Dynamic Characteristics and Demonstration of an Integrated Linear Engine Generator with Alternative Electrical Machines

: A linear engine generator with a compact double-acting free piston mechanism allows for full integration of the combustion engine and generator, which provides an alternative chemical-to-electrical energy converter with a higher volumetric power density for the electriﬁcation of automobiles, trains, and ships. This paper aims to analyse the performance of the integrated engine with alternative permanent magnet linear tubular electrical machine topologies using a coupled dynamic model in Siemens Simcenter software. Two types of alternative generator conﬁgurations are compared, namely long translator-short stator and short translator-long stator linear machines. The dynamic models of the linear engine and linear generator, validated with lab-scale prototypes, are applied to investigate the inﬂuence of alternative topologies of the generator on system performance. The coupled model will facilitate the early design phase and reveal the optimal match of the key parameters of the engine and generator. Then, experimental tests on an integrated compressor cylinder-generator prototype were successfully performed, and it is shown that this concept is feasible and electrical power and compressed working ﬂuid, such as air, can be generated by this prototype.


Introduction
A Linear Engine Generator (LEG) is a special type of combustion engine that represents a new approach concerning the conversion of chemical energy into electrical energy directly without a crank mechanism. Instead of using conventional engines, LEG hires a linear engine and linear generator to generate electricity directly with the linear movement of the piston-translator. The direct drive technology of a linear electrical machine is a perfect way to enhance power density and dynamic performance. Linear machines eliminate the need for mechanical transmissions. Thus, it dramatically reduces the volume, weight, friction, and complexity of a power generation system. The LEG's efficiency is estimated to be higher than the efficiency of other systems, such as diesel generators, as shown in Figure 1, implying that using a LEG should increase the total system efficiency [1,2].
LEG is a potential alternative power supply in hybrid powertrains. The proposed hybrid electric system configuration is illustrated in Figure 2, which shows an example of using the LEG concept in an automotive application to propel electric motors and has been embedded into the tires of the vehicle. Alternatively, LEG can be developed as a range-extending device in electric vehicles to work as a battery charger. Figure 1. Efficiency from fuel to electrical power to the DC-link for an FPEG and a typic generator [1,2]. This figure has been reproduced with permission from IEEE ©2006 IEEE LEG is a potential alternative power supply in hybrid powertrains. The p hybrid electric system configuration is illustrated in Figure 2, which shows an exa using the LEG concept in an automotive application to propel electric motors and h embedded into the tires of the vehicle. Alternatively, LEG can be developed as extending device in electric vehicles to work as a battery charger.
From 1999 to 2003, Sandia National Laboratories [3,4] studied a type of Fre Engine Generator (FPEG) with a numerically homogeneous charge compression combustion in terms of a previous FPEG prototype developed in 1998 [5]. West University studied a two-stroke FPEG numerically [6] and an experimental stu carried out with a power output of up to 316 W [7]. In 2008, Roskilly et al. [8] at Ne University simulated the performance of a spark ignition FPEG. A FPEG system veloped as a range-extending device in electric vehicles at the German Aerospace in 2012. The FPEG works at 21 Hz with a measured power output of 10 kW [9]. Toyota developed a two-stroke FPEG prototype with a gas spring chamber, which strated 42% thermal efficiency, and 10 kW could be achieved [10,11]. In 2020, t research team from Newcastle University [12] reported a preliminary prototype drogen-fueled FPEG with a compression ratio of 3.7, engine speed between 5 Hz Hz, and different equivalence ratios. With the increasing pressure of de-carbonization in transport sectors, hydro ammonia are viewed as promising zero carbon fuels. The internal combustion o gen and ammonia in a well-controlled manner poses difficulties on FPEGs that ventional internal combustion engines. Researchers from Newcastle University p an external combustion Linear Joule Engine Generator (LJEG), and a working pr Efficiency from fuel to electrical power to the DC-link for an FPEG and a typical dieselgenerator [1,2]. This figure has been reproduced with permission from IEEE ©2006 IEEE.
using the LEG concept in an automotive application to propel electric moto embedded into the tires of the vehicle. Alternatively, LEG can be develop extending device in electric vehicles to work as a battery charger.
From 1999 to 2003, Sandia National Laboratories [3,4] studied a type Engine Generator (FPEG) with a numerically homogeneous charge compr combustion in terms of a previous FPEG prototype developed in 1998 [5] University studied a two-stroke FPEG numerically [6] and an experimen carried out with a power output of up to 316 W [7]. In 2008, Roskilly et al. [ University simulated the performance of a spark ignition FPEG. A FPEG s veloped as a range-extending device in electric vehicles at the German Ae in 2012. The FPEG works at 21 Hz with a measured power output of 10 k Toyota developed a two-stroke FPEG prototype with a gas spring chamber, strated 42% thermal efficiency, and 10 kW could be achieved [10,11]. In research team from Newcastle University [12] reported a preliminary pro drogen-fueled FPEG with a compression ratio of 3.7, engine speed betwee Hz, and different equivalence ratios. With the increasing pressure of de-carbonization in transport sectors, ammonia are viewed as promising zero carbon fuels. The internal combu gen and ammonia in a well-controlled manner poses difficulties on FPEG ventional internal combustion engines. Researchers from Newcastle Unive an external combustion Linear Joule Engine Generator (LJEG), and a wor has been developed with a 4.47-kW mechanical power output when the 32.2% [13]. Wu et al. [14] presented a coupled dynamic model of a linear jou generator, which enabled an integrated design of a linear engine and linea et al. [15] conducted a modeling study on the dynamic and thermodynamic of a LJEG and found that the system pressure was the most effective par the system power output. Ngwaka et al. [16] built a numerical model of the From 1999 to 2003, Sandia National Laboratories [3,4] studied a type of Free Piston Engine Generator (FPEG) with a numerically homogeneous charge compression ignition combustion in terms of a previous FPEG prototype developed in 1998 [5]. West Virginia University studied a two-stroke FPEG numerically [6] and an experimental study was carried out with a power output of up to 316 W [7]. In 2008, Roskilly et al. [8] at Newcastle University simulated the performance of a spark ignition FPEG. A FPEG system was developed as a range-extending device in electric vehicles at the German Aerospace Center in 2012. The FPEG works at 21 Hz with a measured power output of 10 kW [9]. In 2014, Toyota developed a two-stroke FPEG prototype with a gas spring chamber, which demonstrated 42% thermal efficiency, and 10 kW could be achieved [10,11]. In 2020, the same research team from Newcastle University [12] reported a preliminary prototype of a hydrogen-fueled FPEG with a compression ratio of 3.7, engine speed between 5 Hz and 11 Hz, and different equivalence ratios.
With the increasing pressure of de-carbonization in transport sectors, hydrogen and ammonia are viewed as promising zero carbon fuels. The internal combustion of hydrogen and ammonia in a well-controlled manner poses difficulties on FPEGs that use conventional internal combustion engines. Researchers from Newcastle University proposed an external combustion Linear Joule Engine Generator (LJEG), and a working prototype has been developed with a 4.47-kW mechanical power output when the efficiency was 32.2% [13]. Wu et al. [14] presented a coupled dynamic model of a linear joule cycle engine generator, which enabled an integrated design of a linear engine and linear generator. Jia et al. [15] conducted a modeling study on the dynamic and thermodynamic characteristics of a LJEG and found that the system pressure was the most effective parameter to alter the system power output. Ngwaka et al. [16] built a numerical model of the friction forces and it was validated by experiments using a compressed air driven linear engine prototype. More recently, Ngwaka et al. proposed a closed-loop LEG concept with Argon-Hydrogen-Oxy external combustion to tackle the challenge of using zero carbon fuels in LEGs. Both external combustion and internal combustion engines may find their applications in the electrification and de-carbonization of transport sectors.
The research teams at Newcastle University have developed a linear engine prototype and a linear electrical machine prototype to validate the dynamic models before a coupled model is developed, respectively. The dynamic characteristic of the coupled system is defined by four interlinks, namely engine design, engine performance, electric machine design, and electric load.
This paper is to address the potential impact caused by the topologies of alternative Permanent Magnet (PM) generators on the performance of the LEG system. The structure of the paper is as follows. In Section 2, linear engine generators have been proposed. In Section 3, a coupled dynamic system of LEG has been investigated. In Section 4, performance validation has been carried out for the integrated system. Sections 5 and 6 give the simulation and experimental results of the proposed integrated linear engine generators. Lastly, the paper has been concluded in Section 7 with a brief summary. Figure 3 illustrates a LEG system that is comprised of an expander with a doubleacting free piston mechanism, a compressor with a smaller diameter and similar mechanism, a combustor, and a generator. The only moving part of the LEG is two double-acting pistons and the translator of the generator. As the piston-translator reciprocates back and forth, air is compressed in the compressor cylinder before entering the combustor. Fuel (e.g., hydrogen and ammonia mixture) is injected into the combustor for the heat addition process. Hot exhaust gas from the combustor enters into two chambers of the expander cylinder alternatively to generate an expansion force. The expansion work deduces the work spent on the compression process to obtain the net force for electricity generation. A lab-scale prototype in terms of the illustrated LEG system was presented in detail in [14].

Linear Engine Generator Development
type. More recently, Ngwaka et al. proposed a closed-loop LEG concept with Ar drogen-Oxy external combustion to tackle the challenge of using zero carbon LEGs. Both external combustion and internal combustion engines may find their tions in the electrification and de-carbonization of transport sectors.
The research teams at Newcastle University have developed a linear engin type and a linear electrical machine prototype to validate the dynamic models coupled model is developed, respectively. The dynamic characteristic of the coup tem is defined by four interlinks, namely engine design, engine performance, elec chine design, and electric load.
This paper is to address the potential impact caused by the topologies of alt Permanent Magnet (PM) generators on the performance of the LEG system. The s of the paper is as follows. In Section 2, linear engine generators have been prop Section 3, a coupled dynamic system of LEG has been investigated. In Section 4 mance validation has been carried out for the integrated system. Sections 5 and 6 simulation and experimental results of the proposed integrated linear engine gen Lastly, the paper has been concluded in Section 7 with a brief summary. Figure 3 illustrates a LEG system that is comprised of an expander with a acting free piston mechanism, a compressor with a smaller diameter and similar nism, a combustor, and a generator. The only moving part of the LEG is two doubl pistons and the translator of the generator. As the piston-translator reciprocates b forth, air is compressed in the compressor cylinder before entering the combus (e.g., hydrogen and ammonia mixture) is injected into the combustor for the heat process. Hot exhaust gas from the combustor enters into two chambers of the e cylinder alternatively to generate an expansion force. The expansion work ded work spent on the compression process to obtain the net force for electricity gen A lab-scale prototype in terms of the illustrated LEG system was presented in [14]. In the previous study's [17] modelling and design of three alternative gen which is composed of feasible PM arrangements, have been performed to react same LEG driving force in order to identify the superior generator for integration LEG system. Three different topologies, namely radially magnetiszed, axially mag and Quasi-Halbach magnetized PM linear machines, which is shown in Figure 4 signed, optimized, and compared within the volumetric constraints of the LEG Consequently, in terms of the parameter comparison results, the axially-magnet linear machine (Figure 4b) offered a better performance. The design process has ported and the results were previously validated in [18]. In the previous study's [17] modelling and design of three alternative generators, which is composed of feasible PM arrangements, have been performed to react with the same LEG driving force in order to identify the superior generator for integration with the LEG system. Three different topologies, namely radially magnetiszed, axially magnetized, and Quasi-Halbach magnetized PM linear machines, which is shown in Figure 4, are designed, optimized, and compared within the volumetric constraints of the LEG system. Consequently, in terms of the parameter comparison results, the axially-magnetized PM linear machine (Figure 4b) offered a better performance. The design process has been reported and the results were previously validated in [18].

Linear Engine Generator Development
Two configurations of the linear machine are considered in this paper, namely the long and short translator versions with different translator masses. The lab-scale generator prototype with a long translator was carefully simulated and examined [19][20][21][22].  Two configurations of the linear machine are considered in this paper, namely the long and short translator versions with different translator masses. The lab-scale generator prototype with a long translator was carefully simulated and examined [19][20][21][22]. Figure 5a shows a long translator generator, which is the reference design with the moving mass of 9 kg (Model 'A') and with a slot/pole combination of 6/7. This design is also the configuration of the lab-scale prototype that has been used for experimental validation. Figure 5b shows the decreasing moving mass of the longer translator generator (reference design) to 5.2 kg (Model 'B'); Figure 5c shows the short translator generator with fixed sheer stress and electrical machine design and the same active electromagnetic interaction as the reference design (doubled the stator length and halved the translator length) with the moving mass of 5.2 kg (Model 'C'); and Figure 5d shows the increasing moving mass of the short translator generator to 9 kg (Model 'D'). For the same mechanical force input profile from the linear engine, the generator with a lighter translator will have a higher velocity, hence it generates a greater back EMF and a potentially larger electrical power output. Although Model 'A' and 'D' have the same weight of the translators a large initial electromagnetic force is generated by model 'D' due to the bulk amount of PMs, which makes the LEG system fail to start properly. Therefore, the comparison study focuses on the rest of the three designs. Furthermore, due to engine limitations, Model 'A is unable to run on loads less than 4 Ohms.    Figure 5a shows a long translator generator, which is the reference design with the moving mass of 9 kg (Model 'A') and with a slot/pole combination of 6/7. This design is also the configuration of the lab-scale prototype that has been used for experimental validation. Figure 5b shows the decreasing moving mass of the longer translator generator (reference design) to 5.2 kg (Model 'B'); Figure 5c shows the short translator generator with fixed sheer stress and electrical machine design and the same active electromagnetic interaction as the reference design (doubled the stator length and halved the translator length) with the moving mass of 5.2 kg (Model 'C'); and Figure 5d shows the increasing moving mass of the short translator generator to 9 kg (Model 'D'). For the same mechanical force input profile from the linear engine, the generator with a lighter translator will have a higher velocity, hence it generates a greater back EMF and a potentially larger electrical power output. Although Model 'A' and 'D' have the same weight of the translators, a large initial electromagnetic force is generated by model 'D' due to the bulk amount of PMs, which makes the LEG system fail to start properly. Therefore, the comparison study focuses on the rest of the three designs. Furthermore, due to engine limitations, Model 'A' is unable to run on loads less than 4 Ohms.  Two configurations of the linear machine are considered in this paper, namely the long and short translator versions with different translator masses. The lab-scale generator prototype with a long translator was carefully simulated and examined [19][20][21][22]. Figure 5a shows a long translator generator, which is the reference design with the moving mass of 9 kg (Model 'A') and with a slot/pole combination of 6/7. This design is also the configuration of the lab-scale prototype that has been used for experimental validation. Figure 5b shows the decreasing moving mass of the longer translator generator (reference design) to 5.2 kg (Model 'B'); Figure 5c shows the short translator generator with fixed sheer stress and electrical machine design and the same active electromagnetic interaction as the reference design (doubled the stator length and halved the translator length) with the moving mass of 5.2 kg (Model 'C'); and Figure 5d shows the increasing moving mass of the short translator generator to 9 kg (Model 'D'). For the same mechanical force input profile from the linear engine, the generator with a lighter translator will have a higher velocity, hence it generates a greater back EMF and a potentially larger electrical power output. Although Model 'A' and 'D' have the same weight of the translators, a large initial electromagnetic force is generated by model 'D' due to the bulk amount of PMs, which makes the LEG system fail to start properly. Therefore, the comparison study focuses on the rest of the three designs. Furthermore, due to engine limitations, Model 'A' is unable to run on loads less than 4 Ohms.

Model Structure and Simulation Implementation
To investigate the dynamic characteristics of the overall system, it is required to use an integrated model to consider the mutual effects of electrical and mechanical responses based on the work in [23,24]. A flowchart of a novel integrated model is shown in Figure 6. It is clear that there is a dynamic interaction between the engine, generator, and resistive load, and any variation in the sub models will affect the system performance. It has been shown elsewhere that, in FPEG, the translator mass should be kept to a minimum for the optimum performance of the engine [25].

Model Structure and Simulation Implementation
To investigate the dynamic characteristics of the overall system, it is required to use an integrated model to consider the mutual effects of electrical and mechanical responses based on the work in [23,24]. A flowchart of a novel integrated model is shown in Figure  6. It is clear that there is a dynamic interaction between the engine, generator, and resistive load, and any variation in the sub models will affect the system performance. It has been shown elsewhere that, in FPEG, the translator mass should be kept to a minimum for the optimum performance of the engine [25]. The electromagnetic force behaviour of the generator while the generator is connected to the resistive load is obtained by FEA analysis, and then data are transferred to AMESim software for modelling purposes by using a series of look-up tables. In other words, data from the look-up tables are extracted from MagNet software when the generator is connected to a variety of resistive loads for a number of different velocity points. In this case, the electromagnetic force of the electrical machine is considered as a function of three inputs, namely velocity, position, and resistive load (current). Using this novel technique to model the dynamic interaction between the engine, generator, and load, it is possible to investigate the performance of the whole system in a real-time situation for further optimisation. In addition, the real generator behavior interacts with the engine rather than an ideal damper approximating a linear generator, which has been used in the literature so far. Figure 7 shows the dynamic modelling block diagram of the engine-generator. The electromagnetic force behaviour of the generator while the generator is connected to the resistive load is obtained by FEA analysis, and then data are transferred to AMESim software for modelling purposes by using a series of look-up tables. In other words, data from the look-up tables are extracted from MagNet software when the generator is connected to a variety of resistive loads for a number of different velocity points. In this case, the electromagnetic force of the electrical machine is considered as a function of three inputs, namely velocity, position, and resistive load (current). Using this novel technique to model the dynamic interaction between the engine, generator, and load, it is possible to investigate the performance of the whole system in a real-time situation for further optimisation. In addition, the real generator behavior interacts with the engine rather than an ideal damper approximating a linear generator, which has been used in the literature so far. Figure 7 shows the dynamic modelling block diagram of the engine-generator.

Model Structure and Simulation Implementation
To investigate the dynamic characteristics of the overall system, it is required to use an integrated model to consider the mutual effects of electrical and mechanical responses based on the work in [23,24]. A flowchart of a novel integrated model is shown in Figure  6. It is clear that there is a dynamic interaction between the engine, generator, and resistive load, and any variation in the sub models will affect the system performance. It has been shown elsewhere that, in FPEG, the translator mass should be kept to a minimum for the optimum performance of the engine [25]. The electromagnetic force behaviour of the generator while the generator is connected to the resistive load is obtained by FEA analysis, and then data are transferred to AMESim software for modelling purposes by using a series of look-up tables. In other words, data from the look-up tables are extracted from MagNet software when the generator is connected to a variety of resistive loads for a number of different velocity points. In this case, the electromagnetic force of the electrical machine is considered as a function of three inputs, namely velocity, position, and resistive load (current). Using this novel technique to model the dynamic interaction between the engine, generator, and load, it is possible to investigate the performance of the whole system in a real-time situation for further optimisation. In addition, the real generator behavior interacts with the engine rather than an ideal damper approximating a linear generator, which has been used in the literature so far. Figure 7 shows the dynamic modelling block diagram of the engine-generator.

Linear Engine Sub-Model
The linear engine dynamic model implementation with an ideal damper, which approximates the linear generator, can be found in the previous publications and the main engine geometrical parameters have been parametrized for optimal performance [14,18,23,24]. Based on Newton's second law, the piston motion is determined by the forces acting on the Energies 2022, 15, 5295 6 of 20 moving mass, i.e., the gas force within the cylinders of the expander and compressor, the friction force, and the load force. Therefore, the piston dynamic equation can be written as Equation (1), where F g is gas force, F f is friction force, F l is load force, m is moving mass, and a is acceleration.
The gas force can be calculated from the pressure within the cylinder, which is governed by the first law of thermodynamics and expressed by Equations (2)-(5) with an ideal gas assumption, where F g is gas force, p is in-cylinder pressure, A is piston area, Q is heat input, γ is specific heat ratio, V is in-cylinder volume, . m i is mass flow rate considering the inlet or outlet of the cylinder, h i is the enthalpy of the inlet or outlet flow, and the subscripts exp and com represent the expander side and compressor side, respectively.
In order to calculate the heat transfer from the expander, compressor, and pipes to the environment, the heat transfer coefficient is obtained. The relevant equations are written below, where h is the convective heat transfer coefficient (subscripts i, o, cyl, and pipe stand for inside, outside, cylinder, and pipe, respectively), α is the overall heat transfer coefficient, A ht is the characteristic heat transfer area, T is the temperature (subscripts g, w, and 0 represent gas, wall, and environment, respectively), d is the wall thickness, k is the thermal conductivity of the wall, D is the cylinder bore diameter, Nu is the Nusselt number, and Re is the Reynolds number [26].
The friction force of a free piston engine is mainly due to the piston ring and cylinder liner, and some from the bearing/shaft [16]. As non-lubricant graphite piston rings with back-bone springs were used for this study, the friction from the piston ring mainly consists of performance of the engine [27]: dry friction caused by the tension force of the piston ring (F f d ) and the friction due to the in-cylinder pressure loading (F f p ). The Stribeck model [28] is used to calculate F f d as expressed in Equation (11), where F f c and F f s are the Coulomb friction force and maximum static friction force, and Cs is the Stribeck constant. F f p is derived from Equation (12), where µ f p is pressure friction coefficient, p is in-cylinder pressure, D is cylinder bore diameter, and W is piston ring width.

Generator Sub-Model
The force generated from the thermodynamic Joule Cycle acts as a prime mover to drive the linear generator. The piston velocity, i.e., the translator velocity, and the total force from the working gas in the cylinders are fed into the linear generator. These two input variables to the linear generator are affected by responding forces from the linear generator, which in turn influence the dynamic balance of the linear motion of the joule engine. The linear generator responding forces F la can be divided into its components (Equation (13), [29]).
where F ele : electrical force, F cog : cogging force, F co : core loss force, F ed : eddy current force, F cp : copper loss force, and F ar : armature reaction force. For simplicity and accurate results, the linear generator responding forces (F la ) are obtained by the help of the Finite Element Analysis (FEA) modelling method, and then look-up tables are created and used to model the aggregated linear generator responding forces.

Input Parameters of the Coupled Model
The parameters of the three models are shown in Table 1.

Linear Engine Sub-Model Validation
It is necessary to verify the prototype dynamic model before extensive parameter analysis. The verification is based on the experiment results, and the detail of the prototype has been previously presented [14,23]. In the prototype engine, a moving mass load is used to replace a linear generator, and compressed air from outside is used to start the engine. When the expander piston reaches its Top Dead Centre (TDC), the expander inlet valve opens, and then the piston is pushed to its Bottom Dead Centre (BDC) by the hightemperature and high-pressure working fluid to complete an expansion stroke. At the same time, the compressor piston connected by the shaft with the expander piston moves synchronously and completes a compression stroke. The exhaust valve of the expander begins to open at the start of the expansion stroke and closes near the TDC position, which is controlled by the engine control unit and the compressor valves open and close according to the set value of the pressure in the compressor. Comparisons of the piston movement characteristics of the test and simulation results are presented in Figure 8. same time, the compressor piston connected by the shaft with the expander piston moves synchronously and completes a compression stroke. The exhaust valve of the expander begins to open at the start of the expansion stroke and closes near the TDC position, which is controlled by the engine control unit and the compressor valves open and close according to the set value of the pressure in the compressor. Comparisons of the piston movement characteristics of the test and simulation results are presented in Figure 8.  Figure 9 describes the gas force and friction force comparisons, respectively. The comparison of gas forces shows that the test and simulation results have the same trend and a relatively small gap. The gas force is measured indirectly, which is based on the dynamic balance of the moving mass. When the piston reaches TDC and BDC, the maximum gas forces of the test and simulation reach 2255.42 N and 3140.20 N, respectively, which could be explained by the high pressure in the chambers. The errors of the gas forces and friction forces will cancel each other and not be passed onto the electric side. The difference between the test and simulation results may be due to the possibility of leakage near the TDC in the experiment. More consideration for the effects of leakage in the simulation model may further improve the model. In addition, it shows that the simulation results and the test result of the friction force are not as consistent as the previous parameters. The simulation friction result shows the friction increases from 120N to 476 N with the piston movement and changes direction when the piston turns. The test friction has a larger fluctuation but has a rough consistency with the simulation friction. Hence, the dynamic behaviour of the prototype engine has been understood.

PM LSM Sub-Model Validation
In this test, the prototype was directly driven by a ball screw (i.e., actuator) with a maximum velocity of 5.7 mm/s. No-load back EMF waveforms obtained from the simulation and experimental results for one phase are plotted on the same graph, as shown in  Figure 9 describes the gas force and friction force comparisons, respectively. The comparison of gas forces shows that the test and simulation results have the same trend and a relatively small gap. The gas force is measured indirectly, which is based on the dynamic balance of the moving mass. When the piston reaches TDC and BDC, the maximum gas forces of the test and simulation reach 2255.42 N and 3140.20 N, respectively, which could be explained by the high pressure in the chambers. The errors of the gas forces and friction forces will cancel each other and not be passed onto the electric side. The difference between the test and simulation results may be due to the possibility of leakage near the TDC in the experiment. More consideration for the effects of leakage in the simulation model may further improve the model. In addition, it shows that the simulation results and the test result of the friction force are not as consistent as the previous parameters. The simulation friction result shows the friction increases from 120N to 476 N with the piston movement and changes direction when the piston turns. The test friction has a larger fluctuation but has a rough consistency with the simulation friction. Hence, the dynamic behaviour of the prototype engine has been understood.
ing to the set value of the pressure in the compressor. Comparisons of the piston mo ment characteristics of the test and simulation results are presented in Figure 8.  Figure 9 describes the gas force and friction force comparisons, respectively. T comparison of gas forces shows that the test and simulation results have the same tre and a relatively small gap. The gas force is measured indirectly, which is based on dynamic balance of the moving mass. When the piston reaches TDC and BDC, the ma mum gas forces of the test and simulation reach 2255.42 N and 3140.20 N, respective which could be explained by the high pressure in the chambers. The errors of the g forces and friction forces will cancel each other and not be passed onto the electric si The difference between the test and simulation results may be due to the possibility leakage near the TDC in the experiment. More consideration for the effects of leakage the simulation model may further improve the model. In addition, it shows that the si ulation results and the test result of the friction force are not as consistent as the previo parameters. The simulation friction result shows the friction increases from 120N to 4 N with the piston movement and changes direction when the piston turns. The test frict has a larger fluctuation but has a rough consistency with the simulation friction. Hen the dynamic behaviour of the prototype engine has been understood.

PM LSM Sub-Model Validation
In this test, the prototype was directly driven by a ball screw (i.e., actuator) wit maximum velocity of 5.7 mm/s. No-load back EMF waveforms obtained from the simu tion and experimental results for one phase are plotted on the same graph, as shown

PM LSM Sub-Model Validation
In this test, the prototype was directly driven by a ball screw (i.e., actuator) with a maximum velocity of 5.7 mm/s. No-load back EMF waveforms obtained from the simulation and experimental results for one phase are plotted on the same graph, as shown in Figure 10. Soft magnetic composite (SMC)-based stator components might change their magnetic properties whilst they are machined in real life. This might be one of the reasons that the measured and simulated results in Figure 10 do not match perfectly. Figure 10. Soft magnetic composite (SMC)-based stator components might chan magnetic properties whilst they are machined in real life. This might be one of the that the measured and simulated results in Figure 10 do not match perfectly. The peak value of the predicted no-load beck EMF is 14 mV, where a d rounding can be approximately (≈9.5%) seen, however, this may be considered the existing noise in the measured signal at this very low speed. In addition, the teristics of the material used in the FEA model may not match the characteristi real material used in the prototype. Design tolerance in the manufacturing pro plays a significant role, which may result in inaccurate dimensions.

Performance Prediction of the LEG System with Long Translator Generator (Model
The electric power generated from the Model 'A' generator is depicted in F The associated mechanical power generation versus the load resistance is also sho Model 'A' generator is capable of generating about 1.8 kW of electric power from mechanical power input that is generated in the thermodynamic process. The g efficiency and the LEG system efficiency are also given in Figure 11.  The peak value of the predicted no-load beck EMF is 14 mV, where a deviation rounding can be approximately (≈9.5%) seen, however, this may be considered fair with the existing noise in the measured signal at this very low speed. In addition, the characteristics of the material used in the FEA model may not match the characteristics of the real material used in the prototype. Design tolerance in the manufacturing process also plays a significant role, which may result in inaccurate dimensions.

Performance Prediction of the LEG System with Long Translator Generator (Model 'A')
The electric power generated from the Model 'A' generator is depicted in Figure 11. The associated mechanical power generation versus the load resistance is also shown. The Model 'A' generator is capable of generating about 1.8 kW of electric power from 2 kW of mechanical power input that is generated in the thermodynamic process. The generator efficiency and the LEG system efficiency are also given in Figure 11.  The peak value of the predicted no-load beck EMF is 14 mV, where a deviation rounding can be approximately (≈9.5%) seen, however, this may be considered fair with the existing noise in the measured signal at this very low speed. In addition, the characteristics of the material used in the FEA model may not match the characteristics of the real material used in the prototype. Design tolerance in the manufacturing process also plays a significant role, which may result in inaccurate dimensions.

Performance Prediction of the LEG System with Long Translator Generator (Model 'A')
The electric power generated from the Model 'A' generator is depicted in Figure 11. The associated mechanical power generation versus the load resistance is also shown. The Model 'A' generator is capable of generating about 1.8 kW of electric power from 2 kW of mechanical power input that is generated in the thermodynamic process. The generator efficiency and the LEG system efficiency are also given in Figure 11. Using the dynamic model, the variation of the phase voltages, phase currents, and power dumped in the load resistance, at peak load condition of 5 Ohms, are shown in Figure 12a-c. It shows the amplitude imbalance over the entire mechanical cycle with variable electrical frequency ( = 130 Hz) operations. Using the dynamic model, the variation of the phase voltages, phase currents, and power dumped in the load resistance, at peak load condition of 5 Ohms, are shown in Figure 12a-c. It shows the amplitude imbalance over the entire mechanical cycle with variable electrical frequency (fe = 130 Hz) operations.
An ideal damper that mimics the linear generator omits the effects of the detailed electromagnetic force, machine losses, and magnetic force ripples, which presents a very smooth overall electromagnetic force versus the piston displacement and time, which is illustrated in Figure 13. These results enable the system designers to investigate the effect of the actual generator reacting force on the linear engine performance, rather than assuming the electrical machine behaves simply as a damper, where the reacting force varies linearly with velocity acting against the engine's driving force. The effects of the machine inductance, saturation, tooth/slots, and finite length of the stator/translator cause disturbances. The resultant actual reacting force with fluctuations will have an impact on the thermodynamic performance of the engine. An ideal damper that mimics the linear generator omits the effects of the detailed electromagnetic force, machine losses, and magnetic force ripples, which presents a very smooth overall electromagnetic force versus the piston displacement and time, which is illustrated in Figure 13. These results enable the system designers to investigate the effect of the actual generator reacting force on the linear engine performance, rather than assuming the electrical machine behaves simply as a damper, where the reacting force varies linearly with velocity acting against the engine's driving force. The effects of the machine inductance, saturation, tooth/slots, and finite length of the stator/translator cause disturbances. The resultant actual reacting force with fluctuations will have an impact on the thermodynamic performance of the engine.
With the coupled model of the LEG, the linear engine is connected to the generator, which is in an open circuit condition to look at the ripple force of the generator. This ripple force, i.e., the cogging force, is due to the non-uniformity of the reluctance path in the air gap area (slot effects) and oversizing of the translator or stator (end effects), as well as the velocity effect/core loss (iron loss and eddy current loss). The cogging force of the Model 'A' generator versus time and piston position can be seen in Figure 14.   An ideal damper that mimics the linear generator omits the effects of the deta electromagnetic force, machine losses, and magnetic force ripples, which presents a v smooth overall electromagnetic force versus the piston displacement and time, whic illustrated in Figure 13. These results enable the system designers to investigate the ef of the actual generator reacting force on the linear engine performance, rather than suming the electrical machine behaves simply as a damper, where the reacting force va linearly with velocity acting against the engine's driving force. The effects of the mach inductance, saturation, tooth/slots, and finite length of the stator/translator cause distu ances. The resultant actual reacting force with fluctuations will have an impact on thermodynamic performance of the engine.
With the coupled model of the LEG, the linear engine is connected to the genera which is in an open circuit condition to look at the ripple force of the generator. This rip force, i.e., the cogging force, is due to the non-uniformity of the reluctance path in the gap area (slot effects) and oversizing of the translator or stator (end effects), as well as velocity effect/core loss (iron loss and eddy current loss). The cogging force of the Mo 'A' generator versus time and piston position can be seen in Figure 14.  With the coupled model of the LEG, the linear engine is connected to the generator, which is in an open circuit condition to look at the ripple force of the generator. This ripple force, i.e., the cogging force, is due to the non-uniformity of the reluctance path in the air gap area (slot effects) and oversizing of the translator or stator (end effects), as well as the velocity effect/core loss (iron loss and eddy current loss). The cogging force of the Model 'A' generator versus time and piston position can be seen in Figure 14. An ideal damper that mimics the linear generator omits the effects of the deta electromagnetic force, machine losses, and magnetic force ripples, which presents a v smooth overall electromagnetic force versus the piston displacement and time, whic illustrated in Figure 13. These results enable the system designers to investigate the e of the actual generator reacting force on the linear engine performance, rather than suming the electrical machine behaves simply as a damper, where the reacting force va linearly with velocity acting against the engine's driving force. The effects of the mach inductance, saturation, tooth/slots, and finite length of the stator/translator cause dist ances. The resultant actual reacting force with fluctuations will have an impact on thermodynamic performance of the engine.
With the coupled model of the LEG, the linear engine is connected to the genera which is in an open circuit condition to look at the ripple force of the generator. This rip force, i.e., the cogging force, is due to the non-uniformity of the reluctance path in th gap area (slot effects) and oversizing of the translator or stator (end effects), as well as velocity effect/core loss (iron loss and eddy current loss). The cogging force of the Mo 'A' generator versus time and piston position can be seen in Figure 14.

Alternative Topologies of PM Generator-MagNet FEA Analysis
Electric power versus resistive load, which is characteristic of two configurations of short and long translator generators, can be seen in Figure 15. In the FEA software, the applied velocity to the translator was kept constant for both configurations regardless of the mass of the translator, and it is equal to 5 m/s. Figure 15 illustrates that model 'A' generates approximately 3.8 kW of electric power, which is double the amount of electric power generation compared to model 'C'. The reason behind this is that in the model 'A' generator, all coils are active at any time instant, contributing to generate output power, whereas in the model 'C' generator half the number of coils are inactive at any time instant and act as an external consumer of load, reducing electrical power generation. In the model 'B' generator, since the number of PMs is halved compared to the PMs in the model 'A' generator and the electrical power is also approximately halved.

Alternative Topologies of PM Generator-MagNet FEA Analysis
Electric power versus resistive load, which is characteristic of two configura short and long translator generators, can be seen in Figure 15. In the FEA softw applied velocity to the translator was kept constant for both configurations regar the mass of the translator, and it is equal to 5 m/s. Figure 15 illustrates that mo generates approximately 3.8 kW of electric power, which is double the amount of power generation compared to model 'C'. The reason behind this is that in the m generator, all coils are active at any time instant, contributing to generate output whereas in the model 'C' generator half the number of coils are inactive at any time and act as an external consumer of load, reducing electrical power generation model 'B' generator, since the number of PMs is halved compared to the PMs in th 'A' generator and the electrical power is also approximately halved.  Figure 16 represents the comparison of the velocity of three models versu displacement. Model 'A' has the lowest peak velocity of 4.9 m/s for the heavies mass. Model 'C' has a peak velocity of 7.1 m/s and model 'B' has the highest valu m/s. This could reflect the reality that model 'B' has the highest frequency whi models have a nearly equal stroke. However, the position of the peak velocity is n center of the stroke and the velocity versus displacement curve is not a standard which is related to the reality that the balanced position of the piston is not in th due to load force, friction, and valve timing. In more detail, due to the valve contro anism, the gas force is relatively large at the beginning of the stroke and gradu creases to the value of the sum of other forces in different directions. This is th balance point where the piston exceeds the stroke center, and the velocity reache value.   Figure 16 represents the comparison of the velocity of three models versus piston displacement. Model 'A' has the lowest peak velocity of 4.9 m/s for the heaviest piston mass. Model 'C' has a peak velocity of 7.1 m/s and model 'B' has the highest value of 7.9 m/s. This could reflect the reality that model 'B' has the highest frequency while three models have a nearly equal stroke. However, the position of the peak velocity is not in the center of the stroke and the velocity versus displacement curve is not a standard ellipse, which is related to the reality that the balanced position of the piston is not in the center due to load force, friction, and valve timing. In more detail, due to the valve control mechanism, the gas force is relatively large at the beginning of the stroke and gradually decreases to the value of the sum of other forces in different directions. This is the force balance point where the piston exceeds the stroke center, and the velocity reaches a peak value. the mass of the translator, and it is equal to 5 m/s. Figure 15 illustrates that mode generates approximately 3.8 kW of electric power, which is double the amount of ele power generation compared to model 'C'. The reason behind this is that in the mode generator, all coils are active at any time instant, contributing to generate output po whereas in the model 'C' generator half the number of coils are inactive at any time in and act as an external consumer of load, reducing electrical power generation. In model 'B' generator, since the number of PMs is halved compared to the PMs in the m 'A' generator and the electrical power is also approximately halved.  Figure 16 represents the comparison of the velocity of three models versus p displacement. Model 'A' has the lowest peak velocity of 4.9 m/s for the heaviest p mass. Model 'C' has a peak velocity of 7.1 m/s and model 'B' has the highest value o m/s. This could reflect the reality that model 'B' has the highest frequency while t models have a nearly equal stroke. However, the position of the peak velocity is not in center of the stroke and the velocity versus displacement curve is not a standard ell which is related to the reality that the balanced position of the piston is not in the ce due to load force, friction, and valve timing. In more detail, due to the valve control m anism, the gas force is relatively large at the beginning of the stroke and gradually creases to the value of the sum of other forces in different directions. This is the f balance point where the piston exceeds the stroke center, and the velocity reaches a value.  The air is compressed in the compressor part and the pressure increases with the decrease of the volume of the compressor, which can be seen in Figure 17. Model 'B' has the highest pressure (9.78 bar) when the volume reduces to the position near TDC and BDC, while model 'A' has the lowest peak pressure (7.49 bar). The pressure amplitude in Model 'B' is the largest among the models. The three cases (i.e., Model 'A'-'C') apply roughly the same valve timings, therefore the velocity profiles, and, in turn, the frequencies of the systems, play a key role in pressure build-up. With the heaviest moving mass, Model Energies 2022, 15, 5295 12 of 20 'A' develops the lowest peak pressure in the compressor and the lowest frequency of the system, which leads to the lowest peak pressure after the pressure balance is established. For Model 'B' and 'C', which have the same weight for their moving masses, the slight difference of stroke length causes the difference in peak pressure. With less resistance than Model 'B', it has the longest stroke compared to the target stroke of 120 mm, which results in its top peak pressure in the thermodynamic cycles. In Figure 18, the peak pressure discrepancy is also derived from the abovementioned reasons.

The Linear Engine Spontaneous Response to Alternative Topologies of PM Generator
Model 'A' develops the lowest peak pressure in the compressor and the lowe of the system, which leads to the lowest peak pressure after the pressure bala lished. For Model 'B' and 'C', which have the same weight for their moving slight difference of stroke length causes the difference in peak pressure. W sistance than Model 'B', it has the longest stroke compared to the target strok which results in its top peak pressure in the thermodynamic cycles. In Figure pressure discrepancy is also derived from the abovementioned reasons. Figure 18 describes the pressure changes in the expander with the ch expander volume. In the expander part, the high-temperature and high-pr input in the expander from point 'a' to point 'b' to push the expander pisto has the highest pressure of 9.78 bar, while Model 'A' and Model 'C' are 7.49 bar, respectively.

Energy Inputs and Outputs
The variation in the combustion heat input due to applying different ex tive loads to the generator have been studied, which is shown in Figure 19. I that the combustion heat input is progressively increased with the load resista for Model 'A', whereas for the other two generator models they are constan bustion heat inputs versus resistive loads in the Model 'B' and 'C' generator generally greater than the Model 'A' design. This indicates that combustion directly linked with moving mass. At a load of 4 Ohms connected to the term erator Model 'B' and 'C', the generators require about 34% more combustio compared to Model 'A'. In Figure 20, it is shown that the Model 'C' generator about 15% more electric power compared to other generators. Model 'A' develops the lowest peak pressure in the compressor and the lowes of the system, which leads to the lowest peak pressure after the pressure balan lished. For Model 'B' and 'C', which have the same weight for their moving slight difference of stroke length causes the difference in peak pressure. W sistance than Model 'B', it has the longest stroke compared to the target stroke which results in its top peak pressure in the thermodynamic cycles. In Figure pressure discrepancy is also derived from the abovementioned reasons. Figure 18 describes the pressure changes in the expander with the cha expander volume. In the expander part, the high-temperature and high-pre input in the expander from point 'a' to point 'b' to push the expander piston has the highest pressure of 9.78 bar, while Model 'A' and Model 'C' are 7.49 b bar, respectively.

Energy Inputs and Outputs
The variation in the combustion heat input due to applying different ex tive loads to the generator have been studied, which is shown in Figure 19. It that the combustion heat input is progressively increased with the load resistan for Model 'A', whereas for the other two generator models they are constant bustion heat inputs versus resistive loads in the Model 'B' and 'C' generator generally greater than the Model 'A' design. This indicates that combustion h directly linked with moving mass. At a load of 4 Ohms connected to the termi erator Model 'B' and 'C', the generators require about 34% more combustion compared to Model 'A'. In Figure 20, it is shown that the Model 'C' generator c about 15% more electric power compared to other generators.  Figure 18 describes the pressure changes in the expander with the changes of the expander volume. In the expander part, the high-temperature and high-pressure air is input in the expander from point 'a' to point 'b' to push the expander piston. Model 'B' has the highest pressure of 9.78 bar, while Model 'A' and Model 'C' are 7.49 bar and 8.73 bar, respectively.

Energy Inputs and Outputs
The variation in the combustion heat input due to applying different external resistive loads to the generator have been studied, which is shown in Figure 19. It is revealed that the combustion heat input is progressively increased with the load resistance increase for Model 'A', whereas for the other two generator models they are constant. Peak combustion heat inputs versus resistive loads in the Model 'B' and 'C' generator models are generally greater than the Model 'A' design. This indicates that combustion heat input is directly linked with moving mass. At a load of 4 Ohms connected to the terminals of generator Model 'B' and 'C', the generators require about 34% more combustion heat input compared to Model 'A'. In Figure 20, it is shown that the Model 'C' generator can generate about 15% more electric power compared to other generators.   Figure 21 illustrates the velocity profiles of the piston/translator assembly in cycle (two strokes). The lighter moving mass demonstrates a shorter cycle time an frequency compared to the heavier moving mass. Due to the reduced frequen intake valves, the overall combustion heat input of the LEG system with the heav ing mass decreases.  Table 2 reveals a comprehensive comparison of alternative generators. Mod produce 2120 Watts output power, which is about 16.5% and 19% more than m and 'B', respectively. However, the Model 'A' generator can achieve the highes efficiency of 30% among other generators. In terms of the ratio of power versus power versus volume, Model 'C' is superior, however Model 'A' is better for th versus weight of the electrical machine.    Figure 21 illustrates the velocity profiles of the piston/translator assembly in cycle (two strokes). The lighter moving mass demonstrates a shorter cycle time an frequency compared to the heavier moving mass. Due to the reduced frequenc intake valves, the overall combustion heat input of the LEG system with the heavi ing mass decreases.  Table 2 reveals a comprehensive comparison of alternative generators. Mode produce 2120 Watts output power, which is about 16.5% and 19% more than m and 'B', respectively. However, the Model 'A' generator can achieve the highest efficiency of 30% among other generators. In terms of the ratio of power versus c power versus volume, Model 'C' is superior, however Model 'A' is better for th versus weight of the electrical machine.   Figure 21 illustrates the velocity profiles of the piston/translator assembly in a single cycle (two strokes). The lighter moving mass demonstrates a shorter cycle time and higher frequency compared to the heavier moving mass. Due to the reduced frequency of the intake valves, the overall combustion heat input of the LEG system with the heavier moving mass decreases.   Figure 21 illustrates the velocity profiles of the piston/translator assembly in cycle (two strokes). The lighter moving mass demonstrates a shorter cycle time an frequency compared to the heavier moving mass. Due to the reduced frequenc intake valves, the overall combustion heat input of the LEG system with the heav ing mass decreases.  Table 2 reveals a comprehensive comparison of alternative generators. Mode produce 2120 Watts output power, which is about 16.5% and 19% more than m and 'B', respectively. However, the Model 'A' generator can achieve the highes efficiency of 30% among other generators. In terms of the ratio of power versus power versus volume, Model 'C' is superior, however Model 'A' is better for th versus weight of the electrical machine.   Table 2 reveals a comprehensive comparison of alternative generators. Model 'C' can produce 2120 Watts output power, which is about 16.5% and 19% more than model 'A' and 'B', respectively. However, the Model 'A' generator can achieve the highest system efficiency of 30% among other generators. In terms of the ratio of power versus cost and power versus volume, Model 'C' is superior, however Model 'A' is better for the power versus weight of the electrical machine. 6. Discussion on System Integration 6.1. Proposed Integrated Prototype Figure 22 shows how the electrical machine is intended to fit within the FPEG air compressor. The short translator generator saves space and has the potential for an integrated design, high efficiency, compact size, and flexibility in renewable energy integration. 6. Discussion on System Integration Figure 22 shows how the electrical machine is intended to fit within the FPEG air compressor. The short translator generator saves space and has the potential for an integrated design, high efficiency, compact size, and flexibility in renewable energy integration. The fundamental issue of integrating an electrical machine with a compressor cylinder is ensuring that the fluid does not skip from chambers for the piston/translator to compress the air or working fluid into a high compression ratio. When the temperature in the compressor cylinder rises, materials with a high working temperature point must be  The fundamental issue of integrating an electrical machine with a compressor cylinder is ensuring that the fluid does not skip from chambers for the piston/translator to compress the air or working fluid into a high compression ratio. When the temperature in the compressor cylinder rises, materials with a high working temperature point must be employed. Furthermore, incorporating valves on end plates and shaft sealing are the remaining issues that were thoroughly explored and addressed in [30,31]. Figure 23 depicts the laboratory assembly setup, in which the linear prototype machine (i.e., compressor cylinder-generator) is attached to a crankshaft mechanism, prime mover, and drive unit to simulate the operation of the combustor and expander cylinder. It was not possible to build and integrate this generator-compressor cylinder prototype with an engine's expanding cylinder, hence the translator/piston assembly must be connected to a linear motion prime mover to mimic the expander cylinder performance. A crankshaft is used in the conversion of rotary to linear motion. It is one of the hardest-working components and converts the prime mover's rotary movement into linear motion. The specifics are as follows: Direct intake, bell-shaped, Stroke is 50.0 mm, Conrod is 110.0 mm, Pin is 15 mm, and Conrod pin is 21 mm.  Figure 23 depicts the laboratory assembly setup, in which the linear prototype machine (i.e., compressor cylinder-generator) is attached to a crankshaft mechanism, prime mover, and drive unit to simulate the operation of the combustor and expander cylinder. It was not possible to build and integrate this generator-compressor cylinder prototype with an engine's expanding cylinder, hence the translator/piston assembly must be connected to a linear motion prime mover to mimic the expander cylinder performance. A crankshaft is used in the conversion of rotary to linear motion. It is one of the hardestworking components and converts the prime mover's rotary movement into linear motion. The specifics are as follows: Direct intake, bell-shaped, Stroke is 50.0 mm, Conrod is 110.0 mm, Pin is 15mm, and Conrod pin is 21 mm.

No-Load Electrical Testing
The results of an open circuit test with a continuous rotational speed of 600 rpm and a peak speed of 1 m/s are shown in Figure 24. Since both sides of the compressor cylinder were vented to the atmosphere, this was strictly an electrical test rather than an electromechanical test. Since the three phases of the machine are well balanced, there is confidence in the assembly of the SMC stator components and the concentricity of the bearings. Table 3 gives the key results of the open circuit test. A comparison between the predicted and simulated back EMF at a fixed speed of 0.3 m/s is shown in Figure 24. The model is seen to overpredict by around 10% compared to an idealized finite element analysis simulation; reasons for this will include damage to the SMC material and possible parasitic air gaps in the stator assembly. To investigate just one of these effects, a small air gap was inserted between the SMC teeth and coil carrying coreback components in the finite element analysis model, as shown in Figure 25. The results of the back EMF prediction for a gap of 0.05 mm were also shown in Figure 25 and bring the agreement between the measured and simulated results closer.

No-Load Electrical Testing
The results of an open circuit test with a continuous rotational speed of 600 rpm and a peak speed of 1 m/s are shown in Figure 24. Since both sides of the compressor cylinder were vented to the atmosphere, this was strictly an electrical test rather than an electro-mechanical test. Since the three phases of the machine are well balanced, there is confidence in the assembly of the SMC stator components and the concentricity of the bearings. Table 3 gives the key results of the open circuit test. A comparison between the predicted and simulated back EMF at a fixed speed of 0.3 m/s is shown in Figure 24. The model is seen to overpredict by around 10% compared to an idealized finite element analysis simulation; reasons for this will include damage to the SMC material and possible parasitic air gaps in the stator assembly. To investigate just one of these effects, a small air gap was inserted between the SMC teeth and coil carrying coreback components in the finite element analysis model, as shown in Figure 25. The results of the back EMF prediction for a gap of 0.05 mm were also shown in Figure 25 and bring the agreement between the measured and simulated results closer.  The difference between the simulation and experimental re be due to several reasons: uneven machine air gap length in real translator affected by the components' tolerance, and the electro the SMC components machined before assembly.

On-Load Electrical Testing
To electrically load the generator, the three phases were nected three-phase resistive load, as shown in Figure 26, and   The difference between the simulation and experimental results in Figure 25a could be due to several reasons: uneven machine air gap length in real life, manufacturing of the translator affected by the components' tolerance, and the electromagnetic performance of the SMC components machined before assembly.

On-Load Electrical Testing
To electrically load the generator, the three phases were connected to a star-connected three-phase resistive load, as shown in Figure 26, and the voltage, current, and electric power of one phase when operating at 300 rpm and a peak speed of 0.5 m/s were recorded ( Figure 27). Figure 28 compares the measured and simulated power output for a variation in load resistance. It is found that for both measured and FEA, the maximum power of 30W occurred at 6Ω. The simulated power using the model excluding the parasitic air gaps (Simulation-1) overpredicts the output power by almost 10%. The difference between the simulation and experimental results in Figure 25a could be due to several reasons: uneven machine air gap length in real life, manufacturing of the translator affected by the components' tolerance, and the electromagnetic performance of the SMC components machined before assembly.

On-Load Electrical Testing
To electrically load the generator, the three phases were connected to a star-connected three-phase resistive load, as shown in Figure 26, and the voltage, current, and electric power of one phase when operating at 300 rpm and a peak speed of 0.5 m/s were recorded ( Figure 27). Figure 28 compares the measured and simulated power output for a variation in load resistance. It is found that for both measured and FEA, the maximum power of 30 W occurred at 6 Ω. The simulated power using the model excluding the parasitic air gaps (Simulation-1) overpredicts the output power by almost 10%.

Compression Test
In order to test the compressor cylinder's pressure capability, the inl valves were installed in the endcap, and two exhaust valves were piped

Compression Test
In order to test the compressor cylinder's pressure capability, the inlet and valves were installed in the endcap, and two exhaust valves were piped to a vessel, as shown in Figure 29. The air was stored in an accumulator, and the press seen increasing with each compression stroke. For safety considerations, the stopped after a few cycles once the pressure hit 1 bar. Thus, the concept of a co

Compression Test
In order to test the compressor cylinder's pressure capability, the inl valves were installed in the endcap, and two exhaust valves were piped vessel, as shown in Figure 29. The air was stored in an accumulator, and th

Compression Test
In order to test the compressor cylinder's pressure capability, the inlet and exhaust valves were installed in the endcap, and two exhaust valves were piped to a pressure vessel, as shown in Figure 29. The air was stored in an accumulator, and the pressure was seen increasing with each compression stroke. For safety considerations, the test was stopped after a few cycles once the pressure hit 1 bar. Thus, the concept of a combined generator/compressor cylinder was successfully proven in the prototype. In-let valve and exhaust valve connection on endcap of prototype (two inlet-two exhaust).
Pressure gage on compressor vessel shows 1 bar Figure 29. Compression testing.

Conclusions
Experimental tests on a novel integrated compressor cylinder-generator system prototype were successfully completed in this study, demonstrating that the concept is feasible and that the prototype can generate electrical power and compressed air simultaneously. As a result, this paper claims that a linear generator can be integrated into a compressor cylinder while overcoming mechanical challenges.
The dynamic and thermodynamic characteristics of a LJEG system with an alternative generator configuration are presented in detail. By decreasing the moving mass of the system, more power can be generated in a short translator generator (i.e., Model 'C') at the expense of consuming more fuel or combustion power compared to long translator generators. Short translator generators generate more electric power with lower efficiency and higher combustion power compared to a long translator generator (i.e., Model 'A' and 'B'), which generates a little less power with higher efficiency at lower combustion power.
A short translator generator has a higher frequency compared to a long translator generator, implying that if the frequency is high, the valves will open and close more frequently and more hot air is drawn from the combustor. This results in the requirement of more combustion power to warm up the air in the combustor before moving to the engine for expansion-compression purposes. Therefore, Model 'C' is more promising in terms of electric power generation.
It might be concluded that during the launching of the FPEG system, the short translator (i.e., Model 'C') can consume less fuel because of its lighter mass compared to a long translator generator (i.e., Model 'A' and 'B'). In other words, in the transient condition of the system, the short translator consumes less combustion power to drive/push the piston-

Conclusions
Experimental tests on a novel integrated compressor cylinder-generator system prototype were successfully completed in this study, demonstrating that the concept is feasible and that the prototype can generate electrical power and compressed air simultaneously. As a result, this paper claims that a linear generator can be integrated into a compressor cylinder while overcoming mechanical challenges.
The dynamic and thermodynamic characteristics of a LJEG system with an alternative generator configuration are presented in detail. By decreasing the moving mass of the system, more power can be generated in a short translator generator (i.e., Model 'C') at the expense of consuming more fuel or combustion power compared to long translator generators. Short translator generators generate more electric power with lower efficiency and higher combustion power compared to a long translator generator (i.e., Model 'A' and 'B'), which generates a little less power with higher efficiency at lower combustion power.
A short translator generator has a higher frequency compared to a long translator generator, implying that if the frequency is high, the valves will open and close more frequently and more hot air is drawn from the combustor. This results in the requirement of more combustion power to warm up the air in the combustor before moving to the engine for expansion-compression purposes. Therefore, Model 'C' is more promising in terms of electric power generation.
It might be concluded that during the launching of the FPEG system, the short translator (i.e., Model 'C') can consume less fuel because of its lighter mass compared to a long translator generator (i.e., Model 'A' and 'B'). In other words, in the transient condition of the system, the short translator consumes less combustion power to drive/push the piston-translator, however in the steady state condition, the short translator generator (i.e., Model 'C'), due to having a lighter mass and higher frequency, consumes more fuel or combustion power. In the start mode of the system, the short translator perhaps consumes less energy compared to the long one because, initially, the engine is required to push the translator to reach a certain frequency, so the one with a heavier mass would consume more fuel.
Depending on the requirements of the application, a short or long translator generator can be adapted. A short translator is preferable since it occupies less volume and is good for compact systems, however, if the weight is important, a long translator can be chosen. In terms of cost, a short translator is more economical because of the use of overhanging stators with 50% less permanent magnet material. Furthermore, an FPEG system with a short translator generator (i.e., Model 'C') is preferable in terms of system cost and volume, whereas Model 'A' is a better option in terms of system efficiency in comparison to Model 'B' and 'C'. Funding: This work was funded by EPSRC (Engineering and Physical Sciences Research Council) Impact Acceleration Account with funding reference number: EP/N509528/1.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Conflicts of Interest:
The authors declare no conflict of interest.