What Is the Hertzian Elastic Contact Pressure & Contact Spot Calculator?
Hertzian contact theory calculates local elastic stress fields and deformations when curved solid bodies touch under normal loads.
How Does the Hertzian Elastic Contact Pressure & Contact Spot Calculator Work?
Combines equivalent radius R_eff and effective composite modulus E* to solve the cubic relation for circular contact patch radius a.
Hertzian Elastic Contact Pressure & Contact Spot Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
a = left[ rac{3 F R_{ ext{eff}}}{4 E^*}
ight]^{1/3}, quad p_0 = rac{3 F}{2 pi a^2}, quad delta = rac{a^2}{R_{ ext{eff}}}
Classical Hertzian spherical elastic contact equations.
How to Use the Hertzian Elastic Contact Pressure & Contact Spot Calculator
- Input normal force in kN, contact radii in mm (0 for flat surface), and elastic moduli in GPa.
Step-by-Step Example Calculation
Steel Ball Bearing on Flat Steel Race
Input Values:
loadKn:15
radius1Mm:40
radius2Mm:0
youngsModulus1Gpa:210
youngsModulus2Gpa:210
Worked Steps: Contact radius a = 1.39 mm, Peak pressure p0 = 3,695 MPa, Elastic approach delta = 0.048 mm.
Understanding Your Result
Displays circular contact spot radius a, peak central pressure p0, mean pressure, and mutual elastic indentation depth delta.
Factors That Affect the Result
- Peak shear stress occurs subsurface at depth ~0.48*a, making subsurface rolling contact fatigue the dominant failure mode.
When Should You Use This Calculator?
- Sizing ball and roller bearings, gear tooth meshing contact, railway wheel-rail contact, and spherical indentation hardness testing.
Assumptions & Limitations
- Assumes frictionless, non-conforming, linear elastic half-space contact with small contact area relative to body dimensions.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Classical analytical Hertzian solution.