Hi all, Before I throw myself out of the office window could someone please help me out a bit here...I'm sure I used to handle these sort of calcs years ago but now I'm not sure of anything! Got a pneumatic press module here and I'd like to calc the force on the piston at 1mm from TDC, I've drawn it out here as clear as possible and it's like this: A formula I came across in many of the books I've been looking through said Fp = T/OM I worked out OM as OM=OC(Sin(17.13+4.34)/Sin(90-4.34); then transposed and came up with Fp=3935N Could some one please let me know if I'm along the right lines or am I going mad? Many thanks I've just previewed the post and it looks a lot like a school/college homework question...I can assure you it's not, although that doesn't make me feel any better about my maths!
Phew, that's good to know. Thanks Erich I'd be interested to know the way you approached it - I originally did it a different way, got a crazy answer which completely threw me and then it went downhill from there!
I just broke the problem down and drew Free body diagrams. Calculated the Force in the conrod as a function of the piston force. The I went up to the crank and applied that force to the crank. I broke that force into a component normal to the crank and a component in line with the crank. Came up with equation relating Torque to Conrod force. substituted and solve for Fp vs T
Got it...finally! Thanks for explaining your methods and also thanks very much for taking the time and trouble to help me out, it is very much appreciated.
Looking at the diagram but applogies in advance if anyone thinks I am slightly off the mark, but the obtuse triangle appears to me that the length I would not equate to 70mm?
Yep I was thinking about something should be done with the value of I, but I found this method works as well; Working with trig, POC triangle OC = 18mm, theta = 17.13 degress, Phi = 4.34 degress. Using the sine rule we have; PC = 18(sin 17.13/sin4.34) = 70.06 which is I. OCM triangle = angle C = Phi + theta = 21.47 degress POM = 90 degress Angle m = 85.66 degress Using the sine rule we get; OM = 18(sin 21.47/sin 85.66) = 6.61 So Fp = 26 / 6.61 x 10^3 = 3.94 x 10^3 N
A simpler approach to solve is: the applied moment is constructed of vectors, which are the applied force, Fp, and the moment arm, r, or, T = r X F = r * F * sin(angl OCP). Since the sum of angles in a triangle is 180 degrees, angle OCP = 180 - 4.34 - 17.13 = 158.53 degrees. So Fp = T / r sin(158.53) = 26 Nm / [18mm * sin(158.53)] = 26000 Nmm / (18mm * 0.3660) = 3946.42 N. QED!
I would'nt of thought that was a simpler approach. Idiotic gave a result of 3935N and asked for the force Fp acting on the piston, other posters said he was close to it and should go with it, however my worked out example showed how he did it, but the method showed how to calculate the compoent force, and not the force acting on the piston, which is the force 3946.4N, and is a different force acting.