Frequency Analysis of a rotating shaft

AIM:

To model a shaft and then perform frequency analysis on the part and find its natural frequency to avoid resonance during its function.

INTRODUCTION:

In this simulation, we run a frequency analysis simulation study on a shaft with madeup geometry and find the frequency at different nodes with which it vibrates. This way, we get to know about the natural frequency of the part. By this test, we can avoid resonance by preventing the natural frequency of the part.

THEORY:

Everything in the universe is always under a vibrational motion because of the energy that they possess and the motion of the atoms and the frequency with which it vibrates is known as its natural frequency. In general, we cant observe the vibration of the objects which might be due to the very low magnitude of the amplitude of the vibrations. But, if they are brought to a vibrating motion with an external force at the same frequency as the natural frequency of the object, we would observe that the vibration amplitude is higher than it should be. This happens due to resonance. Resonance is defined as the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force is equal or close to the natural frequency of the system on which ithe force is applied on.

This phenomena might not seem to be of any importance, but it crucially affects functioning of every working machine aroung us. If the machine is vibrating at a particular frequency and the frequency matches the natural frequency of one its parts, then it would cause a catrastrophic result as the resonance would cause vibration of high amplitude which might hinder the performance of the machine as it would create vibration in the resonating part of the machine which is a huge red flag regarding safety. That natural frequency of the part depends on its weight, mass, shape and material properties. Hence, it is very important to find the natural frequency of the part and caliber the machine in such a way that, it never vibrates at the natural frequency of its constituent parts.

The mode of vibration is the type in which the system tries to oscillate naturally, i.e. without any excitation force. The frequency of oscillation is termed as modal frequency (or natural frequency) and the shape made by the system is called mode shape.

A rotating shaft is a type of simple rod that is used to transfer power from one axis to another. It plays a great role on the functioning of any machine. If it is encountered by resonance, it will vibrate with a high amplitude and willl severely damage the functioning of the machine.

Hence, preventing resonance for the shaft gets very crucial.

MODELLING AND SIMULATION:

The modelling of the shaft was simply done by extruding the base sketches on the concerning planes and faces with the following dimentions:

After modelling the part, we create a new simulation study and select the frequency study.

Then, we define the material of the part by adding the alloy steel via the 'add material' feature.

We then define the boundary conditions of our study by applying a bearing fixture on the stepped face of the rod at the two ends of the shaft with the help of the 'fixed geometry' feature. This condition is applied ti replicate the conditions of the shaft in its actual working environment.

Meshing is an important part of any simulation. Appropriate mesh should be created accordding to geomeetry of the part to get accurate results. The following mesh settings are good enough for our simulation.

RESULTS:

amplitude distribution at mode-1:

amplitude distribution at mode-2:

amplitude distribution at mode-3:

amplitude distribution at mode-4:

amplitude distribution at mode-5:

OBSERVATIONS AND CONCLUSIONS:

From the above study, we got the values of the natural frequencies at which the shaft vibrates. If the machine which the shaft is a part of, vibrates at the same frequencies as one of the values, resonnance would occur and it would cause failure of the machinne. Hence, it should be made sure that the machine doesnt vibrate with any of those frequencies.

The part can also be designed so that they have a preffered natural frequency as the the natural frequency depends on the shape and material of the part.