Frequency Analysis of a rotating shaft

AIM: To find out the critical or resonant frequencies of a rotating shaft in Solidworks.

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.

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.

Material: 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)

• For doing a frequency analysis on this rotational shaft apply bearing fixtures on both the ends of the shaft.

• Standard mesh used

RESULT:

MODE 1: In radial direction

MODE 2: In Y direction

MODE 3: In Z direction

MODE 4: In Y direction(3 nodes)

MODE 5: In Z direction(3 nodes)

The different resonant or critical frequencies obtained are as follows:

CONCLUSION:

From this analysis it is clear the the frequency varies for different mode shapes and its amplitude is directly propotional to the frequency inducing the resonance. The frequencies in Y and Z directions are almost identical; for same number of nodes since the structure is identical for both cases