The Determination of Effects of Primary and Secondary Geometry of Tubular Linear Generator

IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE)
e-ISSN: 2278-1676,p-ISSN: 2320-3331, Volume 12, Issue 1 Ver. I (Jan. – Feb. 2017), PP 06-11
www.iosrjournals.org
DOI: 10.9790/1676-1201010611 www.iosrjournals.org 6 | Page
The Determination of Effects of Primary and Secondary
Geometry of Tubular Linear Generator
Serdal Arslan1
, Osman Gürdal2
, Sibel Akkaya Oy3
1
Birecik Vocational Higher School, Harran University, Birecik, Turkey
3
Faculty of Marine Sciences, Ordu University, Turkey
Abstract: In this paper, general information on the construction of tubular generators are given. Also, the
numeric analyses were conducted by using 2D and 3D finite elements software. The output power, iron loss and
cogging force change were compared by sensing the primary and secondary structural geometry of generator.
Instead of the annular magnets, the magnets in the form of block were used mobile (secondary) part of
generator. Also, analyses were conducted on the generator for two primary geometries.
Keywords: tubular linear generator, linear motor, generator design, electromagnetic design
I. Introduction
As known, the machines which transforms the mechanical energy into electric energy are named as the
generator. It directly affects the topology of generator to be used whether the mechanical energy consists of
circular or linear motion. As the linear induction generators have a variable speed force characteristic, they are
used in the systems which produces electric from heat (instead of strling engine) and in Archimedes’ wave
swing system [1], [2]. As the vernier generator which is evaluated within the class of variable reluctance and the
diagonal transverse have high force density, they become widespread in the wave energy applications
(Archimedes Wave Swing) [3]. The permanent magnet synchronous generators may be adapted to almost all
linear secondary systems in terms of speed and force characteristic and the power density. Although these
creates a disadvantage in terms of that the performances of continuous magnets decrease at high temperature
and the prices are high, they are preferred due to their high efficiencies. In this regards, the permanent magnet
linear generator was preferred as the generator type. The tubular structure is preferred due to hat it has less stray
flux and higher electromagnetic force (emf) compared to the flat structure [4,5]. They have some other
advantages: there will be very low pressure on the linear bed due to that the high forces between the armatures
(normal) are balanced (the sum of normal forces is equal to zero). Therefore, their life will be extended [6].
Other advantages are as follows: they have high compressive force and they show a perfect servo characteristic
along with that the final effect at flat linear generators (final coil effector) is not seen, generally they are easily
constructed, the requirement for using motion transformation mechanisms is eliminated, the mechanical losses
are decreased and the reliability increases. It is desired that the forces of linear generators should not be
asymmetric. Therefore, one-sided flat type is not preferred [7,8]. While the magnetic flux density at the air range
of tubular generators have a stable value, the magnetic flux density changes at tetragon structure due to that the
airway length is higher. Compared to the tubular generator, the iron and copper losses are much more at tetragon
structure. Therefore, their efficiencies are lower [9]. Also, the tubular machines are classified depending on the
flux direction (radial, axial, halbach). In this paper, the flux direction is determined as the neodymium magnets
with radial flux. In this paper, the primary and secondary part of reciprocal collective coil wye-connected
generator which had 6/4 hollow to pole ratio were changed. By using 2D and 3D finite elements software, the
numeric analyses of tubular generator were conducted. By changing the primary and secondary structural
geometry of generator, the change of output power, iron loss and cogging force were compared. Instead of the
annular magnets, the block magnets were used at the mobile part (secondary) of generator. The analyses were
conducted also for the two primary geometries of generator.
II. Tubular Linear Generator Structures
The magnets used at the permanent magnet tubular linear generators (PMTLG) are used as the
neodymium magnets which have a high-energy density. For example; it is also required to take desired magnetic
performance, operation temperature range, external demagnetized areas, weight, cost and positioning to the core
into consideration. When the specifications of Neodymium-Iron-Boron magnets (energy density, magnetic flux
density, etc.) are considered, they are commonly used in the generator applications. These magnets are
demagnetized under the temperature and mechanical effects. Therefore, the magnets of which Cruie temperature
is high (T>200) or UH-EH-VH/AH coded magnets are preferred. At PMTLGs, Samaloy 8SMC) core material
and siliceous sheets are generally used. SMCs are the materials which have low starting permeability, low
saturation induction and high loss compared to the laminated siliceous sheets. But it has lower losses at high

The Determination of Effects of Primary and Secondary Geometry of Tubular Linear Generator
frequencies compared to the siliceous sheets. Although the hysteresis losses are bad when it is compared with a
single laminated siliceous sheet, their dynamic behaviors are better due to the loss of decreased eddy currents.
Tansil300 (3.5% SiFe lamination) showed a better performance compared to Somaloy 500 and Somaloy 700
materials in terms of force and power factor [10]. Also, the magnetic flux was equally distributed to all axes as
SMCs had isotropic specifications [11]. The use of anisotropic amorp-fe alloy materials at tubular machines will
change the dynamic effect of machine. The cost of a core material significantly depends on the magnetic
characteristic. The core materials may be characterized as linear and nonlinear. The parameters which determine
the specification of core material may be expressed as follows: magnetic permeability, saturation point,
permanent magnetism, electrical resistance and coercivity.As known, the siliceous sheets are manufactured up
to 0.65 mm and pressed at desired dimensions (by taking eddy loss into consideration). In this paper, M43
siliceous sheet was selected and analyses were conducted. In Table 1, the general specifications of this sheet
were given in comparison with SMC.
Table 1. The Specifications belonging to M43-SMC materials
GENERAL SPECIFICATIONS M43 Core Material
Specifications
SMC (Somaloy 700)
Core Material Specifications
Units
Alloy 3% SiFe Inorganic insulated iron particles
Magnetic Flux Density at
H=10KA/m
1.79
1.56 T
Electrical Resistance 0,42 400 μΩm
Density 7,7 7,45 g/cm3
Packing Factor 0,96 solid mm
Core Loss-50Hz 3.57 (1.5T-50Hz) 10 (1T-100Hz) W/Kg
Figure 1. Different Primary and Secondary Images
Here, the basic primary image defined at 2D rz plane given with A are given. The image given with B
is seen as the longitudinal sheet package is seen. It was accepted that the sheets were packed in the way that it
will set 30-degree angle around z axis. By placing 12 units from sheet package, P1 primary given with C was
obtained. P2 primary was created by cutting the siliceous sheets in the form of round and aligned along z axis.
The secondary part was created in two ways. Steel 1020 material was defined in the form of dodecagon for
placing block magnets. The neodymium magnets were placed on the material by taking the pole step and
magnetization into consideration. This design was named as S1. Traditional tubular machine circular magnet
structure and cylinder steel material are named as S2.
Table 2. Sizing Data
Sizing Parameters Dimension Units
Pole Step 0.0275 m
Hollow Step 0.0183 m
Primary external diameter 0.1589 m
Primary length 0.1466 m
Magnet length 0.020 m
Rod diameter 0.038 m
III. The Analysis of Finite Elements and Analysis Results
Ansys-Maxwell; is one of the programs which are commonly preferred for the electromagnetic
analyses that it shows approximate results given in the literature about that it has a wide drawing infrastructure,
the solution options are redundant (The Transient State, Magnetostatic, Eddy currents Electrostatic, DC
transmission, AC transmission), the analysis may be conducted by using finite elements methods, the machine
model designed may be conducted with the auxiliary programs (Simplorer, Matlab, Ansys Workbench, etc.)
which may perform the dynamic and analytical analysis. Therefore, the numerical analyses were conducted by

using Ansys-Maxwell. As some geometries of primary and secondary core materials may not be transformed
into 2D rz plane, 3D analysis was applied. With the aim of searching for the advantages and disadvantages that
the geometries given in Figure 1 have provided against each other, the hollow height, back iron thickness,
hollow width, internal diameter and external coil spirea number, magnet width and magnet thickness were taken
equally.
Magnetostatic Analysis: If the motion of load in a closed circuit will be limited in the way that time-varying
electric current will be stable. As known, the static magnetic analysis does not take the time-dependent effects
such as eddy currents, transient state, etc. The density of magnetic flux is relevant to the determination of
magnetic flux and energy stored in the magnetic field. In the static magnetic analysis, the magnetic models
which both may saturate and may not saturate may be modelled. The FEM solvent may conduct 2D and 3D
static magnetic analysis. The time-relevant parts of Maxwell Equations are accepted as zero. In the two-
dimensional analysis, the energy is calculated by calculating the vector analysis.
The magnetic flux entering a closed surface is equal to the flux leaving the closed surface.
0B.  (1)
A vector of which divergence is zero may be referred as the rotational of a vector unit:
AB  (2)
Here, A is referred as the magnetic vector potential (Wb/m). By calculating the magnetic vector potential, the
magnetic flux density is calculated. The equality between the magnetic field density and magnetic field intensity
(H) is given in (3). With this equation, the magnetic flux density is calculated.
HB  (3)
The current density in the areas where magnetic field intensity is fixed and stable, the current density is taken as
zero. The point form of Amper’s Law is given in (4).
JH  (4)
The magnetic flux densities of primary and secondary combinations with magnetostatic analysis in given in
Figure 2. When the figures are reviewed, it is seen that the magnets have not subjected to demagnetization.
Also, the radial magnetic geometry provides much more flux transition in the core threads compared to block
magnet. But the saturation of core material is out of question.
Figure 2. The magnetic flux density distribution of primary and secondary combinations

In order to understand the structural differences, Line1 is defined along the primer as shown in Fig. In addition,
Line2 is defined as a half circle (180°
) on the magnet (middle point of the air gap).
The flux density variation along these lines was investigated.
Figure 3. Fluctuation of flux density along Line1 and Line 2
In the P2-S2 configuration, the flux density in the air gap remains constant. However, the magnetic flux density
along the corner points of the poles is reduced in the segmented primary and block magnet secondary
configurations. This is most likely the P1-S1 configuration.
Transient Analysis: Ansys-Maxwell 3D transient solvent uses the formulation of T

. The Maxwell
equations used in the transient analysis are as follows:
JH  (5)
EH  (6)
Here, the correlation between the conductivity ( ) and electric field (E) indicates the current density (J). The
correlation between the current density and electric field is valid for the homogenous isotropic substances. The
correlation between the current density and magnetic field intensity (H) is due to the Ampere’ Law. In the time-
varying systems, the rotational of magnetic field intensity is referred as the change of magnetic flux density:
t
B
H



(7)
The correlation between equation 5, 6 and 7 refers that the time-varying magnetic field will create the electrical
field. The equation 8 may be indicated by using these two equations:
0
t
B
H
1






(8)
The vector fields are represented with first order edge elements and the scalar fields are represented with the
second order node unknowns. The current at the conductor defined as the surface may be defined in two ways:
the spirea is defined for every phase coil. The first definition neglects the eddy effects. It allows for defining the
coil parameters of generator (resistance, capacitance, inductance). Due to that the current is known at the time
when the voltage is applied, the voltage drop for the surface defined current may be calculated for i. conductor
node of current in (9) [12]:
dR)BvE(JV
)i(Rc
oiRi  
(9)
Here, J0i current density corresponds to the 1A net cycle i current and the external cycle i will disappear and
RiV is given as the voltage drop. The induced e voltage may be calculated for every Rc(i) value:
BdR.He i
Rci
i 
(10)
Here, the integration is made on all conductor area. For the three-dimensional (3D) nonlinear transient state
applications, the classical Newton-Raphson method is used [12]. In the transient analyses conducted, the
operating speed and change of primary iron losses are given in Fig. 4:

Figure 4. The speed-position change and the change of primary iron losses
No significant change was observed in the P1-S1 and P2-S1 configurations (the induced maximum
stresses were 89.3 and 91.2, respectively), despite the variation of the flux density variation given in Fig.
Because the effective magnetic flux density throughout the air gap is very close to each other. However, the
maximum induced voltage in P1-S2 was 101.7V and the maximum induced voltage in P2-S2 was 93.4V.
Figure 5. Induced voltage and phase current change according to combinations of primer and secondary
As the missing data of Secondary Steel 1020 material (W/kg) could not be obtained, only BH curve
was defined. Therefore, the change of primary losses was only calculated. The cogging force and change of
output power in accordance with the primary and secondary structures are given in Fig. 6.
Figure 6. Cogging force, output power change
As known, it is desired that the cogging force as a result of attraction force between the primary core
thread and secondary magnet shall be low without current at the coils. In order to decrease the cogging force,
some techniques (hollow/pole combination [13], final thread width setting [14], hollow type [15], pole slip [16])
are applied. These methods significantly decrease the cogging force. In order to review the effect of primary
and secondary structures, the methods were not applied in the study. The output power is 595 W for traditional
P1-S2 and 481 W for P2-S2. Due to that the structure modelled at 2D rz had same geometric structure with P2-
S2, the output power was determined as approximately equal. The secondary structure created with block
magnets led to a decrease on cogging force at the amount approximately 13% as well as that it did not
significant differences in terms of output power. In this regards, using block magnets instead of ring magnets
provides advantage. In Fig.7, the siliceous sheet and dodecagon secondary is given in order to create the
generator geometry at the structure of P1-S1 and P2-S2.

Figure 7. The image of P1-S1 and P2-S1 generator parts, respectively for prototype production
IV. Conclusion
In this paper, the effects of tubular alternator primary and secondary geometry on the output power,
cogging force and iron losses were reviewed. As distinctive from the traditional geometry, the use of block
magnets at secondary part will not change the output power. But it decreases the demagnetization of magnets as
well as that it leads to a decrease on the cogging force. The generator prototype production will be provided by
combining the secondary and traditional primary structures with block magnet which will be produced in the
future studies. The no-load and loaded experimental tests will be conducted.
References
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The Determination of Effects of Primary and Secondary Geometry of Tubular Linear Generator

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The Determination of Effects of Primary and Secondary Geometry of Tubular Linear Generator