Frequency Analysis of a rotating shaft
AIM
To conduct frequency analysis of a rotating shaft and determine 5 mode shapes and the resonant frequencies.
THEORY
When a body oscillates under absence of any continuous or repeated load, the frequency of oscillation of the body is known as natural frequency.
When a load is applied to the body, it can vibrte at various frequencies. When this frequency becomes equal to the natural frequency of the body, it is known as resonating frequency. A body vibrating at resonating frequency can undergo large deformations which can be dangerous for the body and can lead to failure. This phenomenon in which the body vibrates at the resonating frequency under applied load is termed as resonance. It is preferred to determine and avoid resonance while designing the component.
Modes of vibration
A mode shape is a specific pattern of vibration executed by a mechanical system at a specific frequency. Different mode shapes will be associated with different frequencies. The experimental technique of modal analysis discovers these mode shapes and the frequencies.
Modes are the properties of a particular structure that depends upon the following:
1) Mechanical properties of the structure like damping, stiffness etc.
2) Boundary conditions applied.
If material of the structure changes, mode of vibration also changes.
Critical speed of shaft
In solid mechanics, in the field of rotor-dynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear. As the speed of rotation approaches the object's natural frequency, the object begins to resonate, which dramatically increases system vibration. The resulting resonance occurs regardless of orientation. When the rotational speed is equal to the numerical value of the natural vibration, then that speed is referred to as critical speed.
All rotating shafts, even in the absence of external load, will deflect during rotation. The unbalanced mass of the rotating object causes deflection that will create resonant vibration at certain speeds, known as the critical speeds. The magnitude of deflection depends upon the following:
(a) Stiffness of the shaft and its support
(b) Total mass of shaft and attached parts
(c) Unbalance of the mass with respect to the axis of rotation
(d) Amount of damping in the system
In general, it is necessary to calculate the critical speed of a rotating shaft, such as a fan shaft, in order to avoid issues with noise and vibration.
Like vibrating strings and other elastic structures, shafts and beams can vibrate in different mode shapes, with corresponding natural frequencies. The first vibrational mode corresponds to the lowest natural frequency. Higher modes of vibration correspond to higher natural frequencies. Often when considering rotating shafts, only the first natural frequency is needed.
Critical speed depends upon the magnitude and location of the shaft unbalance, the length of the shaft, its diameter, and the kind of bearing support. Many practical applications suggest as good practice that the maximum operating speed should not exceed 75% of the critical speed; however, there are cases that require speeds above the critical speed to work correctly. In such cases, it is important to accelerate the shaft through the first natural frequency quickly so that large deflections don't develop.
OBJECTIVE
The objective of this project is to perform the frequency analysis on the rotating shaft and determine different modes of vibration and natural frequency.
The shaft is created according to the given design and frequency study is selected from the simulation. The material provided to the shaft is alloy steel.
The stepped faces of the rod are given bearing fixture from the connections and the mesh is created. The study is run.
RESULT
Mode 1
Mode 2
Mode 3
Mode 4
Mode 5
Naatural frequencies
OBSERVATION AND CONCLUSION
As discussed earlier, the natural frequency is minimum for first mode and increases with every subsequent mode.
REFERENCES