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Mass-Spring Impact Duration

  1. Jun 27, 2005 #1
    This is a simple(?) problem but my ability to perform basic calculus disappeared long ago. I am working thru the equations for a spring response to a dropped weight. My primary reference is Shigley (for just about everything!!) and I've validated the eqn's for deflection and max force. However, I am trying to work out the duration of the event for purposes of estimating simulation time in explicit FEA. Solving for time to max deflection from eqns in Shigley yields exactly 1/200th of the time reported by 2 mechanism simulation tools...who nail the deflection and force as noted above.

    Has anyone solved this "compression time" and, if so, can you share the eqn?
  2. jcsd
  3. Jun 27, 2005 #2


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    Not that you're giving a whole lot of info, but based on what you have listed, I would guess that:
    1. You've got one side dealing with the whole colision, and the other dealing with half of it (introducing a factor of 2)
    2. There's some sort of unit issue providing a factor of 100.

    Note that this is a relatively wild guess.
  4. Jun 27, 2005 #3
    I've beat up the units issue so I don't think that's the problem. The system is pretty simple and I've been staring at it for a couple of hours so it didn't occur to me to give more detail... Essentially, I'm looking at a spring to ground with K=238.1 #/in. A weight (W) of 7.43# is being dropped a height (h) of 12 inches onto the spring.

    Compression (D) = (W/k)+(W/k)*SQRT[1+((2*h*k)/W)] = 0.897 in.

    Force (F) = K*D = 213.6 lbf

    Both these calcs agree with the simulation results.

    In Shigley "Mechanical Engineering Design", D is determined by assuming a Cosine term in a longer eqn is unity...

    Cos[(kg/W)t - Phi] = 1


    (kg/W)t-Phi = 0 or (kg/W)t = Phi or t = (Phi*W)/KG

    Phi = Pi/2 + SQRT[atan(W/(2kh))] = 1.84

    thus... t = 0.00015 sec

    which is 1/100th (not 1/200th...sorry) the duration reported by simulation.

    Can anyone see where I messed up? I, of course, waited until the last minute before deciding I wanted to add this to a slide in a webcast tomorrow.

  5. Jun 27, 2005 #4


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    ...is your calculator set to degrees?
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