calculating contact pressure between a sphere and a cylindrical sleeve 2

[MShineV]

Hello everybody,
I need to design a joint consisting of a steel ball stud able to slide and spin in a plastic sleeve bearing with the same diameter. How does one approximately calculate the contact pressure between the ball and the sleeve? The only examples I found are for the contact between two spheres or two cylinders.

Thank You in advance.

 

[kingnero]

Roark's has the equations for (Hertzian) contact stress, where the 4 radii are parameters. This should allow you to use this equation in your case, if I understand your problem correctly.

 

[MShineV]

Thanks kingnero, with your little push in the right direction I was able to find what I needet. For example this neet site:

http://www.amesweb.info/HertzianContact/SphereInCircularRace.aspx#.VLUH5yuG_eE

.
Second question. According to what I read, the contact pressure can easily exceed the yield strenght of the material and that the max safe contact stress is determinet via experiment. Is there a way to roughly approximate the max safe contact stress?

 

[BrianPetersen]

Situations analogous to what you have described are found in every ball bearing, and the situation that you just described is why rolling-element bearings have a finite life that is dependent on the load and the number of rotations.

In your case, the plastic sleeve is likely to be the one taking the bulk of the deflection, and will likely fail first.

 

[CoryPad]

Plane strain indentation (an approximation of contact conditions such as yours) requires the applied surface pressure to be 3 times the yield stress before gross deformation. That is for elastic-plastic materials like metals. Viscoelastic polymers will have lower limits, and physical measurements are the traditional approach.

 

[MShineV]

Thank You all a lot,
How do you think will the murtfeld plastic (yield strenght 76 MPa) handle the 144,3 MPa of contact pressure? I will inform you of the results once the prototype of our machine is tested. Can anybody recomend me some easy literature on this matter?