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

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ravishankar on 13 Mar 2013
Answered: Steve Miller on 4 Aug 2020
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 on 13 Mar 2013

Steve Miller on 4 Aug 2020
There are a set of transmission templates in Simscape Driveline that would be a good starting point:
The equations you cite could be put into a custom Simscape language block to handle the nonlinear effects.

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