Frequency Analysis of a rotating shaft

AIM:  To do frequency analysis on the rotating shaft with pulley using solidworks.

Objective:

To create the model with assigning appropriate dimensions.

To do frequency analysis for the model.

To plot the frequency amplitude for different mode shape.

Introduction:

Resonance is a condition that can occur in mechanical structures and can be described as sensitivity to a certain vibration frequency.

Resonance occurs when a natural frequency is at or close to a forcing frequency, such as rotor speed.

For machinery—such as pumps, turbines and electric motors—resonance can amplify the small vibratory forces from machine operation, and severe vibration levels can result. 

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.

The magnitude of deflection depends upon the following:

(a) stiffness of the shaft and its support

(b) total mass of shaft and attached parts

(c) unbalance of the mass with respect to the axis of rotation

(d) the amount of damping in the system

In general, it is necessary to calculate the critical speed of a rotating shaft, such as a fan shaft, in order to avoid issues with noise and vibration.

Modelling:

To create the model, start new part file in the solidworks.

Start new sketch in the front plane.

Then using the front plane mid-point, create the circle with appropriate dimension.

Then use the smart dimension and assign your dimension for the model.

I've using 50 mm for the inner most circle.

Then extrude this circle with using midplane option and assign your assumed dimension for the extrusion.

I've using 1000 mm value for the extrusion of this circle.

Then we want to create hub or stepped part for this shaft, again go to the front plane and start sketch.

And create a circle using mid point of the front plane and make a circle of diameter larger than the shaft(earlier circle) diameter so that it can act as a stepped part of the shaft and enclose the shaft in it.

Now, extrude the circle using extrude option in features tab and extrude it to a length less than the earlier length of the shaft(>1000mm, as it was shaft diameter).

Here, i am extruding upto a 900 mm of length.

Note use mid plane option to extrude the circle.

Now, our shaft stepped part is created now we will sketch the wheel or pulley, whatever you name it.

To create the pulley, again go to the front plane and create a new sketch.

Create a wheel diameter larger than the hub and using smart dimension give your assumed dimension.

Here, I am using 80 mm for the wheel diameter.

Now, extrude it using mid plane option and note use proper assume dimension.

Now, your model will looks similar to this:

Note that all the circles should be concentric and extrude via mid plane should be selected while extrusion.

Dimension for the model

Simulation:

To do frequency simulation click on the solidworks add-ins and click on the simulation and go to the simulation tab which was added now. 

Add click on the new study and a vertical tab will open on the leftside and click on the frequency as we are meant to do frequency analysis. 

Now, add some material to the model, here i am using the default material which is alloy steel, for our analysis.

Now, after that add some fixtures to the model.

Note use the hub face(the stepped face of rod) at the end for fixtures as shown below:

Now, create mesh using create mesh option.

I'm using a mesh refinement of 6 mm you can go with default option or can opt for more refinement as per your computer specifications.

Now, run the somulations and wait for the results.

Results:

Now after sometime we get the five different shape models for our frequency analysis of our model:

The frequency amplitude is obtained automatically by the software.

Here in the below figure the model is reciprocates in the axis and the frequency ontained for this has amplitude of 0.1602.

Similarly for second shape model, the frequency amplitude is in Y-direction and the value of the amplitude is 0.16015

Similarly the frequency shape model obtain in the Z-direction along the pulley.

Now, here in the mode shape 4, we are getting frequency amplitude along X-Z plane.

Now, in the shape mode 5, we get the frequency amplitude in YZ plane.

Resonant Frequencies:

Mode Shape No.	Frequencies(rad/sec)	Frequency(Hertz)	Period(seconds)
1	1705.7	271.48	0.0036835
2	1705.9	271.5	0.0036833
3	2184.4	347.66	0.0028764
4	5241.9	834.27	0.0011986
5	5242.3	834.33	0.0011986

So this is the resonant frequency at which when the shaft frequency at which it rotates matches at this frequency then it will create resonance.

Here, the speed mentioned is the critical speed of the shaft. At critical speed the natural frequency and the rotational frequency matches and creates a resonance.

For real model, the shaft should not be equal to the critical speed and should be rotate at a frequency lower than natural frequency.