Frequency Analysis of a rotating shaft

Objectives

• To find out the resonance frequencies of a rotating shaft in Solidworks.
• Design the model in solidworks according to any desired dimension.
• Model it in Solidworks according to the image shown below.
• Find out 5 mode shapes and list the resonant frequencies

Theory

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

Natural frequencies are those frequencies with which a body oscillates when there is no repeated or continous load acting on it , when a body vibrate at the natural frequencies it can undergo large deformation which are often destructive

Mode Shapes : - A material vibrating at natural frequency has a tendency to displace in any direction this tendency is studied by looking at the mode shape at the vibrating frequency , The displacement produced at the natural frequency of motion are refer to as mode shape this mode shape depends on the material of the body and the different load applied on the body

Procedure

1. Create a sketch in front plane as shown below
   
2. Exit the sketch and revolve it around the construction line to create desired model
3. Go to simulation new study and select frequency simulation
4. Right click on part name and apply material as alloy steel
5. Right click on fixture select bearing fixture and apply it on both the stepped face of the rod at the two end .
6. Go to mesh and create a mesh of size 2mm
7. Run the study

Results

Mode shape 1

Vibration in radial direction

Mode shape 2

vibration in z direction

Mode shape 3

vibration in y direction

Mode shape 4

Vibration in x-z plane

Mode shape 5

Vibration in x-y plane

Resonant frequencies

• The resonant frequency is lowest for mode shape 1 in which the rod is vibrating in radial direction
• The resonant frequency for mode shape 2 ,3 and 4,5 is approximately equal due to the symmetry of rod along central axis
• The resonant frequency for mode 4 and 5 is highest in which there is an additional node at middle and rod is vibrating along a plane.