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


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


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


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


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


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)



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

)





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

)





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


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

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Figure 13. LG mechanical simulation results using different values of constant-magnitude motoring force

Displacement vs Time (280 N Continuous Flat Force)

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0.00000 0.10000 0.20000 0.30000 0.40000 0.50000 0.60000 0.70000 0.80000 0.90000 1.00000

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Displacement (mm)


0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Time (s)


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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

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Displacement (mm)

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00


Time (s) -40

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0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

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Displacement vs Time (350 N Continuous Flat Force)Displacement vs Time (400 N Continuous Flat Force)

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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)

linear engine motor

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