Threading depth - 2. 2

[dulmant]

Dear All,

First of all I would like to thank everybody that answered my previous thread (31st of January).

I need now to take this subject further, as I still didn't get to any conclusive results.

Apparently there is no theoretical way to relate the percentage of load the first thread of a nut gets and the height of the nut, however this amount can generally be considered around 34% ("Chaddock", "Bickford", and I also found this in some Russian-"Orlov" and Romanian-"Minoiu" books).
It looks like the amount of load that acts on the first thread depends on the elastic properties of the material and on the number of threads. But is the second part really true, if this amount is always 34%? In this case it can be argued that it doesn't depend on the number of threads as long as there are more than 3! If this is so, and if the thread stripping calculations should be made taking this percentage into account, then again it is not important how many more than 3 threads the nut has, as we are calculating as if 3 would be enough!
How does VDI 2230 deal with this?

Furthermore, how can I calculate the height of the nut function both of the material of the nut and of the bolt?
I tried retrieving the max. axial force function of the material of the bolt, through its tensile strength and its stress area (Fmax.bolt = Sigma02xAstress) and then introducing it into the formula indicated by VDI 2230 for the nut, but I am not sure this is the right way as the results I got seem unrealistic.

Note that generally, for example for a bolt class 8.8 and a nut class 8, the height of the nut is h= 0.8xd, and 0.8 is the ratio between the bolt's yeld limit sigma02 (640N/mm2) and the nut sigma02 (800N/mm2); also when the bolt and nut are made of the same material it is recomended that the engagement length to be equal to the diameter of the thread, h= 1xd.
Related to this, Niemann suggests that the engagement length should be calculated like this:
h= 0.8xdx(sigma02-bolt/sigma02-nut)
But this also leads to unrealistic results, for example for a M24 class 12.9 bolt screwed into a plate steel St37, the height of the plate should be 0.8x24x(1080/240) = 86.4mm! Considering the pitch of this bolt, 3mm, the plate should have 29 threads but, as shown by the several authors, generally the load it is not distributed beyond the 10th thread.

I hope somebody can bring more light over this issues.

 

[CoryPad]

You are correct that there is no published theoretical method to relate first thread force ratio and required thread engagement. You have taken a big step when you say that only 3 threads are needed because the first thread supports ~ 1/3 of the force. Required thread engagement calculations are used to predict thread stripping (a fracture event, not a yielding event), so elastic force distribution is no longer appropriate. VDI 2230 deals with this by stating:

"In addition, the calculation model assumes that, on account of the plasticization at the instant of fracturing - stripping of the thread turns - there is a uniform distribution of forces over the thread turns inside the nut."

Thus, the calculation uses thread shear area (a function of thread form, diameter, pitch and height) and material strength to calculate a stripping force.

Usually, it is preferable to have the screw fracture before stripping the nut, so one should use the screw fracture strength, not its yield strength.

I am not familiar with Niemann, but that equation does produce unrealistic answers. Using VDI2230 for your example (assuming St37 has R_m = 400 MPa, and R_{m, screw} = 1220 MPa), I get required engagement = 30 mm, or h/d ~ 1.2. This seems very realistic to me.