Help on Calculating Flange Stress?

[tharding247365]

This is not for sealing purposes. This is purely for transmitting torque. I've designed an Aluminum Flange that bolts onto the back of a steel rear differential flange. How would I go about calculating stresses purely from the bolt preload, thermal preloads in extreme conditions, and also in service when the assembly is transmitting torque? I don't want the bolt to lose bolt preload and eventually undo itself.


To simplify this, you could almost envision 2 plates that are bolted together. One steel, one aluminum. Socket head bolts if that matters.

Any help would be appreciated, it's been awhile since I've been in school. I usually don't need to calculate any of this, but the question arose.

Aluminum Flange I designed is 6061-T6 Aluminum. Steel is an existing OEM part, which I'm sure won't be the weak link in this equation, however I'm not sure of the exact grade of steel. Bolts are steel as well.

 

[Screwman1]

I don't have time today to get into the details that you are askiing but the first thing to do is to get rid of the Sacket head screws and change them to flange bolts to spread out the load and reduce the hardness level to the point where you won't have a stress corrosion failure- there is a reason why class 12.9 is no longer in the SAE std.

 

[tharding247365]

I agree with your suggestions, however the intention of the part was for the customer to reuse existing bolts. They actually prefer the socket head screws. They do however, sometimes use washers to spread out the load.

 

[SwinnyGG]

As stress calculations go, this is an easy one for a few reasons.

If you are transmitting torque (and your description, and use of the term 'OEM' sounds like you're mating a drive shaft) than your flanges are small, which means they are stiff, which means they won't deflect very much and put a bending load into your bolts.

All you really need to know is the service temperature. Calculate how much the flanges will grow in thickness at that temperature- if this is in fact a drive shaft on a car, the change in thickness will be very small since the flanges are outside rotating quickly in open air.

This change in thickness multiplied by the modulus of the bolts will tell you the additional stress imparted.

There should be zero additional bolt loading due to torque in service, if you assume that any slipping of the flanges constitutes a failure (as I would...). As a result of that, you just need to ensure that the clamp loading between the flanges is sufficient to withstand the service load in torsion.

 

[tharding247365]

We're not so much worried about withstanding the service load in torsion, we've actually tested that.

I'm more concerned about the rigid joint's clamping load being too much for the aluminum, and possibly have the bolt work itself out over time due to yielding of the aluminum flange, and or expanding and contracting. How would I go about figuring this one out?

 

[SwinnyGG]

So you're trying to make sure that the heat cycles don't add to the bolt preload enough to cause the flange to fail?

1) determine localized stress on the flange due to bolt preload. This is easy. Bolt preload force divided by contact area between the flange and bolt head.

2) check this stress, reduced by your safety factor of choice, and ensure that the flange does not yield

3)estimate service temp, with a safety factor of your choice

4) determine how much the flange grows at this temp

5) determine the added preload created in the bolt at this new length (easy as long as the bolts are in their elastic region which they almost certainly should be)

6) repeat steps 1 and 2 with this new preload number

 

[tharding247365]

Hi guys, think I figured this out. jgKRI pointed me in the right direction.

Found some other literature online as well to help with some of the equations.

1. Clamping Force due to preload: T=PKD, solve for P T = Torque, P = Force K = Coefficient of Friction D = Diameter of Bolt
2. Pressure exerted on Flange P = F/A P = Pressure F = Force A = Area under bolt head
3. Solve for change in length due to temperature for each member. L =IL * a(t1 - t0) L = Change in Length IL = Initial Length a = Linear Expansion Coefficient T1 = Final temperature t0 = Initial Temperature

4. Solve joint stiffness to use in thermal loading equation in the next step. This part was the hard part. I needed to solve for the stiffness of each frustra, the bolt, and the total joint. This guide helped a ton. Been awhile since I've done this in school.

http://portal.ku.edu.tr/~cbasdogan/Courses/MDesign/course_notes/Joint_Stiffness.pdf

5. Thermal Loading Ft = ((kb*kj)/(kb + kj))*(Lj - Lb)

http://www.roymech.co.uk/Useful_Tables/Screws/Preloading.html

6. Add your Ft back into the equation in step 2. Ft + your original F will give you preload force + thermal force, solve again for the new pressure.
7. Check to see if that new pressure exceeds yield strength.

This whole problem was a lot more involved than I thought. If you find anything wrong in the way I went about this, let me know!