Frequency Analysis of a rotating shaft

AIM:

• To find out the critical or resonant frequencies of a rotating shaft in Solidworks.
• Design the model using solidworks based on any desired dimensions.

INTRODUCTION:

Resonant frequency is the oscillation of a system at its natural or unforced resonance. Resonance occurs when a system is able to store and easily transfer energy between different storage modes, such as Kinetic energy or Potential energy as you would nd with a simple pendulum.

Resonance - "The increase in amplitude of oscillation of an electric or mechanical system exposed to a periodic force whose frequency is equal or very close to
the natural undamped frequency of the system."

Mode:-

The mode is a statistical term that refers to the most frequently occurring number found in a set of numbers. The mode is found by collecting and organizing, data in order to count the frequency of each result. The result with the highest count of occurrences is the mode of the set, also referred to as the modal value.

Mode Shapes The deformed shape of the structure at a speci c natural frequency of vibration is termed its normal mode of vibration. Some other terms used to describe the normal mode are mode shape, characteristic shape, and fundamental shape. Each mode shape is associated with a speci c natural frequency.

Modes are inherent properties of a structure, and are determined by the material properties (mass, damping, and stiffness), and boundary conditions of the structure. Each mode is de ned by a natural (modal or resonant) frequency, modal damping, and a mode shape (i.e. the so-called “modal parameters”).

Procedure:

Creating a geomettry

Property Values 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 Coe cient - 1.3e-05 /K
Thermal Conductivity - 50 W/(m·K)
Speci c Heat - 460 J/(kg·K)

Mass Properties:

Density = 0.01 grams per cubic millimeter
Mass = 4160.73 grams
Volume = 540353.94 cubic millimeters
Surface area = 62831.85 square millimeters
For doing a frequency analysis on this rotational shaft, we must the input bearing xtues on both the ends of the shaft.

Creating a basic mesh

RESULT:

The results we get would be 5 different modes each measured using different amplitude or natural frequencies.

Mode 1:

Mode 2

Mode 3

Mode 4

Mode 5

The different resonant or critical frequencies obtained are as follows:

Study name:Frequency 1
Mode No.	Frequency(Rad/sec)	Frequency(Hertz)	Period(Seconds)
1	0	0	1.00E+32
2	3262.9	519.31	0.0019256
3	3264.1	519.49	0.001925
4	14883	2368.7	0.00042217
5	14885	2369.1	0.00042211

CONCLUSION:

From this analysis it is clear the the frequency varies fo different mode shapes and its amplitude is directly propotional to the frequency inducing the resonance.