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The authors propose an analytical modelling approach for the linear transverse flux permanent magnet motor using the magnetic equivalent circuit method. The main focus of this study is to predict the phase flux‐linkage characteristic of the motor. Essential equations required for implementation of the model and how to solve it are described clearly so that someone can use it easily. A typical motor is selected to apply the proposed model and simulation results, including static characteristics of flux‐linkage and thrust, are presented. To validate the developed analytical model, the discussed motor is also analysed with 3D finite element method using MAXWELL software and the obtained simulation results are compared to each other. [ABSTRACT FROM AUTHOR]

2‐D air‐gap magnetic field distribution is the essential prerequisite of electrical machine analysis. Because of the natural periodicity of rotary machines, Fourier analysis is a suitable choice for air‐gap field prediction. However, due to the end‐effect, periodicity is not present in linear machines and the Fourier series is not appropriate. In engineering mathematics, a rigorous method of solving partial differential equations is the separation of the variables method (SVM) which is based on the hypothesis that the field solution is in the form of the product of two functions of orthogonal directions; for example, in an axisymmetric structure, a longitudinal harmonic function (LHF) and a radial harmonic function (RHF). A particular case of these functions is trigonometric functions, which result in the Fourier series. SVM is imposed in a different manner, where RHF is approximated by the Bessel–Fourier series and consequently LHF has a (piecewise) exponential behaviour. This choice of basis functions not only serves the purpose of modelling the end‐effect but also removes the Gibbs phenomenon, that is, it precisely models discontinuities of flux density at the surface of PMs. A numerical case‐study of a slotless double‐sided linear tubular surface‐PM machine shows that the piecewise exponential approximation can attain 1% error while utilising only three harmonics, whereas the trigonometric approximation, due to the Gibbs phenomenon, slowly arrives at 20% error with 100 harmonics for approximating flux density. Results of both methods were validated using the finite element method (FEM). Additionally, it was discovered that the computational complexity of the model is independent of varying position; therefore, the analytical method could yield the back electromotive force and electromagnetic thrust force for a number of 320 positions at merely 0.2 s while the FEM software required 5 min. [ABSTRACT FROM AUTHOR]

Abstract The authors propose an analytical modelling approach for the linear transverse flux permanent magnet motor using the magnetic equivalent circuit method. The main focus of this study is to predict the phase flux‐linkage characteristic of the motor. Essential equations required for implementation of the model and how to solve it are described clearly so that someone can use it easily. A typical motor is selected to apply the proposed model and simulation results, including static characteristics of flux‐linkage and thrust, are presented. To validate the developed analytical model, the discussed motor is also analysed with 3D finite element method using MAXWELL software and the obtained simulation results are compared to each other.

Abstract 2‐D air‐gap magnetic field distribution is the essential prerequisite of electrical machine analysis. Because of the natural periodicity of rotary machines, Fourier analysis is a suitable choice for air‐gap field prediction. However, due to the end‐effect, periodicity is not present in linear machines and the Fourier series is not appropriate. In engineering mathematics, a rigorous method of solving partial differential equations is the separation of the variables method (SVM) which is based on the hypothesis that the field solution is in the form of the product of two functions of orthogonal directions; for example, in an axisymmetric structure, a longitudinal harmonic function (LHF) and a radial harmonic function (RHF). A particular case of these functions is trigonometric functions, which result in the Fourier series. SVM is imposed in a different manner, where RHF is approximated by the Bessel–Fourier series and consequently LHF has a (piecewise) exponential behaviour. This choice of basis functions not only serves the purpose of modelling the end‐effect but also removes the Gibbs phenomenon, that is, it precisely models discontinuities of flux density at the surface of PMs. A numerical case‐study of a slotless double‐sided linear tubular surface‐PM machine shows that the piecewise exponential approximation can attain 1% error while utilising only three harmonics, whereas the trigonometric approximation, due to the Gibbs phenomenon, slowly arrives at 20% error with 100 harmonics for approximating flux density. Results of both methods were validated using the finite element method (FEM). Additionally, it was discovered that the computational complexity of the model is independent of varying position; therefore, the analytical method could yield the back electromotive force and electromagnetic thrust force for a number of 320 positions at merely 0.2 s while the FEM software required 5 min.

This paper proposes a new double mover configuration of a linear switched reluctance motor (LSRM). The proposed design is established for optimization of the motional forces and to ensure a high-grade electromechanical energy conversion process. The major drawback of the traditional linear machine is that its force densities within and throughout its area is produced in its radial direction of the yoke and does not contribute to its motion or twisting force of the rotor. If these normal forces happen to be in the direction of motion, a larger motional force profile for SRM is yielded. Based on these guidelines, a new LSRM is developed. In order to compare the energy conversion efficiency of LSRM with that of the conventional SRM, a finite element model is constructed. The proposed system is simulated using the FEM software and tested under four conditions. Further, an experimental prototype of the proposed machine is also developed and tested in the laboratory. The results obtained from the prototype indicate that the proposed geometry offers superior performance in terms of high-power density and higher percentage of the national forces. [ABSTRACT FROM AUTHOR]

Abstract An alternative way to generate electricity from solar energy is through the use of generators comprising Stirling engines with a parabolic collector. This study describes a parabolic collector with Stirling engine and investigates the design of a linear mobile generator for these systems. Especially for direct drive in free piston mechanisms proposed for these systems, linear generators are important due to their advantages such as compact structure, light weight, high efficiency and high power intensity. Although conventional one‐phase and three‐phase multi slot/pole models are widely available in the literature, three phase is considered for lower PM cost and to reduce the cost of power electronics and 3/2 slot/pole combination is considered for high speed and frequency. In this study, a new 3/2 slot/pole three‐phase tube‐type linear generator was designed and evaluated for performance and manufacturability. Objective functions were defined for power and efficiency increase to reduce generator power ripple, and the results of Mixed‐Integer Sequential Quadratic Programming, Multi‐Objective Genetic Algorithm (MOGA), and Screening methods were compared and examined. Performance of the two‐dimensional and optimized models was evaluated in terms of induced voltage, power density, efficiency, and output power. The best results were found with MOGA compared to other methods. When compared with the initial value, there was a 97.3% increase in power density for a 32.4% increase in moving weight. Moreover, the efficiency of the MOGA model is improved by 16.2% compared with the initial model. Additionally, significant improvements were shown in terms of thrust coefficient, voltage coefficient, power, and no‐load voltage. A prototype of the model was made and a motor‐driven crank mechanism system was used in place of the Stirling engine to undertake practical measurements.

An alternative way to generate electricity from solar energy is through the use of generators comprising Stirling engines with a parabolic collector. This study describes a parabolic collector with Stirling engine and investigates the design of a linear mobile generator for these systems. Especially for direct drive in free piston mechanisms proposed for these systems, linear generators are important due to their advantages such as compact structure, light weight, high efficiency and high power intensity. Although conventional one‐phase and three‐phase multi slot/pole models are widely available in the literature, three phase is considered for lower PM cost and to reduce the cost of power electronics and 3/2 slot/pole combination is considered for high speed and frequency. In this study, a new 3/2 slot/pole three‐phase tube‐type linear generator was designed and evaluated for performance and manufacturability. Objective functions were defined for power and efficiency increase to reduce generator power ripple, and the results of Mixed‐Integer Sequential Quadratic Programming, Multi‐Objective Genetic Algorithm (MOGA), and Screening methods were compared and examined. Performance of the two‐dimensional and optimized models was evaluated in terms of induced voltage, power density, efficiency, and output power. The best results were found with MOGA compared to other methods. When compared with the initial value, there was a 97.3% increase in power density for a 32.4% increase in moving weight. Moreover, the efficiency of the MOGA model is improved by 16.2% compared with the initial model. Additionally, significant improvements were shown in terms of thrust coefficient, voltage coefficient, power, and no‐load voltage. A prototype of the model was made and a motor‐driven crank mechanism system was used in place of the Stirling engine to undertake practical measurements. [ABSTRACT FROM AUTHOR]

Abstract An analytical method is proposed to model the magnetic field distribution across a slotless tubular interior permanent magnet machine. In order to consider the permeability of both permanent magnets and iron poles of the slider, in the proposed approach, instead of choosing each one as an individual sub‐domain, they are taken as an integrated sub‐domain. Therefore, the governing partial differential equation alters from Poisson equation to the governing magnetostatics equation for inhomogeneous (space‐dependent permeability) materials. The solution is derived through separation of variables method in which a Sturm‐Liouville problem is encountered. The solution and its important mathematical properties, such as the orthogonality and generalised Fourier series, are fully addressed. These properties are very helpful for creating linear interface equations in terms of the integral coefficients. In addition, since the number of sub‐domains is decreased, the total number of the unknowns of the final matrix of equations is reduced effectively. To validate the proposed method, a case study is simulated by the aid of computer software and its results are compared with those of finite element method. It has been observed that the results are in good agreement.

An analytical method is proposed to model the magnetic field distribution across a slotless tubular interior permanent magnet machine. In order to consider the permeability of both permanent magnets and iron poles of the slider, in the proposed approach, instead of choosing each one as an individual sub‐domain, they are taken as an integrated sub‐domain. Therefore, the governing partial differential equation alters from Poisson equation to the governing magnetostatics equation for inhomogeneous (space‐dependent permeability) materials. The solution is derived through separation of variables method in which a Sturm‐Liouville problem is encountered. The solution and its important mathematical properties, such as the orthogonality and generalised Fourier series, are fully addressed. These properties are very helpful for creating linear interface equations in terms of the integral coefficients. In addition, since the number of sub‐domains is decreased, the total number of the unknowns of the final matrix of equations is reduced effectively. To validate the proposed method, a case study is simulated by the aid of computer software and its results are compared with those of finite element method. It has been observed that the results are in good agreement. [ABSTRACT FROM AUTHOR]

Ocean wave energy is sustainable and renewable energy, wave energy conversion (WEC) effectively solves the disadvantage of traditional power system with fossil energy. WEC system is the power generation process that converts wave kinetic energy of undulation and swing into electric energy, and direct‐drive WEC system (D‐DWEC) converts wave energy into electric power directly by linear generator to improve the efficiency. At present, the research of WEC system has the characteristic of interdisciplinary, multi‐system integration, engineering application, and commercial operation. This paper summarizes the types, principle, and classification of WEC system, mainly focusing on the aspects of the kinds and characteristics of linear generators used in D‐DWEC system, power post‐processing, and power control methods. At the end of the paper, giving the development trend and challenges of D‐DWEC technology, the research of ocean complementary energy generation platform with offshore wind, solar and ocean wave energy is analysed. It shows that the platform has advantages owing to stable power output, efficient utilization, ocean saving‐space, and power generation cost reduction. [ABSTRACT FROM AUTHOR]

Thrust ripple and density greatly impact the performance of the linear machine and other linear actuators, causing positioning control precision, dynamic performance, and efficiency issues. Generalized pole-pair combinations are difficult to satisfy both the thrust and ripple for double salient reluctance linear machines. In this paper, a DC-Biased vernier reluctance linear machine (DCB-VRLM) is proposed to solve the abovementioned issues. The key to the proposed design is to reduce the ripple and enhance the thrust density with non-uniform teeth by utilizing and optimizing the modulated flux in the air gap. To effectively verify the proposed design, the DCB-VRLMs with different winding pole pairs and secondary poles are compared. The 12-slot/10-pole combination is chosen to adopt a non-uniform air gap structure. Moreover, the energy distribution of AC/DC winding is studied and optimized to further enhance the performance of the proposed DCB-VRLM. The results indicate that the DCB-VRLM with the non-uniform air gap has a lower thrust ripple, better overload capability, and higher thrust density, which confirms its superiority in long-stroke linear rail transit and vertical elevator applications. [ABSTRACT FROM AUTHOR]

A discrete stator hybrid excited flux switching linear machine (DSHEFSLM) is proposed in this paper. The proposed DSHEFSLM uses a discrete stator to reduce the iron loss and overall cost of the machine. Assistant teeth are used at both ends of the mover to overcome the unbalance in the three phases, which is a global issue in linear machines. Field excitation (FE) is used, which adds field regulation capability to the proposed machine and makes it suitable for a wide speed operation range. A magnetic equivalent circuit model is used to find the suitable coil combination and no-load flux linkage. The multiobjective genetic global optimization is used to optimize the design parameters of the whole machine while keeping the slot area, electric and magnetic loadings constant. A correlation table is drawn to show the impact of different design parameters on average thrust force. The optimization has increased the peak-to-peak flux linkage by 11%, average thrust force by 34.60%, thrust force density by 34.60%, decreased thrust force ripples, and detent force by 21.05% and 8.58% respectively. The proposed machine has reduced the volume of the permanent magnet by 39.18% and offers 28.09% higher average thrust force and thrust force density compared to the flux switching permanent magnet machine proposed in the literature.

Linear switched-flux machines are a kind of permanent magnet machine with a passive ferromagnetic secondary. Therefore, they can achieve both a good performance and a low cost in long stroke applications. However, due to the end effect, these machines generate high detent force and on load thrust force ripples. There are several solutions in the literature that aim to minimise the thrust ripple. One of those solutions is the placement of additional poles in the ends of the machine. These can be passive, i. e. simple ferromagnetic teeth, or active, with additional magnets. The former is the most common solution in the literature. In this article, the optimal configuration of the additional poles is discussed via 4 additional pole sizing strategies, and the influence of the design variables and optimisation objectives is analysed. Then, a generic additional pole configuration is proposed, which combines a high effectiveness and a simple design. Finally, an experimental validation is carried out, and the measurements confirm the results from the optimisation. [ABSTRACT FROM AUTHOR]

Abstract Considering the growing environmental issues, the use of renewable energy converters such as solar cogeneration systems has received more attention during recent years. Solar cogeneration systems convert the thermal energy of solar radiation into mechanical energy (by means of a free‐piston Stirling engine) and then into electrical energy (by means of a linear generator). This paper introduces the novel yokeless mover permanent magnet linear generator (YMPMLG) to reduce mover mass, increase power density, increase thrust and decrease the normal force on the mover, which can make this generator a more suitable structure for operating in solar cogeneration systems. This paper is initiated with a comparative study of a YMPMLG with two reported prototypes in this field. Three generators with similar characteristics are simulated by the finite element method (FEM). The magnetic field flux density, power density, thrust coefficient, normal force, and efficiency parameters are analysed and compared in three generators. Following that, some dimensional parameters of the YMPMLG, including generator diameter and length and permanent magnet dimensions are optimized to achieve the highest possible power density and thrust coefficient using the ‘hybrid genetic and pattern search’ algorithm. The highest power density and efficiency are 0.58 kW/kg and 90.3%, respectively. In the end, the YMPMLG prototype has been tested to validate the results of the FEM method.

This paper proposes double sided complementary modular field excited flux switching linear machine (FEFSLM). FEFSLM offers the low cost, variable flux capability for a wide speed range, a compact and robust stator which is suitable for the long stroke application. Compared to other linear machines, complementary modular design has more sinusoidal and symmetrical flux linkage and lower detent force. Initially, the topology and machine working principle is thoroughly discussed. To maximize the thrust force of the machine and optimize the geometric parameters, built-in genetic algorithm (GA) of JMAG ver. 20 is utilized. Furthermore, the modular design incorporates the concept of fault-tolerant capabilities to provide the required decoupling between phases. 2D finite element analysis (FEA) is used to analyze the machine performance. Comparatively the optimized design exhibits higher thrust force, lower thrust force ripples and higher efficiency than the initial design.

In this work, a novel dual‐stator hybrid excited linear flux switching machine (DSHELFSM) is proposed. The proposed machine is suitable for long‐stroke applications as all the excitation sources are mounted on a short mover and the stator is completely passive. Second, the proposed machine uses ferrite magnets rather than the expensive rare earth permanent magnets (PMs) with the addition of field excitation to achieve flux‐regulation capability at various field currents. An iron bridge that provides an additional path for flux linkage to complete its circuit is used. Various design parameters such as split ratio, stator pole width, width and height of PM, the width of the iron bridge, width of mover's tooth, and stator slot depth are optimised using multivariable geometric optimisation (MGO) while keeping the slot area, electric and magnetic loading constant. The optimised design has improved the performance as compared to the initial design. Furthermore, the results obtained by 2D analysis are verified by 3D analysis. Thermal analysis is carried out to set the operating limit of the proposed machine. [ABSTRACT FROM AUTHOR]

Operation of Vernier machines is based on flux modulation. They have some advantages including maintaining the rated torque in motor applications and the rated output power in generator applications at low speeds, high torque density and relatively low torque ripple due to their magnetic gear property and fault‐tolerance. In recent years, the motor with various topologies has been developed for different applications. Therefore, analysing and monitoring different faults is essential in the design and implementation stages. This study has two main purposes. First, to introduce an accurate frequency index independent of load variations for detecting the turn‐to‐turn short circuit (TTSC) faults in the stator windings of a permanent magnet Vernier machine. Second, modelling the machine in a healthy condition and in the presence of TTSC faults to investigate its effect on machine performance and output characteristics. An analytical model is presented using the modified winding function theory under the TTSC fault by taking into account the effect of stator slots which enhances the accuracy of the air‐gap permeance function estimation. In the process of calculating the fault index, frequency components of the output characteristics of the machine are obtained from the mathematical equations of the magnetic field. It is shown that the proposed indicators are robust against load variations. [ABSTRACT FROM AUTHOR]

This document reviews the current state of the art in the linear machine technology. First, the recent advancements in linear induction, switched reluctance and permanent magnet machines are presented. The ladder slit secondary configuration is identified as an interesting configuration for linear induction machines. In the case of switched reluctance machines, the mutually-coupled configuration has been found to equate the thrust capability of conventional permanent magnet machines. The capabilities of the so called linear primary permanent magnet, viz. switched-flux, flux-reversal, doubly-salient and vernier machines are presented afterwards. A guide of different options to enhance several characteristics of linear machines is also listed. A qualitative comparison of the capabilities of linear primary permanent magnet machines is given later, where linear vernier and switched-flux machines are identified as the most interesting configurations for long stroke applications. In order to demonstrate the validity of the presented comparison, three machines are selected from the literature, and their capabilities are compared under the same conditions to a conventional linear permanent magnet machine. It is found that the flux-reversal machines suffer from a very poor power factor, whereas the thrust capability of both vernier and switched-flux machines is confirmed. However, the overload capability of these machines is found to be substantially lower than the one from the conventional machine. Finally, some different research topics are identified and suggested for each type of machine.

Thrust ripple and density greatly impact the performance of the linear machine and other linear actuators, causing positioning control precision, dynamic performance, and efficiency issues. Generalized pole-pair combinations are difficult to satisfy both the thrust and ripple for double salient reluctance linear machines. In this paper, a DC-Biased vernier reluctance linear machine (DCB-VRLM) is proposed to solve the abovementioned issues. The key to the proposed design is to reduce the ripple and enhance the thrust density with non-uniform teeth by utilizing and optimizing the modulated flux in the air gap. To effectively verify the proposed design, the DCB-VRLMs with different winding pole pairs and secondary poles are compared. The 12-slot/10-pole combination is chosen to adopt a non-uniform air gap structure. Moreover, the energy distribution of AC/DC winding is studied and optimized to further enhance the performance of the proposed DCB-VRLM. The results indicate that the DCB-VRLM with the non-uniform air gap has a lower thrust ripple, better overload capability, and higher thrust density, which confirms its superiority in long-stroke linear rail transit and vertical elevator applications.

The thermal design is one of the most important stages in the design process of electrical machines. Thanks to software packages, like Motor-CAD, rotating machine designers can predict the thermal operation of the machines with high precision. However, a Motor-CAD equivalent for linear machines does not exist. Thus, linear machine designers must develop specific thermal analysis tools when designing the machines. In this article, a generic thermal analysis tool for different kinds of linear machines is presented. The model has been designed in MATLAB Simulink. Hence, it should be easy to implement for most engineers. The article describes the configuration of the different elements of the tool. The calibration parameters and procedure, and typical values of the calibration variables, are also given in the document. Finally, in order to demonstrate the generic nature of the tool, the model is experimentally validated via DC thermal tests to a linear induction machine and a linear switched-flux permanent magnet machine. The results show that, despite being simple and easy to implement, the model can predict the thermal operation of different machines with high precision. [ABSTRACT FROM AUTHOR]

Summary: Although Vernier machines have been introduced a long ago, their description, applications, and design improvement have been recently proposed. This paper reviews different types of linear Vernier machine. Their description and theoretical base of the performance are presented. The performance of the motor is improved by reducing the cogging force, increasing the power factor, and enhancing force density. Stator and translator structures, the arrangement of magnets, and the type of coils of permanent magnet (PM) Vernier machines are reviewed and classified. Then, the electromagnetic performance prediction and energy conversion process in the machine is described. The magnetic field distribution and air gap permeance analysis indicate that such analysis is very complicated than that of other PM machines. Impacts of variations of dimensions in the machine such as the number of modulators on the modulus width and thickness of the mover PMs on the load characteristics (cogging torque and Back‐EMF) are addressed. Besides, principles of operation of flux modulation machines are presented and the shape and dimensions of the modulators are optimized. Finally, a 150 W linear PM Vernier generator is designed and prototyped to the energy harvested by the ocean wave. [ABSTRACT FROM AUTHOR]

A novel dual three‐phase permanent‐magnet linear synchronous machine (DTP‐PMLSM) is proposed for the large capacity ropeless elevator, where two sets of windings have 30 electrical degrees phase shift in space. First, the topology of DTP‐PMLSM with 12‐slot/11‐pole (12 s/11p) combination is introduced. Second, the influence of each main parameter on thrust force performance is investigated by single variable sweeping method, and then DTP‐PMLSM is optimised by global optimisation method. Moreover, the electromagnetic performance is predicted and analysed by two‐dimensional (2D) finite element method (FEM) in detail. Compared with conventional single three‐phase PMLSM, the proposed DTP‐PMLSM shows better force performance. Furthermore, the analysis results are compared with 3D FEM which includes the transverse end effect. Finally, a 12 s/11p prototyped machine is built and tested to validate the theoretical analyses. [ABSTRACT FROM AUTHOR]

It is commonly acknowledged that a direct‐drive linear wave energy converter (DDLWEC) will achieve maximum power extraction in the resonance state, which can be realised through impedance matching under the assumption that the wave is regular. While the real ocean waves are hardly regular. Considering swell, a relatively regular type of real ocean wave, by approximating it with a sum of multiple frequency components, the DDLWEC can be forced resonance to the swell through velocity control, the optimal velocity is derived based on the dynamical model of the DDLWEC through frequency domain analysis. The stability of velocity control is proven and the float equilibrium position deviation due to the velocity control is analysed and countered through compensation control. In real‐time control, the excitation force is approximated by the sum of four sinusoids, simulation and experiment results demonstrate that the proposed method is valid, stable, capable of achieving a high‐power extraction efficiency, and superior to some existing methods. [ABSTRACT FROM AUTHOR]

Linear hybrid excited flux switching machines (LHEFSM) combine the features of permanent magnet flux switching machines (PMFSM) and field excited flux switching machines (FEFSM). Because of the widespread usage of rare-earth PM materials, their costs are steadily rising. This study proposes an LHEFSM, a dual stator LHEFSM (DSLHEFSM), and a dual mover LHEFSM (DMLHEFSM) to solve this issue. The employment of ferrite magnets rather than rare-earth PM in these suggested designs is significant. Compared to traditional designs, the proposed designs feature greater thrust force, power density, reduced normal force, and a 25% decrease in PM volume. A yokeless primary structure was used in a DSLHEFSM to minimize the volume of the mover, increasing the thrust force density. In DMLHELFSM, on the other hand, a yokeless secondary structure was used to lower the secondary volume and the machine’s total cost. Single variable optimization was used to optimize all of the proposed designs. By completing a 3D study, the electromagnetic performances acquired from the 2D analysis were confirmed. Compared to conventional designs, the average thrust force in LHEFSM, DSLHEFSM, and DMLHEFSM was enhanced by 15%, 16.8%, and 15.6%, respectively. Overall, the presented machines had a high thrust force density, a high-power density, a high no-load electromotive force, and a low normal force, allowing them to be used in long-stroke applications.

This study presents comparative researches on performances of a double‐sided switched reluctance linear machine (DSRLM) under different winding connection modes. The static self/mutual inductances of a 6/4 yokeless DSRLM under two winding connection modes are calculated through the finite element method (FEM). This DSRLM can work either as a motor or as a generator. Now the performances of the DSRLM under different winding connection modes, including the force ripple in the electric model and the output voltage ripple in generation model, are compared through an established electric model and an established generation model. In addition, the iron losses under different winding connections are also investigated. Dynamic magnetic flux density waveforms of the DSRLM are calculated via FEM, and an iron loss computation module is established. Simulation results indicate that the advantages of both winding connections reflect in different aspects. This study summarises how to select a proper winding connection mode of DSRLMs for different performance demands responding to different applications. The experimental validations are conducted on a prototype DSRLM finally. [ABSTRACT FROM AUTHOR]

Snake‐like wave energy conversion (WEC) is a new type of WEC that combines raft WEC and magnetoelectric transducer. This type of WEC uses the magnetoelectric transducer, which is designed based on the permanent magnet linear generator and Halbach permanent magnet array, as its power take‐off unit. The purpose of this study is to design a matching magnetoelectric transducer for WEC in common wave conditions and test its performance. The hydrodynamic model of the snake‐like WEC is established to study the motion of WEC in regular waves. The equivalent magnetic circuit model of the magnetoelectric transducer is set up to optimise its ability to harvest wave energy in the ocean. Taking the maximum damping coefficient (cm·max) as the optimisation goal of the magnetoelectric transducer, the induced voltage and output power of the magnetoelectric transducer in relatively uniform and sinusoidal motion can be calculated by simulation software. Finally, a prototype of the magnetoelectric transducer was made and its performance was tested. The experiment shows that the magnetoelectric transducer has a good ability to harvest wave energy, and snake‐like WEC has wide applicability. [ABSTRACT FROM AUTHOR]

This article describes a novel approach to the design of linear machines that are not run at a steady-state operating point. The focus lies on minimizing the power loss to achieve highest possible efficiency. First analytical considerations reveal the potential of designing electrical machines and spring mechanisms for periodic, accelerated motion. It shows the influence of the machine size on the power losses due to the dependence of machine force as well as moving mass on this parameter. Based on these findings, a simulation model was created that can be used with an optimization algorithm. The simulation consists of a stationary and a time-dependent finite-element analysis of the linear machine in conjunction with an operational model that includes a given movement cycle. It was used to design a flat-type linear machine for a free-piston linear generator. The simulation results validate the analytical calculations and illustrate the differences to conventional design approaches for linear machines. [ABSTRACT FROM AUTHOR]

This article presents a design of a high thrust density moving magnet linear actuator for linear refrigerator compressor. The shape of permanent magnet (PM) shows great effect on cost, fabrication and magnetic flux density generation in the actuator. Axially magnetised disk shaped PMs are low cost and convenient for fabrication. Moreover, axially magnetised PMs generate high flux density in a specific direction compared to radial magnets. This paper investigates the design of axially magnetised moving magnet linear oscillating actuator (LOA) which operates on single phase alternating supply. Additionally, an alternative path is proposed for the return of magnetic flux from mover to the stator. Using finite element method (FEM) tools, all the parameters of LOA are optimised. Moreover, with the help of a specially designed experimental setup, FEM simulation results are validated. This actuator demonstrates great advancement in thrust force density, motor constant and output power compared to the size of proposed LOA. [ABSTRACT FROM AUTHOR]

The longitudinal end effect (LEE) has a negative influence on the performance of the flat‐type switched‐reluctance linear machines (SRLMs). For example, it can give rise to the imbalance of peak currents of different phases and the aggravation of the force ripple. This study proposes a modified current estimation model and an adaptive adjustment method (AAM) of turn‐on position to compensate for the LEE of SRLMs. The modified current estimation model considers not only the self‐inductance characteristics but also the mutual inductance characteristics. Some simulation results demonstrate that this modified estimation model has better estimation accuracy than a previous one. Then, the AAM of turn‐on position is proposed based on this modified current estimation model. It can balance the peak currents of different phases so that the negative impact of the LEE is greatly reduced. This new control method is easy to implement and requires little test, and its effectiveness in compensating for the peak currents and reducing force ripple is experimentally verified. [ABSTRACT FROM AUTHOR]

This study presents a novel technique for modelling of linear primary permanent‐magnet (PM) vernier machine wave converter based on an improved magnetic‐equivalent‐circuit (MEC) method. Saturation effect is considered by a new method, where the B–H curve fitting is performed using a novel non‐linear function. The machine properties such as the number of PMs, number of slots, magnets size, and all other machine parameters can be selected arbitrarily in the proposed model. The machine structure is considered by 12 individual zones. Each of the flux tubes in core and air gaps is modelled by a non‐linear reluctance, and the machine performances in both transient and steady‐state conditions are studied. Various machine properties such as magnets size and winding configuration are analysed and the dynamic behaviour is compared in various cases. Comparison to finite‐element method (FEM) shows the effectiveness and accuracy of the proposed MEC method and its much shorter processing time compared with FEM. [ABSTRACT FROM AUTHOR]

The linear permanent‐magnet synchronous generator (LPMSG) for direct‐drive wave energy conversion (WEC) suffers from many drawbacks that have not yet been overcome, such as a low power density and a bulky system volume. Therefore, a magnetic field‐modulated linear permanent‐magnet generator (FMLPMG) with a simple structure has been designed and manufactured. First, the operating principle of the FMLPMG is demonstrated by the equivalent magnetic circuit method, which explains the high power density of the FMLPMG. Second, at a constant speed and a sinusoidal speed, the electromagnetic characteristics of the FMLPMG under the no‐load and load conditions are analysed by the finite‐element method. Finally, a direct‐drive WEC test platform is built to simulate the process of wave action on the FMLPMG. No‐load and load experiments of the FMLPMG are conducted on the test platform, and the results are compared with those of an LPMSG with the same volume and operating conditions. The results show that the FMLPMG with a high power density converts wave energy effectively and solves the problem of low power density faced by the LPMSG in direct‐drive WEC. [ABSTRACT FROM AUTHOR]

Ocean waves are an abundant source of energy. This energy of the ocean can be converted into useful electrical energy using electrical generators. Linear generators have received tremendous attention in energy harvesting technology due to its unique ability to convert the energy without any intermediate converter. The principal objective of this study is to present the various types of linear electrical generators which have been investigated so far for direct drive ocean wave energy conversion and describe the working principle of each type with the difference. In this study, after a brief description of the basic electrical generator, various types of generators, including the linear and flat generators available in the literature are reviewed and discussed based on the design configuration of different types of magnet arrangements. Linear generators have been compared in terms of core type, flux path, the location of PMs, etc. The research gaps have been identified and future research directions have been suggested. [ABSTRACT FROM AUTHOR]

This study presents a non‐linear modelling method for a switched reluctance linear machine (SRLM), which achieves high modelling precision while requiring no prior knowledge regarding the specific structural dimensions of an SRLM. The proposed modelling method provides accurate flux linkage data based on limited experimental measurements through an interpolation process using a variant sigmoid function. The accuracy of the interpolation process is further increased by considering mutual coupling among the three phases. The performance of the proposed method is validated experimentally by comparing it with the performances of the Fourier series method and the two‐dimensional finite element method. The results demonstrate that the proposed method achieves greater modelling precision than the other methods considered in modelling an SRLM. [ABSTRACT FROM AUTHOR]

The thermal design is one of the most important stages in the design process of electrical machines. Thanks to software packages, like Motor-CAD, rotating machine designers can predict the thermal operation of the machines with high precision. However, a Motor-CAD equivalent for linear machines does not exist. Thus, linear machine designers must develop specific thermal analysis tools when designing the machines. In this article, a generic thermal analysis tool for different kinds of linear machines is presented. The model has been designed in MATLAB Simulink. Hence, it should be easy to implement for most engineers. The article describes the configuration of the different elements of the tool. The calibration parameters and procedure, and typical values of the calibration variables, are also given in the document. Finally, in order to demonstrate the generic nature of the tool, the model is experimentally validated via DC thermal tests to a linear induction machine and a linear switched-flux permanent magnet machine. The results show that, despite being simple and easy to implement, the model can predict the thermal operation of different machines with high precision.

Wave Energy Converters (WECs) generally use a Mechanical Power-Take-Off (MPTO) involving hydraulics or gearing to optimise the extraction of energy from the incoming waves before converting it into electrical energy via a high speed rotating generator. This simplifies the design of the Electrical Power Conversion System (EPCS). Further, it facilitates the use of mechanical energy storage such as hydraulic accumulators to reduce the peaky nature of the power flow and allows the WEC resonant frequency to be tuned for maximum energy capture. This work compares two power electronic converter topologies for an Electrical PTO (EPTO). This EPTO is intended to replace the aforementioned MPTO and generator with a Permanent Magnet Linear Machine (PMLM) directly coupled to the WEC. The compared topologies comprise either a Current Source Converter (CSC) or a Voltage Source Converter (VSC) as the generator interface working in combination with a DC-DC converter and an Energy Storage System (ESS). The principle differences between the two topologies are explored and losses are evaluated in a modular EPCS working with a WEC. Wide-bandgap power electronic switches are assumed for both topologies over a range of switching frequencies. The evaluation concludes that the CSC topology is advantageous at higher switching frequencies.

This work presents a new wave energy converter power take off (PTO) system that combines two recent developments in drive train technology, the consequent pole linear vernier hybrid permanent magnet machine and the linear magnetic gear. The combined system is fully realised in three-dimensional finite element method and compared to a similar direct drive machine. While the resulting system is lighter, reducing the active material mass by 30%, and more efficient, the system requires larger amounts of high cost permanent magnet material and increased PTO complexity. It is summarised that while such a system could be recommended in certain conditions, it is not viable for general application.

This article proposes a new topology of double-sided linear Vernier permanent magnet (LVPM) machine with segmented translator structure. A combination of a typical Halbach array consists of two horizontally magnetised permanent magnets (PMs) sandwiched between a salient iron tooth and adjacent vertically magnetised PM pole with the aim of improving its electromagnetic performance. The coreless partitioned translator contributes to a significant reduction in mass and the associated cost. With the aid of finite element analysis (FEA), two LVPM machines with the same PM, and stator volume have been investigated, analysed, and compared. The results imply that the proposed LVPM is capable of producing higher force density, while it exhibits lower cogging force and force ripple compared to its counterpart.

This study discusses the topology development of a cylindrical transverse flux linear machine for use with a free piston engine. Despite its three-dimensional flux path, the stator of this topology can be made from regular laminated components and only the translator includes soft magnetic composites. The detailed design development is discussed, including stator tooth combination, alternative winding, and fabrication techniques. Results from both finite element analysis and experimental measurement are compared, which gives a validation of the feasibility of the building process.

In this study, a linear synchronous machine is compared with a linear transverse flux machine. Both machines have been designed and built with the intention of being used as the power take off in a free piston engine. As both topologies are cylindrical, it is not possible to construct either using just flat laminations and so alternative methods are described and demonstrated. Despite the difference in topology and specification, the machines are compared on a common base in terms of rated force and suitability for use as a generator. Experience gained during the manufacture of two prototypes is described.

Free-piston engines have the potential to offer a compact machine capable of delivering electrical power. In this work, the design and modelling of a linear tubular generator are presented and used to investigate the effect of the electrical machine design on engine performance. A cogging-force-reduction technique is presented and used as a case study to demonstrate the importance of the integrated design.

This study addresses double-sided stationary stators in a linear electric generator with similar operation to a linear oscillatory motion electric machine. The plate mover in the linear electric generator's double-sided stationary stators is powered by the acoustic power output of the thermoacoustic engine's acoustic line. The main originality of this structure resides in the linear guidance used for the moving part. The mover is made up of a plate of sandwich magnets between two stators. This plate is in magnetic balance between the two stators through a controlled friction device.

This paper presents a linear variable reluctance permanent magnet (LVRPM) machine where the armature winding and inset Halbach array permanent magnets (PMs) are mounted on E-core stators. The Halbach array consists of a vertically magnetised PM pole and a salient ferromagnetic iron pole (split tooth) sandwiched between two horizontal PMs. The translator consists solely of laminations with salient iron poles. As a variable reluctance machine, it exhibits inherent magnetic gearing and a higher force and power density than the conventional synchronous PM machines. Finite element analysis (FEA) has been used to investigate the effect of machine parameters. The logical development of the LVRPM from the more conventional Vernier Hybrid machine is presented, including a near 50% reduction in magnetic flux leakage and a higher flux per unit magnet mass.

Different topologies of Vernier permanent magnet (PM) machines have been proposed for direct drive low-speed applications due to their high thrust and power density. However, this type of machine can suffer from low power factor (PF). In this study, a flux concentrated doubly salient linear permanent magnet machine with V-shape PM arrays is proposed and compared to a consequent pole (CP) type machine. Using the configuration of V-shaped PMs allows the flux to be concentrated in iron spacers located between two pieces of PMs. This feature is shown to result in an improvement of the airgap flux density, which allows a reduction in electrical loading and hence an improvement in power factor. In order to achieve a fair comparison, two doubly salient linear permanent magnet machines with different PMs’ configurations have been analysed and compared using transient FEA. The investigated machines have the same overall machine and, crucially, magnet volume. The results confirm that the proposed V-shape machine is capable of higher thrust force, higher no-load back EMF and can achieve a higher PF of 42% compared to the consequent pole machine, while it consumes the same amount of the PM material.