Electromagnetic Loss Analysis of a Linear Motor System Designed for a Free-Piston Engine Generator

electronics

Article Electromagnetic Loss Analysis of a Linear Motor System Designed for a Free-Piston Engine Generator

Yunqin Hu 1,* , Zhaoping Xu 2 , Lijie Yang 2 and Liang Liu 2

1 Department of Communication Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China 2 School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; [email protected] (Z.X.); [email protected] (L.Y.); [email protected] (L.L.) * Correspondence: [email protected]

Received: 8 March 2020; Accepted: 4 April 2020; Published: 8 April 2020

Abstract: A free-piston engine generator is a new type of power generating device, which has the advantages of high efficiency and simple structure. In this paper, a linear motor system composed of a moving-coil linear motor with axial magnetized magnets and a H-bridge pulse-width modulation (PWM) rectifier is designed for portable free-piston engine generators. Based on the finite-element model of the motor and physical model of the rectifier, the combined electromagnetic model is presented and then validated by the prototype-tested results. The electromagnetic processes of the linear motor system are simulated. The electromagnetic losses during the standard working cycle are analyzed. Under the rated reciprocating frequency of 50 Hz and the rated reciprocating stroke of 36 mm, the mechanical-to-electrical energy conversion efficiency of 86.3% can be obtained by the linear motor system, which meets the requirement of portable free-piston engine generators.

Keywords: electromagnetic analysis; electromagnetic loss; modeling and validation; moving-coil linear motor; PWM rectiﬁer; free-piston engine generator

1. Introduction A free-piston engine generator (FPEG) is a novel power generating device, which is a combination of a free-piston engine and a linear motor [1]. This new type of power generating device has attracted more and more scholars’ attention due to its potential advantages of high eﬃciency, simple structure and renewable alternative fuels adaptability [2]. The device can be used in portable power generation, electric vehicles and communication base stations [3]. The structure of a portable FPEG, studied in this paper, is shown in Figure1. The device consists of a mechanical body, a rectiﬁer for power conversion, a battery for energy storage and a controller. The mechanical body includes a free-piston engine, an air-spring for kickback, and a linear motor. Compared with the traditional engine generator, the crankshaft is canceled, and the free-piston is directly connected to the mover of a linear motor. The piston-mover assembly is the only moving part of the device [4]. This structure has the advantages of compact, low mass, easy manufacture, and low maintenance cost.

Electronics 2020, 9, 621; doi:10.3390/electronics9040621 www.mdpi.com/journal/electronics Electronics 2020, 9, x FOR PEER REVIEW 2 of 11 piston-mover assembly moves up from the bottom turning center (BTC) to the top turning center (TTC), and the mixture of air and fuel in the combustion chamber is compressed. In the expansion stroke, the compressed mixture of air and fuel is burned and releases heat instantly, so the piston- mover assembly moves down from the TTC to BTC driving by the combustion pressure. During the stable running, the linear motor works in generating mode all the time. The electromotive force (EMF) in the coil of the motor is quasi-sine wave, and the generating current in the coil is controlled as standard sine wave by the rectifier, and the electrical energy will be stored in Electronicsthe battery2020 in, 9 the, 621 form of direct current. During the starting of the device, the linear motor must work2 of 11 briefly in motoring mode to start the motion of the piston-mover assembly. Electronics 2020, 9, x FOR PEER REVIEW 2 of 11 piston-mover assembly moves up from the bottom turning center (BTC) to the top turning center (TTC), and the mixture of air and fuel in the combustion chamber is compressed. In the expansion stroke, the compressed mixture of air and fuel is burned and releases heat instantly, so the piston- mover assembly moves down from the TTC to BTC driving by the combustion pressure. During the stable running, the linear motor works in generating mode all the time. The electromotive force (EMF) in the coil of the motor is quasi-sine wave, and the generating current in the coil is controlled as standard sine wave by the rectifier, and the electrical energy will be stored in the battery in the form of direct current. During the starting of the device, the linear motor must work briefly in motoring mode to start the motion of the piston-mover assembly.

Figure 1. Free-piston engine generator sketch. Figure 1. Free-piston engine generator sketch. As the free-piston is not limited by the crankshaft, the reciprocating motion of the piston-mover assembly completely depends on the instantaneous forces acted on it. The forces include combustion pressure, electromagnetic force and spring force. The compression ratio of a FPEG is variable, thus multiple renewable alternative fuels can be used by the device without any structural changes. These features make the development of a FPEG competitive and valuable. A working cycle of the portable FPEG, studied in this paper, is shown in Figure2. A working cycle has two strokes: compression stroke and expansion stroke. In the compression stroke, the piston-mover assembly moves up from the bottom turning center (BTC) to the top turning center (TTC), and the mixture of air and fuel in the combustion chamber is compressed. In the expansion stroke, the compressed mixture of air and fuel is burned and releases heat instantly, so the piston-mover Figure 1. Free-piston engine generator sketch. assembly moves down from the TTC to BTC driving by the combustion pressure.

Figure 2. Working cycle of the free-piston engine generator.

The linear motor and the rectifier make up the linear motor system of the FPEG. Its performance affects the energy utilization efficiency of the FPEG. Many researchers have been working on the design of the linear motor for an FPEG [5–7]. Wang [8] proposed and designed a three-phase moving- magnet linear motor for the application of an FPEG. Its electromagnetic characteristics were predicted by analytical expressions and verified by finite element methods. Xu [9] proposed a single-phase moving-coil linear motor with radial magnetized magnets for the application of an FPEG, its analytical model was created, and its thrust force and the coil inductance were investigated. This kind of single-phase moving coil linear motor has the advantage of less moving mass, faster response and better controllability, but the generating efficiency is not Figure 2. Working cycle of the free-piston engine generator. high enough as there is Figurea high 2. eddy Working loss cyclein the of radial the free-piston magnetized engine magnets. generator. Chen [10] proposed a single-phase, short-stroke and large thrust axial magnetized linear motor. During the stable running, the linear motor works in generating mode all the time. A combined electromagnetic model composed of a finite element model and mathematical model of The electromotiveThe linear motor force and (EMF) the rectifier in the make coil up of the lin motorear motor is quasi-sine system of wave, the FPEG. and Its the performance generating affects the energy utilization efficiency of the FPEG. Many researchers have been working on the current in the coil is controlled as standard sine wave by the rectifier, and the electrical energy will be storeddesign inof thethe batterylinear motor in the for form an FPEG of direct [5–7]. current. Wang During [8] proposed the starting and designed of the device, a three-phase the linear moving- motor mustmagnet work linear briefly motor in for motoring the application mode to of start an theFPEG motion. Its electromagnetic of the piston-mover charac assembly.teristics were predicted by analyticalThe linear expressions motor and and the rectifierverified makeby finite up element the linear methods. motor system of the FPEG. Its performance affectsXu the [9] energy proposed utilization a single-phase efficiency moving-coil of the FPEG. linear Many researchersmotor with have radial been magnetized working on magnets the design for ofthe the application linear motor of foran anFPEG, FPEG its [5 –analytical7]. Wang [8model] proposed was andcreated, designed and aits three-phase thrust force moving-magnet and the coil inductance were investigated. This kind of single-phase moving coil linear motor has the advantage of less moving mass, faster response and better controllability, but the generating efficiency is not high enough as there is a high eddy loss in the radial magnetized magnets. Chen [10] proposed a single-phase, short-stroke and large thrust axial magnetized linear motor. A combined electromagnetic model composed of a finite element model and mathematical model of

Electronics 2020, 9, 621 3 of 11 linear motor for the application of an FPEG. Its electromagnetic characteristics were predicted by analytical expressions and verified by finite element methods. Xu [9] proposed a single-phase moving-coil linear motor with radial magnetized magnets for the application of an FPEG, its analytical model was created, and its thrust force and the coil inductance were investigated. This kind of single-phase moving coil linear motor has the advantage of less moving mass, faster response and better controllability, but the generating efficiency is not high enough as there is a high eddy loss in the radial magnetized magnets. Chen [10] proposed a single-phase, short-stroke and large thrust axial magnetized linear motor. A combined electromagnetic model composed of a finite element model and mathematical model of the controller was built, and the simulated results were compared with the tested results. This kind of single-phase axial magnetized linear motor was reported to have higher efficiency than radial magnetized. In this research, the electromagnetic loss in the power converter was not considered. Zheng [11] proposed a 1 kW moving-magnet linear motor for the FPEG application. The power densities, thrust fluctuation, and thermal field of the linear motor were investigated, but the electromagnetic efficiency of the linear motor was not reported in the paper. Xu [12] designed a similar 3 kW linear motor with I-shaped and rectangular designs for the same application. The theoretical efficiency of 90% to 95% was reported under the reciprocating moving speed of 3 to 5 m/s. In reference [13], a single-phase moving-magnet linear motor was proposed for an FPEG. The three-dimensional finite element model was established, and its boundary conditions were presented and explained in detail. By using the model, an electromagnetic analysis was carried out. The performance of the linear motor under reciprocating frequency 75 Hz was investigated and analyzed. The electromagnetic efficiency of 82% was obtained by the linear motor. As per the literature review above, some informative works about the linear motor designed for a FPEG have been reported. Analytical and finite element models have been created to analyze the efficiency of the linear motor, but few works try to research the linear motor and its power driving system as a whole system. The authors believe that a combined electromagnetic loss analysis is an efficient path to assess and optimize the total efficiency of a linear motor system [14,15]. In order to meet the requirements of a portable FPEG, this paper will present a novel linear motor system, which is considered to have the advantages of low moving mass, fast response, easy controllability and high efficiency. Based on the finite-element model of the motor and physical model of its power driving system, a combined electromagnetic model is presented and validated by the prototype. Then the electromagnetic loss of the motor system is analyzed in detail.

2. System Design

2.1. Linear Motor Design The linear motor system is the most important component of the FPEG. It must meet some special requirements of the FPEG, such as low moving mass, fast response, easy controllability and high energy conversion eﬃciency [16,17]. A single-phase moving-coil linear motor with embedded axial magnetized magnets is designed in this paper. As shown in Figure3, the motor can be divided into three parts: the stator, the mover and the shell. The stator is made up of an inner stator and an outer stator, each stator includes an axial magnetized magnet and two iron cores, and the magnet is located between the two iron cores. The magnetization direction of magnet in the inner and outer stators is opposite. The mover is made up of two reverse series moving-coils and a high strength plastic support. The mover is located in the air gap between the inner and outer stators. Electronics 2020, 9, x FOR PEER REVIEW 3 of 11 the controller was built, and the simulated results were compared with the tested results. This kind of single-phase axial magnetized linear motor was reported to have higher efficiency than radial magnetized. In this research, the electromagnetic loss in the power converter was not considered. Zheng [11] proposed a 1 kW moving-magnet linear motor for the FPEG application. The power densities, thrust fluctuation, and thermal field of the linear motor were investigated, but the electromagnetic efficiency of the linear motor was not reported in the paper. Xu [12] designed a similar 3 kW linear motor with I-shaped and rectangular designs for the same application. The theoretical efficiency of 90% to 95% was reported under the reciprocating moving speed of 3 to 5 m/s. In reference [13], a single-phase moving-magnet linear motor was proposed for an FPEG. The three-dimensional finite element model was established, and its boundary conditions were presented and explained in detail. By using the model, an electromagnetic analysis was carried out. The performance of the linear motor under reciprocating frequency 75 Hz was investigated and analyzed. The electromagnetic efficiency of 82% was obtained by the linear motor. As per the literature review above, some informative works about the linear motor designed for a FPEG have been reported. Analytical and finite element models have been created to analyze the efficiency of the linear motor, but few works try to research the linear motor and its power driving system as a whole system. The authors believe that a combined electromagnetic loss analysis is an efficient path to assess and optimize the total efficiency of a linear motor system [14,15]. In order to meet the requirements of a portable FPEG, this paper will present a novel linear motor system, which is considered to have the advantages of low moving mass, fast response, easy controllability and high efficiency. Based on the finite-element model of the motor and physical model of its power driving system, a combined electromagnetic model is presented and validated by the prototype. Then the electromagnetic loss of the motor system is analyzed in detail.

2. System Design

Figure 3. Sketch of the designed linear motor. Figure 3. Sketch of the designed linear motor. Table1 lists the main parameters of the linear motor in detail. Additionally, the neodymium iron boron “N42SH” is a choice for the magnet material to achieve higher residual magnetic ﬂux density, temperature stability and coercive force. The electrical pure iron “DT4” is a choice for the core material. Compared with silicon steel sheets and low carbon steel, the electrical pure iron is more suitable for this kind of moving-coil linear motor. It has lower manufacturing costs and better permeability performance. A kind of aluminum alloy is a choice for the shell material for low density and low magnetic permeability. A kind of high strength plastic “PTFE” is a choice for the coil support material. It has the advantages of non-magnetic, non-conductive and high strength.

Table 1. Parameters of the designed linear motor.

Items Value Diameter of outer stator 114 mm Thickness of outer stator 12 mm Diameter of inner stator 68 mm Thickness of inner stator 24 mm Length of core 15 mm Length of PM 30 mm Length of coil area 37 mm Width of air gap 10 mm Turns of two coils 128 Max stroke 40 mm

2.2. Rectifier Design The rectifier used in the FPEG not only must have high efficiency, but also must have two additional functions. The first function is that the rectifier must be controllable for adjusting the generating current of the motor. The second function is that the rectifier must be used as an inverter during the starting process of the FPEG to start the motion of the piston-mover assembly. This is because the reciprocating motion of the piston-mover assembly in a FPEG completely depends on the instantaneous forces acted on it. Between the forces of combustion pressure, electromagnetic force and spring force, the electromagnetic force is the only one which can be controlled to adjust the piston motion. The control of electromagnetic force of the motor is to control the coil current of the motor according to every stroke, so the rectifier must be controllable. An H-bridge pulse-width modulation (PWM) rectifier is designed to meet the requirements of the FPEG. As shown in Figure4, this is a voltage source PWM rectifier. During the stable running of the FPEG, the linear motor works in generating mode all the time, and the rectifier works in rectify and boot mode. The electromotive force (EMF) in the coil of the motor is quasi-sine ware. When the EMF of the motor is positive, K3 will be controlled by PWM signals and the others remain off, and its Electronics 2020, 9, 621 5 of 11

current path of PWM on and PWM oﬀ is presented in Figure4. When the EMF is negative, K1 will be Electronicscontrolled 2020 by, 9, PWM x FOR signalsPEER REVIEW and the others remain oﬀ. 5 of 11

Figure 4. Designed rectifier and its typical current path. Figure 4. Designed rectifier and its typical current path. During the starting process of the FPEG, the linear motor can briefly work in motoring mode. At thisDuring point ,the the starting PWM rectifier process works of the as FPEG, a PWM the inverter. linear motor When thecan linearbriefly motor work needs in motoring to be motoring mode. Atfrom this bottom point, tothe up, PWM K1 keeps rectifier on, K4works will as be a controlled PWM inverter. by PWM When signals, the linear and the motor others needs remain to obeff . motoringWhen the from linear bottom motor needsto up, toK1 be keeps motoring on, K4 from will up be to controlled bottom, K3 by keeps PWM on, signals, K2 will and be the controlled others remainby PWM off. signals, When andthe linear the others motor remain needs otoff .be We motoring call this from type ofup control to bottom, the limitedK3 keeps unipolar on, K2 controlwill be controlledmethod. This by PWM control signals, method and can the reduce others the remain electromagnetic off. We call this loss type as much of control as possible. the limited unipolar controlTable method.2 lists This the main control parameters method can of thereduce designed the electromagnetic PWM rectifier loss in detail, as much including as possible. the control parametersTable 2 and lists electromagnetic the main parameters parameters of the of designed the power PWM switch rectifier devices. in detail, As shown including in the table,the control metal parametersoxide semiconductor and electromagnetic field effect parameters transistors (MOSFET) of the power are switch a choice devices. for the As power shown switch in the to table, reduce metal the oxideelectromagnetic semiconductor loss. Thefield parameters effect transistors will be (MOSFET) used by the are model a choice in the for next the section.power switch to reduce the electromagnetic loss. The parameters will be used by the model in the next section. Table 2. Parameters of the designed pulse-width modulation (PWM) rectifier. Table 2. Parameters of the designed pulse-width modulation (PWM) rectifier. Items Value RatedItems voltage of the batteryValue 120 V RatedCapacitance voltage of ofthe filter battery capacitor 120 400 VµF CapacitanceMax of Current filter capacitor of K1~K4 400 70 μ AF Max CurrentOn-resistance of K1~K4 of K1~K4 25.5 70 A m Ω Turn-on time of K1~K4 24 ns Ω On-resistanceRise time of ofK1~K4 K1~K4 25.5 16 m ns Turn-onTurn-o timeff timeof K1~K4 of K1~K4 24 62 ns ns Rise timeFall timeof K1~K4 of K1~K4 16 45 ns ns Turn-offDiode forward time of voltage K1~K4 of K1~K4 62 1.3 ns V FallPWM time Frequency of K1~K4 of K1~K4 45 40 kHzns Diode forward voltage of 1.3 V 3. Modeling and Validation K1~K4 PWM Frequency of K1~K4 40 kHz 3.1. Linear Motor Model

3. ModelingThe electromagnetic and Validation model of linear motors can be divided into an analytical model and finite element model. Compared to the analytical model, the finite element model has the advantages of 3.1.being Linear easy Motor to model Model and quick to calculate. Additionally, the finite element model can consider the end effect and take magnetic flux leakage into account and calculate more accurately. In this paper, a The electromagnetic model of linear motors can be divided into an analytical model and finite transient finite element method with a motion solver is used to model the linear motor designed for element model. Compared to the analytical model, the finite element model has the advantages of the FPEG. being easy to model and quick to calculate. Additionally, the finite element model can consider the end effect and take magnetic flux leakage into account and calculate more accurately. In this paper, a transient finite element method with a motion solver is used to model the linear motor designed for the FPEG.

Electronics 2020, 9, x FOR PEER REVIEW 6 of 11 Electronics 2020, 9, 621 6 of 11 Electronics 2020, 9, x FOR PEER REVIEW 6 of 11 The model of the linear motor is shown in Figure 5. This model is a two-dimensional transient finite element model with a motion region. At this point, the mover is in the middle of the stroke, and TheThe modelmodel ofof thethe linearlinear motormotor isis shownshown inin FigureFigure5 5.. This This model model is is a a two-dimensional two-dimensional transient transient the position is defined as the original point of the mover, as shown in Figure 5. The magnetic field is finitefinite elementelement modelmodel withwith aa motionmotion region.region. AtAt this point,point, thethe mover isis in the middle of the stroke, and mainly distributed in ferromagnetic materials, and the leakage flux is relatively small. In order to thethe positionposition is defined defined as as the the original original point point of of the the mover, mover, as as shown shown in in Figure Figure 5.5 .The The magnetic magnetic field field is display the internal structure, the meshes in the air box of the calculation region are hidden. ismainly mainly distributed distributed in in ferromagnetic ferromagnetic materials, materials, and and the the leakage leakage flux flux is is relatively small. In order toto displaydisplay thethe internalinternal structure,structure, thethe meshesmeshes inin thethe airair boxbox ofof thethe calculationcalculation regionregion areare hidden.hidden.

Figure 5. Finite element model of the linear motor, (a) mesh, (b) flux density. Figure 5. Finite element model of the linear motor, (a) mesh, (b) flux density. Figure 5. Finite element model of the linear motor, (a) mesh, (b) flux density. 3.2. Combined Simulation Model 3.2. Combined Simulation Model 3.2. CombinedIn order toSimulation analyze theModel electromagnetic loss of the designed PWM rectifier, its physical model is establishedIn order by to using analyze the thepower electromagnetic electronics toolbo loss ofx in the the designed software PWM of MATLAB. rectifier, itsSupported physical modelby the In order to analyze the electromagnetic loss of the designed PWM rectifier, its physical model is isfinite established element bysoftware using thewe powerused to electronics create the toolboxmodel of in the the linear software motor, of MATLAB. the finite element Supported model by the of established by using the power electronics toolbox in the software of MATLAB. Supported by the finitethe linear element motor software is embedded we used into to create the MATLAB the model software. of the linear The motor, MATLAB the finite software element calls model the offinite the finite element software we used to create the model of the linear motor, the finite element model of linearelement motor software is embedded in every intotime the steps, MATLAB so the real software. combined The MATLABsimulation software can be realized. calls the finite element the linear motor is embedded into the MATLAB software. The MATLAB software calls the finite softwareAs shown in every in timeFigure steps, 6, the so thecombined real combined model consis simulationts of four can beparts: realized. linear motor finite element element software in every time steps, so the real combined simulation can be realized. model,As rectifier shown inmodel, Figure rectifier6, the combined controller, model and consistsfree-piston of fourengine parts: model. linear The motor rectifier finite controller element As shown in Figure 6, the combined model consists of four parts: linear motor finite element model,provides rectifier PWM signals model, to rectifier the four controller, power switch and de free-pistonvices of the engine rectifier model. model. The The rectifier PWM signals controller are model, rectifier model, rectifier controller, and free-piston engine model. The rectifier controller providescalculated PWM based signals on the tocurrent the four feedback power of switch the motor, devices and of a thediscrete rectifier proportional model. The integral PWM differential signals are provides PWM signals to the four power switch devices of the rectifier model. The PWM signals are calculated(PID) algorithm based onis used the current in this feedback paper. The of the free- motor,piston and engine a discrete model proportional is created integral according differential to the calculated based on the current feedback of the motor, and a discrete proportional integral differential (PID)difference algorithm equations is used described in this paper. in [16]. The The free-piston free-pist engineon engine model model is created is used according to output to the the diff pistonerence (PID) algorithm is used in this paper. The free-piston engine model is created according to the equationsmotion trajectory described to indrive [16]. the The linear free-piston motor enginefinite element model is model. used to output the piston motion trajectory difference equations described in [16]. The free-piston engine model is used to output the piston to drive the linear motor finite element model. motion trajectory to drive the linear motor finite element model.

Figure 6. Combined model of the linear motor system. Figure 6. Combined model of the linear motor system.

Figure 6. Combined model of the linear motor system.

Electronics 2020, 9, x FOR PEER REVIEW 7 of 11

3.3. Model Validation A prototype of the linear motor system designed in the last section is developed. Figure 7 shows the prototype and its test platform. The test platform consists of five parts: the developed linear motor, prototype, the developed PWM rectifier, an air spring, a free piston engine and a battery. The piston bore of the engine is 48 mm with the max stroke of 38 mm and the effective compression ratio of 7.8. It uses gasoline direct injection and spark ignition combustion under the Electronics 2020, 9, 621 7 of 11 excess air ratio of 1.1. The indicated power of the engine is about 1.5 kW, and the indicated thermal efficiency is 37% [17]. The piston bore of the air spring is 65 mm, which is bigger than the piston bore Electronics 2020, 9, x FOR PEER REVIEW 7 of 11 3.3.of Model the engine. Validation The moving mass of both the piston and cylinder is about 0.5 kg. A displacement sensor is connected to the mover of the linear motor, and a current sensor is 3.3. Model Validation installedA prototype in the alternating of the linear current motor side system of the designed rectifier, inso thethe lastreal-time section piston-mover is developed. position Figure and7 shows the thecoil prototype currentA prototype andof the its linear testof the platform. motor linear can motor The be tested. testsystem platform Base designedd on consists the in test the of platform,last ﬁve section parts: the is the combineddeveloped. developed model Figure linear created 7 shows motor, prototype,in thethe prototypelast the section developed and is validated its test PWM platform. by rectiﬁer, comparing The an test air the platform spring, simulated consists a free results piston of five with engine parts: the prototype the and developed a battery. tested linear results. motor, prototype, the developed PWM rectifier, an air spring, a free piston engine and a battery. The piston bore of the engine is 48 mm with the max stroke of 38 mm and the effective compression ratio of 7.8. It uses gasoline direct injection and spark ignition combustion under the excess air ratio of 1.1. The indicated power of the engine is about 1.5 kW, and the indicated thermal efficiency is 37% [17]. The piston bore of the air spring is 65 mm, which is bigger than the piston bore of the engine. The moving mass of both the piston and cylinder is about 0.5 kg. A displacement sensor is connected to the mover of the linear motor, and a current sensor is installed in the alternating current side of the rectifier, so the real-time piston-mover position and the coil current of the linear motor can be tested. Based on the test platform, the combined model created in the last section is validated by comparing the simulated results with the prototype tested results.

FigureFigure 7. 7.Prototype Prototype ofof thethe linearlinear motor system and and its its test test platform. platform.

TheFigure piston 8 shows bore of the the simulated engine is 48and mm tested with movement the max stroke of the ofpiston-mover 38 mm and theassembly. effective As compression shown in ratiothe of figure, 7.8. It a uses simplified gasoline testing direct cycle injection is used. and sparkThe stroke ignition of the combustion testing cycle under is the14 mm, excess and air the ratio ofreciprocating 1.1. The indicated frequency power is about of the 23engine Hz. The is testing about cycle 1.5 kW, has andtwo theprocesses. indicated In the thermal first process, efficiency the is 37%linear [17]. motor The piston works bore in motoring of the air mode, spring the is 65 PWM mm, rectifier which is works bigger as than an PWM the piston inverter bore to of drive the engine. the Thelinear moving motor mass move of bothfrom thetop pistonto bottom, and and cylinder the gas is aboutspring 0.5brakes kg. the motion. In the second process, theA gas displacement spring drives sensor the linear is connected motor move to thefrom mover bottom of to the top, linear the PWM motor, rectifier and a works current in sensorrectify is installedand boost in the mode, alternating and the linear current motor side works of the rectifier,in generating so the mode real-time to brake piston-mover the motion. position and the coil current of the linear motor can be tested. Based on the test platform, the combined model created in the last section is validatedFigure 7. by Prototype comparing of the the linear simulated motor system results and with its test the platform. prototype tested results. Figure8 shows the simulated and tested movement of the piston-mover assembly. As shown Figure 8 shows the simulated and tested movement of the piston-mover assembly. As shown in in the figure, a simplified testing cycle is used. The stroke of the testing cycle is 14 mm, and the the figure, a simplified testing cycle is used. The stroke of the testing cycle is 14 mm, and the reciprocating frequency is about 23 Hz. The testing cycle has two processes. In the first process, reciprocating frequency is about 23 Hz. The testing cycle has two processes. In the first process, the the linear motor works in motoring mode, the PWM rectifier works as an PWM inverter to drive the linear motor works in motoring mode, the PWM rectifier works as an PWM inverter to drive the linearlinear motor motor move move from from top top to bottom, to bottom, and and the the gas gas spring spring brakes brakes the the motion. motion. InIn thethe secondsecond process, the gasthe spring gas spring drives drives the linear the linear motor motor move move from from bottom bottom to top, to thetop, PWMthe PWM rectifier rectifier works works in rectify in rectify and boostand mode, boost and mode, the linearand the motor linear works motor inworks generating in generating mode tomode brake to brake the motion. the motion.

Figure 8. Comparison of tested and simulated movement.

Figure 8. Comparison of tested and simulated movement. Figure 8. Comparison of tested and simulated movement.

ElectronicsElectronics2020 2020, 9,, 6219, x FOR PEER REVIEW 88 of of 11 11 Electronics 2020, 9, x FOR PEER REVIEW 8 of 11 Figure 9 shows the simulated and tested coil current of the linear motor during the testing cycle. In FigureeachFigure stroke,9 shows 9 shows the the coil the simulated currentsimulated is and controlledand tested tested coil tocoil current standard curre ofnt theofsine the linear wave linear motor by motor the during PWM during the rectifier. the testing testing The cycle. cycle. root InmeanIn each each stroke,square stroke, the (RMS) the coil coil currentcurrents current is in controlled isthe controlled two toprocesses standard to standard are sine 16.8 wave sine A and bywave the9.8 by PWMA. theThe rectiﬁer.PWM difference rectifier. The between root The mean root the squaretwomean (RMS)RMS square currents currents (RMS) iniscurrents thedue two to in processes thethe twolosses processes are during 16.8 A are andthe 16.8 9.8reciprocating A.A and The di9.8ﬀ erenceA.motion The between difference cycle, theincluding between two RMS the currentselectromagnetictwo RMS is due currents to theloss losses discussedis due during to inthe thethe losses reciprocatingpaper andduring the motion mechanicalthe reciprocating cycle, loss. including motion the electromagneticcycle, including loss the discussedelectromagnetic in the paper loss anddiscussed the mechanical in the paper loss. and the mechanical loss.

FigureFigure 9. 9.Comparison Comparison of of tested tested and and simulated simulated current. current. Figure 9. Comparison of tested and simulated current. FigureFigure 10 10 shows shows the the simulated simulated and and tested tested PWM PWM ratio ratio of of the the PWM PWM rectiﬁer rectifier during during the the testing testing cycle.cycle. AsFigure As shown shown 10 shows in in the the the ﬁgure, figure, simulated the the resultsresults and aretestedare consistent,cons PWMistent, ratio especiallyespecially of the PWM whenwhen rectifier the linear during motor the system testing is isoperatingcycle. operating As shownin in the powerin the figure,generation the results state. This Thisare consconsistency consistencyistent, especially validates validates when the the combined combined the linear model modelmotor created createdsystem inis intheoperating the last last section, section, in the and andpower indicates indicates generation that that the state. the most most This elec electromagnetic consistencytromagnetic validates loss loss of ofthe the the linear combined linear motor motor modelsystem system created has has been in beenmodeledthe modeledlast section, by bythe theand combined combined indicates model, model,that the so so mostthe the combined combinedelectromagnetic model model losshas of enoughenough the linear precisionprecision motor to tosystem carry carry outhas out thebeen the electromagneticelectromagneticmodeled by the loss losscombined analysis analysis inmodel, in the the next nextso section.the section. combined model has enough precision to carry out the electromagnetic loss analysis in the next section.

Figure 10. Comparison of the tested and simulated PWM ratio. Figure 10. Comparison of the tested and simulated PWM ratio. 4. Electromagnetic LossFigure Analysis 10. Comparison of the tested and simulated PWM ratio. 4. Electromagnetic Loss Analysis 4. ElectromagneticBased on the validated Loss Analysis model in the last section, the electromagnetic loss and power conversion eﬃciencyBased of the on linearthe validated motor system model designed in the last for section, the FPEG the areelectromagnetic simulated and loss analyzed and power in this conversion section. ConsideringefficiencyBased of thaton the the the linear validated linear motor motor model system system in the designed workslast section, in fo generatingr thethe FPEGelectromagnetic mode are simulated all the loss time andand during power analyzed the conversion stable in this runningsection.efficiency of Considering the of FPEG,the linear a that standard motor the linear cyclesystem motor is designeddesigned system ﬁrstlyfo worksr the according inFPEG generating are to thesimulated mode rated operatingall and the analyzedtime conditions during in thisthe ofstablesection. the FPEG. running Considering As shown of the that inFPEG, Figure the lineara 11standard, the motor linear cycle system motor is designedworks system in worksfirstlygenerating inaccording generating mode toall the modethe ratedtime all during theoperating time the duringconditionsstable the running standard of the of FPEG. the cycle. FPEG, As The shown workinga standard in Figure frequency cycle 11, is the ofdesigned thelinear standard motor firstly system cycle according is works 50 Hz, to inthe which generating rated is equaloperating mode to allconditions the time ofduring the FPEG. the standard As shown cycle. in Figure The workin 11, theg frequencylinear motor of thesystem standard works cycle in generating is 50 Hz, whichmode all the time during the standard cycle. The working frequency of the standard cycle is 50 Hz, which

ElectronicsElectronics2020 2020, 9,, 6219, x FOR PEER REVIEW 99 of of 11 11 Electronics 2020, 9, x FOR PEER REVIEW 9 of 11 is equal to 3000 turns per minute of conventional engines. The coil current amplitude of the linear is3000 motorequal turns tois 22 per3000 A, minute andturns the ofper reciprocating conventional minute of conventional engines.stroke of Thethe engines.piston-mover coil current The amplitude coil movement current of amplitude theis 36 linear mm. motor of the is linear 22 A, motorand the is reciprocating22 A, and the stroke reciprocating of the piston-mover stroke of the movementpiston-mover is 36 movement mm. is 36 mm.

Figure 11. Standard cycle for electromagnetic loss analysis. Figure 11. Standard cycle for electromagnetic loss analysis. Figure 11. Standard cycle for electromagnetic loss analysis. FigureFigure 12 12 shows shows the the simulated simulated instantaneous instantaneous electromagnetic electromagnetic loss loss power power in the in linear the linear motor motor of the of standardtheFigure standard cycle. 12 showscycle. Between Betweenthe the simulated losses, the losses, the instantaneous copper the copper loss ofelectromagnetic coilloss accounts of coil accounts for loss 87% power offor the 87% in total theof loss.thelinear total The motor loss. copper ofThe thelosscopper standard depends loss cycle. ondepends the Between winding on the the winding wire losses, diameter wirethe copper diameter and is loss limited and of coil is by limited accounts the maximum by forthe 87% maximum allowable of the totalallowable mass loss. of The mass the coppermoving-coil,of the loss moving-coil, depends thus it is onthus di ﬃthe cultit windingis todifficult reduce. wire to The reduce.diameter eddy The loss and eddy of is the limited loss magnet of bythe isthe magnet small, maximum and is small, this allowable helps and this prevent mass helps oftheprevent the magnet moving-coil, the from magnet high thus temperaturesfrom it is high difficult temperatures and to reduce. demagnetization. and The dema eddygnetization. Theloss eddyof the loss magnetThe of eddy the is iron small,loss core of and the is acceptable. thisiron helps core is preventThisacceptable. indicates the magnet This that indicates the from electrical high that temperatures purethe electrical iron “DT4” andpure isdema iron a suitable gnetization.“DT4” choice is a suitable The for eddy the choice core loss material forof thethe ironcore and corematerial sheets is acceptable.areand not sheets necessary. This are indicatesnot The necessary. ﬁgure that also the The indicateselectrical figure also thatpure indicates the iron aluminum “DT4” that is the alloya suitable aluminum is not choice a goodalloy for choiceis the not core a for good thematerial shellchoice andmaterial,for sheets the shell as are the material, not eddy necessary. loss as isthe higher Theeddy figurethan loss expected.isalso higher indicates than expected.that the aluminum alloy is not a good choice for the shell material, as the eddy loss is higher than expected.

Figure 12. Electromagnetic loss in the linear motor. Figure 12. Electromagnetic loss in the linear motor. Figure 13 shows the simulated instantaneous electromagnetic loss in the rectifier of the standard Figure 12. Electromagnetic loss in the linear motor. cycle. ItFigure can be 13 seen shows that the the simulated loss power instantaneous of each MOSFET electrom is diagneticfferent, andloss in it isthe related rectifier to theirof the working standard states.cycle.Figure Take It can 13 the be shows first seen half thethat ofsimulated the the loss cycle power instantaneous to analyze. of each The MOSF electrom EMFET and isagnetic different, current loss ofand in the the it linearis rectifier related motor of to the their are standard positive, working cycle.sostates. the It K3 can Take is controlledbe the seen first that half by the PWM of loss the signalspowercycle to of and analyze. each the MOSF others TheET EMF remain is different,and o ffcurrent. The and current of it the is related linear flows motor pastto their the are working diode positive, of states.K1so all the theTake K3 time, isthe controlled andfirst itshalf loss of by the is PWM the cycle biggest. signals to analyze. When and the The the othe K3EMF PWMrs andremain iscurrent off off., the ofThe current the current linear flows motorflows past pastare the positive, diodethe diode of sotheof the K4,K1 K3 andall is the itscontrolled time, loss is and the by its second PWM loss is biggest.signals the biggest. and No current theWhen othe the flowsrs K3remain past PWM the off. is K2 off,The during the current current the flows first flows half past past of the the the diode cycle, diode ofsoof K1 its the all loss K4,the is time,and zero. its and By loss analyzing its is loss the is second the the biggest. results, biggest. weWhen No can thecurre conclude K3nt PWM flows that is past theoff, diodesthe currentK2 induring the flows rectifier the past first shouldthe half diode of be the ofimproved,cycle, the K4, so and asits they lossits loss accountis zero. is the forBy second mostanalyzing biggest. of the the loss No results, in curre the PWMntwe flows can rectifier. concludepast the K2that during the diodes the first in halfthe rectifierof the cycle,should so itsbe improved,loss is zero. as By they analyzing account forthe mostresults, of thewe losscan inconclude the PWM that rectifier. the diodes in the rectifier should be improved, as they account for most of the loss in the PWM rectifier.

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Figure 13. Electromagnetic loss in the PWM rectifier. Figure 13. Electromagnetic loss in the PWM rectifier. Table3 lists the main parameters and the e fficiency of the linear motor system designed by this paper forTable a FPEG. 3 lists Under the main the standardparameters working and the cycle efficien of ratedcy of frequency the linear 50 motor Hz and system rated designed stroke 36 by mm, this thepaper generating for a FPEG. efficiency Under of the linearstandard motor working and the cycle power of rated conversion frequency effi ciency50 Hz ofand the rated rectifier stroke are 36 91.6%mm, andthe generating 94.1%, respectively. efficiency Theof the effi linearciency motor of the an lineard the power motor systemconversion is 86.3%. efficiency Considering of the rectifier the indicatedare 91.6% thermal and 94.1%, efficiency respectively. of engine The is efficiency about 37% of [the17], linear the e ffimotorciency system of the ischemical-to-electrical 86.3%. Considering the energyindicated conversion thermal of efficiency about 31% of can engine be obtained is about by 37% the [17], FPEG the system, efficiency when of it the uses chemical-to-electrical the motor system. energy conversion of about 31% can be obtained by the FPEG system, when it uses the motor system. Table 3. Parameters and efficiency of the linear motor system. Table 3. Parameters and efficiency of the linear motor system. Name Value Name Value Rated motion frequency 50 Hz Rated motionRated frequency motion stroke 50 36 Hz mm Rated motionRated output stroke power 36 540 mm W Rated outputMass ofpower the mover 540 1.2 W kg MassEffi ciencyof the ofmover the linear motor 1.2 91.6% kg EfficiencyEfficiency of the of linear the rectifier 94.1% Efficiency of the motor system91.6% 86.3% Specificmotor power of the motor 118 W/kg Efficiency of the rectifier 94.1% Efficiency of the motor 5. Conclusions 86.3% system In this paper, a linear motorSpecific system power composed of the of a moving-coil linear motor with axial magnetized 118 W/kg magnets and an H-bridge PWM rectifiermotor is designed for a portable free-piston engine generator. A combined electromagnetic simulation model is presented and validated by the prototype tested results.5. Conclusions The electromagnetic loss of the linear motor system is analyzed by using the validated model. Under the rated working frequency of 50 Hz, the efficiency of 86.3% can be obtained by the proposed In this paper, a linear motor system composed of a moving-coil linear motor with axial linear motor system, which meets the requirement of the design. magnetized magnets and an H-bridge PWM rectifier is designed for a portable free-piston engine The electromagnetic analysis indicates that the copper loss is the main loss of the linear motor, generator. A combined electromagnetic simulation model is presented and validated by the and the diode loss is the main loss of the rectifier. The copper loss and the diode loss account for more prototype tested results. The electromagnetic loss of the linear motor system is analyzed by using the than 90% of the total loss. In the future, we will try to improve the performance of the linear motor validated model. Under the rated working frequency of 50 Hz, the efficiency of 86.3% can be obtained system by optimizing the moving-coil of the linear motor and using independent diodes to replace the by the proposed linear motor system, which meets the requirement of the design. internal diode of the MOSFET. We will test the efficiency of the linear motor system under the 50 Hz The electromagnetic analysis indicates that the copper loss is the main loss of the linear motor, rated working cycle after manufacturing a more powerful mechanical drive system. and the diode loss is the main loss of the rectifier. The copper loss and the diode loss account for more than 90% of the total loss. In the future, we will try to improve the performance of the linear motor system by optimizing the moving-coil of the linear motor and using independent diodes to replace the internal diode of the MOSFET. We will test the efficiency of the linear motor system under the 50 Hz rated working cycle after manufacturing a more powerful mechanical drive system.

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Author Contributions: Y.H. completed the model analysis and finished the manuscript; Z.X. designed the rectifier and provided the guidance; L.Y. designed the linear motor and completed the test; L.L. revised the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This work is supported by the National Natural Science Foundation of China (NO. 51875290, 51975297). Conflicts of Interest: The authors declare no conflict of interest.

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