Impact force

Engineering Fundamentals


Bodies collide e.g. when play is present in the design. This collision causes elastic or plastic deformations to the colliding bodies.

Impact force

Collision Stiffness

If both are ‘rigid’ take the local Hertzian stiffness.

Max. Collision Force


Max. Approach


Deceleration Time

$t=\frac{\pi}{2}\sqrt{\frac{m}{c}} $

Deceleration to $v=0$


Collision of bodies

Differential Equation:

$v\left(0\right)=k_2\sqrt{\frac{c}{m}}=v_0$ with $k_2=v_0\sqrt{\frac{m}{c}}$

Distance, velocity, and acceleration:
$x\left(t\right)=v_0\sqrt{\frac{m}{c}}\sin{\left(\sqrt{\frac{c}{m}}t\right)} $

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