Frequency Analysis of a rotating shaft

Aim:- To study the mode shapes and the critical frequencies of the shaft.

Theory:-

Natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all parts of the system move sinusoidally with that same frequency).

If the oscillating system is driven by an external force at the frequency close to a natural frequency of the system, this frequency is called resonant frequency. Resonance describes the phenomena of amplification that occurs when the frequency of a periodically applied force is in harmonic proportion 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 which can fail the components.

Thus to design a system operating at a frequency other than the natural frequencies, the natural frequency of the system is necessary. This project involves the study of the mode shapes and determining the critical frequencies of the shaft.

Steps of FEA simulation:-

1. Create the 3D model of shaft and apply material(alloy steel).

2. Create the mesh and apply boundary conditions (bearing surfaces at ends and centrifugal force to shaft).

3. Run the frequency analysis study and find out 5 mode shapes and list the resonant frequencies.

Results:-

Mode shape: 1

Mode shape: 2

Mode shape: 3

Mode shape: 4

Mode shape: 5

Observation:-

We can see the frequency at different modes listed below.

From the above frequency analysis it is understood that the shaft should not be operated in the given frequencies of 15.907Hz, 140.12Hz, 140.12Hz, 700.77Hz and 700.79Hz and would result in resonance phenomenon and failure of the shaft.