Pump Jack force - fracture mechanics

  • #1
Hey everyone,

Im having some major trouble with an assignment that I just cant 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 dont 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
 

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