Cellular phones have not only function to communicate, but also have e-banking, web surfing, music, and entertainment. The performance of the smartphone has improved because of various functions of smartphone, and capacity of battery has also improved gradually. Although smartphone batteries have been improved compared to conventional batteries, the available usage time of a phone’s rechargeable battery is getting shorter because of the demands of various applications. Therefore, we propose a new tubular permanent magnet linear generator that uses a Halbach array, to send a message or emergency call when the battery is discharged. In order to increase the power generation of existing tubular linear generators, we changed the axial-direction permanent magnet array to a Halbach-type array. When using the Halbach array, it is possible to generate a strong magnetic field without additional magnetic material. In this research, we compared the Halbach array that uses axially and radially magnetized permanent magnets with an existing model that uses an axially magnets. We verified improvement in the amount of power generated with no-load analysis through simulation using the Maxwell commercial electromagnetic analysis software

Jin Ho Kim

Joonsoo Jun

Yujeong Shin

English

Journal of Vibroengineering

  © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. FEB 2016, VOL. 18, ISSUE 1. ISSN 1392-8716 587 
1914. Linear electric generator with Halbach array to 
self-charge a smartphone 
Joonsoo Jun1, Yujeong Shin2, Jin Ho Kim3 
Department of Mechanical Engineering, Yeungnam University, Gyeongsan, Gyeongbuk, 38541, Korea 
3Corresponding author 
E-mail: 1jsjun1223@gmail.com, 2syuj1217@naver.com, 3jinho@ynu.ac.kr 
(Received 14 March 2015; received in revised form 4 December 2015; accepted 13 December 2015) 
Abstract. Cellular phones have not only function to communicate, but also have e-banking, web 
surfing, music, and entertainment. The performance of the smartphone has improved because of 
various functions of smartphone, and capacity of battery has also improved gradually. Although 
smartphone batteries have been improved compared to conventional batteries, the available usage 
time of a phone’s rechargeable battery is getting shorter because of the demands of various 
applications. Therefore, we propose a new tubular permanent magnet linear generator that uses a 
Halbach array, to send a message or emergency call when the battery is discharged. In order to 
increase the power generation of existing tubular linear generators, we changed the axial-direction 
permanent magnet array to a Halbach-type array. When using the Halbach array, it is possible to 
generate a strong magnetic field without additional magnetic material. In this research, we 
compared the Halbach array that uses axially and radially magnetized permanent magnets with an 
existing model that uses an axially magnets. We verified improvement in the amount of power 
generated with no-load analysis through simulation using the Maxwell commercial 
electromagnetic analysis software. 
Keywords: smartphone, generator, Halbach array, permanent magnet. 
1. Introduction 
A cellular phone is the most commonly used mobile device for transferring information among 
people. Although battery capacity has improved, the dramatically increased usage of cellular 
phones makes the battery service time shorter and shorter. 
In order to address this problem, an embedded linear generator for a self-rechargeable 
smartphone has been developed by Park et al. [1]. The linear generator's operation is based on a 
resonance phenomenon, the electromagnetic force is generated based on Faraday's law, and the 
smartphone battery is charged by electromagnetic force. In the case of existing smartphone 
generators [1], the battery usage time generated by walking motion is not enough to power an 
urgent call because of low efficiency. There are many array types of permanent magnet(PM) in 
linear generator. The radius direction array was introduced by Ishiyama et al. The PM is placed 
face-to-face, and there is a mutual repulsion [2]. The axial direction array, which is different than 
Ishiyama’s array, was introduced by Murphy [3]. A Halbach array is an arrangement of permanent 
magnets that augments the magnetic field on one side of the array while cancelling the field to 
nearly zero on the other side. The rotating pattern of the PM (left, up, right, down) is used [4, 5]. 
In this study, we developed a built-in linear generator system for a smartphone with a Halbach 
array permanent magnet in order to maximize the power generation with respect to the 
aforementioned problems. The Halbach array is a sequence that arranges an alternately radially- 
and axially-magnetized permanent magnets. In this paper, we analyzed Halbach-type magnetic 
characteristic and compared with conventional axially magnetized permanent magnet. Finite 
element analysis (FEA) using the commercial software Maxwell (Ver. 16, ANSYS, Southpointe 
2600 ANSYS Drive Canonsburg, PA 15317 USA) is performed to simulate the electric generation. 
The results of the simulation and experiment show that the proposed generation system has enough 
potential to be considered for practical use.  
1914. LINEAR ELECTRIC GENERATOR WITH HALBACH ARRAY TO SELF-CHARGE A SMARTPHONE.  
JOONSOO JUN, YUJEONG SHIN, JIN HO KIM 
588 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. FEB 2016, VOL. 18, ISSUE 1. ISSN 1392-8716  
2. Generation system 
2.1. Structure and principle of Halbach array generator 
Fig. 1 shows a schematic diagram of a tubular linear generator. A conventional tubular linear 
generator consists of a slider and stator. The slider consists of axially-magnetized permanent 
magnets and a pole shoe, which functions as a conductor of the magnetic field. 
The stator consists of a coil and coil housing, and a 2-pole 3-phase coil winding. Two springs 
enable the slider to produce resonance. 
 
Fig. 1. Schematic diagram of conventional  
tubular linear generator 
 
Fig. 2. Schematic diagram of tubular linear 
generator applying Halbach array 
Fig. 2 shows a schematic diagram of a Halbach array tubular linear generator. The Halbach 
array generator consists of both axial magnetized permanent magnets and radial magnets. One 
sided magnetic fluxes were introduced by John C. Mallinson [6], and Halbach array was 
developed by Kaus Halbach [7]. In the case of the Halbach array generator shown in Fig. 3, if the 
axial and radial permanent magnets were magnetized alternatively, magnetic flux is concentrated 
in only one direction [8-10] because the opposite direction is offset. Thus, it maximizes the amount 
of power generation compared to conventional models without the addition of magnetic material  
[11]. The pole shoe functions as a conductor of the magnetic field to replace the radial magnetized 
permanent magnet on a conventional generator. The coil winding is formed with a 4-pole 3-phase 
that is different from the existing generator with the 2-pole 3-phase. 
 
Fig. 3. Principle of superposition of Halbach array 
Fig. 4 shows a diagram of the energy conversion principle. The electromotive force is 
generated at the stator coil terminals as the slider vibrates up and down by the shaking motion and 
1914. LINEAR ELECTRIC GENERATOR WITH HALBACH ARRAY TO SELF-CHARGE A SMARTPHONE.  
JOONSOO JUN, YUJEONG SHIN, JIN HO KIM 
 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. FEB 2016, VOL. 18, ISSUE 1. ISSN 1392-8716 589 
walking motion of the user. The EMF is calculated by using Faraday’s law and can be expressed 
as follows: 
݁ሺݐ) = െܰ݀߶݀ݖ
݀ݖ
݀ݐ		,	 (1)
where ܰ is the number of turns per coil, ߶ is the flux passing in each turn in real time ݐ, ݀ݖ/݀ݐ is 
the slider speed, and ݖ  is the distance along the ݖ -direction. So, the electromotive force is 
proportional to the number of coil windings, the variation of magnetic flux that interlinks the coil 
winding to the displacement of the slider, and the speed of the slider [12]. 
 
Fig. 4. Energy conversion diagram 
2.2. Analysis of the linear generator and resonance phenomenon 
Excitation by the user’s motion produces base excitation. Fig. 5 is a free body diagram for the 
analysis of base excitation. In Fig. 5, ݉ is the mass of the slider, ݇ is the spring coefficient, and ܿ 
is the coefficient of damping. The base excitation can be expressed by Eq. (2). ݕሺݐ) is ܻsin߱௕ݐ, 
representing the displacement of the base, and the displacement and velocity of the slider are 
denoted as ݔሺݐ) and ݒሺݐ), respectively. The amplitude of ݔሺݐ) is calculated by using Eq. (3). In 
Eq. (3), ߞ represents the damping ratio of the linear generator. The frequency of walking motion 
is in the range of 2 to 2.2 Hz [13], and the frequency of shaking motion is in the range of 3.0 to 
5 Hz [1]. 
݉ݔሷ ൅ ܿሺݔሶ െ ݕሶ) ൅ ݇ሺݔ െ ݕ) = 0, (2)
ݔ = ݕ ቈ 1 ൅ ሺ2ߞݎ)
ଶ
ሺ1 െ ݎଶ)ଶ ൅ ሺ2ߞݎ)ଶ቉
ଵ
ଶ
, ݎ = ߱௡߱௕,
(3)
where ߱௡ is the natural frequency and ߱௕ is the base excitation frequency. 
 
Fig. 5. Free body diagram for the analysis of the base excitation 
1914. LINEAR ELECTRIC GENERATOR WITH HALBACH ARRAY TO SELF-CHARGE A SMARTPHONE.  
JOONSOO JUN, YUJEONG SHIN, JIN HO KIM 
590 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. FEB 2016, VOL. 18, ISSUE 1. ISSN 1392-8716  
In the case of walking motion, the displacement amplitude of the base excitation is less than 
2 cm, which does not create enough displacement for adequate electric generation. To maximize 
the mechanical energy from the motion, the resonance phenomenon is exploited by matching the 
motion frequency to the mechanical natural frequency of the generator. It is possible to check the 
displacement amplitude in accordance with the input frequency by using Eq. (3), as shown in 
Fig. 6.  
According to Fig. 6, the vibration characteristic is different for each natural frequency. In the 
case of walking or shaking motion (2 to 5 Hz), we confirmed that mechanical resonance occurs 
when the natural frequency (߱௡) is 15 rad/s. Then, we determined the optimal mass of the slider, 
the coefficient of the spring, and other specifications for sufficient vertical motion using this result.  
 
Fig. 6. Displacement amplitude versus input frequency 
3. Finite element analysis 
In order for the proposed device to be installed inside the smartphone, the overall size of the 
generation system must be less than 60 mm in length and 7 mm in diameter. Accordingly, the 
magnetic circuit (e.g., the permanent magnet, pole shoe, and electromagnetic coil) is designed to 
satisfy the size specification with large electricity generation. In order to validate the change in 
the number of magnets while meeting the size requirements, we conducted a parameter study 
using no-load analysis with the commercial electromagnetic analysis software Maxwell to 
determine the back electromotive force with no load simulation when the ideal current is zero. 
Table 1 shows the specifications for the linear generator. We determined the specifications 
based on the parameter study. After determining the diameter of the coil that can accommodate 
the allowable current in a limited space, and determining the required number of windings, the 
winding resistance is determined according to number of coil windings.  
Table 1. Specifications of the linear generator 
Quantity Value  
Capacitance 200 µF 
Number of coil windings 1044 turns 
Coil winding resistance 225 Ω 
We assumed that the walking speed is 5 km/h, the peak-to-peak size of the displacement due 
to walking is about 3 cm, the frequency is 2 Hz, and the operational shaking frequency range is 3 
to 5 Hz. We used a frequency of shaking motion of 3.3 Hz to compare with the generating 
characteristics of a conventional model. Dynamic finite-element analysis using the nonlinear FEM 
solver Maxwell was executed. A 2-D dynamic finite-element model was created to assist in 
modeling three-coupled systems. Fig. 7 show FE model of two-pole 6 permanent magnets. Total 
number of mesh elements is 108107. For the magnetic system, the nonlinear magnetic B-H 
1914. LINEAR ELECTRIC GENERATOR WITH HALBACH ARRAY TO SELF-CHARGE A SMARTPHONE.  
JOONSOO JUN, YUJEONG SHIN, JIN HO KIM 
 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. FEB 2016, VOL. 18, ISSUE 1. ISSN 1392-8716 591 
properties of steel 1010 were assigned to the core. The magnetic properties of Neodymium ferrite 
(Ne-Fe35) were assigned to the permanent magnet. The boundary of air surrounding the actuator 
is assigned zero magnetic vector potential (ܣݖ = 0). 
 
Fig. 7. Mesh plot of FE model 
Fig. 8 shows (a) a conventional model uses two-pole 6 permanent magnets, and (b), (c), (d) 
models of a Halbach array each uses four-pole 6, 7 and 8 permanent magnets. That is, each model 
uses 12, 24, 28, and 32 permanent magnets. 
 
a) 
 
b) 
 
c) 
 
d) 
Fig. 8. Model of the proposed generator 
Fig. 9 shows the magnetic flux line plot at initial position. Fig. 10 shows the results of no-load 
analysis, which shows an electromotive force induced in each model. Phase A, B, and C are shown 
for each coil. 
The root mean square (RMS) value of the induced voltage is an average of value that divided 
by the square root. The RMS average value of the induced voltage of the conventional model is 
2.21 V. The RMS average value of the induced voltage for the model with 6, 7, and 8 permanent 
magnets of 4 poles is 3.29, 3.37, and 3.7 V, respectively. We confirmed that the Halbach array 
generator exhibited better performance than the existing generator. When using eight permanent 
magnets, RMS average value of the induced voltage has an approximately 20 % larger than that 
of the conventional model. 
1914. LINEAR ELECTRIC GENERATOR WITH HALBACH ARRAY TO SELF-CHARGE A SMARTPHONE.  
JOONSOO JUN, YUJEONG SHIN, JIN HO KIM 
592 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. FEB 2016, VOL. 18, ISSUE 1. ISSN 1392-8716  
 
Fig. 9. Magnetic flux line plot at initial position 
 
a) 
 
b) 
 
c) 
 
d) 
Fig. 10. Induced voltage in each coil winding at no load 
1914. LINEAR ELECTRIC GENERATOR WITH HALBACH ARRAY TO SELF-CHARGE A SMARTPHONE.  
JOONSOO JUN, YUJEONG SHIN, JIN HO KIM 
 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. FEB 2016, VOL. 18, ISSUE 1. ISSN 1392-8716 593 
4. Conclusion 
We propose a smartphone embedded linear generator that uses a Halbach array. We analyzed 
and compared the characteristics of the magnetic field with a conventional smartphone generator 
by considering the linear generator as the base excitation. In order to produce more power than 
the conventional generator of a smartphone, we conducted a parameter study for the Halbach array 
generator in order to select appropriate permanent magnets. To obtain the optimum number of 
permanent magnets, we conducted an FEA performance analysis. We confirmed FEA by using 
4-pole permanent magnets (a total of 32 permanent magnets), RMS value of the induced voltage 
has approximately 20.24 % larger than the conventional model. Our simulation results show that 
the proposed design is suitable for practical use. 
Acknowledgements 
This research was supported by Basic Science Research Program through the National 
Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2059513). 
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1914. LINEAR ELECTRIC GENERATOR WITH HALBACH ARRAY TO SELF-CHARGE A SMARTPHONE.  
JOONSOO JUN, YUJEONG SHIN, JIN HO KIM 
594 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. FEB 2016, VOL. 18, ISSUE 1. ISSN 1392-8716  
 
Joonnsoo Jun received B.E. degree in Mechanical Engineering from Yeungnam 
University, Korea, in 2013. Now he works at Yeungnam University. His current research 
interests include control, dynamics and electromagnetics. 
 
Yujeong Shin received B.E. degree in Mechanical Engineering from Yeungnam 
University, Korea, in 2013. Now she works at Yeungnam University. Her current research 
interests include control, dynamics and electromagnetics. 
 
Jin Ho Kim received Ph.D. degree in Mechanical Engineering from University of 
California, Berkeley, USA, in 2005. Now he works as the Associate Professor at School 
of Mechanical Engineering, Yeungnam University, Korea. His research interests include 
electric machine, vibration, and design. 
 


Linear electric generator with Halbach array to self-charge a smartphone

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Linear electric generator with Halbach array to self-charge a smartphone

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