# Squirrel-cage rotor

The Phelps Dodge magnet wire chart Table 2. Views Read Edit View history. Guarded motors have mesh or wire over the openings to prevent objects being pushed or reaching into the motor. Slip ring induction motor are used where high starting torque is required i. The simulated stator is presented in Figure 1. The brushes are used to carry current to and from the rotor winding. The induction motor is also called a synchronous motor as it runs at a speed other than the synchronous speed.

## The Impact of the Rotor Slot Number on the Behaviour of the Induction Motor

This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The impact of the rotor slot number selection on the induction motors is investigated. Firstly, analytical equations will reveal the spatial harmonic index of the air gap magnetic flux density, connected to the geometrical features and the saturation of the induction motor.

Then, six motors with different rotor slot numbers are simulated and studied with FEM. The stator is identical in all motors. Their electromagnetic characteristics, such as electromagnetic torque, stator current, and magnetic flux density, are extracted and compared to each other.

The analysis will reveal that the proper rotor slot number selection has a strong impact on the induction motor performance. During the last years, ships have become increasingly dependent on electricity. The new trend to the electric ship design, the integrated electric ship, combines the propulsion system and the ship service electrical system, into a single power system.

In this system, the induction motor is used in several applications. Such applications are the propulsion motor, the thrusters, and other various drives, such as pumps and hoists [ 1 ].

It is known that the application of electric machines in an electric ship should meet special requirements [ 2 ]. Reliability and improved efficiency come first, where there is also a great need for low-noise operation. In the past, the design and analysis of electric machines were carried out with the use of equivalent circuits and analytical equations. Those methods did offer sufficiently accurate results for a reasonable amount of time. Despite that, those methods did not take into consideration the geometric features of the machine, as well as the complex nonlinear behavior of the magnetic materials.

The rapid advance in computer science, in the last years, gave the opportunity for computational methods to evolve. One of those methods is the finite-element method FEM. With the aid of a FEM software, an engineer can design accurately the machine, by also providing the conducting and magnetic properties of the materials used. Then, the simulation carried out solves the Maxwell equations, in space and time, offering a much more accurate solution than the classical methods.

The induction motor design is strongly connected to the power electronics design, since different motor configurations strongly affect its electromagnetic characteristics. This is the reason for extensive research worldwide [ 3 , 4 ]. This paper constitutes a study of the impact of the rotor slot selection on the electromagnetic characteristics of the 4-pole, 3-phase, and aluminum cage induction motor, with the use of FEM. In the past, with the aid of analytical calculations and experimental results, many empirical formulas have been proposed concerning the proper selection of the rotor slot number and its influence on cage induction motors [ 5 — 7 ].

The use of FEM offers an insight into the motors' electromagnetic behavior as well as a quantitative representation of their electromagnetic variables and puts the analytical methods under test. In order to perform a realistic comparison between the designed motors, several aspects had to be taken into consideration.

Firstly, the stator of all simulated motors should be exactly the same. Secondly, most geometrical rotor variables had to be intact in all motors. So, the rotor shaft diameter, the depth of the rotor bars, and the air gap length are the same in every case.

Furthermore, there should be an analogy between the number of the rotor slots and their surface as well as their slot openings. For example, if one doubles the number of rotor slots, he should also have half the slot opening as well as half the bar surface.

In this way, the motors have equal rotor resistance and at the same time equal equivalent air gap. It is obvious that the rotors should be parameterized. For this purpose, a code was written and implemented in the design software. The code was transformed from a previous version [ 8 ], which was created in the Laboratory of Electromechanical Energy Conversion, in order to serve this study's requirements.

The stator used for the simulations is chosen from a real motor in the Laboratory, whose resistance was calculated through DC current injection and also whose geometrical variables were known.

The simulations carried out are AC time-harmonic and take into account the nonlinear magnetic characteristic of the rotor and stator iron core. In this work, the authors will firstly present the harmonic index of the radial component of the air gap magnetic flux density with analytical calculations, in a 3-phase induction motor. Then, with the aid of FEM, the results from six simulated induction motors with different rotor slot numbers will be shown and discussed.

Five of the motors have even rotor slot numbers, where one has odd. The selected numbers are 24, 28, 30, 40, 41, and The motors are considered to be unskewed for every case. The identification of each harmonic's origin is of great value, as it will offer an insight of the air gap magnetic flux density, as well as it will be used later in this work, in order to validate the FEM results. According to [ 10 ], the air gap relative permeance is given by where and are related to the stator and rotor slot geometrical variables.

Two analytical formulas have been proposed to describe them. The first one is by Dabrowski [ 11 ] and Voldek [ 12 ] and the second by Heller and Hamata [ 13 ] and Weber [ 14 ]. So if we introduce 7 , 8 , and 9 into 6 , then where. The radial component of the air gap magnetic flux density can be calculated by or if is divided into the stator and rotor MMF contribution to the magnetic flux density: In order to examine each term of 12 , is divided into four components: From 17 and 19 , the space harmonics which depend on the stator and rotor MMF and the rotor and stator slot numbers , are presented, respectively,.

The equations shown in 20 offer useful information about the magnetic field's distribution. The motors that will be simulated have 4 magnetic poles and 36 stator slots. As a consequence, and , which is a multiple of 3 and 4. So, if the number of rotor slots is also a multiple of 4, there will be only odd harmonic rank numbers in the magnetic flux density.

If the number of rotor slots is a multiple of 2 e. According to [ 15 , 16 ], the air gap relative permeance takes the following form in order to take into account the iron core saturation, considering the fundamental harmonic: So, the influence of the rotor and stator MMF on the magnetic flux density due to the saturation will be. Equation 23 due to 22 results in. From 24 , one may observe that the harmonic ranks of the air gap magnetic flux density due to saturation obey to.

From 20 and 25 , we get that harmonic numbers such as 3, 5, and 9 are produced from both the stator slots existence and the iron core magnetic saturation. Furthermore, the analytical solution leads to the result that the space harmonic rank of the air gap magnetic flux density, because of saturation, is always an odd number, as expected.

The six simulated motors have the same stator, whose geometrical and electromagnetic variables are known as it is a real stator. The simulated stator is presented in Figure 1.

It has 36 stator slots and the 3 phases are delta connected. The rotors are created using a parameterized code developed in the Laboratory. The selected rotor slot numbers are 24, 28, 30, 40, 41, and The numbers are selected after a research with analytical equations and previously published works [ 17 ].

The created rotors are presented in Figure 2. Many of the initial design activities for various winding patterns can be traced back to the s and earlier based on work done on three-phase ac windings. This subsection reviews the various winding line connections, the key winding patterns and hookups, various winding constants, and winding selection and design techniques.

There are other basic decisions that must be made by the design engineer before a BLDC motor design can commence. Previously defined is the number of phases, which is three here. Next in importance is the number of poles. The use of two poles is waning, and the use of six or eight poles is increasing. Four-pole BLDC motors are among the most popular used today. Two-and four-pole BLDC motor designs are used here, but the rules for two and four poles can be extended to higher pole counts.

The number of stator slots and teeth and the winding pattern are key design decisions. This section is dedicated to reviewing the important parameters of these two design decisions. The three-phase winding always develops positive starting torque, no matter where the rotor starts its motion.

There are many winding line connections that can be used in three-phase drive systems. The half-wave wye is the simplest three-phase line configuration Fig. It uses three power lines and one return line four leads. The excitation is shown adjacent to the schematic in Fig. Only 33 percent one lead of the half-wave wye windings are energized at any time in operation. The second wye winding, the full-wave wye Fig. The excitation scheme is shown to the right of the schematic.

The third major winding connection pattern is the delta, shown in Fig. It possesses the same excitation scheme as the full-wave wye. The wye is more popular with the larger-sized integral-horsepower BLDC motor users.

The final winding to be reviewed is the independent winding line connection Fig. In this scheme, each winding is independent of its neighbor. The excitation scheme is more complicated, but each winding can be operated in parallel, thereby distributing the total current. This winding configuration has seen limited use to date. The most popular winding line configurations are the full-wave wye and the delta. There are many types of winding patterns that can be utilized. Four major winding patterns are listed here: Constant integral pitch—lap winding full 2.

Variable pitch—concentric winding 3. Constant fractional pitch—lap winding for even or odd stator slots 4. Half-pitch Each of these winding patterns has two coils per stator slot. There is one winding type designated, a consequent pole winding where there is only a single coil per slot.

Consequent pole windings are very popular in single-phase ac motors of fractional-horsepower size. It displays the various sta-tor slot and rotor pole combinations along with the maximum number of parallel circuit combinations with a specific slot and pole combination.

For purposes of simplicity, either or slot stators are used here to illustrate the various winding patterns.

In one case, a slot stator is used to illustrate an odd-slot fractional-pitch lap winding. If one uses a slot stator winding, there are two full-pitch integral lap windings available, one for two poles and the other for four poles.

The coil pattern for this winding configuration is shown in Figs. There are really 12 coils used in this design, but only 6 are shown.

There are two 1- to 7-throw coils—one inserted on the right side CW direction , the second inserted on the left side CCW direction , and doubles on the other five coils also, inserted as described previously. Note the position of the teeth for the slot stator. So the 1, 2, 3 winding phase hookups displayed in Fig. The series and parallel hookup options are very important from a practical aspect of magnet wire size selection.

BLDC stator slot than larger ones. Since total turns per phase are directly proportional to torque, putting all the needed turns N per phase in a single coil with smaller magnet wires and then paralleling the coils will yield extra space for more turns. This is a packing factor consideration. The disadvantage of using parallel coils is that both sets of coil leads must be used to properly connect the coils see Fig. Remember that there are 2 slots per coil per phase for this 2-pole stator-slot winding pattern.

It is also possible to connect two coils in series and two coils in parallel to achieve a series-parallel hookup. Note the shorter length of these coils because the end turns are shorter while the segments of the turns conductors within the appropriate stator slots remain the same length. The variable-pitch winding was developed to reduce the stator end-turn height caused by the numerous adjacent coil crossovers by nesting the coils inside each other, as shown in Fig.

This pattern can be used only when coils per phase per pole n is 2 or greater. The actual winding pattern is shown in Fig. The following equation describes the method used to determine the two variable winding pitches: The average of these two variable-pitch coils should equal the integral winding pitch for a 3-phase 2-pole slot design, which is 6.

This winding pattern will reduce end-turn height and coil lengths by 10 to 15 percent.