Force calculation of sphere against plane

[davidrdguez]

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,

 

[davidrdguez]

Another picutre

 

[ztengguy]

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.

 

[davidrdguez]

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,

 

[prex]

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

 

[bmrossetti]

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

 

[JStephen]

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.

 

[dhengr]

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.

 

[msquared48]

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

 

[paddingtongreen]

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.

 

[GregLocock]

irfanview

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[davidrdguez]

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 Johnson/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

 

[paddingtongreen]

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.

 

[rb1957]

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

 

[rb1957]

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).

 

[davidrdguez]

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 Johnson/PartI_4.pdf

I think it's wrong!

cheers,

 

[rb1957]

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

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

 

[davidrdguez]

;-)

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

 

[prex]

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

 

[davidrdguez]

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,