Why bolt torque is T = (Friction factor) x F x D and not the radius? 2

[Abhijeet242]

We know that the torque is Force x moment arm. Here in this case why the moment arm is not radius. The real problem for me is that, I am calculating friction torque required by the rotating disc to overcome.
Here the I have done the calculations with below 2 methods:

1. In close approximation with Bolt torque :

Its a plain disc in Martensitic SS rotating on the fixed Bronze plate and acting as a bearing. The axial load is 500 kg including weight of the rotor. Hence like in case of bolt torque, we can say, the Axial force = 500 x 10 = 5000 N ( assuming g = 10 m/s2).
Now, T = 0.3 x 5000 x Avg. dia of the disc ( ( Inner dia. + Outer dia.)/2)

T = 0.3 x 5000 x ((0.119+0.0767)/2)
= 146.77 N-m
2. Considering simple approximation,

T = F x r = 0.3*5000*Avg. radius
= 73.38 N-m

So which one is correct? 73 or 146 Nm of torque?

 

[desertfox]

Hi Abhijeet242

watch the first part of this video it covers your rotating disc problem

https://www.youtube.com/watch?v=UX-2gwiLzFQ

Further more its much easier to watch the above than me type it all out.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[hacksaw]

The total frictional force is proportional to the contact area or pi*Deff.

 

[hacksaw]

Area = pi*Deff*(width of contact)

 

[rb1957]

"The axial load is 500 kg including weight of the rotor." ... is that kg mass or weight (like a bag of sugar) ?

the difference numerically is moot, but the difference in understanding is significant.

I think you have 500kgf weight, and 1kgf = 10N (near enough) ... you're changing the unit of force, as opposed to determining force from mass.

Can you please explain what it is you're doing ? "bolt torque" is usually the installation torque, to develop a preload. How do you go from weight to torque ??

another day in paradise, or is paradise one day closer ?

 

[desertfox]

Hi Abhijeet242

The bolt torque calculation using the bolt diameter is an empirical formula obtained from observations and practical tests rather than a theoretical proof.
If you look in any mechanics book and look for lead screws and stuff you will see they use the mean radius for the friction torque.


“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[drawoh]

Abhijeet242,

When I am analysing a bolt or screw, I know the diameter, not the radius.

--
JHG

 

[btrueblood]

What drawoh said, you buy bolts sized on the diameter, and/or measure them by checking the diameter with a pair of calipers. If you need the radius, divide by two.

 

[drawoh]

What drawoh said, you buy bolts sized on the diameter, and/or measure them by checking the diameter with a pair of calipers. If you need the radius, divide by two.

I don't want to divide by two![ ]

--
JHG

 

[goutam_freelance]

@Desertfox is right. In machine design you analyse a thread, derive the tangential force(P) developed due to axial forces and resulting reaction and frictional forces.

The torque is

T=Pr

r=average radius of thread.

 

[rb1957]

if that's what yu want to calculate. But the OP is taking the load applied (500kg = 5kN) and trying to find a torque. I don't see what he's trying to accomplish.

another day in paradise, or is paradise one day closer ?

 

[r13]

Torque is related to force couple as shown.

 

[goutam_freelance]

I think your case is different from screw thread case. Refer derivation below:

 

[r13]

...Now, T = 0.3 x 5000 x Avg. dia of the disc...

T = 5000µ(2R/3) = 0.333*5000*µ*(2R)= 0.333*5000*µ*D

 

[goutam_freelance]

Further to my post above where I have considered circular disk, I have refined the derivation for annular disk (which may be the case with you). The coefficient of friction is 0.3, assumed.

It appears that your calculation is approximately true.

 

[abhishek sutar]

I only know diameter of a bolt or a screw when analyzing it, and not radius.

 

[rb1957]

"I am calculating friction torque required by the rotating disc" where's the screw thread ?

what's weight got to do with a spinning disc ? the MMoI of the disc would be more relevant.

another day in paradise, or is paradise one day closer ?

 

[desertfox]

Hi rb1957

The OP who doesn’t seem to be responding of late, was confused by the fact that finding the bolt torque involved the bolt diameter and not bolt radius, whereas on this friction disc he should be using 2/3 R for the disc radius, which falls in line with the video link I posted and at the end of this post there is a link to the notes which are from the video link.
The mass of the disc is required I believe, so that he can calculate the frictional torque can be calculated.

http://mechanicsmap.psu.edu/websites/6_friction/disc_friction/discfriction.html

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[rb1957]

mass/weight required if that's the normal load, P.

If someone's pushed down on the disc, then it'll be higher.

So this is the torque that needs to be applied to the disc to overcome static friction ... and then it'll start spinning and then MMoI will be important.

another day in paradise, or is paradise one day closer ?

 

[desertfox]

Yes rb1957 I think at this stage he just wants the required friction torque.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein