Frequency analysis of a rotating shaft using FEA in Solidworks

Aim:- Frequency analysis of a rotating shaft using FEA in Solidworks

Objective:-

1. Create the model as per the assumed dimensions.

2. Find out 5 mode shapes and list the resonant frequencies.

Introduction:-

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. If your design is subjected to dynamic environments, static studies cannot be used to evaluate the response. Frequency studies can help you avoid resonance and design vibration isolation systems. They also form the basis for evaluating the response of linear dynamic systems where the response of a system to a dynamic environment is assumed to be equal to the summation of the contributions of the modes considered in the analysis.

A real model has an infinite number of natural frequencies. However, a finite element model has a finite number of natural frequencies that are equal to the number of degrees of freedom considered in the model. Only the first few modes are needed for most purposes. The natural frequencies and corresponding mode shapes depend on the geometry, material properties, and support conditions. The computation of natural frequencies and mode shapes is known as modal, frequency, and normal mode analysis.

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.

Whirling speed is also called a Critical speed of a shaft. It is defined as the speed at which a rotating shaft will tend to vibrate violently in the transverse direction if the shaft rotates in a horizontal direction. In other words, the whirling or critical speed is the speed at which resonance occurs.

In the field of rotor dynamics, the critical speed is the theoretical angular velocity which excites the natural frequency of a rotating object, such as a shaft, propeller, 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.

Whirling Speed is due to the unbalanced forces acting on a rotating shaft.

Procedure:-

1. Create a sketch as needed. Here the roller diameter is 200 mm with a thickness of 20 mm. Rod diameter of 50 mm and half-length of 300 mm from the face of the roller. The bearing support rod is of 25 mm diameter and length of 30 mm.
2. From the simulation menu, a new study is opened and frequency analysis is selected.
3. Alloy steel material is selected.
4. Then, bearing fixture of Rigid type is selected for each end face of 30 mm length.
5. Fine mesh is created for better results.
6. After that, run the study till 5 modes using FFE Plus solver.

3D Model:-

Mesh and Bearing fixture:-

Mass Properties:-

Frequency Study Properties;-

Mode 1-

Mode 2-

Mode 3-

Mode 4-

Mode 5-

Study Results:-

Mass Participation of the system:-

Frequency vs Mode number plot:-

Resonant Frequency List:-

Mode No.		Frequency(Rad/sec)	Frequency(Hertz)	Period(Seconds)
1		0.081998	0.01305	76.626
2		3194.2	508.38	0.001967
3		3195.1	508.51	0.0019665
4		9272.6	1475.8	0.00067761
5		9277.9	1476.6	0.00067722

From this table, we obtained various resonance frequencies of the created shaft which are 0.013 Hertz for mode 1, 508.38 Hertz for mode 2, 508.51 Hertz for mode 3, 1475.8 Hertz for mode 4 and 1476.6 for mode 5. The mechanical assembly or system in which this shaft will be used must not operate at or around these frequencies for safe operations unless the system may oscillate and the result may be catastrophic.

Conclusion:-

1. Mechanical resonance is the tendency of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings, and airplanes. This is a phenomenon known as resonance disaster.

2. By this study, we came to know the “resonance frequencies” of our geometry. It isn’t related to loading at this stage, only to the geometry. Resonance frequencies change due to the shape of the model and the way it is constrained only.
3. After analyzing the resonance frequencies, we concluded that the mechanical assembly or the system to be used must not operate at these obtained frequencies of this shaft unless it will lead to failure of the system. So we can design our other models according to it so that the whole assembly must operate at safe frequency.

Reference:-

http://help.solidworks.com/2017/English/SolidWorks/cworks/c_Frequency_Analysis.htm

https://en.wikipedia.org/wiki/Mechanical_resonance#:~:text=Mechanical%20resonance%20is%20the%20tendency%20of%20a%20mechanical,resonant%20frequency%29%20than%20it%20does%20at%20other%20frequencies.