I am dealing with rope friction and the so-called Capstan equation.

Situation: A rope wraps around a cylinder with a wrap angle. It depends on the input force.

There are very comprehensive approaches by other colleagues, where the friction value depends on the normal force or pressure.

They are presented in the following publications.

Capstan equation including bending rigidity and non-linear frictional behaviour", Jae Ho Jung, Ning Pan, Taewook Kang, doi: 10.1016/j.mechmachtheory.2007.06.002 Equation 11

" Constraint ability of superposed woven fabrics wound on capstan " , Junpeng Liu Murilo Augusto Vaz Anderson Barata Custódio, doi: 10.1016/j.mechmachtheory.2016.05.014, equation 8.

Both equations have the problem described in the illustrations. If the incoming force becomes 0, then an outgoing force other than 0 will still be output. This is not possible if rope stiffness is neglected.

Symbols for Jung et al.: Incoming force T.1=0 kN. If the wrap angle theta and friction coefficient alpha are large enough, the outcoming force T.2 is already almost 0.8 kN.

Symbols for Liu et al.: Incoming force T.0=0 kN. If the wrap angle theta and friction coefficient a.1 are large enough, T.1 is already almost 3 kN.

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## winch1

Dear colleages,

I am dealing with rope friction and the so-called Capstan equation.

Situation: A rope wraps around a cylinder with a wrap angle. It depends on the input force.

There are very comprehensive approaches by other colleagues, where the friction value depends on the normal force or pressure.

They are presented in the following publications.

Capstan equation including bending rigidity and non-linear frictional behaviour", Jae Ho Jung, Ning Pan, Taewook Kang, doi: 10.1016/j.mechmachtheory.2007.06.002 Equation 11

" Constraint ability of superposed woven fabrics wound on capstan " , Junpeng Liu Murilo Augusto Vaz Anderson Barata Custódio, doi: 10.1016/j.mechmachtheory.2016.05.014, equation 8.

Both equations have the problem described in the illustrations. If the incoming force becomes 0, then an outgoing force other than 0 will still be output. This is not possible if rope stiffness is neglected.

Symbols for Jung et al.: Incoming force T.1=0 kN. If the wrap angle theta and friction coefficient alpha are large enough, the outcoming force T.2 is already almost 0.8 kN.

Symbols for Liu et al.: Incoming force T.0=0 kN. If the wrap angle theta and friction coefficient a.1 are large enough, T.1 is already almost 3 kN.

Does anyone know the problem?

Best regards

Paul Schumann

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