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. The motors are examined under time-harmonic analysis at starting and at 1440 rpm. 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 [
It is known that the application of electric machines in an electric ship should meet special requirements [
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 [
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 [
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 [
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 used motor is a 3-phase, 4-pole, 4 kW, and 400 V aluminum cast-cage induction motor.
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 48. The motors are considered to be unskewed for every case.
The following calculations will lead to a precise formula of the harmonic content of the magnetic flux density in the induction motor’s air gap. 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 [
According to [
So if we introduce (
The first term of (
The radial component of the air gap magnetic flux density can be calculated by
In order to examine each term of (
From (
The equations shown in (
According to [
So, the influence of the rotor and stator MMF on the magnetic flux density due to the saturation will be
Equation (
From (
From (
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
The simulated stator.
The rotors are created using a parameterized code developed in the Laboratory. The selected rotor slot numbers are 24, 28, 30, 40, 41, and 48. The shape of the bars is chosen to belong to NEMA’s class A design specification. The numbers are selected after a research with analytical equations and previously published works [
The simulated rotors with: (a) 24, (b) 28, (c) 30, (d) 40, (e) 41, and (f) 48 rotor slots.
For the appropriate meshing of the models, the skin and proximity effects are taken into consideration. The mesh for the motor with 28 rotor slots is presented in Figure
The mesh distribution in the motor with 28 rotor slots.
The simulated motors are studied in this paragraph at their starting. The magnetic flux lines distribution is presented in Figure
The magnetic flux lines distribution at starting for the motor with: (a) 24, (b) 28, (c) 30, (d) 40, (e) 41, and (f) 48 rotor slots.
In order to sufficiently compare the starting behavior of the motors, the starting torque and stator current were extracted for each case and they are presented in Table
The starting torque and starting current for all studied cases.
Rotor slot |
Starting |
Starting |
---|---|---|
24 | 66.3 | 65.6 |
28 | 73.3 | 67.2 |
30 | 76.4 | 65.3 |
40 | 72.4 | 65.6 |
41 | 71.9 | 65.7 |
48 | 74.4 | 65.7 |
In this paragraph, the authors will show the air gap harmonic content for every case at 1440 rpm. The spatial harmonic content is the result of the stator and rotor MMF harmonics index, the slot existence, and the saturation of the iron cores. The magnitude of the air gap magnetic flux density is presented for every case in dB in Figure
The magnitude of the air gap magnetic flux density at 1440 rpm for the motor with: (a) 24, (b) 28, (c) 30, (d) 40, (e) 41, and (f) 48 rotor slots.
Firstly, it is obvious that there is a resemblance between Figures
The THD for every studied case.
Rotor slot |
THD (%) |
---|---|
24 | 25.75 |
28 | 22.64 |
30 | 24.23 |
40 | 18.4 |
41 | 25.34 |
48 | 19.03 |
From Table
The motor with 41 rotor slots is obviously a motor with odd rotor slot number. As a consequence, the even higher harmonics have increased amplitudes. This agrees with ignore. Previous work state that motors manufactured with odd rotor slot number are very noisy and have increased mechanical oscillations [
Best cases seem to be the motors with 40 and 48 rotor slots. Their rotors have many slots, and as a consequence their rotor-slot-related harmonics are met in higher ranks and so they have less impact. Also, both numbers are multiples of 4, a fact that has strong impact on the reduction of the rotor and stator-MMF-related higher harmonics, since the motors have four magnetic poles, as already mentioned in Paragraph 2.
In this paragraph, the characteristics of the six motors are presented for speed 1440 rpm. This speed is chosen as a typical value for motors of this size and characteristics. The calculated results are shown in Table
Characteristics of the motors at 1440 rpm.
Rotor slots | Torque (N*m) | Current (A) | Cos |
Pin ( |
Pout ( |
|
---|---|---|---|---|---|---|
24 | 44.93 | 12.79 | 0.85 | 8764 | 6772 | 77.3 |
28 | 48.2 | 12.61 | 0.81 | 8201 | 7264 | 88.6 |
30 | 48.52 | 12.61 | 0.85 | 8693 | 7313 | 84.1 |
40 | 49.09 | 12.55 | 0.87 | 8770 | 7399 | 84.3 |
41 | 48.95 | 12.53 | 0.86 | 8713 | 7378 | 84.7 |
48 | 50.73 | 12.49 | 0.86 | 8704 | 7646 | 87.8 |
Moreover, the motor with 28 rotor slots is characterized by the highest efficiency but on the other hand by a poor power factor.
Furthermore, the motor with 41 rotor slots has an acceptable behavior, since its characteristics are literally an average as compared to the others.
The motor with 40 rotor slots is characterized by the greatest power factor, but by lower efficiency than the motors with 28 and 48 rotor slots.
Finally, the motor with 48 rotor slots presents the greatest electromagnetic torque and output power. At the same time, this motor draws the least stator current. The power factor and the efficiency are the second best. If one takes into consideration the results from the previous paragraphs, it is reasonable to claim that for the stator used, the rotor slot number 48 offers the best motor behavior in general, which means good starting characteristics, high efficiency and power factor, low stator current, and less vibrations and mechanical oscillations at nominal speed.
In order to gain insight of the numerical results presented in Sections
The spatial distribution of the amplitude of the magnetic flux density for the motor with: (a) 24, (b) 28, (c) 30, (d) 40, (e) 41, and (f) 48 rotor slots.
It is clear that the motor with 40 rotor slots presents the greatest amplitude of the magnetic flux density, where the motor with 24 rotor slots presents the least. Moreover, the motor with 24 rotor slots seems to be more saturated and especially at the tooth tips. Furthermore, in the motors whose numbers are not a multiple of 4, such as in Figures
This work studies the influence of several rotor slot numbers on the behavior of the induction motor. FEM analysis indicates that for the selected number of stator slots and number of magnetic poles, the rotors with slot number multiple of 3, do not have higher harmonics multiples of 3 in the air gap magnetic flux density. Also, the extracted results lead to the conclusion that the motor with 48 rotor slots is the best case, while it presents good starting behavior along with low air gap magnetic flux density harmonic content and improved characteristics at nominal speed.
Geometrical angle
Component of the air
Stator slot pitch
Stator angular frequency
Rotor angular frequency
Air
Air
Mechanical angular frequency
Total, stator, and rotor airgap magnetic flux density radial components
Stator frequency
Air
Carter’s coefficient
Synchronous speed
Number of pole pairs
Number of stator slots per phase and pole
Slip.
Stator and rotor slot numbers, respectively
Stator and rotor MMF, respectively
Stator and rotor MMF amplitude, respectively.
This work has been supported by the Research Program “K. Karatheodori 2010” of the Research Committee of the University of Patras, Greece.