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The purpose of this paper is to present an analysis of the force ripples of an open slot permanent magnet linear synchronous motor (PMLSM). A calculation procedure using 2D finite elements method (2D‐FEM) is then evaluated with experimentations.

First, the studied PMLSM and its main features are introduced. Then, the 2D‐FEM model used to study the motor is presented. The methods used to calculate the force and the meshing procedures are also highlighted. The calculated no‐load force is compared to measurements. Lastly, the validated model is used to study the influence of the current magnitude on the force ripples at load.

In addition to the no‐load case, the influence of the current magnitude on these forces is presented.

The paper is orientated with a sound industrial background. For that reason, the impact of the current saturation on the thrust generation is presented via the evolution of the thrust coefficient, which is the force to the RMS currents ratio.

Permanent magnet linear synchronous machines (PMLSMs) have large thrust ripple due to the longitudinal end effect caused by the finite length of the armature compared with rotary machines. The purpose of this paper is to analyze the influence of electric loading on thrust ripple performances based on a 12 slots/14 poles (12S/14P) PMLSM. Furthermore, the method of skewed PMs to reduce thrust ripple is investigated based on multi slices 2D finite element (FE) models.

The thrust ripple of PMLSM under open-circuit condition results from the slotting and the longitudinal end effects. Therefore, periodical model has been designed to clarify the effect of the longitudinal end effect. Under on-load condition, the thrust ripple increases and exhibits an effective component of thrust force. To analyze the thrust ripple under on-load condition, frozen permeability (FP) technique is employed. In addition, the method of skewed PMs is analyzed in this paper to obtain more smooth thrust force performance. The effectiveness of skewing accounting for skew angles, step skew numbers and slot/pole number combinations was highlighted.

The longitudinal end effect dominates the thrust ripple of PMLSM in both cases, i.e., open-circuit and on-load conditions. Under on-load condition, the second harmonic component of thrust ripple related to flux linkage harmonics increases significantly. Moreover, the effectiveness of skewed PMs is largely reduced with the increase of magnetic saturation. At last, a proper skew angle and step skew number are obtained for the conventional PMLSM with fractional-slot winding.

By 60 electrical degrees and two or three step skewed PMs, the thrust ripple can be decreased to a tolerable limite for conventional PMLSM. The thrust ripple harmonics contributed by longitudinal end effect and flux linkage harmonics are analyzed, respectively, which is beneficial to exploring other techniques such as adding end auxiliary teeth to obtain lower thrust force pulsation.

The purpose of this paper is to propose the complementary design rules, give a quantitative comparison and analyze the force production mechanism of two kinds of primary wound field flux-switching linear (PWFFSL) motors.

PWFFSL motors have the merits of no use of rare-earth magnet, low cost and a wide operation range in which the armature windings and the field windings are all located at the short primary mover and the secondary is very robust. Hence, the PWFFSL motor is ideal for rail transportation systems which need a long stator and a wide speed range. To overcome the disadvantages of the existing PWFFSL motors, new complementary design rules will be proposed. Also, to offer a better PWFFSL motor for the rail transportation systems, it is necessary to investigate different structures of PWFFSL motors and give a comprehensive comparison. To predict the force performance of two kinds of PWFFSL motors with different secondary types, their flux density analysis and force production mechanism will be presented and compared.

The comparison result shows that the PWFFSL motor with toothed secondary can offer larger thrust force, higher force density and higher efficiency, whereas the PWFFSL motor with segmented secondary has the merits of lower force ripple, less use of stator iron, higher power factor and less critical saturation.

Many PWFFSL motors with different primary/secondary pole pitches based on the proposed design principle have not been considered in this paper.

This paper has presented the air-gap flux analysis, proposed the complementary design rules for two kinds of PWFFSL motors with different secondary types and compared the electromagnetic performance of the two motors.

The optimisation of a tubular linear motor with interior permanent magnets is described. For a rapid design the whole process is divided in three parts: an analytical approach for the a preliminary investigation, a parametric analysis by means of a finite element method and an optimisation. The obtained results show that the adopted optimisation process is efficient for rapid and effective optimisation of the tubular linear motor.

This paper deals with the study of the influence of the phase shift between currents and back-electromotive forces (back-EMF) on torque ripple and radial magnetic forces for a low power synchronous machine supplied with 120 degrees square-wave currents. This paper aims to establish a good compromise between efficiency, harmonics of torque and harmonics of radial forces at the origin of the electromagnetic noise.

Based on a finite element approach, torque and magnetic pressure harmonics versus space and frequency are evaluated for different angle values. The evolutions of the different harmonics against the load angle are analyzed and compared to those of experimental measurements.

Depending on the load torque, field-weakening or field-boosting can be used to reduce current harmonics contributing the most to the radial magnetic forces responsible for the noise. Besides, a compromise can be found to avoid deteriorating too much the performances of the machine, thus being suitable with an industrial application.

This study concerns low power permanent magnet synchronous machines with concentrated windings and driven with a trapezoidal control, while having sinusoidal back-EMF.

The use of a simple mean and suitable with a large-scale manufacturing industry to reduce the identified electromagnetic-borne noise of a specific electric drive makes the originality.

This paper aims to investigate three low-evaluation-budget optimization techniques: output space mapping (OSM), manifold mapping (MM) and Kriging-OSM. Kriging-OSM is an original approach having high-order mapping.

The electromagnetic device to be optimally sized is a five-phase linear induction motor, represented through two levels of modeling: coarse (Kriging model) and fine.The optimization comparison of the three techniques on the five-phase linear induction motor is discussed.

The optimization results show that the OSM takes more time and iteration to converge the optimal solution compared to MM and Kriging-OSM. This is mainly because of the poor quality of the initial Kriging model. In the case of a high-quality coarse model, the OSM technique would show its domination over the other two techniques. In the case of poor quality of coarse model, MM and Kriging-OSM techniques are more efficient to converge to the accurate optimum.

Kriging-OSM is an original approach having high-order mapping. An advantage of this new technique consists in its capability of providing a sufficiently accurate model for each objective and constraint function and makes the coarse model converge toward the fine model more effectively.

The purpose of this paper is to investigate torque ripple and magnetic force on the teeth in interior permanent magnet (IPM) machines over a wide range of speed operation for electrical power steering (EPS) applications.

The flux-weakening capability of IPM machines has been analysed by finite element method considering the effect of cross-coupling between d- and q-axis current. The traditional method of analysing torque ripple is based on constant torque and flux-weakening region. However, the cross-coupling need to be considered when applying this technique to flux-weakening region. Meanwhile, the torque ripple with current amplitude and angle and with different speed in the flux-weakening region is also investigated. In addition, the magnetic force on the teeth due to the separated teeth with stator yoke is also investigated during the constant torque and flux-weakening region.

The torque ripple and magnetic force on teeth in IPM machine are dependent on current and current angle. Both the lowest torque ripple and magnetic force on teeth exist over the whole torque-speed region.

The purely sinusoidal currents are applied in this analysis and the effects of harmonics in the current on torque ripple and magnetic force on teeth are not considered in this application. The 12-slot/10-pole IPM machine has been employed in this analysis, but this work can be continued to investigate different slot/pole number combinations.

This paper has analysed the torque ripple and magnetic force on the teeth in IPM machines for EPS application over a wide range of operation speed, which are the main cause of vibration and acoustic noise. The variation of torque ripple with current amplitude and angle as well as speed in the flux-weakening region is also investigated. In addition, the magnetic force on the teeth is also investigated over the whole torque-speed region.

Force output is extremely important for electromagnetic linear machines. The purpose of this study is to explore new permanent magnet (PM) array and winding patterns to increase the magnetic flux density and thus to improve the force output of electromagnetic tubular linear machines.

Based on investigations on various PM patterns, a novel dual Halbach PM array is proposed in this paper to increase the radial component of flux density in three-dimensional machine space, which in turn can increase the force output of tubular linear machine significantly. The force outputs and force ripples for different winding patterns are formulated and analyzed, to select optimized structure parameters.

The proposed dual Halbach array can increase the radial component of flux density and force output of tubular linear machines effectively. It also helps to decrease the axial component of flux density and thus to reduce the deformation and vibration of machines. By using analytical force models, the influence of winding patterns and structure parameters on the machine force output and force ripples can be analyzed. As a result, one set of optimized structure parameters are selected for the design of electromagnetic tubular linear machines.

The proposed dual Halbach array and winding patterns are effective ways to improve the linear machine performance. It can also be implemented into rotary machines. The analyzing and design methods could be extended into the development of other electromagnetic machines.

The purpose of this paper is to investigate the electromagnetic performances of the permanent magnet linear synchronous machines (PMLSM) with sine and third harmonic (SIN + 3rd) shaping mover in comparison with the PMLSM with sine (SIN) shaping mover and conventional shaping mover.

The optimal amplitude of the injected third harmonic to re-shape the SIN + 3rd shaping permanent magnet (PM) for maximizing the thrust force is analytically derived and confirmed by finite element method (FEM). Furthermore, the PM edge thickness, the pole arc to pole pitch ratio and the tooth to slot ratio are optimized. It is found that the optimal amplitude of the injected third harmonic is one-sixth of the fundamental one, the optimal PM edge thickness, the pole arc to pole pitch ratio and the tooth to slot ratio are 0, 0.85 and 0.5 mm, respectively. In addition, the electromagnetic performances are analyzed and quantitatively compared for the PMLSM with SIN + 3rd shaping mover, SIN shaping mover and conventional shaping mover.

The average thrust force and efficiency of the PMLSM with SIN + 3rd shaping mover are improved significantly, while the thrust ripple is not increased, comparing to those of the PMLSM with SIN shaping mover. Meanwhile, the thrust ripple is lower than that of the conventional shaping mover.

The purely sinusoidal currents are applied in this analysis and the influences of harmonics in the current on electromagnetic performances are not considered.

This paper presents a PMLSM with SIN + 3rd shaping mover to improve the thrust force and efficiency without increasing the thrust ripple, considering the effects of the amplitude of the injected third harmonic to re-shape the SIN + 3rd shaping PM, the PM edge thickness, the pole arc to pole pitch ratio and the tooth to slot ratio.

Due to linear structure, linear switched flux permanent magnet machines (LSFPMMs) also may have odd pole primary, such as 9, 15, 21, etc., without unbalanced magnetic force in equivalent rotary machines. The paper aims to discuss these issues.

In order to increase the thrust force density, the influence of some major design parameters, including split ratio, PM thickness, primary slot width and secondary pole width, are investigated by finite element analysis. For reducing the thrust force ripple under on-load condition, the end auxiliary teeth are adopted and their positions are also optimized.

This novel 9/10 primary/secondary poles LSFPMM has high average thrust force and low thrust force ripple by optimization. The results demonstrate that the odd pole primary may be a good candidate for long-stroke linear direct drive application.

A novel 9/10 primary/secondary poles linear switched flux permanent magnet machine is developed in this paper. The similar conclusions could be obtained for other LSFPMMs with odd pole primary.