Dynamic analysis of pneumatic cylinder
Dynamic analysis of pneumatic cylinder
(OP)
Hi,
First I'll say that I am not a mechanical engineer (electrical
)so please bear with me as I have been assigned to investigate the problem below.
We have a pneumatic cylinder configured with an inlet port, a piston attached to a rod, and an outlet vent. The inlet port is connected to a valve which provides a burst of air pressure. (not constant)
The rod drives a sharpened component into an external second material. The constituent equations that I have used to study this are:
F= A *P; Eq1
where A=area and P= pressure
Alternatively, F= m*a; Eq2
Where m= mass and a = acceleration
Using a high speed camera, we were able to determine the velocity by applying the following:
v=d/t; Eq3
Where d= displacement and t = time
Acceleration was determined using the following:
a= (v-u)/t; Eq4
Where v= final velocity, i.e., 0m/s, Initial velocity, t= time
Finally, momentum, p = m*v; Eq5
Where m= mass and v = velocity
The above calculations are all static, however, to understand this dynamically, I would like to calculate the force, velocity, and momentum as a function of displacement of the rod in the cylinder as well as the calculation of force, velocity, and momentum as a function of time.
It would also be good to factor in the friction of the piston and cylinder wall as well if possible.
There are two cases:
1) In the first case there is a small separation distance (gap) between the rod and the driven slug when the rod has reached its full stroke travel.
2) In the second case, the rod drives the slug of material into the second material and the rod and slug are in contact at the end of the rod's stroke. (no gap)
The contention is that the loss in momentum (the rod and piston no longer in contact with the slug) is significant because the mass of the slug is very small compared to the mass of the rod and piston. The counter argument is that the slug's velocity is sufficient to cause it to continue to drive into the external material after loss of contact.
This is an interesting problem but I am stuck. Any help from the Forum would be greatly appreciated.
Thanks,
Art
First I'll say that I am not a mechanical engineer (electrical
We have a pneumatic cylinder configured with an inlet port, a piston attached to a rod, and an outlet vent. The inlet port is connected to a valve which provides a burst of air pressure. (not constant)
The rod drives a sharpened component into an external second material. The constituent equations that I have used to study this are:
F= A *P; Eq1
where A=area and P= pressure
Alternatively, F= m*a; Eq2
Where m= mass and a = acceleration
Using a high speed camera, we were able to determine the velocity by applying the following:
v=d/t; Eq3
Where d= displacement and t = time
Acceleration was determined using the following:
a= (v-u)/t; Eq4
Where v= final velocity, i.e., 0m/s, Initial velocity, t= time
Finally, momentum, p = m*v; Eq5
Where m= mass and v = velocity
The above calculations are all static, however, to understand this dynamically, I would like to calculate the force, velocity, and momentum as a function of displacement of the rod in the cylinder as well as the calculation of force, velocity, and momentum as a function of time.
It would also be good to factor in the friction of the piston and cylinder wall as well if possible.
There are two cases:
1) In the first case there is a small separation distance (gap) between the rod and the driven slug when the rod has reached its full stroke travel.
2) In the second case, the rod drives the slug of material into the second material and the rod and slug are in contact at the end of the rod's stroke. (no gap)
The contention is that the loss in momentum (the rod and piston no longer in contact with the slug) is significant because the mass of the slug is very small compared to the mass of the rod and piston. The counter argument is that the slug's velocity is sufficient to cause it to continue to drive into the external material after loss of contact.
This is an interesting problem but I am stuck. Any help from the Forum would be greatly appreciated.
Thanks,
Art





RE: Dynamic analysis of pneumatic cylinder
Ted
RE: Dynamic analysis of pneumatic cylinder
Thanks for your response and suggestions. What you suggest would provide a partial answer, but I really need a more comprehensive analytical foundation for this problem.
Already getting the time/distance information was incredibly arduous because it involved counting thousands of frames from the high-speed video. I really want a mathematical representation of the physical system so that I can play the "what if" game.
Any chance that you could help with that? I'll help you with an electrical engineering problem in exchange.
Thanks,
Art
RE: Dynamic analysis of pneumatic cylinder
Other than that you are looking at a complicated system.
For example, when the valve opens, the gas in the supply line expands with a negative pressure wave at the speed of sound in the supply line; the gas accelerates, and the conditions in the supply line change so the speed of sound changes. The supply line itself will contract as the pressure initially drops, possibly until choke flow develops somewhere in the supply.
The gas in the cylinder is compressed by the incoming gas,; a complicated jet forms that transitions from laminar to turbulent flow, also at the speed of sound, possibly with the development of a shock wave at the inlet. The volume of the cylinder will change as the force on the piston increases beyond the ability of static friction to hold the piston in place and then the mass of the piston and rod will begin to accelerate, allowing the volume to increase, with an attendant negative pressure wave and it's effects upstream to the choke.
There will be various temperature related interactions with pressure and volume.
I'd suggest sticking with the experiments or hire a high-end analysis company.
RE: Dynamic analysis of pneumatic cylinder
Your Eq.2. above will change in something like:
F = Ap * p1 - Apr * p2 - Fw = m * a
wherein:
Ap = surface area of piston
p1 = air pressure on piston
Apr = surface area of piston on the rod-side
p2 = air pressure on piston rod-side (dependent of v squared)
Fw = friction of piston seals en rod bearing
m = mass of all moving parts
RE: Dynamic analysis of pneumatic cylinder
Thanks for your response and suggestions. One problem with components like the LVDT is that the cylinder is 5mm in diameter with the piston proportionately smaller. We were looking into some some software to analyze the high speed camera fottage.
Art
RE: Dynamic analysis of pneumatic cylinder
Thanks for pointing out the additional areas to consider in this calculation. Any chance that you would be able to provide a time dependent model?
Thanks again,
Art
RE: Dynamic analysis of pneumatic cylinder
You need to take into account that the flow rate through the valve orifice can be choked at the beginning and changes to uncooked when the pressure inside the cylinder rises. Therefore, you are dealing with a quite complicated problem which needs an assistance from an expert with theoretical and practical experience. Such expertise is rarely exists in the aerospace and military industry and is not common in the commercial industry.