Frequency Analysis of a Rotating Shaft using Finite Element Analysis

AIM

To perform Frequency Analysis on a rotating shaft.

OBJECTIVES

• To create the model of the shaft with the given dimensions in SolidWorks.
• To simulate the Frequency Analysis for the rotating shaft using given conditions.
• To find out the 5 mode shapes and list the resonant frequencies.

INTRODUCTION

Finite element analysis (FEA) is the process of simulating the behaviour of a part or assembly under given conditions so that it can be assessed using the finite element method (FEM).

The simulations used in FEA are created using a mesh of millions of smaller elements that combine to create the shape of the structure that is being assessed. Each of these small elements is subjected to calculations, with these mesh refinements combining to produce the final result of the whole structure.These approximate calculations are usually polynomial, with interpolations occurring across the small elements, meaning that values can be determined at some but not all points. The points where the values can be determined are called nodal points and can usually be found at the boundary of the element.

Frequency Analysis

A shaft is a rotating machine element, usually circular in cross-section,which is used to transmit power from one part to another, or from a machine which produces power to a machine which absorbs power.

Resonance is a state of a system in which an abnormally large vibration is produced in response to an external stimulus, occurring when the frequency of the stimulus is the same, or nearly the same, as the natural vibration frequency of the system. Typically a structure will have many resonant frequencies. When a structure is in resonance, a small force can produce a large vibration.

THEORY

Resonance in a shaft can occur when the natural frequency of the shaft matches with the frequency of the external vibrating force.The greater the mass or density of the material the lower the fundamental frequency of vibration.

Some important terminologies to be understood are-

1. Resonance- A phenomenon in which an external force or a vibrating system forces another system around it to vibrate with greater amplitude at a specified frequency of operation.
2. Resonant frequency- It is the natural frequency of vibration determined by the physical parameters of the vibrating object.
3. Modes are inherent properties of a structure that are determined by the material properties(mass,damping and stiffness), and boundary conditions of structure. Each mode is defined by a natural (modal or resonant) frequency,modal damping and a mode shape(these are called modal parameters)
4. Mode shapes-A mode shape is a specific pattern of vibration executed by a mechanical system at a specific frequency. Different mode shapes will be associated with different frequencies. The experimental technique of modal analysis discovers these mode shapes and the frequencies.

ASSUMED DATA

The dimensions for the shaft are assumed as shown:

Boundary conditions

Bearing Fixture on both ends at stepped face

CASE SETUP

1. First, the sketch of the Shaft is made with the dimensions as assumed.
2. Then, using the ‘Revolve Boss’ feature, the 3D model is made.
3. Then a new study is created by clicking on ‘Frequency’ after enabling SOLIDWORKS Simulation from SOLIDWORKS Add-ins.
4. Then, the simulation is carried out-

1. The material is defined as the default ‘Alloy Steel’.
2. Then using the Fixtures option, the Bearing support is provided on both side using ‘Bearing Fixtures’ option
3. Then the mesh is created with a Mesh size of 6mm.
4. Then, finally the simulation is run and the results are obtained.

Shaft with the Mesh,Fixtures and Load applied

RESULTS & OBSERVATION

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

List of resonant frequencies

CONCLUSION

Therefore, on the basis of Frequency Analysis,the mode shapes are found out and their respective resonant frequencies are listed .