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-magnettranslator 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 enginegenerator - is a potential alternative to conventional rotary generators, as on-board power house in serieshybrid electric vehicles (S-HEV) or as portable power generators for commercial and domestic use.

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]. Cylinder Head

Cylinder Block This research work was supported by the Ministry of Science, Technology and Innovation (MOSTI), Malaysia under IRPA grant 0399-02-0001 PR0025/04-01.

Translator Shaft

Permanent Magnets & Back Iron

Scavenge Chamber Piston

Engine Mounting

Figure 1. LG cross-section showing major components

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) 2 A 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-massspring 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. Non-linear air-spring nature of engine cylinders prior to combustion Translator mass (piston, shaft & magnets)

m Fmotoring

Electromagnetic motor force always provided in the direction of natural bouncing motion can effectuate mechanical resonance for LG starting Figure 2. Spring-mass representation and mechanical resonance process

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. Electrical Motoring via Rectangular Current Commutation To provide for the force to reciprocate the piston assembly, LG is operated as a brushless, permanentmagnet 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 unoptimized 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.

Right Scavenge Chamber

Right Engine Cylinder

Stator Left Iron and Scavenge Coils Chamber Left Engine Cylinder

B.

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 squarewave. 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). Field Direction: Downwards

Current Direction: Into Plane of Paper

Linear Displacement Encoder Figure 4. UTP Linear Generator prototype

Inside: Permanent Magnets on Linear Translator

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) : 5-kW Linear Generator Prototype

Stator Coils

PXI Embedded Controller & Data Acquisition System

Stator Iron Laminations

Resultant Motor Force

Instrument Driver Board

Permanent Magnets

Translator Shaft

Figure 3. Interaction of magnetic fields to produce linear motoring force (reprinted and modified from UM Report, 2005)

Figure 5. LG control room with view of 5-kW LG

IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China

Piston 2

Piston 1 Friction, Compression, Cogging

m

Expansion, Motoring, Cogging

x 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: (1) P1V 1 k = P2V 2k , 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  K  (2) Fcompression ( x) = K1 ⋅  2  ,  x+l 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  K  (3) Fexp ansion ( x ) = K 3 ⋅  4  . x+l CYLINDER 2 Intake Port

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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

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:

∑F

x

= ma x = m

d 2x . dt 2

(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): Pressure (Bar)

Engine Compression Pressure vs. Volume

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Ideal Model

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Experimental Data Ideal (No leakage)

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Improved Model with Leakage

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4

∑F

x

d 2x dt 2 + Fexp − Fcomp − Fcog − f

= ma x = m

= Fmot

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  Fcomp ( x ) = K 1 ⋅  2   x+l 

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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

k

(6) k

 K4  (7) Fexp ( x ) = K 3 ⋅    L− x+l  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: d 2x (8) Fmot + Fexp ( x) − Fcomp ( x) − Fcog ( x) − f = m 2 dt k k d 2x  K4   K  Fmot + K3 ⋅   − K1 ⋅  2  − Fcog ( x) − f = m 2 (9) dt  L− x +l   x +l 

Considering

non-linearity

of

Fcog

k

(x), k

 K 4  , it is  K  Fcomp ( x ) = K 1 ⋅  2  and Fexp ( x ) = K 3 ⋅    x+l   L− x+l 

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: Fstarting _ required ( x) = m

2

(5)

= Fmot ( x) + Fexp ( x) − Fcomp ( x) − Fcog ( x) − f

d 2x − Fexp ( x) + Fcomp ( x) + Fcog ( x) + f dt 2

(10)

IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China

Figure 10. Matlab Simulink program to determine starting force profile Desired Displacement Profile (Displacement vs Time)

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Figure 11. Program to investigate mechanical resonating strategy 6000

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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 springmass 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

IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China

REFERENCES

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.

[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.

VI. CONCLUSION This paper has presented the starting problem of a specific configuration of the free-piston linear enginegenerator (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. Displacement vs Time (400 N Continuous Flat Force)

Displacement vs Time (350 N Continuous Flat Force)

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0.40

0.45

00 0.0000 0.10 0.1000 0.50 0.00

-10

-10

-20

-20

-20 -20

-30

-30

-30 -30

-40

-40

Time (s)

0.20 0.2000

0.30 0.3000

0.40 0.4000

0.50 0.5000

0.60 0.6000

-10 -10

Time (s)

-40 -40

0.70 0.7000

0.8000 0.80

0.9000 0.90

1.0000 1.00

D is p la c e m e n t ( m m )

30

20

D is p la c e m e n t (m m )

30

10 10

00 0.00000 0.10 0.10000 0.20 0.20000 0.30 0.30000 0.40 0.40000 0.00

0.50000 0.50

0.60000 0.60

-10 -10

-20 -20

-30 -30

Time Time (s)(s)(s) Time

-40 -40

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

Time Time (s)

(s)

0.70000 0.70

0.80000 0.80

0.90000 0.90

1.00000 1.00