Modeling a (rotating) mass impact on a preloaded (rotational) spring

[vipers120]

TL;DR Summary

Numerical modeling of a system in which there is a mass rotating freely up to a certain point at which there is a preloaded spring.

I am trying to model numerically the following system:
A rigid body mass is rotating freely around an axis (no rotational stiffness/damping) within a range, let's assume plus-minus 3 degrees for now.
Case A. The external forces on the mass are low and keep changing which results in the situation the angle of the rotating mass is within the range.
Case B. When the external forces on the mass are increasing, we hit a kind of end-stop at 3 degrees. From this point onwards, there is a (rotational) spring which is preloaded relatively high, let's say we have 10 000Nm of pre-load. After this pre-load, the spring stiffness is very low which means there will be not so much more than 10 000Nm given back to the mass.

I'm having issues modeling Case B, especially the time of hitting, i.e. the impact.

My thinking is:
If the incoming velocity (and thus Kinetic Energy) is high enough, the energy is higher that is stored in the pre-loaded spring and thereby will start to deform.
If the incoming velocity (and thus Kinetic Energy) is low, the energy is lower then stored in the pre-loaded spring and thereby will not deform.

1. Is this thinking correct in the first place? I was also thinking trying to approach this problem in terms of moments, because the pre-load is in terms of moments. However, then I don't know how to obtain the moment related to the impact.
2. How to calculate the energy stored in a pre-loaded spring?
3. If the incoming velocity is low, how to approach the impact: how do I model the impact correctly?

I've been trying to look into this topic online and on this forum but did not find similar problems.

 

[jrmichler]

Start with the simplest approach. Assume an impact with a perfectly rigid surface, and a constant torque of 10,000 Nm after any deflection. The calculation is simply the rotation angle to decelerate to zero velocity at constant torque. If the impact energy is small, the deflection will be small, but there will be deflection. There must be deflection because otherwise a finite mass with finite energy impacting a rigid surface would have infinite torque.

The more complex approach is to assume a contact stiffness. Any real object in contact with another real object will have a deflection that is some function of the contact force. Search contact mechanics to find some good information on this. In that case, you would calculate the contact stiffness and use that contact stiffness to calculate a peak deflection, use that peak deflection to calculate the peak torque. If the peak torque exceeded 10,000 Nm, the spring would deflect. The spring torque would be a constant 10,000 Nm during spring deflection.

The even more complex approach is to take the above approach, and add in the spring stiffness. If the total spring deflection is small, this adds complexity without adding accuracy.

There are interesting numerical challenges when modelling contact. Those challenges can easily suck you down into a black hole. Try very hard to make the simplest approach work.

 

[vipers120]

Start with the simplest approach. Assume an impact with a perfectly rigid surface, and a constant torque of 10,000 Nm after any deflection. The calculation is simply the rotation angle to decelerate to zero velocity at constant torque. If the impact energy is small, the deflection will be small, but there will be deflection. There must be deflection because otherwise a finite mass with finite energy impacting a rigid surface would have infinite torque.

The more complex approach is to assume a contact stiffness. Any real object in contact with another real object will have a deflection that is some function of the contact force. Search contact mechanics to find some good information on this. In that case, you would calculate the contact stiffness and use that contact stiffness to calculate a peak deflection, use that peak deflection to calculate the peak torque. If the peak torque exceeded 10,000 Nm, the spring would deflect. The spring torque would be a constant 10,000 Nm during spring deflection.

The even more complex approach is to take the above approach, and add in the spring stiffness. If the total spring deflection is small, this adds complexity without adding accuracy.

There are interesting numerical challenges when modelling contact. Those challenges can easily suck you down into a black hole. Try very hard to make the simplest approach work.

Many thanks for your reply. I think I understand what you mean with your approaches.

I still have a little bit doubts in comparing the simplest approach with the more complex approach.

Using the simplest approach, you assume the restraint torque given to the mass would be 10 000Nm, constantly. This, depending on the velocity and inertia of the system, of course for a small time.
Using the more complex approach, you assume the restraint torque given to the mass could be somewhere ranging between 0 - 10 000Nm, using a finite stiffness in the case the deflection (in combination with the stiffness) would lead to a lower than 10 000 Nm.

These are, in my opinion, two quite different approaches with quite different solutions, aren't they?

 

[jrmichler]

Try the simplest approach. If the results are satisfactory, stop. If not, go to a more sophisticated approach. Repeat until the results are satisfactory.

Trying to figure out what is the best approach before actually trying the simplest approach is an example of "paralysis by analysis". A lot of numerical analysis is like that. Get something to work, then decide if you really need to make it better.