// multi-utility computation suite · offline · instant · precise
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sci.hertz-contact-sphere Calculator
Calculates Hertz contact stress between two spheres: contact radius a = (3FR_eff/4E_eff)^(1/3) and peak pressure p₀ = 3F/(2πa²). Contact radius scales as F^(1/3) — doubling load increases contact area by 59% and peak pressure by 26%; bearing life follows the inverse cube of Hertz pressure.
Inputs
R1 Mm
Distance from centre to edge of a circle. Radius = diameter / 2.
R2 Mm
Distance from centre to edge of a circle. Radius = diameter / 2.
E1 Gpa
Material stiffness (GPa). Stress divided by strain in the elastic range. Steel: 200 GPa. Aluminium: 70 GPa. Rubber: 0.01–0.1 GPa.
Nu1
Reference formula or conversion factor shown for context.
E2 Gpa
Material stiffness (GPa). Stress divided by strain in the elastic range. Steel: 200 GPa. Aluminium: 70 GPa. Rubber: 0.01–0.1 GPa.
Nu2
Reference formula or conversion factor shown for context.
F N
Push or pull (N). F = ma. Net force determines acceleration. Account for all forces including gravity and friction.
Results
contact radius a (μm)
The computed radius -- half the diameter.
central contact pressure P₀ (MPa)
Sample size or count used in the calculation.
elastic approach δ (nm)
Sample size or count used in the calculation.
effective modulus E* (GPa)
Reference formula or conversion factor shown for context.
effective radius R* (mm)
The computed radius -- half the diameter.
a = (3FR*/4E*)^(1/3)
Reference formula or conversion factor shown for context.