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+# Wind turbine gearbox simulator
+![Static Badge](https://img.shields.io/badge/Octave-11.1.0-orange)
+![Static Badge](https://img.shields.io/badge/Arch%20Linux-6.19.12-blue)
+![Static Badge](https://img.shields.io/badge/Gnuplot-6.0%20patchlevel%204-yellow)
+![Static Badge](https://img.shields.io/badge/Gitlab-repo-red?logo=Gitlab)
+
+
+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
+```bash
+$ 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
+```bash
+: '
+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
+![Model](images/kinematicscheme.png)
+
+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 :
+$$
+\{q\} = \{x_1, y_1,\theta _{11},\theta_{12},x_2,y_2,\theta_{22},\theta_{21}\}
+$$
+
+### Equations of movement
+
+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:
+$$
+\left[M\right]\{\ddot{q}\} + \left(\left[K_{mesh}\right](t)+\left[K_{cst}\right]\right) \{q\} = \left\{F(t)\right\}
+$$
+Where $K_{cst}$ represents the constant terms $k_{i_j}$ and $K_{mesh}$ the terms related to the gear mesh stiffness $K_e(t)$.
+
+### Mesh stiffness
+
+
+
+### Forces
+
+
+
+## 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
+