Download - linear engine motor
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
Starting of a Free-Piston Linear Engine-Generator
by Mechanical Resonance and Rectangular
Current Commutation
Saiful A. Zulkifli*, Mohd N. Karsiti** and A. Rashid A. Aziz◊
Universiti Teknologi PETRONAS, Bandar Sri Iskandar, Malaysia
Email: *[email protected] **[email protected] ◊ [email protected]
Abstract—Starting a free-piston linear engine-generator
(LG) involves reciprocating a freely moving piston-magnet-
translator assembly between two oppositely placed engine
cylinders for combustion to occur. The machine is operated
as a brushless linear motor to produce the required motion.
However, due to the very large peak compression force
during starting, limited current rating of stator coils and
insufficient motor force constant, it is not possible to push
the translator end to end in a single stroke. A strategy is
proposed which utilizes the air-spring quality of the engine
cylinders prior to combustion. Energizing the coils with
fixed DC voltage and open-loop, rectangular commutation
of injected current, sufficiently high motoring force is
produced to reciprocate the translator in small amplitudes
initially. Due to repeated compression-expansion of the
engine cylinders and constant application of motoring force
in the direction of natural bouncing motion, the translator’s
amplitude and speed is expected to grow - due to mechanical
resonance - to finally reach the required parameters for
combustion. This work discusses the starting problem and
its mechanical aspects for a specific LG configuration,
builds a mechanical model of LG and presents simulation
results on the viability of the starting strategy using
different values of constant-magnitude motoring force.
Keywords—Free-Piston Linear Engine; Linear Electric
Generator; Linear Generator Starting; Rectangular
Commutation; Permanent-Magnet Brushless Motor
I. INTRODUCTION
A free-piston, linearly reciprocating internal
combustion engine offers many advantages over the
conventional crank-slider engine. Benefits include
improved efficiency, higher power-to-weight ratio and
multiple fuel capability [1]-[4]. When the linear engine is
made as platform to convert mechanical to electrical
energy through a particular arrangement with a linear
generator, the end product - a free-piston linear engine-
generator - is a potential alternative to conventional
rotary generators, as on-board power house in series-
hybrid electric vehicles (S-HEV) or as portable power
generators for commercial and domestic use.
This research work was supported by the Ministry of Science,
Technology and Innovation (MOSTI), Malaysia under IRPA grant 03-
99-02-0001 PR0025/04-01.
One critical task in the operation of the linear machine
is the initial process of starting the engine. A linear
engine cannot be started by an ordinary starter motor
since it has no flywheel, crankshaft or any mechanical
coupling which can accept the rotating push of the starter
motor. The starting method must utilize some form of
linear mechanism that uses available stored energy to
reciprocate the LG at the required starting speed (200-400
cycles per minute.) A possible approach is to use
compressed air, along with appropriate control valves and
control strategy to produce the required motion [5], [6].
However, unless the application of the linear engine is as
an air compressor, this starting method would require
having a separate auxiliary compressor system, which
will add complexity and cost to the system.
For linear engines designed as prime mover for
electricity generation, a practical starting method is to
energize the LG electrically: using stored electrical
energy and an effective control strategy, the LG is run as
a linear motor to produce the required reciprocating
motion. Some research work on linear engine-generators
have mentioned employing this starting method,
consisting of either electrical motoring only [1], [4] or
mechanically assisted by other inherent mechanism such
as a resonating spring-mass system [7]. However,
detailed investigation on the starting process has not been
reported, as most of the research work concentrate on
design, simulation or analysis of the linear machine in
steady-state operation. Criticality of implementing an
effective starting strategy is nevertheless acknowledged
[1]-[3], [8].
Figure 1. LG cross-section showing major components
Translator
Shaft
Permanent
Magnets &
Back Iron
Scavenge
Chamber
Piston
Cylinder
Head
Cylinder
Block
Engine
Mounting
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
II. STARTING OF LINEAR GENERATOR
Starting process of any internal combustion engine
requires optimum piston speed and engine compression
pressure. In a conventional engine whose constrained
motion ensures the same piston top dead centre (TDC)
position in every cycle, the starting system needs only to
ensure that the optimum speed is achieved, since the
resultant compression pressure is related to TDC and the
TDC is fixed. In contrast, in a free-piston linear engine,
piston motion is not kinematically constrained, but
dynamically coupled to combustion pressures and forces
[1]-[3]. Thus, the translator - the single-moving part
consisting of a straight shaft carrying permanent magnets
in the center and connected to pistons at both ends (Fig. 1)
- does not follow a fixed displacement profile and has no
fixed TDC. In addition to optimum speed to ensure
effective scavenging of air and fuel mixture, the
translator’s amplitude in a free-piston engine needs to be
regulated to achieve sufficient compression pressure.
Another key difference between conventional and
linear engines lies in the delivery of the starting force.
The major force that the piston needs to overcome is
compression force, which is due to pressure build-up in
the cylinder after the exhaust port closes. During starting,
the crankshaft of a conventional engine turns as the
flywheel is turned by the starter motor, whose pinion is
engaged with the flywheel’s teeth. Thus, a certain torque
is required to turn the crankshaft and push the piston up
into the cylinder; which is provided by the starter motor.
Due to the crank-slider configuration, large flywheel
diameter and gear action, a relatively low torque is
required of the starter motor, so that magnitude of the
force required to overcome compression and crank the
engine is shrunk to a fraction of the compression force.
The bigger the flywheel radius, the smaller is the torque
and force required for cranking1.
In contrast, there is no crank-slider configuration or
gear action in a linear engine. The required starting force
is applied directly in the direction of linear motion,
opposite the resistive compression force. There is no
mechanism which reduces the required starting force
(dominated by compression), so the entire force must be
provided by the starting system. In the case of LG, whose
piston diameter is 76 mm, the resultant compression force
has a peak in the order of 5 kiloNewtons. This is way
beyond the maximum motor force that can be supplied by
the present design of LG, determined by its motor
constant (24.2 N/A maximum, using six-step
commutation: two phases energized at one time) and the
coils’ current capacity (34 Amps maximum continuous
rating.) Considering the peak compression force of 5 kN,
a peak current of 200 Amperes would be required2. Thus,
a strategy needs to be devised which could nevertheless
1 Since power is torque multiplied by angular speed, the starter
motor’s speed is much higher than the engine’s cranking speed, so that
power is conserved (power in = power out) 2A full dynamic analysis of LG starting is given in [12]
utilize a lower-magnitude motoring force to produce the
required reciprocating motion for starting.
III. PROPOSED STARTING STRATEGY
A plausible method to start the LG is proposed, which
consists of two basic principles: 1) mechanical resonance
via reciprocation and 2) electrical motoring via
rectangular current commutation.
A. Mechanical Resonance via Reciprocation
In the absence of combustion, engine cylinders exhibit
an air-spring behavior, so that at sufficient piston speed,
air inside the cylinder is compressed and expands as the
piston moves into and out of the cylinder, absorbing and
dissipating energy respectively. Thus, the cylinders act
just like ordinary mechanical springs, capable of storing
and delivering energy within one cycle, effectively
creating a bounce phenomenon at each end of the stroke
[5], [7]. Fig. 2 shows how the dual-opposed cylinder
configuration of LG can be likened to a spring-mass-
spring system: a mass in the center sandwiched by two
springs attached to a fixed reference.
Thus, if very little energy is lost in the bounce process,
it is possible to apply motoring force of low but sufficient
magnitude to reciprocate the piston assembly in small
amplitudes initially. Over time, its amplitude and speed
will grow - due to resonance - to achieve the final
required stroke length (69mm), speed (3-5 Hz cyclic
frequency) and compression pressure (about 7-9 bars).
However, there is one fundamental problem: at low
starting speeds, the air-spring characteristic of an engine
cylinder is heavily affected by the piston’s speed [1], [5].
This is due to air leakage around the piston rings, referred
to as piston blow-by. The slower the piston speed, the
more is the quantity of air that leaks through, so that it
becomes possible to push the piston assembly by hand
from end to end (which will occur very slowly, due to the
large compression force).
This is in contrast to ordinary mechanical springs,
whose spring force depends on displacement only and not
on the speed of the moving mass. For LG, the
dependence on piston speed due to piston blow-by affects
the cylinders’ effectiveness to absorb and release energy
during the reciprocation process.
Figure 2. Spring-mass representation and mechanical resonance process
m
Fmotoring
Non-linear air-spring nature of engine
cylinders prior to combustion
Translator mass
(piston, shaft
& magnets)
Electromagnetic motor force always provided in the direction of natural
bouncing motion can effectuate mechanical resonance for LG starting
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
Thus, the lower the starting push of the motoring force,
the lower is the piston velocity and the less effective is
the bounce process as more energy is lost during the
bounce. Even at the final required starting frequency of 3
to 5 Hz, the piston is still operating in the low-speed
region where compression-expansion process is much
affected by speed. Effectiveness of the air-spring property
is a very important concern in the present investigation.
B. Electrical Motoring via Rectangular Current
Commutation
To provide for the force to reciprocate the piston
assembly, LG is operated as a brushless, permanent-
magnet linear motor. Essentially, current is injected into
the stator coils which create a magnetic field whose
strength is proportionate to the level of the injected
current. The resultant magnetic field interacts with the
existing magnetic field of the permanent magnets to
create a mechanical motor force, which will push on the
translator shaft in a certain magnitude and linear direction
depending on the relative position of the permanent
magnets with respect to the fixed stator coils. Fig. 3
shows a schematic of this motor force phenomenon.
This relative position is critical to the effective
motoring of LG, as interaction between the two fields is
different at different positions along the stroke. Injecting
a fixed level of current at different positions creates a
force that varies not only in magnitude but also direction.
Thus, inappropriate current injection will result in un-
optimized motoring force and in the worst case, force in
the wrong direction, opposing translator’s motion. This is
the problem of commutation - knowing exactly when and
where and to which coils current should be injected - and
is the other area of concern of this starting investigation.
C. Research Objectives and Methodology
This research investigates feasibility and effectiveness
of mechanical resonating strategy and rectangular current
commutation to start a certain LG configuration. It
consists of modeling, simulating and implementing the
proposed strategy using fixed DC bus voltage and two
variants of rectangular commutation: 6-step and square-
wave. The LG prototype under investigation (Fig. 4) is a
5-kW linear machine designed and developed by
Universiti Teknologi PETRONAS (UTP), in collaboration
with two other universities: Universiti Malaya (UM) and
Universiti Kebangsaan Malaysia (UKM).
Figure 3. Interaction of magnetic fields to produce linear motoring
force (reprinted and modified from UM Report, 2005)
Figure 4. UTP Linear Generator prototype
Simulation of LG starting is implemented on Matlab
Simulink, with the following motivation: inability to
solve LG dynamic equation in closed algebraic form and
ease in adjusting various system parameters to analyze
and predict system behavior. In addition, due to hardware
limitation and safety reasons, some experimentation runs
are not possible and this is where simulation is beneficial.
For modeling and simulation objective, the LG system
can be decomposed into mechanical and electrical
subsystems. To ensure validity and reliability of
simulation results, the component subsystem models need
to be validated and verified against field experimentation,
which takes place in the LG laboratory at UTP (Fig. 5).
Both data acquisition and controls are implemented on a
common hardware and software platform: National
Instruments’ PXI embedded controller and LabView
Real-Time software.
IV. MECHANICAL SUBSYSTEM MODELING
Mechanical modeling of LG requires identifying the
mechanical forces and setting up a dynamic mechanical
equation. In this initial stage, motoring force appears as
just another mechanical force contributing to the total net
force; thus, electrical current injection responsible for
creating the force is not considered.
A. LG Mechanical Forces
During starting and in the absence of combustion, the
translator is subject to the following forces, neglecting
vibration, as it moves from the right end to the left end of
the stroke (Cylinder 1 TDC to Cylinder 2 TDC) :
Figure 5. LG control room with view of 5-kW LG
Translator
Shaft
Stator
Coils
Stator Iron
Laminations
Current Direction:
Into Plane of Paper
Field Direction:
Downwards
Resultant
Motor
Force
Permanent
Magnets
Right
Scavenge
Chamber Right
Engine
Cylinder Stator
Iron and
Coils
Linear
Displacement
Encoder
Left
Engine
Cylinder
Inside:
Permanent
Magnets on
Linear
Translator
Left
Scavenge
Chamber
5-kW Linear Generator Prototype
PXI Embedded Controller & Data
Acquisition System
Instrument Driver Board
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
Figure 6. LG free-body diagram
1. Compression force Fcompression of Cylinder 2,
opposing translator motion
2. Expansion force Fexpansion (suction force for the initial
stroke) of Cylinder 1, assisting translator motion
(opposing for the initial stroke)
3. Friction forces f between piston ring and cylinder
liner and between translator shaft and linear bearing
4. Magnetic cogging force Fcogging pushing or pulling on
the translator
5. Electrical motoring force Fmotoring which should be in
the same direction as translator motion in order to
effectuate a successful resonating strategy
Fig. 6 shows a simplified free-body diagram indicating
the above translational forces. Fig. 7 shows a schematic
diagram indicating the intake and exhaust ports and a
graph of the mechanical forces against displacement, for
the 69-mm total stroke length.
Compression and expansion forces arise from air
pressure acting on the piston surface, which develop
within the combustion chambers with the inward and
outward motion of the translator. Magnetic cogging force
results from static interaction between the permanent
magnets’ magnetic field and the iron-cored stator.
Depending on translator position, it may be positive or
negative, thus assisting or resisting translator motion. Fig.
8 shows cogging force over the entire stroke, obtained via
finite-element analysis performed by the Universiti
Malaya team. Due to symmetry of LG design, it can be
seen that the profile is symmetrical with respect to the
reference center position. It has zero values at certain
positions of the stroke, around which are probable and
stable rest positions in the absence of external force.
Instantaneous values of friction force cannot be obtained
accurately, due to hardware limitation. For the purpose of
the present analysis, a fixed value of 200 N is used,
acquired from a relatively simple but reliable set of
experiments. Adjustments to this value are made in the
later stages of validation and analysis.
Cogging and friction are static forces with no
dependency on translator speed, while compression and
expansion forces are dynamic, with a heavy speed
dependency below certain cyclic speeds. For an ideal gas,
both compression and expansion processes are governed
by the same relationship between pressure and volume
inside the engine cylinder when the exhaust port is closed: kk
VPVP 2211 = , (1)
where P is pressure, V is volume and subscripts 1 and 2
denote instantaneous values of pressure or volume at
different times or displacements. The constant k is the
adiabatic constant of the medium undergoing the
compression-expansion process - air in the present case -
and has different values for different gases3 [1], [5].
Consider the case in which one cylinder is compressed
while the other cylinder’s exhaust port is already open.
Assume that the resultant compression pressure acting on
the piston’s surface is uniform across the piston’s surface
area and can thus be taken as a one-dimensional function
of displacement. We thus obtain the following equation
for the cylinder undergoing compression [1], [8]: k
ncompressiolx
KKxF
+
⋅=2
1)( , (2)
where K1 and K2 are constants determined by atmospheric
pressure, piston surface area and cylinder trapped volume.
Parameter l is the equivalent crevice length of the
cylinder head and is thus another system constant, while x
is the instantaneous piston distance from TDC and is the
only variable in the equation. Derivation for the cylinder
undergoing expansion results in a similar equation: k
ansionlx
KKxF
+
⋅=4
3exp )( . (3)
Figure 7. LG schematic and mechanical forces vs. displacement
Figure 8. Magnetic cogging force
3 Several factors affect slightly the value of k, which are assumed
negligible and thus ignored in the present analysis and modeling of LG.
The constant value of k used in this study is 1.38
Magnetic Cogging Force vs Displacement
-300
-200
-100
0
100
200
300
-35 -30 -25 -20 -10 -5 0 5 10 15 20 25 30 35
Displacement (mm)
Force (N)
CCooggggiinngg
FFoorrccee
CCYYLLIINNDDEERR 11
EExxhhaauusstt PPoorrtt
IInnttaakkee PPoorrtt CCYYLLIINNDDEERR 22
IInnttaakkee PPoorrtt
EExxhhaauusstt PPoorrtt
-500
0
500
1000
1500
2000
2500
3000
3500
-34 -30 -26 -22 -18 -14 -10 -6 -2 2 6 10 14 18 22 26 30 34
TDC 2 TDC 1
OOvveerrllaapp
RReeggiioonn
CCyylliinnddeerr 22
CCoommpprreessssiioonn
FFoorrccee
Exhaust Port 2
Exhaust Port 1
Force
(N)
CCyylliinnddeerr 11
EExxppaannssiioonn
FFoorrccee
FFrriiccttiioonn
FFoorrccee
CCooggggiinngg
FFoorrccee
OOvveerrllaapp
RReeggiioonn
Expansion,
Motoring,
Cogging
Friction,
Compression,
Cogging x
m
Piston 1 Piston 2
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
From the expressions of Fcompression and Fexpansion above,
the non-linearity of these forces with respect to
displacement is apparent. However, the above equation
holds for an adiabatic and isentropic process in which no
heat or mass is gained or lost. In the present system
which involves piston rings, air compression-expansion
inside engine cylinders cannot be taken as isentropic
because at low operating speeds, it is not a strictly closed
system. This is due to the piston blow-by mentioned
above: air leakage through the piston rings from the
higher-pressured to the lower-pressured region, which
should otherwise be completely isolated from one another
by the piston rings. Thus, the ideal relationship above is
not sufficient for the present modeling of LG during
starting. An improved compression-expansion model has
been developed 4, which incorporates an air mass transfer
algorithm to account for the air leakage.
This improved model has been correlated and validated
with experimental data. Fig. 9 shows simulation results of
the final validated model, compared to experimental data
of cranking the LG at 440 cycles/minute, along with the
ideal case without leakage. The improved model shows a
difference (reduction) of 28 % in compression pressure
compared to the ideal case. Since force is pressure
multiplied by piston area, this reduction translates to a
difference of more than 2 kN. Thus, if leakage were not
accounted for, simulation results would be invalid.
B. LG Dynamic Equation
For a dynamic mechanical equation of LG during
starting, Newton’s second law of motion is used. Let m
be the total mass of the translator (shaft, pistons and
magnets) and a its acceleration, we thus have:
2
2
dt
xdmmaF xx ==∑ . (4)
During starting, motion is possible along a single axis
only (x), ignoring vibration along the other axes.
Incorporating the mechanical forces above, we therefore
have the following equation to represent LG during
starting, for motion from TDC 2 to TDC 1 (Fig. 7):
Figure 9. Comparison between experimental data, ideal model and
improved compression-expansion model
4 Improved compression-expansion model was developed by Abdul
Rashid Abdul Aziz and Syaifuddin Mohd of UTP
2
2
dt
xdmmaF xx ==∑
fFFFF cogcompmot −−−+= exp
fxFxFxFxF cogcompmot −−−+= )()()()( exp (5)
Fmot (x) represents motoring force resulting from current
injection into the LG coils. If we let the motoring force to
be constant-magnitude, we have Fmot (x) = Fmot. From (2)
and (3), assuming adiabatic and isentropic process and x
= 0 at TDC 2 (Fig. 8), Fcomp(x) and Fexp(x) are given by:
k
complx
KKxF
+
⋅=2
1)( (6)
k
lxL
KKxF
+−
⋅=4
3exp )( (7)
where K1, K2, K3, K4 and l are all system constants, and so
is L, which is the total stroke length from TDC2 to TDC1.
Thus, the dynamic equation for LG becomes:
2
2
exp )()()(dt
xdmfxFxFxFF cogcompmot =−−−+ (8)
2
2
21
43 )(
dt
xdmfxF
lx
KK
lxL
KKF cog
kk
mot =−−
+
⋅−
+−
⋅+ (9)
Considering non-linearity of Fcog (x), k
complx
KKxF
+
⋅=2
1)( and k
lxL
KKxF
+−
⋅=4
3exp )( , it is
not possible to solve the above equation for x in closed
algebraic form; even worse if velocity dependency of
compression-expansion due to air leakage is incorporated
into the Fcomp (x) and Fexp (x) terms and if the motoring
force is not constant but having some relation to other
system parameters.
V. DETERMINATION OF STARTING FORCE AND SIMULATION
WITH CONSTANT-MAGNITUDE MOTORING FORCE
LG dynamic equation (8) is incorporated in a
simulation program implemented in Matlab Simulink
(Fig. 10), with two objectives. The first objective is to
determine the required starting force profile, as a function
of displacement, to push the translator assembly from one
end to the other, in a single stroke. The effect of speed on
piston ring leakage and thus compression-expansion force
and required starting force can also be assessed. The
desired motion profile (displacement vs. time) is input of
the simulation. The program then generates the required
profiles of velocity, acceleration and net effective force.
Through summation of forces, the final required starting
force profile can then be extracted, as reflected below:
fxFxFxFdt
xdmxF cogcomprequiredstarting +++−= )()()()( exp2
2
_ (10)
Volume (cc)
Engine Compression Pressure vs. Volume
0
2
4
6
8
10
12
14
16
18
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Pressure (Bar)
Experimental Data Ideal (No leakage) Improved Model with Leakage
Experimental
Improved
Model
Ideal
Model
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
Figure 10. Matlab Simulink program to determine starting force profile
Figure 11. Program to investigate mechanical resonating strategy
Desired Displacement Profile (Displacement vs Time)
-40
-30
-20
-10
0
10
20
30
40
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (s)
Dis
pla
ce
me
nt
(mm
)
0.125-s Stroke (4 Hz or 240 rpm)
0.25-s Stroke (2 Hz or 120 rpm)
0.5-s Stroke (1 Hz or 60 rpm)
5-s Stroke (0.1 Hz or 6 rpm)
Engine Compression Force vs Displacement
-1000
0
1000
2000
3000
4000
5000
6000
-40 -30 -20 -10 0 10 20 30 40
Displacement (mm)
Fo
rce
(N
)
0.125-s Stroke (4 Hz or 240 rpm)
0.25-s Stroke (2 Hz or 120 rpm)
0.5-s Stroke (1 Hz or 60 rpm)
5-s Stroke (0.1 Hz or 6 rpm)
Required Motoring Force vs Displacement
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
-40 -30 -20 -10 0 10 20 30 40
Displacement (mm)
Fo
rce
(N
)
0.125-s Stroke (4 Hz or 240 rpm)
0.25-s Stroke (2 Hz or 120 rpm)
0.5-s Stroke (1 Hz or 60 rpm)
5-s Stroke (0.1 Hz or 6 rpm)
Figure 12. Desired displacement profiles for 4 starting speeds, engine compression force vs. displacement and required starting force vs. displacement
Fig. 12 (leftmost) shows four desired displacement
profiles against time representing the starting speeds of 6,
60, 120 and 240 cycles per minute. The middle and
rightmost graphs show simulation results of engine
compression force and required starting force
respectively. It is observed that the higher the starting
speed, the larger is the required starting force, due to
larger resultant compression force of the engine cylinder.
This proves significance of speed dependency on piston
ring leakage and blow-by phenomenon. Compression
force is seen to dominate not long after the exhaust port
closes, for all starting force profiles, since compression
force is up to 7 times higher than all other forces
combined (Fig. 8). For a 240-cpm (4-Hz) starting speed,
the required starting force has a peak value exceeding 5
kiloNewtons.
The second simulation objective is to investigate
viability of the proposed resonating strategy to start the
LG, by using constant-magnitude motoring force. The
previous simulation program is rearranged so that the
graphical order of the simulation blocks (Fig. 11) follows
the same order as LG dynamic equation (8). Although
motoring force is produced by electrical current injection,
it is still considered at this stage as just another
mechanical force. It is provided by a subsystem block
that produces constant force with velocity detection
(zero-crossing detector) to ensure that the applied force is
always in the same direction as piston motion. Fig. 13
shows simulation results using different magnitudes of
motor force: 400N, 350N, 300N and 280N.
It is observed that for all force values, the cyclic
frequency when the translator reaches the required
amplitude is the same, around 25 Hz. Since the LG
system during starting is much like a resonating spring-
mass system, this could very well be its resonant
frequency. Although there exist cogging and friction
forces, compression force dominates after several cycles
so that their spring-like property - although non-linear
and velocity-dependent - characterizes the LG system.
Similar to a spring-mass system with an external forcing
function, the different motoring force magnitudes in the
starting of LG affect the initial piston speeds, the length
of time and the number of cycles before the final required
amplitude and cyclic frequency are reached. The 25-Hz
resonant frequency could not have been obtained
analytically from LG dynamic equation, proving a benefit
of the above dynamic simulation.
After inclusion of the electrical subsystem model of
LG, the proposed strategy will be further investigated
through experimental validation of both electrical and
mechanical models using low excitation energy (low DC
bus voltage) in motionless coil energization tests and
single-stroke motoring tests without compression. Further
experimentation and simulation will be implemented with
higher DC bus voltage (multiple batteries) to validate the
compression model and the final integrated LG model.
Throughout this process, analysis of experimental and
simulation results will be carried out to interpret and
understand system behavior under different motoring
conditions and to analyze system response to rectangular
current commutation. Extensive experimentation and
simulation results, validation details, model refinement
and system analysis are provided in [12].
Ultimately, the system is designed to operate as a
linear generator as well as motor. When functioning as a
generator, it is expected to have sufficient output to drive
0.1 Hz
4 Hz 2 Hz 1 Hz
4 Hz
2 Hz
1 Hz
0.1 Hz
4 Hz
2 Hz
1 Hz
0.1 Hz
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
the vehicle with sufficient energy left over to also
recharge the battery pack. The current work focuses on
the issue of starting problem, which is considered as part
of the transient response, while the study on the
recharging aspect of the system is part of the steady-state
response, which is beyond the scope of the current work.
VI. CONCLUSION
This paper has presented the starting problem of a
specific configuration of the free-piston linear engine-
generator (LG). A strategy is proposed that employs the
air-spring character of the engine cylinders prior to
combustion and mechanical resonance to reciprocate the
translator up to the required amplitude. Characterization
and modeling of the mechanical subsystem of LG are
provided. An improved compression-expansion model
incorporating piston blow-by shows a 28% difference in
compression pressure from the ideal model. Mechanical
simulation is implemented to determine the required
starting force profile and to assess the effect of speed, due
to piston blow-by, on the compression-expansion force
and the required starting force. Simulation results show
that if a sufficiently large, fixed-magnitude force is
constantly applied on the translator in the direction of
motion, the system can be reciprocated and resonated to
the full required amplitude of 34.5 mm, although at a
much higher-than-required final frequency of 25 Hz,
confirming viability of the proposed starting strategy.
ACKNOWLEDGMENT
Contributions from the following persons are highly
appreciated: Dr. Khalid Nor of Universiti Teknologi
Malaysia, Dr. Hamzah Arof and Dr. Hew Wooi Ping of
Universiti Malaya, Syaifuddin Mohd of UTP and LG
project team members from UTP, UM and UKM.
REFERENCES
[1] Aichlmayr, H.T., “Design Considerations, Modeling and Analysis of Micro-Homogeneous Charge Compression Ignition Combustion Free-Piston Engines,” Ph.D. Thesis, University of Minnesota, 2002.
[2] Arshad, W.M., “A Low-Leakage Linear Transverse-Flux Machine for a Free-Piston Generator,” Ph.D. Thesis, Royal Institute of Technology, Stockholm, 2003.
[3] Cawthorne, W.R., “Optimization of a Brushless Permanent Magnet Linear Alternator for Use With a Linear Internal Combustion Engine,” Ph.D. Thesis. West Virginia University, Morgontown, 1999.
[4] Nemecek, P., Sindelka, M. and Vysoky, O., “Modeling and Control of Linear Combustion Engine,” Proc. of the IFAC
Symposium on Advances in Automotive Control, p. 320-325, 2004.
[5] Hoff, E., Brennvall, J.E., Nilssen, R. and Norum, L., “High Power Linear Electric Machine - Made Possible by Gas Springs,” Proc.
of the Nordic Workshop on Power and Industrial Electronics, Norway, 2004.
[6] Johansen, T.A., Egeland, O., Johannessen, E.A. and Kvamsdal, R., “Free Piston Diesel Engine Timing and Control – Towards Electronic Cam-and Crankshaft,” IEEE Transactions on Control
Systems Technology, 2002.
[7] Annen, K.D., Stickler, D.B. and Woodroffe, J., “Miniature Internal Combustion Engine (MICE) for Portable Electric Power,” Proc. of the 23rd Army Science Conference, Florida, 2002.
[8] Nandkumar, S., “Two-Stroke Linear Engine,” Master’s Thesis, West Virginia University, Morgontown, 1998.
[9] Arof, H., Eid, A.M. and Nor, K.M., “On the Issues of Starting and Cogging Force Reduction of a Tubular Permanent Magnet Linear Generator,” Proc. of the Australasian Universities Power
Engineering Conference (AUPEC2004), Brisbane, 2004.
[10] Nor, K.M., Arof, H. and Wijono, “Design of a Three Phase Tubular Permanent Magnet Linear Generator,” Proc. of the 5th
IASTED International Conference on Power and Energy Systems (EUROPES2005), Benalmadena, Spain, 2005.
[11] Ohm, D.Y., Park, J.H., “About Commutation and Current Control Methods for Brushless Motors,” Proc. of the 29th Annual IMCSD
Symposium, San Jose, 1999.
[12] Zulkifli, S.A., “Modeling, Simulation and Implementation of Rectangular Commutation for Starting of Free-Piston Linear Generator,” M.Sc. Thesis, Universiti Teknologi PETRONAS, Malaysia, 2007.
Figure 13. LG mechanical simulation results using different values of constant-magnitude motoring force
Displacement vs Time (280 N Continuous Flat Force)
-40
-30
-20
-10
0
10
20
30
40
0.00000 0.10000 0.20000 0.30000 0.40000 0.50000 0.60000 0.70000 0.80000 0.90000 1.00000
Time (s)
Dis
pla
ce
me
nt
(mm
)
Time (s) -40
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0
10
20
30
40
Displacement (mm)
Displacement vs Time (280 N Continuous Flat Force)
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Time (s)
Displacement vs Time (300 N Continuous Flat Force)
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0
10
20
30
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0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000
Time (s)
Dis
pla
ce
me
nt
(mm
)
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0
10
20
30
40
Displacement (mm)
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Displacement vs Time (300 N Continuous Flat Force)
Time (s) -40
-30
-20
-10
0
10
20
30
40
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Time (s)
Displacement (mm)
Displacement vs Time (350 N Continuous Flat Force)Displacement vs Time (400 N Continuous Flat Force)
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10
20
30
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0
0.0 0.05 0.10 0.15 0.2 0.25 0.30 0.35 0.40 0.45 0.50
Time (s)
Displacement (mm)