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Leonardo Electronic Journal of Practices and Technologies
ISSN 1583-1078
Issue 23, July-December 2013
p. 19-40
Design Criteria of Tubular Linear Induction Motors and Generators:
a Prototype Realization and its Characterization
Vincenzo DI DIO1*, Giovanni CIPRIANI1, Rosario MICELI1, and Renato RIZZO2
1 DEIM – Università degli Studi di Palermo, Viale delle Scienze s.n., 90128 Palermo Italy
2 DIETI – Università degli Studi di Napoli Federico II via Claudio 21, 80125 Napoli Italy
E-mails: vincenzo.didio@unipa.it *; giovanni.cipriani@unipa.it ; rosario.miceli@unipa.it ; renato.rizzo@unina.it
* Corresponding author: Phone: 003909123860299; Fax: 0039091488452
Abstract
In this paper a mathematical model of tubular linear induction machines
(TLIM) with hollowed induced part is recalled. Moreover the design criteria
of a TLIM with hollowed iron induced part are presented as well as the
technological processes to be adopted and the choice of materials to construct
the various parts. The methodologies for mechanical assembling and electric
wiring are considered too. A prototype with bimetallic induced part has been
designed and built. Finally some experimental results on electrical and
mechanical variables, when the machines are used as motors, are shown.
Keywords
Linear machines; Cylindrical coordinates; Mathematical model; Tubular
induction motors; Tubular induction generators; Lamination.
Introduction
Efficient energy consumption is a key factor to Europe’s ambitious goals for
sustainable development and activities related to air pollution and climate shifting.
In order to tackle the increasing electricity demand, a number of solutions for efficient
19 http://lejpt.academicdirect.org
Design Criteria of Tubular Linear Induction Motors and Generators: a Prototype Realization and its Characterization
Vincenzo DI DIO, Giovanni CIPRIANI, Rosario MICELI, Renato RIZZO
energy consumption, generation of energy from renewable sources, and new power
distribution business models for active energy control have been considered and some of them
have been even pushed via regulations in national and European level.
Since photovoltaic (PV) installed power increases all over the world, solar technology
is now strongly present in the electricity market, and it cannot be seen only as a vision of the
future. As solar energy is one of the most abundant free sources in nature, the generation of
electrical energy, compared with other counterparts, is effectively convenient, in particular in
countries of the Mediterranean area, for the greater part of the year. PV generation systems
are actually available in different power sizes covering the range from domestic applications
to large power generation plants [1-6].
Many different improvements have been proposed and experimented to enhance
efficiency not only in energy conversion (PV fields) but also in energy management (power
converters). In recent times, multi-level inverters such as H bridge multi-cell cascaded
inverter, Neutral Point Clamped (NPC) and Active Point Clamped (APC) have also been used
for a more efficient and effective PV power conversion. Many inverter topologies have been
patented, within the market development, to solve some common problems of the PV plants
such as leakage currents due to parasitic capacitance of the panel and efficiency losses due to
the transfer of reactive energy between the grid filters and the DC bus capacitor. Moreover,
some particular topologies have been conceived for the fault tolerant operation of PV plants [7-9].
In renewable energy sources state of the art an important role is now played from sea
electric energies generators [10-11], one of the most interesting is the direct generation with a
tubular linear generator.
In this paper the design of a tubular linear induction machine is presented because
from this theory the dual generator machines can be in a simple way developed [12-13].
In tubular linear machine the magnetic flux flows, from pole to pole, along the
direction of the motion, crossing the air-gap in radial direction [14-15]. The cross-section of a
tubular machine is not always circular, but can have the shape of regular polygon (square,
hexagon, etc.) [16-17].
The most used configurations are those in which the cross-section is square or
circular; in this case the machine is called cylindrical. The most used structure has a short
inductor which is fixed to a basement, while, the induced part, usually longer than the
inductor, is the moving one.
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Leonardo Electronic Journal of Practices and Technologies
ISSN 1583-1078
Issue 23, July-December 2013
p. 19-40
The lamination of the inductor can be either longitudinal or transversal with respect to
the direction of motion. In case of transversal lamination the magnetic core of the inductor is
composed of one block in which each sheet has a crown shape or of more blocks in which
each sheet has the shape of a crown sector. The main disadvantage of longitudinal lamination
is the difficulty to align the sheets of each core with precision, because of their length. The
main disadvantage of transversal lamination is the thickness between the sheets which
increases the reluctance of the magnetic circuit [18].
The aim of this research was focused on a 3-phase machine with circular cross-
section, with short inductor fixed to a basement whose core (one block) has a transversal
lamination and a hollowed long induced part, as a moving part.
The Mathematical Model and the Design Criteria of TLIM's
In this section, a mathematical model in cylindrical coordinates of a TLIM (used as
motors) with a hollowed induced part depending on electrical, magnetic and geometrical
parameters in cylindrical coordinates (just suggested by the geometry of the tubular motor) is
recalled. Such construction criteria of the induced part is much more preferred in comparison
to those with full induced part, considering that the contribution to the thrust due to the
elementary volume of the induced part has large values in the part of the cylinder close to the
external surface [18-20]. The scheme of an indefinitely long tubular linear induction motor
with go air-gap, re and ri respectively outer and inner radius of induced part is represented in
figure 1.
Figure 1. Schematic outline of an indefinitely long TLIM
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Design Criteria of Tubular Linear Induction Motors and Generators: a Prototype Realization and its Characterization
Vincenzo DI DIO, Giovanni CIPRIANI, Rosario MICELI, Renato RIZZO
Some simplifying hypotheses have been made in expanding the mathematical model:
at first, the magnetic field is assumed radial and uniform along all the air-gap, then, the
magnetic saturation of the inductor and the iron cores of the induced part has been neglected,
finally the inductor is thought as being a cylindrical sheet so that it is possible to obtain a
sinusoidal magnetic field waveform along the air-gap [18].
The mathematical model considers the generalised form of the Ohm's equation, the
Maxwell's equations and the definition of the vector magnetic potential (because the magnetic
field is solenoidal), obtaining the following vector set of equations:
[ ]BVE ∧+σ=ℑ (1)
ℑ=Hrot (2)
tBErot∂∂
−= (3)
ArotH = (4)
where ℑ = surface density current, σ = electric conductivity, E = electric field, V = linear
velocity, B = magnetic induction, H = intensity of magnetic field, A = vectorial magnetic
potential.
Hence the equation of distribution of the vector magnetic potential is obtained:
⎥⎦
⎤⎢⎣
⎡∧−
∂∂
μσ=∇ ArotVtAA2
(5)
where µ = absolute permeability.
From this last equation, the cylindrical symmetry of the tubular motor suggests the
following solving vector function:
( ) ( ) ( )kztjerAt,z,rA −ωϕ= (6)
where r, z, φ = the variables of a cylindrical coordinate system and k is the propagation
coefficient of the synchronous wave defined starting from the electric pulsation:
sV/k ω= (7)
where ω = synchronous wave defined starting from the electric pulsation, Vs = the
synchronous linear velocity.
Then the vector differential equation of distribution of the vector magnetic potential is
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Leonardo Electronic Journal of Practices and Technologies
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p. 19-40
obtained:
0Ar1ja
rA
r1
rA
22
2
2
=⎟⎠⎞
⎜⎝⎛ +−
∂∂
+∂∂
(8)
where j = imaginary unit,
( )ωμσ=α s (9)
where s = motor slip.
The solving vector function is:
( ) ( ) ( )[ ] ( )kztj2/112
2/111 erjKCrjICrA −ω⋅α⋅+⋅α⋅ϕ= (10)
where I and K are modified Bessel function respectively of first and second kind.
The constants C1 and C2 can be determined using the above hypotheses and recalling
the properties of conservation of the vector magnetic field at the surface of separation
between two media with different permeability.
Bearing in mind the Maxwell's equations, the final expression of the magnetic
induction vector is as follows:
( ) ( ) ( ) ( )( ) ( ) ( ) ( )
( )kztjM
i2/1
1e2/1
1e2/1
1i2/1
1
2/11i
2/11
2/11i
2/11 eB
rjKrjIrjKrjIrjIrjKrjKrjIrB −ω⎥⎦
⎤⎢⎣
⎡⋅α⋅⋅⋅α⋅−⋅α⋅⋅⋅α⋅⋅α⋅⋅⋅α⋅−⋅α⋅⋅⋅α⋅
= (11)
The thrust developed by a tubular motor is determined from the electromagnetic force
per unit volume of the induced part, fe, as defined by the formula:
[ ]2
BRef*
e⋅ℑ
= (12)
where *B = the complex conjugate of the radial component of the magnetic induction in the
induced part of the machines.
This, after some mathematical simplifications, can be simplified to the following
expression:
( )[ ] ( )[ ]( )[ ] ( )[ ]ieie
iies2M
err028.81cosrr2cosh
rr028.81cosrr2coshr
srVB21f
−α−−α
−α−−ασ=
(13)
The integral of this force per unit volume between the inner and the outer volume
provides the thrust developed by the motor:
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Design Criteria of Tubular Linear Induction Motors and Generators: a Prototype Realization and its Characterization
Vincenzo DI DIO, Giovanni CIPRIANI, Rosario MICELI, Renato RIZZO
∫ ⋅⋅π=τe
i
r
re drrfl2
(14)
where l = the length of the machine.
After other simplifications, the final expression of the thrust, T, is obtained [18]:
[ ]d2tanh2
srVlBT es2M α⋅α
σπ≅
(15)
where d = the induced sheet thickness.
From eq. (15), the design criteria, which are shown in the following, have been
developed.
After choosing the synchronous speed of the motor to be designed on the basis of the
specific application, after fixing the air-gap flux density to a maximum value that is typical
for linear electric machines, after fixing the supply frequency, a set of curves (figure 2), which
gives the thrust divided by the length of the inductor vs. the external radius of the induced
part, is obtained. Figure 2 refers to the prototype described in the following paragraph.
0 0.02 0.04 0.06 0.08 0.1 0
200
400
600
800
1000
1200
external radius [m]
T h r u s t
p.u.
of l e n g t h
[N/m]
s=0.4 mm
s=0.6 mm
s=0.7 mm
s=0.75 mm
s=0.8 mm
s=0.9 mm
S
Figure 2. Thrust in p.u. vs. external radius (parameter: slip) Vs=8 m/s, BM=0,4 Wb/m2, f=50Hz
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The thrust and the speed of the motor, as well as the kind of supply (1-phase or 3-
phase) and the value of the voltage, are fixed taking into account the application and the
mechanical performance required to the machine and also taking into account the voltage
level at the place where the machine has to work. The number of pole pairs is then fixed; thus,
after knowing the rated frequency, f, and the synchronous speed, the pole pitch and the length
of the machine are chosen on the basis of the following formulae:
τ==τ p2l;f2
Vs (16)
Thus, after fixing the length of the inductor, the external radius of the hollow irony
induced part is derived from the set of curves in figure 2. After knowing the external radius of
the irony induced part, after fixing the thickness of the air-gap between the stator teeth and the
translator, the internal radius of the inductor is fixed. The air-gap is chosen as little as possible
taking into account the constructive tolerances of the moving parts. The kind of mechanical
working, exploiting which it is possible to obtain the best precision, is the shearing under
pressure by stamp. In case of construction of only one prototype, the stamp could be too
expensive. In this case laser cutting can be used or, in order to reduce the global cost at the
expenses of a product of worse quality, numerically controlled machines can be used too. For
the construction of the iron part of the stator core some sheets, cut differently as shown in
figure 3, can be used. Figure 3 refers to the built prototype. By alternating one kind of sheets
with the other, it is possible to obtain a pack in which there is a succession of teeth and slots.
Figure 3. Sheets of the iron core
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Design Criteria of Tubular Linear Induction Motors and Generators: a Prototype Realization and its Characterization
Vincenzo DI DIO, Giovanni CIPRIANI, Rosario MICELI, Renato RIZZO
The thickness both of the teeth and the slots is due to the thickness of the sheets and to
the number of sheets of the same kind. The holes in the sheets permit the tightening of the
sheets themselves. In each hole a cut, which permits the terminals of the wiring in the slots of
the core to come out, is made.
The adopted lamination is better than the other, even if it causes an increase of the
thickness of the air-gap, because it permits a better assembling of the sheets.
The mentioned structure of the inductor, however, is worse from the point of view of
the produced heat for Joule effect in the induced part because of the circulating currents. This
aspect is not so important from the point of view of the behaviour of the motor as TLIM's
usually work with discontinuous or alternative cycles. The turns of the inductor have a
circular shape. They can be constructed as 1-layer or 2-layer windings. In case of a 2-layer
winding two concentric winding parts can be placed in each slot of the inductor. To design the
cross-section of the copper conductor of the winding, the mechanical power produced by the
motor is computed, then the input apparent power is computed, after having given typical
values to the efficiency and to the power-factor; finally the rated current is computed. For the
insulation of the different turns composing the winding, an external cover of enamel is
sufficient (double or triple layer). To determine the number of turns of each winding, the
scheme of the magnetic circuit of the machine shown in figure 4 is considered.
Figure 4. Core schematic outline of a TLIM
The dimensions of the radial paths of the magnetic circuit depend on the depth of the
slot, and therefore on the dimension of the winding to be successively determined. Therefore
one possible dimension of the depth of the slot and of the iron radial paths is fixed, after
verifying the proper positioning of the winding. After fixing the length Lf of the iron path of
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Leonardo Electronic Journal of Practices and Technologies
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the magnetic circuit, after taking into account the air-gap go, the f.m.m. of the translating
magnetic field is computed on the basis of the following formula:
00
Mf
f
M00fftrif g2BlBg2HlH.m.m.f
μ+
μ=+=
(17)
From the f.m.m. of the translating magnetic field, after knowing the current absorbed
by the motor, the number of turns for each pole pair is computed. Considering the number of
slots available in each pole and the number of turns which will be allocated in each slot, the
number of turns for each winding is computed. In order to build the insulation between each
turn and the magnetic core and among each turn in each slot, some sheet spacers can be built
and properly allocated so as to cover the surfaces of the slots; other spacers can be allocated
among the windings (Figure 5 which refers to the built prototype). After knowing the
diameter of each conductor of the turn and the thickness of the spacers, the depth and the
width of the slots are computed.
Figure 5. Constructive detail of the inductor
In particular the slot must have a width bigger than the sum of the dimensions of the
number of conductors, horizontally placed, and of the dimensions of the two spacers. The slot
is built placing one after the other some sheets of type a in figure 3; therefore the width of the
slot is an integer multiple of the thickness of the sheets. The depth of the slot must be
designed so as to allocate one or some turns and the spacers. The depth of the slot determines
also the difference between the internal radius of the sheets of a and b type (figure 3). The
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Design Criteria of Tubular Linear Induction Motors and Generators: a Prototype Realization and its Characterization
Vincenzo DI DIO, Giovanni CIPRIANI, Rosario MICELI, Renato RIZZO
computed depth of the slot must be coherent with the initial hypothesis on the dimensions of
the radial iron path of the magnetic circuit. Subsequent trials permit to achieve good results.
After knowing the length of the machine and fixing the minimum width of the slot and the
number of slots, the thickness of the teeth is computed. They will be built laying, one after the
other, some sheets of b type (figure 3). The end of the turns can be connected with one
another by using, for the allocation of the connection, the cuts present in the core. The ends
can be drawn out the core of the inductor and connected with a connection board made up of
insulating material. This solution, even if it is not so good from the industrial application
standpoint, permits the easy modification of the typology of the winding so as to be very
suitable from the point of view of experimental applications [19,21-24]. In particular it is
possible to build both 1-phase and 3-phase windings either with one layer or two layers.
Design and Construction of a TLIM Prototype with hollowed Induced Part
The prototype of the designed TLIM is 3-phase machine with rated voltage and
frequency respectively of Vn = 400V and fn = 50Hz. After choosing a synchronous speed of
Vs = 8m/s, assuming a thickness of the induced part of d = 2mm, fixing an air-gap flux
density equal to BM = 0.4Wb/m2, assuming a conductivity of the iron of the induced part of σ
= 0.15·µ·Ω/m and a iron relative permeability equal to µ = 1000, the set of curves of figure 2
is derived from (15). For the design of the motor, whose translator must have a short
movement with alternative cycles, an equivalent working condition in steady-state can be
considered even if with a large slip. The hypothesis is then that a motor has to be designed to
be able to give a thrust T = 150N with a speed V = 2m/s. The mechanical power developed in
this condition is P = 300W. If a 2 pole-pair machine must be built (p=2) the pole pitch and the
length of the machine are determined on the basis of the following relationships:
m08.0502
8f2
Vs =⋅
==τ (18)
m32.0008.022p2l =⋅⋅=τ⋅⋅= (19)
The thrust divided by the length of the inductor is then computed (which is more or
less 470N/m) and from figure 2 (characteristic with s=0.75) it can be deduced that the external
radius of the inductor must be bigger than 0.04 m. After fixing the air-gap between the stator
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Leonardo Electronic Journal of Practices and Technologies
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teeth and the translator to 0.8 mm, the internal radius of the inductor is then computed equal
to 8.16 cm. Sheets of both shapes in figure 3 have been used. The obtained lamination is then
transversal with respect to the direction of the motion. Laying one block of sheets of a type
after another of the other type, the global stator core is obtained in which there is a succession
of teeth and slots. The circular turns are placed in the slots and the connections can be made
outside the stator core. The apparent reference power is:
VA78055.07.0
300cosPA ≅
⋅=
ϕ⋅η=
(20)
Thus the reference current is:
A2.14003
780V3
AIn
≅⋅
=⋅
= (21)
with an efficiency of 0.7 and a power factor of 0.55. The conductor, chosen on the basis of the
thermal criteria and consequently on the basis of the computed current value, has a cross-
section of S = 1mm2 and it creates a concentric winding with 2 layers. The turns are allocated
in the 24 slots of the inductor. The number of slots for pole and phase is then two. The
insulation among the turns of the winding is then guaranteed by triple layer enamel. The
conductor in itself has a diameter of 1.128mm; after having applied the triple layer insulation
the diameter is then 1.3mm. To determine the number of turns of each part of winding, the
fact the magnetic circuit has two paths in air and four paths in iron (two longitudinal and two
radial) is considered. The two longitudinal iron paths are equal to the pole pitch (figure 4). A
trial-and-error method is then used under the hypothesis that the radial paths have half the
length of the longitudinal paths.
If If is the length of the iron path of the magnetic circuit then:
m24.008.0332
22lf =⋅=τ⋅=τ
+τ⋅≅ (22)
on the basis of equation (17) the f.m.m. is then computed corresponding to the translating
magnetic field:
AS5860008.021044.024.0
1044.0g2BlB.m.m.f 740
0
Mf
f
Mtrif =⋅
⋅π+
⋅π=
μ+
μ= −−
(23)
This value, considered the absorbed current, permits to compute the number of turns
for each pole pair which is then 326. As two slots for each pole are available and two different
parts winding are allocated in each slot, the number of turns for each part of winding is 40,75,
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Design Criteria of Tubular Linear Induction Motors and Generators: a Prototype Realization and its Characterization
Vincenzo DI DIO, Giovanni CIPRIANI, Rosario MICELI, Renato RIZZO
then approximated to 42. 14 layers of 3 turns each are then posed as shown in figure 5. In
particular the slot has a width (lslot) bigger than the sum of the dimensions of the conductors
together (the diameter of each one is Dc) and of the spacers (the thickness of which is Sd); then
it can be written:
mm4.575.023.13S2D3l dcslot =⋅+⋅=+> (24)
The slot is built placing one after the other some sheets of the type (figure 3) each
0.5mm thick; thus the width of the slot is an integer multiple of 0.5. In the end the slot is built
laying 11 sheets of the type which guarantee a width of 5.5 mm (figure 5). The slot depth pslot
is computed so that two windings and the spacers can be allocated; thus it can be written:
( ) ( ) mm4.3975.023.1142S2D142p dCslot =⋅+⋅⋅=+⋅> (25)
In the end the depth of the slot, which is due to the difference between the internal
radius of the a and b type, is about 4 cm (figure 3). This datum is coherent with the initial
hypothesis on the dimension of the radial iron path of the magnetic circuit. If the sheet a of
figure 3 has a depth of the crown of 3 cm, needed for the robust shutting of the core, its
external radius is about 19.2 cm.
As the length of the machine is about 0.32 m, the minimum width of slot is 5.5 mm,
the teeth have a thickness of 8 mm and they will be built laying one after the other 16 sheets
of the b type (figure 5). The terminals of the 48 parts of winding have been drawn out of the
core of the inductor and connected to an insulating basement. Figure 6 shows the scheme of
the basement and the electrical connections whilst figure 7 is its photograph. A 3-phase 2-
layer winding with the pitch reduced of 5/6 has been built.
30
Figure 6. Schematic outline of the basement and the electrical connections
Leonardo Electronic Journal of Practices and Technologies
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Figure 7. The basement and the electrical connections
Finally figure 8 shows the prototype of the TLIM built on the basis of the design here
fully explained.
Figure 8. The prototype of TLIM
Experimental Measure on the Prototype
In the following the author exposes the experimental data supplied by the prototype
and useful for the characterization. The procedures to measure electrical and mechanical data
are also explained [25-27].
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Design Criteria of Tubular Linear Induction Motors and Generators: a Prototype Realization and its Characterization
Vincenzo DI DIO, Giovanni CIPRIANI, Rosario MICELI, Renato RIZZO
Experimental Measure of the Electrical Characteristics of the TLIM
The measure of electric data, useful for characterising the motor, has been carried out
with locked and running translator. With the aid of a net analyser and three LEM's, separately
for the three phases of the motor, in the conditions of locked translator: the voltages, the
absorbed active power and currents, and the power factor have been measured. The analyser
has, besides, provided the average values and the absorbed 3-phase active power. The values
of measured electric data are shown in Table 1.
Table 1. Values of measured electric data in the conditions of locked translator Voltage
[V] Current
[A] Power factor
Power [W]
V1=224,5 8,048 0,569 1028 V2=221,8 7,690 0,577 985,4 V3=224,5 7,881 0,554 980,6 Average value - 7,873 0,554 - The absorbed 3-phase active power is 2994 W
With the aid of the LEM, in the conditions of running translator, the current absorbed
from each phase of the motor, have been measured. Figure 9 shows the currents diagram
when the motor rums with no power loading. Figure 10 shows a zoom of the same diagram of
figure 9 in the range zero to 200 ms.
Figure 9. Absorbed currents vs. time
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Figure 10. Absorbed currents vs. time (in the first transient)
From both the diagrams we can notice that initially the currents have values more
elevated than in the following. Subsequently such values increase in correspondence to a
value of abscissa equal to 1600 ms, time in which the translator has finished to run. Now the
motor is in the condition of locked translator; this explains the increase of the values of the
currents that persists till the currents die out.
Experimental Measure of the Mechanical Characteristics of the TLIM
In order to carry out the measures of the mechanical characteristics of the motor, a
mechanical system, which permits to load the motor with different calibrated weights, has
been built. A hook has been joined at the end of the translator of the motor to connect a steel
rope that, through a pulley, sustains the weights. An encoder able to acquire the rotational
speed and send the signal to the computing board, on the shaft of the pulley, has been
mounted. The illustrated system is represented in figure 11.
The measured mechanical data are the speed and the acceleration of the translator.
Figures 12-14 show the speed vs. time after having loaded mechanically the motor with
weights of values equal respectively to 3, 5 and 7 kg. Figures 15-17 show the acceleration vs.
time after having loaded mechanically the motor with weights of values equal respectively to
3, 5 and 7 kg.
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Design Criteria of Tubular Linear Induction Motors and Generators: a Prototype Realization and its Characterization
Vincenzo DI DIO, Giovanni CIPRIANI, Rosario MICELI, Renato RIZZO
Figure 11. Scheme of the linking system of the load
Figure 12. Velocity vs. time (3 kg)
Figure 13. Velocity vs. time (5 kg)
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Figure 14. Velocity vs. time (7 kg)
Figure 15. Acceleration vs. time (3 kg)
Figure 16. Acceleration vs. time (5 kg)
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Design Criteria of Tubular Linear Induction Motors and Generators: a Prototype Realization and its Characterization
Vincenzo DI DIO, Giovanni CIPRIANI, Rosario MICELI, Renato RIZZO
Figure 17. Acceleration vs. time (7 kg)
Another investigation, on the prototype of TLIM, has focused on determining the
start-up thrust. So the motor has been submitted to a number of starting tests with increasing
load forces. The experimental results permits to estimate a start-up thrust of 115 N (maximum
load at which the motor is still able to start).
Conclusions
This paper, after describing some useful tools for designing hollowed tubular linear
induction machines, recalls a particularly suitable mathematical model: moreover an
experimental prototype has been built and tested. By the study of the experimental curves it
can be deduced that tubular linear induction motors with hollowed induced part produce a
high start-up thrust and an excellent mechanical characteristic more or less linear in the first
part and then decreasing. This kind of characteristics makes them particularly suitable for
such industrial applications as press, solenoid valves, robot linear axles, electric switches,
alternative compressors, liquid metal pumps, and hammers.
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Acknowledgements
Paper supported by the contribution of SDES (Sustainable Development and Energy
Savings) Laboratory at University of Palermo - D.E.I.M. department.
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