Wind turbine gearbox simulator

Wind turbine gearbox simulator is a matlab/octave simulator for a lumped parameters mechanical model of wind turbine gearbox. It implements varying wind profile, defects, varying gear mesh, and compute numerically the dynamical behaviour of the system using a Newmark's scheme.

Dependencies

Development language: Octave 11.1.0

Compatibility: Matlab v2026-a (delete all graphics_toolkit("gnuplot") mentions in the code)

Plot engine: Gnuplot 6.0 patchlevel 4

Usage

$ git clone https://gitlab.com/afoucaultc/wind_turbine_gearbox
$ cd wind_turbine_gearbox
$ octave
$ octave:1> run main.m
$ # or run any standalone (starting by a "_")
$ octave:1> >>> run _[standalone].m

File tree

: '
Main process takes the main parameters and compute the
whole process of calculations. It prints every figure
into .svg files, into folder print/run_print/. The
number of periods to calculate are asked as input when
the code is started.
"class_" are static functions used to calculate and plot
see in-code comments for more informations
'
## Main process
├── main.m
├── main_parameters.m
    ├── run_main.m
    │   └── _convergence.m
    ├── run_display.m
    │   └── class_display.m
    └── run_print.m
: '
Standalone files are files that do a single specific task
that cannot be done by the main process. These starts by
a "_" and can be ran using ">>> run _file.m"
- _init_speed.m calculates the optimal initial speed to 
    avoid the transitionnal regime.
- _rms-analysis.m gives a .csv (in /data) containing the 
    RMS, STD and Kurtosis for different defects conditions
- _animation.m is showing a visual animation of the diff-
    -erent shaft rotations and vibrations
- _gear-mesh-var.m plots the difference of mesh stiffness
    between different center distance error values
- _convergence.m plots the convergence between a high
    sample rate and other sample rates to determine which
    one to choose for minimal numerical error and comput-
    -ational
    time
'
## Standalone functions
├── _init_speed.m
├── _rms-analysis.m
├── _animation.m
├── _gear-mesh-var.m
└── _convergence.m
: '
Rendering folders stores the .csv datasheet and .svg plots
'
## Rendering folders
├── data
│   └── rms.csv
└── print
    ├── _convergence
    ├── _gear-mesh-var
    └── run_print

## Others
├── octave-workspace
└── README.md

Model

As showed on the image, the model is based on 2 shaft with 4DDL each (x, y, input and output \theta), as a lumped parameters model. The parameters are listed as a q vector : {q} = {x_1, y_1,\theta {11},\theta{12},x_2,y_2,\theta_{22},\theta_{21}} The equations of movement are given by the Lagrange formulation, using the kinetic and potential energies.

\left[\frac{\partial E_p}{\partial q_i}\right] + \left[\frac{d}{dt}\left(\frac{\partial E_k}{\partial\dot{q}i}\right)\right] = \frac{\partial W}{\partial q_i} \label{eq:reformlagrange} \ E_k = \frac{1}{2} \left( m_1{\dot{x}1}^2+ m_1{\dot{y}1}^2+ I{11}{\dot{\theta}{11}}^2+ I{12}{\dot{\theta}{12}}^2+ m_2{\dot{x}2}^2+ m_2{\dot{y}2}^2+ I{22}{\dot{\theta}{22}}^2+ I{21}{\dot{\theta}{21}}^2 \right) \ E_p = \frac{1}{2} \left( k{x_1}{x_{1}}^2+ k_{y_1}{y_{1}}^2+ k_{\theta_1}(\theta_{11}-\theta_{12})^2+ k_{x_2}{x_{2}}^2+ k_{y_2}{y_{2}}^2+ k_{\theta_2}(\theta_{21}-\theta_{22})^2+ K_e(t){\delta}^2 \right)

The derivative of these equations is taken to directly get the movement, using: \frac{\partial E_p}{\partial q_i}+\frac{d}{dt}\left(\frac{\partial E_k}{\partial \dot{q}_i} \right) = F_i(t)

The different terms (k and m) are regrouped into matrices, to give the following system: \left[M\right]{\ddot{q}} + \left(\left[K_{mesh}\right]+\left[K_{cst}\right]\right) {q} = \left{F\right} Where K_{cst} represents the constant terms k_{i_j} and K_{mesh} the terms related to the gear mesh stiffness K_e(t).

Development machine specification

Hardware: Thinkpad E560, CPU Intel(R) Core(TM) i5-6200U(4)@2.8GHz, 3.70GiB RAM OS: Arch Linux 6.19.12

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