Mechanical design considerations for conventionally-laminated, high-speed, interior PM synchronous machine rotors

The increase of pole numbers of the interior permanent magnet (IPM) synchronous machine can boost its air gap flux density, raise its efficiency and torque, and reduce its volume and weight. With the help of geometry module, this paper analyzes the relation between "flux concentration function" and the pole pair numbers of IPM synchronous machine, discusses connections between pole numbers and air gap flux density, per pole flux, non-load electric potential, flux density of rotor lead magnet material, flux density of stator tooth, flux density of stator yoke, and power which permanent magnet of unit volume produce respectively. Finally, authors point out: (1) when the saturation of lead magnet material was considered, the air gap flux density and the sums of the per pole flux will produce a the maximum with the increase of pole pairs, that is, IPM machine has a suitable pole pairs; (2) IPM machine bears "flux concentration function", when its pole pairs is more than or equal to 3, B/sub /spl delta///B/sub M/>1 or 4, B/sub /spl delta///B/sub r/>1; (3) the pole pairs of the IPM machine, which be from 3 to 6, is suitable. (4) the inner flux density of permanent magnet and power produced by the permanent magnet of unit volume will drop with the increase of pole pairs of the IPM machine.

– The paper presents a systematic comparison of four topologies of the interior permanent magnet machine (IPMM) designed for low speed applications. This comparative study investigates the suitability of the concentrated winding and distributed winding in the stator and the flat-shaped or V-shaped magnets in the rotor poles. The paper also studies the inductance characteristics of the designs using finite element analysis. Various steps taken to minimize the cogging torque and torque ripple in the studied machines were also discussed in details. Keywords : AC standstill saliency test, Cogging torque, Concentrated winding, Distributed winding, Direct-drive, Interior Permanent Magnet Machine, PM machine, Torque ripple 1. Introduction I n direct drive wind turbine systems, intermediate gear boxes are eliminated to increase the efficiency and reliability of the whole system, as well as reducing maintenances down-time. The generator used in such systems needs to have a low rated speed. This demand for an increase in the number of pole pairs of the generator. A review done in [1], [2] on direct-drive wind turbines suggests that permanent magnet (PM) machines are the most favorable for direct-drive wind turbine. While the most common type of PM machines used in the wind industry is the radial flux surface mounted magnet (SPM) type, an interior PM synchronous machine (IPMSM) offers a number of advantages over the SPM type. The most commonly cited advantages are: the presence of reluctance torque ( ) as shown in (1) in an IPM machine is beneficial in achieving a higher torque with lower magnet volumes and IPMSM has a mechanically and magnetically robust rotor. It should be noted that the presence of saliency in the IPSM results in the reluctance torque and also contributes toward the constant power speed range. A recent study carried out in [3] found that the use of an IPM machine in a small scale direct drive wind turbine can provide quicker return of investment compared to a SPM machine, especially in sites where average wind speed is low. According to [3] the return of investment can be achieved by taking advantage of provision for a constant power speed range available in IPMMs. But cogging torque in an IPMM is generally greater compared to a SPM machine due to the greater variation of reluctance between the stator and rotor [4]. This makes reduction of the cogging torque crucial in a low speed IPM machines [5]. The IPMSM with radially magnetized V-shaped (V-S) magnets has a better flux concentration and higher saliency ratio than its counter-part flat-shaped (F-S) magnet designs which makes it more attractive for traction drives [6]. The torque components of an IPM machine is (1) where, = magnet alignment torque, = cogging torque, and reluctance torque. The majority of IPM machines are designed with distributed windings (DW). Recently, the concentrated winding (CW) for the IPMSM is getting attention from the research community due to its high slot-fill factor, high tolerance to phase fault, simplified manufacturing process, non-overlapping coils resulting in shorter end-windings and reduced copper usage. In spite of having these advantages, the CW was not widely used in the past due to its characteristics in producing EMF and MMF waveforms with unacceptably high total harmonic distortion. However, in recent years, it has been shown that through appropriate choice of slot and pole combinations [7], the CW stator has the ability to produce sinusoidal EMF waveform with high a winding factor, and smooth average torque. In this paper, four design topologies of IPMSM were considered for investigation which includes (a) conventional distributed winding in the stator and flat-shaped IPM structure in the rotor( DW FS-IPMM), (b) distributed winding in the stator and V-shaped IPM structure in the rotor (DW VS-IPMM), (c) concentrated winding in the stator and flat-shaped IPM structure in the rotor (CW FS-IPMM), (d) concentrated winding in the stator and V-shaped IPM structure in the rotor(CW VS-IPMM). Fig. 1 shows the cross-section of the four topologies and no-load flux distribution. The objective of this paper is to present a detailed comparison of the major performance characteristics of all the four topologies illustrated in Fig.1. The selection process of the major dimensions and winding structure of the proposed IPMM is described in Section 2. Section 3 presents the cogging torque and torque ripple minimization of all the four investigated designs.

The increase of pole pairs numbers of the interior permanent magnet (IPM) synchronous machine with concentration structures can boost its air gap flux density, raise its efficiency and torque, and reduce its volume and weight. But there exists a suitable value. With the help of geometry module, this paper analyzes the relation between concentration function and the pole pair numbers of IPM synchronous machine, and, by the use of finite element analyze (FEA) software, discusses connections between pole pair numbers and air gap flux density, per pole flux, non-load electric potential, flux density of rotor lead magnet material, flux density of stator tooth, flux density of stator yoke, and power which permanent magnet of unit volume produce respectively. Furthermore a suitable pole pair numbers value for IPM synchronous machine with concentration function is presented

This paper investigates a driving method for a Permanent Magnet (PM) Synchronous six-phase machine by using its consecutive three phases. The torque of PM synchronous machine is the division of instantaneous power (I-power) of the machine to the rotor speed. The I-power of a machine gives information about the torque. The torque output of a PM synchronous machine can be predicted by looking at the I-power. This study investigates the torque of a PM synchronous six-phase machine by exciting its phase coils for the combination of conventional three-phase, double conventional three-phase, consecutive three phases of six-phase machine and double consecutive three phases of six-phase machine. This paper also investigates the way of driving a six-phase machine using the balanced three-phase supply. Firstly, analytical studies have been done for these exciting combinations. These analytical results indicate that symmetric six-phase machine can be driven using these combinations. Secondly, a PM synchronous six-phase machine has been designed in a finite element analysis (FEA) software. Lastly, that designed six-phase machine excited with these combinations to observe the torque wave form of the machine. As a result of this study, a symmetric six-phase machine can be run by its consecutive three phases without torque ripple.

A magneto-structural combined dimensional and topology optimization approach for interior permanent magnet synchronous machine (IPMSM) rotor design is proposed using the Solid Isotropic Material Penalization (SIMP) density-based topology optimization method. This method optimizes the location and dimensions of the permanent magnets (PMs) embedded in the rotor, while simultaneously optimizing the lamination flux barriers using topology optimization.To allow for the location and dimensions of the PMs to change while retaining the same number of mesh elements and connectivity, the mesh must be deformed. Mesh deformation is accomplished using a Laplace smoothing technique. To increase the range of PM displacement and size changes, the non-PM areas of the rotor design domain are divided into sub-regions along whose boundaries the mesh nodes are redistributed also using a Laplace smoothing algorithm. Three examples of IPMSM rotor optimizations are presented to demonstrate the proposed approach.

This paper presents the design and experimental verification of a 6 kW interior permanent magnet (IPM) synchronous machine intended for an automotive direct-drive starter/alternator application. The machine was designed using a saturable lumped-parameter magnetic circuit model in combination with a Monte Carlo optimization process that minimized the machine-plus-converter cost. An experimental IPM machine has been constructed based on the resulting design specifications. Laboratory tests have confirmed the accuracy of the analytical models for predicting the q-axis inductance L/sub q/ (including saturation effects) and the torque production characteristics, but discrepancies between the predicted and measured d-axis inductance L/sub d/ were revealed. The impact of these differences on machine performance is discussed, as well as potential adjustments in the IPM analytical model to improve the performance of future machines.

A method for fast calculating the high-frequency harmonic loss (HFHL) in the permanent magnet (PM) of interior PM synchronous machine under the pulsewidth modulated voltage source inverter supply is proposed. The combination of the frozen differential reluctivity tensor method and the linear frequency finite-element analysis (FEA) is proposed to investigate the relationship between the high-frequency harmonic voltages (HFHVs) in the rotor reference frame and the flux density variations in the PM, which is described quantitatively with the proposed analytical model using several dimensionless parameters. Then, the PM HFHLs are calculated analytically with the models using the flux density variations as input. The relative errors between the HFHLs calculated analytically and those obtained from the time-stepping FEA are within 15% at eight arbitrary working conditions. The proposed method can be used to calculate the PM HFHL in both two- and three-dimensional cases, which is testified with the experiment. Quadratic polynomial is used to fit the relationship between the dimensionless parameters and the fundamental currents. With the fitted polynomial and the analytical spectra of the HFHVs obtained from the double Fourier integration method, the PM HFHL map over entire working range can be calculated in one hour.

An experimental investigation is conducted to determine the behaviour of brushless PM synchronous machine parameters in the high speed flux weakening operating range. Real-time operating characteristics are determined for two commercially available 4 Nm interior PM synchronous machines. Special computer assisted measuring techniques are employed using an experimental vector controlled drive, capable of providing sinusoidal excitation waveforms at up to 8000 RPM. Perturbation analysis is performed on the measured data and results are applied to a variation of the classical d-q axis equivalent circuit model. The experimental results are repeatable and show a significant variation in the machine parameters as a function of the torque angle. Magnetic nonlinearities are also identified and accounted for through recomputation of the machine model over a wide range of operating points. The authors demonstrate that all tests can be performed with no previous knowledge of manufacturer proprietary information or results from finite element simulation.

In order to describes an investigation of interior permanent magnet (IPM) synchronous machines with higher winding factor, this paper presents a detailed comparisons of the 18-slot/10-pole IPM machine equipped with two coil pitches with conventional one coil pitch fractional slot 18-slot/10-pole machine for applications that require optimal flux-weakening operation, which are including the predicted air gap flux density, back-EMF, average torque, torque ripple and d-axis and q-axis designed by finite element analysis (FEA). With this result, a better structure is carried out to determine the coil pitch, compared with the one coil pitch machine, the two coil pitches increase the winding factor and have better performance in the machine without significant increases in the ripple torque.

Closed-form expressions are available to predict the torque-speed performance limits of interior permanent magnet (IPM) synchronous machines under various simplifying assumptions. This paper compares the performance that is predicted by using these closed-form expressions and that directly calculated by finite element analysis (FEA) considering maximum limits in both the constant-torque and flux-weakening operating regimes. It confirms that the closed-form expressions cause substantial errors in the constant-torque regime where magnetic saturation effects are large. However, the accuracy of the closed-form predictions improves significantly at elevated speeds in the flux-weakening regime due to the reduced impact of magnetic saturation as flux levels are decreased.

This paper investigates the transient magnetic behavior of an interior permanent magnet (IPM) synchronous machine following a large transient current caused by a fault condition. A combination of finite element (FE) analysis and numerical integration of the machine equations is used to calculate the currents resulting from a symmetrical three-phase short-circuit fault at the machine terminals, including magnetic saturation effects. FE analysis is further used to simulate the magnetic behavior of the machine when subjected to the fault currents, with a particular focus on the propagation of the demagnetizing MMF throughout the conductive laminations as well as the conductive PM material. Eddy currents induced in the laminations and magnet material are shown to impede the progression of the demagnetizing MMF. However, the transient analysis illustrates the manner in which the fault currents ultimately trigger the onset of irreversible demagnetization of significant portions of the rotor magnets in the analyzed machine. The transient demagnetization analysis method is extended to investigate the influence of several key design variables, including machine operating temperature and segmentation of the rotor magnets.

A new magnetic circuit model is presented for an interior permanent magnet (IPM) synchronous machine, using a machine with three-phase distributed stator windings and three layers of flux barriers in the rotor as an example topology. The model accounts for: i) the effects of cross-coupled magnetic saturation caused by the salient rotor; ii) variation of magnetic saturation levels in the iron rotor bridges that are key elements of the unitary rotor laminations; iii) the effects of stator lamination slots on the airgap mmf distribution; and iv) the local variation of airgap permeance due to the stator slotting and the relative position of the rotor with respect to the stator. As a result of these features, the new model is capable of significantly improving the accuracy of electromagnetic performance predictions for aggressively-designed IPM machines compared to previously-available magnetic circuit models. Comparisons with finite-element analysis and measurement results are provided showing that the new model is much faster while delivering appealing accuracy compared to the FE method.

The equivalent circuit parameters of an interior permanent magnet synchronous machine (PMSM) vary under different operating conditions due to magnetic saturation and temperature rise. Knowledge of accurate machine parameters is of paramount importance for high performance PMSM control and condition monitoring. Therefore, this paper presents a novel parameter estimation method, which employs both the electrical and mechanical model of an interior PMSM (IPMSM) for simultaneously estimating three parameters; namely, the d- and q-axis inductances and permanent magnet flux linkage. Specifically, the proposed parameter estimation approach is mathematically justified at first. Thereafter, by using the machine mechanical model with the speed measurement, a third equation in addition to the dq-axis voltage equations is developed to make the estimation model full-rank for simultaneously estimating three parameters. Lastly, the proposed approach is implemented with the recursive least square algorithm to estimate machine parameters and it is validated with simulations and experimental tests on a laboratory IPMSM drive system.

The tracking of optimal current trajectories in an interior permanent magnet (IPM) synchronous machine is traditionally realized by a complex online tracking, inaccurate analytical equations, or tiresome offline calibration methods. This paper proposes a modified hybrid feed-forward/feedback flux-weakening algorithm for IPM synchronous machines. In this paper, the utilized power converter is a standard T-type multilevel inverter, and hence, the voltage and current harmonics contents of the conventional two-level inverter are improved. The control algorithm utilizes the optimal current profile for maximum torque per ampere (MTPA) operation and a voltage regulation (VR) feedback control for efficient flux-weakening operation. For infinite-speed IPM machine drives, the d-q current components are limited to follow the maximum torque per voltage (MTPV) trajectory. A low-complexity model predictive control (MPC) is employed to minimize the conflict that arises from using cascaded PI control loops for current and speed control. The performance of the drive is investigated based on the Prius 2004 IPM parameters. Extensive simulation scenarios were performed using the MATLAB/SIMULINK which validates the effectiveness of the proposed algorithm. Real-time simulations based on the dSPACE DS 1103 platform are conducted to confirm the system validity for real hardware implementation. The proposed IPM drive system proves simple structure, fast response, and low harmonic contents.

A fast hybrid analytical model is presented to predict the on‐load performance of double‐layer interior permanent‐magnet synchronous machines (IPMSMs) considering both iron bridges saturation and slotting effects. The saturation of the iron bridges is defined by a constant flux in the magnetic equivalent circuit method. The slotting effect is defined by a flux path function and virtual surface currents (VSCs) in one‐dimensional (1‐D) and two‐dimensional (2‐D) analytical methods, respectively. For the no‐load condition, double‐layer IPMSMs are modelled via surface‐mounted permanent magnet synchronous machines with two types of the permanent magnet model and the Magnetic Islands method are used to calculate the armature reaction. The effect of the stator slots is considered by using VSCs. To increase the computation speed in the 2‐D analytical method, the amount of VSC is calculated by 1‐D analysis. The 1‐D and 2‐D analytical results for a double‐layer IPMSM are compared with those of finite element analysis and experimental set‐up.