Construction of a model of a hydraulic damper

[magicfrog]

TL;DR

Study of a hydraulic brake based on the flow of hydraulic oil through an adjustable orifice. The aim is to develop a computational model that closely matches the simulation results.

Hi everyone, I’ve tried searching the forum for similar topics but I don’t think I’ve found anything relevant to my specific situation. That’s why I’m here to start this new thread.

I am currently studying a hydraulic brake. The spring-operated system is capable of varying its speed (e.g. linear motion) by opening and closing an orifice, which alters the flow rate of the hydraulic fluid. This is a classic choking valve problem.

Using SolidWorks software and with access to the Motion module, I can simulate this mechanism by applying linear or rotational damping, specifying a value and a law (linear, quadratic, cubic).
What I would like to do is relate this hydraulic damper – caused by oil flowing through an orifice – to a coefficient that can be used in the equations, and find an equivalence with the values I can simulate using the software. I wonder: are there any examples where a damping coefficient can be derived from the analysis of a choked valve problem? Are there any theories and practical examples that have been tested?

The idea is to build a model that can determine a motion damping coefficient based on changes in the airflow passing through the orifice.

I hope I have explained my question clearly enough; if not, please accept my apologies, and thank you to anyone who can help.

 

[Chestermiller]

Damping is often approximated using an ideal dashpot. Is that what you are searching for: an approximate equation for the dashpot coefficient as a function of the damping fluid and hydraulic damper design? Are you considering doing experiments to measure the damping coefficient in independent tests?

 

[magicfrog]

Yes, I would like to develop a mathematical model that can describe the behaviour of a hydraulic damper with an adjustable nozzle, and that I can verify both through testing (if only I could figure out how – I’m thinking of measuring deceleration, or how time varies with and without damping, or simply by varying the flow cross-section) and using the simulation software I have available.

Because I still believe we can derive a relationship that actually describes what I can simulate using the software. For example, if I set a linear damping of 4 N/(mm/s), what does that correspond to in reality? What geometry would give me this approximate damping value? Or, conversely, given a geometry ‘x’, what damping value do I obtain? And how does it vary as the geometry changes?

Are these just observations I can draw from tests, or can I build a detailed mathematical model? And if so, how? What assessments would I need to make?

I imagine this isn’t something that can be developed straight away.

 

[jrmichler]

I am currently studying a hydraulic brake. The spring-operated system is capable of varying its speed (e.g. linear motion) by opening and closing an orifice, which alters the flow rate of the hydraulic fluid.

The idea is to build a model that can determine a motion damping coefficient based on changes in the airflow passing through the orifice.

It's not clear exactly what you are trying to do, but it sounds like you are simulating a damper, then using the results to derive a damping coefficient. If so, damping coefficients refer to systems where the damping force is a linear function of velocity. Search term damping coefficient leads to many good sources. Air is more complicated than hydraulic because air is compressible.

I can simulate this mechanism by applying linear or rotational damping, specifying a value and a law (linear, quadratic, cubic).

When you do this with a linear law, you are defining the damping coefficient. You just need to work out the units. If the damping force is other than linear to velocity (such as quadratic), then the term damping coefficient no longer applies because the damping force is not a linear function of velocity.

If you are trying to simulate real world components, you absolutely positively need to start by measuring some real world components. You will quickly learn that the real world does not necessarily follow any simple model. Try searching shock absorber testing machine to learn more.

 

[Chestermiller]

I'm thinking of a cylinder with a piston in which the clearance between the piston and the cylinder wall is finite. The piston is long, and the cylinder is oriented vertically, with a viscous liquid between the base of the piston and the cylinder. The length of the clearance between the piston and the cylinder wall is large, and, in addition to the liquid being present at the base, it also fills the length of the gas. You press down on the piston, and measure the force as a function of the piston when ward velocity.

You basically have pressure/drag flow between parallel plates, and can analyze the problem to get the piston pressure as a function of the piston velocity.

 

[magicfrog]

So, if I’ve understood correctly, I should first build a fairly realistic prototype without the hydraulics, test it, and then, once I’ve added the hydraulic components, assess the system’s deceleration and, based on that, determine a damping value?

 

[magicfrog]

Isn’t the use of simulation software or other computational methods sufficient on its own to derive an initial value to be tested subsequently using the prototype?

 

[gmax137]

What do you have in mind for 'simulation software?'

 

[magicfrog]

I mean software that allows me to carry out fluid dynamics analyses as CFD analyses.

 

[Chestermiller]

The viscous damper I described in post #2 does not require CFD analysis to quantify its behavior. It can solved analytically for the damping force as a function of the piston velocity.

Are you willing to accepts this kind of device as a model for what your are trying to describe. What are your objective for this work? Are you just trying to get a better understand on how a damper might work, or are you actually trying to design a specific system to perform a specified function, and you need to be able to design a damper?

 

[gmax137]

My suggestion is to do it Chet's way first. Before diving into a CFD. The more you understand the physics, the better your CFD model will be. I've seen spectacularly bad (though colorful) results.

 

[magicfrog]

The goal is to design the damper. But in order to do that, I first need to clearly understand what it actually implies, and above all the physics behind it.
My basic idea was to describe the relationships governing this phenomenon and to generalize them, not only for this specific case study.


So yes, as a first step, what I could do is measure the advancement speeds (or advancement times) at different settings of the adjustment nozzle and then extract a curve as a function of velocity. I assume that from this it should be possible to identify a trend.

 

[Chestermiller]

The goal is to design the damper. But in order to do that, I first need to clearly understand what it actually implies, and above all the physics behind it.
My basic idea was to describe the relationships governing this phenomenon and to generalize them, not only for this specific case study.


So yes, as a first step, what I could do is measure the advancement speeds (or advancement times) at different settings of the adjustment nozzle and then extract a curve as a function of velocity. I assume that from this it should be possible to identify a trend.

I would first derive and solve the equations for the fluid dynamics of the system. Do you know how to solve axial annular laminar flow of a viscous fluid?

 

[magicfrog]

I should rewrite and simplify the continuity and momentum equations for the case at hand, probably reducing it to a two-dimensional problem.


I do not have the relevant ready-to-use equations in front of me, so I would need to sit down and derive them myself :)