Investigation of a tubular dual-stator flux-switching

Investigation of a tubular dual-stator flux-switching permanent-magnet linear generator for free-piston energy converter Yi Sui, Ping Zheng, Chengde Tong, Bin Yu, Shaohong Zhu, and Jianguo Zhu Citation: Journal of Applied Physics 117, 17B519 (2015); doi: 10.1063/1.4916186 View online: http://dx.doi.org/10.1063/1.4916186 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/117/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Algorithm for the calculation of the translator position in permanent magnet linear generators J. Renewable Sustainable Energy 6, 063102 (2014); 10.1063/1.4900553 A novel single-phase flux-switching permanent magnet linear generator used for free-piston Stirling engine J. Appl. Phys. 115, 17E711 (2014); 10.1063/1.4862397 Investigation of a 7-pole/6-slot Halbach-magnetized permanent-magnet linear alternator used for free-piston stirling engines J. Appl. Phys. 111, 07E711 (2012); 10.1063/1.3672084 Measuring air gap width of permanent magnet linear generators using search coil sensor J. Appl. Phys. 101, 024518 (2007); 10.1063/1.2403964 Electromagnetic forces in the air gap of a permanent magnet linear generator at no load J. Appl. Phys. 99, 034505 (2006); 10.1063/1.2168235

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JOURNAL OF APPLIED PHYSICS 117, 17B519 (2015)

Investigation of a tubular dual-stator flux-switching permanent-magnet linear generator for free-piston energy converter Yi Sui,1 Ping Zheng,1,a) Chengde Tong,1 Bin Yu,1 Shaohong Zhu,1 and Jianguo Zhu2 1

School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150080, China Center for Electrical Machines and Power Electronics, University of Technology Sydney, Sydney, NSW2007, Australia 2

(Presented 6 November 2014; received 22 September 2014; accepted 15 November 2014; published online 25 March 2015) This paper describes a tubular dual-stator flux-switching permanent-magnet (PM) linear generator for free-piston energy converter. The operating principle, topology, and design considerations of the machine are investigated. Combining the motion characteristic of free-piston Stirling engine, a tubular dual-stator PM linear generator is designed by finite element method. Some major structural parameters, such as the outer and inner radii of the mover, PM thickness, mover tooth width, tooth width of the outer and inner stators, etc., are optimized to improve the machine performances like thrust capability and power density. In comparison with conventional single-stator PM machines like moving-magnet linear machine and flux-switching linear machine, the proposed dual-stator flux-switching PM machine shows advantages in higher mass power density, higher volume power C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4916186] density, and lighter mover. V Owing to the advantages of wide power sources, high efficiency, high reliability, and low maintenance cost, freepiston energy converter, which integrate a free-piston Stirling engine (FPSE) with a linear generator, has great potential in application fields like electric vehicle and aerospace.1,2 As the key component of free-piston energy converter, the linear generator operates under high-frequency oscillating motion conditions, and such characteristics like low mover mass and fast dynamic are required.3,4 More importantly, lower mover mass enables higher resonant frequency, consequently leads to higher power density. Due to the high efficiency and high power density, tubular permanent-magnet (PM) linear machines are widely adopted in free-piston energy converter.5–7 Flux-switching PM linear machine can overcome the thermal demagnetization which exists in the conventional mover-PM linear machine. It has a simple and robust mover, but its power density still needs further improvement.8–10 In the past decade, there is an emerging PM machine family that features dual-rotor or dual-stator structure. Compared with singlestator PM machine, dual-stator PM machine has higher power density. However, most published works about this kind of machine focus on rotating PM machine,11–15 and few literatures can be found working on the tubular dual-stator PM linear machine. Herein, we propose a single-phase tubular dual-stator flux-switching PM linear generator that features low mover mass and high power density. And this paper focuses on the operation principle and design optimization of the machine. The proposed tubular dual-stator flux-switching PM linear generator consists of three cylindrical components, i.e., outer stator, mover, and inner stator, as shown in Fig. 1. The mover is similar to that of a conventional switchedreluctance linear machine, and its structure is simple and a)

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robust, which is beneficial for high-frequency oscillatory motion. Differing from conventional mover-PM linear machine, magnets of flux-switching PM linear machine are placed in stator instead of mover. The outer stator and inner stator have similar mechanical structures. For both the outer and inner stators, the axially magnetized PMs with opposite magnetization directions are sandwiched between the slotted stator modules, and the annular outer and inner windings are inserted in the slots of both the inner and outer stators, respectively. The outer stator and mover can be considered as one typical flux-switching linear machine, and the inner stator and mover can be considered as another flux-switching linear machine, these two machines share the common mover. Through adopting the dual-stator structure, the mover mass can be reduced, which is useful for improving the resonant frequency of the FPSE system. Since the proposed dual-stator machine can be considered as an integrated machine that integrates two singlestator flux-switching PM linear machines together, so a single-stator flux-switching PM linear machine is taken as an example to illustrate the operation principle of the proposed machine. Fig. 2 shows the vector plots of no-load flux distribution when the mover is at two different positions. As the mover moves to the top limiting position, the flux linkage is excited by the PM in the upside of the stator, and the flux linkage in the outer winding flows in counterclockwise direction, as shown in Fig. 2(a); as the mover moves to the bottom limiting position, the flux linkage is contributed by the PM in the bottom side of the stator, and the flux linkage in the outer winding flows in clockwise direction, as shown in Fig. 2(b). As the mover moves from one limiting position to the other one, the flux linkage in the outer coil changes with the relative motion between mover and stator, and the flow direction of the flux linkage also changes from one direction to the opposite one. When the mover oscillates in a certain frequency, voltage is induced in the winding.

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FIG. 1. Topology of the dual-stator flux-switching PM generator: (a) 3-D view and (b) 2-D view.

Unlike conventional single-stator flux-switching PM linear machine, the proposed dual-stator machine has PMs in both the inner and outer stators, these PMs simultaneously provide magnetomotive force (MMF) for the machine, and the PMs in the same side of the two stators can have opposite or consistent magnetization direction, as shown in Fig. 3. In Fig. 3(a), as the PMs in the same side of the two stators have opposite magnetization directions, the flux linkages generated by the outer and inner stators have opposite flowing directions in the mover, and they can cancel each other, then the mover yoke can be thinner. In Fig. 3(b), as the PMs in the same side of the two stators have consistent magnetization directions, the flux linkages generated by the outer and inner stator have consistent flowing directions in the mover, and the flux linkages superimpose in the mover, then the mover yoke should be thick enough to avoid saturation. As the PMs in the same side of the two stators have opposite or consistent magnetization direction, the corresponding vector plots of no-load flux distribution and no-load flux density are calculated by finite element method (FEM), as shown in Figs. 4 and 5. In comparison with the case of opposite magnetization direction, the mover yoke of consistent magnetization direction case is more saturated, which means thicker mover yoke is needed and the mover mass is increased, further leading to lower power density. Hence, the PMs in the same side of the two stators should have opposite magnetization direction. The machine performance like force capability and power density is mainly influenced by several structural parameters like the outer and inner radii of the mover Rm1 and

FIG. 2. Vector plots of no-load flux distribution.

Rm2, the PM thickness of the outer and inner stators hM1 and hM2, the mover tooth width wtm, the tooth width of the outer and inner stators wts1 and wts2, the width of the outer and inner stators yoke wys1 and wys2, the outer and inner radii of the mover yoke Rym1 and Rym2. The aforementioned design parameters are optimized with some structural parameters fixed, i.e., the active length and stator outer diameter are 63 mm and 100 mm, respectively. Considering the machine manufacturability, the air gap length is chosen to be 1 mm. Through changing the outer and inner radii of the mover (Rm1 and Rm2), the force and power density are calculated, as shown in Fig. 6. For a certain inner radius of the mover Rm2, with the increase in outer radius of the mover Rm1, both the force and power density first increase and then decrease. The maximum force and power density occur when Rm1 and Rm2 are about 27 mm and 13 mm, respectively. Hence, Rm1 and Rm2

FIG. 3. Schematic diagram of flux linkage path when PMs in the same side of the two stators have opposite or consistent magnetization direction: (a) opposite magnetization direction and (b) consistent magnetization direction.

FIG. 4. Vector plots of no-load flux distribution, when PMs in the same side of the two stators have opposite or consistent magnetization direction: (a) opposite magnetization direction and (b) consistent magnetization direction.


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FIG. 8. The force and power density vs. wtm. FIG. 5. No-load flux density distribution, when PMs in the same side of the two stators have opposite or consistent magnetization direction: (a) opposite magnetization direction and (b) consistent magnetization direction.

FIG. 6. The force and power density vs. Rm1 and Rm2.

are chosen to be 27 mm and 13 mm, respectively, which means a good balance between electrical and magnetic loading. With the optimal Rm1 and Rm2 of 27 mm and 13 mm, the force and power density with respect to the PM thickness of the outer and inner stators (hM1 and hM2) are calculated, as shown in Fig. 7. For a certain PM thickness of the inner stator hM2, with the increase in PM thickness of the outer stator hM1, both the force and power density first increase and then decrease. The maximum force and power density occur when hM1 and hM2 are about 4 mm and 3.5 mm, respectively. Hence, hM1 and hM2 are chosen to be 4 mm and 3.5 mm, respectively. By choosing different mover tooth width wtm, the force and power density are calculated, as shown in Fig. 8. With the increase in wtm, both force and power density first increase and then decrease. When wtm is less than 6 mm, the mover tooth is saturated, both the force and power density increase sharply with the increase in wtm; as wtm exceeds 9 mm, the flux leakage increases, so both the force and power density decrease. The maximum force and power density occur when wtm is 8 mm. Hence, the mover tooth width wtm is chosen to be 8 mm.

FIG. 7. The force and power density vs. hM1 and hM2.

The force and power density with respect to the outer and inner stators’ tooth width (wts1 and wts2) are calculated, as shown in Fig. 9. For a certain inner stator tooth width wts2, with the increase in inner stator tooth width wts1, both the force and power density first increase and then decrease. Both the force and power density reach maximum values when wts1 and wts2 are 6 mm and 4 mm, respectively, thus wts1 and wts2 are chosen to be 6 mm and 4 mm. By choosing different outer stator yoke width wys1, both the force and power density are calculated, as shown in Fig. 10. With the increase in wys1, both the force and power density first increase and then decrease; when wys1 is 4 mm, both the force and power density achieve maximum values. Hence, the outer stator yoke width is chosen to be 4 mm. Through changing outer and inner radii of the mover yoke (Rym1 and Rym2), the force and power density are calculated, as shown in Fig. 11. For a certain inner radius of mover yoke Rym2, with the increase in outer radius of mover yoke Rym1, both the force and power density first increase and then decrease, and they achieve maximum values as Rym1 and Rym2 are 22.5 mm and 14.5 mm, respectively, thus Rym1 and Rym2 are chosen to be 22.5 mm and 14.5 mm. Fig. 12 shows the variation of both the force and power density with respect to the inner stator yoke width wys2. With the increase in wys2, the power density first increases and

FIG. 9. The force and power density vs. wts1 and wts2.

FIG. 10. The force and power density vs. wys1.


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J. Appl. Phys. 117, 17B519 (2015) TABLE I. Comparison of dual-stator flux-switching PM linear machine and two single-stator PM linear machines.

Parameter

FIG. 11. The force and power density vs. Rym1 and Rym2.

FIG. 12. The force and power density vs. wys2.

then decreases, and the force gradually increases. Considering the balance between electromagnetic performance and manufacturability, the inner stator yoke width is chosen to be 6 mm. Two single-stator PM linear machines, which include a radially magnetized moving-magnet PM machine and a single-stator flux-switching PM machine, have been used to compare with the proposed dual-stator machine. The comparison details of both the proposed and the single-stator machines are listed in Table I. As can be seen from Table I, the proposed machine features advantages in mover mass, volume, and mass power density. Owing to the special dual-stator structure, the proposed machine has low mover mass, and this is achieved by integrated design of magnetic circuit of the two stators. The lighter and robust mover is beneficial for high-frequency oscillating motion. Besides, the proposed topology improves the utilization rate of space and machine material, and the dual stator concept can be extended to other types of PM linear machines. A tubular dual-stator flux-switching PM linear generator has been investigated for free-piston energy converter where a robust and a light mover are required. For the proposed machine, PMs in the same side of the two stators should have opposite magnetization direction. The influence of several major structural parameters on both force capability and power density has been studied. The dimensions of both the outer stator and mover have significant impact on both the force capability and power density. The dimensions of inner stator have limited influence on both force capability and power density. In comparison with conventional single-stator PM linear machines, the proposed dual-stator flux-switching

Phase number Power (kW) Current density (A/mm2) Average speed (m/s) Frequency (Hz) Stroke (mm) Stator outer diameter (mm) Air gap length (mm) Axial length of stator (mm) Axial length of mover (mm) Stator core mass (kg) Copper mass (kg) Mover core mass (kg) PM use (kg) Mover mass (kg) Total mass (kg) Volume (m3) Mass power density (kW/kg) Volume power density (kW/m3)

Radially magnetized

Flux-switching (single-stator)

Flux-switching (dual-stator)

Three 0.988 7.701

Single 0.915 7.8

Single 1.095 7.8

2.8

1.6

1.6

100 14 100

100 8 100

100 8 100

0.8 63

1 63

1 63

81

51

55

0.831 0.842 0.491 0.622 1.113 2.786 5.457 10 0.355 1.81 103

4

1.396 0.446 0.631 0.292 0.631 2.765 4.948 10 0.331 1.85 103

4

1.382 0.769 0.493 0.349 0.493 2.993 4.948 10 0.366

4

2.21 103

PM linear machine shows advantages in higher volume power density, higher mass power density, and lighter mover. This work was supported by National Natural Science Foundation of China under Projects 51325701 and 51377033. 1

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