Frequency Analysis of a rotating shaft
Aim: To find out the critical frequencies of a rotating shaft in Solidworks.
Finite Element Analysis
The Finite Element Analysis (FEA) method, originally introduced by Turner et al. (1956), is a powerful computational technique for approximate solutions to a variety of “real-world” engineering problems having complex domains subjected to general boundary conditions. FEA has become an essential step in the design or modeling of a physical phenomenon in various engineering disciplines. A physical phenomenon usually occurs in a continuum of matter (solid, liquid, or gas) involving several field variables. The field variables vary from point to point, thus possessing an infinite number of solutions in the domain. Within the scope of this book, a continuum with a known boundary is called a domain. The basis of FEA relies on the decomposition of the domain into a finite number of subdomains (elements) for which the systematic approximate solution is constructed by applying the variational or weighted residual methods. In effect, FEA reduces the problem to that of a finite number of unknowns by dividing the domain into elements and by expressing the unknown field variable in terms of the assumed approximating functions within each element. These functions (also called interpolation functions) are defined in terms of the values of the field variables at specific points, referred to as nodes. Nodes are usually located along the element boundaries, and they connect adjacent elements.
The finite element analysis method requires the following major steps:
- Discretization of the domain into a finite number of subdomains (elements).
- Selection of interpolation functions.
- Development of the element matrix for the subdomain (element).
- Assembly of the element matrices for each subdomain to obtain the global matrix
- for the entire domain.
- The imposition of the boundary conditions.
- The solution of equations.
- Additional computations (if desired).
Description:
Vibration:
Vibration is the periodic motion of a body or system of connected bodies displaced from a position of equilibrium. In general, there are two types of vibration, free and forced. Free vibration occurs when the motion is maintained by gravitational or elastic restoring forces, such as the swinging motion of a pendulum or the vibration of an elastic rod. Forced vibration is caused by an external periodic or intermittent force applied to the system. Both of these types of vibration can either be damped or undamped. Undamped vibrations can continue indefinitely because frictional effects are neglected in the analysis. Since in reality, both internal and external frictional forces are present, the motion of all vibrating bodies is actually damped.
Mode shape:
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.
Objective:
- To find out 5 mode shapes and list the resonant frequencies.
Figure: Flow of the project.
Steps Followed:
- 3D CAD Models are created on the basis of the drawings provided by skill Lync.
- Simulation add-in is selected and a new frequency study is created.
- Material is provided to the model as alloy steel(default).
- Bearing fixture constraints is provided on the stepped sides of the shaft.
- Discretization is done using the meshing command.
- The study is run and results are saved.
- Mode shapes are defined.
- The results are studied.
Results:
Mode Shape 1
Mode Shape 2
Mode Shape 3
Mode Shape 4
Mode Shape 5
Frequency v/s Mode Shape:
Frequencies of Mode shapes
Conclusions:
Resonant frequencies are as follows:
Link for CAD files: https://drive.google.com/file/d/1-b_QDU47k80A3UEkAmb-_y_oLOUUcdP8/view?usp=sharing