KEVOS® MAKEOS · Strength
Hertz Contact Stress
What contact pressure develops between these curved bodies under load?
Contact width, maximum contact pressure and maximum subsurface shear stress for sphere (point) or parallel cylinder (line) contact by Hertz theory.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Contact type | choice | Point contact for balls; line contact for rollers and wheels on flat tracks. |
| Radius of body 1 | mm | Radius of the convex body (ball or roller radius). |
| Radius of body 2 (0 = flat, negative = concave) | mm | Radius of the mating body: 0 for flat, negative for a concave seat or groove. |
| Normal load | N | Normal load across the contact. |
| Contact length (line contact only) | mm | Length of line contact (roller or wheel width). |
| Materials | ||
| Elastic modulus, body 1 | GPa | Modulus of body 1. |
| Poisson’s ratio, body 1 | Poisson’s ratio of body 1. | |
| Elastic modulus, body 2 | GPa | Modulus of body 2. |
| Poisson’s ratio, body 2 | Poisson’s ratio of body 2. | |
| Allowable contact pressure | MPa | Allowable contact pressure for the material, hardness and number of cycles, from your design data. |
Method and formulas
- E* = 1 ÷ ((1 − ν₁²) ÷ E₁ + (1 − ν₂²) ÷ E₂); 1/R = 1/R₁ + 1/R₂.
- Point: a = (3FR ÷ 4E*)^(1/3); p₀ = 3F ÷ 2πa²; τmax ≈ 0.31 p₀ at 0.48a.
- Line: b = √(4FR ÷ πLE*); p₀ = 2F ÷ πbL; τmax ≈ 0.30 p₀ at 0.786b.
- Example: a 50 mm radius roller, 20 mm long, on a flat with 10000 N gives p₀ = 606.04 MPa.
Limitations
- Elastic, frictionless, smooth contacts with dimensions much larger than the contact area.
- Edge loading at roller ends raises pressure well above the line-contact value.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check wheels on rails, cam followers and rollers
- Size ball transfer units and pivots
- Compare materials and radii
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Contact radius or half-width
- Maximum contact pressure
- Maximum subsurface shear and its depth
- Approach (point contact)
Interpreting the result
- Compare with allowable values for the actual hardness and cycle count; surface fatigue governs repeated contacts.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2301–2309. Topic reference; no source tables or recommended settings are reproduced.
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