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Engineers: Check my math

Jared_Solomon

Well Known Member
Hey All,

i've been plugging away at my RV-14 and I've run into a snag. After installing the main landing gear and performing the toe-in/toe-out measurements it appears that my left landing gear has a twist in it resulting in 2.8 degrees of toe-in. I decided to machine myself a shim to take the twist out (I have the equipment, so why not!). I installed the shim and it went on no problem. It got me thinking about the preload I might be putting on the bolts with the 2.8 degrees of deflection. I reached out to Van's. I spoke with Gus who in turn spoke to engineering. His response was engineering felt it should be fine, but he thought it was best to replace the gear. There shipping me out a new gear leg today. As a side hobby i've been trying to learn more about mechanical engineering. So I decided to try and run some calculations of my own to see how how much pre-load, particularly in shear I am putting on the bolts with the shim. I used an online beam stress calculator to run my calculations. Am I in the ballpark?

Beam Length (Bolt Length) = 2.25
Center of the deflection = 1.125 (half way point)
Area Moment Of Inertia = 0.00019
Young's Modulus = 30E+6 * .38 (reduced for shear) = 11400 KPSI


I also ran the calculation for the full Young's Modulus of 30E+6, which brought the shear force to 0.7 KPSI.

2017-06-01%2020.56.34.jpg


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extremes.png


shear.png
 
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Interesting issue. I'm not an engineer, but studied Aero E many many years ago. I would look at this more as tension vs shear. I'd guess your numbers are good - also consider the direction of the preload is horizontal since you're correcting for toe in/out. Any operational loads are going to be primarily vertical with landing unless you really hammer the brakes or hit something hard. Anyway - non issue since they are sending a new leg. Van's is very good about that sort of thing. I expect I will need about .75 degree correction on my left leg. Van's says they tend to do some warping with the heat treatment.

I had no luck at all with their "dangling bobs" method for lining things up. I found a little magnetic laser at Harbor Freight I used with the initial set up of the gear, and plan to use it again for the final correction when I get it up on the gear permanently.

Happy building!
 
adding a shim between flanges will create bolt bending when the axle is loaded. that is bad. bolts should be loaded in tension only unless it's an interference fit. I doubt this is an interference fit. adding a tapered shim between flanges is even worse because when you torque the bolt the tension itself creates bolt bending because the flanges will slide along the shim. basically, all you have to remember is do not bend bolts. but if you do have potential for bending bolts, like a carb lever attachment, put the shank in bending and not the threads. good call to replace the gear leg. ( I can't see the pictures to comment on the calculations but I wouldn't bother with this kind of calculation, just correct the issue. )
 
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I can not see the pictures, but will assume the wedge is located between two flat pieces through which the bolt acts. If that is the case the 2.5 deg is not much for the bolt bending, but the head and nut is another matter. Either a wedge, or spherical, self aligning washer on each end would address that. Then you would have been fine if needed. The proper loading case of the bolt would be to assume no friction, look at the wedge angle and calculate the shear loading of the wedge trying to spit it self out using static forces resolved orthogonal or parallel to the surfaces. Reality is that with a .2 friction factor, you should have enough normal force to resist a slip, but this would get you the worst case shearing force. Then you can look up the acceptable shear load in the MIL-HDBK-5J tables. You might want to add this pdf to your collection. Mr. Google can find a copy for download.
 
Shims are standard practice

adding a shim between flanges will create bolt bending when the axel is loaded. that is bad. bolts should be loaded in tension only unless it's an interference fit. I doubt this is an interference fit. adding a tapered shim between flanges is even worse because when you torque the bolt the tension itself creates bolt bending because the flanges will slide along the shim. basically, all you have to remember is do not bend bolts. but if you do bend bolts, like a carb lever attachment, put the shank in bending and not the threads. good call to replace the gear leg. ( I can't see the pictures to comment on the calculations but I wouldn't bother with this kind of calculation, just correct the issue. )

Hey Steve,

Using tapered shims on the RV-14, RV-8 and RV-12 is standard practice. I fixed the pictures so you should be able to get a better idea of what I was describing. Van's sells shims in 0.25, 0.50 and 0.75 degree increments to fix this problem. They suggest stacking them as needed. I don't think they had something as large as 2.8 degrees in mind. But 1 - 1.5 degrees is not uncommon for these airplanes. My solution was to machine a shim to the correct angle instead of stacking a bunch of shims. The question is whether 2.8 degrees is "just too much". Van's took the conservative route and simply offered to replace the gear leg, even though the engineers at Van's said it should be fine. I thought it would be educational to run the calculations though and see if the engineering department's position that it should be fine could be demonstrated via calculations.
 
Thanks!

I can not see the pictures, but will assume the wedge is located between two flat pieces through which the bolt acts. If that is the case the 2.5 deg is not much for the bolt bending, but the head and nut is another matter. Either a wedge, or spherical, self aligning washer on each end would address that. Then you would have been fine if needed. The proper loading case of the bolt would be to assume no friction, look at the wedge angle and calculate the shear loading of the wedge trying to spit it self out using static forces resolved orthogonal or parallel to the surfaces. Reality is that with a .2 friction factor, you should have enough normal force to resist a slip, but this would get you the worst case shearing force. Then you can look up the acceptable shear load in the MIL-HDBK-5J tables. You might want to add this pdf to your collection. Mr. Google can find a copy for download.

Hi Bill,

Thanks for the tip about MIL-HDBK-5J. I downloaded a PDF copy. Looks like it's got some great info in it.I fixed the pictures so the calculations can be seen. Would the head and nut experience more load due to the wedged shim? The nut is torqued to the correct spec (85 in/lb), so I would expect the clamping pressure at both the nut and bolt head to be the same as if the joint didn't have the wedge. Am I missing something?
 
Hey Steve,

Using tapered shims on the RV-14, RV-8 and RV-12 is standard practice. I fixed the pictures so you should be able to get a better idea of what I was describing. Van's sells shims in 0.25, 0.50 and 0.75 degree increments to fix this problem. They suggest stacking them as needed. I don't think they had something as large as 2.8 degrees in mind. But 1 - 1.5 degrees is not uncommon for these airplanes. My solution was to machine a shim to the correct angle instead of stacking a bunch of shims. The question is whether 2.8 degrees is "just too much". Van's took the conservative route and simply offered to replace the gear leg, even though the engineers at Van's said it should be fine. I thought it would be educational to run the calculations though and see if the engineering department's position that it should be fine could be demonstrated via calculations.

well, a tapered shim between bolted flanges may be OK for building a barn or something like that.
 
There are tens of thousands of 150 year old barns that were built without engineers and are held together with tapered wooden pegs.
 
GIGO

Your math is right but the formula is wrong. What you have is not a beam with two point loads on it but more like a beam with a single point load in the center. When assembled and torqued, the midpoint of the bolt is going to be forced to deflect about .040 to conform to the 2.8 degree angle. My sense is that this won't be a problem, but I can't prove that mathematically. Since you're a machinist, if you were worried about the bending load on the bolt, you could always ream out the holes on one side. But since they're sending you a new gear leg this is all an intellectual exercise, isn't it?
 
In the certified world they have been wedge shimming Cessna's axles for 60 plus years (with much steeper angles than your 2,8 degrees). Although it does put a bending load on the head and nut, I have never seen it to be an issue.
 
Some ME thoughts on the soon to be obsolete shim...

The loading scenario is essentially identical to the same system without a shim, assuming both sides of the shim are flat surfaces. The previous post is right in pointing out that your analysis model is not correct.

As others have said, the bolts will have some amount of bending strain in their center, depending on how much clearance the holes have. Additionally, one or both ends of the bolts (head and nut ends) could contain a bending moment. Whether or not these latter two exists depends on how much clearance the holes have. Without analysis and understanding the exact bolt geometry upon torquing, it is not possible to know how much margin is consumed by the angular deformations.

Additionally, understanding cyclic fatigue loading of bolts in systems like this is not simple, and requires understanding the elasticity of all members in the stack, among other variables.
 
Re-Ran the calculations

Thanks everyone for your replies. I re-ran the calculations with a different model based on your feedback. Which can be seen down below. The tolerances on the holes in both the axle flange and gear leg flange are very small, around -0.002. The contact points of both the bolt head and nut are perpendicular to the bolt axis(flat). Due to the small tolerances i'm thinking that the majority of the load (shear) is being applied uniformly along the bolt shank and the walls of the flange holes on both the axle and the gear leg. Therefore I'm thinking any moments on the bolt head and nut would be minimal.

The latest calculations show a 0.500 KPSI load on the center of the bolt, to deflect it 2.8 degrees (0.055in displacement) with a max shear force of 0.250 KPSI.

The NAS1304-29 bolts used in this joint have a min shear rating of 96KPSI. A 0.250KPSI pre-load seems negligible on the bolts, the flanges and the shim. The loads appear to be lower then I would have expected based on pure "intuition". I'm beginning to think that Van's engineering dept's position may be supported by the data. Unless my calculations are still way off :D

calc2.png


extreme2.png


shear2.png
 
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when is the last time you have seen a barn landed at 6 ft/sec? Buildings are built with generous factors of safety of 3 or 4, whereas airplanes are built generally with 1.5. You have to be much more careful.

I would put a tapered washer under the nut, assuming that there is enough clearance in the hole that the bolt doesn't bind when tightened. That would ensure that the bolt is in tension only.

Most shims that I have seen for gear axles have been for 1 deg or less. 2.8 seems like a lot. If VANS will provide a new one then that is the right answer.
 
The July 2016 issue of Kitplanes has an article, starting on page 46, about the things that a designer has to consider regarding bolted joints. It includes some decent references. It does not include actual analysis.

Caveat, I wrote the article.

Many of the comments in this thread are excellent, by the way.

How would I approach this joint? Simple - I'd contact Van's and ask them what to do, and then do that. Period.

Dave
 
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"when is the last time you have seen a barn landed at 6 ft/sec?"

Not to drag out my perhaps ill placed barn comments but you asked the question. A 1500 lb steer/cow/bull, at five mph, which they can easily do, would be 7.33 ft/sec.
Cattle do run into the side of buildings, it happens all the time when they are frightened or feeling frisky.
 
It is not the load on the beam that would concern me but, rather, the loads on the joint. Joints are far more complex to analyze than a beam. The design loads are based on intimate contact between flanges and you cannot guarantee that your shims are going to give you anything approaching full contact. For such a critical joint I would make sure the assembly matches the design.

Good luck!
 
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