Frequency Analysis of a rotating shaft

AIM:

To perform Finite Element Analysis (FEA) by designing a Rotating shaft and determine critical frequencies using SOLIDWORKS.

THEORY:

Vibration is a mechanical phenomenon, periodic back and forth motion of particle of an elastic body or medium, commonly resulting when almost any physical system is displaced from its equilibrium condition and allowed to respond to the forces that tend to restore equilibrium. It occurs in two categories: Free vibrations and Forces vibrations.

Free vibrations occur when the system is disturbed momentarily and then allowed to move without restraint. For example a weight suspended from a spring. In equilibrium, the system has minimum energy and the weight is at rest. If the weight is pulled down and released, the system will respond by vibrating vertically and then damps down to motionlessness.

Forced vibrations occur if a system is continuously driven by an external agency. For an example a child’s swing is pushed on each downswing. This makes the system undergo in SHM and driven by sinusoidal forcing. This leads to the phenomenon of resonance.

Resonance occurs when the driving frequency approaches the natural frequency of free vibrations. The result is a rapid take up of energy by the vibrating system, with an attendant growth of the vibration amplitude.

Natural frequency is the rate at which an object vibrates when it is not disturbed by an outside force. These frequencies are dependent on the way mass and stiffness is distributed inside the body.

Mode is a statistical term that refers to the most frequently occurring number found in a set of numbers. The mode is found by collecting and organizing data in order to count the frequency of each result. The result with the highest count of occurrences is the mode of the set, also referred to as the modal value.

Modes are inherent properties of a structure, and are determined by the material properties (mass, damping and stiffness) and boundary conditions of the structure. Each mode is defined by a natural (modal or resonant) frequency, modal damping, and a modal shape (i.e. the so called modal parameters)

Mode shapes is the deformed shape of the structure at a specific natural frequency of vibration is termed its normal mode of vibration. Some other terms used to describe the normal mode are mode shape, characteristic shape, and fundamental shape. Each mode shape is associated with a specific natural frequency.

Frequency analysis is done if your design is subjected to dynamic environments, static studies cannot be used to evaluate the response. Frequency studies can help you 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.

A real model has an infinite number of natural frequencies. However, a finite element model has a finite number of natural frequencies that is equal to the number of degrees of freedom considered in the model. Only the first few modes are needed for most purposes.

The natural frequencies and corresponding mode shapes depend on the geometry, material properties, and support conditions. The computation of natural frequencies and mode shapes is known as modal, frequency, and normal mode analysis.

PROCEDURE:

• Create a 3D model with suitable dimensions.

• Now start with the frequency study simulation.
• Now assign the material to the part i.e. Alloy steel.

• Now for fixing the part right click on ‘Fixtures’ and then select ‘Bearing Fixture’. Then select the cylindrical face of the stepped shaft. The ‘Bearing Fixture’ takes only one face at a time, therefore again set the fixture for the other side of the rotor shaft.

• Now create a mesh with 2 mm mesh size.

• Now run the simulation.

RESULTS:

• Mode 1 - Animation - Mode 1

• Mode 2 - Animation - Mode 2

• Mode 3 - Animation - Mode 3

• Mode 4 - Animation - Mode 4

• Mode 5 - Animation - Mode 5

• Critical Frequencies

CONCLUSION:

• We can see from the results the critical frequencies of rotating shaft are 0.11935 Hertz, 315.86 Hertz, 315.88 Hertz, 1125.8 Hertz, and 1126 Hertz.
• Thus shaft should not be operated near these frequencies since it can result in resonance which can have a drastic effect on the life of the shaft.
• However mode 1 frequency is a bit peculiar as it is of an extremely low range.