Rope Tension on Pulley System

[nedders]

Hi

I'm trying to explain, justify, calculate

I have a cable that S-shapes under and over a series of pulleys, and I'm trying to calculate how much extra tension is required to pull the rope through the snakey pattern.

In my mind, if the pulleys are frictionless (ie. bearings), then bending the rope around a series of pulleys won't make any difference what-so-ever.

If there is a weight of say 10kg on one end, then surely it's only 10kg force required to pull through.

I want to know if changing the shape so there is more wrap around the pulleys, if it will make any difference to require tension to pull the rope

 

[rb1957]

sounds about right, 'cept for using "kg" as a unit of force ... we Engineers understand Newtons !

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[3DDave]

There is some resistance to bending in the rope but that will be on a per-rope basis as to how much. And there will be some friction in the contact between the rope and the pulley - for example V-belt pulleys are designed to force friction to occur while plain pulleys are designed to produce less, though some is often there from guides to keep the rope from sliding off the sides of the pulleys.

Mostly, pulleys always have some resistance to turning so adding more pulleys will add more tension to pull the rope through.

 

[nedders]

Hi sorry, yes Newtons!

Is there anyway to calculate or even approximate the resistance due to bending rope?

I can't find / remember of any useful equations.

I thought possible Euler's, or even "beam deflection theorem", but I think these are irrelevant

 

[BrianE22]

There looks to be brake calipers on some of the pullies. Are you applying a torque?

 

[rb1957]

can you show the rope path ? just so as we're clear what you mean.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Tmoose]

The attached pdf scan is from the Third edition of Marks Handbook. CA 1930.

 

[3DDave]

Per-rope means there's no formula. You might get that information from the maker of the selected rope or run your own experiment.


Hint on scanning - back the page with black paper. It prevents the reflection from behind the sheet that is partly absorbed by ink on the reverse side. The improvement in contrast is significant.

 

[nedders]

Please see crude sketch of red line showing rope path.

Basically they asked me what force would be required to pull the rope through the snaking pattern, if say a 200kg weight was attached to the other end

 

[LittleInch]

At 200 kg presumably vertical mass hanging off the pully system, I think any rope bending "friction" is basically negligible.

In terms of multiple pulleys used on cranes and lifting equipment etc, I can't recall a rope factor in any of them in determining the reduction in force for multiple pulley blocks.

If you need to just add 5% to the pull force o account for this and the starting fiction of the pulleys.

At no rope velocity it is zero extra force. Just can't see it being significant.

Looks like on for testing to me or luck up block and pulley design.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[rb1957]

"Basically they asked me what force would be required to pull the rope through the snaking pattern, if say a 200kg weight was attached to the other end" ... none ? the weight a 200kg is (IMHO) certainly more than enough to have that rope moving (at speed) through those blocks. Of course if by "rope" you mean a 8" dia cable then maybe there is a friction/stiffness issue ... what I don't know about ropes and blocks would fill a lot of very big books ...

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[nedders]

Hi. thanks for your answers.

Sorry, I should have given more detail.

Let's say we are pulling the rope to the left in the diagram.
The 200kg weight is hanging off the right hand side resisting.

I just wanted to know if the force required would be 200x9.81, or more than that.
Obviously it would be more, but would it be significantly more or not.

My theory was if bearings are "frictionless" then, any snaking pattern would be irrelevant.

Not sure what else I could calculate to get an expected value.

 

[Tmoose]

That 1930 Marks Handbook empirical efficiency value looks to be over 90% except for hemp rope over 1-1/2".

With 7 pulleys involved I'd expect 7X "not very much" would total " something" .

 

[LittleInch]

But the angle is much less than 180 degrees and there are no sides on the rollers - sheave efficiency. Plus nedders has invented frictionless rollers.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Scuka]

How bad would it be if you give the wrong answer?
I don't see anything in this system that would cause any sort of significant resistance to that rope, provided you're not pulling some thick metal cable.

But you need to be sure? Make a simple test rig.

Buy 2 metal sheets or wooden boards for a few bucks.
Buy 7 roller bearings for a few bucks.
Buy 7 bolts and nuts for a few bucks.
Drill 7 holes in your plates.
Put it all together.
Pull the rope through and see what happens.
Drill another 7 holes further apart for a deeper S shape and see if that changes things.

 

[nedders]

Hi
Actually we do plan to make a test rig.

It's just that my boss wanted me to provide some calculations on what I expect the answer to be prior to this.

In his mind, he expects a huge resistance, which to me seems like a small miracle.

We do intend to test at various cable sizes up to a 64mm metal cable I believe

 

[MintJulep]

Bending stiffness of wire rope given here.

http://documentation.dsaocean.com/tutorials/Tutorials/PDS-AAQ.html

Lot's of formulas.

https://www.mdpi.com/1996-1944/13/17/3842