Bond Graphs Modelling of Electromagnetic Actuators International Journal of Mechatronics and Applied Mechanics, 2017, Issue 1 118 BOND GRAPHS MODELLING OF ELECTROMAGNETIC ACTUATORS Constantin Niţu 1 , Bogdan Grămescu 2 , Mihai Avram 3 1,2,3 University POLITEHNICA of Bucharest 313, Splaiul Independenţei, 060042-Bucharest, Romania constantin.nitu@upb.ro Abstract. The paper presents the model of an electromagnetic actuator, developed in 20 sim environment, by use of Bond Graph method. The software facilities are exploited by using both signal block diagram and the power bond graph elements within the same model. The models of the flux raising stage, when the armature doesn’t move and the dynamic period, until the armature ends its stroke are presented. These ones take into account only the saturation of the core magnetization curve, but not its nonlinearity. The data used for simulation are from an experimental tested device, so, both calculated and measured results can be compared. Keywords: Bond Graphs, Mechatronics, Electromagnetic Actuator, Dynamic Behaviour, 20 SIM. 1. Introduction Many industrial applications make use of binary state actuators, with limited displacement, which are electrically driven. Hydraulic/pneumatic distributors, intake/exhaust valves for camless variable distribution of the spark ignition engines, electric power switching devices or mobile robots are common examples [1], [2], [3]. Their main feature is quick switching between two stable positions, one stroke being obtained by electromagnetic forces, while the return is accomplished by help of springs. Sometimes, they have to keep one of the two stable positions for a shorter or longer period, according to the operation cycle of the system to which they belong. Some applications, like electromagnetic actuation of the intake and exhaust valves of the automobile engines, meant to contribute to the fuel economy, power increasing and pollution diminishing, enable computer control of the valves motion as concerns stroke, duration of the movement and frequency, following programmable laws as the essential difference from the actual mechanisms which have fixed and previously determined laws [4]. 2. Actuator Model An electromagnetic actuator is, in fact, a mechatronic system, which operates in transient regime. It consists of the driving circuit, the electromagnet and the driven mechanism. Its regular use is for the applications which require small strokes, constant amplitude and high frequency. Some typical examples are related to the hydraulic/pneumatic valves and electromechanical switching devices. During the last years, a special interest for this type of actuating was shown in the automotive industry for actuating the intake/exhaust valves of the thermal engines. When modeling the operation of such actuators, one should take mainly into consideration the position, velocity and acceleration of the moving parts, in different stages of an operation cycle, as well as the current and generated force evolution, power consumption, duration and settling time. Mechatronic approach is obviously because the equations describing the electric circuit, magnetic behavior and the mechanism dynamics have to be solved simultaneously. The simplest driver for an inductive load, with a constant voltage applied to the coil, is shown in figure 1. It is based on the switching operation of the transistor, which is open for the period , when the electric circuit equation is: Ri dt d u    (1) where: =N - magnetic flux linkage in the coil; N- number of coil turns; i – current; R – electric resistance of the coil; u = VC – VCE .