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Rotating Bodies - Stress

Stress in rotating disc and ring bodies.

Stress in a Rotating Disc

Stress in rotating disc

Stress in a rotating disc can be calculated as

σ z = ω2r2ρ / 3

= v2ρ / 3

= ( 2 π n / 60)2r2ρ / 3 (1)


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 rotating ring

Stress in a rotating ring can be calculated as

σ z = ω2ρ ( r12+ r1 r2+ r2 2 ) / 3                     (2)


r1 = outer radius of ring (m)

r2= inner radius of ring (m)

For a thin ring the equation can be simplified to

σ z = ω2ρ r                    (3)


r  = mean radius of ring (m)

Design Stress for materials used in Flywheels

Design Stress Flywheel Materials
(kg/m3 )
Typical Design Stress
( MPa)
Aluminum alloy 2700
Birch plywood 700 30
Composite carbon fiber - 40% epoxy 1550 750
E-glass fiber - 40% epoxy 1900 250
Kevlar fiber - 40% epoxy 1400 1000
Maraging steel 8000 900
Titanium Alloy 4500 650
"Super paper" 1100
S-glass fiber/epoxy 1900 350

Related Topics

  • Dynamics

    Motion of bodies and the action of forces in producing or changing their motion - velocity and acceleration, forces and torque.

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