Spring Piston Simulator Project

[MartyMcFly]

mikeyb, you're probably right about shorter "lock time" being a myth. We often make extrapolations based on how we perceive or feel the shot. To me the gas ram feels quicker/snappier, but this could all be an illusion of the recoil dynamics.  If/when I get the gas ram code incorporated, we will be able to get a better analytical comparison of the two power types. I hope there is someone on this forum that has the new Diana 34 EMS, it would be a great test platform for comparing the gas ram vs. metal spring due to its convertibility.

I will say this though, if we assume that the ram's seal friction is negligible (a big IF) then the gas ram does have some advantages in terms of potential efficiency gains relative to the metal spring. With the metal spring we have hysteresis, un-uniform coil deflection, and/or vibrations - all of which can bleed off energy. BUT all of this is just hypothesizing on my part, the effect of the ram's seal and the scale of the differences is the real determinant of efficiency gains/losses in real life.

One last thing, I previously mentioned that bringing the adiabatic index down from 1.4 to 1.35 resulted in better performance. I've played around with this number and the performance drops when we go below or above 1.35. This is a very interesting finding, because it means that having a little bit of a heat loss in the rifle can help performance, up to a point. My educated guess is that it's probably due to changes in the timing of the pressure impulse. (For those reading who are confused about the adiabatic index, it acts as a coefficient that approximates how heat is lost into the body of the rifle). For some reason, keeping the air slightly cooler has a positive impact on performance. Maybe this is due to the rifle going from a "pop" phase to a "blow" phase. These phases might be just myths - but there might be some trade-off between when the pellet becomes dislodged due to pressure vs. when it is being accelerated by the velocity of the air behind it.

To all: keep the critiques coming. It's very helpful to my understanding of what is and isn't a good model and how to interpret the output.

-Marty

[MartyMcFly]

Marty, Thank you for posting the curve.
It was interesting to compare your model results to the test results I posted the link to.
In both cases the pellet passes through 200 mm pretty much towards the end of the pressure spike. In your model, it looks like it takes about 1.4 ms to get there. In my tests it was about 1.8 ms. I was shooting a .22, 14.7 gr pellet, so the slower start make sense. It is also a gas ram which has a different pressure rise curve. It may be that your friction model is not that far off. How does it compare to the bounding "no pellet friction" case?

Stan, below is a comparison of the pellet stiction vs. no pellet stiction, all other frictions (i.e., seal and barrel frictions) were kept on. Unsurprisingly the pellet starts moving immediately, but this results in approximately a 10 fps velocity increase. The timing of pellet exits is about the same in both scenarios.

Pellet Position vs. Pressure (all frictions engaged)


Pellet Position vs. Pressure (pellet stiction turned-off)


Pellet Acceleration vs. Pressure (all frictions engaged)


Pellet Acceleration vs. Pressure (pellet stiction turned-off)


-Marty

[MartyMcFly]

Correction, I showed the wrong graph for Pellet Acceleration vs. Pressure (pellet stiction turned-off).

Here the corrected one:
Pellet Acceleration vs. Pressure (pellet stiction turned-off)



-Marty

[rgb1]

Marty, gamma changes thru the compression cycle. To get an appreciation
use this website......


         www.wolframalpha.com/


......enter in the box (for example)     "specific heat ratio  air  800F  1200psi"
The compute button is on the right.   Hope this helps.


                          Ron

[MartyMcFly]

Marty, gamma changes thru the compression cycle. To get an appreciation
use this website......


         www.wolframalpha.com/


......enter in the box (for example)     "specific heat ratio  air  800F  1200psi"
The compute button is on the right.   Hope this helps.


                          Ron

Thanks Ron! The current code makes a few simplifications, which I intend to sharpen as I go along. This link is very helpful.

-Martyrs

[MartyMcFly]

Not much in terms of analytical updates, but I did want to provide a brief update on the progress made with the code:

• Fixed the spring extension going beyond the chamber walls - it was a bug that didn't properly account for the spring preload.
• Added functionality to distinguish between a piston bounce and piston slam. The difference is important because a bounce can occur on a cushion of air, while a piston slam results in the piston making contact with the end of the compression chamber.
  
• Turned various simulation components into objects. This will make it easier to "build" different versions of a rifle from said components (i.e., barrel, spring, pellet, etc.)
• Began adding boiler plate code for a Gas Ram. The goal is to have the capability of testing rifles with different power plants side-by-side.

Thanks for visiting!
-Marty

[MartyMcFly]

Marty, gamma changes thru the compression cycle. To get an appreciation
use this website......


         www.wolframalpha.com/


......enter in the box (for example)     "specific heat ratio  air  800F  1200psi"
The compute button is on the right.   Hope this helps.


                          Ron

Ron, I've done some more research on gamma behavior. What I found is that the value of gamma falls as the temperature gets higher. Using Wolfram, the estimate is that it falls somewhere into the vicinity of 1.33 at peak compression and temperature. In my code I assumed that gamma was constant at 1.35 to account for heat sinking into the chamber walls. That said, I think this value comes close to what is probably the average gamma throughout the piston stroke, since we are starting with a value of 1.4 at ambient pressure/temperature and it will fall as we compress the air.

I'm experimenting with some codes that can vary the gamma based on the temperature, but I'm doubtful that it will make a big difference. I expect the most visible difference to be in the predicted temperature of the air. Since gamma is falling during compression, it will have a negative effect/feedback on the temperature, which in turn will also result in slightly lower peak compression.

One last thing to mention... The inner surface area of the compression chamber is shrinking during the piston stroke, which means that the conductive area for heat to sink into is also shrinking. This likely implies that although some heat is lost into the steel, there isn't enough time for the gun to absorb much of it.

-Marty

[MartyMcFly]

Time for some updated graphs!

As mentioned in the prior post I've made some improvements to the code. The following simulation graphs incorporate the following improvements:

• Spring correctly stops at the end of the comp chamber
• Piston bounce detection
• Piston slam detection
• Comp chamber walls absorb heat dynamically based on changing volume of the compression chamber as the piston moves
• Gamma (ratio of specific heats) is no longer static, it changes based on the air temperature in the compression chamber

Notes:
Friction coefficients are still estimates from other papers, they need to be measured for accuracy given my rifle.
Friction model for rifling and pellet spin is simplified, it needs to be improved to better account for changes in pellet inertia due to spin.
Code that calculates energies for a gas ram needs to be added.
The transfer port is still treated as an extension of the compression chamber. This needs to become its own volume with transfer of gases.
There is no code to simulate rifle recoil at this point. It's still on the drawing board.

Current output:
Pellet weight 8.44gr
First piston bounce at: 8.99 ms
Piston slam at: 25.51 milliseconds
Pellet exited at: 10.28 ms, velocity: 254.41 m/s (834.68 ft/s)

-Marty

PS. The addition of the dynamic gamma rather than using a static 1.35 cost about 4 fps in terms of velocity. It's a small impact but still large enough to detect.

[WhatUPSbox?]

Nice.
Is the pellet friction model a linear function of pressure? Is there a stiction term?

[mikeyb]

Some parameters look consistent, but IMO there is a problem with piston velocity.

After the piston bounces off the initial plug of air the spring eventually stops the piston rebound and sends the piston forward again. Plot is OK so far.
 
At some time well AFTER the pellet exits, my sim suggests ~15-20 ms after t=0, the piston comes to REST at the end of the comp tube.
You call it piston slam? Much of the system energy has dissipated by this time so the final piston stop is nowhere near as violent as a dry-fire.

The pellet is long gone so air pressure in front of piston is small.

The plot shows the piston velocity settles to 10 m/s.

I don't think this is correct. It should be 0 m/s.

[MartyMcFly]

Some parameters look consistent, but IMO there is a problem with piston velocity.

After the piston bounces off the initial plug of air the spring eventually stops the piston rebound and sends the piston forward again. Plot is OK so far.
 
At some time well AFTER the pellet exits, my sim suggests ~15-20 ms after t=0, the piston comes to REST at the end of the comp tube.
You call it piston slam? Much of the system energy has dissipated by this time so the final piston stop is nowhere near as violent as a dry-fire.

The pellet is long gone so air pressure in front of piston is small.

The plot shows the piston velocity settles to 10 m/s.

I don't think this is correct. It should be 0 m/s.

You're right, the piston should stop around 25ms. Perhaps it's just a coincidence, but suspiciously it's coming out to be 9.8 m/s... Time to do some more debugging!

-Marty

[MartyMcFly]

Nice.
Is the pellet friction model a linear function of pressure? Is there a stiction term?

Yes, to both. Working on a more advanced friction model which will increase the inertia as the pellet spins up.

-Marty

[MartyMcFly]

mikeyb, thanks for your sharp eyes! The piston graph was showing ~10ms (9.8 m/s) because that's the velocity the piston was traveling at just before slamming into the end of the compression chamber. The integration routine is doing adaptive time stepping so it doesn't register when I force the spring velocity to zero upon contact with the end of the comp chamber.

I'm not sure how I'm going to fix this yet. The proper but harder way is to try to stop the piston via a large deceleration force. This may ultimately result in another 'tiny' bounce and should depend on the elastic properties of the piston seal. The other solution is to pause and save the system state, reset the velocities and forces to zero, and then continue. I'd like to make it as realistic as possible, so I'm inclined to do the former, but it will require some more research on my part.

That said, for the moment you can interpret the piston velocity graph as going to zero at 25 milliseconds rather than staying at 10 m/s level. It does not impact the pellet velocity.

-Marty

[MartyMcFly]

Attached are the updated graphs using the 'pause and save' method to fix the issue with the piston not stopping at impact. Now, the piston velocity graph has a sharp drop in velocity at the end of the stroke. This is hopefully a temporary fix. That said, the air temperature drops a bit too much subsequent to piston stop. I doubt that the compression chamber walls can draw heat away that quickly, especially since I don't have the transfer port modelled yet. This can be fixed by putting a floor on the chamber heat at ambient temperature, but the proper way is to keep track of how hot the internal walls have gotten because at some point their ability to draw heat away from the air slows down and may even reverse. Oh boy, all of these little details are starting to add up!

-Marty

[WhatUPSbox?]

Nice.
Is the pellet friction model a linear function of pressure? Is there a stiction term?

Yes, to both. Working on a more advanced friction model which will increase the inertia as the pellet spins up.

-Marty

I was thinking that with the stiction term present, it should be visible int the force curves. Shouldn't the net force be zero until pellet launch?
On a related topic, it may be interesting to compare both in modelling and test how a slug compares to a skirted pellet. On first order, the slug friction model would not be pressure dependent.

[MartyMcFly]

The net force is the pressure acting on the pellet minus the bore frictions, which are pellet elastic deformation, skirt friction and rifling friction. Pellet stiction is implemented differently and acts a little bit like a delay, it prevents the pellet from accelerating until about 30 Newtons of force is generated in pressure. Out of a peak ~220 Newtons about 120 Newtons is stolen by bore friction (not including stiction). I hope that helps.

-Marty

[WhatUPSbox?]

I was thinking net force is analogous to acceleration and should be zero until the pellet starts to move. Usually, stiction is higher than the subsequent sliding friction (at least for a while) and when it releases there would be a glitch in the curve.

[MartyMcFly]

I was thinking net force is analogous to acceleration and should be zero until the pellet starts to move. Usually, stiction is higher than the subsequent sliding friction (at least for a while) and when it releases there would be a glitch in the curve.

There is a glitch in the acceleration curve (see reply #62). I'll put in more acceleration curves in the future. Moreover, the stiction is dominated by the deformation friction, because the deformation friction acts on the pellet longer.

-Marty

[MartyMcFly]

Trials and Tribble-ations

As noted previously the output of the simulation was showing a drastic drop in air temperature (way below ambient) after the initial spike. My first guess was that the code for heat transfer into the chamber walls was drawing heat away too quickly or that I was improperly keeping track of the walls' changing temperature. Although, that code may still need adjusting I found a simpler explanation for the temp drop. You see, when the compression chamber shrinks the total volume of air in the system initially shrinks too (thus temp spike), but as the pellet moves the volume behind it starts expanding. It's this fast volume expansion in the barrel that is causing the temperature to fall so much. Not only that, what I should have done is capped the volume expansion at the moment the pellet exits the barrel, because that's when the pressure equalizes with the outside. But I didn't do that and as a result the volume just kept expanding as the pellet went on its merry way to kiss the squirrel.

Thoughts on next steps beyond volume control

Currently, the volume of air is treated as a lumped sum of the compression chamber, the transfer port, and the area in the barrel behind the pellet. This is obviously a simplistic approach, but it works pretty well in getting us accurate figures for the pellet energy. That said, it does not allow us to closely study the impact of the transfer port on air temperature, piston bounce, or timing of pellet release. To fix that here is an outline of the approach I'm thinking about next:

• Separate the lumped volume into three independent volumes: 1. comp chamber 2. transfer port 3. barrel volume behind the pellet

• Next extend the ODE integration to keep track of the mass of air and the air temperature in each volume

• Implement mass flow calculations between compartments based on pressure differences

• Code the energy balances for each compartment (taking into account work, heat transfer, and mass flow enthalpy)

• Profit!

I think the difficult part of this approach will be defining the air mass flow between compartments. This is typically where fancy-pants math like the Navier-Stokes equations and Computational Fluid Dynamics (CFD) comes in. Such math deals with the conservation of energy, momentum, and mass of a fluid/gas flow. Having said that, I'm not planning to mess with Navier-Stokes directly, but instead I plan to apply some empirically derived approximations for orifice discharge rates, which I hope will get us close enough to a real-world figures for each of the volumes.

Thanks for dropping by!
-Marty

[MartyMcFly]

Sunday, Sunday, Sunday!

You guessed it, its Sunday and I finally have some time to post. I haven't made much headway with the changes discussed in the previous post yet, but I did make some progress in other areas.

First, I added a graph that shows the temperature change in the compression chamber walls. As you can see, due to the speed of the compression stroke the temp increase is miniscule, in fact I had to go to the 6th decimal place to show it. So, although the air temperature gets pretty hot, most of it is not absorbed by the rifle. I guess that's a good thing, more heat = more power, in general.

Second, I improved the pellet friction code. The bore has three component frictions, which initially were done as follows:

• Elastic pellet deformation friction, modelled as a constant based on pellet push through force and a friction coefficient.
• Skirt expansion friction, modelled as the skirt contact area, pressure and a friction coefficient.
• Rifling friction, modelled using a log function with pressure and pellet position, combined with the pellet's inertia and angular twist rate

The initial version was a bit of a messy implementation, it didn't do a proper energy balance between forward pellet movement and its angular movement.

The new version still breaks it up into three components but with the following changes:

• Pellet deformation friction is still a constant, but it is only dependent on the push through force, no more friction coefficient.
• Skirt expansion friction has stayed the same.
• The rifling friction has been simplified to avoid logs and rewritten to compute an induced torque (based on the pellet’s inertia, twist rate, and pellet velocity) and then it converts that torque to an axial force using the bore radius and the cosine of the rifling angle.

I still want to improve the friction code further. Firstly, I don't like a constant deformation friction. It should vary based on the softness of the pellet and the acceleration. Second, I'd like to add a resisting force from the air that is being compressed in front of the pellet.

As a result of the changes I can now also keep track of the pellet's angular velocity (how fast its spinning). The spin might not be a huge part of the pellet's total energy, nevertheless the true energy of the pellet is a sum of the forward motion and spin, which we should keep track of to properly compute efficiency.

Attached are the latest graphs. Please note that I have not recalibrated the coefficients, so the numbers are a little off compared to the previous graphs. That will be done later once the math is in better shape.

-Marty