Design of a 5 kW Tubular Permanent Magnet Linear Generator Khalid Mohamed Nor, Senior Member, IEEE, Wanizah Arof, and Wijono
ABSTRACT A tubular permanent magnet linear generator with the output power of 5 kW and output voltage of 200 V with minimum cogging force is designed, simulated and fabricated. Specific design criteria are employed to meet exclusive requirements rclated to its stator and translator. A simple model of the electromagnetic analysis of the cogging force and generated emf is presented. Finite elemcnt software is used to simulate the machine. The linear machine is developed based on the results of finite element simulation. A radially magnetized magnet is chosen to give a high performance and to solve the cogging force-voltage problem.
Keyword: Cogging Force, Finite Element Simulation, Linear Generator, Permanent Magnet Tubular Linear Generator.
optimization of models involves the permanent magnet, the coil and the stator dimension. A srnaller generator of 0.3 kW,200V was also designed and constructed [2]. The voltage induced in the coil is derived from the flux calculated with the finitc element method and the dynamic performance of the generator is examined using the electric circuit simulation software.
1. INTRODUCTION
Prospective applications of linear engine are for industrial, conmiercial and personal purposes especially where a stand alone power generation is needed. It is also vital when grid power utility is unavailable. It can also be used as an alternative power generator for hybrid vehicles.
,
NASA Glenn Research Center, Cleveland, Ohio, the Department of Energy (DOE), and Stirling Energy Company [ 3 ] developed a lightweight and highly efficient linear generator driven by a stirling engine for space applications. The generator consists of a moving part and a stator where the coil is wound on its outer surface. A 3D parametric finite element method is used to simulate and evaluate the open circuit voltage and the flux density of the generator.
In this paper, design and simulation aspects of a tubular permanent magnet linear generator intended to be driven by a free-piston internal combustion engine are outlined. Specific design criteria are employed to meet exclusive requirements related to its stator and translator. In our previous design, axially magnetized permanent magnets are used as magnetic flux sources. Due to cogging force problem, a series of modifications and improvements have been made. In normal circuinstances, reduction in cogging force yields lower output voltage. However, in using radially magnetized permanent magnets, we hope to achieve low cogging force and high output voltage. Optimization is performed to maximize the flux density in the magnetic core and minimize the dimension while avoiding saturation. The tooth shoe is introduced to minimize the cogging force. Finite element software is used to siinulatc the machine
Blarigan [4] at Sandia National Laboratories, Livermore
designed and constructed an efficient linear generator, The generator is driven by a high speed hydrogen fuel free piston engine. This speed is achieved by increasing the compression ratio. With an oriented-grain silicon steel lamination stator, NdFeB radial magnetized permanent magnets and 25 coil slots, the generator produces 40 kW of output power, with an efficiency of 96%.
Cawthome [I] developed two models of 5 kW, 220V iron and air core tubular permanent magnet linear generators driven by a linear internal combustion engine. In the previous design, the generator and engine are designed independently with thc only link between the design of the two systems being the stroke length and the estimated speed of oscillation. The design method includes an optimization that maximizes the efficiency and minimizes the volume of the alternator while providing the desired output power and output voltage. The 2D parametric finite element method is used in generator parameters calculation. The
11. LINEAR GENERATOR DESIGN
The combustion engine has a single internal combustion chamber. It has stroke length of 76 inm, The generator is designed to have 4 winding slots. As the square wire is used, the slot fill factor is assumed to close to one, and the air gap in the winding slot is ignored in the simulation model. The generator is nominally designed to run at 3000 rpm.
The stator is constructed of non-oriented silicon steel
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laminations. The radially stacking combined with axially slotting is applied to get a better electromagnetic pcrformancc of the stator as well as to provide easy assembly. The translator consists of a shaft, backiron and pcrmanent magnets separated by aluminum spacers A high power rare earth permanent magnet, NdFeB is used to providc a high density niagnetic field. Magnets are radially magnetized and mounted alternately on the shaft. In order to activate all of the coils, the translator is made to be two pole pitches longer. The translator back iron provides a path In which the magnetic field flows through the stator circuit. The silicon steel material is chosen for translator back iron as this material has high rclative permeability. Thc mild steel is used as shaft material to give higher cross section area in which the magnetic flux flows. The 3D drawing is shown in thc Fig. 1.
poles pitch every stroke. The maximum (or minimum) flux is calculated by involving the flux density and surface area of the magnet and flux reduction factors. Fig. 2 shows the axial cross sectional representation of a one pole generator.
#-
I
FE
Fig. 2. Flux in one pole generator representation
Referring to Fig. 2, the flux generated by the magnet can be denvcd from its magnetic remanence and normal surface area.
where B , = flux density on the permanent magnet surface. B, = magnetic remanence KI= flux density factor A , , , = surfacc area of permanent magnet I;,,,,,~,,~,~,,~~ = permanent magnet inner radius (it i s the same length as rshan).
Fig. 1. Tubular linear generator diagram
Ill. AKALYSIS
The peak flux linkage in the coil can be calculated from,
Anuiytical Calcirlulion
Some parameters are used as constants; others are optimized for best results. In the analytical calculation a simplified model is used to get the general characteristic of the generator parameters. The flux linkage in the coil is changed from positive maximum to negative minimum in a one pole pitch translator movement. It is assumed to change linearly. The induced voltage of the coil is thercfore a square wave form.
(5
where
Kfrz,,g,,s= flux fringing factor Kpm= magnet length factor, due to air gap and lamination insulation existence, ie
For a given flux linkage as a function of the h e a r translator motion, the induced voltage can be calculated as, e = -N-+(t) (1)
2g,,,3= lamination insulation thickness for both sides g =airgap distance
The translator is moved forward and backward, two
After the maximum flux is found, the next calculation is flux wave shape correction. It is known that the flux
dt
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does not actually change linearly. The sinusoidal approach is used to correct the wave shape. Then,
F,
an
I (1
a as
F~(v + o /B'dF)-d(vd) )
= 111
0s
'(11
(9) 4toiisin
( 1 ) = 4cojl
sin(#')
where: F, = force in element in the s direction
(7'
The induced voltage is then calculated by using Eq. (I). In this simulation, the sinusoidal speed is used instead of linear speed. For arbitrary speed function, the induced voltage is now written as,
a P = derivative of field dS
intensity with respect to
displacement s = virtual displacement of the nodal coordinates
e = -N--
d#(x) dlr d ( x ) dt
taken alternately to be in the X , Y , Z global direction vol= volume of the element.
(8)
Finile Element Analysis
IV. RESULTS
Under no-load condition, the back emf is derived froin the magnetic field produced by the permanent magnets, and under load operation the output voltage is the result of interaction of the flux from the permanent magnets and the output current.
A . F / L ~Lirrkuge X and Induced Voliage
The position of translator in one stroke of mot,on is shown in the Fig. 3, The gives the maximum (or minimum) flux flowing in the circuit.
-
The magnetic potentia1 vectorA , instead of flux d e n s i t y z , is often used in the field analysis. The magnetostatic field principle is used to calculate magnetic flux and voltage. Gauss's law is applied in this situation. For problems considering saturable material with permanent magnets, the flux density is a hnction of field intensity
6 I
1-1
I"
LLMYXl i(
vx?x**,
i 7.
1
Fig. 3. Translator movement
The flux linkage over a closed loop can be simply derived as the integration of flux density over the area encircled by the coil. The total flux linkage of coil having N turn is thus Nq$
At position 1, coil 1 and 3 have maximum flux linkage and coil 2 and 4 have minimum flux linkage. Ai position 2, the situation is reversed. At position 3, the configuration goes back to the situation as at position I . Fig 4 shows the flux linkage curve for forward and backward translator movement, and Fig 5 shows the induced voltage in the cods.
The no-load voltage or the back emf is derived froin flux linkage to coils. If the fringing flux of the machine is ignored, the flux flowing in back iron can be used to calculate the back emf. If not, the flux linkage can be calculated using magnetic vector potential. The cogging force is due to the magnetic attraction between the permanent magnets mounted onto the shaft and the stator teeth. The force attempts to maintain the alignment between the permanent magnet and the teeth. This force exists even if there is no current flowing in the coils. it becomes an important parameter since its peak value is significantly high. The virtual work method is used in the force calculation. In this method, the force acting on a ferromagnetic object can be determined as the sum of forces in the air layer surrounding it. The force of an air material element in the s direction is given by [ 7 ] :
Fig. 4. Flux linkage of coib
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I
Two Phase Output Voltage 250
__
_.
._
s
1W
.
k
.........
Fig. 5. Induced voltage
1
....... t
(4
Fig. 8. Simulation two phase output voltage
We use Kr= 0.7 and Kfringing = 0.8 in the calculation. The flux linkage in coil is shown in Fig. 6. The coil induccd voltage is shown in Fig. 7.
Series Output Voltage ................................
-$
..................................
200 100 0
'-lw -m -MO
....
II.
I
l.ll.l
-
......... ."l..._l_.l..:
t IS)
Fig. 9. Simulation series output voltage
tl.1
Fig. 6. Flux linkage B. Cogging Force The maximum cogging force is expected to be around 150N. The cogging force is shown in Fig. 10.
CO11V * l P
Cogging Force
200 7-
,(*I
Fig. 7. Coil voltage
Coils can be connected into single and two phase system. The output voltages from simulation are shown in Fig. 8 and Fig. 9.
J........................................................................................................ J Translator Posirion(mm)
Fig. 10 Cogging force
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v.
191 Boldea, Ion, Syed A. Nasar, Lirwar Eleciric
DISCUSSlOh’ The radially magnetized permanent magnet appears to give high output voltage and low cogging force when used in the generator design. This radial flux naturally avoids the concentration of flux density in the magnet edge which can create a high cogging force. This flux is also contributes better flux changing and thus higher induced voltage.
VI.
Actuators and Generafors, Cambridge: Cambridge University Prss, 1997, pp. 201-233. Wang , Jiabin, Weiya Wang, Geraint W. [I01 Jewell, and David Howe, “A Low-Power, Linear, Permanent - Magnet Generatori Energy Storage System”, IEEE Transactions On Indiisrrial Electronics, Vol. 49, No. 3, June 2002.
Khalid Mohamed Nor Department of Electrical Engineering Faculty of Engineering University of Malaya 50603 Kuala Lumpur Malaysia Email: !&alid@uni.edu.my
coKcLusIoN
The design of a generator using radial magnets is presented. The cogging force and induced voltage are calculated as well as simulated. The results appear EO be similar.
VII. ACKNOWLEDGMENT The authors gratehlly appreciate and thank the Ministry of Science, Technology and Environment, Malaysia for funding of this research project under IRPA Grant 33-02-03-30 13. REFERENCE Cawthome , William R., Optimization of U Brushless Permanerif Mugnet Linear Alter~atorfor Use With a Linear Inrernal Combustion Engine, PhD Thesis, Department of Computer Science and Electrical Engineering, West Virginia University, Morgantown, West Virginia, 1999 Cawthome, William R., at al., “Development of a Linear Altemator-Engine for Hybrid Electric Vehicle Applications”, IEEE Transactions On Vehicular Technology, Vol. 48,No. 6 , November 1999 Geng, Steven M, and Gene E. Schawrzc, A 3 0 Magnelic Analysis of a Linear Alternator for a stl?“li?lgPower Sysfein, NASA John H. Glenn Research Center, Ohio, unpublished. Blarigan, Pcter Van, “Advanced Internal Combustion Eiectrical Generator”, Proceeding of the 2001 DUE Hj:drogen Progrum Review, NRELiCP-570-30535, Sandia National Laboratories, Livermore, Ca 94550 Zyl, AW van, and CF Landy, Reductiun of Cogging Forces in U Tubular Linear Syncronous Motor by Uptimising the Seconday Design, ,!LEE Africon,
2002 Yoshimura, T., H.J. Kim, M. Watada, S. Torii, D. Ebihara, Analysis ofrhe Rediiction of Detent Force in a Pemiaiient Magner Linear Syricronow Motor, TEEE Transaction on Magnetic, Vol. 31, No. 6, November 1995. ANSYS Release 7.1 Documentation, 2003 Boldea, Ion, S.A. Nasar, Linear Mtion Electroinagrretic Device, New York: Taylor & Francis, 2001.
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