Frequency Analysis of a rotating shaft

AIM : To find out the critical frequencies of a rotating shaft in Solidworks.

OBJECTIVES :

1. To create 3D model of a rotating shaft.
2. To perform frequency analysis on the rotating shaft and find out the critical frequencies.

INTRODUCTION:

Resonance:

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 the resonant frequency of another system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.

Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system. Small periodic forces that are near the intrinsic resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy.

Mode shapes:

mode shape is the shape of the beam at different natural frequencies.

The mode shapes of a system are obtained when you calculate its response due to initial conditions only. If you get a guitar string, for example, at rest and give it initial conditions (then release the string), it will vibrate in a specific way that depends on its eigenfrequencies, and each of them is related to a specific mode shape.

Hence, for the homogeneous response (initial conditions only), you can say that the response of your string is the sum of the response of its mode shapes, each one vibrating at its own eigenfrequency. You can think of them as standard movements that your system may perform.

Eg: Beam

PROCEDURE :

• Geometry Modelling of Rotating Shaft -
• At first, a shaft and a disc were sketched and then assembled to form a rotating shaft assembly. For sketching shaft, there can be multiple way, i.e., either circles can be drawn and extruded or a line of desired length is sketched and revolved around it's axis to form a shaft. Here latter one was used.
• The shaft was sketched according to following dimensions, and was revolved around `1000mm` line as cental axis.
• Shaft -

• Disc -

• Assembly of Rotating Disc -
• For assembly of these component, they were inserted in the assembly window and mated accordingly.

• Simulation Setup -
• For frequency analysis, Solidworks Simulation was setup. Here frequency analysis was carried out for two different materials namely 'Alloy Steel (SS)' and 'Aluminium Alloy 6061-T6 (SS)' respectively. Bearing fixtures were provided at the two stepped faces of the shaft at the two ends. The properties of 'Alloy Steel (SS)' and 'Aluminium Alloy 6061-T6 (SS)' are as follows:

• Meshing were done on the part bodies for simulation. The global mesh size was set to `7.5mm` and the simulation was made to run. The properties of meshing are,

• The study settings were kept as default setting. The number of mode shapes were kept as `5` and rest of settings can be viewed here,

RESULT :

• Case 1. : Frequency Analysis for 'Alloy Steel (SS)' ,
• The study was carried out for `5` mode shapes, and amplitudes for each study was observed.
• Mode Shape 1 :

• Mode Shape 2 :

• Mode Shape 3 :

• Mode Shape 4 :

• Mode Shape 5 :

• List of Resonant frequencies :

• Plot for Frequency versus Mode number :

• Case 2. : Frequency Analysis for 'Aluminium Alloy 6061-T6 (SS)' ,
• The study was carried out for `5` mode shapes, and amplitudes for each study was observed.
• Mode Shape 1 :

• Mode Shape 2 :

• Mode Shape 3 :

• Mode Shape 4 :

• Mode Shape 5 :

• List of Resonant frequencies :

• Plot for Frequency versus Mode number :

• Comparison between both materials for different modes-

Conclusion:

1. From the result obtained for 'Alloy Steel (SS)' , it can be concluded that the above system has resonant frequencies at `0`Hz, `101.33`Hz, `480.78`Hz . If the above system is made to run at or near the resonance frequencies, Whirling of shafts occurs due to rotational imbalance of a shaft, even in the absence of external loads, which causes resonance to occur at certain speeds, known as critical speeds.
2. Similarly from the result obtained for 'Aluminium Alloy 6061-T6 (SS)', it can be concluded that the above system has resonant frequencies at `0.0676`Hz , `98.71`Hz , `465.51`Hz. If the above system is made to run at or near the resonance frequencies, there is a chance of failure of the structure due to Whirling of shaft. The system will work fine for all other frequencies.