FREQUENCY ANALYSIS OF A ROTATING SHAFT USING FINITE ELEMENT ANALYSIS (using SOLIDWORKS)

AIM:

To find the critical frequencies of a rotating shaft in SOLIDWORKS

OBJECTIVES:

1. To understand the working of the rotating shaft alongwith the flywheel on it
2. To find out resonance frequencies for different modal positions of the rotating shaft
3. To accomplish the aforementioned using SOLIDWORKS

INTRODUCTION:

Resonant vibration in mechanical structures such as pumps, turbines and motors occurs when a natural frequency is at or close to a forcing frequency such as rotor speed. When present, this condition can cause severe vibration levels by amplifying small vibratory forces from machine operation. Such problems often develop after a speed change has been implemented, as with retrofitting a machine with an adjustable-speed drive (ASD) or operating a 50 Hz motor on 60 Hz power. The solution frequently depends on the ability to distinguish between structural resonance and a rotor critical speed.

Structural resonance: Structural resonance refers to excessive vibrations of non-rotating components, usually machine parts or supporting structures. Due to the complexity of these components, it is the more common resonant condition and usually occurs at or near the rotating speed of the machine. Even slight vibratory forces from residual unbalance and misalignment effects of the machine can excite the resonant base structure, resulting in severe vibration.

Rotor critical speed: A rotor critical speed exists when a machine’s rotating element is the resonant component and its speed matches the natural frequency of the rotor.

PROCEDURE OF COMPLETION:

• First, the rotating shaft was made with the following dimensions using rotating shaft method:

• Then, the flywheel is designed as per the following dimensions:

• Then, both the parts were assembled such as the shaft and the flywheel rotates as follows:

• Next, the simulation is setup for the frequency analysis.
• First, material is applied i.e. Alloy steel. The properties are as follows:

• Next, bearing fixture is added to the ends of the rotating shaft as follows:

• Next, a finer mesh of `3mm` mesh element was used for better accurate results as follows:

• The simulation is perfectly setup and run for the frequency analysis for `5` different modes.

OBSERVATIONS:

• At first mode, the amplitude of the vibration is as follows:

• At second mode, the amplitude of the vibration is as follows:

The simulation is as follows:

https://youtu.be/0Q5CSGwUv7k

• At third mode, the amplitude of vibration is as follows:

The simulation is as follows:

https://youtu.be/ufuJmCH-BHw

• At fourth mode, the amplitude of the vibration is as follows:

The simulation is as follows:

https://youtu.be/LLiS_SAbbMY

• At fifth mode, the amplitude of vibration is as follows:

The simulation is as follows:

https://youtu.be/0x2WtkuLbP8

CONCLUSIONS:

The comparative study of the first four modes is as follows:

The comparative study of the last 4 modes are as follows:

The resonant frequencies of each of the modal number is as follows:

MODE NUMBER	FREQUENCY (rad/s)	FREQUENCY (hz)	PERIOD (seconds)
`1`.	`0`	`0`	`1.00E+32`
`2`.	`1726.1`	`274.72`	`0.00364`
`3`.	`1726.2`	`274.73`	`0.00364`
`4`.	`7095.8`	`1129.3`	`0.000885`
`5`.	`7095.9`	`1129.4`	`0.000885`

So, we can conclude that the rotating shaft cannot be rotated at the above mentioned frequencies as it will break down or rupture. The first mode is uncharacteristically very low compared to the other modal cases.