Resonant Combustion Start Considering Potential Energy of Free-Piston Engine Generator

Article Resonant Combustion Start Considering Potential Energy of Free-Piston Engine Generator

Mitsuhide Sato *, Takumi Goto, Jianping Zheng and Shoma Irie Faculty of Engineering, Shinshu University, Nagano-City, Nagano 380-8553, Japan; [email protected] (T.G.); [email protected] (J.Z.); [email protected] (S.I.) * Correspondence: [email protected]; Tel.: +81-26-269-5211

Received: 30 August 2020; Accepted: 1 November 2020; Published: 3 November 2020

Abstract: Free-piston engine generators without a crank mechanism are expected to be used in series hybrid vehicles because of their lower losses. The series hybrid system requires a low starting thrust because the engine frequently starts depending on the battery state. This study clarifies the effectiveness of the constant thrust resonance starting method that utilizes the compression pressure of the engine and the spring thrust. The piston must pass the combustion starting point with a predetermined speed to start combustion. Herein, we present a thrust setting method that uses the energy state diagram to optimize the velocity at the combustion start point. A simulation is performed assuming output when mounted on a vehicle. Consequently, the simulation results show that the maximum thrust can be reduced by more than 90% compared to that without resonance. Moreover, the speed at the combustion start point is in agreement with the value obtained using an energy state diagram. An impulse-like combustion pressure is generated in 180 ms, and combustion can be started using resonance, as shown in an experiment using a small-output engine and linear motor. The effectiveness of the constant thrust resonance starting method was confirmed.

Keywords: free-piston engine; mechanical resonance; potential energy; mechanical energy; linear motor; combustion starting

1. Introduction Transportation equipment emits large quantities of harmful gasses such as carbon dioxide and nitrogen oxide; therefore, the electrification of automobiles is progressing to improve the fuel efficiency of vehicles [1–5]. The development of pure electric vehicles, which are expected to be highly efficient, is progressing in countries around the world [6,7]. A series hybrid vehicle equipped with a dedicated engine for power generation and a rotary generator has been drawing attention in recent years because of a longer cruising range and lower costs [8–10]. In this system, the generator is driven by gasoline engine power, and the electric power obtained drives the vehicle propulsion motor to drive the vehicle. This is an electric vehicle that can extend the cruising range while generating electricity with a power generation engine. The energy density of fossil fuels, such as gasoline, is much higher than that of batteries. The number of batteries installed in the vehicle can be reduced by using a fossil fuel-based power generation system. On the contrary, this system requires a linear motion conversion mechanism, such as a crank/camshaft, to convert the linear power of the engine into a rotational motion for the generator. The direct rotation conversion mechanism leads to mechanical loss and size increase. Therefore, studies on the free-piston engine linear generator system (FPEG) for improving the overall fuel efficiency are in progress [11–18]. The FPEG is an internal combustion engine that does not use a direct-drive rotation conversion mechanism. Using the combustion force of the engine and the repulsive force of the spring, the mover reciprocates to generate electricity with a linear generator.

Energies 2020, 13, 5754; doi:10.3390/en13215754 www.mdpi.com/journal/energies Energies 2020, 13, 5754 2 of 17

The linear motion of the piston has been reported to be directly converted into energy without using the linear–rotation conversion mechanism, and the friction loss of the FPEG is improved by approximately 40% [11]. The efficiency of applying premixed compression ignition combustion was calculated using a combustion simulation, and an energy conversion efficiency of 42% was achieved under the conditions of 19.0 compression ratio and 12.7 kW power generation output [12]. The thrust is adjusted and the piston (i.e., the mover) without the crank can be operated arbitrarily by using the inverter current control of the linear generator [19]. Up to now, improvements in thermal and power generation efficiencies have been reported by taking advantage of arbitrary operability of piston [19–21]. The FPEG mainly required power generation; however, the linear generator is motored to drive the piston to start the engine from the time it is stopped until the engine is ignited [21]. Series hybrid vehicles do not keep the engine running all the time; instead, they turn on and off depending on the battery charge state. Therefore, a method for efficiently and steadily starting combustion is required considering many times of engine starting. In other words, resonance using the repulsion spring and the spring effect with engine compression is appropriate for the combustion start process [22,23]. In ordinary spring resonance, the potential energy is bilaterally symmetrical at the center of vibration. In contrast, the potential energies of FPEGs in single-side engine type with different spring properties are not symmetrical, and the spring effect with the engine compression is nonlinear. Obtaining the amplification effect with a simple resonance is difficult because the resonance frequency during vibration is not constant. Thus, a constant thrust force is applied in the action direction to resonate the piston in opposed engine with symmetric potential energy [24]. An appropriate thrust must be given to start combustion at the combustion start point in single-side engine type; however, the method of setting the thrust has not yet been reported. This study proposes a method of setting the constant thrust starting method using the energy state diagram concept. The thrust reduction effect of the constant thrust starting method is clarified by a simulation. We also perform experiments using an engine to verify whether or not the constant thrust resonance method can start an engine.

2. FPEG Operation Principle

2.1. Structure Figure1 presents the physical model of the FPEG consisting of a free-piston engine, a linear generator, and a repulsion spring. A major feature of the FPEG is the absence of a mechanical constraint, unlike the piston of the crank mechanism. The combustion force (Fc) of the engine acts on the piston, causing the free piston to move toward the spring repulsion chamber. The spring repulsion force (Fg) acts in the direction opposite to the combustion force and pushes the piston back into the combustion chamber. The piston reaches the combustion start point (xs) near the top dead center (TDC) of the compression stroke and starts the combustion. The piston reciprocates between the TDC and the bottom dead center (BDC) to generate electricity by repeating this operation. The free piston engine burns properly by passing at the ideal piston speed at the combustion start point (xs)[24]. The permanent magnet is attached to the piston, and the coil is wound on the stator, which constitutes a moving magnetic linear synchronous generator. The power is generated by the reciprocating motion of the piston, and the braking thrust (Fl) is applied to the piston. The dynamic braking thrust can be adjusted by power generation control using an inverter that controls the output to the battery. The linear generator thrust under vector control is expressed by the product of the q-axis current (iq) and the thrust constant (Kf) of the generator. The equation of motion is described by Equation (1) with the piston displacement (x) and the piston mass (m). Energies 2020, 13, x FOR PEER REVIEW 3 of 17 to the thermodynamic law based on the heat generated and the volume of the combustion chamber. The pressure before the combustion behaves like an adiabatic compression air spring. The pressure on Energies the starting2020, 13, 5754 process is expressed by Equation (4), with the pressure and volume3 of 17 at the scavenging point expressed as pa (atmospheric pressure) and Va, respectively. Combustion Spring chamber Linear generator/ motor chamber

Coil

2 Ac (m ) Free-piston

Fc (Combustion Permanent magnet thrust) Fg x x (m) (Spring thrust) x0 0 xs a (TDC) (BDC) F (Linear motor thrust) l FigureFigure 1. 1.PhysicalPhysical model model of of the the free free-piston-piston engine linear linear generator generator system system (FPEG) (FPEG consisting) consisting of of a a free-piston engine, a linear generator, and a repulsion spring. The position x = 0 means top dead center free-piston engine, a linear generator, and a repulsion spring. The position x = 0 means top dead (TDC), x = x0 means the leftmost end of the cylinder, x = xa means the scavenging point, and x = xs center (TDC), x = x0 means the leftmost end of the cylinder, x = xa means the scavenging point, and x = means the combustion start point in the compression stroke. xs means the combustion start point in the compression stroke.

The spring repulsion force is expressed by Equation (2) with the spring repulsion coeﬃcient (Kg). EquationThe combustion (4) describes thrust the is the starting product process of the combustion before the chamber start of pressure the combustion and the cross-sectional and assumes area, that the compressias shownon in behavior Equation (3).of the The combustion pressure after chamber the combustion is a quasi changes-static according air spring to thethat thermodynamic does not exchange heatlaw with based the on the outer heat environment. generated and the Therefore, volume of Eq theuation combustion (4) is chamber. based on The Poi pressuresson’s before equation the and describescombustion the state behaves at which like an the adiabatic same compressiongas is compressed. air spring. Equation The pressure (4) is ontransformed the starting into process Equation is expressed by Equation (4), with the pressure and volume at the scavenging point expressed as pa (5) with the scavenging point (xa) and the length (x0) from the TDC (x = 0) to the leftmost wall. The (atmospheric pressure) and V , respectively. combustion thrust has a nonlineara relationship with the piston position [23]. Equation (4) describes the starting process before the start of the combustion and assumes that the compression behavior of the combustion chamber푑2푥 is a quasi-static air spring that does not exchange 푚 = 퐹 − 퐹 + 퐹 (1) heat with the outer environment. Therefore, Equation푑푡2 (4)푐 is푔 based푙 on Poisson’s equation and describes the state at which the same gas is compressed. Equation (4) is transformed into Equation (5) with the scavenging point (xa) and the length (x0) from the퐹푔 TDC= 퐾푔 (x푥= 0) to the leftmost wall. The combustion (2) thrust has a nonlinear relationship with the piston position [23].

퐹푐 = 퐴푐푝푐 (3) d2x m = Fc Fg + Fl (1) dt2 훾− 훾 푝푎푉푎 = 푝푐푉푐 (4) Fg = Kgx (2) 훾 훾 푝푎푉푎 푝푎(푥푎 + 푥0) −훾 푝푐 = 훾Fc = Acpc 훾 ∝ 푥 (3) (5) 푉푐 (푥 + 푥0) γ γ paVa = pcVc (4) where m: piston mass (kg); x: piston position (m); Fc: combustion force (N); Fg: spring force (N); Fl: γ γ paVa pa(xa + x0) 2 motor thrust (N); Kg: spring constantp = (N/m)=; Ac: combustionx γchamber cross-sectional area(5) (m ); pc: c V γ γ − combustion chamber pressure (Pa); Vc: c combustion(x + x 0 chamber) ∝ volume (m3); γ: heat capacity ratio

(generallywhere m :air piston standard mass (kg);conditionx: piston 1.4) position; pa: atmospheric (m); Fc: combustion pressure (Pa) force; V (N);a: scavengingFg: spring force point (N); volume 2 (m3F)l :; motorand xa thrust: scavenging (N); Kg :point spring position constant (m) (N./ m); Ac: combustion chamber cross-sectional area (m ); 3 pc: combustion chamber pressure (Pa); Vc: combustion chamber volume (m ); γ: heat capacity ratio 3 2.2.(generally Starting air standard condition 1.4); pa: atmospheric pressure (Pa); Va: scavenging point volume (m ); and xa: scavenging point position (m). The piston must be operated from the stopped state to the combustion start point to burn the engine2.2. Startingand start power generation in the FPEG. Therefore, the linear generator is driven as a linear motor onThe the piston engine must start be operated-up process from ( theFigure stopped 2). The state piston to the combustionis accelerated start to point a combustible to burn the speed usingengine battery and startpower. power generation in the FPEG. Therefore, the linear generator is driven as a linear motorHowever, on the enginethe piston start-up speed process must (Figure be increased2). The piston up isto acceleratedthe piston to driving a combustible frequency speed (hig usingher than 10 batteryHz by power.overcoming the repulsive spring thrust [11,12]. A large starting thrust is required to start the combustion in one stroke. A larger thrust increases the generator size and the power consumption. A hybrid vehicle particularly turns the engine on and off according to the remaining battery level. The starting thrust must be reduced because the number of engine starts in the hybrid vehicles is high.

Energies 2020, 13, 5754 4 of 17 Energies 2020, 13, x FOR PEER REVIEW 4 of 17

Generator mode Gasoline Electric Indicated Energies 2020, 13, x FOR PEER REVIEWenergy energy 4 of 17 work

Thermal GeneratorGenerator loss lossmode + - Gasoline Electric Indicated energy Motor energy work mode Motor loss

Thermal Generator Figure 2. Energy flow of the FPEG. The linear generator is driven as a linear+ - motor on the engine Figure 2. Energy flow of the FPEG. Theloss linear generatorloss is driven as a linear motor on the engine start-up process with battery power. start-up process with battery power. Motor mode However, the piston speed must be increasedMotor loss up to the piston driving frequency (higher than 2.3. Resonance10 Hz by overcoming Start-Up the repulsive spring thrust [11,12]. A large starting thrust is required to start the combustion in one stroke. A larger thrust increases the generator size and the power consumption. FigureMechanical 2. Energy resonance flow of is the effective FPEG. Thefor thelinear starting generator thrust is driven reduction as a .linear Figure motor 3 shows on the a comparison engine Astart hybrid-up process vehicle with particularly battery power. turns the engine on and off according to the remaining battery level. of theThe potential starting thrustenergies must of be a reducedgeneral because spring the–mass number system of engine and the starts FPEG. in the Th hybride left vehicles and right is high. springs are given the same coefficient; therefore, the potential energy is line-symmetric with respect to the 2.3. Resonance Start-Up vibration2.3. Resonance center point Start-up in the spring–mass system model. On the contrary, the potential energy does not haveMechanicalMechanical line symmetry resonance resonance becauseis iseffective effective the for forFPEG the the starting is composed thrust thrust reduction. reduction of a linear Figure. Figure mechanical3 shows 3 shows a comparison springa comparison and a ofnon the-oflinear potential the potential compression energies energies spring of of a a gen general effecteral spring–massinspring the combustion–mass system system andchamber and the FPEG.the. When FPEG. The a left Thsymmetrical ande left right and springs rightlinear aresprings spring areforce givengiven is applied thethe same same, and coe coefficient ffithecient; thrust therefore,; oftherefore Equation the potential, the (6) potential isenergy applied isenergy line-symmetricat the isresonance line-symmetric with frequency respect with to the of respect vibrationEquation to the(7), vibrationthe equationcenter center point of inmotion point the spring–mass in becomes the spring Eq systemuation–mass model. (8).system The On the modelgeneral contrary,. On solution thethe potentialcontrary of Equation energy, the potential(8) does becomes not haveenergy Eq lineuation does not(9), andsymmetry have amplification line because symmetry the occurs FPEG because in is composedthe thesecond FPEG of-term a linear is component. composed mechanical of springHowever, a linear and at mechanicalhe non-linear resonance compression spring frequency and is a nonnot -constantspringlinear ecompressionff ectand in changes the combustion spring depending effect chamber. inon thethe When combustionvibration a symmetrical state chamber because linear. When springthe potential a force symmetrical is applied,energy linear of and the the spring FPEG forceis asymmetric.thrust is applied of Equation , Tandhe the resonance (6) isthrust applied of frequency Eq at theuation resonance (6) of is the applied frequency spring at changes ofthe Equation resonance in (7),the frequency the FPEG equation with of of Eq asymmetricmotionuation (7), becomes Equation (8). The general solution of Equation (8) becomes Equation (9), and amplification thepotential equation energy, of motion and the becomes resonance Equation is difficult (8). The to obtaingeneral with solution Equat ofion Eq (6).uation (8) becomes Equation occurs in the second-term component. However, the resonance frequency is not constant and changes (9), and amplification occurs in the secondF -termF component.F However, the resonance frequency is depending on the vibration state because thec potentiall energy ofg the FPEG is asymmetric. The resonance not constantfrequency and of the changes spring depending changes in the on FPEG the vibration withPiston asymmetric state because potential the energy, potential and energy the resonance of the isFPEG is asymmetric.difficult to obtain The with resonance Equation frequency (6). of them spring changes in the FPEG with asymmetric potential energy, and the resonance is difficult to obtain with Equation (6). Non-linearity Linearity Kg F F x Fc l g x = 0 Piston

m Asymmetric

Non-linearity potential energyLinearity Kg

(J) x E x = 0

Symmetrical Energy Energy potential energy Asymmetric

potential energy (J)

Center point of vibration x0 E 0 Position x (mm) Symmetrical Energy Energy potential energy Figure 3. Comparison of the potential energies of a general spring–mass system and the FPEG. The Center point of vibration potential energy does not have line symmetry in the FPEG.x0 0 Position x (mm) Accordingly, a constant thrust is applied in the moving direction of the piston to amplify the Figure 3. Comparison of the potential energies of a general spring–mass system and the FPEG. pendulumFigureThe amplit3. potential Comparisonude energy, as of doesshown the not potential havein Figure line energies symmetry 4, which of ina general thepresent FPEG. springs the –constantmass system thrust and resonancethe FPEG. Thestarting methodpotential. The tenergyhrust actsdoes tonot the have left line in thesymmetry expansion in the stroke FPEG. from the TDC to the BDC, and to the right in the compression stroke from the BDC to the TDC. The thrust command gives a constant value by changingAccordingly plus and, a constant minus according thrust is applied to the absolutein the moving piston direction speed value of the. A piston rightward to amplify thrust the is pendulumapplied on amplita positiveude, pistonas shown speed, in Figureand whereas 4, which a leftwardpresents thrustthe constant is applied thrust on resonance a negative starting piston methodspeed (.Fig Theure thrust 1). Th actsis to starting the left method in the expansion realizes astroke resonance from the state TDC. T heto the piston BDC, then and reaches to the right the incombustion the compression start point stroke with from a small the BDCthrust. to the TDC. The thrust command gives a constant value by changing plus and minus according to the absolute piston speed value. A rightward thrust is 퐹 = 퐹 푐표푠 휙 푡 (6) applied on a positive piston speed, and whereas푙 a leftward thrust is applied on a negative piston speed (Figure 1). This starting method realizes a resonance state. The piston then reaches the combustion start point with a small thrust.

퐹푙 = 퐹 푐표푠 휙 푡 (6)

Energies 2020, 13, 5754 5 of 17

Accordingly, a constant thrust is applied in the moving direction of the piston to amplify the pendulum amplitude, as shown in Figure4, which presents the constant thrust resonance starting method. The thrust acts to the left in the expansion stroke from the TDC to the BDC, and to the right in the compression stroke from the BDC to the TDC. The thrust command gives a constant value by changing plus and minus according to the absolute piston speed value. A rightward thrust is applied on a positive piston speed, and whereas a leftward thrust is applied on a negative piston speed (Figure1). This starting method realizes a resonance state. The piston then reaches the combustion Energies 2020, 13, x FOR PEER REVIEW 5 of 17 start point with a small thrust. Fl = F cos φt (6)

r 퐾g0 휔 = 휙 = K√g0 (7) ω = φ = 푚 (7) m 2 d x 2 m 푑 +푥 ω2x = F cos φt (8) 푚2 + 휔2푥 = 퐹 푐표푠 휙 푡 (8) dt 푑푡2 F x(t) = C cos(ωt + δ) + t퐹sin ωt (9) 푥(푡) = 퐶 푐표푠( 휔푡 + 훿) 2+ω 푡 푠푖푛 휔 푡 (9) where F: thrust amplitude (N); ω: resonance angular frequency2휔 (rad/s); φ: thrust angular frequency (radwhere/s); andF: thrustKg0: spring–massamplitude (N); system ω: resonanc spring constante angular (N frequency/m). (rad/sϕ thrust angular frequency (rad/s); and Kg0: spring–mass system spring constant (N/m). Constant thrust

resonance (N)

l Sine wave resonance

Thrust

(mm) x

Combustion

Position Initial position start position 0 Time t (ms) FigureFigure 4. 4.Constant Constant thrust thrust resonance resonance starting starting method method for for the the FPEG. FPEG A. A constant constant thrust thrust is is applied applied in in the the movingmoving direction direction of of the the piston. piston. 2.4. Consideration of Potential Energy 2.4. Consideration of Potential Energy The thrust of the constant thrust resonance starting method must be set considering the The thrust of the constant thrust resonance starting method must be set considering the characteristics of the spring and the speed of the combustion start point. However, a general characteristics of the spring and the speed of the combustion start point. However, a general solution solution for obtaining an appropriate thrust cannot be simply obtained because the combustion for obtaining an appropriate thrust cannot be simply obtained because the combustion chamber chamber pressure and spring force have nonlinear. Therefore, the state diagram of the potential energy pressure and spring force have nonlinear. Therefore, the state diagram of the potential energy given given by the combustion chamber pressure and the spring force shown in Figure5 is used. by the combustion chamber pressure and the spring force shown in Figure 5 is used. Point a is the initial piston position. The piston advances to point b, where it balances with the E potential energy while increasing the mechanical energy with a constant thrust by a linear motor to Kinetic energy K the piston in the direction of the BDC. After the piston changes its traveling direction, a constant U thrust force acts in the direction of the TDC and the piston moves to point c. The piston then reaches the combustion start point z while increasingMechanical the mechanical energy by repeating this operation. energy of piston E The potential energy depends on thez spring coeﬃcient. The gradient of the mechanical energy of the

piston depends on the starting thrust(J) magnitude. E

Potential energy U

Energy Energy c b a Combustion Center point of vibration start point x s (Initial position) x0 0 Position x (mm)

Figure 5. Energy diagram in the FPEG. The piston reaches the combustion start point z while increasing the mechanical energy by the given thrust of the linear motor.

Point a is the initial piston position. The piston advances to point b, where it balances with the potential energy while increasing the mechanical energy with a constant thrust by a linear motor to the piston in the direction of the BDC. After the piston changes its traveling direction, a constant thrust force acts in the direction of the TDC and the piston moves to point c. The piston then reaches the combustion start point z while increasing the mechanical energy by repeating this operation. The potential energy depends on the spring coefficient. The gradient of the mechanical energy of the piston depends on the starting thrust magnitude.

Energies 2020, 13, x FOR PEER REVIEW 5 of 17

퐾g0 휔 = 휙 = √ (7) 푚

푑2푥 푚 + 휔2푥 = 퐹 푐표푠 휙 푡 (8) 푑푡2

퐹 푥(푡) = 퐶 푐표푠( 휔푡 + 훿) + 푡 푠푖푛 휔 푡 (9) 2휔 where F: thrust amplitude (N); ω: resonance angular frequency (rad/sϕ thrust angular frequency (rad/s); and Kg0: spring–mass system spring constant (N/m). Constant thrust

resonance (N)

l Sine wave resonance

Thrust

(mm) x

Combustion

Position Initial position start position 0 Time t (ms) Figure 4. Constant thrust resonance starting method for the FPEG. A constant thrust is applied in the moving direction of the piston.

2.4. Consideration of Potential Energy The thrust of the constant thrust resonance starting method must be set considering the characteristics of the spring and the speed of the combustion start point. However, a general solution for obtaining an appropriate thrust cannot be simply obtained because the combustion chamber pressureEnergies and2020 spring, 13, 5754 force have nonlinear. Therefore, the state diagram of the potential energy6 of 17 given by the combustion chamber pressure and the spring force shown in Figure 5 is used.

Kinetic energy K U

Mechanical energy of piston E

(J) E

Potential energy U

Energy Energy c b a Combustion Center point of vibration start point x s (Initial position) x0 0 Position x (mm) Figure 5. Energy diagram in the FPEG. The piston reaches the combustion start point z while increasing Figurethe 5. mechanical Energy energydiagram by the in giventhe FPEG thrust. ofThe the linear piston motor. reaches the combustion start point z while increasing the mechanical energy by the given thrust of the linear motor. The potential energies of the mechanical spring and the compression spring eﬀect of the combustion Pchamberoint a is are the given initial by piston Equations position. (10) and The (11) piston by integrating advances Equations to point (2)b, where and (4), it respectively.balances with the potentialThe potentialenergy while energy increasingU in Figure 5the is themechanical sum of Equations energy (10)with and a constant (11), as shown thrust in Equationby a linear (12). motor to The linear motor gives a constant thrust to the piston with the constant thrust resonance starting method. the piston in the direction of the BDC. After the piston changes its traveling direction, a constant The piston gradually stores mechanical energy and can start combustion when the potential energy thrustat force the combustion acts in the start direction point isof exceeded. the TDC Theand mechanical the piston energy moves E to of thepoint piston c. The is the piston sum ofthen the reaches the combustionpotential U andstart kinetic pointK z energies,while increasing as shown inthe Equation mechanical (13). Theenergy diﬀerence by repe betweenating thethis potential operation. The potentialenergy energy at the depends combustion on start the point spring and coefficient the mechanical. The energy gradient is the of kinetic the mechanical energy. The startingenergy of the pistonthrust depends must beon set the to starting obtain the thrust speed requiredmagnitude for a. proper start of combustion. The starting thrust can be set such that the velocity at the combustion start point vs is ideal with the energy state diagram and the kinetic energy of Equation (14). 1 U = K x2 (10) g 2 g

R h ixa = xa = ( + )γ 1 ( + ) γ+1 ( ) Uc x Fcdx paAc xa x0 γ+1 x x0 − γ , 1 R − x (11) = xa = [ ( + ) ( + )]xa ( = ) Uc x Fcdx paAc xa x0 ln x x0 x γ 1

U = Ug + Uc (12) E = U + K (13) r 2K v = (14) s m

where Ug: potential energy of the mechanical spring (J); Uc: potential energy of compression in the combustion chamber (J); x0: distance between the TDC and the leftmost point (m), U: total potential energy (J); E: mechanical energy (J); K: kinetic energy (J); and vs: velocity at the combustion starting position (m).

3. Starting Thrust Reduction Effect This chapter clarifies the thrust reduction effect of the constant thrust resonance starting method using a simulation. We also show herein that the velocity at the combustion start point reaches a desired value by setting the thrust using the energy state diagram. The simulation was conducted at an output of 10 kW, simulating the conditions of installing this system in a car. Energies 2020, 13, 5754 7 of 17

3.1. Simulation Conditions The simulation is performed by assuming a 10 kW output considering vehicle installation [11,12]. Figure6 shows a block diagram of the motion analysis constructed using MATLAB-Simulink. The simulation combines the electric circuit of the motor, vector control and, equation of motion, as shown Equation (1) [19]. The linear generator (linear motor) uses vector control. The starting thrust can be controlled by changing the q-axis current. Table1 presents the mechanical conditions of the simulation. As the frictional force before combustion is small and does not show significant fluctuations [11], the friction Energies 2020, 13, x FOR PEER REVIEW 7 of 17 was not considered in the simulation. Mechanical springs have low damping [25]. Damping action vehicleis expected mounting when [26 the–30 combustion] and is a chamber magnet- ismovable used as ancylindrical air spring linear before synchronous the start of combustion. generator. A However, in the experiment described in Section4, the pressure damping of the air spring before rectangular wire is used as the coil wire to increase the space factor. It has a concentrated winding the start of combustion was small. Therefore, the damping of the spring was not considered in structure put in one tooth to reduce the copper loss [31–33]. The magnetic flux of the magnet is the simulation. The starting point is set to the position at which the potential energy is minimum. concentrated on the stator side with a Halbach array to improve the thrust constant [34–36].

* Constant thrust i * = 0 V * Vu resonance d d dq PI V * PWM i * * v iq* (v>0) q Vq ↓ control V * generator -iq* (v<0) uvw w v θ

id uvw i 푠 q ↓ dq x

F i Combustion c u Inverter Battery thrust + Linear i synchronous v - motor iw Spring Fg thrust Electrical circuit model

FigureFigure 6. 6. BlockBlock diagram diagram of thethe FPEGFPEG simulation. simulation. Table 1. Mechanical conditions of the simulation. Linear generator Combustion chamber Item Value Piston and mover mass m 5.25 kg Distance between TDC and the leftmost point x0 7 mm 2 Bore cross sectionFree-pistonAc 0.00363 m Exhaust point position xa 70 mm

Figure7 depicts the basic configuration263 of the linear generator [ 20]. Table2 shows the linear generator specifications obtained with the electromagnetic field analysis software JMAG-Designer. Permanent The linear generator is designed considering themagnet copper loss reduction and miniaturization for the vehicle mounting [26–30] and is a magnet-movable cylindrical linear synchronous generator. A rectangular wire is used as the coil wire to increase the space factor. It has a concentrated winding structure put in one tooth to reduce the copper loss [31–33]. The magnetic flux of the magnet is Coil concentrated on the stator side with a Halbach array to improve the thrust constant [34–36].

Figure 7. Basic configuration of the linear generator for the 1 kW output.

Table 1. Mechanical conditions of the simulation.

Item Value Piston and mover mass m 5.25 kg Distance between TDC and the leftmost point x0 7 mm Bore cross section Ac 0.00363 m2 Exhaust point position xa 70 mm

Energies 2020, 13, x FOR PEER REVIEW 7 of 17 vehicle mounting [26–30] and is a magnet-movable cylindrical linear synchronous generator. A rectangular wire is used as the coil wire to increase the space factor. It has a concentrated winding structure put in one tooth to reduce the copper loss [31–33]. The magnetic flux of the magnet is concentrated on the stator side with a Halbach array to improve the thrust constant [34–36].

* Constant thrust i * = 0 V * Vu resonance d d dq PI V * PWM i * * v iq* (v>0) q Vq ↓ control V * generator -iq* (v<0) uvw w v θ

id uvw i 푠 q ↓ dq x

F i Combustion c u Inverter Battery thrust + Linear i synchronous v - motor iw Spring Fg thrust Electrical circuit model

Energies 2020, 13, 5754 8 of 17 Figure 6. Block diagram of the FPEG simulation.

Linear generator Combustion chamber

Free-piston

263

Permanent magnet

Coil

FigureFigure 7. 7.BasicBasic configuration conﬁguration of the linearlinear generator generator for for the the 1 kW 1 kW output. output.

Table 2. Linear generator speciﬁcations. Table 1. Mechanical conditions of the simulation. Item Value Item Value Stator external dimensions 168 263 mm Piston and mover mass m × 5.25 kg Outer dimensions of mover 128 130 mm × DistanceArmature between resistance TDC and the leftmost 108 point mΩ (perx0 phase)7 mm ArmatureBore inductance cross section Ac 1.8 mH (per phase)0.00363 m2 ThrustExhaust constant point position xa 22 N/A 70 mm

3.2. Simulation Results Figure8 shows the thrust that started the engine with one stroke, in which the engine was immediately driven at 20 Hz from the piston stopped state to the combustion start point. A very large Energiesthrust 2020 of, 13 3.5, x kNFOR is PEER required REVIEW at 80 mm stroke and 20 Hz drive frequency. 9 of 17

4 60

)

) 2 40

(

F 1

0 20

Thrust Thrust

Position  1

 2 0 0 50 100 150 200 0 50 100 150 200 Time t (ms) Time t (ms)

(a) (b)

FigureFigure 8. Simulation 8. Simulation results results with with the the starting starting engine engine in in one one stroke: stroke: ( (aa)) linear linear motormotor thrustthrust and and (b) piston(b) position. piston position. A large A largethrust thrust of more of more than than 3 3kN kN is is required required toto reachreach the the combustion combustion start start point point in in one onestroke. stroke. The sinusoidal thrust of Equations (6) and (7) is applied by the linear motor to reduce the starting300 thrust. Figure9 shows the simulation results. A sinusoidal60 thrust with 150 N amplitude and 20 Hz frequency is applied as shown in Figure8. In the ﬁgure, panel (b) illustrates the displacement.

) 45 ) 150

k (N)

(

F 0 x 30

Thrust Thrust

 150 Position 15

 300 0 0 100 200 300 400 0 100 200 300 400 Time t (s) Time t (ms)

(a) (b)

6 2.5

2.0

)

N 4

(

k 1.5

(

1.0 2

Thrust Thrust

Thrust Thrust 0.5

0 0.00 0 100 200 300 400 0 100 200 300 400 Time t (ms) Time t (ms) Time t (ms) (c) (d)

Figure 9. Simulation results with sinusoidal thrust: (a) linear motor thrust; (b) piston position; (c) combustion chamber thrust; (d) spring thrust. The piston position can gradually increase up to 250 ms, but the amplitude attenuates after 250 ms.

Figure 11 shows the simulation results of the constant thrust resonance starting method. The first to fifth lines depict Cases 1–5, respectively. Column (a) shows the starting thrust of the linear motor, which acts uniformly in the direction of the piston action in all conditions. Figure 11b,c shows the piston displacement and speed. The amplitude gradually increases because of resonance, and the piston can reach the combustion start point with a thrust much smaller than that in Figure 8. Using resonance is practically considered to have no issues because the piston can reach the combustion start point within 0.2 s in all cases. The number of vibrations required before starting is also the same as the number of times assumed in Table 3. Increasing the thrust is effective in shortening the starting time and reducing the number of start-up vibrations.

Energies 2020, 13, x FOR PEER REVIEW 9 of 17

4 60

)

) 2 40

(

F 1

0 20

Thrust Thrust

Position Energies 2020, 13,1 5754 9 of 17

 2 0 0 50 100 150 200 0 50 100 150 200 The displacement can graduallyTime t (ms) increase up to 250 ms, but the amplitudeTime attenuates t (ms) after 250 ms

because the compression spring(a) effect in the combustion chamber is nonlinear,(b and) the spring resonance frequency is not constant. The spring effect the combustion chamber compression has no linearity, and theFigure potential 8. Simulation energy is results not line-symmetric; with the starting therefore, engine in the one resonance stroke: (a)using linear themotor sinusoidal thrust and thrust (b) is difficultpiston in the position. FPEG. A Consequently, large thrust of reaching more than the 3 kN combustion is required starting to reach point the combustion in a stable start manner point in in the sinusoidalone stroke. thrust starting method is difficult.

300 60

) 45 ) 150

k (N)

(

F 0 x 30

Thrust Thrust

 150 Position 15

 300 0 0 100 200 300 400 0 100 200 300 400 Time t (s) Time t (ms)

(a) (b)

6 2.5

2.0

)

N 4

(

k 1.5

(

1.0 2

Thrust Thrust

Thrust Thrust 0.5

0 0.00 0 100 200 300 400 0 100 200 300 400 Time t (ms) Time t (ms) Time t (ms) (c) (d)

FigureFigure 9. 9.Simulation Simulation resultsresults withwith sinusoidalsinusoidal thrust:thrust: ( (aa)) linear linear motor motor thrust; thrust; (b (b) )piston piston position; position; (c) (c)combustion combustion chamber chamber thrust; thrust; (d (d) )spring spring thrust. thrust. The The piston piston position position can can gradually gradually increase increase up up to to250 250ms, ms, but but the the amplitude amplitude attenuates attenuates after after 250 250 ms. ms.

TheFigure propriety 11 shows of amplification the simulation and results the thrust of the reduction constant e ffthrustect of resonance the constant starting thrust method. resonance The startingfirst to method fifth lines described depict inCase Sections 1–5,2 have respectively. been confirmed. Column Table (a) shows3 presents the thestarting simulation thrust conditions. of the linear Nos.motor, 2 and which 3 change acts uniformly the starting in the thrust direction with of the the same piston spring action constant in all conditions. as no. 1, Figure while the11b spring,c shows constantthe piston of thedisplacement mechanical and spring speed. and The starting amplitude thrust gradually change nos. increase 4 ands because 5. The starting of resonance, thrust and is set the usingpiston the can energy reach state the diagramcombustion in Figure start 10point and with the energya thrust law much in Equation smaller than (13), suchthat in that Fig theure number 8. Using ofresonance vibrations is and practically the starting considered speed would to have be no the issues expected because values. the Casespiston 1, can 2, andreach 3 havethe combustion the same springstart point characteristics, within 0.2 buts in diallff cases.erent The starting number thrusts; of vibrations therefore, required the potential before energiesstarting i ares also the the same, same andas the the mechanical number of energy times assumed gradient in is diTablefferent. 3. Increasing In Cases 4 the and thrust 5, the is potential effective energy in shortening differs by the changingstarting thetime spring and reducing characteristics, the number but theof start number-up vibrations. of starts is the same as in Case 1. In addition, the starting point speed vs was 1.2 m/s under these conditions. This speed reflects the readiness to combust at minimum starting displacement, which depends on the conditions.

Energies 2020, 13, x FOR PEER REVIEW 10 of 17

EnergiesFigure2020, 13 12, 5754 illustrates a diagram of the piston position and velocity with an enlarged view10 of of the 17 vicinity of the combustion start point. The amplitude increases while passing points a, b, and c from the starting point, and Tablethe piston 3. Conditions reaches for the the combustion simulation andstarting expected poin results.t z. The piston velocity at the combustion start point reaches 1.2 m/s, which is the expected result. The phase diagram appears Spring Starting Expected Number of Expected Velocity at the distortedCase because the potential energies in cases 4 and 5 were different from those in cases 1–3. Constant Thrust Vibrations to Start Combustion Start Point The constant thrust starting method using resonance reduces the maximum thrust required to start1 the engine 41,453 from N/m 3.5 kN to 125 several N hundred N. It 4is also practically effective for changing the 2 41,453 N/m 168 N 3 thrust3 value 41,453 considering N/m the combustion 256 N start time. In 2addition, the number of reciprocations1.2 m/s up to − the 4start and 30,000 the Nvelocity/m at the 167 combustion N start point 3 predicted using the energy state diagram agree5 with 50,000 the simulation N/m results. 175 N Therefore, the thrust 3 can be set considering the conditions required for starting using the energy state diagram.

100 100 100

90 90 90

)

J J 80 80 80

(

U 70 70 70

60 60 60

Energy

50 50 50

40 40 40 0 20 40 60 0 20 40 60 0 20 40 60 Position x (mm) Position x (mm) Position x (mm)

(a) (b) (c)

100 100

90 90

)

J 80

80 (

(

U 70 70

60 Energy

Energy

50 50

40 40 0 20 40 60 0 20 40 60 Position x (mm) Position x (mm) (d) (e)

FigureFigure 10.10. EnergyEnergy statestate diagram:diagram: ((aa)) CaseCase 1,1,( (bb)) CaseCase 2, 2, ( (cc)) CaseCase 3, 3, ( (dd)) Case Case 4, 4, and and ( e(e)) Case Case 5. 5. TheThe blackblack curvecurve is is potential potential energy. energy. The The red red line line is is the the mechanical mechanical energy energy of of the the piston. piston.

4. EngineFigure Start 11 shows Experiment the simulation results of the constant thrust resonance starting method. The first to fifth lines depict Cases 1–5, respectively. Column (a) shows the starting thrust of the linear motor, This chapter shows that the constant thrust resonance start method can start combustion by which acts uniformly in the direction of the piston action in all conditions. Figure 11b,c shows the piston using an experimental device with a small engine and a linear motor. displacement and speed. The amplitude gradually increases because of resonance, and the piston can reach the combustion start point with a thrust much smaller than that in Figure8. Using resonance is 4.1. Experimental Method practically considered to have no issues because the piston can reach the combustion start point within 0.2 s inFigure all cases. 13a shows The number the moving of vibrations part of the required engine before experimental starting isdevice also thecomprisin same asg thea linear number motor of timesthat gives assumed a starting in Table thrust,3. Increasing an engine, the and thrust a mechanical is e ffective inspring. shortening The engine the starting piston time andand the reducingmover of thethe numberlinear motor of start-up are mechanically vibrations. connected. A mechanical spring is attached to the other side of the engine. The spring constant Kg and spring preload were 9940 N/m and 150 N, respectively. Figure 13b shows the overall structure of the engine test equipment. A shaft motor (S350-1S-100st-L480, GMC Hillstone co., Ltd., Yamagata, Japan) is used as the linear motor giving the starting thrust. An FPGA real-time controller and a servo amplifier are used for the linear motor thrust control. The servo amplifier controls the current flowing through the linear motor by the PWM control based on the thrust command created by the FPGA. A combustion pressure sensor (CAS-15K, CITIZEN FINEDEVICE Co., Ltd., Yamanashi, Japan) is attached to the engine to measure

Energies 2020, 13, x FOR PEER REVIEW 11 of 17

Energiesthe 2020pressure, 13, 5754 inside the combustion chamber. A magnetic linear encoder (LA11D, Renishaw plc)11 of is 17 used to measure the piston position.

400 100 3

300 2 80

)

200 ) ) 1

m/s

(

mm 100

(

l l

F 0 x 0

-100 40

Thrust Thrust -1

-200 Velocity

Position 20 -300 -2

-400 TDC -3 0 50 100 150 200 0 0 50 100 150 200 0 50 100 150 200 Time t (ms) Time t (ms) Time t (ms)

(a)

400 100 4

300 3 80

) 2 200 )

)

m/s

(

( 1 100

(

l l 60

x F 0 0

-100 40 -1

Thrust Thrust

Velocity -200 Position -2 20 -300 -3

-400 0 TDC -4 0 25 50 75 100 125 150 0 25 50 75 100 125 150 0 25 50 75 100 125 150 Time t (ms) Time t (ms) Time t (ms) (b)

400 100 4

300 3 80

) 200 ) 2

)

m/s

(

100 ( 1

(

l l 60

F 0 x 0

100 40 -1

Thrust Thrust

Velocity 200 Position -2 20 300 -3 TDC 400 0 -4 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Time t (ms) Time t (ms) Time t (ms)

(c)

400 100 4 300 3 80

200 )

) 2

)

( 100 m/s

(

l l 1

v 0 0

40 -100 -1

Thrust Thrust

Position -200 Velocity -2 20 -300 -3 TDC -400 0 -4 0 25 50 75 100 125 150 175 0 25 50 75 100 125 150 175 0 25 50 75 100 125 150 175 Time t (ms) Time t (ms) Time t (ms) (d)

400 100 4 300 3 80

)

200 ) 2

)

m/s

( ( 1

100

(

l l 60

F 0 x 0

-100 40 -1

Thrust Thrust

Velocity -200 Position -2 20 -300 -3 TDC -4 -400 0 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 Time t (ms) Time t (ms) Time t (ms) (e)

Figure 11. Simulation results of the thrust of the linear motor, piston position, and piston velocity with the constant thrust resonance starting method: (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4, and (e) Case 5. The amplitude gradually increased because of resonance. The piston can reach the combustion start point with much a smaller thrust. Energies 2020, 13, 5754 12 of 17

EnergiesFigure 2020, 1123, x illustrates FOR PEER REVIEW a diagram of the piston position and velocity with an enlarged view12 of of the 17 vicinity of the combustion start point. The amplitude increases while passing points a, b, and c from Figure 11. Simulation results of the thrust of the linear motor, piston position, and piston velocity the starting point, and the piston reaches the combustion starting point z. The piston velocity at the with the constant thrust resonance starting method: (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4, and combustion start point reaches 1.2 m/s, which is the expected result. The phase diagram appears (e) Case 5. The amplitude gradually increased because of resonance. The piston can reach the distorted because the potential energies in cases 4 and 5 were diﬀerent from those in cases 1–3. combustion start point with much a smaller thrust.

4 4 4

3 3 3

)

2 ) 2 ) 2

m/s

( 1 ( 1

(

v 0 c a b 0 c a b 0 c a b

z z z -1 -1 -1

Velocity

Velocity -2 Velocity -2 -2

-3 -3 -3

-4 -4 -4 0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Position x (mm) Position x (mm) Position x (mm)

4 4 4

3 3 3

) ) 2 2 ) 2

m/s

( ( 1 1

(

v 0 0 0

-1 z -1 z -1 z -1.2 -1.2 -1.2

Velocity

Velocity -2 -2 Velocity -2

-3 -3 -3

-4 -4 -4 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 Position x (mm) Position x (mm) Position x (mm) (a) (b) (c) 4 4

3 3

) ) 2 2

m/s

( ( 1 1

v 0 c a b 0 c a b

z z -1 -1

Velocity -2 Velocity -2

-3 -3

-4 -4 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Position x (mm) Position x (mm) 4 4

3 3

) ) 2 2

m/s

( ( 1 1

v 0 0

-1 z -1 z -1.2 -1.2

Velocity -2 Velocity -2

-3 -3

-4 -4 0 1 2 3 4 5 0 1 2 3 4 5 Position x (mm) Position x (mm) (d) (e)

Figure 12.12. SimulationSimulation results of a diagram of the pistonpiston positionposition andand velocity.velocity. The bottom of each ﬁgurefigure shows an enlarged enlarged view view of of the the vicinity vicinity of of the the combustion combustion start start point point:: (a)( aCase) Case 1, ( 1,b) (Caseb) Case 2, (c 2,) (Casec) Case 3, ( 3,d) (Cased) Case 4, and 4, and (e) (Casee) Case 5. The 5. The piston piston velocity velocity at the at thecombustion combustion start start point point was was 1.2 1.2m/s, m as/s, aspredicted predicted in inthe the energy energy state state diagram. diagram.

TheFigure constant 13c display thrusts the starting engine method interior using cross resonance-section. Table reduces 4 shows the maximum the engine thrust specifications. required toA startglow the-ignition, engine two from-cycle 3.5 kN engine to several (180X hundred TN, Enya N. Metal It is also Products practically Co., eLtd.ﬀective, Saitama, for changing Japan) thewas thrust used valueto confirm considering reaching the the combustion TDC and startstarting time. the In combustion addition, the by number using resonance of reciprocations without up adjusting to the start the ignition time. The fuel used KLOTZ for a small glow engine, which is mainly composed of methanol, nitromethane and oil. The fuel contains 15% nitromethane and 22% oil. The target velocity at the start of combustion is set at 0.5 m/s, which is obtained from the engine operation test results.

Energies 2020, 13, 5754 13 of 17 and the velocity at the combustion start point predicted using the energy state diagram agree with the simulation results. Therefore, the thrust can be set considering the conditions required for starting using the energy state diagram.

4. Engine Start Experiment This chapter shows that the constant thrust resonance start method can start combustion by using an experimental device with a small engine and a linear motor.

4.1. Experimental Method Figure 13a shows the moving part of the engine experimental device comprising a linear motor that gives a starting thrust, an engine, and a mechanical spring. The engine piston and the mover of the linear motor are mechanically connected. A mechanical spring is attached to the other side of Energies 2020, 13, x FOR PEER REVIEW 13 of 17 the engine. The spring constant Kg and spring preload were 9940 N/m and 150 N, respectively.

Engine Reciprocating

Spring

Linear motor

(a)

chamber

(b) (c)

Figure 13. EExperimentalxperimental device: ( (aa)) a appearanceppearance of of moving moving parts parts,, ( (bb)) o overallverall structure structure,, and ( (c)) c crossross section ofof thethe engine engine interior. interior. This This device device consists consists of aof linear a linear motor motor that givesthat gives a starting a starting thrust, thrust, an engine, an engine,and a mechanical and a mechanical spring. Thespring. output The of output the engine of the is aboutengine 1.7 is kW, about and 1.7 the kW, linear and motor the linear controls motor the controlsthrust with the anthrust FPGA with and an an FPGA ampliﬁer. and an amplifier.

Figure 13b shows the overallTable structure 4. Engine of specifications. the engine test equipment. A shaft motor (S350-1S-100st-L480, GMC Hillstone co., Ltd., Yamagata, Japan) is used as the linear motor giving Item Value the starting thrust. An FPGA real-time controller and a servo amplifier are used for the linear motor Displacement 36 cm3 thrust control. The servo amplifier controlsBore thediameter current flowing34 mm through the linear motor by the PWM control based on the thrust commandExhaust created point by position the FPGA. 25 A mm combustion pressure sensor (CAS-15K, CITIZEN FINEDEVICE Co., Ltd., Yamanashi,Piston Japan)stroke is attached40 mm to the engine to measure the pressure inside the combustion chamber. A magneticMaximum linear output encoder 1.73 (LA11D, kW Renishaw plc) is used to measure the piston position. 4.2. ExperimentalFigure 13c displaysResults the engine interior cross-section. Table4 shows the engine specifications. A glow-ignition, two-cycle engine (180X TN, Enya Metal Products Co., Ltd., Saitama, Japan) was used Figure 14 illustrates the experimental results. Panel (a) depicts the thrust applied to the piston, to confirm reaching the TDC and starting the combustion by using resonance without adjusting the panel (b) shows the piston displacement, panel (c) exhibits the combustion chamber pressure, panel (d) shows combustion pressure vs. piston position in the starting process in about 100 ms, and panel (e) exhibits the piston position calculated by simulation. A thrust of 280 N was applied in the same direction of the mover movement while using the start method that employs resonance. The piston movement amplitude gradually increases because of the spring resonance. The compression and expansion pressures at the engine starting stroke have approximately the same curve with damping energy less than 1J and a small effect of damping effect. The combustion chamber pressure operates like an air spring before the start of combustion. The inside of the cylinder was compressed with approaching TDC and a state close to combustion occurred at approximately 150 ms. An impulsive combustion pressure is generated at 180 ms due to the piston reaching TDC, and the engine combustion is confirmed to have been started using the spring resonance. The maximum combustion pressure at this time was 5.6 MPa. The number of reciprocations up to the start of the combustion is four, and the combustion start speed was 1.22 m/s, which is in close agreement with the set conditions. The speed error is approximately 1.7%, which is within acceptable range. The cause of the error in the combustion start speed is the effect of friction and damping effect of air spring.

Energies 2020, 13, 5754 14 of 17 ignition time. The fuel used KLOTZ for a small glow engine, which is mainly composed of methanol, nitromethane and oil. The fuel contains 15% nitromethane and 22% oil. The target velocity at the start of combustion is set at 0.5 m/s, which is obtained from the engine operation test results.

Table 4. Engine speciﬁcations.

Item Value Displacement 36 cm3 Bore diameter 34 mm Exhaust point position 25 mm Piston stroke 40 mm Maximum output 1.73 kW

4.2. Experimental Results Figure 14 illustrates the experimental results. Panel (a) depicts the thrust applied to the piston, panel (b) shows the piston displacement, panel (c) exhibits the combustion chamber pressure, panel (d) shows combustion pressure vs. piston position in the starting process in about 100 ms, and panel (e) exhibits the piston position calculated by simulation. A thrust of 280 N was applied in the same direction of the mover movement while using the start method that employs resonance. The piston movement amplitude gradually increases because of the spring resonance. The compression and expansion pressures at the engine starting stroke have approximately the same curve with damping energy less than 1J and a small effect of damping effect. The combustion chamber pressure operates like an air spring before the start of combustion. The inside of the cylinder was compressed with approaching TDC and a state close to combustion occurred at approximately 150 ms. An impulsive combustion pressure is generated at 180 ms due to the piston reaching TDC, and the engine combustion is confirmed to have been started using the spring resonance. The maximum combustion pressure at this time was 5.6 MPa. The number of reciprocations up to the start of the combustion is four, and the combustion start speed was 1.22 m/s, which is in close agreement with the set conditions. The speed error is approximately 1.7%, which is within acceptable range. The cause of the error in the combustion start speed is the effect of friction and damping effect of air spring. Figure 14d shows the relationship pressure of the combustion chamber and the piston stroke on the starting process around 100 ms. Similar curves were obtained during compression and expansion, and the effect of attenuation is small. Moreover, the specific heat ratio of both pressure-curves were calculated using an approximate curve, they were 1.21 and 1.23 at the time of expansion and compression, respectively. Contrary to the simulation, the specific heat ratio during the actual operation slightly differs between compression and expansion. This is one of the causes of the error of 1.7% of the combustion start speed. Thus, the accuracy of combustion start velocity can be increased by obtaining the specific heat ratio in advance using the pressure history. The simulation was conducted under the conditions simulating the experimental environment. The simulation results confirmed that the piston movement was amplified by the constant thrust starting method and reached the TDC after four reciprocating movements as in the experiment. The amplitude of the simulation was slightly larger than that of the experiment because the damping effect and friction of the combustion chamber were not taken into consideration. Energies 2020, 13, x FOR PEER REVIEW 14 of 17

Figure 14d shows the relationship pressure of the combustion chamber and the piston stroke on the starting process around 100 ms. Similar curves were obtained during compression and expansion, and the effect of attenuation is small. Moreover, the specific heat ratio of both pressure-curves were calculated using an approximate curve, they were 1.21 and 1.23 at the time of expansion and compression, respectively. Contrary to the simulation, the specific heat ratio during the actual operation slightly differs between compression and expansion. This is one of the causes of the error of 1.7% of the combustion start speed. Thus, the accuracy of combustion start velocity can be increased by obtaining the specific heat ratio in advance using the pressure history. The simulation was conducted under the conditions simulating the experimental environment. The simulation results confirmed that the piston movement was amplified by the constant thrust starting method and reached the TDC after four reciprocating movements as in the experiment. The Energiesamplitude2020, 13of, 5754the simulation was slightly larger than that of the experiment because the damping15 of 17 effect and friction of the combustion chamber were not taken into consideration.

400 60 6 ) Combustion 300 50 MPa 5

(

c c

200 )

)

N 40 4

( 100 mm

(

l l

x 0 30 3

-100

Thrust 20 2

-200 Position (d) -300 10 1

Combustion pressure -400 0 0 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Time t (ms) Time t (ms) Time t (ms) (a) (b) (c)

1.0 60

)

MPa 50 ( 0.8

c c

)

p 40

(

0.6

x 30

0.4 20

Compression Position 0.2 Expansion g= 1.21 10 g= 1.23

Combustion pressure 0.0 0 0 10 20 30 0 50 100 150 200 Position x (mm) Time t (ms) (d) (e)

FigureFigure 14.14.Experimental Experimental results results with with the the constant constant thrust thrust resonance resonance starting starting method: method: (a) linear (a) motorlinear thrust,motor (thrustb) piston, (b) position,piston position (c) combustion, (c) combustion pressure, pressure (d) combustion, (d) combustion pressure pressure vs. piston vs. piston position position in the in startingthe starting process, process and, ( eand) piston (e) piston position position calculated calculated by simulation. by simulation An impulse-like. An impulse combustion-like combustion pressure couldpressure be generated could be generated in approximately in approximately 180 ms with 180 the ms constant with the thrust constant starting thrust method. starting method.

5.5. ConclusionsConclusions ToTo startstart powerpower generationgeneration withwith thethe FPEG,FPEG, thethe pistonpiston mustmust bebe givengiven thrustthrust upup toto thethe strokestroke andand speedspeed atat which which combustion combustion can can start. start. A veryA very large large thrust thrust is required is required to make to make the stopped the stopped piston piston ready forready combustion. for combustion. Therefore, Therefore, we used herein we used spring herein resonance spring to resonance gradually increase to gradually the amplitude. increase the amplitude.The piston resonates by utilizing the compression spring effect of the combustion chamber and the springThe piston effect ofresonates the spring by chamber.utilizing the However, compression the potential spring energyeffect of of the the combustion FPEG is not chamber symmetrical and aboutthe spring the center effect of vibration of the spring and using chamber. a simple However, spring–mass the resonancepotential energysystem is of di thefficult. FPEG Therefore, is not wesymmetrical used the constant about the thrust center resonance of vibration starting and method, using in a which simple thrust spring is applied–mass inresonance the same system direction is asdifficult the piston. Therefore action direction., we used the constant thrust resonance starting method, in which thrust is appliedThe in constant the same thrust direction resonance as the starting piston action method direction. had a maximum thrust reduction effect of more than 90%The comparedconstant thrust to the resonance starting method starting by method one stroke had without a maximum using thrust resonance reduction and enables effect aof stable more amplification.than 90% compared The number to the starting of reciprocations method by and one the stroke combustion without start using speed resonance predicted and usingenables the a energy state diagram were in agreement with the simulation results. The starting thrust can be set appropriately by using the energy state diagram. This method is also effective for the opposed engine model in which the potential energy is symmetrical. We confirmed that the constant thrust starting method can start the engine combustion with a small-output experimental device using a free-piston engine. The amplitude of the piston displacement gradually increased from the position of the natural length of the spring, and the combustion started at the combustion start point when a constant was applied thrust in the direction of the piston action. The combustion can be started by reducing the starting-up thrust through a proper utilization of the constant thrust resonance starting method. Energies 2020, 13, 5754 16 of 17

Author Contributions: Conceptualization and methodology, M.S.; software, M.S., T.G., and J.Z.; validation, T.G., J.Z., and S.I.; writing—original draft preparation, M.S. and T.G.; funding acquisition, M.S. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by JSPS KAKENHI Grant Number 20K14714. This work was partially supported by Nagamori Foundation research grant 2020. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Coloma, J.F.; García, M.; Wang, Y.; Monzón, A. Environmental Strategies for Selecting Eco-Routing in a Small City. Atmosphere 2019, 10, 448. [CrossRef] 2. Serrano, J.R. Imagining the Future of the Internal Combustion Engine for Ground Transport in the Current Context. Appl. Sci. 2017, 7, 1001. [CrossRef] 3. El-Taweel, N.A.; Khani, H.; Farag, H.E.Z. Analytical Size Estimation Methodologies for Electrified Transportation Fueling Infrastructures Using Public–Domain Market Data. IEEE Trans. Transp. Electr. 2019, 5, 840–851. [CrossRef] 4. Monteiro, V.; Afonso, J.A.; Ferreira, J.C.; Afonso, J.L. Vehicle Electrification: New Challenges and Opportunities for Smart Grids. Energies 2019, 12, 118. [CrossRef] 5. Kang, H.; Kim, S.; Lee, K. Multiple Harmonics Reduction Method for the Integrated On-board Battery Charging System of Hybrid Electric Vehicles. IEEJ J. Ind. Appl. 2020, 9, 235–243. [CrossRef] 6. Varga, B.O.; Sagoian, A.; Mariasiu, F. Prediction of Electric Vehicle Range: A Comprehensive Review of Current Issues and Challenges. Energies 2019, 12, 946. [CrossRef] 7. Zhu, J.; Wierzbicki, T.; Li, W. A review of safety-focused mechanical modeling of commercial lithium-ion batteries. J. Power Sources 2018, 378, 153–168. [CrossRef] 8. Yu, Y.; Jiang, J.; Min, Z.; Wang, P.; Shen, W. Research on Energy Management Strategies of Extended-Range Electric Vehicles Based on Driving Characteristics. World Electr. Veh. J. 2020, 11, 54. [CrossRef] 9. Kim, D.; Benoliel, P.; Kim, D.; Lee, T.H.; Park, J.W.; Hong, J. Framework Development of Series Hybrid Powertrain Design for Heavy-Duty Vehicle Considering Driving Conditions. IEEE Trans. Veh. Technol. 2019, 68, 6468–6480. [CrossRef] 10. Passalacqua, M.; Carpita, M.; Gavin, S.; Marchesoni, M.; Repetto, M.; Vaccaro, L.; Wasterlain, S. Supercapacitor Storage Sizing Analysis for a Series Hybrid Vehicle. Energies 2019, 12, 1759. [CrossRef] 11. Jia, B.; Mikalsen, R.; Smallbone, A.; Roskilly, A.P. A study and comparison of frictional losses in free-piston engine and crankshaft engines. Appl. Ther. Eng. 2018, 140, 217–224. [CrossRef] 12. Kosaka, H.; Akita, T.; Moriya, K.; Goto, S.; Hotta, Y.; Umeno, T.; Nakakita, K. Development of Free Piston Engine Linear Generator System Part 1—Investigation of Fundamental Characteristics; SAE Technical Papers 2014-01-1203; SAE International: Warrendale, PA, USA, 2014. 13. Moriya, K.; Goto, S.; Akita, T.; Kosaka, H.; Hotta, Y.; Nakakita, K. Development of Free Piston Engine Linear Generator System Part 3—Novel Control Method of Linear Generator for to Improve Efficiency and Stability; SAE Technical Papers 2016-01-0685; SAE International: Warrendale, PA, USA, 2016. 14. Xu, Z.; Chang, S. Prototype testing and analysis of a novel internal combustion linear generator integrated power system. Appl. Energy 2010, 87, 1342–1348. [CrossRef] 15. Goto, S.; Moriya, K.; Kosaka, H.; Akita, T.; Hotta, Y.; Umeno, T.; Nakakita, K. Development of Free Piston Engine Linear Generator System Part 2—Investigation of Control System for Generator; SAE Technical Papers 2014-01-1193; SAE International: Warrendale, PA, USA, 2014. 16. Hung, N.B.; Lim, O.; Iida, N. The effects of key parameters on the transition from si combustion to hcci combustion in a two-stroke free piston linear engine. Appl. Energy 2015, 137, 385–401. [CrossRef] 17. Li, Q.; Xiao, J.; Huang, Z. Simulation of a Two-Stroke Free-Piston Engine for Electrical Power. Energy Fuels 2008, 22, 3443–3449. [CrossRef] 18. Yuan, C.; Feng, H.; He, Y.; Xu, J. Combustion characteristics analysis of a free-piston engine generator coupling with dynamics and scavenging. Energy 2016, 102, 637–649. [CrossRef] 19. Sato, M.; Nirei, M.; Yamanaka, Y.; Murata, H.; Bu, Y.; Mizuno, T. Operation Range of Generation Braking Force to Achieve High Efficiency Considering Combustion in a Free-Piston Engine Linear Generator System. IEEJ J. Ind. Appl. 2018, 7, 343–350. [CrossRef] Energies 2020, 13, 5754 17 of 17

20. Yamanaka, Y.; Nirei, M.; Sato, M.; Murata, H.; Bu, Y.; Mizuno, T. Design of a Linear Synchronous Generator and Examination of the Driving Range for a Free-Piston Engine Linear Generator System. IEEJ J. Ind. Appl. 2018, 7, 351–357. [CrossRef] 21. Sato, M.; Naganuma, K.; Nirei, M.; Yamanaka, Y.; Suzuki, T.; Goto, T.; Bu, Y.; Mizuno, T. Improving the Constant-Volume Degree of Combustion Considering Generatable Range at Low-speed in a Free-Piston Engine Linear Generator System. IEEJ Trans. Electr. Electron. Eng. 2019, 14, 1703–1710. [CrossRef] 22. Wang, X.; Chen, F.; Zhu, R.; Yang, G.; Zhang, C. A Review of the Design and Control of Free-Piston Linear Generator. Energies 2018, 11, 2179. [CrossRef] 23. Jia, B.; Zuo, Z.; Feng, H.; Tian, G.; Roskilly, A.P. Investigation of the starting process of free-piston engine generator by mechanical resonance. Energy Procedia 2014, 61, 572–577. [CrossRef] 24. Jia, B.; Zuo, A.; Feng, H.; Tian, G.; Smallbone, A.; Roskilly, A.P. Effect of closed-loop controlled resonance based mechanism to start free piston engine generator: Simulation and test results. Appl. Energy 2016, 164, 532–539. [CrossRef] 25. Yan, H.; Wang, D.; Xu, Z. Design and Simulation of Opposed-Piston Four-Stroke Free-Piston Linear Generator; SAE Technical Papers 2015-01-1277; SAE International: Warrendale, PA, USA, 2015. 26. Sun, P.; Zhang, C.; Chen, J.; Zhao, F.; Liao, Y.; Yang, G.; Chen, C. Decoupling design and verification of a free-piston linear generator. Energies 2016, 9, 1067. [CrossRef] 27. Wang, J.; West, M.; Howe, D.; Parra, Z.D.L.; Arshad, W.M. Design and experimental verification of a linear permanent magnet generator for a free-piston energy converter. IEEE Trans. Energy Convers. 2007, 22, 299–306. [CrossRef] 28. Zheng, P.; Tong, C.; Bai, J.; Yu, B.; Sui, Y.; Shi, W. Electromagnetic design and control strategy of an axially magnetized permanent-magnet linear alternator for free-piston stirling engines. IEEE Trans. Ind. Appl. 2013, 48, 2230–2239. [CrossRef] 29. Cao, R.; Cheng, M.; Mi, C.C.; Hua, W. Influence of leading design parameters on the force performance of a complementary and modular linear flux-switching permanent-magnet motor. IEEE Trans. Ind. Electr. 2014, 61, 2165–2175. [CrossRef] 30. Zheng, P.; Tong, C.; Chen, G.; Liu, R.; Sui, Y.; Shi, W.; Cheng, S. Research on the magnetic characteristic of a novel transverse-flux pm linear machine used for free-piston energy converter. IEEE Trans. Magn. 2011, 47, 1082–1085. [CrossRef] 31. Wang, Q.; Zhao, B.; Zou, J.; Li, Y. Minimization of Cogging Force in Fractional-Slot Permanent Magnet Linear Motors with Double-Layer Concentrated Windings. Energies 2016, 9, 918. [CrossRef] 32. Song, J.; Lee, J.H.; Kim, D.; Kim, Y.; Jung, S. Analysis and Modeling of Concentrated Winding Variable Flux Memory Motor Using Magnetic Equivalent Circuit Method. IEEE Trans. Magn. 2017, 53, 1–4. [CrossRef] 33. Ura, A.; Sanada, M.; Morimoto, S.; Inoue, Y. Influence of Structural Differences on Motor Characteristics of Concentrated Winding IPMSMs Obtained by Automatic Design. IEEJ J. Ind. Appl. 2019, 8, 458–464. [CrossRef] 34. Wang, J.; Howe, D. Tubular modular permanent-magnet machines equipped with quasi-halbach magnetized magnets-part i: Magnetic field distribution, emf, and thrust force. IEEE Trans. Magn. 2005, 41, 2470–2478. [CrossRef] 35. Sim, M.-S.; Ro, J.-S. Semi-Analytical Modeling and Analysis of Halbach Array. Energies 2020, 13, 1252. [CrossRef] 36. Duong, M.-T.; Chun, Y.-D.; Bang, D.-J. Improvement of Tubular Permanent Magnet Machine Performance Using Dual-Segment Halbach Array. Energies 2018, 11, 3132. [CrossRef]

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