linear elastic and inextensible beam. An exact mathematical model
is derived and the analytical solution is obtained. Both the beam-body contact and two
noncontact regions are analyzed. From the equilibrium equation of force and bending
moment, the derived model has three compatible ordinary differential equations, and one
algebraic equation from the Euler beam theory with four unknown parameters. From the
solutions, the relationship between incoming and outgoing tension is obtained, and we call
this the modified capstan equation. The results show the correction connecting the capstan
equation and its applications. For example, in a typical case, the capstan equation
underestimates the effect of bending rigidity, which renders the only physically possible
situation of tension in a real capstan to be the equilibrium of inclined tension. Moreover,
the sensitivity of the tension ratio on the variation of the inclined angle is extensive. For
instance, the difference in the tension ratio between the classical and modified results may
be the maximum 71 % value for a mere 100 variation of the inclined angle direction. Also,
it is directly applicable to fiber contact with a body whose surface has a noncircular
convex profile. Several further topics are suggested for discussion.
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College of Engineering/Engineering Practice School (공과대학/대학원)Dept. of Material Science and Engineering (재료공학부) Journal Papers (저널논문_재료공학부)
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