Frequency Analysis of a rotating shaft

AIM:

To find out the critical or resonant frequencies of a rotating shaft in Solidworks.

Design the model using solidworks based on any desired dimensions.

To create a solid model of a rotating flywheel on a shaft and identify 5 critical frequencies by generating 5 mode shapes using Solidworks Simulation’s Frequency analysis feature.

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:

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:

`Wo=sqrt(k/m)`

Procedure:

1. Creating the shaft with required dimensions.
2. Setting up simulation study.
3. Select the material as alloy steel.
4. Apply geometric fixtures.
5. Create mesh of required size.
6. Go to study properties and make changes as per requirement.
7. Run the study and get the results.

Modelling:

Simulation Setup:

Results:

Mode 1:

Mode 2:

Mode 3:

Mode 4:

Mode 5:

Table:

Study name: Frequency 1
Mode No.	Frequency(Rad/sec)	Frequency(Hertz)	Period(Seconds)
1	5142.8	818.5	0.001222
2	5157	820.77	0.001218
3	5342.6	850.3	0.001176
4	13205	2101.7	0.000476
5	13218	2103.7	0.000475

Conclusion:

It is not safe to run the component in this above frequencies. By observing the values, we can say that there is high risk of failure between 820 to 850 Hertz and near 2102 Hertz