Frictional Moment produced by contact between rotating and non-rotating surfaces

[Kreat-Impulse]

1. This problem is part of an engineering model I am working on for a class. I am ultimately trying to model the torque applied to a bottle as a function of the static/kinetic coefficient of friction between it and the rubber cone it is being torqued by (The reason for this being bottle caps and jar lids are not all made of the same material, so the c.o.f. will change)

The rubber cone is glued to a gear connected to the pawl of a ratchet configured for a 4:1 mechanical advantage. For every time a force is applied to the ratchet, there will be an impulse generated on the gear and thus the rubber cone causing it to turn and producing friction between it and the bottle cap (which will hopefully, or theoretically, turn the bottle cap).

My question is how to calculate this frictional moment.

2. Torque is given by Tau=Force x Radius=I x alpha

where I is the moment of inertia of (in this case) the center of mass, and alpha is the angular acceleration.

The applied force to the ratchet (and thus the torque), the surface area of contact between the cone and the bottle cap, the dimensions, mass, and inertial properties of the cone and bottle cap are all known. The variable is the coefficient of friction.

3. My guess would be that you would integrate the Torque over the surface area of contact and multiply that by the coefficient of friction.

In the end my frictional moment looks like:

M(f) = (mu)*tau*A = (mu)*F*r*pi*d*t

where mu is the c.o.f., F is the force applied to the ratchet, r is the radius of the gear glued to the cone, d is the diameter of the bottle cap, and t is the width of the surface contact area.

Thanks for you input.

Kreat-Impulse

 

[Dr.D]

You have a lot of terms, a lot of variables, etc. all of which are entirely clear to you but which do not come across clearly to the reader. You really need a figure with clear labels to show what each of your variables represents.

For example, you speak of the moment of inertia, the angular acceleration, etc., but you don't say what moment of inertia, what angular acceleration, etc. you are speaking about. Now before you say that I am just being picky, let me also remind you that you have also talked about a bottle, a bottle cap, a ratchet, etc., so there really are several different bodies involved, each of which has a possible motion and physical properties. In short, you need to learn to communicate before anyone can be of much help to you.

 

[thomate1]

I would like to commend you on your thorough approach to this engineering problem. Your understanding of the relationship between torque, force, and friction is correct. To calculate the frictional moment in this scenario, you can use the equation M(f) = (mu)*tau*A, where mu is the coefficient of friction, tau is the applied torque, and A is the surface area of contact between the cone and the bottle cap. You can also take into account the dimensions and properties of the cone and bottle cap to get a more accurate calculation. It is important to note that the coefficient of friction can vary depending on the materials and surface conditions, so it may be helpful to conduct experiments or use a range of possible values in your calculations. Overall, your approach is sound and I believe you will be able to accurately model the torque applied to the bottle. Good luck with your project!