1. INTRODUCTION

A shaft is a rotating machine element, usually circular in cross-section, which is used to transmit power from one part to another, or from a machine that produces power to a machine that absorbs power. These are mainly used in power transmissions.

2. AIM

To model a stepped shaft using Solidworks and perform a frequency analysis to determine the critical frequency of the shaft.

3. OBJECTIVE

To find out the critical frequencies of a rotating shaft in Solidworks. You will have to create the model in Solidworks according to the dimensions that you see fit. Model it in Solidworks according to the image shown below

4. PROCEDURE

• The 3D model is created using assumed dimensions.
• D1=50mm L1=1000mm; D2=80mm L2=900mm; D3=300mm L=25mm

• Once the model is created alloy steel is added as the model material.

Material Properties Model Reference Properties Name: Alloy Steel (SS) Model type: Linear Elastic Isotropic Yield strength: 6.20422e+08 N/m^2 Tensile strength: 7.23826e+08 N/m^2 Mass density: 7700 kg/m^3 Elastic modulus: 2.1e+11 N/m^2 Poisson's ratio: 0.28 Thermal expansion coefficient: 1.3e-05 /Kelvin

• Once the material is added simulation study is opened by selecting a frequency option under a new study option and bearing fixture is given to the stepped bar on both the ends.

Model Reference Connector Details Bearing Support-1 Entities: 1 face(s) Type: Bearing Bearing Support-2 Entities: 1 face(s) Type: Bearing

• After fixing the ends, the study is meshed and run.

5. RESULT

MODES Name Type Min Max Amplitude1 AMPRES: Resultant Amplitude Plot for Mode Shape: 1(Value = 0 Hz) 5.719e-04 Node: 4588 3.519e-01 Node: 8092 Name Type Min Max Amplitude2 AMPRES: Resultant Amplitude Plot for Mode Shape: 2(Value = 140.385 Hz) 2.959e-04 Node: 2359 1.797e-01 Node: 2569 Name Type Min Max Amplitude3 AMPRES: Resultant Amplitude Plot for Mode Shape: 3(Value = 140.392 Hz) 5.539e-04 Node: 2359 1.797e-01 Node: 3866 Name Type Min Max Amplitude4 AMPRES: Resultant Amplitude Plot for Mode Shape: 4(Value = 631.729 Hz) 3.621e-04 Node: 2568 2.871e-01 Node: 811 Name Type Min Max Amplitude5 AMPRES: Resultant Amplitude Plot for Mode Shape: 5(Value = 631.792 Hz) 3.367e-04 Node: 2122 2.871e-01 Node: 331 Mass Participation (Normalized) Mode Number Frequency(Hertz) X-direction Y-direction Z direction 1 0 1.8976e-11 2.4481e-12 8.8892e-33 2 140.39 0.37419 0.4737 1.4963e-10 3 140.39 0.47369 0.3742 9.2783e-13 4 631.73 1.1523e-12 4.4144e-10 5.3447e-09 5 631.79 9.0761e-10 1.057e-10 1.8392e-08 Sum X = 0.84789 Sum Y = 0.84789 Sum Z = 2.3887e-08

6. CONCLUSION

Frequency Number	Rad/sec	Hertz	Seconds
1	0	0	1e+32
2	882.07	140.39	0.0071233
3	882.11	140.39	0.0071229
4	3969.3	631.73	0.001583
5	3969.7	631.79	0.0015828

After performing frequency analysis on the shaft, the critical frequencies have been calculated and it is found that if the shaft vibrates at 140.33 Hz or 631.79 Hz it would damage the shaft. Hence it is advisable to operate the shaft such that it does not reach these frequencies during its operation to increase the life and reduce the damage of the shaft.