Frequency Analysis of a rotating shaft (Solidworks) FEA

OBJECTIVE

• To find out the critical frequencies of a rotating shaft in Solidworks.
• To create the model in Solidworks according to dimensions that you see fit.

INTRODUCTION

FEA

Finite Element Analysis or FEA is the simulation of a physical phenomenon using a numerical mathematic technique referred to as the Finite Element Method, or FEM. This process is at the core of mechanical engineering, as well as a variety of other disciplines. It also is one of the key principles used in the development of simulation software. Engineers can use these FEM to reduce the number of physical prototypes and run virtual experiments to optimize their designs.

Complex mathematics is required in order to understand the physical phenomena that occur all around us. These include things like fluid dynamics, wave propagation, and thermal analysis.

Analyzing most of these phenomena can be done using partial differential equations, but in complex situations where multiple highly variable equations are needed, Finite Element Analysis is the leading mathematical technique.

Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. 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.

Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamical system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.

Natural frequency, also known as Eigen frequency, is the frequency at which a system tends to oscillate in the absence of any driving or damping force.

The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all parts of the system move sinusoidally with that same frequency).

In a mass-spring system, with mass m and spring stiffness k, the natural frequency can be calculated as:

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

From this analysis we get the five different modes of frequency and the minimum frequency is 1. 0 Hz. and maximum frequency is 5. 1637.9 Hz.

REFFERENCES

• https://en.wikipedia.org/wiki/Resonance
• https://en.wikipedia.org/wiki/Natural_frequency#:~:text=Natural%20frequency%2C%20also%20known%20as,sinusoidally%20with%20that%20same%20frequency).