FEA in SOLIDWORKS - Frequency Analysis of a rotating shaft

AIM:

To find out the critical frequencies of a rotating shaft Solidworks simulation.

INTRODUCTION:

What is simulation?

Simulation mimics the real process under certain condition in computer software using Finite Element Analysis FEA. FEA basically divides the object into number of small parts. This process is known as meshing. The size of mesh element size indirectly proportional to accuracy and execution time. On the small elements load conditions applied using partial diffirential equations mathematical model of given conditions.

What are Natural frequency/critical frequencies, mode shapes?

All stable, unforced, mechanical systems vibrate harmonically at certain discrete frequencies, known as natural frequencies of the system. Complex systems have several natural frequencies. All rotating shafts, even in the absence of external load, will deflect during rotation. The unbalanced mass of the rotating object causes deflection that will create resonant vibration at certain speeds, known as the critical speeds. During this 'resonance' the frequency of rotation matches with natural frequency of the object which results in amplifying vibration to high unacceptable values which eventually may destroy the object.

The magnitude of deflection depends upon the following:

1. stiffness of the shaft and its support
2. total mass of shaft and attached parts
3. unbalance of the mass with respect to the axis of rotation
4. the amount of damping in the system

The special initial displacements of a system that cause it to vibrate harmonically are called mode shapes for the system. If a system has several natural frequencies, there is a corresponding mode of vibration for each natural frequency.

The natural frequencies and mode shapes are arguably the single most important property of any mechanical system.

PROCEDURE:

1. Open solidworks and create new part.

2. Design the rotaing shaft with disc as below:

3. Goto simulation, create new study and choose frequency analysis

4. Define material, here alloy steel

5. In the fixtures select bearings and select each stepped end of the shafts.

6. Create mesh

Note: Here default values selected as it balance accuracy with computer specs (which here very basic). To improve accuracy reduce the element size (finer mesh) and based upon the computer specs the evaluation time will increase than default values.

7. Now the mesh and run the simulation to get the results.

(Models attached in its dedicated secton, under 'choose file' option)

RESULTS:

Mass of this shaft: 1.2kg

List of resonance frequencies with different mode shapes

Mode Shape 1 Amplitude

Mode Shape 2 Amplitude

Mode Shape 3 Amplitude

Mode Shape 4 Amplitude

Mode Shape 5 Amplitude

CONCLUSION:

From this analysis, the shaft should not run at frequencies ~364 Hz and ~1642 Hz, if it reaches these frequency resonance occurs and the vibration increases tremendously thus the catastropic repurcussions occur.