A moving-coil linear generator with dual axial-magnetized stator for free-piston engines

Abstract

Free-piston engine coupled with linear generator is a new type of thermoelectric energy converter, which has the advantages of high efficiency and simple structure. In this paper, a novel moving-coil linear generator with dual axial-magnetized stator is proposed for this kind of short-stroke high frequency oscillation generating applications. Finite-element (FE) model of the generator is created, the static and transient characteristics are analyzed, and the losses in different components are compared. A full-bridge power converter is designed to meet the control requirements of reversible operation. A 540 W experimental prototype is developed and tested to validate the FE analysis. According to the tested and simulated results, the generator has advantages of high efficiency and fast response. The generating efficiency of 92% can be obtained at the rated generating power. The average inductance of the proposed generator is about 0.7 mH, which benefits from the low armature effect and ensures a very quick electromagnetic response.

Keywords

Electromagnetic characteristics free-piston engine moving-coil linear generator power converter

1. Introduction

Free-piston energy generator (FPEG) is a new type of thermoelectric energy converter composed of free-piston engine and linear generator. It can directly convert chemical energy into electrical energy. This device can be used in hybrid electric vehicles, emergency power supply, portable power generation, etc. [1,2]. It has the advantages of high efficiency, low emissions, simple structure, and convenient maintenance [3]. Therefore, such energy converter device has attracted much attention from worldwide scholars, and various types of FPEGs have been proposed and studied in recent years [4,5]. This paper concentrates on a novel FPEG with a two-stroke free-piston engine, a gas spring, and a linear generator, as shown in Fig. 1. The piston is directly connected to the mover of the linear generator as a piston assembly. Without rotating crankshaft and flywheel, a back spring is used to store energy. Compared to the mechanical springs, the gas spring has good thrust characteristics, and it is more suitable for FPEG. The piston assembly motion depends on the instantaneous force acting on it, including combustion pressure, spring force, electromagnetic force, and friction. The compression ratio is variable and controllable. This characteristic means the FPEG can use traditional fuels such as petrol, diesel, or alternative fuels such as hydrogen, synthetic fuel, etc. [6]. Furthermore, the variable compression ratio also offers a potential possibility to realize promising Homogeneous Charge Compression Ignition (HCCI) [7]. These features make the FPEG more competitive and valuable.

Fig. 1.

Free-piston engine coupled with linear generator.

The working cycle of the free-piston engine is described in Fig. 2. A complete cycle includes compression stroke and expansion stroke. The positive direction is shown by the arrow on the piston assembly in Fig. 1. During the compression stroke, the gas spring releases stored energy, the piston moves from the bottom dead center (BDC) to top dead center (TDC), and the fuel mixture is compressed. During the expansion stroke, the piston moves in the opposite direction, and part of kinetic energy of the piston assembly is stored in the gas spring to prepare for the next compression stroke. Figure 2 also shows the working mode of the linear generator. “Down” means the mover moves down, “Up” means the mover moves up. In most time, the free-piston engine works in fire cycle, the linear generator works in generating mode, the generating current is a sinusoidal curve, and negative sign indicates current direction. Once the misfired or abnormal combustion is occurred, the free-piston engine works in no-fire cycle. The linear generator works in motoring mode during the expansion stroke so that the piston can move to the aimed position.

Fig. 2.

Two-stroke working cycle of Free-piston engine.

Linear generator is the key element of an FPEG, many strict requirements such as low moving mass, high thrust force, high efficiency, fast response, and good controllability should be fully considered [8]. In order to develop a suitable linear generator for free-piston engines, many scholars have made a deep research on its theory and applications. Jiabin Wang et al. [9] discussed a tubular linear permanent magnet generator equipped with a modular stator winding and a quasi-Halbach magnetized armature, and the author optimized it through three key dimensional ratios. The analysis results show this machine topology has attractive features of high-power density, high efficiency, and low cogging force. Thu Thuy Dang et al. [10] presented a sizing optimization approach for maximizing the performance and demonstrates that the linear tubular linear induction generator is a good choice for free-piston Stirling micro generator systems. Ping Zheng et al. [11] presented a transverse-flux PM linear machine, the parameters of the machine are optimized by finite element method (FEM). In the end of the article, the authors concluded that the proposed machine has advantages in simple mechanical structure, low cogging force, low thrust fluctuation, and high efficiency.

So far, most studies have focused on moving magnet linear generator (MMLG) [12–14], it has the advantages of compact structure and high-power density. However, this machine still has the drawbacks like high moving mass, bad thermal conditions, difficulty in cooling, and PM demagnetization resulted from combustion heat. Some scholars studied a moving-coil linear generator (MCLG) [15–17], this generator can avoid the drawbacks occurred in MMLG. However, the current proposed MCLG have complex PM structure. They are costly and difficult to manufacture and install.

This paper presents a simple structure and high efficiency MCLG with dual axial-magnetized stator. Finite-element model of the generator is built, the static and transient characteristics are analyzed, and the losses in different components are compared. A full-bridge power converter is designed to meet the control requirements of reversible operation. An experimental prototype is developed and tested to validate the FE analysis.

2. Structure design

This paper proposes a single-phase MCLG with dual axial-magnetized stator. It consists of a stator, a mover, a shell, and two covers. Figure 3 shows the detailed components and structure of this machine. The whole stator is divided into two parts: inner stator and outer stator. Every part includes two iron cores and an axial magnetized PM. The PM is located between two iron cores, its material is N42SH. The magnetization direction of inner PM and outer PM is opposite. Different from MMLG, in the proposed MCLG structure, PM as the stator part is far away from the combustion chamber, and its cooling is achieved by the flow of air in the airgap, so it is less affected by temperature. The iron core as the path way of the magnetic flux, its material is DT4. The mover includes a non-magnetic coil skeleton with two slots, two moving-coils, a lead column, and a shaft. Two moving-coils are wound in series on two slots. Its terminals are led out along lead column. The current direction in the two moving-coils is opposite. The right end of coil skeleton is placed in the gap between the inner and outer stator. Its left end is connected to the shaft. A threaded hole is reserved at the left end of the shaft to install the piston. The coil skeleton and shaft use low density, high strength, and non-magnetic material. This moving-coil with coreless structure has two distinct advantages: First, compared to use PM as a mover in MMLG, the moving mass in the proposed structure is lower, which helps to increase the operating frequency and response speed. Second, the eddy current loss is small, which helps improve generating efficiency. The rectangular shell with an internal arc surface and two covers are made of aluminum alloy. There are several cooling holes on the right cover, cold air flows through these holes into linear generator to cool it. Table 1 lists the detailed structural parameters of the MCLG.

Fig. 3.

Three-dimensional structure of the MCLG.

Table 1

Main structure parameters of the MCLG

Parameter	Dimensions
Inner diameter of inner core	20 mm
Outer diameter of inner core	68 mm
Length of inner core	15 mm
Inner diameter of Outer core	90 mm
Outer diameter of Outer core	114 mm
Length of Outer core	15 mm
Inner PM length	30 mm
Outer PM length	30 mm
Moving-coil area	37 mm * 8 mm * 2 mm
Coil turns	64 * 2

3. Electromagnetic analysis

An accurate calculation of the magnetic field distribution is required to analyze the performances of the proposed MCLG [18]. The most commonly used method is FEM or formula method. Due to the FEM can take complicated structures, magnetic paths saturation, nonlinearity and other factors into account, its results have the merits of high accuracy and reliability [19]. In this paper, the designed MCLG is calculated by FEM. The FE model is built and the magnetic field distribution, electromagnetic force, and other electromagnetic characteristics is analyzed.

The FE model of the proposed MCLG is shown in Fig. 4(a). Different colors represent different materials and components. This model consists of PM, coil skeleton, coil, iron core, air box, cover, and shell. In order to see the internal structure, the air box is hidden. The position of the mover demonstrated in Fig. 4(a) is defined as 0 mm (x = 0), and the arrow on the coil skeleton is the positive direction of motion. The max stroke is 40 mm. The arrow on the PM represents the magnetization direction. Figure 4(b) shows the flux distribution under the active of PM alone. The magnetic field is mainly distributed near the ferromagnetic material. The main magnetic path passes through the inner core, air, outer core, outer PM, outer core, air, inner core and inner PM. The flux is evenly distributed in the air gap. This figure also shows there are some magnetic flux leakage circuits, and leakage flux is relatively small. For comparison, Fig. 4(c) describes the on-load flux distribution, which is generated by the energized coil and PM. The value of on-load flux is a little bigger than that of no-load. This indicates the axial magnetized PM distributed in the inner stator and outer stator can evidently reduce the armature effect [20].

Fig. 4.

(a) FE model, (b) No-Load flux distribution, (c) On-Load flux distribution.

Air gap is an important place for energy conversion, the distribution and magnitude of the magnetic field in the air gap have a direct impact on the power density, thrust fluctuation, and controllability of the linear generator. Figure 5 describes the change of the flux density along the gap position when the mover is in the middle position (x = 20 mm). Xg = 0 mm is shown in Fig. 4(a). As is shown in Fig. 5, when the current is 0 A, the flux density in the work air gap is almost equal except for the ends. This is because there is a little magnetic leakage at the end. The value of the flux density is about 0.5 T. The curve of I = 0 A is center symmetric about the point (30, 0) due to the symmetry of magnetic circuit structure. When the current is not 0 A, the flux density curve at I = 22 A and I = −22 A slightly deviate the curve at I = 0 A due to the influence of armature effect.

Fig. 5.

Flux density distributing in the air gap.

Figure 6 shows the thrust coefficient and EMF coefficient versus moving-coil position when different current is applied. The curve is non-linear. The values at both ends are less than the value at the middle. This is because the stator length is small, which results in the effective working length of the moving-coil at both ends is smaller than that at the middle. In the FPEG device, the speeds of the piston assembly is low at the ends, and the power generation mainly occurs in the middle area, thus, the proposed MCLG is suitable for this device. The average thrust coefficient and average EMF coefficient is 8.5 N/A and 8.5 V/(m ⋅ s⁻¹), respectively. This indicates the armature effect is very small. After finite element calculation, the inductance value is 0.7 mH. The inductance is low, which benefits from the low armature effect and ensures a very quick electromagnetic response.

Fig. 6.

Thrust coefficient and EMF coefficient vs. Moving-coil position.

4. Power converter design

In order to prevent the piston assembly from hitting the cylinder, solve the problem of misfire, and adjust the compression ratio, it is necessary to control the linear generator accurately. A control strategy that takes the end point of the stroke as the control target is presented in this paper, the control block is shown in Fig. 7. Based on the aimed position x ^∗, the tested position x and the tested in-cylinder pressure Pc, the aimed current i ^∗ is calculated and compared to the tested current, then the current PID produces PWM wave according to the error between the aimed current and tested current. The PWM wave controls the MOSFETs of the power converter circuit to complete the control of the linear generator.

Fig. 7.

The current control block of MCLG.

Fig. 8.

Full-bridge reversible power converter circuit.

The full-bridge reversible power converter circuit mentioned above is shown in Fig. 8. The whole circuit includes a supercapacitor, a filter capacitor, four insulated gate MOSFETs, and four diodes. The supercapacitor has merits of fast charging, high discharge capacity, and high-power density. The turn-on and turn-off of MOSFETs is determined by the PWM signal. Table 2 lists four working modes of the linear generator and the corresponding values of the MOSFETs. In the table, ‘K = 1’ means the MOSFETs is on, ‘K = 0’ means the MOSFETs is off. The state of “Motoring-Up” is not mentioned in Fig. 2. This state occurs only when the gas spring energy is too low to successfully complete the compression stroke. The working modes of ‘Motoring-Down’ and ‘Generating-Up’ will be tested in the following experiments. Figure 8 also shows the current flow direction in the two states. The dotted line represents the freewheeling circuit.

Table 2

The main parameter of power converter

Working modes of MCLG	The value of MOSFETs
Motoring-up	K1 = k4 = 0, k2 = 0 − Duty(<0), K3 = 1
Generating-up	K1 = 1 + Duty(<0), K2 = K3 = K4 = 0
Motoring-down	K1 = 1, k2 = K3 = 0, k4 = Duty(>0)
Generating-down	K1 = K2 = K4 = 0, K3 = 1 − Duty(>0)

5. Prototype experiment

A prototype has been developed according to the design parameters listed in Table 1. Figure 9 shows the prototype motoring and generating test platform. The arrow on the mover indicates the positive direction of motion, which is consistent with the above definition. Figure 10 shows the components of the prototype test system. It includes a proposed MCLG, a gas spring with vent holes, a supercapacitor, a DSP controller, a power converter, and a contact displacement sensor. The MCLG prototype main includes an inner stator, a mover, and an outer stator. The bore of the gas spring is 65 mm. The measuring range of the displacement sensor is 0–50 mm, and its linearity is less than 0.4 FS. This sensor is connected to the shaft of the mover. Thus, the real-time position and speed can be obtained through the processing of the controller. A current sensor with a sampling resistance of 400 Ω and a linearity of 0.1 FS is used to obtain the tested current of MCLG. The terminal voltage of supercapacitor is about 23V. Based on the hardware platform, the performance of the proposed MCLG is tested. This test includes two processes: in the first process, the MCLG working in “Motoring-Down” modes, the gas spring is compressed under the electromagnetic force. In the second process, the MCLG working in “Generating-Up” modes, the linear generator generates electricity under the action of gas spring. The tested results shown in Fig. 11 to Fig. 13.

Fig. 9.

Prototype motoring and generating test platform.

Fig. 10.

Components of the prototype test system.

Fig. 11.

Tested and simulated MCLG motion.

Figure 11 shows the tested and the simulated trajectory of the piston assembly during the two processes. The piston assembly moves between 13 mm and 27 mm. The working frequency in generating process is 23 Hz. Figure 12 compares the armature current of the tested and simulated during the two processes. The RMS current in the two process are 16.8 A and 9.8 A, respectively. The results show the linear generator with dual axial-magnetized stator has the advantages of fast response and good controllability. Figure 13 describes the PWM duty curves in the two processes. There are differences between the tested curve and the simulated curve. This is because the pulse width modulation has a delay during the experiment. Figure 11 to Fig. 13 show the designed power converter can meet control requirement, and the correctness of the FE analysis is verified.

Fig. 12.

Tested and simulated MCLG current.

Fig. 13.

Tested and simulated MCLG PWM duty.

6. Performance analysis

The correctness of the FE analysis has been proved. The performance of the proposed MCLG is conducted according to FE analysis. Figure 14 shows the generating power versus the current when different frequencies and stroke length are set. The position of stroke center is x = 20 mm. As can be seen, the generating power improves with the increase of current, frequency and stroke length. The generating power at tested point is 56 W. RMS current, operating frequency and stroke length at rated working point are 15.4 A, 50 Hz and ±18 mm, respectively. Due to the lack of a combustion chamber, the working frequency and speed cannot reach rated working point, thus, the experiment was not done under such conditions. The generating power at rated working point is 540 W.

Fig. 14.

Generating power of MCLG.

The generating efficiency of the MCLG is calculated by: $\begin{eqnarray}\displaystyle {\eta}=\frac{P_{0}}{P_{in}}=\frac{P_{0}}{P_{0}+P_{loss}}\ast 100\% & & \displaystyle\end{eqnarray}$ (1) Where P ₀ is the generating power, P _loss is the total loss of the linear generator.

When the friction loss is neglected, the total loss is calculated by: $\begin{eqnarray}\displaystyle P_{loss}=P_{PM}+P_{core}+P_{copper}+P_{shell} & & \displaystyle\end{eqnarray}$ (2) Where P _PM is the loss in PM, P _core is the loss in core, P _copper is the loss in coil, and P _shell is the loss in the shell and cover.

Figure 15 shows the generating efficiency versus the power when different frequencies and stroke length are set. The shape of the curve is similar to inverted C. In the low frequency and short stroke region, both generating power and generating efficiency is low. The generating power and generating efficiency improve with the increase of generating frequencies and stroke length. The generating efficiency at tested point and rated working point is 75% and 92%, respectively. Figure 16 shows the loss composition of MCLG at the rated point. It is clearly that the most loss comes from copper loss, accounting for 87% of the total loss. The loss in the core and PM caused by eddy current is small. Table 3 lists the main performance parameter of the proposed MCLG. Compared to a linear generator with single-side PM reported in [3] and a plate moving-magnet linear generator reported in [12], the MCLG proposed in this paper has the advantages of simple structure, low armature effect, low inductance, fast response.

Fig. 15.

Generating characteristics of MCLG.

Fig. 16.

Loss composition of MCLG.

Table 3

Main performance parameters of MCLG

Items	Value
Rated frequency	50 Hz
Rated stroke	±18 mm
RMS current	15.4 A
Coil resistance	0.177 Ω
Moving mass	1.2 kg
Average thrust coefficient	8.5 N/A
Average EMF coefficient	8.5 V/(m ⋅ s⁻¹)
Average inductance	0.7 mH
Electromagnetic time constant	3.9 ms
Generating power	542 W
Generating efficiency	92%

7. Conclusion

A novel MCLG with dual axial-magnetized stator has been proposed and investigated in this paper. The static and transient characteristics have been analyzed by FEM, and a full-bridge power converter has been designed. A 540 W experimental prototype was developed, and the correctness of FE analysis has been verified. According to the tested and simulated results, the generating efficiency of 92% can be obtained at the rated generating power. The average inductance of the proposed generator is about 0.7 mH, which benefits from the low armature effect and ensures a very quick electromagnetic response. From these works, it can be seen that the proposed MCLG has the advantages of simple structure, low moving mass, low armature effect, low inductance, fast response, and high efficiency.

The performance of the proposed MCLG needs to further study when it coupled with a free-piston. The fired cycle will be simulated and tested. Besides, long time stable operation of the FPEG also requires further research.

Footnotes

Acknowledgement

This work is supported by the National Natural Science Foundation of China (grant no. 51875290).

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