At work I have been given the task of finding force of ball bearing hitting a pick up finger in a ball nut. If you have no idea what that is then to simplify the scenario I am trying to model a ball bearing hitting a steel plate and the force that ball exerts on the plate.(adsbygoogle = window.adsbygoogle || []).push({});

Back to physics 101 I know that F=ma=m(dv)/dt

To simplify some more we can say a=a=∆v/∆t

where ∆v is the change in velocity and ∆t is the time the ball is in contact with the surface of the plate.

I know the mass of the bearing and initial velocity, I can assume an elastic collision so the exit velocity is the same as the entrance velocity. The big problem is determining how long the ball is in contact with the surface.

Here is my first attempt at the calculation.

I converted the 'ball' to a cylinder with the same mass and same height but different diameter for simplicity. I also assumed that there was no radial expansion of the cylinder (ignoring Poissons ratio)

The speed of sound in a solid is σ= (E^.5)/ ρ

Where E is Young’s Modulus for the material and ρ is the density

∆t=2L/ σ

From there it is easy to calculate force using F=m*∆v/∆t

Source for these equations http://www.jw-stumpel.nl/bounce.html" [Broken]

The problem that I am encountering is the resulting force from these set of initial conditions.

diameter of ball=.141"

∆t=1.44E-5 sec

v=103 in/sec

m=1.27E-5 slugs

E=30500 ksi =3.05E7 psi

density=.282 lb/in^3

the result is a force of 181 pounds. I know this can not be the case because FEA analysis of this force on the mating part will cause a failure. Since these nuts can run for millions of inches of travel without failure this can't be an accurate result.

Is there a flaw in my calculations or assumptions or am I even close to the correct path?

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# Bouncing Ball Bearing

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