×
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!
  • Students Click Here

*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.

Students Click Here

Jobs

Mechanical engineering general discussion FAQ

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 general discussion FAQ Index
Back to Mechanical engineering general discussion Forum

My Archive


Resources

eBook - Mastering Tolerances for Machined Parts
When making CNC machined parts, mastering tolerances can be challenging. Are general tolerances good enough? When does it make sense to call out for tighter tolerances? Do you need a better understanding of fits, datums, or GD&T? Learn about these topics and more in Xometry's new e-book. Download Now
eBook – How to Choose the Correct Corrosion Testing Method
When designing a metal component, engineers have to consider how susceptible certain alloys are to corrosion in the final product’s operating environment. In a recent study by NACE (National Association of Corrosion Engineers), it was estimated that the direct and indirect costs of corrosion in the United States is approximately 6.2% of the GDP. In 2016, that cost exceeded $1 trillion dollars for the first time. Download Now

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