A cylindrical roller pressed against a raceway forms a Hertzian line contact of half-width b carrying peak pressure p₀. For load per unit length Q′ and effective radius R (1/R = 1/rrace + 1/rroller) and effective modulus E* = E/(2(1−ν²)):
b = √(4·Q′·R / (π·E*))
p₀ = 2·Q′ / (π·b)
Below the surface, the Hertz solution gives a full subsurface stress field. The orthogonal shear stress τxz — the component that reverses sign every time a roller rolls overhead — is what Lundberg–Palmgren rolling-contact-fatigue theory identifies as the driver of subsurface crack nucleation:
τxz(x,z)/p₀ = -n·[1-(m²-z²)/(m²+n²)], with
m²,n² from (1-(x/b)²+(z/b)²)² + 4(x/b)²(z/b)²
This sim numerically searches that field for its peak κ = max|τxz/p₀| and location — it reaches its maximum below and to the side of the contact, not at the surface. That subsurface, alternating shear is why rolling-contact fatigue cracks in clean, well-lubricated bearings start a few tens of micrometres under the raceway and grow upward, popping out a flake of material — a spall — once they break through.
- Radial load Fr — distributed across loaded rollers by Stribeck's equation Q(ψ) = Qmax·cos1.5ψ inside a ±100° load zone (shown as the orange arc); it sets Q′, b and p₀.
- Shaft speed — sets how fast the inner race and rollers rotate, i.e. how many stress cycles per second the tracked raceway point (the small dot) accumulates.
- Fatigue shear strength τlim — a stand-in for steel cleanliness/hardness. Damage per cycle is modelled as (τ₀/τlim)9, the steep power-law exponent Lundberg–Palmgren theory uses for rolling-contact life — a small change in stress or material quality moves the spall time by orders of magnitude. This constant and its calibration are illustrative, not a certified L10 life calculation.
- Once accumulated damage reaches 100%, a spall pit forms at the tracked point and stays until you reset.