Torque In Permanent Magnet Machines 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.

Analytical Analysis of Cogging Torque in Permanent Magnet Machines With Unequal North and South Poles, With Particular Reference to Consequent Pole Machines

In this paper, a general analytical model is developed to analyze the cogging torque accounting for unequal north and south poles as well as pole shifting, which can be applied to consequent pole permanent magnet (CPPM) machines and other rotor PM machines. The optimal slot opening and optimal pole-arc to pole-pitch ratio with/without pole shifting for minimum cogging torque are then analytically derived and verified by finite element analyses and experiments. It shows that in contrast to conventional PM machines with equal north and south poles, of which the fundamental cogging torque order is the least common multiple (LCM) between slot number <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N_s</i> and pole number 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> , the fundamental cogging torque order for the PM machines with unequal north and south poles (as often the case in CPPM machines), is the LCM between <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N_s</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> , which has been derived analytically. However, in the special case when the slot number in one submachine is even, the LCM between <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N_s</i> and 2 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> has the same value as the LCM between <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N_s</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> .

Zeroization of Cogging Torque of Permanent Magnet Machines by Optimizing Rotor Surface Shape: Comparison Between Surface and Interior Types

In this paper, we investigate the mechanism of cogging torque reduction by optimizing the rotor surface of permanent magnet synchronous machines. The optimizations of both the surface and interior permanent magnet machines are carried out. It is clarified that the cogging torques of both the machines can be reduced to be nearly zero by optimizing the rotor surfaces, whereas the mechanisms of cogging torque reduction of these machines are completely different from each other.

Cogging Torque Suppression of Modular Permanent Magnet Machines Using a Semi-Analytical Approach and Artificial Intelligence

The cogging torque of permanent magnet machines with a modular stator is affected by additional harmonic components due to the segmentation of the stator lamination. This paper proposes a novel approach based on the shaping of the stator tooth tips with sinusoidal profiles to minimize the cogging torque of such machines. A theoretical study and a design formula are proposed to determine the spatial frequency of the sinusoidal profiles, while an optimization procedure based on genetic algorithm and artificial neural networks is adopted to determine their amplitudes and phase shifts. The proposed method is validated through finite element analysis considering two different case studies. Also, a comparison with other approaches from the literature is presented to highlight the effectiveness of the proposed technique. Finally, an additional analysis is reported to demonstrate the effectiveness of the proposed method against manufacturing and assembling tolerances.

Impact of Selected Methods of Cogging Torque Reduction in Multipolar Permanent-Magnet Machines

This paper focuses on the matter of cogging torque reduction by combining various methods of cogging torque minimization. Due to the high costs of prototype construction, cogging torque is minimized during the design phase by using numerical methods, while computer simulations are used to find a magnetic circuit arrangement for which the cogging torque has the smallest possible value. Cogging torque occurs as a result of combined impact of the magnetic field of a permanent magnet located at rotor and stator with variable magnetic conductivity depending on an angle of rotation. It is a pulsating torque and occurs permanently during machine operation, impacting the operation of the entire device cooperating with the electric machine and causing vibrations, tension, and noise. It results in braking torque and subsequent power losses and leads to faster wear and tear of machine structural elements. High cogging torque values cause problems with rotational speed adjustment. In the case of electric generators used in wind power plants, it impedes the start-up of power plants at high wind speeds. Considering the above, the reduction of cogging torque in permanent-magnet machines is extremely important.

Using and enhancing the cogging torque of PM machines in valve positioning applications

In this study, it is aimed to use the cogging torque of permanent magnet (PM) machines for providing the load torque in the valve positioning applications. The policy is to use the machine cogging torque to overcome the load torque at the steady-state condition (fixed valve position). Therefore, there is no excitation, and no armature Joule losses at the steady-state condition and consequently lower thermal stress for the machine. To have a more compact actuator, it is tried to increase the machine cogging torque. Two well-known types of PM machines, i.e. surface-mounted PM (SPM) and flux-switching PM (FSPM) machines are studied to be applied in this application. Some techniques such as applying auxiliary slots and PM segmentation (for the SPM machine) and two-part rotor topology (for both SPM and FSPM machines) are proposed to increase the machine cogging torque. The impact of each technique on the developed cogging torque is studied by means of finite element analysis. Finally, the SPM and FSPM machines are compared together in the terms of the torque density. The validity of the proposed concept of providing the load torque by the cogging torque is investigated by experimental tests.

Study of The Effect of Height and Length of Slotting in Magnet Edge on the Cogging Torque Reduction of Fractional Slot Number in Permanent Magnet Machine

Cogging torque generated in permanent magnet machine effects to some undesirable vibration and noises. In order to minimize the cogging torque in permanent magnet is the most important issues recently. This paper investigated the influence of the value of height and length of slotting in magnet edge on the cogging torque reduction. For purpose of study the structure of 24 slot/10 pole of permanent magnet machines have been chosen. The 2-D finite element based on FEMM 4.2 software was implemented to compute the permanent magnet machine performance. Simulation results showed that by optimising the height and length of slotting in magnet edge can reduce the cogging torque of permanent magnet machine significantly. The most effective way by employing a-two step slotting with 2.5 mm of height and 0.7 mm of length of the slotting in magnet in the first step of slotting. In the second step of in magnet edge, the length of slotting has been assigned as much as 2.3 mm and the height of slotting was 0.588635 mm. By employing the FEMM, three of different magnet structures of permanent magnet machine were analysed. It was found that the cogging torque of permanent magnet machine proposed magnet structure as much as 99.7 % compared with the initial structure of the permanent magnet machine.

Improving a Cogging Torque Reduction Technique for Fractional Slot Numbers in a Permanent Magnet Machine

For this paper, an improvement to a cogging torque reduction technique was studied in regards to integral slot numbers in a permanent magnet machine. An 18 slot/8 pole permanent magnet machine structure was selected and developed, and some axial channels were introduced to the machine’s rotor core. The effects the axial channels had on cogging torque reduction were not studied in detail; however, it was noted that the channels did not disturb the machine’s normal magnetic flux in regards to an air gap. Two slotting steps were used on the edge of the machine’s permanent magnet with slot opening widths of 2 mm and air gap lengths of 1 mm; this was done in order to minimize cogging torque. Three different magnet structures for the permanent magnet machine were then analyzed and compared. The two steps for slotting were found to be best for cogging torque reduction among the three different structures. Finally, simulation results showed that improving slotting steps for magnet edges could significantly reduce cogging torque in permanent magnet machines by up to 98.80%.

Design and Simulation of Two Phase Doubly Salient Permanent Magnet Machine with a Dual Stator Structure

A new type of doubly salient permanent magnet machine with a dual stator structure is proposed. The motor is designed by staggering two stators by 45°on a 4/6 pole structure of double-salient pole motor. The motor has the advantages of high power density, small pulsation and high efficiency. The basic structure and working principle of the motor are introduced. The air-gap flux is calculated by the simple magnetic circuit method. The no-load magnetic field distribution, air gap flux density and permanent magnet Flux, back EMF, inductance characteristics of the machine are analyzed by using finite element simulation software. The inherent cogging torque of permanent magnet machine is analyzed. The simulation results verify the rationality of the new structure machine.

Effect of Relative Slot-Opening Shift on Cogging Torque and Performance of an Axial Flux Permanent Magnet Machine

Cogging torque in permanent magnet machines is a source of acoustic noise, vibrations and one of the reasons behind output torque ripple. Its reduction is of prime importance in automotive and positioning applications. Several techniques are available in the literature for cogging torque reduction in both radial and axial flux machines. This paper presents the effect of relative displacement of consecutive slot-openings on cogging torque of an axial flux permanent magnet machine. In addition, its influence on several performance parameters such as stator flux linkage, no-load induced emf, emf harmonics and rated electromagnetic torque of the machine is also analysed and compared. A 3-D finite element model of the machine is simulated to obtain various analysis results. A maximum reduction of 51.67% in cogging torque is obtained for 0 or 1 displacement factor. However, the rms-induced emf and average torque showed deterioration by 4.05% and 5.8%, respectively.

Influence of Pole and Slot Number Combinations on Cogging Torque in Permanent-Magnet Machines With Static and Rotating Eccentricities

With the aid of finite-element and analytical methods, this paper investigates the influence of static/rotating eccentricities on the cogging torque of permanent-magnet machines having various pole/slot number combinations (2p/N 8 ), including fractional-slot topologies, such as 2p = N 8 ± 1, 2p = N 8 ± 2, and 2p/N 8 = 8/12, as well as an integer-slot machine 2p/N 8 = 4/12. It is found that the influence of eccentricity reduces significantly with the number of structure cyclic symmetry, which is equal to the greatest common divisor of slot and pole numbers. Hence, the eccentricity shows the largest influence in machines having 2p = N 8 ± 1, small influence in machines having 2p = Ne ± 2, and the smallest influence in the other machines. The static and rotating eccentricities result in cogging torque components multiples of (2p)th and (N 8 )th orders, respectively. Both static and rotating eccentricities produce similar cogging torque magnitude. The experimental results validate the FE and analytical investigation.

A New Method for Minimizing Cogging Torque in Permanent Magnet Machines Using Genetic Algorithm

Cogging torque is one of the main reasons which cause ripple in motor's speed and torque. So the reduction of cogging torque must be considered in the design of permanent magnet machines. This paper presents a new method for cogging torque minimization by optimizing pole-arcs combined with varying the thickness in magnets. With the combination of different pole-arcs of each PM slice to achieve the minimum cogging torque while without being harmful to the average torque. Thus, optimize the offset value which varies the thickness of magnets to further reduce the amplitude of cogging torque. In this paper, it used genetic algorithm (GA) to optimize pole-arcs and magnet offset on the basis of Finite Element Method (FEM).

Minimization of cogging torque in permanent magnet machines using the topological gradient and adjoint sensitivity in multi-objective design

The paper presents an application of the topological derivative and continuum sensitivity analysis for the optimal design of the permanent magnet excited machines with the adjustable excitation. In our work we applied a topological optimization in order to find a general shape of rotor poles consisted of an iron and magnet part. An essential advantage of the proposed method is its numerical effectiveness. In order to verify results, three-dimensional models were developed and thoroughly analyzed. Aspresented in thecomparative analysis of 3D results, theapplied method lead to thesignificant reduction of both, the cogging torque and a level of higher harmonics in the voltage induced in the armature windings.

Integrated Optimization of Two Design Techniques for Cogging Torque Reduction Combined With Analytical Method by a Simple Gradient Descent Method

This paper presents an integrated optimization process to minimize cogging torque in permanent-magnet (PM) machines by a simple Gradient Descent method. The presented optimization method can be easily achieved in machine design. The design techniques of nonuniformly distributed magnets and teeth are presented to illustrate the optimization process. First, with the assistance of an analytical model deduced, the initial solution and feasible domain of the optimization can be easily identified. Then a simple Gradient Descent method is combined with finite element analysis to perform the optimization within the identified feasible domain. Four representative PM machines-including surface-mounted permanent-magnet synchronous machine (SPMSM), brushless DC machine (BLDC), and interior permanent-magnet synchronous machine (IPMSM)-are designed and optimized by the presented method, respectively. The results verify that the presented optimization process can greatly reduce the cogging torque in PM machines. In addition, it is easily achieved and very time-saving. At last, the influence of the nonuniformly distributed magnets method on load torque is examined.

Analytical Methods for Minimizing Cogging Torque in Permanent-Magnet Machines

Cogging torque in permanent-magnet machines causes torque and speed ripples, as well as acoustic noise and vibration, especially in low speed and direct drive applications. In this paper, a general analytical expression for cogging torque is derived by the energy method and the Fourier series analysis, based on the air gap permeance and the flux density distribution in an equivalent slotless machine. The optimal design parameters, such as slot number and pole number combination, skewing, pole-arc to pole-pitch ratio, and slot opening, are derived analytically to minimize the cogging torque. Finally, the finite-element analysis is adopted to verify the correctness of analytical methods.

Cogging Torque Reduction in Permanent Magnet Machines

This paper examines two methods - magnet shifting and optimizing the magnet pole arc - for reducing cogging torque in permanent magnet machines. The methods were applied to existing machine designs and their performance was calculated using finite-element analysis (FEA). Prototypes of the machine designs were constructed and experimental results obtained. It is shown that the FEA predicted the cogging torque to be nearly eliminated using the two methods. However, there was some residual cogging in the prototypes due to manufacturing difficulties. In both methods, the back electromotive force was improved by reducing harmonics while preserving the magnitude.

Torque production in permanent-magnet synchronous motors

An analytical method was developed to determine cogging as well as commutating torque in permanent-magnet machines of both buried and surface-mounted magnet types. A detailed analysis of the torque production in a permanent magnet synchronous motor drive with rectangular current excitation is presented. The effect of skewing is considered. The proposed method takes advantage of the knowledge of the flux density distribution in the air gap as a function of design parameters. The equations can be programmed easily and are very useful for parametric studies and optimization.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>