What is Hertz contact stress?

Hertz contact stress is the localized stress that develops when two curved bodies are pressed together. The contact area is very small and the maximum pressure occurs at the center. This theory applies to elastic, non-conforming contacts like ball bearings, gears, and wheel-rail interfaces.

What is the maximum contact pressure formula for spheres?

For two spheres: p_max = (1/π)·(6F·E*²/R*²)^(1/3), where E* is the combined elastic modulus and R* is the combined radius. The contact area is circular with radius a = (3FR*/(4E*))^(1/3).

What is the combined elastic modulus E*?

The combined (effective) elastic modulus accounts for both bodies: 1/E* = (1-ν₁²)/E₁ + (1-ν₂²)/E₂. It represents the combined elastic compliance of both contacting surfaces.

When does Hertz theory apply?

Hertz theory assumes: elastic material behavior, contact area much smaller than body dimensions, frictionless contact, smooth surfaces, and non-conforming geometries. It does not apply to plastic deformation, rough surfaces, or conforming contacts.

Where is Hertz contact stress important?

Rolling element bearings, gear teeth, cam-follower systems, wheel-rail contact, indentation testing, and any machine element where curved surfaces press against each other. Contact fatigue (pitting) is often governed by Hertzian stress.

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गोळा-वर-गोळा आणि सिलिंडर-वर-सिलिंडर लवचिक संपर्कासाठी कमाल Hertz संपर्क दाब, संपर्क क्षेत्र आणि जवळ येणे मोजा.

गोळ्याचा संपर्कसिलिंडर संपर्क#171

संपर्क प्रकार

त्रिज्या R₁ (mm) — सपाटासाठी ∞

त्रिज्या R₂ (mm) — सपाटासाठी ∞, 0 = सपाट

बल F (N)

E₁ (GPa)

ν₁ (Poisson चे गुणोत्तर)

E₂ (GPa)

ν₂ (Poisson चे गुणोत्तर)

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कमाल संपर्क दाब p₀

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संयुक्त E*

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संयुक्त R*

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⚠️ Note: सपाट पृष्ठभागासाठी R₂ = 0 प्रविष्ट करा (R₂ → ∞). Hertz सिद्धांत लवचिक संपर्क, वस्तूच्या आकाराच्या तुलनेत लहान संपर्क क्षेत्र आणि घर्षणरहित पृष्ठभाग गृहित धरतो.

Hertz Contact Stress Calculator | Free Online Tool

Published by Nikolai Shelkovenko on फेब्रुवारी 15, 2026 एप्रिल 5, 2026

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