hzgzh / flywheel

Finite element tool for gyroscopic systems

Flywheel

Finite element method (FEM) formulation of rotating equipment in Julia language, featuring lateral dynamics with 1-D Euler-Bernoulli beam shaft segments, gyroscoping coupling and linear bearing impedance.

Features:

• Importing of custom machinery geometry from file
• Calculation of inertia, gyroscopy, damping & stiffness matrices
• Estimation of resonance frequencies and deformation due to gravity
• Time-transient numerical simulation with stiff ODE solvers

Usage

Edit the blueprint file "Rotor_Sample.txt", cf. headers file "Rotor_Sample_Entries.txt" for the meaning of each column.
Hint: Flywheel_blueprint("Rotor_Sample") shows a machine overview, bearings are depicted as triangles, solid discs as grey elements.
M,G,D,K=Flywheel_fematrices("Rotor_Sample") returns the finite element matrices based on your rotor dynamic system:
\

GravForce=Flywheel_gravity("Rotor_Sample",9.806,K) depicts the static deformation due to gravitational acceleration of 9.806m/s^2:

Flywheel_waterfall(M,G,D,K,1000,500,10000) creates a waterfall diagram of eigenfrequencies between the rotational speeds 1000 and 10000 rev/min, in 500-steps:

A,B=Flywheel_statespace(M,G,D,K,800) generates the state matrix A and input matrix B in the state-space domain, at a rotational speed of 800rev/min:
Flywheel_modes("Rotor_Sample",A,9) illustrates the 9th lowest natural bending mode:

Installation

• Fetch the code from github locally, place it into your directory.
• In Julia, run as: (v1.5) pkg> add "C:\Users\myusername\.julia\dev\Flywheel".
• Then add the package with using Flywheel and place the "Rotor_Sample.txt" blueprint in your current Julia directory.

References

• Linear and Nonlinear Rotordynamics: A Modern Treatment with Applications, Second Edition by Y. Ishida and T. Yamamoto (ISBN 978-3-527-40942-6)
• Dynamics of Rotating Systems" by G. Genta (ISBN 978-0-387-28687-7)

License

GPL-3.0 License

Author

Lysandros Anastasopoulos