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

• knight92
In summary, 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.

#### knight92

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.

Bump..

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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knight92
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.

## 1. What is Tribology?

Tribology is the study of friction, wear, and lubrication of interacting surfaces in relative motion.

## 2. What is Contact Curvature Sum?

Contact Curvature Sum is a mathematical concept used in tribology to calculate the total curvature of two surfaces in contact.

## 3. How is Contact Curvature Sum calculated?

Contact Curvature Sum is calculated by summing the individual curvatures of each surface at the point of contact.

## 4. What is the importance of understanding Contact Curvature Sum?

Understanding Contact Curvature Sum is important in tribology as it helps determine the level of contact between two surfaces and can impact friction, wear, and lubrication behavior.

## 5. Can you provide an example of Contact Curvature Sum in real-world applications?

One example of Contact Curvature Sum in real-world applications is in the design and testing of car tires. By understanding the curvature of the tire and the road surface, engineers can optimize the tire's performance and reduce wear and tear on both the tire and the road.