AIM : To find out the critical frequencies of a rotating shaft in Solidworks.

OBJECTIVES :

1. To create 3D model of a rotating shaft.
2. To perform frequency analysis on the rotating shaft and find out the critical frequencies.

INTRODUCTION :

Frequency is the number of occurrences of a repeating event per unit of time. Frequency is measured in units of hertz (Hz) which is equal to one occurrence of a repeating event per second. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency.

When the applied frequenccy becomes equal to or greater than the natural frequency then the objet tends to vibrate greater. This phenomenon is called as resonance.

The mode is not affected by extreme values. The mode is easy to identify in a data set and in a discrete frequency distribution. The mode is useful for qualitative data.

Here the frequency analysis is carried out in a fly wheel setup. Flywheel is the mechanical device which is used to store the energy in it.

2D sketch

All dimensions are in mm

PROCEDURE

• First we are going to create the 3d model of a part.
• Go to the simulation and click on new case study then select the frequency.
• After that fixed the both the ends with bearings.
• Select the material as alloy steel by right clicking on a part.
• Create a new mesh and set the manual mesh as 3mm fine mesh.
• And then click on mesh and run and the run.
• We will get the five different types of modes and frequencies.

Model Information

Treated As	Volumetric Properties
Solid Body	Mass:1.19742 kg Volume:0.000155509 m^3 Density:7700 kg/m^3 Weight:11.7347 N

Material Properties Model Reference 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 Connector Definitions Pin/Bolt/Bearing Connector Model Reference Connector Details Bearing Support-1 Entities: 1 face(s) Type: Bearing Bearing Support-2 Entities: 1 face(s) Type: Bearing

Mesh information

Mesh type	Solid Mesh
Mesher Used:	Standard mesh
Automatic Transition:	Off
Include Mesh Auto Loops:	Off
Jacobian points	4 Points
Element Size	3 mm
Tolerance	0.15 mm
Mesh Quality Plot	High

Study Results Name Type Min Max Amplitude1 AMPRES: Resultant Amplitude Plot for Mode Shape: 1(Value = 0 Hz) 0.000 Node: 33751 1.784 Node: 1310 Part1-Frequency 1-Amplitude-Amplitude1 Name Type Min Max Amplitude2 AMPRES: Resultant Amplitude Plot for Mode Shape: 2(Value = 364.047 Hz) 0.004 Node: 59017 1.058 Node: 33251 Part1-Frequency 1-Amplitude-Amplitude2 Name Type Min Max Amplitude3 AMPRES: Resultant Amplitude Plot for Mode Shape: 3(Value = 364.091 Hz) 0.002 Node: 5352 1.058 Node: 33251 Part1-Frequency 1-Amplitude-Amplitude3 Name Type Min Max Amplitude4 AMPRES: Resultant Amplitude Plot for Mode Shape: 4(Value = 1637.63 Hz) 0.001 Node: 26043 2.094 Node: 1382 Part1-Frequency 1-Amplitude-Amplitude4 Name Type Min Max Amplitude5 AMPRES: Resultant Amplitude Plot for Mode Shape: 5(Value = 1637.94 Hz) 0.000 Node: 17902 2.093 Node: 50156 Part1-Frequency 1-Amplitude-Amplitude5 Mode List Frequency Number Rad/sec Hertz Seconds 1 0 0 1e+032 2 2287.4 364.05 0.0027469 3 2287.7 364.09 0.0027466 4 10290 1637.6 0.00061064 5 10291 1637.9 0.00061052 Mass Participation (Normalized) Mode Number Frequency(Hertz) X direction Y direction Z direction 1 0 7.595e-043 1.192e-012 7.9221e-013 2 364.05 4.0932e-011 0.71766 0.17666 3 364.09 1.0751e-010 0.17666 0.71767 4 1637.6 1.4755e-008 1.4491e-009 7.9474e-010 5 1637.9 1.3662e-008 8.7812e-010 3.1336e-009 Sum X = 2.8565e-008 Sum Y = 0.89432 Sum Z = 0.89434

CONCLUSION :

1. From the result obtained for 'Alloy Steel (SS)' , it can be concluded that the above system has resonant frequencies at `0`Hz, `101.33`Hz, `480.78`Hz . If the above system is made to run at or near the resonance frequencies, Whirling of shafts occurs due to rotational imbalance of a shaft, even in the absence of external loads, which causes resonance to occur at certain speeds, known as critical speeds. Whirling speed is also called as Critical speed of a shaft. It is defined as the speed at which a rotating shaft will tend to vibrate violently in the transverse direction if the shaft rotates in horizontal direction. In other words, the whirling or critical speed is the speed at which resonance occurs.
2. Similarly from the result obtained for 'Aluminium Alloy 6061-T6 (SS)', it can be concluded that the above system has resonant frequencies at `0.0676`Hz , `98.71`Hz , `465.51`Hz. If the above system is made to run at or near the resonance frequencies, there is a chance of failure of the structure due to Whirling of shaft. The system will work fine for all other frequencies.
3. To avoid the effect of resonance, the system can be incorporated with dampers or springs. Two movable nylon bushes also help to prevent the shaft whirling amplitude from reaching excessive levels.
4. The material should be selected carefully for designing such systems as different materials can have different resonant frequencies and such materials should be selected which have high natural frequencies as it can be concluded that Alloy Steel system have higher resonant frequencies as compared to Aluminium Alloy. They can be employed for their purposes according to requirement.