Bending around sheave or pulley

[DeereAdam]

I need to calculate how much tension it would require to bend large insulated cable of various sizes around a pulley. The Conductor would be made of aluminum or copper and solid. The Insulation would be of various thicknesses depending on the cable. I was looking at breeaking this problem down to calculations for a rod and calculations for a pipe. I hope to arrive at a formula that I can plug in the diameter of the conductor and wall thickness of the insulation.

The pulley diameter is 3.43 meters
The Cable will bend 180 degrees around the pulley
This can be a static calculation... One end of cable may be assumed as fixed and the other being pulled until the cable forms snugly around the pulley.

Thanks for any help.

 

[Studiot]

Hello Adam, welcome to Physics Forums.

Perhaps you would like to elaborate on your question and the mechanical arrangements.
Tension straightens wires, it doesn't bend them.
Tension as a force is axial to the wire, you need a transverse force to bend it round a curve of any description.

 

[DeereAdam]

I agree with the description of applied force... I hope this will help clarify what I am trying to calculate. This could be thought of upside down with a weight attached to one end of the cable... how much weight applied in a straight direction to bend the cable around the pulley. The Pulley is 3.42m diameter. Thanks again -Adam-

 

[Studiot]

But you have shown the stiff wire already bent.

Assuming it is straight up and down on the left hand side to start with you need a sideways force, initially acting left to right.

Since this force needs to be tangential it is usually provided by a rotating arm or crank.
You would then be into a moment calculation, not a tension one.


Look at pipe bending apparatus in a plumbing catalog.

 

[DeereAdam]

I think you understand what I am trying to achieve... I understand what you are saying about the actual bending of the cable... How would you go about calculating this... if it is possible... Is there an accurate way to calculate this? However this is figured it must be converted back to a tension value because of how this system works... Thanks for your help -Adam-

 

[Studiot]

Have a look a this document, in particular look at equation 3 on sheet 37.

sorry missed the reference

http://eng.sut.ac.th/metal/images/stories/pdf/06_Sheet-metal forming.pdf

 

[DeereAdam]

This Calculation looks promising but it does not calculate the moment... and it is calculating for sheet metal... trying to tie this back to rod and pipe calculations and make it correct? I do like the simplicity but I am not sure if this could be changed to calculate for rod or pipe. I do appreciate the reference tough and will study it more. I am sure that most of the people on this form have more background in these calculations. I must make sure that this is calculated correctly. Are there more complex calculations for bending moments and can those be broken up over a radius? Thanks again for your help. -Adam-

 

[256bits]

Maybe you can use calculator this for a torsional spring to help you out.

http://www.tribology-abc.com/calculators/t14_4.htm

Only problem is that your wire would not act as a spring but would most likely have some plastic deformation around the sheave.