Frequency Analysis of a rotating shaft

Objective-

In this study, we will do the frequency analysis on the shaft contaning disc. There is most important to find the natural frequency because if the rotating shaft frequency matched with the natural frequency then a large amplitutde displacement will occured and shaft will distorted. So we will find the natural(critical) frequency and we will also find the different mode shapes of shaft and list the resonant frequencies.

Introduction-

Natural frequency- the frequency at which a system oscillates when not subjected to a continuous or repeated external force.

Forced vibrations and resonance- forced vibrations occur when the object is forced to vibrate at a particular frequency by a periodic input of force. If an object is being forced to vibrate at its natural frequency, resonance will occur and large amplitude vibrations can be observed.

Mode shapes of vibration- a mode shape is a specific pattern of vibration executed by a mechanical system at a specific frequency. Different mode shapes will be associated with different frequencies. The structure tends to vibrate with a particular \'mode shape\' at each frequency.

Natural Frequencies and Modal shapes depend on-

-Geometry
-Material Properties and Mass
-Support conditions(fixtures)
-In-Plane loads

Procedure-

• Create a 2-D sketch with appropriate dimensions.
• Using Revolve tool, create a 360 degree revolve of the sketch to make a 3-D model.
• Now click on the Simulation then click on New Study then select the frequency analysis.
• Now right click on Part then click on Apply material and choose the Alloy Steel material.

Property of Alloy Steel-

Elastic Modulus- 2.1e+11 N/m^2
Poisson\'s Ratio- 0.28
Shear Modulus- 7.9e+10 N/m^2
Mass Density- 7700 kg/m^3
Tensile Strength- 723825600 N/m^2
Yield Strength- 620422000 N/m^2
Thermal Expansion Coefficient- 1.3e-05 /K
Thermal Conductivity- 50 W/(m·K)
Specific Heat- 460 J/(kg·K)

Mass Properties-

Mass = 93.18 kg
Volume = 0.01 m^3
Surface Area = 0.67 m^2

• Then right click on Fixtures then click on Bearing Fixture
• After bearing fixture, select the on the stepped face of the rod at the two ends.
• Now create a standard mesh of the model.

Mesh Details-

Mesh type- Solid Mesh
Element size- 16.0734 mm
Mesh quality- High
Total nodes- 33067
Total elements- 20580

• Then click on Mesh and Run.

Results-

Mode 1-

Mode 2-

Mode 3-

Mode 4-

Mode 5-

Frequency at each mode-