(Tribology) Can someone explain Contact Curvature Sum to me?

  • Thread starter knight92
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I am having a hard time grasping contact curvature sums. Can someone give me a link to where there is a guide or a youtube video? or can someone help me here please.

Here are the equations:

1/Rx = 1/rax + 1/rbx

1/Ry = 1/ray + 1/rby

1/R = 1/Rx + 1/Ry

The question is this:

The ball-outer race contact of a deep groove ball bearing has 10mm ball diameter, a 5.5 mm outer race concave groove radius and a 45 mm radius from the bearing axis to the bottom of the groove. The load on the ball is 500 N and the race and the ball are made of steel (E=206 GPa, v = 0.30). Apply Hertzian Contact Analysis to determine.

(a) - Curvature Sum (Include diagrams to define contact geometry).

From this I reckon it is talking about a rolling element bearing?

I know how to do the rest of the questions but I really don't understand how to find the curvature sum. I have searched on google and youtube but all I find is reports and simulations, none of which actually explain anything.
 

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Baluncore
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Where two curved surfaces are in hertzian contact they may be treated as a single sphere in contact with a flat plate. The curvature of the sphere is equivalent to the sum of the curvatures of the two surfaces in contact. So two balls in contact will have a greater equivalent curvature while a ball in a groove will have a lower curvature because the groove contributes negative curvature to the sum.

Extract attached; Tribology in Machine Design. T. A. Stolarski. Pages 64 to 72
 

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Where two curved surfaces are in hertzian contact they may be treated as a single sphere in contact with a flat plate. The curvature of the sphere is equivalent to the sum of the curvatures of the two surfaces in contact. So two balls in contact will have a greater equivalent curvature while a ball in a groove will have a lower curvature because the groove contributes negative curvature to the sum.

Extract attached; Tribology in Machine Design. T. A. Stolarski. Pages 64 to 72
Thank you.
 

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