Effects of cogging torque reduction techniques applied to surface mounted PMSMs with distributed windings

A nonlinear model is proposed representing air-gap magnetic flux density distribution in a synchronous machine with magnetic saturation in the pole tips. In order to explain the effect of magnetic saturation in a synchronous machine, the authors have measured air-gap flux in a specially designed synchronous machine, and recently proposed a model for the air-gap flux density distribution, concentrating on magnetic saturation in the field pole iron cores. In this paper, we propose an adaptation of our model for calculating air-gap flux, specifically addressing the magnetic saturation in the pole tips. By regarding the saturation as a consumer of m. m. f. similar to a virtual winding, we construct a magnetic circuit which represents the flow of magnetic flux inside the synchronous machine, and derive expressions which represent air-gap flux density distribution. Close agreement is obtained between the theoretically calculated results, and the results measured using search coils placed at the teeth of the armature.

In order to investigate the effect of nozzle on stress concentration in pressure vessels, three dimensional finite element analyses were performed. The results were compared with those for corresponding two dimensional axisymmetric finite element analyses. A three dimensional finite element model with a surface crack was also designed to evaluate the effect of internal pressure and heat transfer on crack face, and the resulting stress intensity factors from the finite element analyses were compared with those for ASME Sec. XI and Raju-Newman's stress intensity factor solution. As a result, the validity of currently available stress intensity factor solutions for a surface crack was reviewed in the presence of geometrical complexity, heat transfer and internal pressure.

Permanent magnet synchronous motors (PMSM) generate high-frequency electromagnetic vibration and noise when powered by inverters, and the cause is high-frequency electromagnetic exciting force (EMEF). In this paper, the frequencies and orders of EMEF are analyzed. The expression of EMEF acted on the stator inner surface is derived and the frequencies and orders of main components of vibration are listed. The high-frequency vibration experiments are conducted on a surface mounted 8-pole and 12-slot PMSM. The high-frequency vibrations near switch frequency and its multiples are main components of vibrations of motors when powered by inverters, and experiments are conducted to study the influence of switch frequency on the vibration acceleration. The impacts of periodic frequency PWM and random frequency PWM on the vibration acceleration and peak value of its frequency spectrum are studied by experiments. Introduction The vibration of motors is one of the most important performance indicators. The noise generated by vibration will pollute our working and living environment. A severe vibration can even destruct the machine structure. There are higher requirements for vibration in special applications. While the application of inverter improves the dynamic performance of the motor, it causes high frequency vibration and noise. Many researchers have done a lot of work about the vibration and noise of motors. The frequency of noise of inverter-fed induction machine is calculated[1,2]. The influence of inverters on the vibration of axial flux PM motors is studied by finite element method(FEM) and experiments. The impacts of random PWM and harmonic injection is studied[4-6]. The effect of pulse frequency modulation(PFM) in reducing noise of induction motor is studied[7]. When powered by inverters, the stator current has a lot of time harmonics which increases the complexity of air gap flux. The air gap flux determines the magnitude and frequency of electromagnetic exciting force (EMEF) acted on the inner surface of stator. In this paper, the flux distribution is derived by magnetic circuit method firstly. Then, the expression of radial of EMEF is obtained by Maxwell’s stress tensor. The frequency, order and sources of the main EMEF are listed. The high-frequency vibration experiments are conducted on a surface mounted 8-pole and 12-slot PMSM. The high-frequency vibrations near switch frequency and its multiples are main components of vibrations of motors when powered by inverters, and experiments are conducted to study the influence of switch frequency on the vibration acceleration. The impacts of periodic frequency PWM and random frequency PWM on the vibration acceleration and peak value of its frequency spectrum are compared by experiments. Calculation of EMEF in PMSM The vibration of stator of PMSM is mainly determined by radial EMEF acted on the inner surface of the stator. Neglecting the effect of magnetostriction and assuming 0 Fe μ μ  , the EMEF acted on the inner surface can be expressed as[8]: 2nd International Conference on Electrical, Computer Engineering and Electronics (ICECEE 2015) © 2015. The authors Published by Atlantis Press 1580 2 0 1 2 n n o F B μ = (1) where 0n B is the radial air gap flux density in the inner surface of stator. So the air gap flux distribution need to be obtained before calculating the EMEF. Neglecting the core magnetic reluctance, the air gap flux distribution can be expressed as ( ) ( ) ( ) , , , b t f t t θ θ λ θ = ⋅ (2) where θ is the mechanical angle, ( ) , f t θ is the air gap magneto-motive force(MMF) and ( ) , t λ θ is the air gap permeance. In a surface mounted PMSM (SPMSM), the air gap permeance does not change with time. It can be approximately expressed as ( ) 0 l θ λ λ = Λ +∑ (3) where 0 Λ is the constant part and l λ is the space periodic part caused by slots. l λ can be expressed as ( ) ( ) ( ) 0 ( 1) sin 1 cos cos ( 1) l l k l k k lZ lZ k l k k δ

This paper proposes an effective assistant model for considering the stator slot-opening effect on air gap flux density distribution in conventional interior-type permanent magnet (IPM) motor. Different from the conventional slot-opening effect analysis in surface-type PM (SPM) motor, a composite effect of slot-opening uniquely existing in IPM motor, which additionally causes enhancement of air gap flux density due to magnet flux path distortion in iron core between the buried PM and rotor surface. This phenomenon is represented by a proposed assistant model, which simply deals with this additional effect by modifying magnetic pole-arc using an effective method. The validity of this proposed analytical model is applied to predict the air gap flux density distribution in an IPM motor model and confirmed by finite element method (FEM).

The proposed technique focuses on the nonsinusoidal power supply control strategy aiming to obtain the optimal air gap flux density distribution. The electrical constraints for the alignment between rotated fundamental and harmonic air gap flux are illustrated in detail. The supporting simulation is performed to analyze the misaligned angles between fundamental and harmonic air gap flux for the traditional methods. Different from traditional flux-oriented methods, the improved algorithm for harmonic currents injection is designed based on rotor flux orientated control in fundamental plane and air gap flux orientated control in harmonic planes. The synchronous and aligned control of the fundamental and harmonic air gap flux is achieved regardless of load condition. The experimental verification is implemented based on a multiphase driving platform using a seven-phase induction machine as prototype. Various scenarios are provided for the proposed control strategy comparing with the traditional ones in terms of induced electromotive force waveforms, harmonic currents, and advance angles of air gap flux. The simulated and experimental results validate the theoretical assumption and the effectiveness of the proposed method.

Outer rotor permanent magnet machines have been applied to low-speed and high-torque applications for their high moment of inertia and torque density. The 12-slot/10-pole outer rotor fractional slot permanent magnet machine model is established by the finite element analysis (FEA) in this paper, and the no-load back EMF, air-gap flux density and flux distribution of the machine are preliminarily simulated and verified. The stator tooth width of outer rotor permanent magnet machine is analyzed, and five different schemes of stator tooth width are designed. It is proved that the torque density can be effectively improved by using reasonable armature tooth width and auxiliary tooth width by FEA. At last, the reason of improving the output torque is explained by the analysis of the magnetic density and the winding coefficient of the armature tooth.

This paper focuses on a dual-motor series system of a double-Y shifted 30° permanent magnet synchronous motor (PMSM) with a salient-pole rotor structure driven by a single inverter. A mathematical model is established considering the non-sinusoidal distribution of the air gap flux density (including the 5th harmonic). A vector control system based on the i d=0 strategy and incorporating torque compensation is proposed. Simulation studies under variable load conditions demonstrate that the series system can achieve decoupled control for PMSMs with a salient-pole rotor structure and non-sinusoidal air gap flux density distribution.

The analysis of laterally loaded piles is generally carried out by idealizing the soil mass as Winkler springs, which is a crude approximation; however this approach gives reasonable results for many practical applications. For more precise analysis, the three- dimensional finite element analysis (FEA) is one of the best alternatives. The FEA uses the modulus of elasticity <TEX>$E_s$</TEX> of soil, which can be determined in the laboratory by conducting suitable laboratory tests on undisturbed soil samples. Because of the different concepts and idealizations in these two approaches, the results are expected to vary significantly. In order to investigate this fact in detail, three-dimensional finite element analyses were carried out using different combinations of soil and pile characteristics. The FE results related to the pile deflections are compared with the closed-form solutions in which the modulus of subgrade reaction <TEX>$k_s$</TEX> is evaluated using the well-known <TEX>$k_s-E_s$</TEX> relationship. In view of the observed discrepancy between the FE results and the closed-form solutions, an improved relationship between the modulus of subgrade reaction and the elastic constants is proposed, so that the solutions from the closed-form equations and the FEA can be closer to each other.

In this paper, comparisons are made on various parameters of electromagnetic fields like air gap flux density (radial), flux distribution, phase currents, speed and torque of a healthy and stator inter-turn fault induction motor (IM). Using FEM (Finite Element Method), the inter-turn short circuit fault analysis of PWM (Pulse Width Modulated) inverter fed 3 phase IM is analyzed. The inter-turn fault is the initial stage of a short circuit in the stator winding and it progresses to a phase to phase fault or phase to ground fault if left undetected. When the IM is directly fed from the mains, the inter-turn fault can be identified using a popular technique known as MCSA (Motor Current Signature Analysis). But this method fails when the IM is fed from a PWM inverter due to rich noise content observed in the current spectrum due to high frequency inverter switching making it difficult to detect the fault. The electromagnetic field analysis of PWM inverter fed 3 phase IM with 12.5% and 25% stator winding inter-turn fault is carried out on a 7.5kW IM using ANSYS Maxwell FEA (Finite Element Analysis) tool. The spatial FFT spectrum of air gap flux density (radial) indicates the presence of stator winding inter-turn fault with rich noise content compared to healthy motor.

This paper studies the effects of the flux modulation poles (FMPs) on the radial magnetic forces in permanent magnet vernier (PMV) machines. The air-gap flux density distribution in the PMV machine is analyzed by using a combination of the finite element analysis and analytical methods. And then, the radial force density is calculated by Maxwell's stress method. At no-load condition, the permeance harmonics by FMPs generate various air-gap flux density harnmonics by interacting with the magneto-motive force (MMF) harmonics of the magnet. As a result, the low order harmonics of the radial force density which may induce significant vibration is caused in the PMV machine. Furthermore, the characteristics of the radial force density under the load condition will be investigated.

This paper analytically derives the optimal third harmonic current to improve the output torque in five-phase surface-mounted permanent magnet (SPM) machines under the constraints of the same peak/rms value. The relationship between the output torque and the third harmonic current is established and its optimal value for maximizing the output torque is derived. It is found that the optimal third harmonic current is dependent on the ratio of the third harmonic back electromotive force (EMF) to the fundamental one but it is not 1/6 of the fundamental one as pulse width modulation in an inverter. In order to improve the output torque by increasing the fundamental and third harmonic winding factors and the third harmonic airgap flux density, the unequal width tooth and permanent magnet (PM) segmentation are employed in the 10-slot/8-pole five-phase SPM machine. The optimal unequal tooth dimensions and the number of PM segmentations are analyzed for maximizing the output torque. The airgap flux density, back EMF, cogging torque, and output torque of the machine with equal/unequal tooth width and unsegmented/segmented PM are compared. Finally, the experiments on the prototype 10-slot/8-pole PM machine with unequal tooth width and segmented rotor are given to verify the analytical and finite element analyses.

This paper summarizes the results of an experimental and analytical investigation of the slot ripples in the damper windings of a salient-pole synchronous machine under steady state operation. A new method of measuring damper winding currents and voltages directly has been established and used to examine the ripples due to the stator slot openings, which appear in the damper bar currents and voltages, air gap flux density distributions and terminal voltages. By examining the physical relationship between air gap fluxes and damper winding currents and voltages both at no load and on load, slot ripples phenomena have been made clearer than before. >

The requirement of stringent environment and fuel efficiency target on automotive demand the use of lighter, smaller and efficient motors. The advantages like higher magnetic properties than ferrite, near net shape magnet production, and no use of heavy rare earth elements makes the use of bonded neo magnet in an automotive accessory motors very attractive. The isotropic nature of bonded neo magnets offers a feasibility to obtain wide range of magnetization profiles. The magnetization of the magnet influences the air-gap flux distribution and hence the motor performance 1. The performance of permanent magnet motors using isotropic bonded neo magnet can be improved by optimizing the air-gap flux profile using magnetization. Based on the magnet circumference touching the motor air-gap and the desired magnetization profile, an appropriate magnetization fixture needs to be designed. In an external rotor permanent magnet brushless (PMBL) DC motor and brushed DC motors, the inner circumference of the magnet touches the airgap and hence the magnet is magnetized using an inner-only fixture which has magnetization coils next to the inner circumference of the magnet. When the radial magnetization is desired, a double sided magnetization can also be used to magnetize bonded neo ring magnets 2. The use of double sided magnetization helps in enhancing the motor performance 3. To ensure that the bonded neo magnet is fully saturated a minimum magnetizing field of around 3T is to be generated throughout the magnet thickness 4. Considering this required magnetizing field, a fixture each offering inneronly and inner-outer magnetization (double sided magnetization) is designed using Finite element analysis (FEA) to achieve the radial magnetization. The simulation based results on the performance comparison of two fixtures is summarized. Figure 1 shows the simulated mid airgap flux density when magnet is magnetized with inner-only and inner-outer magnetizing fixtures. From this figure it is observed that, compared to inner-only fixture, the inner-outer fixture results in flat topped radial wave shape of flux density. Both designed fixtures are fabricated and the measured performance is used to validate the simulation results. It is observed that the peak magnetizing current and the energy required to achieve the magnet saturation in an innerouter fixture is 19.8% and 26.5% less respectively compared to inner only fixture. The reduction in peak magnetizing current and magnetization energy requirement will lead to reduced thermal stress and improved fixture reliability. It will also help in reducing the magnetization cycle time due to better heat dissipation in inner-outer fixture. During magnetization of the magnet, the effectiveness of the inner-outer fixture depends highly on the alignment of the inner and outer magnetization coils. The alignment and hence the performance of the fixture is influenced by the fabrication tolerances 5. Even a small misalignment between the coils on either side of the magnet will result in flux waveform distortion and reduction in magnetic flux. Considering the manufacturing tolerances, the effect of the various misalignment angles between the inner and outer magnetization coils on the magnet flux is arrived at using the FEA based simulation. The magnetization result is also measured by creating various misalignments between the inner and outer magnetization coils in the fabricated inner-outer magnetization fixture. Table I gives the measured magnet flux integral for various misalignment angles. It is observed from Table I that the $\pm 2 ^{circ}$ mechanical misalignment between the coils will not result in significant change in magnet flux and higher misalignment angles will result in considerable reduction of flux per pole. It is also observed that the misalignment effect is symmetric about the aligned position and higher degree of misalignment causes drooping wave shape on one side and a hump on the other side in any given pole depending on the direction of misalignment.

The reactor pressure vessel is usually cladded with stainless steel to prevent corrosion and radiation embrittlement. Number of subclad cracks may be found during an in-service-inspection due to the presence of cladding. It is specified, in ASME Sec. XI, that a subclad crack is characterized as a surface crack when the thickness of the clad is less than 40% of the crack depth. This condition is provided to keep the crack integrity evaluation conservative. In order to refine the fracture assessment procedures for such subclad cracks under a pressurized thermal shock condition, three dimensional finite element analyses are applied for various subclad cracks existing under cladding. A total of 36 crack geometries are analyzed, and the results are compared with those for surface cracks. The resulting stress intensity factors for subclad cracks are 6 to 44% less than those for surface cracks. It is proven that the flaw characterization condition as specified in ASME Sec. XI can be overly conservative for some subclad cracks.

The treatment of atrophic edentulous maxilla with implants becomes complex due to issues such as poor bone quality in the posterior region, insufficient bone volume, and anatomical constraints of the maxillary sinus. Rehabilitation using dental implants placed in the pterygomaxillary region posteriorly and between the maxillary sinuses anteriorly allows overcoming these limitations. The aim of this study is to investigate the stresses generated in the bone, implant, substructure materials, and aesthetic materials of hybrid prostheses prepared from three different substructure materials placed at different lengths in the pterygomaxillary region of completely edentulous maxillae using three-dimensional finite element analysis (FEA). Implants of two different lengths, 11.5 mm and 18.0 mm, were placed in the pterygomaxillary region. The 18.0 mm long implant has bicortical anchorage. Hybrid prostheses were prepared using three different substructure materials: PEEK, Ti, and Zr. A force of 150 N was applied unilaterally at an angle of 30 degrees from the palatal direction to the buccal side. Models with PEEK substructures exhibited greater displacement and shear stress values compared to those with Ti and Zr substructures. An increase in Von Mises stresses was observed in the apical region of the 18 mm long dental implants where cortical anchorage was achieved. In cortical bone, higher Pmax and Pmin values were noted in certain areas of the models with PEEK substructures. Different substructure materials have varying effects on the prosthesis, bone, and implant. It is suggested that the use of substructure materials with high elastic modulus would be more appropriate to reduce potential prosthetic complications in hybrid prostheses and achieve predictable stress distribution in the bone. The use of maxilla-restricted dental implants should be considered when sufficient cortical bone anchorage is present around the neck region of the implants. However, in cases where cortical bone support in the neck region is insufficient, the use of implants providing bicortical anchorage may be more beneficial.