# Dynamic Test Measurements and Simulation on a Series Wound DC Motor
## 3 Measurements
### Dynamic Test Measurements
#### 3.2.1 Determination of Dynamic Input Parameters  
Several different methods [16; 18; 19; 20] exist for the determination of the moment of inertia of the rotor (\(J_{r}\)). A well-known method is when an additional point-like load with precisely known mass is attached to the rotor at a given distance from its axis of rotation [18]. Figure 4: Results of a dynamic test measurement performed on the analysed SWDCM. (\(J_{load}=0.0001576\) kg\(\cdot\)m\({}^{2}\)). (**A**) Battery terminal voltage, (**B**) motor speed, and (**C**) current intensity. If the obtained system is deflected from its equilibrium position, it will be swinging. The unknown moment of inertia of the rotor can be calculated from the measured time period. In our case, because of the relatively high value of friction torque, the above method could not be applied. Without removing the rotor from the motor, the value of \(J_{r}\) can also be determined from the second stage of the run-out experiments [16; 19; 20]. Figure 5 shows the results of the second stage of the run-out experiments. The slope of the measured angular speed-time function gives the angular acceleration (\(\varepsilon\)) of the rotor. Table 1 shows the magnitude of angular accelerations at different mechanical loads. Equation (3) gives the connection between friction torque \(M_{res}\) (bearing plus brush friction) and angular acceleration \(\varepsilon\):  
\[(J_{r}+J_{load})\cdot\varepsilon=M_{res} \tag{3}\]  
It can be seen that both \(J_{r}\) and \(M_{res}\) are unknown in Equation (3). Thus, the results of two independent run-out experiments, applying different mechanical loads (load pair), can be compared and then the values of \(J_{r}\) and \(M_{res}\) can be calculated from the obtained system of equations, providing that \(M_{res}\) has the same value in both cases. The main drawback of this method is the above assumption which can introduce systematic error in the calculated value of \(J_{r}\). The results obtained applying the above method with different load pairs are shown in Table 2. \begin{table}
\begin{tabular}{c c c} \hline
**Load** & \(J_{load}\) [kg\(\cdot\)m\({}^{2}\)] & \(|\varepsilon|\) [rad/s\({}^{2}\)] \\ \hline Disc 1 & 0.0001576 & 30.331 \\ Disc 2 & 0.0018561 & 27.273 \\ Disc 3 & 0.0035496 & 25.516 \\ Disc 4 & 0.06785 & 6.5519 \\ \hline \end{tabular}
\end{table} 
Table 1: Magnitude of the rotor’s angular acceleration at different mechanical loads. Figure 5: Results of the second stage of the run-out experiments. In the scientific literature, there are advised methods to eliminate the above drawback [18]. However, for their application, the realisation/production of an additional experimental set-up is necessary. Another accurate method can be realised by removing the rotor from the motor (Figure 6) and measuring \(J_{r}\) with an independent procedure. Following that, perform a run-out experiment, and then calculate the value of \(M_{res}\) from Equation (3). In our case, the above independent procedure was a roll-down experiment (Figure 7) on an incline made of aluminium. The mass of the rotor (\(m\)), the rolling radius (\(r\)), the incline angle (\(\alpha\)), and the position of the centre of mass of the rotor (\(s\)) as a function of time were precisely measured. The \(s(t)\) function was derived from a video record made by a high-resolution camera. From the position-time function, the velocity-time function, and then the acceleration of the centre of mass of the rotor (\(a_{c}\)) was determined. Since rolling friction between the rotor and the incline is not negligible, two independent roll-down experiments are necessary in applying different incline angles (\(\alpha_{1}\) and \(\alpha_{2}\)). From the two experiments come two equations with two unknowns. One of them is the moment of inertia of the rotor (\(J_{r}\)), and the other one is the arm of rolling friction (\(k\)).