Frequency Analysis of a Rotating Shaft

AIM: Perform frequency analysis on a rotating shaft and list resonant frequencies.

OBJECTIVES:

• Model a rotating shaft.
• Perform a frequency analysis.
• Obtain results and list resonant frequencies.

THEORY:

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. For example: if a new-born baby's heart beats at a frequency of 120 times a minute (2 hertz), its period, T, — the time interval between beats—is half a second (60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

Frequency Analysis

Every structure has the tendency to vibrate at certain frequencies, called natural or resonant frequencies. Each natural frequency is associated with a certain shape, called mode shape, that the model tends to assume when vibrating at that frequency. When a structure is properly excited by a dynamic load with a frequency that coincides with one of its natural frequencies, the structure undergoes large displacements and stresses. This phenomenon is known as resonance. For undamped systems, resonance theoretically causes infinite motion. Damping, however, puts a limit on the response of the structures due to resonant loads.

Resonance frequencies are the natural frequencies at which it is easiest to get an object to vibrate. While setting up vibrations at other frequencies is possible, they require much more energy and constant input to maintain than a resonance frequency. Most objects have several resonance frequencies, and this property must be taken into account because of their positive, as with musical instruments, or negative, as with bridges, effects.

PROCEDURE:

Modelling

A rotating shaft is modelled according to below given dimensions.

Simulation

Alloy Steel is selected as the material of the component.

Bearing friction is applied on the stepped face of the rod at the two ends separately.

Default mesh settings are selected for meshing

Mesh Result

Frequency Analysis

RESULT:

By performing the frequency analysis on the rotating shaft, we obtained 5 mode shapes and resonance frequency. We also obtained three plots viz. Frequency vs Mode number, Frequency vs effective mass participation factor (EMPF) and Frequency vs Cumulative effective mass participation factor (CEMPF)

CONCLUSION:

The critical frequencies of rotating shaft are 0, 107.82, 107.86, 533.42, 533.62 Hertz.