Trouble predicting position equation on spring/mass damped system

[andrew623]

I am analysing a system that consists of a simple damper. The construction starts with a long compression spring; a small mass compresses the spring, and when released, the spring pushes the mass forward, until it hits a column of fluid. The mass has a controlled thru geometry, which allows the fluid to pass through at a linear rate, until the spring reaches its full extension, and the system stops.

I am trying to come up with an equation for position, as a function of time. So far, my general approach has been to find the velocity of the mass as it hits the column of fluid; to do this, I did a basic energy conservation for the the spring-mass system, ie:

KE1 + PE1 = KE2 + PE2

Where PE1 is the spring completely compressed, KE1 is zero (at t=0), and PE2 and KE2 is the spring at distance "X," which is the location of the column of oil. From this, I am able to get a decent value for my velocity @ the time it hits the column of fluid, I think.

Finally, I have tried sticking this value into a generic solution for the SDOF diff. eq., ie:

http://www.efunda.com/formulae/vibrations/sdof_free_damped.cfm

now using "v0" from above, x0=0, and attempting to calculate "x" at a certain point during the damped portion of the stroke. Unfortunately, my mass is very small, and my damping coefficient has been calculated experimentally to be quite high. As a result, I am getting a damping ratio in the hundreds, and it is throwing my calculation for a loop.

I'm curious if my general approach is not correct ? When I plug everything in, my predicted time is a small fraction of a second, while in practice, this damper takes a few seconds to close completely.

 

[Achy47]

Thank you for sharing your analysis of the damper system. Your approach of using energy conservation to determine the velocity of the mass at the point of impact with the column of fluid is a good starting point. However, there may be some other factors that could affect the accuracy of your calculations.

Firstly, it is important to make sure that all the energy in the system is accounted for. In addition to the potential energy stored in the compressed spring, there may also be some energy dissipated due to friction between the mass and the column of fluid. This could potentially affect the velocity of the mass at impact and therefore, the overall behavior of the system.

Secondly, the equation you are using for the SDOF system assumes a constant damping coefficient. However, in real systems, the damping coefficient may vary depending on the velocity or displacement of the mass. This could explain the discrepancy between your predicted time and the actual time it takes for the damper to close completely.

To improve the accuracy of your analysis, you may want to consider using a more sophisticated model that takes into account the varying damping coefficient. You could also try to measure or estimate the amount of energy dissipated due to friction and include it in your calculations.

Overall, your general approach is correct, but it may need some refinement and consideration of additional factors to accurately predict the behavior of the damper system. Keep exploring and experimenting, and I'm sure you will come up with a more accurate solution.

Best of luck with your analysis!