# Impact Force on a Spring or Damper

#### Nick C

Hello Everyone, I'm hoping you can help with this.

I need to set up a test on a dynamic test rig which can simulate shock impacts upon a spring (actually it's a hard rubber based component).

The test has previously been done on a rig which dropped a mass of 78Kg onto the part until destruction, but the equipment is no longer availble. Therefore I want to find a solution which allows me to use the dynamic rig which can provide shock impacts which are controlled by displacement in mm.

So, my question relates to how I can calculate the impact force upon the part when I know the following:

1) Mass of the object being dropped
2) Height of the object being dropped
3) The density of the part being hit, in N / mm (The rubber part)

I can then set the equipment to cycle over a displacement which provides the correct peak loading from the calculation.

I hope I have provided enough info.

Nick

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#### Q_Goest

Homework Helper
Gold Member
Do you mean maximum force? Consider a spring for example. The force on the spring when something impacts it increases until all the kinetic energy of the impacting object has been absorbed by increasing the potential energy in the spring. So the force on the spring varies depending on displacement according to the spring equation:
F = kx

The maximum force is when the spring is fully compressed and has thus absorbed all the energy of impact.
KE object = E spring
.5mV^2 = .5kx^2
Solve for x (spring displacement) then find the force on the spring. Note that this neglects any potential energy from the mass as it compresses the spring which may or may not be significant. That's easy enough to add into the equation and from the sounds of your set up, it may be necessary. You'll need to describe the set up better though.

The same holds true for any elastomer. The elastomer has some spring rate which may or may not change as the elastomer is compressed. There's no easy way I know of to calculate an elastomer's spring value from it's geometry and properties. You may need to measure it.