Calculating Compression Time for Mass-Spring Impact: A Comparison of Methods

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Discussion Overview

The discussion revolves around calculating the compression time of a mass-spring system when a weight is dropped onto the spring. Participants explore different methods and equations to estimate the duration of the compression event, with a focus on discrepancies between theoretical calculations and simulation results.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant describes their approach using equations from Shigley's "Mechanical Engineering Design" to calculate compression time and deflection of a spring under a dropped weight.
  • Another participant suggests potential issues with the calculations, proposing that there might be a factor of 2 discrepancy due to different treatment of the collision and a possible unit issue causing a factor of 100.
  • The original poster clarifies their calculations for compression and force, which align with simulation results, but expresses confusion over the significant difference in calculated compression time compared to simulation data.
  • A later reply humorously questions whether the original poster's calculator is set to degrees, implying a possible oversight in the calculations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the source of the discrepancy in compression time calculations, with multiple competing views and suggestions remaining unresolved.

Contextual Notes

The discussion highlights potential limitations in the assumptions made regarding the equations used, as well as the dependence on specific definitions and parameters such as spring constant and weight. There are unresolved mathematical steps related to the calculation of compression time.

Who May Find This Useful

This discussion may be of interest to those involved in mechanical engineering, particularly in the areas of dynamics and simulation of mass-spring systems, as well as individuals working on related computational modeling tasks.

VinceA
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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?
 
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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)
and
2. There's some sort of unit issue providing a factor of 100.

Note that this is a relatively wild guess.
 
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

thus...

(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.

Thanks!
 
...is your calculator set to degrees?
 

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