×
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

Force calculation of sphere against plane

Force calculation of sphere against plane

Force calculation of sphere against plane

(OP)
Hi there!

I need to check the maximum weight we can put on a platform we have.

There are different parts between this platform and the floor. It doesn't seem difficult to check each part, but the platform is place on the top of three feet like the one in the attached picture: a sphere touching a plane.

In theory the sphere touches the plane in one point.

How can I know the maximum load?

Thank you
Regards,
 

RE: Force calculation of sphere against plane

I would say check your statics...assume as a point load, and check each component. Or, check each component for a max load, and then use the lesser value.   

RE: Force calculation of sphere against plane

(OP)
Hi ztengguy,

Yes, I'll check the statics. and each component. This is not the problem

What I need to know is what happens in between these two parts (spherical and planar)

Cheers,

RE: Force calculation of sphere against plane

You need Hertz's theory of contact pressure. See in the first site below, under Other -> Hertz -> Spheres -> Sph.on flat , but you'll also find plenty of articles by googling.
The allowable stress is defined by the code in effect. It should be at least 3-4 times the allowable stress in tension.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Force calculation of sphere against plane

If you have access to a copy of "Roark's Formulas for Stress and Strain," there are good tables for contact stresses, including your particular case of a sphere on a flat plate.

Regards,

Brandon

RE: Force calculation of sphere against plane

Note that in some similar situations, such as bolts bearing in bolt holes, it is simply assumed that some yielding will be going on and will not be objectionable- something to keep in mind if you get unreasonable results with the Hertz stresses.

RE: Force calculation of sphere against plane

You will get what appear to be unreasonable stress results, and the Hertz stress calcs. do assume that some yielding will take place.  But, it is yielding in bearing, and in a confined and supported bearing area.  The problem becomes significantly more complex if the two materials do not have essentially the same mechanical properties.

RE: Force calculation of sphere against plane

If you are that worried about it, why don't you just make an imbedded concave seat area for the end of the bolt into the plate - it will increase the contact area to a more uniform and quantifiable arrangement.

Mike McCann
MMC Engineering
http://mmcengineering.tripod.com
 

RE: Force calculation of sphere against plane

What program(s) display ".png" files? how do I see the second picture?

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Force calculation of sphere against plane

(OP)
Hi everyone,

Thanks for the answers

 - The xcalcs page is very cool. I made some analysis and I got the following results:
Average compressive stress: 1340 MPa
Maximum compressive stress: 2010 MPa
The contact is steel against steel. Supposing a yield strength of 200 MPa I'm out of the 3-4 times

 - I don't have the Roaks but I found other info. For instance:
http://www.optics.arizona.edu/optomech/Fall08/reports/HW9/opti521/James%20Johnson/PartI_4.pdf
(but I don't get the same result in the equation 11!)

 - I need to have the flat surface, this is an accurate alignment system where these feet have to slide on the flat surface.

Cheers

 

RE: Force calculation of sphere against plane

Cheers Greg. I should have remembered, I had a very early version. It has grown since then, it looks like a great program.

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Force calculation of sphere against plane

IE works fine for me (for showing .png files)

RE: Force calculation of sphere against plane

if you want accurate alignment and a sliding interface, then i guess either you change the steel (a higher strenth steel should get you an Fbru that works) or you change the contact (put a flat on the sphere, and redesign how it attaches to the body so you can ensure the four feet have a common plane).

RE: Force calculation of sphere against plane

(OP)
Hi,

This system is already manufactured and working.

I didn't realise the materials we were using

For the plane (plate) is 16MnCr5 which has a minimum tensile strength of 1000MPa

For the sphere (screw) the quality is 10.9 so 940 MPa

I'll do the calculations, but I'd like to ask someone to check the example in

http://www.optics.arizona.edu/optomech/Fall08/reports/HW9/opti521/James%20Johnson/PartI_4.pdf

I think it's wrong!

cheers,

 

RE: Force calculation of sphere against plane

along the lines of "if it ain't broke, don't fix it" ...

if it's working, don't run a calc on it !

 

RE: Force calculation of sphere against plane

(OP)
winky smile

we want to know if we can put more weight on it; much more

RE: Force calculation of sphere against plane

Nonsense.
E' should be GPa, and a deformation of 1.4 mm under 10 N is ridiculous.
You didn't specify your dimensions for us to check.
Anyway consider that a structural code will normally allow for a permanent deformation under the sphere, but this is of little importance in that case, as the spherical support will normally not move.
In your conditions you risk to degrade the flat surface by the repeated local deformations by the moving sphere, so you should consider a lower allowable.
You should look into the allowables for ball bearings, that should be (maximum stress) of the same order as the fatigue strength.

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Force calculation of sphere against plane

(OP)
Hi there,

I contacted the author of the paper and he agreed there are mistakes.

I have a 50 mm Radius feet (10.9 quality) against a 16MnCr5 plate

The point is I can't say how much weight we place, but what's the maximum one

cheers,

RE: Force calculation of sphere against plane

the problem with "maximum" is that it is hard to calculate with your design; as i see it.

any load is deforming the plate (or sph.) since by analysis you have a point contact  = infinte stress.  in reality you have some localised yielding = load distribution.  but clearly too much local yielding will impact how easy it is to move, degrade the palte/sph., etc ... qualitive requirements. (plus somewhere along the line the structure on the other side of the feet is going to give way.

the easiest thing would be to test a structure,
next easiest would be to redeisgn the feet so that they only stand (the way the great designer intended feet to work) and something else comes into play when moving (castored wheels, a dolly, ...).

RE: Force calculation of sphere against plane

Again, you will get deformations with any significant loads.  It's a fact of life.  But, a possible solution to your problem is as follows: take a 3 or 4" square piece of like material, 1 or 2" thick; the bottom surface is machined flat and polished, the top has a .25" deep spherical hole machined in it to a radius of 50.1mm for your leveling foot to fit into.  If you've done the recommended reading on this subject, as suggested above, not just finding a formula and plugin-n-chugin into it, you should know that the nearer the two spherical surfaces are in their radii the lower the bearing stress will be, and the less the deformation will be.  This will allow you to load the leg to a higher value, without it deforming significantly, and will distribute that load to the base plate to keep it from being deformed by the leveling foot radius.  You figure out the exact sizes, stresses and deformations.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources