matlab code/program to solve 3 dimensional nonlinear variable differential equation using 4-5 order adaptive variable step length RUNGE-KUTTA method

how to get a numerical simulation model using RUNGE kutta nethod in simulink of a nonlinear time varying differential equations. A 3 dimensional nonlinear dynamic model for gear transmission system is to be developed considering the time-varying meshing stiffness,tooth surface friction and backlash and taking into the dynamic distribution of load between each pair of gear. the 4-5 order adaptive variable step length runge-kutta method is to be used to solve the variable differential equations of gear dynamic model.

****Ip(theta double dot p)+rp(k1+k2)s+Tfp=Tp

Ig(theta double dot g)-rg(k1+k2)s+cw(theta dot- theta g dot)+kw(theta-theta g)-Tfg =0

I(theta double dot )-cw(theta dot- theta g dot)-kw(theta-theta g)=-T****

Ip,Ig-moment of inertia of pinion and gear respectively p-pinion ,g-gear k1,k2-meshing stiffness of gear pair, cw,kw-torsional damping coefficent and web torsional stiffness respectively r-radius t-torque theta-angular momentum

the above equations are taken from technical paper"EFFECT OF WEB STIFFNESS AND DAMPING ON THE VIBRATION OF GEAR TRANSMISSION"-2010 2ND international conference on mechanical and electronics engineering

[Ryan G]

Looks like you've got your equations already, check out Seth's post about building ODE's in Simulink.

Answer 1

[Steve Miller]

There are a set of transmission templates in Simscape Driveline that would be a good starting point:

https://www.mathworks.com/help/physmod/sdl/transmissions-1.html

The equations you cite could be put into a custom Simscape language block to handle the nonlinear effects.

https://www.mathworks.com/help/physmod/simscape/lang/what-is-the-simscape-language.html