# Thread: Electronics Engineer needs help with Belleville calculations

1. ## Electronics Engineer needs help with Belleville calculations

I have an alternator with a splined dog bolted to an M10x1.25 threaded shaft. Originally it used a shouldered nut torqued to 40 Nm, but it was prone to loosening so the factory added a Belleville washer and changed the nut from 10 mm A/F to 15 mm A/F.
When I removed this alternator I found that nut was loose, so I plan to upgrade to the new fixing system.

The Belleville washer specified is DiN2093 20x10.2x1.0x1.0 which I believe is flat at 1.0 mm deflection and is 1.0 mm thick.

The axial load on the "bolt" would be,
F = T / c / D
= 40 (N.m) / 0.2 / 0.010 (m)
= 20,000 N
where c = 0.2, the coefficient of friction of a steel thread
(ref: https://www.engineersedge.com/torque.htm)

I understand that the load on a "bolt" should be shared with the Belleville washer, in order for the washer to immediately compensate for the relaxation of the load, due to creep or thermal expansion, so I would expect that the Belleville washer should be sized to flatten at 20,000 N.

The calculator I found:

tribology.png

determines the flattening load of the washer above as 3,300 N when deflected 1.0 mm, using E = 210 GPa, which I understand is that of spring steel, as used in a DIN2093 washer.

So, my question is, assuming the calculations are correct, how useful can this washer be if the axial load must reduce from 20,000 N to 3,300 N before it will begin to move?

2. A Belleville washer is generally used as a spring, or to have a flexible preload range for a bolt or bearing installation.

Belleville washers could be used as a bolt locking method but only in very low dynamic load applications within the range of the Belleville washer spring compression length. You can stack the washers to change the spring rate and depending on the configuration the range where spring load is available.

A Belleville washer is not what you need to lock the bolt/nut on your shaft.

I suggest for locking the fastener, either a split lock washer, thread lockers, or an interference or locking thread. Also, you may be able to modify the shaft to accept a cotter pin and use a castle nut/bolt as a locking method.

3. Belleville washer design calculator I use..

https://www.engineersedge.com/belleville_spring.htm

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