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

AI Thread Summary
Contact curvature sums in tribology involve calculating the equivalent curvature of two surfaces in Hertzian contact, such as a ball and a groove in a bearing. The equations provided illustrate how to derive the curvature sums for the x and y axes, leading to an overall curvature. The discussion highlights the challenge of finding clear resources, with users expressing frustration over the lack of straightforward guides or videos. It emphasizes that the curvature of the sphere is the sum of the curvatures of the contacting surfaces, where grooves contribute negatively to the overall curvature. Understanding these concepts is essential for applying Hertzian Contact Analysis in mechanical design.
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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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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Baluncore said:
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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