Frequency Analysis of a rotating shaft
AIM: To simulate a rotating shaft for frequency analysis to find out the critical frequency.
THEORY: Every object has a natural frequency of vibration given by under root of stiffness to the mass ration of the body.
As we know when a body vibrates, it senses a repeated shift from its mean value which is called Amplitude. If the amplitude remains in the permissible limits no harm is done to the body. In our case, we are dealing with a rotating shaft. As the shaft rotates it will experience vibration due to uneven material distribution.
Let us understand the Resonance phenomenon. When induced vibration's frequency touches the natural frequency of the body the very phenomenon is called Resonance. It is a highly undesirable point as the amplitude shoots to infinity which will break the body. In our case, it is called whirling of the shaft.
The expression for Amplitude is given by:
`A= e/((ω_n/ω)^2-1)`
where,
`A = Amplitude`
`ω=Induced__Frequency`
`ω_n=Natural__Frequency`
`e=Ecentricity`
We can clearly see that if induces frequency will be equal to the natural frequency, the denominator will become zero, and Amplitude shoots to infinity.
General Figure for resonance is given below
Note:
A suitable shaft with a circular disc in the middle is taken as our part, the figure is given below for dimensions
Study Setup: Frequency analysis with bearing fixture on the stepped faces of the shaft.
Let us take a look at the mesh and run our study
We have selected the 5 Frequency mode and FFE Plus iterative solver
Let us see the results
List of resonant frequencies:
Frequency Vs Mode no.
From the results above we can find the critical frequencies at different modes.
While designing the operating conditions we need to take care that the induced frequency must not reach the critical points.
In case the purpose can only be completed by working above the natural frequency, we must consider the duration of the frequencies from the resonance frequency table and pass our system past the natural frequency in less amount of time than given In the table.
For Example, TURBINE shafts rotate at 3000 RPM which is above the natural frequency so we use servomotors to pass the natural frequency time in nanoseconds to avoid Whirling.