## 3 Applications of the Measurement System
### Experimental Procedure
#### 3.1.2 Measurement of the Electric Resistance, Dynamic Self and Mutual Inductance of Motor Windings  
Figure 16 shows an experimental setup for measuring the electric resistance of the stator or rotor winding of an electric motor. Figure 15: Experimental setup for the measurement of the moment of inertia of the rotor of an electric motor. Experimental Procedure  
In the figure, \(R_{w}\) and \(L_{w}\) denote the electric resistance and inductance of the winding. During the experiment, the voltage drops on the winding (\(U_{w}\)) and the shunt resistor (\(U_{shunt}\)) are measured at constant current intensity. The intensity of the current flowing through the winding (\(I_{w}\)) can be calculated from the voltage drop on the shunt resistor. Varying the intensity of the current with the variable load resistor, \(U_{w}\) can be given as a function of \(I_{w}\). If the heating of the winding and shunt resistor is negligible, this function is linear, and its slope gives the electric resistance of the winding. It must be emphasized that in the case of a brushed motor, the voltage drop on the rotor winding cannot be measured through the carbon brushes. If we do this, the brush voltage will also be included, and the function mentioned above will not be linear. The details of this phenomenon and the measurement procedure of the brush voltage can be found in References [26; 30]. In Figure 17, an experimental setup for measuring the self-dynamic inductance of a motor winding is presented. Figure 16: Experimental setup for measuring the electrical resistance of motor windings. Figure 17: Experimental setup for measuring the self-dynamic inductance of a motor winding. Experimental Procedure  
The winding of the analyzed motor is excited by the AC power source presented in Section 2.3. During the measurement, the voltage drops on the shunt resistor (\(U_{shunt}\)) and the winding (\(U_{w}\)) are measured as the function of time. From the voltage drop on the shunt resistor, the current intensity through the winding (\(I_{w}\)) can be calculated. After that, the magnetic flux over the winding is calculated by the following formula:  
\[\psi_{w}(t)=\int_{0}^{t}(U_{w}(t)-R\cdot I_{w}(t))\cdot d\tau+\psi_{w}(0) \tag{3}\]  
From the \(\psi_{w}(t)\) and \(I_{w}(t)\) functions, the self-dynamic inductance can be calculated as a function of current intensity (\(L_{w}(I_{w})\)). The detailed mathematical procedure is presented in [26], together with experimentally determined self-dynamic inductances for a series-wound DC motor. The application of these inductances as input characteristics of a motor simulation program module is also presented in [26]. Figure 18 shows an experimental setup for measuring the mutual dynamic inductance between the stator and rotor windings of a series-wound DC motor. Experimental Procedure  
The stator and rotor windings have to be electrically disconnected during the measurement. The stator winding is supplied with direct current. The armature winding is rotated at a fixed, constant angular speed \(\omega\) in the magnetic field of the stator winding, and the voltage (\(U_{rw}\)) induced in it is measured. For rotating the armature winding, the three-phase induction motor is used in the \"drive motor\" mode (C6, Section 2.2). The intensity of the current flowing through the stator winding (\(I_{sw}\)) is varied, by adjusting the  
Figure 18: Experimental setup for measuring the mutual dynamic inductance between the stator and rotor windings of a series-wound DC motor. resistance of the load resistor \((R_{load})\). The mutual dynamic inductance can be calculated from the quantities above according to the following formula:  
\[L_{s,r}=\frac{U_{rw}}{\omega\cdot I_{sw}} \tag{4}\]  
It must be emphasized that at a given \(I_{sw}\) current intensity, the \(\frac{U_{rw}}{\omega}\) ratio is independent of the value of \(\omega\). Thus, the mutual dynamic inductance is a motor characteristic which depends only on the intensity of the current flowing through the motor.