# Another non-viscous damping thread

• Q_Goest
In summary, the reciprocating pump is running at 350 RPM and has a 2.25" stroke. The piston is double acting and there's a very small clearance between the coupling and the piston. The contact stresses are no more than 2/3 of the yield strength of the materials.
Q_Goest
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I have a reciprocating pump running 350 RPM, 2.25" stroke. Piston is double acting (ie: force in both directions). Load is ~30,000 pounds. There's a very small clearance in the coupling between piston and drive train, and this coupling goes through the same motions as the piston (it is attached to the piston).

There's a ~0.003" gap between coupling and piston, so there's just a tiny bit of slapping going on. Not loud, but distinct. I'd guess the impacting loads are on the order of just a few thousand pounds. Once they come into contact, forces rise to 30,000 pounds.

Contact stresses are no more than 2/3 of yield strength of the materials.

Can this situation lead to non-viscious damping and potential heating of the coupling? If so, how might you calculate it?

I wouldn't necessarily refer to it as non-viscous damping, but the effect you're referring to could well be happening. The degree to which it occurs could vary from significant to barely noticeable.

You have essentially a load-unload cycle associated with the components that are slapping together. If the loading and unloading phases are identical, there will be no energy dissipation in the structure. What you would probably see is that the unloading stresses are slightly lower, indicating that energy is being dissipated within the system.

I'd refer to this as hysteresis in cyclic loading as opposed to non-viscous damping (although it's much the same thing, it's like the difference between using torque and moment). Yes, it could lead to potential heating, and could also have an effect on the fatigue life of your components. As for calculating it, I'm not sure how you'd go about it in service (as you'd have to measure the contact stresses during operation) but you would then have to reconcile the energy losses in loading and unloading to the temperature rise your components would see.

Unfortunately though, the rise in temperature's bound to be pretty small per cycle and your energy loss per cycle might be tiny...and thus very hard to measure!

Hi timmay, Thanks for the response. I think you're correct (should be a small/negligible affect). I’m just trying to see if there's something I'm missing here. I agree the loading/unloading phases (as long as the piston/piston knob) are in contact should counter each other. Those parts are all well below yield, so it’s essentially a spring loading and unloading.

I've thought about it some more and now I'm thinking this energy which is being dissipated as the parts slap together could be estimated from the fact they don't 'bounce' apart (ie: coefficient of restitution is zero or close to it). Question then is, what values should be used in the equation for kinetic energy, specifically mass and velocity?

The pump crosshead is doing all the work. It’s velocity as a function of time is well known and shouldn’t change significantly due to the impact with the piston shaft. Therefore, the velocity used to estimate kinetic energy is the velocity of this crosshead toward the end of each stroke. In other words, assume the piston stops at the end of the stroke, then crosshead moves toward piston and use this velocity for v.

Next problem is estimating mass for the kinetic energy. The piston shaft becomes the part that is ‘not bouncing’ against the crosshead, so the mass of that part seems like the proper one to use for calculating the kinetic energy.

I’m still trying to think through the contribution of the pressure on the piston though. When the piston impacts the crosshead, the force produced is also a function of pressure, so one might be tempted to say that the kinetic energy dissipated during this slapping together of parts, is more than the 1/2mv2 of the piston. I think that although this pressure creates a force during impact (ie: resisting piston motion) the total mass necessary to calculate the kinetic energy being dissipated isn’t a function of this pressure load, so it should be neglected. It would be the same as if there were a spring being compressed, so that additional energy goes directly into the fluid, not the parts slapping together.

I think I’ll try calculating it this way unless someone can point out an error in the logic.

If it is audible, that suggest that some energy is being dissipated in this joint. Have you run this machine long enough to get any benefit from disassembling that connection and looking at the surfaces to see what they look like? You say that the parts are well below yield, but I have to assume that you mean that for the working stresses; impact stresses could be a different matter entirely I would think. Over the long haul, I would worry some about the idea that you are going to suffer long term damage in this connection due to repeated impacts. If you can hear it, it is getting pounded to some degree.

Hi Dr.D. Sorry, must have missed your comment here. The pump/compressor is a prototype design I've just started testing, so I'm looking at every little detail. It's designed for liquid and/or gasseous cryogenic hydrogen with an inlet of 100 psi and discharge of 7000. Anyway, I've taken the coupling apart and there didn't seem to be any damage whatsoever. Also, the heating issue has gone away. I'm now thinking it was just a tight rider band that, once it ran for a bit, got loose enough to eliminate the constant drag on the piston. Seems to be fine now.

## 1. What is non-viscous damping?

Non-viscous damping is a type of damping force that occurs in mechanical systems, which is caused by energy dissipation through elastic deformation rather than friction. This means that the damping force is proportional to the velocity of the system, rather than the displacement.

## 2. How does non-viscous damping affect the behavior of a system?

Non-viscous damping can decrease the amplitude and increase the frequency of oscillations in a system. It can also cause the system to reach equilibrium faster and reduce the amount of energy stored in the system.

## 3. What is the difference between viscous and non-viscous damping?

Viscous damping is caused by friction and is proportional to the velocity of the system. Non-viscous damping, on the other hand, is caused by elastic deformation and is also proportional to the velocity of the system. The main difference is that viscous damping is always dissipative, while non-viscous damping can sometimes be energy-generating.

## 4. How is non-viscous damping calculated?

The non-viscous damping coefficient, also known as the damping ratio, can be calculated by dividing the damping force by the critical damping force. It can also be calculated using the natural frequency and the damping constant of the system.

## 5. What are some real-world applications of non-viscous damping?

Non-viscous damping is commonly used in mechanical and structural engineering to control the vibrations of buildings, bridges, and other structures. It is also used in the design of shock absorbers and damping mechanisms for vehicles, such as cars and airplanes.