Frequency Analysis of a rotating shaft

AIM: To find out the critical frequencies of a rotating shaft in Solidworks i.e. to perform frequency analysis on the shaft.

Theory:
The resonance is 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.
A mode of vibration is characterized by a modal frequency and a mode shape. It is numbered according to the number of half waves in the vibration.

Implementation:
Firstly the shaft model is made using the solidworks where the dimensions are taken on a random basis and the modelled component is used for the frequency analysis where the ends are fixed as bearings. Then the meshed component is analyzed on default setting to obtain 5 modes of frequency possible.

Modelling:
Here multiple sketches are made and extruded and the finally mirrored to ge the end modelled component for the frequency analysis.

This is the modelled component for the frequency analysis where the material is chosen to be as Alloy Steel.

Then the frequency analysis is conducted on the modelled component. Here the mesh is chosen to be as finer as possible in order to get accurate results.

The fixtures are selected to be the bearing fixtures at the 2 ends and then the simulation is ran by default with 5 modes to appear. Then the followinf are the results obtained for different modes. Each mode refers to oscillaton of motion about different axis or in different planes.

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

List of the resonant frequencies is as follows

The following are the animated files

Mode 1 Mode 2

Mode 3 Mode 4

Mode 5

These are the results obtained in different planes and about diffferent axes as per the resonance frequencies.

Conclusion:

From this analysis it is clear the the frequency varies for different mode shapes and its amplitude is directly propotional to the frequency. It can also be concluded that the shaft would fail at the above obtained resonance frequency where the load would be max at corresponding nodes.