INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Jobs

Structural Calculations

How do I work out the forces in an impact of a steel ball and a plate? by GregLocock
Posted: 26 May 06

In the special case of a ball or cylinder bouncing off a hard plate the answer is complex.

Not very surprisingly Timoshenko covers this problem in "Theory of Elasticity".

Unfortunately I didn't copy all the right equations down, so I'll just solve the simpler case of a steel ball bouncing off its twin. If you think about that case it is likely that this is also the same as the steel ball bouncing off an infinitely stiff flat plane.

The time of the contact is

t=2.94(1.25*sqrt(2)*pi*rho*(1-nu^2)/E)^0.4*R*v^-0.2  eqn 244

R=0.031 m
v=3.132 m/s
rho=7843 kg m-3  
E=210*10^9 N m-2
nu=0.3

t=0.1493 ms

The average force, F during the contact is 2*m*v/t (ie the change of momentum divided by the time)

F=42 kN, ie a little over 4 tons force.

Timoshenko actually gives a direct solution for a ball on a flat plate, and the peak force rather than the average force, but it is spread over two pages. This solution assumes that the contact time is long compared with the period of the lowest modes of vibration.  

Back to Mechanical engineering other topics FAQ Index
Back to Mechanical engineering other topics Forum

My Archive


Resources


Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close