solid metal ball design

[dravid]

Hi, i am designing a mechanism, which includes the metal balls (as that of ball bearing). The ball has to withstand two point load acting on its surface. Can anyone provide me a direction to do so.

 

[boo1]

Stresses?
Manufacturing?
what are you looking for?

 

[plasgears]

Pursue the methods of contact stress. I assume that the receptical of the ball is similarly spherical. With sufficiently high stresses, the balls would need to be hardened, and if motion is not great, the balls need not be high precision ground.

 

[arto]

Look in Roark Table 33 case 1c [5th ed]

for allowable stress, maybe use 1.6 x Sallow as in the ASME Code

 

[dravid]

Hi Arto,

Thanks for reply, i am interested in design. Where i can find Roark Table. ?

 

[arto]

Raymond J Roark & Warren C. Young "Formulas for Stress & Strain" McGraw Hill

This is the greatest book ever published in the history of the universe [if you're an ME, that is!! If the ship is sinking, this is the one you bring on the lifeboat to the desert island - maybe Machinery's Handbook, too].

Remember when you watched the back of the professor's head for 4 years when he derived all those equations? Well, Roark has just the results & a lot more too.

Even if you're a high-tech FEA guy, it is great to verify solutions [i.e., "the FEA model produced results within 10% of Roark, so it must be right."]

Get a copy if you can. I think it's up to the 7th edition now - BUT - if you come across Grandpa's old 3rd or 4th edition hang on to that too, because some of the older formulae are more "user friendly" when you want a quick answer.

 

[boo1]

Spotts, Design of Machine Elements, 6th Ed, pp443

Lists contact stress between a sphere and a flat surface as:

Po=0.616*(P/R**2*((E1*E2)/(E1+E2))**2)**3
Po max copressive stress
P=load
R=Rad sphere

 

[mieshko]

Hi
It's sounds like Hertz contact problem. Theoretical background and maths formulas you can find in : Thimoshenko, "Theory of Elasticy"

 

[dravid]

Hi, thanks for the replies.

Now, if there are three point forces, instead of two. is there any solution for finding stresses in metal ball(sphere). or method to find out the dia of ball based on these three forces.

 

[Pekelder]

Calculations on three forces are not different of that on two. The three forces are in one plain (assuming no friction, will come to that), so you can calculate the three forces and/or directions. From the contact-geometry you can, with the Herz formulas, derive the local stress. With a steel ball, the contact stress will always be higher than shear or something like that (at least, you might expect that given you are designing the mechanism) end the deflections are small (again, assuming you calculate the mechanisme so that no plastic deformation will result).

If there is friction (there is bound to be..), you can still work with the Herz formulas, but you will have to take into account that there is shear-stress in the surface. Thimoshenko might have something on that. You might elaborate a bit on the mechanism you are designing so we can have some idea of the forces, dimensions etc.

Regards,

Pekelder