Hertzian Contact Stress Calculator
Calculate maximum Hertzian contact pressure between two contacting bodies
Calculator
Enter the load, radii, and material properties to compute contact radius and maximum Hertzian pressure.
About the Hertzian Contact Stress Calculator
The Hertzian Contact Stress Calculator determines the localized stresses that occur when two curved surfaces—such as spheres, bearings, gears, rollers, or cams—come into contact under an applied load. This tool computes contact radius and maximum pressure using classical Hertz contact formulas.
What You Can Calculate
- Contact Radius (a): The radius of the circular contact patch between two bodies.
- Maximum Hertzian Pressure (p₀): The highest compressive stress at the center of contact.
- Equivalent Radius (R′): Effective curvature from both bodies.
- Equivalent Modulus (E′): Combined material stiffness based on moduli and Poisson’s ratios.
Formulas Used in the Calculator
The calculator uses standard Hertzian equations:
- Equivalent Radius: 1/R′ = 1/R₁ + 1/R₂
- Equivalent Modulus: 1/E′ = (1−ν₁²)/E₁ + (1−ν₂²)/E₂
- Contact Radius: a = [ (3FR′) / (4E′) ]1/3
- Maximum Pressure: p₀ = (3F) / (2πa²)
How to Use the Calculator
- Enter the normal load applied between the surfaces.
- Provide the radii of both contacting bodies.
- Enter the elastic modulus and Poisson’s ratio for each material.
- The calculator instantly displays contact radius and maximum Hertz pressure.
Applications of Hertzian Stress Analysis
Hertzian contact analysis is essential in bearing design, gear tooth contact, cam-follower systems, rail wheels, rolling elements, and any mechanical system where curved surfaces transfer load through small contact areas.