# Inelastic collisions and material properties

I am in the middle of a large project as an undergrad mech. engineering student and my team and I are having some modeling issues. Here is a description of our task:

We must modify the design of a digital spool valve for a company. We have a spool, and 2 electro-magnetic endcaps that the spool moves back and forth between. When the metal spool hits the metal endcaps, there is an unacceptible bounce from the impact force.

Now the problem is more complex then this, but on a basic level for a solution we would like to change the materials of various components of this part and have the impact be absorbed.

Herein lies the problem, we need some equations to model an inelastic collision, but standard equations will not work. We have plenty of information on the current performance of this spool (ie: magnetic force vs. distance graphs, materials and weights, velocities before and after impacts ect...) It would be nice to have some equations that have material properties becasue we could analyze the efffects from our material changes. Does anyone know of any equation that relates an impact to material properties? I've done some research into the Hertz impact theory, does anyone have any more info on this?

Alex T.

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We are using the following equation for a 1-D inelastic equation;

v1= [(Cr+1)M2V2+V1(M1-CrM2)] / [m1+m2]

We know everything besides Cr from testing. v1=1.95 m/s , v2=-.75 m/s , m1=mass spool =7.85 g , m2=mass endcap = 33.5g

So Ive solved for Cr, but get a very different number than solving for Cr using Cr=-v/u = -(-.75)/1.95 =.3846

Shouldnt these 2 Cr's be close to the same?

Also, we need a way to model the impact if we change the materials of components ie. changing the modulus of elasticities. We need a way to compare different concepts and all our ideas involve a material change of some sort. Granted the result will only be a rough estimation, but it would be nice to have some numerical analysis to back our claims before we prototype and test any of our ideas. Does any one know of a way to model an impact using material properties, masses, and velocities? I guess we could find the coefficient of restituion for each material by a drop height test, but could we do with this data? Say I change the endcap to a nylon with a different Cr, how can this change be modeled using the inelastic collision equation?

Also, could this system and impact be modeled in solidworks?

Thanks,