Hand calc. possible for a brake disc?

[321GO]

Hello Guys,

I'm trying to hand calc a brake disc to get some estimate of the stresses in the collar part(the part connecting the actual brake disc to the hub mounting face).

The stress state from FEA results prove very complex and multidirectional(basically a mess).

Does anybody have any experience with such a setup? Any thoughts, suggestions or assumptions to make are more than welcome.

p.s. thermal induces stresses are excluded, pure torgue loading

Thank you all.

 

[desertfox]

Hi 321GO

If its a bolted flange and hub, for a purely torque loading I would do a hand calculation similiar to the calcs done for a shaft coupling.
see this link:-

http://books.google.co.uk/books?id=PISJL2HwOwgC&pg=PA385&lpg=PA385&dq=torsional+

strength+of+bolted+couplings&source=bl&ots=NoJE_egIw-&sig=_roMvkwFW4sQWMQymkQAd0QeH-0&hl=en&ei=7OKcS_jJNZKM0gSUz9jqAQ&sa=X&oi=book_
result&ct=result&resnum=7&ved=0CBgQ6AEwBjgK#v=onepage&q=
torsional%20strength%20of%20bolted%20couplings&f=false

desertfox

 

[321GO]

Hi dessertfox,

first off thank you.

i suppose you're referring to the expression for shear strength of the hub-flange intersection:
d^2*f >= 2T/(pi * Sshear)
d=shaft dia.
f=flange thickness
T = torque

But this assumes torque effects on the complete circumference, which is not the case for a brake disc.
The pad only interacts on (let's say)a quarter of the circumference(90 deg).

Do you think one could simply divide the left part of the equation to counteract this effect?!

Some would probably shoot me for such's a remark, but i only need pallpark value's...

Again, thanks in advance!

 

[desertfox]

hi 321GO

Yes your assumption about my post is correct.
Any chance you can provide a sketch, are you refering to the brake pad pressing against disc during operation? in which case you need to multiply the normal force by the coeff of friction to obtain the force acting tangentially.
Also with the resultant normal force you need to find where it can be considered to act radially from the hub centre, knowing that gives the radius at which the tangential force acts.

desertfox

 

[321GO]

hi desertfox,

pls see attachment.

The problem is that i'm not sure how to correctly cope with the fact that the reaction (to the tangent pad force) is only coming from a part of the circumference(approx 90 deg), due to the pad contacting the disc locally.

 

[desertfox]

hi 321GO

Have a look at this file I have uploaded, I assumed there was a hole in the centre of the collar though in my calculation.

desertfox

 

[TERIO]

As far as doing a hand calc to determine the shear stresses in the collar Tr/J should get you in the right neighborhood. However, it likely won't be very close to your FEA result.

If your collar was long compared to its diameter and you were looking far from the connection between disc and collar (at least a couple diameters) then you could expect the stress to be Tr/J regardless of how the torque is applied due to St. Venant's Principle. Since you are looking at stresses that are near the application of the load this won't be the case. I would expect that you would see shear stresses higher than Tr/J in the collar in areas close to the pad and lower than Tr/J in areas far from the pad (shorter distance -> stiffer -> carries more load).

 

[desertfox]

Hi 321GO

Terio makes a good point about the intersection between the disc and collar, you can use the stress concentration factors from this link below for torsion of a stepped shaft.

http://www.roymech.co.uk/Useful_Tables/Fatigue/Stress_concentration.html

you may need to scroll down to the case that you need.

This combined with the formula in my uploaded file should get you in the ballpark.

desertfox

 

[hydtools]

321GO, the calculations and solution do not care about how large or small the contact angle of the brake pad is. The previous posts show you how to find the forces and solve the hub or collar load. You are making the problem more complicated than it is by trying to resolve your thinking about how large the contact arc may or may not be and how that will influence your solving the problem. It does not matter. The solution of forces and torque do not include any arc of contact or action on the disc or hub.

Ted

 

[TERIO]

Clarification on my last post - I was not intending to point out SCFs although there obviously will be a stress concentration. My point was that I don't think the shear stress (without consideration of SCFs) will be uniformly distributed around the circumference of the collar; the part near the load application will be more highly stressed (see attached).

http://files.engineering.com/getfile.aspx?folder=98cc731e-d034-4710-927d-66a462dfc4a0&file=disc.pdf

 

[321GO]

Hello Terio,
i agree with you, the FEA results also prove your point.

I will try the suggestion from desertfox, regarding the stress concentration factors.

 

[desertfox]

Hi 321GO

Post back and let us know how you get on.


desertfox

 

[TERIO]

Not sure why I didn't explain like this before, but it is not just a pure torque loading; there is a torque and a transverse shear force. Close to the point of loading shear stresses due to torque and transverse shear will be in the same direction and on the other side they will be in opposite directions.

 

[GregLocock]

The problem is more similar to a cranked cantilever than a simple torqued disk problem. Sadly the assumptions you make will have a 1:1 effect on the stresses you see.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[321GO]

I have posted the FEA results for the shear in the collar part, i'm doing some calculations based on the post of TERIO.

Thanks for all the suggestions.

 

[321GO]

Hello Guys,

i did a hand calc. based on the suggestion from TERIO(see attachment).

Not sure if's this simple though...although the result somewhat approaches the FEA.

Thought's more than welcome!

 

[desertfox]

Hi 321GO

I can't understand were the vertical reaction comes from, I am obviously missing something perhaps you can point it out.

desertfox

 

[321GO]

Hi deserfox,

the sole force that the brakepad/disc interface can create is tangent to the circumference, no two ways about it.
Since the pad is assumed on 3 o'clock position(and disc rotating clockwise), the reaction force is vertically upward.

The reaction force is counteracting the torque for equilibrium.

Besides the torque induced shear, there is also shear due to the vertical force, it's trying to shear the friction ring of the collar, upwards(credit to TERIO).

 

[Bobber1]

Just to further complicate things, the forces may be limited by the allowable tire friction. You can have giant brakes but if you have skinny tires, the hub and brake pads will not control the forces.

 

[JStephen]

It seems to me you have two possible approaches here. If the thing is new, never been done before (at least by you), then you take your best shot at a design, make it extra conservative, and probably have a workable if heavy brake. If it's an actual production part, then you likely have 40 years of corporate experience in designing similar parts to draw from, as well as FEM. But taking a part optimized based on experience, and doing hand calcs on it, I'm not sure what you'd really learn from it.