## 1 Introduction

Currently, the electric motors are widely used in industry, transport and households. Depending on needs, they may operate with fixed or variable speed. Among those who work at a constant speed, driving pumps, compressors and fans, it is possible to indicate synchronous reluctance motors [1], induction motors and PM motors. Popularity of reluctance motors stems from a relatively simple rotor structure in relation to e.g. induction motor or permanent magnet motor [2, 3, 4]. In general it leads to higher efficiency, lower manufacture cost with respect to other electric motor types. It should be pointed that synchronous motors typically are not line-start motors, but thanks to design solution a self-start is possible [5]. For low-power and fractional power motors, this is the valuable advantage, because due to their cost, it does not require the use of electronic inverters (which are relatively expensive with respect to the motor). To meet this challenge, the designers create a hybrid motor (combining the features of an induction motor and synchronous reluctance motor) having the ability to self-start. Sometimes the reluctance rotor includes magnets, thus increasing the torque generated by a synchronous motor. The solution of the self-start-up problem, in synchronous reluctance motors, consist in selection one of the possible solutions: additional use of the classic rotor cage (for the "classical" and the flux-barrier rotors [6]), partial or complete filling of rotor recesses using e.g. aluminum [7, 8], which is available for the flux-barrier rotor. Both solutions provide the motor start-up, whereas at work with synchronous speed, they are only a source of the Joule loss in the “cage” (due to the existence of the magnetic field harmonics in the air gap).

For several years the use of SMC materials, as a part of electric motors, was tested [9, 10, 11, 12, 13]. The main reason of these tests is the core loss reduction, which is especially important for motors energized by sources generating waveforms with the frequency greater than 50 Hz (e.g. 400 Hz). Another reason is the possibility of building the cores having shapes not available to “classic” technology (using magnetic laminations), and cores having isotropic magnetic properties in any direction. In the case of the fractional power motors, having relatively small geometrical dimensions and fed by a 50 Hz AC source, the best solution appears to be the use a SMC material in the rotor [14, 15, 16]. Then the mechanical strength of the SMC material (which is lower than that of laminations) plays no important role, whereas the possibility of rotor core design, capable to produce a motor possessing expected dynamics, becomes important. Please note that the “classic” cutting technology “generates” zones of material with worse magnetic properties and this fact should be taken into account in the motor design.

The authors of this paper examine the mass-produced 120 W line-start synchronous reluctance motor (LSSR motor), having a cage rotor ensuring the self-start. The rotor is tested both with two magnetic materials: the magnetic laminations and widely available SMC material.

## 2 Characteristic of examined LSSR motor

Modeling and simulations were carried out for mass-produced 4-pole, three-phase, line-started synchronous reluctance motor of a 120 W nominal power. At the nominal work conditions the motor is energized from 400 V/50 Hz mains. The stator and rotor geometries as well as the slot number of the stator and rotor, have been adopted from the mass-produced induction motor of similar nominal power. The magnetic asymmetry of the rotor (the rotor has "classical" structure) has been achieved thanks to cut out of several teeth in the rotor laminations – Fig. 1. The presence of the rotor cage guarantees self-start of the motor (in a similar manner to a rotor cage existing in an induction motors).

Commercially available reluctance motor is made of commonly used M600-50A magnetic laminations having width of 0.5 mm. The authors dealt with the problem of improving the dynamics of this motor. For this reason, a number of rotor geometries were analyzed and checked whether it is possible to construct motor comprising a core made of a SMC material, without affecting the worsening of dynamics and performance of the motor. So, the simulations were carried out for two types of magnetic materials that can be used in rotor construction: the commonly used material (M600-50A) as well as commonly available on the market the Somaloy500 SMC material.

## 3 FEM modelling activity

For the calculations and simulations, the authors used OPERA 3D commercial software, which guarantee the solution of the non-linear magnetic problem, taking into account the eddy currents induced in the rotor cage as well as rotor movement. The use of 3D model resulted from the existence of rotor slots’ skew. The authors are familiar with 2D solutions, which include, in an approximate way, this parameter. But we decided to use a full 3D model, realizing the extension of computing time. Built models took into account the dynamic phenomena occurring in the electromagnetic field, in electrical circuits and mechanical system of the motor. The built 3D FEM model is described by very well known Maxwell’s equations

where *H⃗*,*J⃗*,*B⃗*,*E⃗* are magnetic field strength, current density, flux density and electric field strength vectors, respectively. Moreover, *u⃗* and *A⃗* are velocity and magnetic potential vectors, respectively.

In regions where the field is only derived from a vector potential, the following equations, as a combination of Eq. 1-5, is used

where *V* is an electric scalar potential, *μ* is the magnetic permeability, and *σ* is the electric conductivity.

In the analyzed FEM model, in the rotor there are conductive elements leading to induced eddy currents. The dimensions of these elements are so large that it is necessary to solve the problem of taking into account the uneven distribution of induced currents. This is achieved by solving an extra equation for each region which leads to induced currents.

where *Ω* is the volume where eddy current exists, *S* is the cross section of the element.

Together with the field equations the circuit and mechanical equations were solved. The voltage equation for the stator winding can be written as:

where *U _{ph}* is the instantaneous phase voltage on the stator winding,

*R*is the winding resistance,

*i*is the instantaneous current in the winding,

*N*is the number of turns,

*Ψ*is the magnetic flux linkage (calculated by field equations). Taking into account the wire diameter of the stator winding, the skin effect was ignored when calculating the resistance.

Equation (8) can be written into a new form, using the calculated vector potential *A⃗*.

where *S _{c}* is the cross section of the stator winding,

*A*is the z-component of vector potential.

_{z}The rotor speed can be calculated based on the mechanical equation

where *T* is the sum of the electromagnetic torque computed by the program, friction and load torques, *J* is the polar moment of inertia, *θ* is the position angle.

The authors considered many rotor’s structures (the stator geometry and the stator winding parameters remained constant), took into consideration the minimization of tools cost. Examples of analyzed rotor geometry are shown in Fig. 2.

The study was conducted by energizing the motor by 50 Hz sinusoidal voltage. The authors studied not only the impact of the rotor geometry on the motor dynamics, but also the possibility of a different magnetic material usage, with respect to the commonly used one (M600-50A). During simulations the SMC material (Somaloy500) available on the market was used. This material has “worse” magnetization curve with respect to the “original” material (see Fig. 3), but thanks to it, we have the possibility to influence the ratio of *d*-axis and *q*-axis reluctances. As it is known, this ratio determines the reluctance torque of the motor, but as shown in the paper, also affects the reduction of parasitic torques that occur during motor start-up (this is the Gorges phenomenon, where there is a significant decrease in the asynchronous torque generated by the motor, existing at half synchronous speed). The proposal to use a SMC material does not increase too much the whole motor cost [15]. Unfortunately, the use of the SMC material significantly increased the magnetizing component of the current, which is of great importance for fractional power motors, where the magnetizing component is a dominant in the consumed current – see Table 1. To reduce this negative effect, we increased the core length by 10% and reduced the air gap thickness by 20%, with respect to the reference motor. In this way we limited the increase in current consumption to 6%, while improving the motor dynamics. A comparison of the rotor speed during start-up, for the geometries shown of Fig. 2a and 2b, is presented in Fig. 4.

Comparison of consumed currents at nominal load

Variant of the rotor geometry | Consumed current (RMS value) [A] | Cage loss [W] |
---|---|---|

Reference motor, M600-50A (Fig. 2a) | 0.434 | 0.976 |

SMC material (Fig. 2a) | 0.480 | 1.145 |

SMC material, wider outher teeth, (Fig. 2c) | 0.467 | 1.227 |

SMC material, core longer of 10%, (Fig. 2a) | 0.478 | 1.143 |

SMC material, air-gap reduced of 20%, (Fig. 2a) | 0.465 | 1.114 |

SMC material, core longer of 10%, air-gap reduced of 20%, (Fig. 2a) | 0.457 | 1.106 |

Additional teeth, M600-50A material (Fig. 2b) | 0.458 | 1.119 |

SMC material, core longer of 10%, air-gap reduced of 20%, additional teeth, (Fig. 2b) | 0.462 | 1.187 |

SMC material, additional horizontal teeth (Fig. 2d) | 0.495 | 2.040 |

A problem, which exists in the test motor, is currents flowing in the rotor cage, even for a synchronous speed – Table 1. They cause Joule losses both in the rotor cage and in the stator winding. Since the rotor cage has a specific structure, so the authors determined current waveforms for the bar located in the “classical” rotor slot, and for the bar located in a “wide” slot. Examples of waveforms are shown in Figs. 5-6.

The dynamics of the reference and the proposed motors can be compared using dynamic curves – see Fig. 7, where faster access to the synchronous speed by motor having the proposed structural solution (specified geometry-Fig. 2b, the SMC material in the rotor, the package longer of 10%, the air-gap width reduced by 20%) is clearly visible. According to the authors, this is the best solution among the analyzed variants.

## 4 Conclusions

The authors dealt with reluctance motor of fractional power, adapted for direct start-up from the mains. The start-up is possible thanks to the rotor construction, which combines the features of an induction and a reluctance motor. Before starting the test the strict limits were imposed with respect to the possible structural changes. The main limitation was to minimize the cost of new tools necessary to build the motor. It was assumed, on the basis of previous works carried out by the authors, that the change will be subject to the rotor only, both in terms of construction and the material from which it is made. We examined the effect of the material change using available on the market SMC material - Somaloy500. The operating conditions were selected as sinusoidal supply voltage, 400 V, 50 Hz, and the rated load torque. The results of the computer simulations lead to the following conclusions:

- –for the motor dynamics improvement, the best solution is the change of the rotor material to the SMC material, supplemented by the package extension by 10%, the air gap reduction by 20% and adding additional teeth (the teeth are a part of the rotor lamination impression, which in the "classical" construction are removed) – see Fig. 2b,
- –to minimize the amplitude of the current flowing through the rotor bars placed in "classical" and “wide” slots (at steady state), the best solution is the rotor made of the "classic" material having additional teeth - see Fig. 2b,
- –to minimize the consumed current (at steady state), the best solution (except reference motor) is the rotor made of SMC material, having an extended package by 10%, reduced the air-gap width by 20%, and having no additional teeth - see Fig. 2,
- –the use of the SMC material in the rotor and the core extension (the length of the stator winding change a bit too), resulted in a reduction of the rated motor efficiency from 70% (for the reference motor) to 68% (for the indicated best solution),
- –additional mechanical studies are needed to confirm possibility of using the proposed SMC material in the rotor (it is known that the mechanical strength of the SMC material is less, than that of the "classic" M600-50A material).

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