Linear PM Research Articles

Design and Multi-Objective Optimization of a Tubular Linear PM Machine for Stirling Generator Based on Gradient Boosting Regression Tree Surrogate Model

Design and Multi-Objective Optimization of a Tubular Linear PM Machine for Stirling Generator Based on Gradient Boosting Regression Tree Surrogate Model

Linear Permanent Magnet Vernier Generators for Wave Energy Applications: Analysis, Challenges, and Opportunities

Harvesting energy from waves as a substantial resource of renewable energy has attracted much attention in recent years. Linear permanent magnet vernier generators (LPMVGs) have been widely adopted in wave energy applications to extract clean energy from oceans. Linear PM vernier machines perform based on the magnetic gearing effect, allowing them to offer high power/force density at low speeds. The outstanding feature of providing high power capability makes linear vernier generators more advantageous compared to linear PM synchronous counterparts used in wave energy conversion systems. Nevertheless, they inherently suffer from a poor power factor arising from their considerable leakage flux. Various structures and methods have been introduced to enhance their performance and improve their low power factor. In this work, a comparative study of different structures, distinguishable concepts, and operation principles of linear PM vernier machines is presented. Furthermore, recent advancements and innovative improvements have been investigated. They are categorized and evaluated to provide a comprehensive insight into the exploitation of linear vernier generators in wave energy extracting systems. Finally, some significant structures of linear PM vernier generators are modeled using two-dimensional finite element analysis (2D-FEA) to compare their electromagnetic characteristics and survey their performance.

Design optimization of a novel linear transverse flux switching permanent magnet generator for direct drive wave energy conversion

Linear transverse flux permanent magnet machines (LTFPMs) are categorized as high force density topologies, which are suitable candidates for direct drive and low-speed applications. This paper introduces a novel LTFPM topology, which also proposes advantages of the flux-switching machines. This proposed linear transverse flux switching PM machine (LTFSPM) has two long passive translators located at the armature's top and bottom sides. The topology offers a high value of force density, and also, it is a cost-effective topology due to its double-sided passive translator. Furthermore, the PMs are fully utilized in the magnetic circuit, the end winding length is negligible, and the iron cores can be laminated easily. In this paper, the operation principle of the topology is explained and its magnetic circuit is discussed. To reduce the computational time of optimization procedure, a double-layer method is adopted, which provides high robustness, low computational time, and high precision. Results of the finite element method indicate that the proposed machine can be considered a potential candidate for linear motion applications especially direct drive wave energy conversion systems, which require high force density values.

A Mesh Design Technique for Double Stator Linear PM Vernier Machine Based on Equivalent Magnetic Network Modeling

Linear permanent magnet Vernier machines (LPMVMs) is an attractive solution for stroke and direct-drive applications. Several LPMVM topologies have been presented for different applications that operate based on magnetic flux modulation. LPMVMs have some advantages including high force, and torque density at low speeds. This paper introduces a double-excited linear Vernier machine for wave energy conversion. To model the machine, finite element analysis and nonlinear equivalent network model are used. To improve the accuracy of the model and compact the network, a new meshing method is proposed. For better continuity in the output waveforms of the machine, special positioning is utilized. The end-effect is modeled using two separate networks. Finally, the modeling and simulation results are compared with each other and validated experimentally.

Combined optimization of a linear PM actuator with trapezoidal PMs and coils considering fringing effect for precision engineering

For precision engineering, a linear PM-moving actuator with trapezoidal PMs and trapezoidal coils considering the fringing effect is proposed. To take into account the effect of the finite-long trapezoidal PM array, an improved Fourier series expansion is developed to calculate the fringing-included magnetic field. Then the full-stroke thrust excited by the trapezoidal coils is accurately predicted and validated by the finite element method. Sensitivity of the trapezoidal parameters of PMs and coils is analyzed, and combined optimization is implemented by the genetic algorithm. Through the Pareto optimal solutions of thrust, the relation of the PM-coil parameter combination is described and formulated by curve fitting. Compared with the traditional rectangular PM actuators or other trapezoidal-typed actuators, the proposed actuator with trapezoidal PMs and coils further decreases the thrust ripple and largely increases the thrust magnitude simultaneously, and reaches an utmost-close effective stroke as well.

Modeling and Decoupling Control of a Linear Permanent Magnet Actuator Considering Fringing Effect for Precision Engineering

In this article, accurate modeling and decoupling control of a linear ironless PM actuator are implemented for precision engineering. Given the fringing effect due to the finite length, the magnetic field of the PMs and the three-phase winding are both calculated by applying an improved Fourier series expansion. Subsequently, based on a distributed model, the associated flux linkage and winding inductances are obtained and validated. Compared with rotary motors of physical symmetry, the winding inductance matrix makes the electrical model of the finite-long linear actuator present a new non-uniform form, to which the classic decoupling technique is inapplicable directly. Therefore, improved decoupling strategies are established utilizing the zeroth-order approximation of the inductances based on the $dq0$ transformation, as well as a real-time updating scheme. Physical experiments show that high-order harmonics are eliminated by applying the non-uniform model, which makes it effective and applicable.

Integrated Design Method of Linear PM Machines Considering System Specifications

The system specifications should be considered in the practical design of linear machines, albeit mostly neglected in the previous studies. The main objective of this article is to propose a systematic design method of a coreless-type permanent magnet linear synchronous machine (PMLSM), satisfying all the constraints resulting from the system specifications. Based on the trapezoidal motion profile, an electromagnetic design model is developed by utilizing the 2-D field solutions and energy conversion principle. The thermal effects are incorporated into the design model by measuring the hot-spot temperature of the static winding coil, thereby setting the upper limits of current density. The differential evolution (DE) is then applied to the design model to search for optimal solutions without violating any of the constraints. As a result, the proposed model combined with DE provides the Pareto-optimal front belonging to the feasible regions where all system specifications (e.g., acceleration profile, maximum speed, maximum allowable temperature, load mass, and supply voltage) are satisfied. Finally, the validity of the design model is verified by both the finite element (FE) and experimental results.

Inductance Calculation of Coreless-Type Linear PM Machines Based on Analytical Field Projection and Coil Separation Method

The analysis of winding inductance in electric machinery is crucial for both design and control implementations. This article presents an accurate and computationally efficient method to calculate the winding inductance in a coreless-type permanent magnet linear synchronous machine (PMLSM). The analysis is based on the novel approach combining the analytical field projection and the coil separation method. After dividing the coil domain into three regions, a two-dimensional winding inductance in the front view is calculated by solving the field governing equations in each subdomain. Subsequently, the model is extended in three dimensions by projecting the side view of the coil onto the 2-D plane, and the interpolation method is involved in accounting for the end-winding inductance. As a result, the proposed model can save much computation time to evaluate the winding inductance without relying on the finite element (FE) method. In the end, the validity of the analytical model is verified by FE and experimental results.

Analysis of the Fractional Pole-Pair Linear PM Vernier Machine for Force Ripple Reduction

Linear permanent magnet Vernier machine (LPMVM) is attracting more and more attentions recently due to its simple structure, high efficiency, and high thrust density at low speed. In this article, a novel fractional pole-pair linear permanent magnet Vernier machine (FP-LPMVM) is proposed, which gives more freedom in the design of the LPMVM to reduce the force ripple of the machine. The operation and force ripple reduction principles of the FP-LPMVM are also given in this article with the help of analytical equations. It is found that some of the proposed FP-LPMVM exhibit inherent good performances such as high EMF symmetry and low thrust ripple due to the combining of the flux modulation effect and the FP-LPMVM. In order to verify the theoretical analysis in this article, two LPMVM prototypes (i.e., 12 slots 20 poles integer pole-pair LPMVM and 18 slots 29 poles fractional pole-pair LPMVM) are manufactured, tested, and compared with each other. The experimental results are consistent with the FEA results, and the validity of the analysis and the superiorities of the proposed FP-LPMVM are verified.

Comparative Study of Novel Doubly-Fed Linear Switched Flux Permanent Magnet Machines With Different Primary Structures

To enhance the thrust force density and move a part of copper loss from the primary to the secondary of linear switched flux permanent magnet machines (LSFPMMs), this paper proposes a novel kind of doubly-fed LSFPMMs (DFLSFPMMs) by adding another set of armature winding on the secondary of LSFPMMs. The design and working principles of the new winding are analyzed first. It is found that the optimal coil pitch depends on the primary structure. Then, the parameters of DFLSFPMMs with U-core, C-core, E-core, and multi-tooth primary structures are globally optimized, and their electromagnetic performances are investigated by 2D finite element method. The result shows that the average thrust force of U-core DFLSFPMM is 30% higher than that of conventional LSFPMM counterpart, and it is also 23%-29% higher than those of DFLSFPMMs with other three primary structures. Besides, the U-core machine with tubular structure is analyzed for the potential application of electromagnetic shock absorbers, which shows the U-core DFLSFPMM has 10% higher peak-to-peak damping force than linear spoken-type PM machine. Finally, a prototype of U-core DFLSFPMM is manufactured and tested to validate the analysis.

Quasi-flat linear PM generator optimization using simulated annealing algorithm for WEC in Indonesia

Linear permanent magnet generator (LPMG) is an essential component in recent wave energy converter (WEC) which exploits wave’s heave motion. It could be classified into tubular-type, flat-tricore type, and quasi-flat type. In previous researches, these three models have been studied and designed for pico-scale WEC. Design optimization has further been conducted for flat-tricore LPMG, by using simulated annealing (SA) algorithm. It modified some parameters to minimize the resulted copper loss. This paper aims to optimize a quasi-flat LPMG design by applying SA algorithm. The algorithm would readjust the initial LPMG parts dimension. Then, the output of the optimized design would be analyzed and compared. The results showed that the optimization could reduce the copper loss by up to 73.64 % and increase the efficiency from 83.2 % to 95.57 %. For various load resistances, the optimized design also produces larger efficiency. However, the optimized design has a larger size and produces larger cogging force than the initial design.

Modeling and Analyzing a Novel Dual-Flux-Modulation Consequent-Pole Linear Permanent-Magnet Machine

A novel dual-flux-modulation consequent-pole linear permanent-magnet (DFM-CP-LPM) machine is proposed in this paper, which can be regarded as the combination of a linear flux-switching PM machine and a linear vernier PM machine. Via two sets of interoperable PMs mounted on both the primary and the secondary, the proposed machine can work in a dual-flux-modulation mode, achieving higher thrust density. Meanwhile, the consequent-pole structure is introduced, reducing approximately half of the PM usage compared to a conventional surface-mounted linear PM vernier machine (LPMVM), which will greatly reduce the cost. In this paper, the configuration and the operation principle of the novel DFM-CP-LPM are presented. Then the optimization and several thrust ripple reduction methods are introduced to improve the performance of the machine. Thermal analysis is also carried out to check the demagnetization risk of primary PMs, due to the heat from coils. Finally, the proposed machine is compared to a conventional LPMVM and a consequent-pole linear vernier permanent magnet machine with only PMs set on the secondary. The results verify the superiority of the proposed DFM-CP-LPM.

Design Optimization and Performance Investigation of Linear Doubly Salient Slot Permanent Magnet Machines

Novel linear doubly salient slot permanent magnet machines (LDSSPMMs) are investigated in this paper. First, the machine topology and operation principle are introduced, and the choices of feasible slot/pole combinations and winding configurations for three armature phases are discussed. Then, the 12 slots and 10/11/13/14 poles LDSSPMMs with double-layer (DL)/single-layer windings are globally optimized using genetic algorithm. The electromagnetic performances including flux linkage, back electromotive force (back EMF), detent force, and static force-current characteristics are comparatively studied using two-dimensional (2-D) finite-element analysis (FEA). It shows that 12 slots/13 poles (12s/13p) and DL winding are the optimal choices to provide higher thrust force as well as lower force ripple. Moreover, the risk of local irreversible demagnetization of PMs is analyzed, which only occurs at very limited corners of the PMs and can be eliminated by PM shaping. Furthermore, the electromagnetic performances between linear variable flux reluctance machines (LVFRMs), linear hybrid-excited slot PM machines, linear primary yoke PM machines, and LDSSPMMs are comparatively studied. It shows that LDSSPMM can provide much higher thrust force than LVFRM at the same copper loss. With the increase of copper loss, LDSSPMM exhibits better thrust force capability than other machines. Finally, a prototype of 12s/13p DL-LDSSPMM is manufactured and tested to validate the 2-D FEA predicted results.

Multiobjective Optimization of a Double-Side Linear Vernier PM Motor Using Response Surface Method and Differential Evolution

This paper designs a double-side linear vernier permanent-magnet motor, which incorporates the merits of high thrust force capability, high power factor, and high efficiency. Since the parameters of the motor are very sensitive and the high thrust force capability comes along with the high force ripple, a framework of multiobjective optimization is proposed to improve the overall motor performances. The sensitivity analysis is used to select significant variables and the multiobjective differential evolution with ranking-based mutation operator is conducted with the response surface models to generate the Pareto solution set. The electromagnetic performances of the optimal motor are compared with the initial motor by simulating step by step based on finite-element analysis. Finally, a prototype motor is manufactured and the experimental results validate the improved motor performances.

Comparative Study of the Dual Layer Magnet Array in a Moving-Coil Tubular Linear PM Motor.

Conventional single-layer magnet arrays are widely utilized in electromagnetic linear machines. The objective of this paper is to analyze various types of novel dual-layer magnet arrays, either in similar or different patterns, to compare their flux field distribution and increase flux density in the machine. High flux density helps to improve the sensitivity of electromagnetic displacement sensors or actuator thrust. The design concept of magnet arrays are presented. The machine space is divided into several regions according to the magnetic properties. The corresponding magnetic field distribution is formulated based on magnetic vector potential and Laplace’s equations. Numerical computation is conducted to validate the developed magnetic field model. A systematic comparison of magnetic field of various magnet arrays is carried out. It shows that the dual Halbach magnet array can generate relatively high and constant flux density, which may help to produce strong signals. A research prototype and an experimental testbed are developed to validate the analytical model of dual Halbach array. This study provides a general framework for the design and analysis of dual-layer magnet arrays with various magnetization patterns. It can be extended to multiple-layer designs in radial direction.

Analysis of a Novel Double-Sided Yokeless Multitooth Linear Switched-Flux PM Motor

A novel double-sided yokeless multitooth linear switched-flux permanent magnet (DYMLSFPM) motor is proposed to improve the electromagnetic performance of conventional double-sided linear switched-flux PM (DLSFPM) motor in terms of force ripple and cogging force. Its feature of structure is the multitooth primary without yoke. First, an analytical method of permeance model is developed for determining the optimal combination of primary slots and secondary poles. For DYMLSFPM motor with six primary slots, there are four available different secondary poles 16/17/19/20, respectively. By comparing the results of four combinations, it shows that the DYMLSFPM motor with 19 secondary poles can have better thrust force performance, which is also verified by the finite-element analysis. After all these four structures are optimized first by single-variable optimization and then by global optimization with genetic algorithm for further analysis, 6-slots/19-poles (6s/19p) combination can have the second highest average thrust force and the lowest thrust ripple. Moreover, it requires significantly smaller volume of PMs and exhibits much lower cogging force than conventional 6s/7p DLSFPM motor. Finally, a prototype of 6s/19p DYMLSFPM motor is manufactured and tested to validate the predicted results.

Optimal Design of 1 Phase Linear Oscillatory PM Motor Series for Small Compressor Like Drives: With FEM and Self-Starting Transients Validation

Refrigerator compressors are currently driven mostly by rotary line start or variable-speed (inverter-fed) motors with mechanical transmission. Direct driving of pistons by linear oscillatory resonant PM 1 phase motors has just been introduced to low power (less than 100 W) such applications. The present paper introduces a 3 pole PM mover 1 phase PM linear oscillatory motors, in terms of optimal nonlinear analytical design methodology, with FEM and dynamics validation. Both 50 and 250 Hz (inverter fed) operation for 2000 and 100 W is exemplified for minimum active materials costs and, respectively, minimum global costs (losses capitalized cost is added). For the line start case study (at 2000 W, 50 Hz) a circuit model for transients is introduced and the motor self-starting transients with full power delivery at above 91% efficiency is available. The 50 Hz motors are heavier around (5.7 kg/kW at 2000 W and 7.5 kg/kW at 100 W, respectively) than the 250 Hz motors around (1.2 kg/kW, 3 kg/kW) but the latter require inverter control.

Analytical Calculation of Back EMF Waveform for Linear PM Motors in Slotted and Slotless Structures

This paper presents the analytical calculation of back electromotive force (EMF) waveform for linear permanent magnet motors in either slotted or slotless structures. The predictions are based on the analysis of the 2-D magnetic field distributions and the 3-D end effects. In the slotted structure, the relative permeance function obtained by the Schwarz-Christoffel conformal mapping is used to take into account the effects of slotting and to calculate the air-gap flux density. Subsequently, to evaluate the leakage components resulting from the slot opening, slot opening factor is introduced to reflect the elements which do not follow the intended path to produce the back EMF. In the slotless structure, the effective values of the magnetic field quantities, together with the extended theory of winding factors, are employed to evaluate the back EMF waveform. For the analysis of the axial end effects, the 3-D leakage factor is incorporated into the analytical solutions by adding the end leakage permeance to the entire magnetic circuit models. The validity of the analytical results for each topology is confirmed by 2-D finite element and experimental results.

An Improved Displacement Measurement Based on Model Reconstruction for Permanent Magnet Synchronous Motor

Permanent magnet synchronous linear motor (PMSLM) and PM synchronous planar motor are important motion devices in the modern precision industry. Their inherent periodic magnetic fields are highly related to motor position. Correspondingly, the magnetic fields can be utilized to determine their own displacement and replace expensive sensors. However, the measurement result of this strategy seriously depends on magnetic field model (MFM) preciseness. To improve measurement accuracy, a novel MFM with Fourier series is proposed in this paper. First, a high-order theoretical model from theoretical derivation is developed. And the analyses show that even harmonics exist in the magnetic field of motor, which are not included in the theoretical model. This model deviation obviously affects measurement accuracy. Hence, the new MFM is reconstructed based on a high-order theoretical model. Comparative experiments with the three different MFMs are carried out to measure the displacement of the PMSLM. In the experiments, a linear hall sensors array containing eight sensors is self-developed to detect motor magnetic field. The root mean square of displacement measurement errors using a reconstruction model, a high-order theoretical model, and a fundamental model is 4.84, 8.42, and $758~\mu \text{m}$ , respectively. The experimental results validate that the measurement result of the proposed reconstruction MFM is better than the other two MFMs.

Force Ripple Minimization of a Linear Vernier Permanent Magnet Machine for Direct-Drive Servo Applications

Linear vernier permanent magnet machines (LVPMMs) for direct-drive servo applications are attracting more and more attentions due to its high force density, easy maintenance, rapid dynamic response, and so on. This paper proposes an LVPMM structure, which has a similar secondary as that of a regular linear PM machine, while its primary mover is composed of three modules, and the modules are separated by flux barriers. Since high-precision servo systems have rigorous demands on the force ripple of the drive motors, two methods are introduced to minimize the force ripple of the LVPMM. One is to choose an optimal length of flux barriers; the other is to change the three-phase winding connection. The effectiveness of both methods is verified by time-stepping finite element analysis. It is found that the force ripple can be reduced from 10.6% to 2.4% by the proposed two methods.