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

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

(OP)

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?

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?

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

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

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

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

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

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

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 ?

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

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

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

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

--

JHG

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

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

I don't want to divide by two!

--

JHG

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

The torque is

T=Pr

r=average radius of thread.

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

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

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

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

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

T = 5000µ(2R/3) = 0.333*5000*µ*(2R)= 0.333*5000*µ*D## RE: Why bolt torque is T = (Friction factor) x F x D and not the radius?

It appears that your calculation is approximately true.

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

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

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 ?

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

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/di...

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

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

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 ?

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

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

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

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

Well, answer from my point of view, is that, both of the things are accomplishing quiet same results only the difference is that, in case of the Bolt, there is the axial elongation force involved and in case of rotating disc, weight of the rotor is involved. I think answer 74 N-m shall be correct for the specific query. Thanks again for the replies.

Now, speaking about the bolt, what i understood is that, Torque universally will always be T = F x r. In case of bolt now, previously what i was missing is, there are 2 surface friction bolt and nut experiences.

1. Friction between the threads

2. Friction between the Nut bottom surface and the surface of the component on which it is being tightened.

Here, the K factor which we use while calculating tightening torque is actually considering both these frictions and during the derivation "/2" has been taken care (i.e. r = d/2). Hence the simplified form what we see is T = K.F.d

where, d = bolt diameter.

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

Usually there are two components causing friction torque - friction between bolt head and surface and friction between bolt threads and mating part.

Maybe the source that supplied the T = KFd formula combined the two. That's quite the simplification though. At any rate, the numbers are all washed out by the choice of K.