Frequency Analysis of a rotating shaft using SOLIDWORKS

AIM -

Frequency analysis of a rotating shaft.

OBJECTIVE - Find out the critical frequencies of a rotating shaft .

Find out 5 mode shapes and list the resonant frequencies.

INTRODUCTION -

A shaft is defined as a rotating member, usually circular, which is used to transmit power. Although normal and shear stresses due to torsion and bending are the usual design case, axial loading may also be present and contribute to both normal and shear stresses. Frequency is an absolute measure of the flex of a shaft. It is defined as how many times per minute a shaft oscillates. The units of frequency measurement are known as cycles per minute, or cpm. A shaft with a higher frequency is stiffer than one with a lower frequency. By using frequency as a method of comparing two different shafts, it is obvious which shaft is stiffer and by how much. Typically there will be 10 cycles between shaft flexes.

VIBRATION - Vibration, periodic back-and-forth motion of the particles of an elastic body or medium, commonly resulting when almost any physical system is displaced from its equilibrium condition and allowed to respond to the forces that tend to restore equilibrium.

RESONANCE - Resonance describes 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. 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.

3D MODEL OF SHAFT -

Above model is drawn in solidworks part modelling tool. First by selecting a front plane simple sketch is drawn as shown in right hand side figure . Then by using the revolve command the shaft is rotated at 360 degree by selecting the horizontal axis as reference . After the part modelling was completed the model was imported to analysis tool for the frequency analysis of the shaft.

MESHING AND PRE-PROCESSING (Material Selection) OF THE SHAFT BEFORE FREQUENCY ANALYSIS -

Here, the selected material for the frequency analysis is Alloy Steel and on the right side we see the meshing of the shaft . The meshed shaft is not too coarse and not to fine.

If we look at the shaft of meshed one we can find that both end part of shaft are applied with bearing fixtures .

DIAGRAMS OF THE FREQUENCIES AFTER PERFORMING THE ANALYSIS -

After the meshing part is done we move for the results here we have five different cases of frequency amplitude where we can find the value of frequency in Hz and the deformation scale of the shaft.

Above is the first frequency that we found and the value for the frequency is 0.0009871 Hz .

Above is the second frequency that we found and the value for the frequency is 0.03458 Hz.

Above is the third frequency that we found and the value for the frequency is 0.0707 Hz.

Above is the fourth frequency that we found and the value for the frequency is 1074.4 Hz .

Above is the fifth frequency that we found and the value for the frequency is 1074.8 Hz.

GRAPH OF NUMBER OF MODES VS FREQUENCY -

Above graph gives us information related to mode number vs frequency. As we can see that as mode number gets increased the frequency also get increased .

List of resonant frequencies -

Mode No.	Frequency(Rad/sec)	Frequency(Hertz)	Period(Seconds)
1	0.0062024	0.00098715	1013
2	0.21707	0.034548	28.945
3	0.44459	0.070758	14.133
4	6750.6	1074.4	0.000931
5	6753	1074.8	0.00093

CONCLUSION -

From the above study we conclude that as the mode increases the frequency of the shaft also increases and thus we see the changes in periods . Now if try to operate the shaft above the mentioned frequency in chart the shaft will get damaged so its better to operate the shaft below the above mentioned frequencies.