Frequency Analysis of a rotating shaft using Solidworks

AIM: To perform the Frequency analysis by creating a model provided to find out 5 mode shapes of the shaft and to list out the resonant frequencies in Solidworks.

THEORY:

Introduction : For a rotating shaft there is a speed at which, for any small initial deflection, the centripetral force is equal to the elastic restoring force. At this point the deflection increases greatly and the shaft is said to "whirl". Below and above this speed this effect is very much reduced. This critical (whirling speed) is dependent on the shaft dimensions, the shaft material and the shaft loads . The critical speed is the same as the frequency of traverse vibrations. The critical speed N of a shaft is simply

`N = (sqrt(k/m))/(2*pi)`

or

where m = the mass of the shaft assumed concentrated at single point .
k is the stiffness of the shaft to traverse vibrations

For a horizontal shaft this can be expressed as

`N = (sqrt(g/m))/(2*pi)`

or

where y = the static deflection at the location of the concentrated mass

Symbols
m = Mass (kg)
N = critical speed (rev/s )
g = acceleration due to gravity (m.s-2 )
L = Length of shaft

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 we 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. Modes are inherent properties of a structure, and are determined by the material properties (mass, damping, and stiffness), and boundary conditions ofthe structure. Each mode is defined by a natural (modal or resonant) frequency, modal damping, and a mode shape (i.e. the so-called “modal parameters”).

PROCEDURE:
1. Creating the rotating shaft.

• Rotating Shaft diameter = 1.00m
  Extrude = 0.20m (from midplane)
• Shaft Diameter = 0.20m
  Extrude = 2.00m (from midplane)
• Smaller Shaft Diameter = 0.10m
  Extrude = 0.10m (from midplane)
• Mass = 215.20 kilograms
  

2. Clicking on the new simulation select the frequency simulation.
3. Here, Alloy material is provided as the material for the rotating shaft.

4. Apply bearing fixture on the stepped face of the rod at the two ends.

5. The study settings were kept as default setting. The number of mode shapes were kept as 5

6. Now create a mesh and run the frequency analysis study to get the different mode shapes of the shaft.

6. Now click on mesh and run option

RESULTS, TABLES & PLOTS-

• MODE SHAPE 1-

• MODE SHAPE 2-

• MODE SHAPE 3-

• MODE SHAPE 4-

• MODE SHAPE 5-

Different Resonant Frequencies are obtained as-

Study name:Frequency 1

Mode No.	Frequency(Rad/sec)	Frequency(Hertz)	Period(Seconds)
1	0	0	1.00E+32
2	264.71	42.13	0.023736
3	264.72	42.132	0.023735
4	1045.6	166.41	0.006009
5	1045.6	166.42	0.006009

CONCLUSION: Thus the following are observed after viewing the results of the frequency analysis on the rotating shaft:

• 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.
• When the shaft vibrates at 42.13 Hz or 166.41 Hz, it would damage the shaft.
• It is suggested to operate the rotating shaft such that it does not reach the above-mentioned frequencies to prevent the shaft from damage.
• By doing so, it reduces the damage to the shaft and hence, it provides the increase in life period to the rotating shaft.