Hertzian Contact Stresses - Please Help!!

[LiamRainbow]

This is my first post to any board. I usually just research till I find the answer, but this is driving me absolutely nuts.

I'm trying to show my working for maximum shear stress for a sphere on a flat plate. The answer is 202.9 MPa.

Please can somebody show me the working out, I'm stuck at calculating the principal stresses and I cannot understand the z value, which is apparently 0.225mm.

When I input the values below into the equation for principal stress, I get 2.57x10¹⁰Pa, which gives me the wrong value when inputted into the shear stress eq.

I'm losing my mind over this!

Radius of sphere = 50mm, E = 200GPa, Poisson's Ratio = 0.3, Force = 300N, Pmax = 654.5MPa, z=0.225mm

 

[Deleted member 4993]

This is my first post to any board. I usually just research till I find the answer, but this is driving me absolutely nuts.

I'm trying to show my working for maximum shear stress for a sphere on a flat plate. The answer is 202.9 MPa.

Please can somebody show me the working out, I'm stuck at calculating the principal stresses and I cannot understand the z value, which is apparently 0.225mm.

When I input the values below into the equation for principal stress, I get 2.57x10¹⁰Pa, which gives me the wrong value when inputted into the shear stress eq.

I'm losing my mind over this!

Radius of sphere = 50mm, E = 200GPa, Poisson's Ratio = 0.3, Force = 300N, Pmax = 654.5MPa, z=0.225mm

What is the reference paper/book you have used to calculate the principal stress/es?