Frequency Analysis of a rotating shaft
AIM
To find out the critical frequencies of a rotating shaft in Solidworks.
THEORY
Natural frequency
In general, frequency is number of times an cycles occurs per unit time. Technically, in vibrations, it is a frequency at which a system tends to oscillate about their mean position 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 an external force is applied and oscillating system is driven at the frequency at which the amplitude of its motion is greatest i.e if the external applied load frequency matches with natural frequency of the material, this frequency is called resonant frequency.Every material has its own natural frequencies, the materials naturally tends to vibrate if it is subjected to a disturbance. Modes and Modes Shapes are obtained when it shaft is rotating at high speeds, i.e deformed shape of the material at natural frequency of vibration is termed its normal mode of vibration.
Resonance
Resonance is the phenomenon of increased amplitude where the external applied load frequency matches with natural frequency of the material . At resonance, the ampliotude of vibration is very high and the material tends to fail at this frequency.
Objective
1. To create a model of a rotating shaft.
2. Run a frequency analysis on the shaft and get the mode shapes.
3. Find the resonance frequencies
FREQUENCY ANALYSIS OF ROTATING SHAFT
Procedure
1. Create a MODEL with appropriate dimensions.
2. Run a Frequency analysis.
3. Apply the matertal as Alloy Steel
4. Apply the fixtures at both ends.
5. Generate a mesh with appropriate parameters.
6. Run the study.
7. Compare the mode shape and get resonance frequencies.
Analysis Setup
Model
SOLIDWORKS model is created with the help of below sketch using Revolute tool.
FINAL 3D MODEL
The below model is obtained after revolving about its centre axis
MATERIAL
Alloy steel is selected as a material and the properties of it are listed below
FIXTURES
Since the bearing are fixed at the stepped shaft, the fixtures are applied at the stepped faces
MESH GENERATION
size=3mm
tolerance=0.25mm
USE OF SOLVERS AND STUDY PROPERTIES
RESULTS
The below result figures represents the showcase of
1. Frequency of oscillation
2. Range of amplitudes
3. Deformation Scales
MODE SHAPE 1
MODE SHAPE 2
MODE SHAPE 3
MODE SHAPE 4
MODE SHAPE 5
The below table represents the list of frequencies and corresponding Time Period of oscillation for particulr mode shapes
| MODE NO | Resonant Frequency (in Hz) | Time Period (in seconds) |
| 1 | 541.56 | 0.001865174 |
| 2 | 543.72 | 0.001839181 |
| 3 | 1029.2 | 0.000976284 |
| 4 | 1772.6 | 0.00056414 |
| 5 | 1776.7 | 0.000562841 |
Conclusion
1.The resonant frequencies obtained are 541.56, 543.72, 1029.2, 1772.6, 1776.7
2. In order to avoid failures we must rotate the shaft in such a way thet the frequency of oscillation should not be near to the resonant frequency, it should be either way less or way more than resonant frequency.
3. But when the frequency reaches above-mentioned values, the system will be in resonance and high amplitude are observerd thereby the system fails.
4. Different materials have different natural frequency we must select the material in such a way that it should not fail due to resonance during operation.
5. The selection of material plays an important role for the material not to fail due to resonance
6. In Bridges, the most suitable material should be used, so that due frequency of oscillation as per the loading conditions the resonant frequency should not be reached in order to in the safer side