Rotordynamics

Critical Speed Simulator

Examine the whirling and critical speeds of a simply supported shaft loaded with a heavy central rotor disk. Control physical sizing and load dynamics.

Material Preset

Steel

200 GPa

Area Moment (I)

30.68

x10⁻⁸ m⁴

Output

CSV

Export ready

Parameters

Shaft Material

Shaft Diameter (d)50 mm

10200

Shaft Length (L)1.00 m

0.55

Central Mass (m)100 kg

101000

Elastic Modulus (E)200 GPa

50300

Shaft Whirl Animation

System Governing Equations

Area Moment of Inertia (I)

I = π * d⁴ / 64

Static Center Deflection (δ)

δ = m * g * L³ / (48 * E * I)

Critical Speed (Nc)

Nc = (30 / π) * √(g / δ)

At L = 1.00 m, the static deflection is 0.333 mm.

Critical speed represents the lowest frequency at which the shaft becomes dynamically unstable (whirls).

Rotor Whirling Simulation

Critical Speed

1639RPM

Static Deflection (δ)

0.333mm

Critical Angular Vel

171.62rad/s

Safe Speed (75%)

1229RPM

Length vs Critical Speed & Deflection

Length Sweep Data Points

Shaft Length (m)	Deflection (mm)	Critical Speed (RPM)
0.50	0.042	4635
0.90	0.243	1919
1.30	0.732	1106
1.70	1.636	739
2.10	3.085	539
2.50	5.204	415
2.90	8.123	332
3.30	11.970	273
3.70	16.872	230
4.10	22.956	197
4.50	30.352	172
4.90	39.187	151