1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Modeling piston/crank with position loop equation, excel plot

  1. Jul 21, 2010 #1
    1. The problem statement, all variables and given/known data

    attachment.php?attachmentid=27075&stc=1&d=1279734347.jpg

    2. Relevant equations
    I would like to know if my work is correct. I thought that the graph would be a sinusoidal, but there is a small irregularity in the middle.

    Am I correct in using θAC = 90 deg and θAB = 36.8699 deg in solving for the constant angular velocity?

    I attached the scratch paper portion because that contains my geometry work for determining the θAB value beyond the symbolic part, and I'm unsure if that's correct.

    I've set up the position, velocity, and acceleration loop equations symbolically as shown below.

    What concerned me about using θAC = 90 deg is that it causes θ'AB = 0 due to the cos term. This ends up making the max angular velocity -60 rad/s.....

    3. The attempt at a solution

    [PLAIN]http://img203.imageshack.us/img203/4069/piston2.jpg [Broken]
    attachment.php?attachmentid=27077&stc=1&d=1279734347.jpg

    Scratch paper

    [PLAIN]http://img827.imageshack.us/img827/9174/pistonscratchpaper.jpg [Broken]

    https://www.physicsforums.com/attachment.php?attachmentid=27079&stc=1&d=1279735274

    [PLAIN]http://img408.imageshack.us/img408/2493/pistongraph.jpg [Broken]


    Thanks in advance for helping out a clueless EE student!

    EDIT:

    Resized images......can resize further if the res is too big for your monitor. Also fixed broken link. Still missing the scratch paper image because I'm away from home. I'll upload when I get home.....but hopefully this should be enough for someone to check my basic equations and graph.
     

    Attached Files:

    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 23, 2010 #2
    It's pretty difficult to follow your steps, so I cannot comment in detail on your work. I think we need not use so many variables (please excuse me if I misunderstand something). Two coordinates are enough: [tex]\phi[/tex] (angle between AC and AB) and x.

    The only geometric condition relating the coordinates is: [tex]b^2=a^2+x^2-2axcos\phi[/tex]

    Plug a=3 and b=5 in, then solve for x (x>0 as the origin is at A): [tex]x=\sqrt{9cos^2\phi +16}+3cos\phi[/tex]

    Thus: [tex]\dot{x}=-(\frac{9sin\phi cos\phi}{\sqrt{9cos^2\phi +16}}+3sin\phi)\dot{\phi}[/tex]

    From here, we can find the constant angular velocity of AC in the range [tex]0<\phi <\pi[/tex] and [tex]\dot{x}<180 in/s[/tex]. Then the rest is simple. The graph I obtained looks akin to yours.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Modeling piston crank Date
Stoner-Wohlfarth model, remanent magnetization Saturday at 10:45 AM
Four-spin interactions the Ising model Mar 9, 2018
Displacement of a spring within a piston Jan 26, 2016