Find critical speed of the shaft:

The rotor of a turbo super charger containing weight 10 kg is keyed to the centre of a 25 mm diameter steel shaft. The span length of the shaft is equal to 50 cm. Find critical speed of the shaft and amplitude of vibration of the rotor at a speed 300 rpm. The eccentricity of mass is equal to 0.015 mm. Let E = 2.0 × 1011 Pa.

Solution

It is given that

Rotating mass = 10 kg

Diameter of shaft = 25 mm

Span length 'l' = 50 cm

E = 2.0 × 1011 Pa

Eccentricity 'e' = 0.015 mm

Speed = 3000 rpm

w = 10 × 9.81 = 98.1 N

I =  (π/64)d⁴  =(π/64)(2.5/64)⁴ = 1.92 × 10- 8  m4

Let shaft to be simply supported

ω= (2π 3000) /60 = 314.16

ω / ωn = 314.16/ 386.15= 0.814

Amplitude of vibration