A non-linear model to approximate the dynamics of a pulse width-modulated spray nozzle

This paper deals with the mathematical model construction of a PWM-nozzle in order to analyse the impact of its dynamics on the flow discharge through multiple simulation tests. A structured analysis is proposed where the system is divided up into two linked subsystems: an electromagnetic subsystem and a mechanical subsystem. Due to the ferromagnetic property of the solenoid, hysteresis effects occur that have been approximately described by third order polynomial functions. The motion of the core inside the solenoid is defined by linear differential equations (mass spring–damper subsystem) with these differences that the displacement is physically restricted, Coulomb friction is appended and the initial preload of the spring is covered so that the final solution is non-linear. An experimental test in which the resulting displacements of the core due to a voltage pulse input are compared with the model simulations demonstrates the exactness of the model.