Rotating Bodies - Stress

Stress in a Rotating Disc

Stress in a rotating disc can be calculated as

σ_z = ω² r² ρ / 3

= v² ρ / 3

= ( 2 π n / 60)²r²ρ / 3                               (1)

where

σ_z = stress (Pa, N/m²)

ω = angular velocity (rad/s)

r = radius of disc (m)

ρ = density (kg/m³)

π = 3.14...

n= revolutions per minute (rpm)

Stress in a Rotating Ring

Stress in a rotating ring can be calculated as

σ_z = ω²ρ (r₁²+ r₁ r₂+ r₂ ²) / 3                              (2)

where

r₁ = outer radius of ring (m)

r₂= inner radius of ring (m)

For a thin ring the equation can be simplified to

σ_z = ω² ρ r ²                               (3)

where

r  = mean radius of ring (m)

Design Stress for materials used in Flywheels