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Internal friction in wire rope


Hi folks, I had a class about friction while winding wire rope around a drum. I'll translate (it's in portuguese) and transcript a text about it:

A rope just can wind up around a drum when it takes the drum's shape due to it internal friction appears and it leads a deviation (it can be estimated, see the image 1) between the rope axis and an axis tangent to drum and parallel to the rope axis (Image 2). The main reasons which lead the internal friction are:

1. The compression of rope fiber next to the drum and tension of rope fiber furthest from the pulley

2. Sliding friction between the rope fibers

3. Elastic deformation of the material.

And this friction can be put into numbers by this formula (Image 3) and the amount of force required to wind up it by this another (Image 4). Given this introduction, my question is do you guys know something or meet this theory? I asked it because I was not able to find anything article about it. I think it is important to make you know the author of the book has passed away for more than one decade so the theory can be outdated.

Image 1

Image 2

Image 3

Image 4

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