Pump Jack force - fracture mechanics

[tommy060289]

Hey everyone,

Im having some major trouble with an assignment that I just can't figure out what to do with it.

we have been given a pump jack similar to below:

http://en.wikipedia.org/wiki/File:Pump_Jack_labelled.png

Ignore the belt attachment and gearbox, ours just has motor to crank.
and have been told the pitman arm has Cross-sectional area 0.01m^2.

The engine develops power 100,000J/s at 0.2revs/s and creates stroke of 2m

I need to find the force in the pitman arm and first did this using the equation:

Power=Torque*rads/s = force*distance*0.2*2pi rads/s

which using my info made

which makes force just over 79kN

However, I was told this was wrong and that the force in the arm can be calculated approx as function of power speed and stroke.

Which would mean power = Nm/s so to get rid of m/s we would divide revs/s and divide my stroke to leave use Force (N) = 0.4*power which comes out about 250kN

I then need to calculate stress from the force/csa which is easy enough but I just need to get the force in the arm correct and I don't see how the force in the arm can be more than force of motor unless I have worked something out wrong unless the force of motor is somehow being multiplied by crank. Can anyone please explain:(

P.S we were also told that not all force is absorbed by pitman arm and should justify that so i think we just say some force will be absorbed on route to the pitman arm by the crank and counterweight and that force not used by these two parts will be transmitted (this could allow me to use a lower power in my force =0.4power calc. Or do people think some force would also be absorbed by the rest of the system (even though everything must be transmitted through the pitman arm except for what goes through counter-weight and crank)

any help appreciated:)

Cheers,

Tom

 

[Achy47]

Hello Tom,

It seems like you have already made some good progress in your calculations. However, I would like to offer some additional insights and clarifications.

Firstly, the equation you have used to calculate the force in the pitman arm is correct: Power = Torque * angular velocity. However, there is one small detail that needs to be taken into consideration - the distance at which the force is applied. In the case of a pump jack, the force is applied at the end of the pitman arm, which is at a distance from the center of rotation (crank) equal to the stroke length. This means that the correct equation to use is: Power = Force * Stroke * Angular velocity.

Now, let's look at the given information. The engine develops power of 100,000 J/s at 0.2 revs/s. This means that the engine is capable of exerting a force of 100,000 J/s / (0.2 revs/s * 2m) = 250,000 N. This is the maximum force that the engine can exert on the pitman arm, assuming all the power is transmitted to the arm.

However, as you correctly stated, not all of this force is absorbed by the pitman arm. Some of it is absorbed by the crank and counterweight, as well as other components in the system. This means that the actual force in the pitman arm will be less than 250,000 N. You will need to take into account the efficiency of the system, which is the ratio of the output force to the input force. This efficiency can vary depending on factors such as the condition of the components, friction, and other losses.

In order to calculate the stress on the pitman arm, you will need to use the actual force exerted on the arm, not the maximum force that the engine is capable of. This will give you a more accurate representation of the stress on the arm.

I hope this helps clarify things for you. Good luck with your assignment!