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

Click For Summary

Discussion Overview

The discussion centers around understanding the concept of contact curvature sums in the context of Hertzian contact analysis, particularly as it applies to rolling element bearings. Participants seek clarification on the equations involved and the geometric interpretation of curvature sums in contact mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses difficulty in understanding contact curvature sums and requests resources or explanations.
  • The equations for curvature sums are presented, indicating how to calculate the equivalent curvature from two surfaces in contact.
  • Another participant explains that in Hertzian contact, the curvature of a sphere in contact with a flat plate can be treated as the sum of the curvatures of the two surfaces, noting that a groove contributes negative curvature.
  • References to a specific text, "Tribology in Machine Design" by T. A. Stolarski, are provided to support the explanation of curvature sums.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the understanding of contact curvature sums, as one participant seeks further clarification while another provides an explanation. The discussion remains unresolved regarding the participant's initial confusion.

Contextual Notes

The discussion includes assumptions about the geometry of the contact surfaces and the application of Hertzian contact theory. There may be limitations in the participant's understanding of how to apply the equations to the specific problem presented.

knight92
Messages
100
Reaction score
0
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.
 
Engineering news on Phys.org
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
 

Attachments

  • Like
Likes   Reactions: 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.
 

Similar threads

What is the Radius of Curvature of the Outer Surface of a Contact Lens?
  • · Replies 1 ·
Replies
1
Views
7K
Undergrad Hi,I hope someone can help me. Looking at a magnetic generator,
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Can someone help me explain these two problems better?
  • · Replies 5 ·
Replies
5
Views
6K