National Power and Energy Conference (PECon) 2003 Proceedings, Bangi, Malaysia 306

Linear Generator: Design and Simulation

H. Arof, Wijono and K. M. Nor, Senior Member, IEEE

AbstrQct--A six-slot tubular permanent magnet linear generator is designed, simulated, fabricated and tested. The finite element method is used in calculation and simulation to get the accurate results. Optimization bf the translator length is carried out to achieve the minimum togging force. Tests are conducted to confirm the simulation results. Better performance is achieved in the propo.sed iniproved generator prototype.

Keywords--Cogging Force, Finite Element, Linear Generator, Permanent Magnet Tubular Linear Generator.

I. INTRODUCfION

RESEARCHES on the linear engines are still conducted until the present day. This engine is a better choice in

relation with energy efficiency issues. Due to the absence of the crank shaft, rod and rotary parts that contribute to friction losses, the linear system becomes compact, highly efficient, and lightweight. In. addition, gas fuel is recommended to achieve low emission.

Linear generator is an electromechanical energy converter driven by a prime mover. It undergoes a reciprocating motion and converts mechanical power into electrical power. The mechanism in the linear generator is the same as the rotary generator except that in the linear generator, there is an end effect. The moving part moves linearly until it reaches the end point where it stops and moves back in reverse direction. On the other hand, a rotary generator never reaches the end point in its motion. The end effect contributes to significant problems including the cogging force.

Cawthorne [1] 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 the 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 optimization

Manuscripl received October 31, 2003. This work is sUPPDrted by Ministry of Science, Technology and Environment, Malaysia under IRPA Grant No. 33·02-03·3013.

Harmah Aror is with the Department Df Electrical Engineering, University of Malaya, Malaysia (phone: +60 37967 5205, fax: +60 37967 5316, email: uhan17llhGi.ll1l1.cdu.mv).

Wijono is with the Department of Electrical Engineering, University of Malaya, Malaysia (email: wijono{iilum.rdI1.1l1Y).

Khalid Mohammed Nor is with the Department of Electrical Engineering, University of Malaya, Malaysia (email: khalid@um.edu.my).

0-7803-8208-0/03/$17.00 ©2003 IEEE.

of models involves the permanent magnet, the coil and the stator dimension. A smaller generator of OJ kW, 200V was also designed and constructed [2]. In both researches, the voltage induced in the coil is derived from the flux calculated with the finite element method. The dynamic performance of the generator is examined using the electric circuit simulation software.

, V'

NASA Glenn Research Genter, 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 ofthe generator.

Blarigan [4] at Sandia National Laboratories, Livermore designed and constructed an efficient linear generator. The generator is driven by a high speed hydrogen fueled 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 slots, the generator can generate 40 kW of output power, with an efficiency of 96%.

Our team is currently investigating the free-piston linear generator. A tubular permanent magnet linear generator driven by a free-piston internal combustion engine is designed, simulated, fabricated and tested. The engine is proposed to be used in many industrial, commercial and personal applications where a stand alone power generation is needed, or there is no power utility provided, It is also proposed to be an alternative power generator used fOf hybrid vehicles.

Fig. I. The linear generator

II. LINEAR GENERATOR DESIGN

Similar to a rotary machine, the stator of the linear generator consists of copper coils and a silicon steel

laminated core. Replacing the rotor is a translator consisting of pennanent magnets and a shaft. The linear generator has six slots, six coils, and a set ofpemlanent magnet translator.

Fig. 2. Tubular Linear Generator Diagram

A. Stator All fluxes generated by permanent magnets are expected

to flow crossing the coils. A low reluctance magnetic circuit material is required. Among ferromagnetic materials, silicon steel is the best material for this purpose.

The stator is constructed from non "oriented silicon steel laminations of grades 35H360 and 50H470. The typical specifications of both materials are shown in Table 1.

TABlE I LAMINATION MATERIAl PROPERTY

Thick· Assumed Max. Core Max. Min. Grade Loss Induction Lmnt. ness Density

WfKg at 5,000 Factor mm kgldm' I.OT I I.5T Aim % 3511360 0.35 7.65 1.451 3.6 1.63 95.0 5()H47() 0.50 7.70 2.00 I 4.70 1.64 96.0

B. Coil

Instead of round wire, the flat copper wire is used to obtain a better coil fill factor. The flattening technique is often used by manufacturer in forming the flat wire from its original round shape. The coil is compact since there is

almost no space between wires. The current carrying capacity of wire used is 27.5 Amperes, and the number of turns per coil is 30.

e. Magnet Arrangement The translator consists of axial permanent magnets and

spacers. These components are mounted onto the shaft. The permanent magnets are made of a high flux density rare earth Neodymium Iron Boron 30EH. The typical properties of the material is shown in the Table 2.

307

TABLE 2

The spacer material is mild steel 1IS S45C which has relative penneability of 2000. The material is easily fabricated and has good penneability although its penneability is much lower than that of the silicon steel. The spacers provide electromagnetic paths between magnet and

stator core.

D. Shaft Since the permanent magnet is axially magnetized, the

stainless steel material which has a relative permeability around 1 is chosen as the shaft material. The low relative penneability shaft causes almost all fluxes to flow through the stator core. Table 3 shows the typical properties of stainless steel material.

TABLE 3 SHAfT MATEiUAL PROPERTY

Electrical Relative Density AISI Composiiion Resistivity rermeabilily gem'] "Ohm em 304 Fe!Cr18INi I 0 70"72 I 7.93

III. GENERATOR MODELING The linear generator system consists of an engine and a

tubular permanent magnet linear generator. The engine is a single internal combustion type, which has one combustion chamber and one air �ickback chamber. The combustion piston and the kickback piston are connected by a stainless steel shaft. The moving parts of the generator are mounted onto this shaft. The flux generated by permanent magnets flows through coils via the air gap and the stator core. Small air gap is required to keep the fringing flux low, with almost all fluxes flow through the core. During translator movement, the quantities of fluxes crossing coils are changed. The changing in flux is used to calculate the induced voltage in the coils.

The linear generator is first modeled as an independent part of the system. The interaction between the generator and the engine, especially in relation with forces, is not considered. Parameters calculations do not include the generator loading. These parameters are flux distribution, cogging force and open circuit voltage.

A. Flux Distribution Flux calculation has two objectives, i.e., to map the flux

density in the generator parts and to calculate the induced voltage in the coils. The shape and the dimension of teeth, the back iron of the stator, and air gap are determined by the flux density. As stated above, the voltage induced in the coils can be derived from the flux changing with respect to time.

The magnetic potential vector A , instead of flux density, is often used in the field analysis. The differential operation to this vector potential gives:

'V·'VxA==O (1)

In parametric simulation, the magnetostatic field principle is used to calculate magnetic flux and voltage. Gauss's law can be applied in this situation:

'V.jj"" 0 'VxH;:::.] 'V.J;:::. 0

(2)

(3)

(4)

w.here B is the magnetic flux density vector, H is the

magnetic field intensity vector and J. is the total current density vector.

Using Equation (I), the flux density B in the equation

(2) can be expressed in terms of vector A as:

B ;:::.'VxA (5) For problems considering saturable material with

permanent magnets, the constitutive relation for the magnetic fields is:

II ;:::. [,u]H + floM 0

floM 0 :::: B, (6)

(7)

where �a is absolute permeability of free space, M 0 is

remanent intrinsic magnetization vector, and B, is remanent flux density. The correlation between. the flux density and the field intensity with absence of the magnet is given by:

(8)

The permeability matrix [P] can be a function of field or temperature. If [u J is only a function of field,

o 1 o �l

The flux flows through an area can be calculated as:

lj/ = JlI. 11"dS (10)

(9)

where B is flux density vector, dS is displacement unit and 11" is unit normal vector of dS.

In RZ coordinate system, the unit normal vector n can be written as,

308

(11)

Thus, the dot product of the flux density and the vector Ii gives: , y'

( 12)

The total flux flowing trough the cross sectional area of the back iron having a thickness LR can be calculated as:

(13)

B. Output Voltage After simulation using the finite element method to obtain

the flux and the flux density over all areas, the induced voltage is calculated from the linkage flux in the coils. This emf is given by Faraday's Law as,

dl.jl e=-N ­dt (14)

where N is number of turns, d'f'ldt is the derivative of flux with respect to time.

The flux flowing in the back iron is considered in the voltage calculation. It is assumed that this flux is the same as the flux linkage to the coil.

C. Cogging Force 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]:

i-r aH

i f - - a Fs = B -d(vol)+ ( Br dH)-d(vol) 01 as 01 as

(16) where: F, = force in element in the s direction

8H as = derivative of field intensity with respect to

displacement s = virtual displacement of the nodal coordinates taken

alternately to be in the X,Y,Z global direction vol = volume of the element.

There are many ways to reduce the cogging force. In this design, the optimization of the magnet length is done. This method is one of the most effective techniques [5],[6].

The basic method of reducing the cogging force is shifting

,V'

the force curve of a pole in order to cancel the force curve of another pole. If the spacers and teeth are in line at the same translator position, both cogging force curves have the same peak position. The sum of these curves gives a high peak value. If curves are shifted, the sum of curves gives a lower peak value. Although it is practically impossible to reduce the cogging force to zero, the curves can theoretically cancel each other.

IV. FINITE ELEMENT SIMULATION

The finite element method gives more accurate results than that of the· analytical calculation especially in the solving field problems of complicated shape objects. In case of a symmetrical problem with a simple shape, a 2D representation gives a sufficient result. If the shape is unsymmetrical, the 3D analysis should be used. To get better results, more number of elements is required. It is important to create fine elements in small and narrow objects. Simulations are performed using finite element simulation programs ANSYS® and Ansoft Maxwell®.

The linear generator with 'normal' or 'standard' permanent magnet arrangement and optimum pennanent magnet arrangement are included in calculations. In the 'normal' arrangement, the position of spacers is in line with that of teeth of the stator.

The movement of the translator is simulated with a sinusoidal waveform. The stator material property is defined from the BH data so that its dynamic permeability is considered. The fringing effect is also taken into account. The starting point of the translator in the optimum permanent magnet arrangement is shifted to get a symmetrical voltage waveform. The speed of motion is 3000 rpm.

As described above, the parametric method is used in the simulation. The mechanism includes a series of simulations where the position of translator is shifted to consider the motion. The time range used in one full stroke of the translator motion is divided into several points. The translator position at every point is defined by the motion equation. For each point, a complete simulation creates the flux and the force value. To calculate the voltage for one full stroke motion, Eq. 14 is changed to a discrete form as: .

61j1 e=-N­I'1t

(15) where tJ.1fI is flu

. x difference between a point and the next

point separated by the time difference tJ.t . The generator is axis-synunetric at plane RZ as shown in

figure 2. The axis-symmetry yield force only in the Z direction, as forces in other directions cancel out. The plane axis-symmetry allows us to analyze flux in the RZ plane only and use the results for the complete geometry.

V. SIMULATION RESULTS

In Fig.3 and Fig. 4, a flux distribution in the generator at

309

the starting position is shown. The diagram is one half of cross sectional area of that in the 3D diagram shown in Fig. 2. The flux mainly distributes in the stator teeth and the back iron. The flux density in the stator is below 2 Tesla - the saturated flux density of the material. The fringing fluxes flow in the other teeth through the air in the inner space of stator and in the air gap. These fluxes lead to the presence of ripples in the voltage waveform. The small air gap keeps fringing effect low.

Fig. 3. Flux Distribution

r-�-�--�-�-------' U!'!n 7.11Cl lOY .:J JOO] IlO.H:U:

Fig. 4. Flux Density

Icm.u. I!IOLLITIOI :n'n·�

In Fig. 5 the cogging force in the generator with the 'nonna!' and the optimized permanent magnet length are compared. The generator with the optimum magnet length arrangement gives the maximum cogging force up to 70% less than that of the maximum cogging force of the generator with normal magnet arrangement.

800 600 400 ZOO

"" 0 "- \ ·200 -400

-1500 .aoo

Cogging Forte

Transl.!or PQ5itiqn [mml Fig. 5. Cogging Force

f=="l �, - - . . --- 1

. The nTIS output voltage of the generator with the optimum

magnet length is reduced to 87.5% compared to that of the generator with the normal magnet length. This lower voltage value is achieved to get the minimum cogging force.

Another advantage of the optimized configuration is the smoother voltage waveform. As shoWn in Fig. 6, a better voltage shape is achieved. The disadvantage is the reduction in nTIS and peak voltage value.

Output Vollag�

·\50 tI·,

fig. 6. Simulated Output Voltage

VI. TEST RESULTS Tests are conducted to confirm the simulation results. The

generator is run by a rotary motor via a crank shaft to provide a linear motion. The movement of the translator as a function of time is sinusoidal.

310

� ...... Fig. 7. Test No-load Output Voltage

In this lest, generator is run at 600 rpm. In order to compare the test result to the simulation result, the estimated value is recalculated with the test speed. It is found that, as shown in Fig. 7, the voltage waveform is similar to the simulation result. .

The test value is lower compared to the simulation result One of the possible reasons is due to the stator construction. In axial stacking, a lot of air gap exists between laminations, and in radial lamination, the sheet insulation gives high

. material reluctance. For simulation purpose, the stator is defined as a solid object. By taking into account the lamination fill factor, the· simulation gives accurate results.

VII. IMPROVED PROTOTYPE

Further improvements to get a better performance of the generator are currently done. A higher output voltage can be achieved by increasing the number of turns and the longer stroke length. Using the same cross sectional area of the wire, the number of slots is decreased. The stroke length is increased so that it becomes longer than the previous one,

and thus the speed is also increased. The new prototype has two-slot stator and three sets of

magnet. The length of the generator is increased since it has longer stroke length. The output voltage is increased to 83% of the targeted vo ltage of 250 volts.

Output Voltage

4OO.DO --�---�-�---�-.---.�-�------

300.00 2C1a.DD

� •• 00 >

-2:DD.DOj---�--�----�--\-�---1

-lOD.OD i---------------,-.;/-----

-400.00

Fig. 8 Simulation Output Voltage of New Prototype

\ r\ \ I I \ '\ \.. i \

\ r '-. \ f \! \ I \ I '-j "'./

/ \ .'"\ i \ i , ! \ r' "

t 'I I \ . \

J \

\ I

\ \"

Fig. 9. Test No-load OUlput Voltage of New Prototype

\ '\.J

The next proposed improvements are increasing the speed of motion and changing the permanent magnet to the new type which has higher remanent flux density. The new magnet arrangement giving the lower reluctance is also proposed to get higher flux.

VIII. CONCLUSION

The six-slot permanent magnet linear generator is designed, simulated, fabricated and tested. The voltage waveform generated is similar to the simulation results. The maximum cogging force is radically dropped if the pennanent magnet length is optimized. The shifting of coil voltage waveforms due to permanent magnet length optimization can give a better shape of output voltage waveform. A new proposed prototype has a better output. Further optimization ofthe generator components dimension will give a better performance.

IX. ACKNOWLEDGMENT

The authors gratefully appreciate and thank the Ministry of Science, Technology and Environment, Malaysia for the funding of this research project under IRPA Grant No. 33-02-03-3013.

REFERENCE [I] Cawthome, William R., Optimization of a Brushless Permanent

Magnet Linear Alternator for Use With a Linear Inlema! Combustion. Engine. PhD Thesis, Department of Computer Science and Electrical Engineering, West Virginia University, Morgan town, West Virginia, 1999

[2] Cawthorne, William R, at aI., "Development of a Linear Altemator­Engine for Hybrid Electric Vehicle Applications", IEEE Transaclions On V.�icul>rTechnology, Vol. 48. No.6, November 1999

[3] Geng, Steven M, and Gene E. Schawne, A 3D Magnelic Analysis of a Lineor Alternatar for a Stirling Power System, NASA John H. G1crm Research Center, Ohio, unpublished.

[4] 8larigan, Peter Van, "Advanced Internal Combustion Electrical Generator", Proceeding of Ihe 2001 DOE Hydrogen Program Review, NREUCP-570-30535, Sandia National Laboratories, Livermore, Ca 94550

[5] Zyl, A W van, and CF Landy, Reduction of Cogging Forces in a Tubulor Linear Syncronous Molor by Oplimising Ihe Secondary DeSign, ,IEEe African. 2002

[6] . Yoshimura, T.,HJ. Kim, M. Watada, S. Torii, D. Ebihara, Analysis of the ReduClion of Detenl Force in a Permanent Magnel Linear

311

Syncronous Motor, IEEE Transaction on Magnetic, Vol. 31, No.6, November 1995.

J7l ANSYS Release 7.! Documentation, 2003 [8) Boldea, lon, S.A. Nasar, Linear Mlion Eleclromagnetic DeYice, New

York: Taylor & francis, 200!. [9J Boldea, lon, Syed A. Nasar, Linear Electric Actuators and

Genera/ors, Cambridge: Cambridge University Prss, 1997, pp. 201-233.

[10) Wang, Ii.bin, Weiya Wang, Geraint W. Jewell, and David Howe, "A Low,Power, Linear, Permanent - Magnet Generatorl Energy Storage System", IEEE Transactions Ollilldustri/11 Electronjcs, Vol. 49, No. 3, June 2002.

Hamzah Arof graduated with Bachelor of Electrical Engineering from University of Michigan, US. He obtained his PhD in Electrical Engineering in 1997 from University of Wales. His current research interests are Signal Processing, Pattern Recognition and Electrica! Power Generation.

Wijono WlIS bom in Malang, Indonesia. He graduated with Sarjana Teknik (Bachelor of Engineering) from Brawijaya University, Indonesia in 1987. He obtained his Master of Technology from Bandung Institute of Technology, Indonesia in 200 l. He is a PhD studenl at Department of Electrical Engineering, University of Malaya, Malaysia since 2002,

Khalid Mohamed Nar was born in Sungai Pelong, Selangor, Malaysia. He graduated with first Class Honors in Bachelor of Engineering from the Universi ty of Liverpool; England. He obtained his /viSc in 1978 and PhD in 1981 from the University of Manchester Institute of Science and Technology, England. He is a lecturer at the University of Malaya, Malaysia since 1981 and he is a professor in the Department of Electrical Engineering. He is a Senior Member of IEEE. His current research interests are Electrical Power System Simulation, Eleclrical Power Gen eration and Electrical Power quality.