FREQUENCY ANALYSIS OF ROTATING SHAFT USING SOLIDWORKS

OBJECTIVE: To model the rotating shaft and calculate the critical or resonant frequencies.

INTRODUCTION:

Resonance:

Resonance describes the phenomena of amplification that occurs when the frequency of a periodically applied force is in harmonic proportion to a natural frequency of the system on which it acts. When an oscillating force is applied at the resonant frequency of another 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 the intrinsic resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy.

Mode shapes:

mode shape is the shape of the beam at different natural frequencies.

The mode shapes of a system are obtained when you calculate its response due to initial conditions only. If you get a guitar string, for example, at rest and give it initial conditions (then release the string), it will vibrate in a specific way that depends on its eigenfrequencies, and each of them is related to a specific mode shape.

Hence, for the homogeneous response (initial conditions only), you can say that the response of your string is the sum of the response of its mode shapes, each one vibrating at its own eigenfrequency. You can think of them as standard movements that your system may perform.

Eg: Beam

Procedure:

• Initially model the rotating shaft using Solidworks modeling.
• Start a new case study in the Solidworks simulation.
• Select frequency analysis and name it.
• Apply the material as alloy steel and use bearing fixtures.
• Create mesh and run.

Property values of alloy steel:

Elastic modulus - 2.1e+011 N/m^2

Poisson ratio - 0.28

Shear modulus - 7.9e+010 N/m^2

Mass density - 7700 kg/m^3

Tensile strength- 723.82e+06 N/m^2

Yeild strength - 620.422e+06 N/m^2

Thermal expansion coefficient - 1.3e-005 /K

Thermal conductivity - 50 W/(m K)

Specific heat - 460 J/(kg K).

Rotating shaft model :

Mass = 336.15 grams.

Volume = 335150.4 mm^3

Surface area = 46495.57 mm^2.

2D diagram of the model which is revolved about the axis:

model:

Bearing fixture:

PLOTS:

Amplitude variation in different mode shapes obtained:

1.

2.

3.

4.

5.

RESULTS:

Different resonant frequencies obtained are as follows:

The frequency varies for different mode shapes.