ELECTROMECHANICAL SYSTEMS
Electromechanical systems such as electric motors and electric pumps are used in most indus- trial and commercial applications. Figure 2.19 shows a simple d.c. motor circuit. The torque produced by the motor is proportional to the applied current and is given by
where T is the torque produced, kt is the torque constant and i is the motor current. Assuming there is no load connected to the motor, the motor torque can be expressed as
As the motor armature coil is rotating in a magnetic field there will be a back e.m.f. induced in the coil in such a way as to oppose the change producing it. This e.m.f. is proportional to the angular speed of the motor and is given by:
where Va is the applied voltage, and L and R are the inductance and the resistance of the armature circuit, respectively. From (2.79),
Models of more complex d.c. motor circuits are given in the following examples.
Example 2.11
Figure 2.20 shows a d.c. motor circuit with a load connected to the motor shaft. Assume that the shaft is rigid, has negligible mass and has no torsional spring effect or rotational damping associated with it. Derive an expression for the mathematical model for the system.
Solution
Since the shaft is assumed to be massless, the moments of inertia of the rotor and the load can be combined into I , where
where Va is the applied voltage and L and R are the inductance and the resistance of the armature circuit, respectively. Substituting (2.80), we obtain
