Frequency Analysis of a rotating shaft

Aim: Frequency analysis of rotating Shaft.

Introduction:

The 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 the 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.

Design and Modelling:

Meshing:

Element Size

6.271 mm

Material Properties:

Name:	Alloy Steel
Model type:	Linear Elastic Isotropic
Default failure criterion:	Max von Mises Stress
Yield strength:	6.20422e+008 N/m^2
Tensile strength:	7.23826e+008 N/m^2
Mass density:	7700 kg/m^3
Elastic modulus:	2.1e+011 N/m^2
Poisson's ratio:	0.28
Thermal expansion coefficient:	1.3e-005 /Kelvin

Boundary Conditions:

Fixtures: 2 Bearing Supports

Angular Velocity:	120 rad/s
Angular Acceleration:	2 rad/s^2

Results:

Mode 1:

Mode 2:

Mode 3:

Mode 4:

Mode 5:

Mode List:

Conclusion:

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