Estimating Impact Force from Rotating Shaft on Collar

[jay_elec]

Hello All,
Some background information: I'm a co-op engineering student and recently my supervisor asked me to do a bit of research on a solution to a problem we had. Essentially, a cardan shaft connecting a motor and a gear box failed at a joint during operation and caused some extensive damage (luckily no one was hurt). A solution to this was to design a collar placed midway of the shaft to "catch" the shaft if it breaks and prevent damage to the surrounding. This shaft is rotating at high speeds so we are assuming precession plays an important factor as the shaft would hit the side of the collar instead of falling straight down if it breaks at a joint.

An important aspect to know before designing the collar is an order-of-magnitude estimation of the impact force from the shaft to the collar. One approach that I have been thinking of is using an energy method where we find the rotational kinetic energy due to precession from the shaft and equating that to the strain energy of the collar when it deforms from impact. Keep in mind that there assumptions that will need to be made (the collar will elastically deform, the shaft is rigid, the collar is circular, there is clearance between the shaft and the collar, etc.). My question is: is this the right approach to find an estimation of the impact force or is there another approach (maybe better) that I can take? If anyone can share any insight on this that would be awesome! I've also included a quick diagram to give a better idea of the shaft and collar.

 

[AlephZero]

I wouldn't worry too much about the initial "impact" of the shaft onto the collar, but what happens after that.

I suppose the worst case would be if the shaft fails at the gearbox end, so it is still being driven by the motor, and the motor might overspeed before something shuts it down.

The simplest situation would be that the shaft is orbiting synchronously with its rotation speed. You could model the shaft as a rigid rotating body with two forces acting on it, the radial force from the collar and a radial reaction at the motor joint.

But if describing it as Cardan shaft means there is a universal joint at the non-failed end, the situation could be worse than that. If the friction force between the rotor and collar is big enough, the rotor and collar will act rather like an epicyclic gear, with the friction replacing the gear teeth. In that case, the rotor will orbit around the shaft much faster than its own RPM in the opposite direction, depending on the radii of the shaft and collar. If the collar is strong enough, that might fail the other joint on the rotor, in which case a single collar might not prevent the rotor somehow getting into "free flight".

It might be better to have two collars one near each end of the shaft, first because from the geometry of the device the same clearance gap will only create half the orbital radius if one end fails, and if both ends fail you have a better chance of retaining the shaft inside the collars.

 

[jay_elec]

Thanks for the reply! I forgot to mention that there is a system that will shut down the motor if there is a sudden drop in current so we don't need to worry about over speed and can treat failure on either ends of the shaft as the same. I'm a bit unclear on how the universal joint at the non failed end would create a worse situation, can you clarify this?

 

[AlephZero]

If you have a universal joint in the shaft, you can get non-synchronous motion - i.e. the shaft can orbit around the collar at a different speed from its RPM.

For example, the joint would let you move the "broken" end of the shaft around in a circle at any speed you choose, even if the shaft was not rotating at all.

That is what could create the "epicyclic gear" type of motion, where the shaft is rolling around the collar without slipping, with a frequency of about ##\text{RPM} \times \dfrac{r_{\text{collar}}} {r_{\text{clearance gap}}}##.

When you kill the power, remember you still have the kinetic energy of the rotating motor to dissipate before everything stops - not just the KE of the rotating shaft.