Slot Pitch Research Articles

Investigation of Key Parameters on Cogging Torque in Permanent Magnet Machines Based on Dominant Harmonic Contents

The investigation of design parameters on the cogging torque has been a classical and common research subject over the last few decades. Nevertheless, an accurate analysis of major contributors to the cogging component is still difficult to find in past published works. This paper aims to address this knowledge gap by identifying the dominant harmonic contents responsible for the amplitude of cogging torque. As a result, a new factor is introduced to denote the level of cogging torque, rectifying the defect of the well-known existing factor called the goodness factor. The correlations between the key parameters (i.e., pole and slot numbers, pole arc to pole pitch ratio, and slot opening to slot pitch ratio) and the cogging torque are clarified by the proposed methodology. Finally, finite element (FE) and statistical results demonstrate the validity of the proposed results. It is expected that the key findings reported in this paper will serve as a valuable reference in the field of electric machines.

A pole-changing flux reversal permanent magnet motor

In this paper, a pole-changing (PC) flux reversal permanent magnet (FRPM) motor is proposed for obtaining a wide speed range. According to the general air-gap field modulation theory, the permanent magnet (PM) magnetic field is modulated into a series of harmonics with different pole numbers by rotor teeth. By introducing an especial PM arrangement, two groups of working harmonics with different pole-pair numbers are generated in the proposed 12-7 PC-FRPM motor due to the modulation of rotor teeth. Based on the calculated slot pitch angles of these harmonics, two winding connections can be obtained for PC operation to achieve two operating modes. The electromagnetic performance of PC-FRPM motor before and after PC are analyzed using finite element analysis and verified by the experimental test results.

Design and Optimization of a Pole Changing Flux Switching Permanent Magnet Motor

A flux switching permanent magnet (FSPM) motor is designed and optimized in this paper to achieve high torque density and expanded speed regulation range from a design viewpoint of pole-changing (PC). Based on the field modulation theory, the PM field in the FSPM motor is modulated by the stator and rotor teeth, generating rich harmonics with different pole-pair numbers in the air-gap flux density. By adopting an appropriate slot pole combination, working harmonics with different slot pitch angles are obtained to establish a basis of the PC-FSPM motor. Then, different working harmonics can be used to achieve different energy conversions with different winding configurations, so the PC operation can be performed to realize the high torque and wide speed regulation range by switching the working modes. Based on the field modulation theory, the operation principle of conventional and PC-FSPM motors are analyzed and compared. Then, according to the design principle of the PC-FSPM motor, a 24/22-pole PC-FSPM motor with the E-core is designed and optimized by a multi-level optimization method. Finally, the electromagnetic performances are analyzed by finite element analysis and the test results of the prototype have verified the feasibility of the motor.

Comparative Study of Various Slot Pitches for 2-Pole 6-Slot Ultra-high-Speed Permanent Magnet Synchronous Motors

The 2-pole 6-slot permanent magnet synchronous motor (PMSM) is an attractive option for ultra-high-speed (UHS) applications due to its excellent manufacturability and balanced magnetic force. UHS PMSMs should be designed with short stack lengths and end coil heights to address rotor dynamics issues. Additionally, given their high frequency, these PMSMs should be designed considering stator iron loss, rotor eddy current loss, and AC copper loss. The performance of the same pole-slot combination varies significantly based on the slot pitch. Hence, we compared the size and efficiency of the 2-pole 6-slot UHS PMSM based on the slot pitch. For a fair comparison, an optimal design was performed for each slot pitch. To reduce computation time, optimization was conducted in two stages: size minimization and efficiency maximization. It was confirmed that in terms of total axial length, the 1-slot pitch UHS PMSM is the shortest due to the advantage of having a short end coil height, even with the lowest winding factor and largest stack length. Furthermore, it was determined that the 2-slot pitch UHS PMSM offers an excellent trade-off between efficiency and size.

An optimized stator and rotor design of squirrel cage induction motor for EMU train

This paper aims to objectively calculate the 480-kW squirrel cage induction motor (SCIM) design for the electric multiple unit (EMU) trains. This is done by optimizing the stator slot and rotor slot design to get efficiency and power factor targets. The stator slot design is achieved by limiting the width and height of the stator slot pitch according to the specified range. A depth-to-width ratio is used according to the range to optimize the design of the rotor bar slot. The design process of the induction motor consists of three steps: it determines the specification design target, calculates the specified parameters of the induction motor, and simulates the design to obtain the most optimal motor design using ANSYS Maxwell. The simulation performance values obtained an efficiency of 92.547 % and a power factor of 0.915. This value is obtained from the optimization of the rotor slot and has met the minimum requirements of efficiency and power factor in designing a SCIM. The design proposed in this paper can be developed and applied in the Indonesian domestic railway manufacturing industry.

Using grey wolf optimizer to minimize voltage total harmonic distortion of a salient-pole synchronous generator

It is important to calculate the optimum design parameters of synchronous generator (SG) to obtain the desired total harmonic distortion (THD). In this study, we aim to determine the optimum rotor design parameters of SG by using grey wolf optimizer (GWO) algorithm. For this purpose regression modelling is performed to mathematically modelling the relationship between the selected rotor design parameters (factors namely slot pitch, center slot pitch, and damper width) and THD (response). This factor combination is not previously investigated in the related literature. Then by using GWO the optimization is performed on this regression equation. Maxwell simulations have been used for numerical experiments. The results of GWO are compared with the results of genetic algorithm (GA). The results indicate that the GWO algorithm can be well adapted to similar optimization processes and can be effectively used. As a result, the voltage THD of the SG is reduced to 0.3951 under the acceptable magnetic flux conditions. This GWO aided optimization study is significant in that it demonstrates how the performance of SG can be improved by making minor changes to the production line that has been adjusted for mass production without changing the outer diameter and dimensions of SG.

Optimalisasi Antena Mikrostrip Tiga Pita Untuk Penerapan Pada WLAN dan WiMAX

Wired WLAN (Wireless Local Area Network) technology emerged as the most widely used network. WLAN is suitable for those who need internet. By using WLAN will be found various advantages for its users. Likewise with WiMAX (Worldwide Interoperability for Microwave Access) wireless technology, WiMAX basically has a function similar to WLAN, but with certain small differences. WLAN can cover one local area, in contrast to WiMAX which can cover a metropolitan area of ​​up to 50km. Antenna is an integral part of WLAN and WiMAX. This paper discusses a three-band microstrip antenna optimized for WLAN and WIMAX technology. The antenna consists of two layers of FR4 (epoxy) printed circuit board (PCB) with a thickness (h) of 1.6 mm, a dielectric constant (εr) of 4.4, and a dielectric loss factor (tan) of 0.02 with dimensions of 35 mm × 48 × 1.6 mm . This antenna is simulated using CST software. The design of the Studio Suite 2018 antenna is done by adjusting the size of the slot spacing, the length of the slot, the size of the ground clearance, and the size of the board length. In this antenna design, the slot size can be increased on the left side of the patch to increase the slot pitch for a deeper return loss, and the right side of the patch to increase the slot pitch for a shorter return loss. The results in the simulation process obtained good working frequency, bandwidth and return loss, the antenna can operate at the expected frequencies, namely 2.4 GHz, 3.2 GHz, 5.1 GHz with a return loss of -42 dB, -44 dB, - 31 dB. Bandwidths 114.4 MHz, 121.2MHz and 287.9MHz.

Method for weakening cogging torque of built-in permanent magnet synchronous motor by auxiliary slot

The cogging torque is an unavoidable property of the permanent magnet motor, which will cause the motor to generate vibration and noise during the movement, and deteriorate the motor performance. In order to decrease the cogging torque of the permanent magnet synchronous motor, by analyzing the cogging torque expression, it is known that opening auxiliary slots in the rotor can decrease the cogging torque. Influence of slot pitch on cogging torque. The simulation results show that when the slot depth is 0.6mm, the slot width is 1.7mm and the slot spacing is 1.56, the cogging torque is most obvious reduced, and the cogging torque is decreased by 53.6% compared to the non-grooved state.

Optimization design and drag reduction characteristics of bionic borehole heat exchanger

As a renewable energy source, geothermal energy has drawn attention because it is clean, low-carbon, resource-rich, stable, and sustainable supply. In the mining and operation of a geothermal energy system, there is a certain amount of fluid resistance in the borehole heat exchanger where the fluid flows. As the resistance in the conventional borehole heat exchanger (CBHE) accumulates with the length increase, the pumping power increases, resulting in energy loss and affecting the operation of the entire geothermal system. A bionic borehole heat exchanger (BBHE) is designed using a circular groove as a bionic unit based on the bionic non-smooth surface hypothesis. Its structural characteristics are the circular groove’s depth, width, and slot pitch. Where the fluid faces the least resistance, minimization of the pressure drop was the optimization goal. Based on the outcomes of a CFD numerical simulation and genetic algorithm optimization study. These are the BBHE’s ideal structural parameters: diameter is 60 mm, 66 mm for the groove width, 418 mm for the slot pitch, and 80 mm for the groove depth. Compared to the CBHE, under identical numerical simulation settings, the fluid resistance reduction rate of BBHE can reach 13%. Increasing fluid velocity in the BBHE can increase the temperature transmission rate. The study’s findings can serve as a reliable source of scientific information for the use and management of geothermal energy.

Optimal design of q ‐axis field winding structure of dual‐excited synchronous condenser

The dual-excited synchronous condenser (DESC) has two field windings whose axes are located at direct and quadrature axes respectively. The DESC has more capacity of absorbing reactive power than that of the traditional synchronous condenser (TSC). However, the q-axis field winding distributed on the d-axis magnetic pole surface can decrease the magnetic circuit area of the rotor core of DESC, thus it may result in the increase of the total harmonic distortion (THD) of the magnetic field and the oversaturation of the rotor magnetic circuit. In order to obtain better electromagnetic characteristics of DESC, a q-axis field winding structure is proposed by optimising the number of slots, slot pitch and slot dimensions. The influences of the number and pitch of slot in q-axis on the air-gap radial flux density and THD of DESC are studied under the d-, q- and dual-axis excitation modes. The dimensions of the q-axis slots are optimised by combining the time-stepping finite element method and Taguchi method, and the optimal structure of q-axis field winding is obtained. A 10-kVar DESC is developed to verify the simulation results. This study provides theoretical basis for the design and manufacture of the DESC.

Optimization Design and Analysis of Bionic Friction Reducing Nozzle in Oil Shale High-Pressure Jet Mining

The borehole hydraulic mining method has unique advantages for underground oil shale exploitation. Breaking rock with a high-pressure water jet is a crucial step to ensure the smooth implementation of borehole hydraulic mining in oil shale. The hydraulic performance of the nozzle determines the efficiency and quality of high-pressure water jet technology. To obtain a superior hydraulic performance nozzle, based on the bionic non-smooth theory, a circular groove was selected as the bionic unit to design a bionic straight cone nozzle. The structural parameters of the circular groove include the groove depth, width, and slot pitch. The optimization objective was to minimize the pressure drop, where the fluid has the least resistance. A genetic algorithm was used to optimize the structural parameters of the circular grooves in the inlet and outlet sections of the bionic straight cone nozzle. The optimal structural parameters of the nozzle were as follows: the inlet diameter was 15 mm, the inlet length was 20 mm, the outlet diameter was 4 mm, the length-to-diameter ratio was 3, and the contraction angle was 30°. In addition, in the inlet section, the groove width, slot pitch, and groove depth were 3.9 mm, 5.2 mm, and 5.5 mm, respectively, and the number of circular grooves was 2. Moreover, in the outlet section, the groove width, slot pitch, and groove depth were 2.25 mm, 3 mm, and 5.5 mm, respectively, and the number of circular grooves was 2. The CFD numerical simulation results showed that under the same numerical simulation conditions, compared with the conventional straight cone nozzle, the bionic straight cone nozzle velocity increase rate could reach 13.45%. The research results can provide scientific and valuable references for borehole hydraulic mining of high-pressure water jets in oil shale drilling.

Rotor design optimization of a synchronous generator by considering the damper winding effect to minimize THD using grasshopper optimization algorithm

The aim of this study is to calculate the optimum factor levels for the design parameters namely slot pitch, center slot pitch, and damper width to keep the magnetic flux density distribution in a desired range while minimizing the total harmonic distortion (THD). For this purpose, the numerical simulations are performed in the Maxwell environment. Then by the aid of regression modeling over this simulation results; the mathematical equations between the responses (THD and magnetic flux density distribution) and the factors are calculated. After the modeling phase, grasshopper optimization algorithm (GOA) is run through these regression equations to determine the optimum values of the rotor design parameters (factors). The confirmations are also performed in the Maxwell environment and the result indicated that the THD is minimized and the magnetic flux density distribution on the teeth is kept in a desired range.

A Pole-Changing Doubly Salient Permanent Magnet Motor

This article presents a new pole-changing (PC) doubly salient permanent magnet (DSPM) motor. According to the general air-gap field modulation theory (GAFMT), the permanent magnet excitation field can be modulated by the stator and rotor teeth to a series of harmonics with different pole-pair numbers and different slot pitch angles. Thus, when the armature winding is connected and reconnected according to the different excitation field harmonics, the PC operation can be realized to obtain a high torque density at the low-speed region and a widened speed regulation range with a simple motor structure. According to the GAFMT, the operating principle of the proposed motor is introduced, and the winding connection is discussed. Then, to verify the validity, the electromagnetic performance of the proposed motor is analyzed by the finite element analysis. Finally, a prototype is built and tested.

Slotless Disk Type Resolver: A Solution to Improve the Accuracy of Multi-Speed Wound Rotor Resolvers

A common solution for increasing the accuracy of wound-rotor (WR) resolvers is to increase the number of poles. To achieve a compact design, fractional slot concentrated winding (FSCW) is used for multi-pole WR resolvers. However, employing such windings leads to rich sub-harmonics in the induced voltages. To suppress these undesirable sub-harmonics, multi-layer windings with an appropriate shifting angle between the layers are suggested. However, the said shifting angle is limited by the slot pitch so that the capability of the multi-layer winding is not utilized fully. To overcome the mentioned deficiency, a slotless disk type configuration is proposed in this article. Then, an optimization based on the winding function (WF) model of the sensor is carried out to achieve an optimal winding configuration. 3-D time-stepping finite element method (FEM) is used to verify the success of the proposed analytical model and the performed optimization. Finally, a prototype of the optimal configuration is built for experimental measurements.

극 슬롯 조합에 따른 영구자석 표면 부착형 동기전동기의 특성 분석 연구

In this paper, the characteristics of SPMSM (Surface mounted Permanent Magnet Synchronous Motor) applied to EPS(Electric Power Steering) systems were analyzed according to the combination of pole slots. In general, fractional-slot permanent magnet synchronous motors using concentrated windings have advantages such as being more economical than distributed windings, having shorter end windings, and high copper fill factor. However, traditional permanent magnet synchronous motor having the fractional slot has a relatively low winding factor due to the slot pitch and pole pitch ratio. One way to compensate for this is to use a modular motor with fewer slots for a given number of poles. The modular motor is a motor with the number of slots per pole per phase less than 0.5, and the winding factor is larger than that of the traditional motor. Therefore, in this paper, three types of motors: fractional slot modular motors, traditional motors, and integer slot motors, were analyzed and the power characteristics were compared using the FEM(Finite Element method).

Novel Quasi-Three-Dimensional Modeling of Axial Flux In-Wheel Motor With Permanent Magnet Skew

This paper presents a characteristic analysis of axial flux permanent magnet machines (AFPMMs) for in-wheel electric vehicles. Preferentially, a novel quasi-3-D model is developed for the fast and accurate design of AFPMMs. In electromagnetic field analysis, combined with field reconstruction method, the computation time of 2-D solutions is significantly reduced. With the use of time sweeping of the basis function, only the static finite element (FE) analysis is performed to calculate the air-gap flux distribution at the entire rotor position, whereas the conventional 2-D solutions require a transient FE analysis. In the shape sweeping process of the basis function, the virtual air-gap section method is introduced to take into account that the ratio of slot opening to slot pitch is different depending on the radius of analysis plane, which causes errors in the analysis results of the conventional quasi-3-D method. The virtual air-gap sections are obtained by interpolation of the spatial field between the mapped cylindrical planes. The proposed technique reduces the number of 2-D analysis planes required for high accuracy in the conventional quasi-3-D method, and it can also predict the air-gap magnetic flux distribution for skewed permanent magnets without additional FE analysis. Finally, using the magnetic fields calculated in the proposed method, the electromagnetic performances of the AFPMM are calculated, such as load torque, cogging torque, attraction force, and back-EMF. The analysis results were verified by comparison with the measurement results.

Stator flux barriers to improving interior permanent magnet motor characteristics

There are many methods to improve the characteristics of permanent magnet motors. One of them is by making flux barriers on the stator or rotor, or both. This paper discusses the adding stator flux barriers on the rectangular-shaped stator of the interior permanent magnet motor. The purpose is to increase the maximum rotation of the machine. The shape of the flux barrier is circular considering the ease of the manufacturing process, with the proposed diameter is one slot pitch. Several diameters of larger and smaller sizes will also be simulated for comparison. Other parameters, which are cogging torque and stator core loss, are also investigated. Design and simulation are carried out analytically and numerically using 2D finite element analysis. The simulation results indicate that the proposed flux barrier diameter can provide the maximum rotation with only a tiny decrease in output torque. In this regard, it can be concluded that the stator flux barriers affect the speed than output torque. Additional advantages are also obtained from the decrease in cogging torque and core loss at the base speed compared to a stator without flux barriers.

Primary Resonance Analysis of Permanent Magnet Synchronous Motors Caused by Unbalanced Magnetic Pull

The dynamic behaviors of permanent magnetic synchronous motors considering unbalanced magnetic pull have been extensively investigated. However, the harmonics and cogging effects are ignored and the stator and the rotor are assumed to be smooth cylinders. In this research, an analytical expression of unbalanced magnetic pull considering harmonics and cogging effects is obtained. Based on the model, the motion equations of the rotor system are established. The natural frequency and frequency-response are analyzed by average method, and stability of periodic solution is investigated by Routh-Hurwitz criterion. The analysis indicates that the natural frequency is closely related to stator slot parameters. The frequency-response shows that the amplitude varies between the two static equilibrium points. Besides, when the ratio of slot width to stator slot pitch is close to the peak value, the amplitude tends to be increasing obviously. It is useful for the design of permanent magnet synchronous motors with high stability and low vibration.

Electromagnetic Analysis and Performance Investigation of a Flux-Switching Permanent Magnet Machine

This paper aims to present a general and effective analytical approach to calculate the air gap flux density and the back electromotive force (EMF) of a flux-switching permanent magnet (FSPM) machine. The proposed analytical expression of the air gap flux density is based on an improved air gap permeance function considering the geometries of slotted stator core pieces and magnets between stator teeth as well as the salient rotor poles. The back EMF equation is accurately derived using the proposed air gap flux density equation expressed in terms of practical machine dimensions and thus it provides the key design factors as well as details of the back EMF production mechanism. To validate the proposed analytical expressions, they are applied to the case study of a 12-slot 10-pole FSPM machine, and the finite element analysis results confirm the analytical predictions. Besides, for the proposed analytical model, the effects of the machine’s geometries on back EMF characteristics are investigated. The investigation shows that the ratio of rotor slot opening to slot pitch has a significant effect on the back EMF, and its optimal value is suggested. The proposed equations also provide a mean to choose the slot and pole combinations to obtain a higher power density.

Механическая прочность и твердость полимерных материалов, радиационно сшиваемых рентгеновским излучением электрического газового разряда

The article considers the design of a homopolar inductor machine excited from an integrated winding that concurrently produces the rotating armature magnetic field and the excitation field. The use of an integrated winding makes it possible to simplify the machine design, to decrease the consumption of insulation and structural steel, which simultaneously serves as part of the externally closed magnetic core for the passage of excitation flux in the axial-radial direction. The integrated winding distribution among the coil phases for the multiphase version is detailed, and the integral MMF distribution curve for the three-phase four-pole version of the winding is plotted. More accurate dependences for calculating the electromagnet torque of a motor with tooth structures on the rotor and stator are proposed that take into account the change of the gap permeance when the rotor is shifted by half the slot pitch. The torque values are substituted in the Arnold constant equations for determining the bore diameter in designing. A formula for estimating the thermal state of the machine with an integrated winding is given. A conclusion about the possible application fields of homopolar inductor motors with the integrated winding has been drawn: for operation in repeated short-term modes, when there is a need to force the torque, and when used in combination with a permanent-magnet machine on a common shaft.