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					                                                            Australasian Universities Power Engineering Conference (AUPEC 2004)

                                                                                       26-29 September 2004, Brisbane, Australia


                                    W. N. L. Wan Mahadi, S. R. Adi and K. M. Nor

                                         Department of Electrical Engineering
                                                University of Malaya


        This paper presents a study of thermal design aspect of Neodymium Iron Boron (NdFeB) magnet in
        the free piston linear generator design. The generator is coupled with the internal combustion engine
        which tends to produce heat. Due to the high temperature from the combustion engine, the
        performance of NdFeB magnet used in the generator is examined. In this paper, heat sources from the
        exhaust of the internal combustion engine, current carrying conductors and friction are studied. The
        heat transfer mechanism such as convection and radiation are also explored. Finite element method is
        used to generate and analyze a thermal model of the NdFeB magnet in the linear generator.

1.        INTRODUCTION                                        Fundamental knowledge of magnet and linear generator
                                                              in various aspects such as electrical and thermal
A linear generator is developed in the University of
                                                              properties has been explored. This paper is written with
Malaya, Malaysia for automotive and stand-alone
                                                              the objective to investigate and analyze thermal
(standby or remote) generator applications. It is driven      properties and simulation of NdFeB magnet in the linear
by an internal combustion engine and converts                 generator design. FEM simulation plays an important
mechanical power into electrical power. It consists of a      role to evaluate thermal performance of the magnet and
stator and a linear translator, which carries axial field     generator. Although the exhaust of the combustion
permanent magnets. The main difference of linear              engine acts as the main contributor in producing
generator to a conventional generator is that the motion      maximum heat, others various heat sources produced in
of the rotor is linear. The linear system gains               the generator have also been investigated.
improvement in efficiency and volume reduction as the
crankshaft is removed.
                                                              2.        PERMANENT MAGNET FOR LINEAR
                                                                        GENERATOR DESIGN

                                                              In order to select the appropriate permanent magnets for
                                                              the linear generator, four major factors are emphasized;
                                                              a) magnetic properties,
                                                              b) corrosion resistance,
                                                              c) material cost and
                                                              d) maximum operating temperature.

     Fig. 1: Linear generator with a free-piston engine       A rare earth permanent magnet NdFeB, is chosen based
                                                              on a number of considerations especially in terms of
The development and investigation of linear generator         producing high energy product. The physical,
have been continuing for a number of years. In order to       mechanical and magnetic properties of the magnet such
design a better performance of linear generator               as thermal conductivity, specific heat, electrical
prototype, previous research has been reviewed. Based         resistivity and magnetic flux density which are affected
on past research at West Virginia University, Sandia          by temperature are investigated. Since NdFeB magnet is
National Laboratories in California, Sunpower Inc. and        brittle, a tin coating is used as a protective layer for the
The Royal Institute of Technology in Sweden, basic            magnet to overcome corrosion resistance.
ideas in designing free-piston generator have been
studied [5,6,10]. Fig. 1 illustrates the principle of the
linear generator with a free-piston combustion engine.

2.1        Magnetic properties                              A detailed study on thermal analysis of linear generator
                                                            is furthered by designing a thermal model using FEM.
The intensity of magnetization and the coercive force       The temperature difference at certain regions in the
are elements which determine the performance of             linear generator is then can be estimated. For thermal
permanent magnets. For a better performance, NdFeB          analysis in the linear generator, various kinds of heat
magnet is a good choice for a linear generator              sources and heat transfer mechanisms are studied. Heat
application. It offers the highest energy product           sources in the linear generator include heat from the
compared to other permanent magnets. The strongest          exhaust of the combustion engine, current carrying
magnet has the highest maximum energy product               conductors and friction are investigated. In this paper,
(BHmax). For the linear generator, NdFeB magnet with        our analysis concentrates on heat sources from the
grade N30EH is used.                                        internal combustion engine and the electromagnetic field
Important parameters for NdFeB permanent magnet             part. The heat transfer mechanisms are also investigated.
with grade N30EH:                                           This analysis can be classified as one of multi-physics
a) Remanance flux density, Br = 1.114 T                     problems which involve conduction, convection,
b) Coercive force, Hcb = 871 kA/m                           radiation, electromagnetic field and friction.
c) Intrinsic force, Hcj = 2411 kA/m
d) Maximum energy product, BHmax = 241 kJ/m3                3.1      Governing equations

                                                            In any applications, before thermal model is designed,
                                                            numerical computation should be considered and the
                                                            load applied to the model should be represented by the
                                                            governing equations. For linear generator, the net
                                                            function of heat, which is considered to be generated can
                                                            be represented as
                                                                      ∑ f (Q) =     f (Qt + Qe + Q f )            (1)

                                                            where Qt is the heat from the combustion engine, Qe is
                                                            the heat from electromagnetic field and Qf is the heat
                                                            produced by piston and sleeve bearing through friction.
                                                            In general, the heat equation is derived from the
                                                            conservation of energy principle, which states that the
                                                            net heat conducted out is equal to the summation of heat
      Fig. 2: Demagnetization curves as a function of       generated and change in energy stored within the
      temperature                                           system. Mathematically, this expression can be
                                                            expressed as [2]
Fig. 2 which is taken from reference [12] shows the                          v        ∂e
demagnetization curves for N30EH NdFeB magnet at                             ∇•q = Q−                             (2)
different temperatures.                                                               ∂t
                                                            where q is the heat conduction, Q is the heat generated
3.         THERMAL ANALYSIS                                 within the system and ∂ e/ ∂ t is the change in energy
                                                            stored. q is described by Fourier’s Law of heat
Thermal analysis is very important in generator             conduction and is given by
application to evaluate the effect of temperature in the                                v
system. The focus of our analysis is to develop a thermal                         q = −κ∇T                         (3)
model and to study the heat distribution in linear          Therefore, the heat transfer in a solid material is
generator. Compared to other materials used, the            expressed by a partial difference equation as follows [2]
permanent magnet temperature is one of the key items to                v     v               ∂T
be emphasized in generator design. A simulation is                     ∇ • (κ∇T ) + Q − ρC p    =0                (4)
developed to ensure that the magnet can be operated at      where κ is the thermal conductivity, Cp is the specific
certain temperature conditions due to the limited           heat capacity, ρ is the mass density, Q is the heat
maximum operating temperature within NdFeB magnet.          generation rate per unit volume and T is the unknown
                                                            temperature distribution that is to be determined.

3.2      Heat transfer mechanisms                             Then, the total heat loss, Qcr by convection and radiation
                                                              in the inner part of linear generator is [5]
To study the behavior of materials at certain                              Qcr = (hc + hr ) A(T − T A )             (8)
temperature, a basic knowledge of heat transfer
mechanism should be studied. Several properties of
                                                              Radiation is usually significant relative to conduction or
materials change with temperature are also can be
                                                              natural convection, but negligible relative to forced
predicted and investigated with the aid of heat
                                                              convection. Thus, radiation in forced convection
distribution estimation from FEM simulation. Heat can
                                                              applications is normally disregarded, especially when
be transferred in three different ways: conduction,
                                                              the surfaces involved have high emissivities and low
convection and radiation.
                                                              temperatures [11]. For this reason, the radiation effect is
                                                              negligible in our simulation because of the high
In order to transfer heat from a solid surface to a cooling
                                                              emissivities of copper and silicon steel materials in the
medium such as air, it is necessary for the surface to be
                                                              generator’s stator, which are 0.63 and 0.7 respectively.
hotter than the surrounding medium. The heat transfer
coefficient is a constant, which depends upon the surface
material, the surrounding medium and the relative
                                                              3.3      Electro-thermal analysis
velocity of the surrounding medium [1]. For convection,
the heat transfer is complicated due to the fact that it
                                                              Electro-thermal simulation has become an essential part
involves fluid motion as well as heat conduction.
                                                              of many engineering applications. Thermal analysis for
Newton determined that the heat transfer through a
                                                              the linear generator is quite complex due to the presence
surface area is proportional to the fluid solid temperature
                                                              of heat source from electromagnetic field part. It
difference. The temperature difference usually occurs
                                                              requires a solution of coupled field analysis. In the
across a boundary layer of fluid adjacent to the solid
                                                              coupled field analysis, heat generation inside the coils is
surface. The Newton’s equation can be represented as
                                                              considered in order to get a prescribed temperature field.
                  Qc = hc A(T − T A )                   (5)   To generate a model that takes into account both
                                                              electrical and thermal effects still remains a challenge.
where, hc is the convection heat transfer coefficient, A is   The relationship between the electromagnetic field and
the heat transfer surface area, T is the temperature of       temperature are studied to analyze the overall system.
the surface area and TA is the ambient temperature. For a
natural convection of air, the range of the heat transfer     In our design, we consider heat produced by the
coefficients is between 2 to 25 W/m2.0C and for a forced      electromagnetic part as a heat generation. Heat
convection, the range is between 25-250 W/m2.0C [11].         generation in linear generator refers to resistance heating
The temperature effect and heat loss at the outer part of     in copper wire where electrical energy is converted to
the linear generator is caused by a natural convection        heat. Heat generation is usually expressed per unit
while the inner part is caused by forced convection and       volume of the medium and it can be represented as
radiation.                                                                                I 2 Rcoil
                                                                           Qe =                                       (9)
The radiation heat transfer is more difficult to calculate,                       π ( r02 L) − π (ri 2 L)
as radiation loss depends on the forth power of the
absolute material temperature. In the inner part of linear    where Rcoil is coil resistance, I is current capacity of wire
generator, the radiation heat transfer coefficient can be     and L is coil thickness. From calculation, heat generated
expressed as [6]                                              in copper coil is 374082.6773 W/m3.
                         σ t ε (T 4 − T A )
                  hr =                                (6)     3.4      Friction
                            (T − T A )
where ε is emissivity of the material and T is the            Friction is associated with bodies in motion. When two
material temperature. The radiation heat transfer to or       bodies in contact are forced to move relative to each
from surface surrounded by an air occurs parallel to          other, a friction force that opposes the motion develops
convection between the surface and the air. Thus, the         at the interface of these bodies. The energy supplied as
total heat transfer is determined by adding the               work is eventually converted to heat during the process
contributions of both heat transfer mechanisms. The           and is transferred to the bodies in contact, as evidenced
radiation heat transfer can be represented as [11]            by a temperature rise at the interface [11]. This
              Qr = εσ t A(T 4 − TA )
                                                   (7)        phenomenon is occurred in linear generator while it is

operating. Piston and sleeve bearing in a cylinder are              ∂T   ∂N 1 ∂N 2 
                                                                    ∂x   ∂x            ...
example of objects, which produce heat through friction.
                                                                    ∂T   ∂N        ∂x     
                                                                          1 ∂N 2                               (16)
Heat generated through friction can be calculated as                    =               ... {T } = [ B ]{T }
                                                                    ∂y   ∂y        ∂y 
                      Q f = ηFν                        (10)         ∂ T   ∂ N 1 ∂ N 2 ... 
                                                                    ∂z   ∂z
                                                                                   ∂z 
where η is friction coefficient, F is frictional force and ν
is sliding velocity.                                           where {T} is the temperature at nodes, [N] is a matrix of
                                                               shape functions and [B] is a matrix for temperature
4.        SIMULATION ANALYSIS                                  gradients interpolation. By using Galerkin method, the
                                                               equation (11) can be written as [3]
4.1 Complete partial differential equations (PDE)                          ∂qx          ∂qy         ∂qz                 ∂T 
    for thermal model                                                ∫  ∂x + ∂y + ∂z
                                                                                                           − Q + ρCp        Ni dV = 0
                                                                                                                         ∂t 

For a basic equation of heat transfer, the equation (5)
can be represented as [3]                                      By applying the divergence theorem to the first three
                                                               terms, the equation can be expressed as [4]
           ∂q x ∂q y ∂q z              ∂T
      −(       +    +     ) + Q = ρC p                 (11)            ∂T             ∂N i ∂N i ∂N i 
            ∂x   ∂y   ∂z               ∂t                                          ∫
                                                                ∫ ρC p ∂t N i dV − V  ∂x ∂y ∂z {q}dV
                                                                V                                     
where qx, qy and qz are components of heat flow through
                                                                = QN dV − { q } { n } N dS  ∫
the unit area and Q = Q(x, y, z, t) is the inner heat                         i                              i
generation rate per unit volume. It is assumed that the          V                          S

boundary conditions can be of the following types [4]          {q}T = [qx qy qz ] and {n}T = [nx                                       ny   nz ]
    a) Specified temperature
               Ts = T1 ( x, y, z, t ) on S1         (12)
                                                               where {n} is an outer normal to the surface of the body.
     b) Specified heat flow                                    After insertion of boundary conditions equations (12) to
          q x n x + q y n y + q z n z = −q s on S2     (13)    (15) into equation (18), then the equations for the overall
                                                               system is [4]
     c)   Convection boundary conditions
      q x n x + q y n y + q z n z = h(Ts − Te )        (14)                           ∂T             ∂N              ∂N i     ∂N i
                                                                     ∫ ρC
                                                                                         N i dV − ∫ [ i
                                                                                                      ∂x              ∂y       ∂z
where Ts is an unknown surface temperature, Te is a                                                                                           (19)
known environment temperature and h is the convection                = ∫ QN i dV − ∫ {q}T {n}N i dS + ∫ q S N i dS −
                                                                          V                     S1                       S2
                                                                     ∫ h(T − T ) N dS − ∫ (σεT                       − αq r ) N i dS
    d) Radiation                                                                        e       i

          q x nx + q y n y + q z nz = σεT − αqr
                                            4                        S3                                S4
                                           s           (15)

where α is the surrounding absorption coefficient and qr       4.2                Finite element model simulations
is incoming heat flow per unit surface area.
For transient problems, it is necessary to specify a           Finite element analysis is a tool used in engineering
temperature field for a body at the time t = 0. A domain       application to determine the physical effects of a given
V is divided into finite elements connected at nodes.          set of boundary conditions will have on a part. The finite
Global equations for the domain can be assembled from          element method is the most useful technique and
finite element equations using connectivity information.       flexible tool to determine the unknown temperature in
Shape functions Ni are used for interpolation of               most industrial applications. The geometry being
temperature and temperature gradients inside a finite          modeled will always be divided up into smaller
element [4]. This can be expressed as follows                  divisions known as elements and the elements are
                                                               connected together to form the finite element mesh.
     T = [ N ]{ T }                                            Each element contains nodes, which are points and the
     [ N ] = [ N 1 N 2 .....]                                  elements are mathematically connected to one another.
                                                               It is actually an approximate mathematical method for
     {T } = {T1 T 2 .....}
                                                               solving differential equations problems.

Theoretical analysis, heat transfer mechanisms,              simulation, the heat source is largely governed by the
electromagnetic-thermal and friction have been               heat conduction from the exhaust of the combustion
discussed. The integral finite element equation that is      engine.
referred to the equation (19) is solved using 2D Finite
Element Analysis. For this purpose, ANSYS 7.1                The heat source from the combustion engine is
software is used as a simulation tool. Since the linear      considered about 7270C (1000K). The heat generation
generator is symmetric about the centerline of the shaft,    from the copper coil, which is governed by equation (9);
it is only necessary to model half of the geometry in        and natural convection at the enclosure of the generator
ANSYS. Therefore, 2D axis-symmetry expansion is              are also applied as thermal load of the linear generator.
used to design and simulate a full model of the linear       For our simulation, it is noticed that the radiation effect,
generator.                                                   forced convection and friction are not considered.
The linear generator dimensions used is given in Table 1     Radiation effect is almost negligible because the
below,                                                       existence of the air gap between the stator and translator
         Table 1: Linear generator dimensions                is very narrow. The effects for these three mechanisms
                                                             will be further investigated in future work.
      Components                     Dimension
      Stator pole pitch                76 mm
      Stator slot pitch                76 mm
      Stator slot depth                30 mm
      Stator tooth width                8 mm
      Stator back iron thickness       6.5 mm
      Magnet outer diameter            55 mm
      Magnet inner diameter            25 mm
      Magnet thickness                 56 mm
      Magnet spacer                    20 mm
      Air gap                           1 mm

            Fig. 3: 2D linear generator model

Starting from a sketch of the geometry, closed regions
have to be identified. Determination of properties of
materials such as specific heat, thermal conductivity and    Fig. 4: Heat distribution in linear generator without
density at different temperatures are important for          cooling fins and permanent magnet part
thermal problem solving. In order to get a final solution,
thermal load as boundary conditions of the model are         Fig. 4 and Fig. 5 show the heat distribution in linear
defined properly. Fig. 3 shows the 2D linear generator       generator as well as permanent magnet. Temperature
model.                                                       region around the permanent magnet has also been
                                                             analyzed to ensure that it is below than its maximum
4.3      Simulation results and discussion                   operating temperature.

From mathematical analysis of thermal model, the heat
sources boundary conditions are applied. In this

                                                               6.     REFERENCES

                                                               [1]    Design of Machines and Drives – Generalised
                                                                       Machine Designed Concept. http://www.staff.
                                                              /dmd Intro.pdf.
                                                               [2]    Efunda        (Engineering      Fundamentals),
                                                                      Conduction:            General          Theory.
                                                               [3]    G.P.Nikishov, “Introduction to the Finite
                                                                      Element Method”, University of Aizu, Japan,
                                                               [4]    Marc T.Thomson, “Electrodynamic Magnetic
                                                                      Suspension – Models, Scaling Laws, and
Fig. 5: Heat distribution in linear generator with cooling            Experimental Results”, IEEE Transactions on
fins and permanent magnet part                                        Education, Vol. 43, No. 3, 2000.
                                                               [5]    N. W. Lane and W.T. Beale, “A 5 kW Electric
From thermal simulation of both linear generators with                Free-Piston Stirling Engine”, Proceedings of 7th
and without cooling fins, it is observed that the range of            International Conference on Stirling Cycle
temperature distribution in permanent magnet is                       Machines, Tokyo, Japan, 1995.
between 43.9010C to 133.7480C (without cooling fins)           [6]    P.     V.    Blarigan,    “Advanced     Internal
and 40.820C to 113.8480C (with cooling fins). This                    Combustion Electrical Generator”, Proceedings
range can be accounted as a safety margin for the                     of U.S DOE Hydrogen Program Review,
permanent magnet which has maximum operating                          NREL/CP-610-32405,          Sandia     National
temperature of 2000C.                                                 Laboratories, Livermore, Ca 94550, 2002.
                                                               [7]    S.R. Trout, “Understanding Permanent Magnet
From the results, the amount of heat to be removed will               Materials: An Attempt at Universal Magnetic
be determined in order to maintain an optimum                         Literacy”, Magnequench International, Inc.
operating temperature. To reduce as much heat within        
the generator, the design of the finned surfaces is still in          techcenter/reference/papers/CoilWinding2000.
the process of improvement. The use of the fins in this               pdf.
application is very effective in order to reduce the           [8]    S.R. Trout and Yuriy Zhilichev, “Effective Use
temperature rise in the linear generator. As a                        of Neodymium Iron         Boron Magnets, Case
continuation, a cooling mechanism design such as                      Studies”,       Proceedings     of      Electric
forced cooling will be investigated and simulated.                    Manufacturing and Coil Winding ’99
                                                                      Conference, 1999.
5.       CONCLUSION                                            [9]    S.R. Trout, “Material Selection of Permanent
                                                                      Magnets, Considering        Thermal Properties
Thermal model from FEM analysis has been studied.                     Correctly”,      Proceedings     of     Electric
The simulation results are required to observe the                    Manufacturing and Coil Winding Conference,
temperature rise within the permanent magnet. The                     Ohio, USA, 2001.
temperature distribution within the permanent magnet           [10]   W. R. Cawthorne, “Optimization of a Brushless
has been determined. To improve the simulation,                       Permanent Magnet Linear Alternator for Use
coupled field analysis, cooling mechanism, radiation,                 with a Linear Internal Combustion Engine”,
forced convection and friction effects will be                        Ph.D. dissertation, Dept. Computer Science and
investigated further. An analysis of thermal, heat                    Elect. Eng., Univ. West Virginia, Morgantown,
transfer and cooling mechanisms will aid in the                       1999.
estimation of heat distribution in the linear generator.       [11]   Y. A. Cengel, “Introduction of Thermodynamics
For further investigation, the data that have been                    and Heat Transfer”, the Mac-Graw Hill
obtained from the simulation is then used in cooling                  Companies Inc., United States of America,
mechanism design by using better fins and forced                      1997.
cooling.                                                       [12]   Electron Energy Corp., EEC Magnetic


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