Frequency Analysis of a rotating shaft using Solidworks

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 find 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 specific 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 specific 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 defined by a natural (modal or resonant) frequency, modal damping, and a mode shape (i.e. the so-called “modal parameters”).

PROCEDURE:

• Create a 2-D Sketch with the basic dimensions of the sketch and then using mirror function complete the 2-D cross sectional sketch.

• Using Revolve Tool, create a 360deg revolve of the sketch making it into a 3-D part model.

3-D Part Model : Rotating Shaft

• Now assign a specific material to the rotating shaft, i.e Alloy Steel

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 Coefficient - 1.3e-05 /K
Thermal Conductivity - 50 W/(m·K)
Specific 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 fixtues on both the ends of the shaft.

• Now create a standard mesh of the model. (7mm mesh used)

Mesh Details:

Mesh Type- Solid Mesh

Element Size- 7mm

Total Nodes- 17348

Total Elements- 10927

Now Run the Frequency analysis

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:

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.