Frequency Analysis of a rotating shaft

Aim:

To perform frequency analysis on the shaft with disc mounted on it and find out the Resonant frequencies.

Introduction:
There is some technical knowledge to be known in this project which is given below:

Frequency:
It is the number of occurrences of a repeating event per unit of time.

Natural frequency:
It is the frequency at which a system tends to oscillate in the absence of any driving or damping force.They usually depend on the way mass and stiffness are distributed within the structure.

Resonance:
Body when acted upon by loads can vibrate at frequencies.When these bodies vibrate at natural frequencies,it can undergo large deformations which are often destructive.This is known as Resonance.

Resonant Frequency:
It is the frequency that is capable of exciting a resonance maximum in a given body or system.
The identification of these resonant frequencies for any object is very important in order to avoid excessive vibration or even failure.

PROCEDURE:

1. Model Design:
Includes making the cad model of the system that is to be analyzed and assigning materials to the components.

2. Applying Boundary Conditions:
Includes setting up the fixed geometry, reactions and external loads.

3. Meshing:
The type, size and various other mesh parameters are setup to get best result for simulation.

4. Simulation/Solver Analysis:
The solver is run giving out the results for Von mises stresses, strains,displacements & Amplitudes at all the nodes and identifying the minimum and maximum values of those to determine the critical regions.

Case Study:

1. Model Design:

The following are the details of the model:
Diameter of Shaft : 30 mm
Diameter of Bearing : 20 mm
Diameter of Disc : 100 mm
Total Length of Shaft : 400 mm
Thickness of Disc : 15 mm
Stepped Thickness : 15 mm from both sides

Fig 1: Top View Of the model

Fig 2: Side View of the model

Material Selection:

The material of the shaft and disc is chosen to be Alloy steel, the properties of which are given in the below table.

Name:	Alloy Steel
Model type:	Linear Elastic Isotropic
Default failure criterion:	Max von Mises Stress
Yield strength:	620422000 N/m^2
Tensile strength:	723825600 N/m^2
Mass density:	7700 kg/m^3
Elastic modulus:	2.1e+11 N/m^2
Poisson's ratio:	0.28
Shear modulus	7.9e+10 N/m^2
Thermal expansion coefficient:	1.3e-05 /Kelvin

Fig 3: Alloy Steel applied to the model

2. Boundary Condition:

Fig 4: Fixed constraint applied to both stepped face ends of shaft

3. Meshing:

Fig 5: Default mesh applied to the model

The parameters of meshing are given in the table below:

Study name	Rotating Disc (-Default-)
Mesh type	Solid Mesh
Mesher Used:	Standard mesh
Automatic Transition:	Off
Include Mesh Auto Loops:	Off
Jacobian points for High quality mesh	16 Points
Element Size	7.23341 mm
Tolerance	0.36167 mm
Mesh quality	High
Total nodes	10902
Total elements	6512
Maximum Aspect Ratio	4.576
Percentage of elements with Aspect Ratio < 3	99.8
Percentage of elementswith Aspect Ratio > 10	0
% of distorted elements(Jacobian)	0
Number of distorted elements	0
Time to complete mesh(hh:mm:ss)	00:00:02

4. Analysis Result:

There are 5 Mode Shape results which are shown below:

i. Mode Shape 1:

Fig 6: Frequency Analysis-Mode Shape 1


ii. Mode Shape 2:

Fig 7: Frequency Analysis-Mode Shape 2

iii. Mode Shape 3:

Fig 8: Frequency Analysis-Mode Shape 3

iv. Mode Shape 4:

Fig 9: Frequency Analysis-Mode Shape 4

v. Mode Shape 5:


Fig 10: Frequency Analysis-Mode Shape 5

Observation:

The following table shows all the resonant frequencies from the analysis:

Mode No.	Frequency(Rad/sec)	Frequency(Hertz)	Period(Seconds)
1	4,038.2	642.7	0.0015559
2	4,050.8	644.71	0.0015511
3	7,563.5	1,203.8	0.00083072
4	13,348	2,124.3	0.00047074
5	13,376	2,128.9	0.00046974

Conclusion:

The shaft must not be rotated at resonant frequencies of 642.7 Hz; 644.71 Hz; 1,203.8 Hz; 2,124.3 Hz; 2,128.9 Hz.As operating at these frequencies may cause resonance thus, resulting in excessive vibration or even failure of the model.