**3. Results**

#### *3.1. Parameters, Optometric Analysis and Steady-State Characteristics*

The computer models for BM, M1, M2, M3 and M4 that allow calculation of motor parameters and steady state characteristics are the first part of an analysis of all motor models. The motor parameters and operating characteristics are obtained as output data from these computer models for analytical calculation of the models. The obtained parameters and operating characteristics are presented in Table 4 for the rated load operating regime.

**Table 4.** Motor parameters and characteristics at rated load.


Models M2, M3 and M4 are derived by taking into consideration the optometric analysis, i.e., the results obtained from it (the value of CPS, MT, MW and ORD for the adequate motor model). The M2 model has the biggest efficiency and overloading capability along with the smallest consumption of the permanent magne<sup>t</sup> material. This model is chosen for further comparison with the model BM. The data for the stator winding of model M2 are presented in Table 5. The data of stator, rotor and magnets geometry for model M2

are presented in Table 6. The presented data in Table 6 are supported by drawings of stator and rotor slot of model M2 presented in Figure 5.

**Table 5.** Data of stator, rotor winding and magnets of model M2.


**Table 6.** Dimensions of stator and rotor lamination and magnets.


The steady-state characteristic of the efficiency, power factor and torque for BM and M2 are presented in Figures 6–8, respectively. The steady-state characteristics should support the data, presented in Table 4, i.e., for the adequate torque angle, the rated values of efficiency, power factor and torque should be obtained.

The impact of each varied parameter (CPS, ORD, MT and MW) on efficiency, power factor, starting torque and maximum output power is analyzed by varying the parameter of interest within the prescribed limits while the rest three parameters are constant and equal to the values presented in Table 4 for the model M2. The analysis originates directly from the optometric analysis and allows for the impact of each parameter on motor operating characteristics to be evaluated separately. The impact of CPS on efficiency, power factor, starting torque and maximum output power is presented in Figure 9.

**Figure 5.** Dimensions (**a**) magnets (**b**) stator slot (**c**) rotor slot.

**Figure 6.** Steady-state characteristics of efficiency (**a**) BM (**b**) M2.

**Figure 7.** Steady-state characteristics of power factor (**a**) BM (**b**) M2.

**Figure 8.** Steady-state characteristics of torque (**a**) BM (**b**) M2.

**Figure 9.** Impact of CPS on (**a**) efficiency (**b**) power factor (**c**) starting torque (**d**) maximum output power.

A similar analysis is performed for determining the impact of ORD, i.e., air gap length, on efficiency, power factor, starting torque and maximum output power. The obtained results are presented in Figure 10. The impact of MW on efficiency, power factor, starting torque and maximum output power of the motor is presented in Figure 11. The similar analysis for the impact of MT is presented in Figure 12.

**Figure 10.** Impact of ORD on motor operating characteristics (**a**) efficiency (**b**) power factor (**c**) starting torque (**d**) maximum output power.

**Figure 11.** Impact of MW on motor operating characteristics (**a**) efficiency (**b**) power factor (**c**) starting torque (**d**) maximum output power.

**Figure 12.** Impact of MT on motor operating characteristics (**a**) efficiency (**b**) power factor (**c**) starting torque (**d**) maximum output power.

#### *3.2. FEM and Transient Models*

The FEM models of the motors allows for the calculation of magnetic flux density distribution in the cross-section of motor models by solving the magnetic vector potential in the small areas of the mesh that are created in the cross-section of motors. The obtained results of magnetic flux density distribution in the motor cross-section are presented in Figure 13.

**Figure 13.** Flux density distribution (**a**) BM (**b**) M2.

The transient characteristics of speed, torque and line current, when the motor is accelerated with the rated load, are presented in Figures 14–16 for models BM and M2, respectively. The motor is supplied with network voltage and accelerated with rated load of 14 Nm coupled to the motor shaft and load inertia of 0.0066 kgm2.

**Figure 14.** Transient characteristics of speed-load torque 14 Nm and inertia 0.0066 kgm<sup>2</sup> (**a**) BM (**b**) M2.

**Figure 15.** Transient characteristics of torque-load torque 14 Nm and inertia 0.66 kgm<sup>2</sup> (**a**) BM (**b**) M2.

**Figure 16.** Transient characteristics of current-load torque 14 Nm and inertia 0.66 kgm<sup>2</sup> (**a**) BM (**b**) M2.

The M2 model is simulated for various loads and load inertia. In Figure 17 is presented the characteristic of speed of acceleration of M2 with load torque of 14 Nm and load inertia of 0.37 kgm2, and with 10 Nm and load inertia of 0.24 km2. For the above-mentioned loads and moments of inertia, the characteristics of torque and current of M2 are presented in Figures 18 and 19. The maximum load inertia allowed for successful starting is 0.37 kgm<sup>2</sup> for M2 and 0.17 kgm<sup>2</sup> for BM.

**Figure 17.** Characteristics of speed of M2 (**a**) load 14 Nm, inertia 0.37 kgm2 (**b**) load 10 Nm, inertia 0.24 kgm2.

**Figure 18.** Characteristics of torque of M2 (**a**) torque 14 Nm, inertia 0.37 kgm<sup>2</sup> (**b**) torque 10 Nm, inertia 0.24 kgm2.

**Figure 19.** Transient characteristics of current of M2 (**a**) load torque 14 Nm, inertia 0.37 kgm<sup>2</sup> (**b**) load torque 10 Nm, inertia 0.24 kgm2.
