Fastened joint - Preload scatter - Bossard calculator

[Juanda]

TL;DR Summary

I don't understand why the Bossard calculator gives greater differences for the resulting preload when the friction variance is more controlled.

Fastened joints are subject to scatter. It's impossible to get exactly the same value every time. This is especially relevant when using methods that rely on friction such as torque wrenches. The scatter is a combination of the possible differences in friction and the precision of the tool.

Bossard is a company that has released some very useful information regarding fastened joints mostly based on VDI 2230. To be precise:

• F_044: Friction and friction coefficients. The document is sometimes referenced as F.049 which is the code of the page shown in the lower right corner.
• F_047: Preload and tightening torques.

Those couple of documents are nice but even nicer is the online calculator they released to make everyone's life simpler because it does a lot of the job for you. You just input the numbers and get the output.

However, I was very surprised when I compared the results of two different joints where the only difference was the “Friction coefficient Class”. According to F.049, the lower (alphabetically ordered) the class, the better because the range is smaller. As you can see in the following picture, the range for the friction coefficient is smaller in the upper classes.

A smaller friction range implies a smaller difference between the possible slopes in the following graph.

Now comes the surprise. I compared the output for two inputs with the only difference being the friction range. I made it so the friction range was equivalent to a “Friction coefficient Class B” vs “Friction coefficient Class D” which is two classes worse.

Input for the class B (0.08 range in friction coefficient)	Input for class D (0.15 range in friction coefficient)
Output for the class B (46 % difference)	Output for the class D (43 % difference)

The necessary torque (maximum tightening torque) to reach the input utilization of yield (80 %) is greater in the D class since there is more friction to overcome. That makes sense. To find that number the online calculator uses the lowest possible friction to make sure you won't over-torque the bolt and brake it while preloading it in case the friction happens to be lower or the utilization is so big that it breaks once it's put in use.

What breaks my mind is the fact that the "Difference" is also lower in the D class. That makes no sense to me. In the D class, we are more uncertain about the joint's friction (0.08 vs 0.15 range). That's what makes it undesirable in the first place since that can produce a lot of variation in the preload. But we're seeing in the calculator that class B is resulting in greater potential differences in preload (46 vs 43 %). As far as I know, these calculations should be linear so the greater certainty in the friction (a smaller friction range) should result in a smaller difference in resulting preloads.

Am I missing something or is there something wrong with the online calculator?
I probably could create an Excel sheet or small Python script to calculate everything but I'd rather not reinvent the wheel and use the tools already available out there. Also, I could commit mistakes I'd hope a big company such as Bossard has made sure to check for.
However, I need to be sure such tools are reliable.

 

[Juanda]

I'm still exploring this. I did the calculations myself following the ECSS-E-HB-32-23A while simplifying some steps and defining targets slightly differently but I got results very similar to the Bossard calculator for the low friction case. The high friction one differs significantly only on the axial preload obtained. I assume it is because Bossard is considering the combined stress due to the torsion while I'm only using the axial stress due to the elongation as part of the simplifications previously mentioned. As a result, for a given target utilization, cases where the friction is greater will end up with a lower axial load.

Still, my main surprise was that I got the same percentual difference in axial preload when using "The Experimental Coefficient Method" which is supposed to be "the accurate method". As a reminder, that is 46 % for class B and 43 % for class D. It still doesn't make much sense to me but getting the same as the calculator from Bossard would be too much of a coincidence. My current explanation for this is that, although the difference in friction is smaller ($0.16-0.08=0.08 \lt 0.35-0.20=0.15$), as a percentage it is a greater difference ($\frac{0.16-0.08}{0.16}=50\% \gt \frac{0.35-0.2}{0.35}=42.85\%$).
Note. I think the 42.85 % from the high friction case being very close to the 43 % previously shown is a mere coincidence. In the low friction case, such similarities do not exist.
Therefore, the difference % in axial preload in the final results will be greater for class B than for class D when using the bottom and top values from the brackets. The conclusion from that result would be that the main advantage of being in a better class is that the axial preload can be greater for a given utilization since there isn't as much energy wasted as torsional deformation although you'll have more uncertainty in the result.

I find that quite strange because that's the conclusion when using "The Experimental Coefficient Method" with the lowest and highest values of friction from the brackets defined in F_044. However, it's known that using lubrication will result in less uncertainty. NOTE: Class D is not non-lubricated. We are comparing MoS2 vs oil lubrication. I'd have used the unlubricated case E to compare it with class B but there is no upper limit for that scenario. Bear with me and consider the oiled case to be unlubricated.
There is another method (The Typical Coefficient Method) that is supposed to be more inaccurate. It uses a nominal value of friction and encapsulates all the uncertainty within "Uncertainty factors of tightening methods". In such a calculation, having lubricated bolts does produce a smaller uncertainty since its uncertainty factor is $\epsilon=0.25$, while for unlubricated ones it's $\epsilon=0.35$. Using this second method considering the nominal friction being the average friction from the bracket results in greater uncertainty in the unlubricated case as normally expected.

So on one hand there is class B with lubricated bolts which will produce a greater axial load for a given utilization than class D with worse lubricated bolts. That's clear.
However, the discrepancy in the difference % depending on the method used is still puzzling me. I assume this is because the brackets from F_044 don't mean the friction coefficient will vary between the two limits. It means the friction coefficient must be inside the bracket to be considered belonging to a class but the variation will be smaller than the full size of the bracket. To be precise, in the case of lubricated bolts, the variation should be in the order of 25% according to the uncertainty factors. This by the way is especially funny because 25% above and 25% below means a 50% difference between the top and bottom which is the same as what I got from the change in the friction coefficient for class B if we consider the nominal friction to be the average between the two limits.

I think my main problem is that I don't understand the friction brackets given by Bossard in F_044 because using the bottom and top values from the brackets gives results that are too strange. Having greater uncertainty with lubricated bolts than with worse lubricated bolts makes no sense.