Calculating resistive torque on vertical shaft

[Luuk0312]

Hi there,

 

For a university project me and my project group have to make a model (in Matlab) of a trifilar pendulum in such a way that it accurately represents the motion of the pendulum in real life. In order to do so we have to come up with all the physics formulas related to the pendulum. One of those is the resistive torque caused by the pendulum disk being in contact with the center shaft. This causes for a resistive torque due to which the disk will be slowed down as it is rotating. My question now is: how can I calculate this resistive torque? I know that Coulumb's friction law equals F_f = μ * N and I am sure I can find out what the friction coefficient between these two materials is, but what I don't know is how to calculate the normal/radial load of the disk on the shaft. I have searched the internet for a couple of hours and could not find anything on how to calculate an actual value for the normal load. What I did find was how to calculate the radial load on a bearing when a horizontally placed shaft with weight W runs through the bearing, but in my case the ''shaft'' is standing vertical and there is no bearing between the contact surfaces.

I would be happy if someone could help me with this problem or at least send me in the right direction, since at the moment I have no idea on how to continue. I will add a picture of the pendulum where it is clearly visible how the disk and the shaft are in contact with each other (red circle).

 

 

[studiot]

If I understand your device correctly, the (horizontal?) disk we see in the pic is the 'bob' of the pendulum, which is suspended by the three wires we see.

The shaft you refer to is really a locating or centering pin and no shaft work is input or extracted.

It is not clear how the motion is driven/activated.

Presumably the oscillatory action is a twisting one.

So is the bob set in motion and then allowd to twist freely back and fore under the influence of the support wires?

Or is the head the head or top end of the wires driven to oscillate back and fore?

 

Either way you are interested in the interaction between the locating pin and the disk.

Have you set up 3D Euler axes in your program?

I say this because the three wires are set at angles so will induce a 3D system of torques in the disk.

In turn the disk will jam against the locating pin to produce counter torques.

It is not practical, if indeed possible, to calculate these counter torques directly, but they will be equal and opposite (good old Newton) to the loading torques from the tnesions in the wires. That is why your search was fruitless.

Presumably the contraption motion is sufficiently gently such that wires all remain taught at all times?

[Luuk0312]

First I want to make clear that we  will not have to model the disk motion in a 3D program so that we see the setup moving on our computer. We want to model the system using Matlab, a mathematics program with lots of different functions we are probably not going to use, and the result we are looking for is a plot of a sine wave which will dampen out over time (due to resistive forces/torques). Then we will do real-life measurements on the disk and compare those to the model. The goal of the project is to make the model as accurate as possible to the real life situation.

Then, I am not sure what you mean by 'bob', but I assume what you are asking is if the disk is the thing that rotates and moves up and down. If so, that is correct.

The motion can either be driven by 1. an external excitation device (unfortunately  I do not know how this device works or what it looks like yet) or 2. twisting the disk and letting it twist freely back and forth. For now we are just looking at modeling the motion of the disk when we let it spin freely back and forth. We started by making a free body diagram including all the forces and torques present in the system, I'll put up a list here:

1. Horizontal component of cable forces applying torque to the disk and causing it to rotate when we let it loose.

2. Gravity which pulls the disk down once it is let loose (gravity force is larger than the vertical component of the cable forces).

3. Center pin resistive torque.

4. Air drag force when the disk moves up and down (although this may be negligible due to extremely low up/down velocity)

5. Friction in the cable joints/hinges (we have no idea how to model this, but we assume this is negligible as well).

I am not sure what you mean by ''Presumably the contraption motion is sufficiently gently such that wires all remain taught at all times?''. Could you elaborate?

And if the center pin resistive torque equals zero, will this mean that the disk could keep spinning forever (assuming air drag and friction in cable joints/hinges is negligible), or did we forget an important force/torque opposing the disk movement?

Edited September 18, 2018 by Luuk0312
Forgot something