Frequency Analysis of a rotating shaft

AIM: To sudy the shapes of the mode and the Critical Frequency of the rotating shaft

THEORETCAL BACKGROUND:

Natural Frequencies:

The frequency with which body oscillates when there is no repeated or continuous load acting on it. The motion pattern of a system oscillating at its natural frequency is called the normal mode.

Resonance:

Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamical system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.

Modes:

They are the properties of a particular structure that depends on material properties and the boundary condition applied to the structure. The modes are defined by resonant frequency, modes shapes and modal damping.

PROCEDURE:

1] Create a sketch of rotating shaft of desired dimensions and revolve it 360 degrees to obtain the solid model.

2] Select a new study and choose frequency analysis.

3] Select "Alloy Steel" as the material

4] Apply the bearing fixtures and mesh the geometry

5] Run the study to get different shapes and resonant frequency.

Sketch:

Model:

Material properties

The properties of "Alloy Steel" are as shown below

Fixtures and Meshing

Mode 1

The maximum and minimum amplitudes are 1.972e-01 and 5.44e-18 respectively

Mode 2

The maximum and minimum amplitudes are 1.309e-01 and 4.79e-04

Mode 3

The maximum and minimum amplitudes are 1.309e-01 and 5.928e-04

Mode 4

The maximum and minimum amplitudes are 2.763e-01 and 1.232e-04

Mode 5

The maximum and minimum amplitudes are 2.763e-01 and 1.109e-04

TABULATION:

The resonant frequencies for different modes are tabulated below

Observation:

The shaft can be operated apart from the above resonant frequencies. Whenever the natural frequencies becomes equal to the frequencies of the applied force the shaft vibrates with high vibration amplitude whicn ultimately fails the system.