Frequency Analysis of a rotating shaft - SolidWorks FEA

 AIM:

The study aims to find the mode shapes and resonant frequencies of a rotating shaft.

OBJECTIVE:

1. To create a model of a rotating shaft.
2. Run a frequency analysis on the shaft and get the mode shapes.
3. Compare the mode shapes and get resonance frequencies for all the modes. 

THEORY:

Frequency

Frequency, in a general sense, is defined as the number of times an event occurs per unit time. However, a more scientific definition is The number of times a point on a wave passes through a fixed reference point in one second is known as frequency. The formula for the frequency is shown below.

; where f = frequency ,and T = Time

Natural Frequency

The Natural Frequencies of a structure are the frequencies at which the structure naturally tends to vibrate if it is subjected to a disturbance. This vibration will cause the structure harm and sometimes the structure might even fail.

Modes and Mode Shapes

The deformed shape of the structure at a specific natural frequency of vibration is termed its normal mode of vibration.

Resonance

In physics, 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. At resonance, the vibration amplitudes are so high that there is a chance that the system might fail.

PROCEDURE:

The procedure used for the analysis is as follows

1. Create a sketch for the rotating shaft and revolve it 360 degrees.
2. Start a new study. Under it, select Frequency analysis and name it Frequency 1.
3. Apply the Alloy Steel Material
4. Apply the fixtures.
5. Generate a mesh with appropriate parameters.
6. Run the study.
7. Compare the mode shape and get resonance frequencies.

MODEL:

The model was created in two steps using SOLIDWORKS 2018 modeling software which are given below

1. First of all, a sketch with appropriate dimensions was made as shown in figure 1.
2. In the second step, the model was completed as shown in figure 2. Figure 3 shows the meshed shaft.

Sketch of the shaft.

Model of the shaft

Meshed Shaft

MATERIAL SELECTION

The material assigned to the model for this simulation or analysis was Alloy steel. The properties of alloy steel are shown in figure 4.

Properties of Alloy steel.

FIXTURE:

The model was given two bearing fixtures or support at the stepped faces to encompass the bearing to be fitted in that place in practice. Figure 5. Shows the bearing support fixtures.

Fixtures in the model.

SETTING

The study settings were kept as the default settings. They are shown in figure 8.

The number of frequencies and modes shapes is kept at 5. The Bonding option is selected as automatic. The solver used by the SOLIDWORKS simulation wizard is FFEPlus.

FStudy Settings.

RESULTS

There were in total 5 mode shapes.

Mode shape 1:

The maximum and minimum amplitudes are 7.55e-01 and 2.344e-09.

Frequency mode shape 1.

Mode shape 2:

The mode shape plot obtained is shown in figure 10. The maximum and minimum amplitudes are 4.379e-01 and 3.679e-04.

Frequency mode shape 2.

Mode shape 3:

The mode shape plot obtained is shown in figure 11. The maximum and minimum amplitudes are 4.378e-01 and 6.524e-05.

Frequency mode shape 3.

Mode shape 4:

The mode shape plot obtained is shown in figure 12.  The maximum and minimum amplitudes are 6.834e-01 and 7.938e-05.

Frequency mode shape 4.

Mode shape 5:

The mode shape plot obtained is shown in figure 13. The maximum and minimum amplitudes are 6.834e-01 and 6.580e-04.

Frequency mode shape 5.

RESONANCE FREQUENCY:

The resonance frequencies for different mode shapes are shown in table.

CONCLUSION:

The resonance frequencies obtained are 0.028136, 149.27, 149.27, 552.18, and 552.23. Apart from these frequencies, the shaft can be operated without any problem. But whenever the frequency is equal to any of the above-mentioned ones, the system will go in resonance and high vibrations amplitude are obtained. This fails in the system. This can easily be prevented by providing Dampers in the system. The material also plays an important role in the determination of the resonant frequency. If a more suitable material is used, the resonant frequency can be increased such that it can never be reached under working conditions.