The diagram and equations (13) and (14), of the behaviour of a DC motor with independent excitation were examined in Figure 8. By simply analysing the rotor circuit of the said figure, the following equation for the rotor's operating voltage "Ur", may be deduced:
From which we can find the value of the current intensity in the rotor "Ir":
And by entering into equation (13), we can find the equation for the motor torque "t", dependent on the angular velocity "co":
By taking equation (18) the following expression can also be found for the angular velocity
By analysing equations (19), (20) and (21), it emerges that:
1. During starting, when "co « 0", the intensity of the current in the rotor "Ir" is very high, since "Ir « Ur/Rr", as the ohmic resistance of the rotor circuit "Rr" is very low. A very high current intensity may burn out the circuits. For this reason, current intensity must be limited during starting.
2. The motor torque "t" during starting is also very high and gradually drops as the motor's angular velocity " " increases. In principal, this is sufficient as the behaviour is similar to that of a constant power hyperbole (remember Figure 5). But during starting, the torque supplied by the motor is so high that it exceeds the wheel-rail adhesion limit. To avoid slip, the starting torque needs to be limited to the allowable values of the adhesion.
3. Consequently, during starting the current intensity must be limited to avoid the circuits burning out and to limit the motor torque, thus preventing the adhesion in the wheel-rail contact from exceeding the limits. The maximum motor torque obtained during starting is called "maximum continuous torque", (see Figure 16). Since the motor torque and the tractive effort "Ft" in the wheel-rail contact are directly related, the maximum available tractive effort "Ft" during starting is also called "maximum continuous effort", (see Figure 5).
Fig. 15. Shunting of DC motors with independent excitation.
When dealing with DC motors with independent excitation the most effective way of reducing motor torque during starting is to reduce the intensity of the current in the stator "Ie", as in equation (20). To this end, a rheostat is placed in series with the stator, with a variable resistance "Re", as can be seen in Figure 15. This is known as "Shunting". As the intensity "Ie" diminishes, the motor speed increases (equation (21), without any excessive increase in the motor torque "t". At the beginning of starting, the value of the Shunting resistance "Re" is maximum, producing a maximum reduction of the current intensity "Ie" and therefore, the magnetic flux induced in the rotor is minimum. This operation is controlled so that the motor torque "t" will be the maximum appropriate one without exceeding the adhesion limits. As the locomotive gradually gathers greater speed, the intensity "Ir" and the motor torque "t" gradually decrease (equations (19) and (20). It is then necessary to increase the motor torque to recover traction capability during starting. To achieve this, the value of the Shunting resistance "Re" is gradually reduced in a controlled manner. Thus, the current intensity "Ie" and the motor torque "t" again increase without exceeding the adhesion limits and recover the locomotive's traction capability (see the "real operational curve” in Figure 16).
Below, we have simulated the operation of a DC motor with independent excitation using the model shown in Figure 9, for different fixed values of the Shunting resistance "Re". The motor has a power of 1200 kW and in the simulation was working under zero load. Figure 16 shows the results of the motor torque obtained for different fixed values of "Re" as a function of the motor's rotational speed, comparing the results with the theoretical torque corresponding to the constant torque hyperbole and also to the maximum continuous torque.
Fig. 16. Simulation results of a DC motor with independent excitation for different values of the Shunting resistance "Re".