## 4 Experimental Results  
The performance of two different IMs (SIEBER LS71, denoted as IM#1 and ATB SEVER 1.2K90 L-6, denoted as IM#2), with the parameters given in Table 10 in the Appendix B, has been investigated to confirm the accuracy of the derived expressions. The experimental setup for testing these machines was realized in the Laboratory for Electric Machines and Drives at the Faculty of Technical Science, University of Kragujevac, Serbia. First, the initial tests (open-circuit and short circuit-tests) have been carried out  
Figure 3: Impact of variation of the bearing loss on the speed-time curve during no-load direct startup (\(J=9.4\) kgm\({}^{2}\), \(U=200\) V). Figure 2: Impact of variation of the supply voltage on the speed-time curve during no-load direct startup (\(J=9.4\) kgm\({}^{2}\) and \(B=0.1\)). to determine the equivalent motor parameters, and the obtained values of the equivalent circuit data are presented in Table 1.  
Second, to determine the friction torque and bearing losses, both motors were powered using a Danfoss frequency converter. A resistance-current compensation was carried on the frequency converter; therefore, the torque was constant for all frequencies, allowing parallel mechanical (i.e., torque-speed) characteristics during recording. Further, the motor load (directly proportional to the friction torque) at different speeds was determined using the triangle similarity rule. With the resistance-current compensation enabled at voltage/frequency (_U/f_) control (and slip compensation disabled), one can roughly assume that all the machine characteristics (the torque as a function in the speed) would be parallel as frequency changes in a speed frame of interest. In that case, any difference in the speed (with an unloaded machine) will reflect the friction torque. Thus, the small changes in speeds at different frequencies have been recorded, and the friction torque was calculated in a wide-speed region. \(B\)'s value was determined from the value of this torque (\(M_{riction}=B^{*}n\)), as shown in Figure 4 for both machines. Catalog data of the value of the moment of inertia was already known for both motors. It should be noted that the friction torque is not linear with speed, especially at low speeds. Stribeck friction cannot be neglected at low speeds. However, in the literature, the friction torque is usually linear with speed as it mainly reflects viscous friction in bearings. This approximation was made in this work, and the friction torque was considered viscous torque because it would be hard to experimentally determine the Stribeck friction component that exists only at low speed. Another way to determine the friction torque is to form the speed response characteristic with a switched-off motor at high speed. However, complex mathematical investigations will be needed to model the non-linear region accurately. A precise recording of the two analyzed machines' run-up was performed. It was realized by an encoder on the motor shaft and a digital signal processor (DSP) that collects data at 100 ms. The speed recording for IM#1 and IM#2 was performed using different voltage values--130 V and 190 V for IM#1 and 125 V and 150 V, for IM#2. All the records were identified where the motor is turned on at 100 ms. The measured and the simulated results are presented in Figures 5 and 6, for both machines. The perfect agreement between all simulated and measured results is apparent. Figure 4: Measured load torque-speed of rotation characteristics: (**a**) experimental setup, (**b**) IM#1, and (**c**) IM#2. Figure 5: Measured and simulated speed-time characteristics of IM#1. The methods presented in [8] and the proposed method based on the Kloss equation provide the most considerable deviations from the measured values. The main reason is that the Kloss equation does not represent an ideal approximation for a real torque-speed curve. However, the proposed method based on the Thevenin theorem gives the best matching results with the experimental results.