Modelling of basic induction motors and source loading in rotor–motor systems with regenerative force field

In this article a short route to arrive at bondgraph model of induction motor is discussed. Creating a model of an induction motor with electrical, magnetic and mechanical ports is a considerably puzzling issue. The usual approach is to view induction motor as an extended transformer with a resistor varying as a function of slip. Such models are inadequate when motors are driving a general class of loads and when electrical input is not a pure harmonic. Though there are several models with intertance fields derived in classical manner they obscure the physics of the system and are often intractable. In this article a general principle of modelling induction motors is presented by viewing the fluctuation of magnetic field from two coordinates, one fixed to stator and other to the rotor. The mechanical port emerges out naturally and the model is computationally efficient and compact. An interesting phenomenon of such a motor driving a rotor with material damping beyond its threshold speed of instability is simulated and discussed. Rotors with internal damping tend to become unstable when driven beyond a speed which is entirely determined by a ratio of external and internal dampings and the critical speed. When such rotors are driven by an induction motor with supply frequency beyond the threshold speed of instability very interesting phenomena are observed in the coupled system like entrainment of rotor speed, existence of limiting oribit of the rotor, small fluctuation of angular speed caused by unbalance and seemingly chaotic behaviour. This example shows the power of bondgraph modelling of induction motor with a mechanical port which can be coupled to a general class of loads.