Author Topic: Measurement of the coefficient of friction for the capstan equation.  (Read 10381 times)

struktor

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Re: Measurement of the coefficient of friction for the capstan equation.
« Reply #30 on: September 01, 2021, 11:00:06 PM »
Hello  agent_smith,

B=Rope-on-metal friction , more then 180deg angle of contact.

In the absence of friction, it can reach 180deg + 90deg = 270deg .

180deg + beta

0 < beta < 90deg


agent_smith

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Re: Measurement of the coefficient of friction for the capstan equation.
« Reply #31 on: September 02, 2021, 02:49:19 AM »
Thanks 'struktor',

The contact angles in my real-world image of a #206 Munter hitch were (obviously) approximations.
I wasn't really intending to say 179.134 degrees, or 189.3256 degrees (or whatever) etc.
The 180 degree U turns in my photo image are just approximations.

Be that as it may, is it within your scope of math knowledge to be able to directly apply the capstan equations directly to the Munter hitch photo image?
Or is this outside of your scope of knowledge? (its a genuine question - not an insult!).

I will have my new load cell late October, and could verify your calculations.

The coefficient of friction for rope-on-rope, and rope on metal is something you would have to work out?

Note also that under load, modern synthetic rope flatten a little bit and so there is more surface area contact (particularly at the rope on metal carabiner interface).

I suppose that if you knew the tension force at the load cell, you could work backwards and derive the coefficient of friction?
There will be static friction to initially overcome and then once the rope is moving, it is now kinetic friction?

I can easily measure the load while the system is in equilibrium.
Not sure how I would measure load at the brake end of the rope while it is moving? Maybe attach the load cell to the free end of the rope, hold it in my hand and then allow the rope to flow through the Munter hitch (and observe the LCD screen display)?

Summary:
What do you think 'struktor' - can you apply the math direct to the real world image of the Munter hitch and try to predict the force on the brake hand end of the rope?
Make your math predictions with calculations directly applied to the Munter hitch image (rather than abstractly on computer generated imagery).
Then I could check your predictions once I have my load cell...

Assumptions:
[ ] Rope would  be EN892 Beal 'Joker' 9.1mm diameter Link: https://sport.beal-planet.com/en/mountain-line/1418-5132-joker-91mm-gd.html#/14-color-blue/58-length-50m
[ ] Carabiner has radius of 5.0mm
[ ] Contact angle (rope-on-rope): Approx 180 degrees / Pi radians)
[ ] Contact angle (rope-on-carabiner 'first' point): Approx 180 degrees / Pi/2 radians) - feel free to be more precise!
[ ] Contact angle (rope-on-carabiner 'second' point): Approx 90 degrees (variable)
[ ] Mass held by Munter hitch belay = 100kg

Challenge accepted?

struktor

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Re: Measurement of the coefficient of friction for the capstan equation.
« Reply #32 on: September 02, 2021, 11:30:46 PM »
Thank you, agent_smith,

Need someone with FEA software (eg. ANSYS).
Examples of the MES program:
  https://youtu.be/3Y0EIBbXHi8
  https://youtu.be/ne9fxOG7f8A
http://personal.strath.ac.uk/andrew.mclaren/Steven%20Welsh%20Technical%20Paper%202013.pdf

I use a large simplification.
How does rope-to-rope friction work?
They can be simplified by adding an insert?
The figure shows a rope friction insert.

KC

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Re: Measurement of the coefficient of friction for the capstan equation.
« Reply #33 on: September 03, 2021, 12:05:18 PM »
Nice eye candy, what are you drawing with please Struktor?
i L-earn from drawing too, is all geometry..
And note that drawing tools basics are always a flat linear face or radial for 2D objects;
as these are important concept differences all across the board into drawing as knotting etc.
Thanks so much for links too!
.
In reply #30 tho, i do look at only the 180 arc opposing the pull from opposite side of the host as the only radial friction component that uses all tensions for seating to host to give then controlling frictions, nips and grips(w/oppsing180).  Using both the byproduct of deformation as side force and the force holding primary against Load too, as 1 for seating forces to host.
But i shy from calling The SPart (that for me ends halfway around the circle where 180 starts) and the pull from Bitter End seize as radial friction but rather more linear parts especially viewable here where 1 end pull towards Load if each of these legs.  But in in any case more linear rope part if endpoints in opposing directions.  Pure axis inline not a harsh point for there is no cross axis resistance, so directional claiming just a directional axis (vertical vs horizontal etc.) not a big point as would be in rigids that do resist on the cross axis.
.
Uniqueness of 180 arc would be that both ends, as center apex does, as in fact the whole component does
>> pull and work all as 1 in the same unique direction, as no other form does. 
>>giving structural arcs to bridges and ropes etc. thru this geometry.
"Nature, to be commanded, must be obeyed" -Sir Francis Bacon
We now return you to the safety of normal thinking peoples.
~ Please excuse the interruption; thanx -the mgmt.~

struktor

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Re: Measurement of the coefficient of friction for the capstan equation.
« Reply #34 on: September 03, 2021, 11:16:14 PM »
Thank you KC,

I am currently using FreeCad.
https://www.freecadweb.org



Good programs cost a lot.
But they can also do a lot.
Finite Element Modeling of Tight Elastic Knots
https://arxiv.org/pdf/2010.09109.pdf

struktor

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Re: Measurement of the coefficient of friction for the capstan equation.
« Reply #35 on: September 05, 2021, 12:05:06 AM »
Angle of friction.
https://en.wikipedia.org/wiki/Friction#Angle_of_friction

The rope slides down the vertical rod.
It will stop before it reaches a right angle.
This is due to the angle of friction.
The same will happen when the rod is replaced with a rope.
« Last Edit: September 08, 2021, 10:30:39 PM by struktor »

 

anything