# Inelastic collisions and material properties

• alext918
In summary: Alex is trying to find equations that relate an impact to material properties. He is also looking for a way to model the impact if he changes the materials of components.
alext918
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.

Specificially, what standard equation are you assuming will not work?

Would it be fruitful to search for coefficient of restitution tables or attempt to measure such values if necessary?

A simple experiment: http://hypertextbook.com/facts/2006/restitution.shtml

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 I've 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 anyone 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,

## 1. What is an inelastic collision?

An inelastic collision is a type of collision where kinetic energy is not conserved. This means that after the collision, the objects involved stick together and move with a common velocity.

## 2. How is an inelastic collision different from an elastic collision?

In an elastic collision, kinetic energy is conserved and the objects involved bounce off each other with no loss of energy. In an inelastic collision, kinetic energy is not conserved and the objects involved stick together and move with a common velocity.

## 3. What factors affect the outcome of an inelastic collision?

The outcome of an inelastic collision is affected by the materials of the objects involved, their masses, and the initial velocities of the objects.

## 4. How do material properties play a role in inelastic collisions?

The material properties, such as elasticity and density, affect the amount of energy lost during an inelastic collision. Objects with higher elasticity will lose less energy during the collision compared to objects with lower elasticity. The density of the materials also affects the outcome of the collision, as denser materials will have a greater impact on the objects involved.

## 5. Can inelastic collisions be useful in real-world applications?

Yes, inelastic collisions are commonly used in real-world applications, such as car crashes and sports equipment. They can also be used in material testing to determine the properties of different materials. Inelastic collisions are also important in understanding the behavior of particles in particle accelerators.

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