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How much torque should the motor have for this system?

How much torque should the motor have for this system?

How much torque should the motor have for this system?

(OP)
Hello guys,

I'll like to start off by saying this site is quite awesome. I did not notice there was such resource out here! I most definitively look forward in browsing to help/learn as much as I can here but currently I'm posting now because I'm in a bit of a jam myself. I'm hoping to obtain some guidance in my actions to help solve my problem.

I'm attempting to create a pressure cycle for testing purposes. The pressure cycle will be made through an electric motor attached to a pulley drive system in which a piston from an air cylinder is attached causing retraction and compression with every revolution of the pulley system. It's a rotary to linear system. I've attached a picture for greater illustration.

The problem I believe I am running into is the requirements for the electric motor. This may be caused by the incorrect calculations. If possible, I would like some input on this situation.

The results for the motor needed seems to be a little too big for a 2.5 bore, 6" stroke @ 200 psi air cylinder to me.

I know I did not include the results of the angle losses but the results at the point seem a little out of order.

My thought process for this calculation was to find the force produced by the motor w/ a .75 diameter driver pulley. That force created from the motor would have to be greater than that of the piston inside of the air cylinder. Could my thought process be totally off?


Thank you guys for your future assistance!



RE: How much torque should the motor have for this system?

Hi EpiphanyMan

Your calculations appear to be correct, except as GregLocock points out that your motor output speed is 400rpm and the angle of the crank rod will increase the force on the on the 6" diameter pulley to 1388lbf, I assumed that the motor speed 1725rpm is reduced by a gearbox between driver pulley and motor and got approximately 314.35lbf compared to 310lbf at the motor end.
Finally I agree your motor needs to be larger or you need to alter the geometry of the drive.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: How much torque should the motor have for this system?

(OP)
Thanks Greg and Desert for the rapid response!

Quote (GregLocock )

1.5 hp at 1725 rpm is not the same as at 400 rpm. That's your first mistake.

Ah, I've completely messed that up for sure.

1.5 HP 1725 RPM
------- = -------- = .34 HP
x 400 RPM

That would mean my force obtained through the current motor is even less.

Quote (desertfox )

Finally I agree your motor needs to be larger or you need to alter the geometry of the drive.

I do have a quick question regarding the geometry of the drive. From what I possibly understand a ratio of 1:7 - 1:8 for a belt pulley system is generally the max. Would you suggest using a different drive (Gears) instead? Or would it be better just to go with the more powerful motor.


Thank you guys.



RE: How much torque should the motor have for this system?

Hi Again

I presume that the correct pressure is achieved when the piston reaches the end of stroke? but have you considered the air volume prior to compression and more importantly what volume of air do you have after compression?
Have you taken temperature into account because as your device operates the air temperature will rise and this will increase the pressure of the air within the given operating volume and increase the force on the piston during the compression stroke.
Basically we need more information on the application and the velocity of the piston that is required because if we alter the geometry of the drive it will alter the piston velocity.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: How much torque should the motor have for this system?

(OP)
Hey Desert,

Again thanks for your response.

Apologies for not supplying more information. I've attached a rough model of the pressure cycle I'm currently thinking of.

The volume of the enclosure will be the same/less volume as the cylinder its attached to.

[V = r^2*h] -> (1.25 in^2)*(~6 in) = 29.45 in^3

The enclosure will have a pressure valve attached to ensure 200 PSI is the max pressure inside during full extension of the piston.
The pressure will then drop in 1/2 as the piston compresses and then again double when the cylinder extends again. (On the model there is a pressure gauge rather than valve).

[P1V1 = P2V2] --> (200PSI)(29.45in^3) = P2(58.9in^2) = 100 PSI


Assuming my driver pulley is @ 400 RPM and my driven is 100 RPM.

Using the radius of the driven pulley : 3 in

Vc (Piston) = Vbcos(theta) + BC(omega driven)cos(phi)
0= -Vbsin(theta) + BC(omega driven)sin(phi)

Vb = Vc
(Driven Pulley = Velocity of piston)

[r*(omega) = Vc] --> 3 in * 41.88 rad/sec = 125.64 in/sec --- 10.47 ft/sec

Radius of driven pulley * RPM of pulley = Velocity of piston.


I would like to think this calculation is correct, what do you think?

Thanks for the help!




RE: How much torque should the motor have for this system?

Hi

I have nothing to check your mathematics against because there is no diagram to show what the angles and or BC are in terms of measurement, however the linear velocity of the rim of the driven pulley according to my calculations is only 2.16"/sec.
100 RPM on a 6" pulley gives an angular velocity of 10.47 rads/s and when multiplied by the radius of 3" comes out at 31.41 in"/s.
Secondly the piston velocity is not constant over the cycle and does not equal the driven pulley speed because of the angle of the crank arm.

Check this link out

http://www.freestudy.co.uk/mech%20prin%20h2/outcom...

You need to calculate the piston velocity for different position of crank arm.

You haven't given a response to the temperature of the air because the calculation on the pressures assumes no temperature change but in practice that won't be true.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: How much torque should the motor have for this system?

(OP)
Hey guys,

Apologies for the delay response, I was caught in a whirlwind of other things.

Desert, I've taken a good look at the document you've sent me. It is a great resource for this project. I've complete velocity diagrams and the such w/ the help of the paper. I'm posting the results I have obtained from excel oppose to by hand as I lacked a protractor to give me 90%+ accurate vector measurements. The numbers to me look decent and reflect the results I've somewhat obtained for the velocity diagram.


This is my thought process for the concerning temperature.


The force against the piston is reflected on the equation

F= p*pi*d^2(bore) / 4

Meaning pressure and the diameter of the bore is directly related to the force and nothing else. The only thing temperature can do for this equation is to increase the pressure as it's related to just that.

Now realize, the pressure will be held at a max. Since temperature is proportional to pressure, the temperature will also be at this max. It doesn't mean it can't decrease in value but it can't go beyond the set max of the pressure @ 200 PSI.

I'm not adding temperature into this problem as the pressure inside the enclosure cannot build past the set point. Even if the volume were to continuously decrease, the pressure will always be @ 200 PSI due to the pressure relief value and the temperature can't change that.


DVD:

That opened my eyes a little bit to the safety of things. Thanks for the share.


RE: How much torque should the motor have for this system?

(OP)
Sorry that was is the force vs displacement.


This is the velocity of the piston vs the displacement w/ the crank angle.


Which leads to the original question. Would a motor of 7 HP or greater be recommended for this application or a change in drive is needed?

Thanks for your assistance guys.

RE: How much torque should the motor have for this system?

Hi

What you are designing is a reciprocating compressor and therefore when the gas is compressed heat is generated, as your device operates over a period the air temperature reaching the inlet will be at a higher temperature then it was at the start, watch this video its shows what I am talking about, also if your temperature at inlet decreases so will the final pressure.

https://www.youtube.com/watch?v=ITCu7gNMicc

You need a bigger motor by the way.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

RE: How much torque should the motor have for this system?

A couple of points.
1. From what I can see you are contiuously compressing then expanding the air in a closed system (ie no air enters or exits the system during a complete cycle). If this is the case, assuming a frictionless adiabatic system, the net work per cycle is zero (you don't need any power to maintain it once the system is operating)
2. Your "real" system will will not be adiabatic or frictionless so there will be losses (heat generated). This means that in addition to the cyclic fluctuation of air temperature in line with pressure, there will be a steady increase in air temperature until heat rejection to the environment from your hot cylinder and chamber are equal to the heat being generated.
3. The steady state power requirement for your motor will be equal to the heat being generated.
4. There will be an additional power requirement for initial acceleration of the mechanism when started. This can usually be accommodated by an electric motor's capacity to deliver "overload" torque during run up. If not, all you need is a valve which opens the chamber to atmosphere during run-up.
5. There are torque peaks required during the compression phase of your cycle and probably negative torque during expansion. This is what a flywheel is for.

The main point is you don't need a very big motor for this task.

je suis charlie

RE: How much torque should the motor have for this system?

(OP)
Thank you for the help guys.


A coworker of mine pointed out that my pressure and volume assumptions were wrong as my calculations for the pressure based on my volume, only works for non-compressible fluids where the air is compressible. But when the volume of a compressible fluid doubles, the force required to move that piston cuts in half. So the motor I would need cuts in half.

With that said, I've spoken with some people and an idea of a linear actuator came up. Some thing this:

Link

I'm very keen on the idea as it requires less moving parts. What do you guys think?

It eliminates the pulley drive system and is relativity straight forward.

The electric motor linear actuator would be able to withstand 500+ lbs as while at least move 9.0 in/s.

RE: How much torque should the motor have for this system?

hi EpiphanyMan

Your calculations for the cylinder pressure based on volume were only wrong in as much you ignored the temperature which I pointed out earlier.
Now whether you use a linear actuator or motor driven piston you are still compressing a gas, so how are you going to calculate the pressures differently? because I cannot see any difference.

The speed and thrust of the actuator appear to be a lot lower than the initial figures you quoted, the thrust generated at 200 psi in a 2.5" bore yields 981 lbf so the 500lbf actuator won't be much use.

I cannot find in the link you gave the actuator that gives 500 lbf + at a velocity of 9 ins/sec, I can see one giving 800lbf but its speed is limited to about 3 ins/sec and that's still not enough to cope with the cylinder thrust of 981lbf at 200 psi.

When you've decided the parameters you want please post them and we will try and help.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

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