FREQUENCY ANALYSIS OF A ROTATING  SHAFT

FREQUENCY ANALYSIS OF A ROTATING SHAFT

1. AIM

• To Create a 3D CAD Model of a ‘Rotating Shaft’ in SOLIDWORKS. And,
• Perform Frequency Analysis to find out the Critical / Resonant frequencies for the same.
  
  

2. INTRODUCTION

2.1 Frequency Analysis:

Every structure has the tendency to vibrate at certain frequencies, called natural or resonant frequencies. Each natural frequency is associated with a certain shape, called mode shape, that the model tends to assume when vibrating at that frequency.

When a structure is properly excited by a dynamic load with a frequency that coincides with one of its natural frequencies, the structure undergoes large displacements and stresses. This phenomenon is known as resonance. For undamped systems, resonance theoretically causes infinite motion. Damping, however, puts a limit on the response of the structures due to resonant loads.

Frequency studies help us avoid resonance and design vibration isolation systems. They also form the basis for evaluating the response of linear dynamic systems where the response of a system to a dynamic environment is assumed to be equal to the summation of the contributions of the modes considered in the analysis.

Note: Resonance is desirable in the design of some devices.

2.2 Rotating Shaft:

A rotating shaft is a 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.

They are mainly classified into two types.

1. Transmission shafts are used to transmit power between the source and the machine absorbing power; e.g. counter shafts and line shafts.
2. Machine shafts are the integral part of the machine itself; e.g. crankshaft.

The material used for ordinary shafts is mild steel. When high strength is required, an alloy steel such as nickel, nickel-chromium or chromium-vanadium steel is used. Shafts are generally formed by hot rolling and finished to size by cold drawing or turning and grinding.

3. PART MODELLING

The geometry used for the part in the analysis is as shown below.

4. FREQUENCY ANALYSIS

4.1 Procedure:

1. Create a frequency study. Right-click the top icon in the Simulation study tree and select Properties. Define the Properties of the study to set the number of frequencies. The program calculates the lowest five modes by default. We have used the default no. of modes fro our analysis.
   
   

   Study name	Frequency 1
   Analysis type	Frequency
   Mesh type	Solid Mesh
   Number of frequencies	5
   Solver type	FFEPlus
   Soft Spring:	Off
   Incompatible bonding options	Automatic
   Thermal option	Include temperature loads
   Zero strain temperature	298 Kelvin
   Include fluid pressure effects from SOLIDWORKS Flow Simulation	Off

2. Define material for Rotating _Shaft_Rupesh component, right-click its icon in the Simulation study tree and select Apply/Edit Material. We have applied 'Alloy Steel' as the material for the shaft. Note that density is a required material property.
   
   

   Properties

   Name: Alloy Steel Model type: Linear Elastic Isotropic Default failure criterion: Unknown Yield strength: `6.20422*10^8 (N/m^2)` Tensile strength: `7.23826*10^8 (N/m^2)` Mass density: `7700 ((kg)/(m^3))` Elastic modulus: `2.1*10^11 (N/m^2)` Poisson's ratio: 0.28 Thermal expansion coefficient: 1.3e-05 /Kelvin

3. Define appropriate restraints. Apply bearing fixture on the stepped face of the rod a the two ends.
   
   
4. Mesh the model and run the study. A 10 mm mesh is used.
   
   

   Mesh type	Solid Mesh
   Mesher Used:	Standard mesh
   Automatic Transition:	Off
   Include Mesh Auto Loops:	Off
   Jacobian points	4 Points
   Element Size	10 mm
   Tolerance	0.5 mm
   Mesh Quality Plot	High

   
   

   Total Nodes	24776
   Total Elements	15209
   Maximum Aspect Ratio	3.5584
   % of elements with Aspect Ratio < 3	99.8
   % of elements with Aspect Ratio > 10	0
   % of distorted elements(Jacobian)	0

   
   
   
5. View the results. Double-click an icon in a Results folder to display the associated plot.
   
   
6. Right-click the Results folder and select List Resonant Frequencies to list the requested number of resonant frequencies.
   
   

4.2 Results & Plots:

4.2.1 Rotating_Shaft_Rupesh-Frequency 1-Amplitude-Amplitude1

Name	Type	Min	Max
Amplitude1	AMPRES: Resultant Amplitude Plot for Mode Shape: 1(Value = 302.339 Hz)	0.000e+00 Node: 346	3.015e-01 Node: 479

4.2.2 Rotating_Shaft_Rupesh-Frequency 1-Amplitude-Amplitude2

Name	Type	Min	Max
Amplitude2	AMPRES: Resultant Amplitude Plot for Mode Shape: 2(Value = 302.723 Hz)	0.000e+00 Node: 346	3.015e-01 Node: 1541

4.2.3 Rotating_Shaft_Rupesh-Frequency 1-Amplitude-Amplitude3

Name	Type	Min	Max
Amplitude3	AMPRES: Resultant Amplitude Plot for Mode Shape: 3(Value = 366.047 Hz)	0.000e+00 Node: 346	5.198e-01 Node: 391

4.2.4 Rotating_Shaft_Rupesh-Frequency 1-Amplitude-Amplitude4

Name	Type	Min	Max
Amplitude4	AMPRES: Resultant Amplitude Plot for Mode Shape: 4(Value = 805.615 Hz)	0.000e+00 Node: 346	7.039e-01 Node: 494

4.2.5 Rotating_Shaft_Rupesh-Frequency 1-Amplitude-Amplitude5

Name	Type	Min	Max
Amplitude5	AMPRES: Resultant Amplitude Plot for Mode Shape: 5(Value = 805.909 Hz)	0.000e+00 Node: 346	7.036e-01 Node: 514

4.2.6 Mode List

Frequency Number	Rad/sec	Hertz	Seconds
1	1,899.7	302.34	0.0033075
2	1,902.1	302.72	0.0033034
3	2,299.9	366.05	0.0027319
4	5,061.8	805.62	0.0012413
5	5,063.7	805.91	0.0012408

5. CONCLUSION

The frequency analysis is performed on the rotating shaft and the different mode shapes with the resulting frequencies have been listed above. The frequency varies for different mode shapes and its amplitude is directly proportional to the frequency inducing the resonance. It is suggested that to prevent the damage, the rotating shaft shoud operate such that it does not reach the above mentioned frequencies. Thus, the life of the rotating shaft is increased.