What is the formula for calculating torque for a motor with a load attached?

[trentw2323]

[SOLVED] Torque Calculation

I am not a mechanical engineer. I am a computer software engineer that likes to learn about different things. (I had to mention it because I was shunned in eng-ti**.com) I am working on a project and need to buy a motor for it. Obviously, before purchasing a motor, I need to know what type to get. My final configuration will be a pulse width modulation speed controller connected to the motor. From the research I have done, I want to be at about 75% of the ability of the motor. The motor will have a wheel 6" in diameter attached to the spindle. Attached to that wheel is a rod connected to a load centered above the motor assembly. The load is 20 lbs. The motor will continuously spin at no more than 60 rpm and will move the load up and down inside of the chamber. I do not know the calculation to determine the torque I will need to move the load. Can someone please help me with the formula? I would like to know the formula used for the calculation as well. I attached a diagram to demonstrate what I am trying to accomplish. Any help is greatly appreciated.
Trent

 

[FredGarvin]

The dynamic loads are going to be a big factor in this calculation. Statically you can see that the worst case torque is only 60 in-Lbf. However, once this thing starts rotating, there will be accelerations that will increase that requirement. Those dynamic forces are going to be dependent on how fast this is going to turn and, I believe, the stroke. Then you do have to add in other losses like frictional and heating.

Start with taking a look here:
http://en.wikipedia.org/wiki/Piston_motion_equations

 

[trentw2323]

I am not to worried about major accuracy. I had looked at that page before and i got really confused. I am not too worried about friction and such, I am looking for a rough estimate. More or less i just need the formula for moving the load taking in the account of the diameter of the circle. I guess an example would be if i had a 20lb piece of metal welded to the edge of the circle, how much torque would the motor need to be able to spin with the weight attached.

 

[Daiquiri]

If you need a very rough estimate, take a look the equation which gives the piston velocity "v" vs. time in that wiki page:
http://en.wikipedia.org/wiki/Piston_motion_equations#Equations_wrt_time

The force (or load) acting on the piston is 20 lbs. Thus, the power required to move that load is

P = 20 \cdot g \cdot v

The power suplied to the piston by the crankshaft is:

P = M \cdot \omega

where \omega is the angular velocity, which is related to RPM by the equation given in http://en.wikipedia.org/wiki/Piston_motion_equations#Angular_velocity
and "M" is the torque which you're looking for.

If you want to neglect the friction and inertial forces, then all the power from the crankshaft is used to move the piston, so you have that

M \cdot \omega = 20 \cdot g \cdot v

and from this one you can calculate the torque M.
Note that your motor will be running against higly oscillating forces, so I recommend you to install a flywheel to this contraption, if it doesn't already have one.

Now... Like FredGarvin said, we don't know nothing about the dynamic forces. They depend on engine components' masses and their geometry.
So, if I were you I would multiply this value of M by a nice "coefficient of ignorance" (say, 1.5 or even 2) and let some VFD do the job of controlling the RPM (is PWM = VFD? don't know much of electronics ).

 

[trentw2323]

Reply

Thank you for the response. I planned on slight multiplication of the answer just to be safe. Thank you very much, this is what i was looking for. As for your question, pwm stands for pulsed width modulation. If you were to look at the result on an o-scope, you would see a definite peak of energy(pulse) followed by no energy as far as a dc is concerned. This provides the proper current to the motor but in short bursts to control its speed. It can be measured as pri(Pulse rate interval) and prf(Pulse rate frequency). PRI measure the entire pulse from the second it appears to the second the next pulse appears. PRF is the inverse of pri. (pri=1/prf and prf=1/pri). This method for controlling the speed of the dc motor is used to provide a constant speed without changing the amps/watts on the motor and works at very low speeds when changing the amps/watts would cause the motor to stop spinning due to the magnets not being charged. I tried to explain it the best i could. Thank you very much for your response once again.