Friction Torque Calculation Question

[Eylon]

I need to spec a servo motor to rotate a heavy load (~1,200 lb).
The bearing surface is a round steel plate rotating on lubricated round bronze plate(6" OD).
Below are the formulas I used for the calculations.
Fn and P are the force and pressure acting on the rotating plate by the mass.
r i&o are the plate diameters. Tb is the required torque.
My questions:
1. Does anybody have experience with a similar application or calculation and can verify the formulas? The resulted torque seems very large to me.
2. Is the friction coefficient (0.2) makes sense?

Thank you.

 

[CoryPad]

Similar equations are used for fasteners to convert applied torque to clamping force with friction at the rotating fastener surface. Your friction coefficient is high if the plate is lubricated well - I would guess your application to be closer to 0.1 than 0.2.

 

[Tmoose]

I anticipate starting from rest the torque will be very high.
Once moving, will it rotate for long periods?

Is the 1200 lb load the result of a process, or the result of a bulky object sitting on top or the thrust bearing?
I am concerned about the bearing set up required to guide and stabilize a bulky object.

A tapered roller bearing of modest size could handle a bunch of axial load and have very low starting and running torque.

https://www.grainger.com/product/NTN-Taper-Roller-Bearing-Cone-1YTX6

 

[LittleInch]

Sounds far too low to me. You've got over half a tonne of mass sitting on a 6" diameter plate any get 60 Nm?? 50 Nm is a fairly easy pull force for a person on 1 m long bar (5kg weight). Would that rotate a mass that big?

Of course there is no appreciation here of starting friction or acceleration which would seem to me be be a significant part of your torque.

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

 

[drawoh]

Eylon,

You said "servo motor". Does this mean the plate is rotated from one position to another, with some degree of accuracy?

T = 1200lb[×]0.2[×]3in[×]4.45N/lb[×].0254m/in = 80N.m

Historically, servo motors are sized by rotor inertia. Once you find one powerful enough to manage your mass inertia accurately, your friction torque may not be serious.

You could use ball or roller bearings.

--
JHG

 

[monkeydog]

As a side note, you will want to check your galling resistance for the two materials.

 

[drawoh]

Eylon,

One more thought, again based on the assumption that this is a servo system.

If you need to move accurately, you need to know what your friction torque is. Low is good, but if it varies reliably between say 81.2 and 81.4N.m, you know how much torque is required to overcome friction and accelerate your load at some precise rate. My understanding is that static friction is something like twice running friction (???). I would appreciate being corrected!

My gut feeling is that friction is variable, depending on surface finishes and the amount of lubricant on your surfaces. This is all the more reason to use some sort of rolling bearing.

--
JHG

 

[chicopee]

Your final answer for Tb matches Beer/Johnston's textbook Statics and Dynamics

 

[gruntguru]

Back of the envelope approximation.
To displace the plate linearly F = uN = 0.2 x 1200 = 240lbf = 1070 N
Lever arm for rotational torque ~ radius of gyration (zz) = D/(2 x 2^1/2) = 6/(2 x 2^1/2) = 2.12" = 0.054 m

Torque = F x r = 1070 x 0.054 = 57.65 Nm

je suis charlie