Understanding Hertzian Contact Stress
When under load, two elastic, curved surfaces do not touch at a single mathematical point or an infinitely thin line. Instead, they deform slightly, flattening out to create a small contact area. Hertzian contact stress refers to the localized stresses that develop within this tiny area of deformation.
This type of interaction between two surfaces is known as non-conformal contact, which is governed by Hertzian theory. If the contact pressure exceeds the material’s limits, it may lead to premature failure. For example, ball bearings and roller bearings can experience Brinelling if the stress exceeds 4,200 MPa and 4,000 MPa, respectively.
Types of Contact & Applications
The shape of the contact area dictates the stress distribution. Our calculators are divided into the three primary contact regimes encountered in the field:
Line Contact (Cylinder on Cylinder / Cylinder on Flat / Roller on Roller — Without any Crown): Under load, the contact area forms a narrow rectangle.
Common Applications: Mating teeth of uncrowned spur gears, roller bearings supporting rotating shafts, and camshafts against flat followers.
Elliptical Contact: When the radii of curvature of the two bodies are different in orthogonal directions, the contact patch forms an ellipse.
Common Applications: Crowned spur/helical and bevel gears, and crowned rollers.
Point Contact (Ball on Ball / Ball on Flat): Under load, the contact area forms a small circle.
Common Applications: Deep groove ball bearings, angular contact bearings, and thrust ball bearings in clutch systems.
Evaluate Your Design
Our tools are created to provide insights into the stress regimes in which real-world components operate, powering the machines we use every day. Choose a calculator below that matches your contact regime to determine the maximum contact pressure, the dimensions of the contact patch, and the depth of the maximum shear stress to evaluate your design.
Disclaimer: The tools and calculators on this site are built on standard engineering textbook principles and are meant for baseline estimation and educational use only. Always seek independent professional validation before taking anything into production. Epiphany Drives doesn't assume any liability for discrepancies, mechanical issues, or accidents resulting from the use of these tools.