*2.5. Windings Clearance*

The clearance between two adjacent windings is calculated as in [14]. Taking a wedge of *hwed* = 4 mm is required to hold the windings in place, the stator pole arc length *ts* at the closest point of the winding to the center of the shaft is given by:

$$t\_s = (\frac{D}{2})\beta\_s + 2h\_{wd\text{\textquotedblleft mm.}}\text{ mm.}\tag{3}$$

Accounting for the wedges that hold the windings in place leads to the calculation of a modified stator pole pitch *pb* as:

$$p\_b = \frac{\pi (D + 2h\_{\text{used}})}{P\_s}, \text{ mm.} \tag{4}$$

Assuming a suitable value of allowable current density (*J* = 6 A/mm2), the area of conductor *ac* is calculated. Hence, the wire diameter (*dw*) including insulation is obtained from standards wires tables. The maximum height of the winding (*hw*) is obtained by subtracting a margin length (*hwed*) from stator pole height (*hs*):

$$h\_{\rm w} = h\_{\rm s} - h\_{\rm wvd} \,\text{mm.}\tag{5}$$

Assuming *Kf* = 0.95 fill factor, the number of layers that can be accommodated in this available winding height is given by:

$$\mathcal{N}\_{\upsilon} = \frac{h\_{w}\mathcal{K}\_{f}}{d\_{w}}.\tag{6}$$

The value of *Nv* is rounded off to the nearest lower integer. Now the number of horizontal layers required for winding is given by:

$$N\_{\rm li} = \frac{T\_{\rm pli}}{N\_{\rm v}}.\tag{7}$$

The space between 2 stator pole tips at the bore is given by:

$$Z = p\_b - t\_\text{ }\text{mm.}\tag{8}$$

The width of the winding *wt* is given by:

$$w\_t = d\_w \frac{N\_h}{K\_f} \text{ mm.}\tag{9}$$

The clearance between the windings at the bore is given by:

$$CL = Z - 2w\_l \text{ mm.}\tag{10}$$

This value has to be positive and preferably greater than 3 mm. Here it is allowed greater than 0.5 mm.

## *2.6. Average Torque Calculation*

Average torque of SRM is calculated based on the assumptions that flux linkage (*λ*) vs. current (*i*) characteristics are available and phase current is kept constant at its maximum value between the unaligned and aligned positions [2].The average torque is the total work done per stroke multiplied by number of strokes of one revolution divided by 2*π*:

$$T\_{av} = \frac{\mathcal{W}P\_s P\_r}{4\pi}, \text{ N.m} \tag{11}$$

$$\mathcal{W} = \mathcal{W}\_{aligunc} - \mathcal{W}\_{unaling\,\,{n}} \tag{12}$$

where *Waligned* and *Wunaligned* are the areas under *λ* − *i* curves at aligned and unaligned positions, respectively. W is the area of energy loop and then calculated as in [22].

#### *2.7. Losses and Efficiency Calculation*

The prediction of switched reluctance motor efficiency requires knowledge of losses [18,24]. The calculation of losses in the SRM, especially the assessment of core losses, is a very difficult task mainly because the flux waveforms are non-sinusoidal and the differences in shape of flux density waveforms in the different sector of SRM's magnetic circuit. Furthermore, core losses are also conditioned by the type of control used and rotation speed(*ω*). For low speeds, the mechanical losses can be neglected. Hence losses may be calculated as:

$$Losses(\omega) = \text{Core Loss} + \text{Copper Loss.} \tag{13}$$

Once the losses are obtained the efficiency is calculated as follows :

$$\eta = \frac{\omega T\_{av}}{\omega T\_{av} + Losses(\omega)}.\tag{14}$$

In this paper, the speed at which efficiency is calculated is the rated speed of 1000 rpm for all SRM designs candidates. Copper losses value depends on the control technique used as it impacts the value of phase current. Considering n is number of phases, *Rj* is phase dc resistance and *Ij* is phase current, total copper loss instantaneous value may be calculated by the equation:

$$P\_{\rm cu}(t) = \sum\_{j=1}^{j-n} I\_j^2(t) R\_j. \tag{15}$$

The average copper losses can be calculated by equation:

$$P\_{cu} = \frac{1}{T} \int\_{0}^{T} P\_{cu}(t)dt,\tag{16}$$

where, *T* is the period of time for *Ps*/2 strokes. For sake of simplification, we assume no overlap between phases. Since the current of phase is not pure dc. The peak value of it (*Ip*) is considered for copper losses calculation as a pessimistic prediction. Copper loss is then calculated straight forwardly by the equation:

$$P\_{\rm cu} = I\_p^2 R\_{\rm plr}.\tag{17}$$

## *2.8. Eddy Currents Losses*

Referring to [25] the eddy current losses in SRM can be calculated by the equation:

$$P\_{t'} = \frac{e^2}{4k\_{\rm circ}\rho\_{fc}\delta} \frac{1}{T} \int (\frac{\partial B}{\partial t})^2 dt \text{ } w/k\text{g}\_{\prime} \tag{18}$$

where *e*: sheet thickness in meter, *kcir*: constant (1 < *kcir* < 3) introduced to account for the fact that paths in the interior of the lamination will have smaller emfs than those near the surface; *ρf e*: the electrical resistivity of the ferromagnetic material (in Ωm); *δ*: density of the ferromagnetic material (in kg/m3).

From Equation (18), the waveform of flux density (*B*) for all SRM sectors must be known. Once they are available, *Pe* is calculated by numerical integration and differentiation. There are a lot of methods to obtain these waveforms and many of them are time consuming. In [18], a mathematical method using matrices is introduced to obtain the waveforms of all the SRM sectors in a systematic manner. The calculation of *B* waveforms for all sectors is achieved by modulation of triangular pulses. The stator poles waveforms consist only of unipolar triangular pulses, while those of the rotor poles contain both positive and negative pulses. The stator and rotor yoke waveforms have more complicated relationship with the triangular pulses. This method is demonstrated in details in [18] and used here for 8/6 and 6/4 SRMs.
