Frequency Analysis of a rotating shaft

Aim: Frequency analysis of rotating shaft.

Introduction :Frequency analysis helps determine critical speed based on resonant frequency and control vibrations in system.

Theory:The critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, lead screw, or gear. As the speed of rotation approaches the object's natural frequency, the object begins to resonate, which dramatically increases system vibration. The resulting resonance occurs regardless of orientation. When the rotational speed is equal to the numerical value of the natural vibration, then that speed is referred to as critical speed.

Setup:

Solid model the setup.

Define simulation as frequency analysis.

Material Properties (Alloy Steel)

Elastic Modulus 210000 N/mm^2

Poisson's Ratio 0.28

Shear Modulus 79000 N/mm^2

Mass Density 7700 kg/m^3

Tensile Strength 723.8256 N/mm^2

Yield Strength 620.422 N/mm^2

Thermal Expansion Coefficient 1.3e-05/K

Thermal Conductivity 50 W/(m·K)

Specific Heat 460 J/(kg·K)

Apply the fixture ie bearing fixture at step end.

Mesh the model.

Define no. of modes for analysis.

Run the simualation

Results:

Resonant Frequency.

Study name:Frequency 1
Mode No.	Frequency(Rad/sec)	Frequency(Hertz)	Period(Seconds)
1	0	0	1.00E+32
2	564.44	89.833	0.011132
3	564.44	89.834	0.011132
4	2588.5	411.98	0.0024273
5	2588.6	411.99	0.0024272