Frequency Analysis of A Rotating Shaft Using SolidWorks

Frequency Analysis Of Rotating Shaft And Comparing It with Number of Modes

Aim:- To calculate resonant frequency of a rotating shaft with fixed at its end and plot it.

Theory:-

In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time-frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform.

The mathematical motivation for this study is that functions and their transform representation are often tightly connected, and they can be understood better by studying them jointly, as a two-dimensional object, rather than separately. A simple example is that the 4-fold periodicity of the fourier transform and the fact that two-fold Fourier transform reverses direction – can be interpreted by considering the Fourier transform as a 90° rotation in the associated time–frequency plane: 4 such rotations yield the identity, and 2 such rotations simply reverse direction (reflection through origin).

Resonant Frequency

In physics 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.

Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system. Small periodic forces that are near a resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy.

Modes

A normal mode of an oscillation system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. In music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "harmonics" or "overtones".

Objectives:-

To calculate resonant frequency at 5 modes and giving bearing fixture to end faces of rotating shaft and also plotting analysis with respect to different amplitude of frequency.

Dimensions of shaft:-

Design of Rotating Shaft:-

Bearing Fixtures at the end faces:-

Plots :-

Material= Alloy Steel

Amplitude 1

Frequency= 0.0089945 Hz

Amplitude 2

Frequency= 518.39 Hz

Amplitude 3

Frequency= 518.46 Hz

Amplitude 4

Frequency= 2367.4 Hz

Amplitude 5

Frequency= 2367.5 Hz

Resonant Frequency for five Different modes:-

Frequency Vs Number of Modes Graph:-

Explaination:-

From above plots it can be seen that the rotor of the rotating shaft has larger deformation with increase in frequency than the middle part.

Conclusion:-

From above study it can be concluded that the frequency increases as mode increases and there is an larger deformation of shaft as frequency increases. From the graph of frequency Vs number of modes it can be seen that at starting the curve increases slightly and then suddenly increases largely then again increases gradually.