AbstractâStarting a free-piston linear engine-generator (LG) requires favorable compression pressure and piston speed for combustion to occur. To produce the ...
Investigation of Linear Generator Starting Modes by Mechanical Resonance and Rectangular Current Commutation Saiful A. Zulkifli*, Mohd N. Karsiti∇ and A-Rashid A-Aziz◊ *∇
Department of Electrical and Electronics Engineering, ◊ Department of Mechanical Engineering, Universiti Teknologi PETRONAS Bandar Sri Iskandar, 31750 Tronoh, Perak, MALAYSIA
Abstract—Starting a free-piston linear engine-generator (LG) requires favorable compression pressure and piston speed for combustion to occur. To produce the required reciprocating motion, the LG is operated as a brushless linear motor. However, the peak force required to achieve the full stroke is beyond the maximum motor force that can be produced, limited by the coils’ current capacity and LG’s motor constant. A starting method is proposed, utilizing mechanical resonance and the air-spring character of engine cylinders prior to combustion. Energizing the coils with fixed DC bus voltage and open-loop, rectangular current commutation, the LG is reciprocated in small amplitudes initially. Due to repeated compression-expansion of the engine cylinders and constant application of motoring force in the direction of natural resonating motion, the translator’s amplitude and speed is expected to grow and reach the final required values for combustion. To investigate viability of the proposed strategy, an integrated model of LG - consisting of mechanical and electrical subsystems - is developed and real-time simulation is performed on Matlab Simulink. The individual models are validated against field experimentation before final simulation and experimentation are implemented. This work discusses simulation and experimental results of the proposed starting strategy.
I.
INTRODUCTION
A free-piston linear engine-generator (LG) is a potential alternative to conventional rotary generators, as onboard power house in series-hybrid electric vehicles (S-HEV) or as portable power generators. It consists of a linear electric generator coupled to a free-piston, linearly reciprocating internal combustion engine (Fig. 1 and 2). Due to the free-piston engine configuration, it offers many advantages such as higher powerto-weight ratio, improved efficiency and multiple fuel capability. One critical task in the operation of LG is the initial process of starting the engine. As prime mover for electricity generation, a practical method to start the engine is to supply electrical power to the linear machine to reciprocate the translator assembly, operating it as a brushless linear motor. The major force that the piston needs to overcome during starting is compression force, in a linear direction opposing
piston motion. In the case of LG, the resultant compression force has a peak in the order of 5 kN. This is beyond the maximum motor force that can be supplied, determined by the LG’s motor constant and current capacity. A starting strategy is proposed which could nevertheless utilize a lower-magnitude motoring force to produce the required motion. It consists of two principles: 1) mechanical resonance via reciprocation and 2) electrical motoring via open-loop, rectangular commutation of injected current. II. MECHANICAL SUBSYSTEM A. Mechanical Modeling and Starting Strategy For modeling and simulation objectives, the LG system is decomposed into mechanical and electrical subsystems. Simulation of LG starting is implemented on Matlab Simulink [1]. To assess viability of the mechanical resonance strategy, mechanical forces acting on the system are identified and a dynamic mechanical equation of LG during starting is derived. A mechanical model is developed consisting of sub-models of compression-expansion force, friction force, magnetic cogging force and motor force. 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.
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.
978-1-4244-4252-2/09/$25.00 ©2009 IEEE
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Cylinder Head
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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 (Fig. 3). Over time, its amplitude and speed will grow, due to resonance, to achieve the final required parameters for combustion [2]. However, at low speeds, the air-spring characteristic of an engine cylinder is heavily affected by piston speed - due to air leakage around the piston rings referred to as piston blow-by. This affects the cylinders’ effectiveness to absorb and release energy during reciprocation. Thus, the compression-expansion model is improved to incorporate an air mass transfer algorithm, which is correlated and validated with experimental data (Fig. 4). The improved model shows a reduction of 28% in compression pressure compared to the ideal case, which translates to a difference of more than 2 kN between the improved and ideal models. B. Preliminary Mechanical Simulation Mechanical simulations are first carried out to determine the required starting force, compression-expansion force and the effect of piston speed on these forces (Fig. 6). It is observed that the higher the starting speed, the larger is the required starting force, due to the larger resultant compression force of the engine cylinder, which in turn is due to less air leakage. This proves the influence of piston speed. Another objective of LG mechanical simulation is to investigate viability of the proposed resonating strategy by using a constant-magnitude motoring force. Non-linear air-spring nature of engine cylinders prior to combustion Translator mass (piston, shaft & magnets)
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Fig. 7 shows simulation results using different magnitudes of constant motoring force. It is observed that for all force values, the cyclic frequency when the translator reaches the required amplitude is the same, around 25 Hertz. Although there exist cogging and friction forces, compression-expansion force dominates so that its spring-like property characterizes the LG system. The 25-Hz resonant frequency could not have been obtained analytically from LG dynamic equation, proving a benefit of the dynamic simulation. III. ELECTRICAL SUBSYSTEM A. Electrical Motoring Strategy To provide for the force to reciprocate the piston assembly, current is injected into the stator coils to create a magnetic field which interacts with the existing magnetic field of the permanent magnets on the translator shaft, resulting in a motor force acting on the shaft (Fig. 5). With 3 phases, the process of current injection needs proper steering of the current into the right coils at the right time. This process is called current commutation and is a critical and integral process of any brushless motor. Two distinct current commutation techniques are possible: rectangular and sinusoidal commutation. Rectangular commutation consists of discrete on-off switching of the transistors at fixed, finite and pre-determined positions of the translator. Field Direction: Downwards
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Electromagnetic motor force always provided in the direction of natural resonating motion can effectuate mechanical resonance for LG starting Fig. 3. Spring-mass representation and mechanical resonance process.
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Fig. 5. Interaction of magnetic fields to produce linear motoring force.
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Sinusoidal commutation also involves energization of certain pairs of transistors based on displacement but it performs the switching at a very high rate, using pulse width modulation (PWM) technique, to allow regulation of the injected current or effective DC bus voltage by varying the duty cycle of the energized transistors [11]. There are thus several control possibilities for LG starting. One option is to have open-loop control: based solely on displacement, the transistors are discretely switched with rectangular commutation to produce motoring force in a certain desired direction and with a certain objective as explained below. No closed-loop current control or motion control is implemented. However, due to inductive and back emf effects, the effective current profile will have sawtoothed or triangle-shaped waveforms, which will in turn result in heavily-rippled force profiles. The proposed starting strategy consists of motoring the translator assembly in small amplitudes initially and resonating it up to the final required amplitude. In this simple strategy, no specific endpoint for each stroke of the translator is targeted nor is there any specific displacement or velocity profile to be achieved. The reason the piston assembly stops in each stroke is that it has exhausted its energy (mostly converted and stored in the air spring of the engine cylinders and slightly lost to friction.) The controller tracks displacement solely for the purpose of commutation and tracks velocity solely for force switching. Whenever the piston assembly stops and changes its direction of natural resonating motion, the flow of injected current will be reversed, so as to provide for force which assists
rather than opposes piston motion. Thus, this paper does not present the study of closed-loop motion control to meet certain motion or velocity profile; instead, this paper investigates open-loop, discrete-switching and rectangular current commutation with fixed DC bus voltage. Two variations of rectangular commutation studied in this work are 6-step and square-wave. B. Electrical Modeling and Simulation During starting, the LG is operated as a linear motor to produce the required reciprocating motion. The particular linear machine studed in this research (designed and built by research team in Universiti Malaya) is a 3-phase permanentmagnet brushless motor, with the following basic design: • Stationary coil: 3-phase, Y-connected, 6-coil • Moving magnet: 7-pole permanent-magnet • Iron-cored stator Hardware responsible for current injection consists of a common type of motor drive used in rotating brushless motor applications: 3-phase, full-wave, full-controlled, MOSFET voltage-source inverter bridge (Fig. 8). For modeling and simulation objectives, the electrical subsystem of LG can be broken down to a DC voltage source model (to represent standard automotive battery bank providing DC bus voltage in multiples of 12V), a brushless motor drive model (MOSFET inverter bridge) and an inductive-resistive (LR) network model. Thus, the electrical part is essentially a network of fixed
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voltage source, resistors and inductors. The remaining part making up the electrical subsystem is the electromagnetic models of flux, KV (emf) and KF (motoring force). Fig. 9 shows an integrated LG block diagram of electrical and mechanical models for the real-time simulation. On the leftmost is a lookup-table providing displacement points throughout the stroke of LG for the rectangular commutation of current. There are thus 2 different pre-determined switching tables, one each for 6-step and square-wave, as discussed below. The next block labeled LG Electrical Model contains a battery model, a MOSFET inverter bridge model, a 3-phase, Yconnected motor model and a back emf model. The back emf model contains profiles of KV against displacement for each phase of LG. Since the resultant back emf voltage is also a function of velocity, the latter is also an input of the back emf model, in addition to displacement. Output of the LG Electrical Model block is the 3 phase currents IA, IB and IC. The 3 phase currents are inputs of the subsequent block - LG Motor Force Model, in which each phase current is multiplied by the corresponding KF profile to produce the final motoring force Fmotoring - a summation of the individual contributions of force. Each force is due to the interaction between the permanent magnets’ magnetic field and the field due to current flowing through the respective phases being energized. The resultant Fmotoring is an input to LG Mechanical Model, which is utilized for LG mechanical simulations described above. It is shown in this integrated block diagram to show the interrelation between motor force, velocity and displacement. The relationships and interconnectivity described above, whose derivation and further explanation can be found in [1], come from general electric motor principles - irrespective of rotating or linear configuration - and are thus not unique to LG. Ref. [3]-[6] are good sources of reference for linear enginegenerator modeling and simulation, while a broad literature on linear generators and free-piston engines can be found in [7][10]. C. KV and KF Models and Switching Matrix Rectangular current commutation means discrete switching of the motor drive transistors based on fixed, pre-determined switching positions. Optimum switching positions to ensure maximum motoring force, Fmotoring, can be determined from the KF and KV profiles – graphs of motor force vs. displacement or back emf vs. displacement, respectively.
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Duality between electromotive force and magnetic force implies that ideally, for each phase of LG, KF has the same magnitude and profile as KV, only the units are different. The 2 different rectangular commutation techniques - 6-step and square-wave - result in different KF profiles and thus, different optimum switching positions. The expected difference in performance between the 2 techniques will thus be due to different effective current profiles flowing through the energized coils, different KF profiles, different switching positions and finally, different effective motor force. One objective of the present work is thus to investigate and compare the performance and effectiveness of the 2 techniques. Fig. 10 below shows KV (x) for all three phases of LG, generated via finite-element analysis (FEA) in the design of the linear electric machine (data provided by Universiti Malaya). With 6-step commutation, 2 phases are energized: one positive while the other negative; with square-wave commutation, all 3 phases are energized: 2 phases having the same polarity while the remaining phase has the opposite polarity. Using this information and the phase KV(x) profiles of Fig. 10, the resultant KV(x) profiles due to multiple-phase energization are generated and from these, the optimum switching positions to obtain maximum motor force can be determined. KV vs Displacement (Simulink 9th Poly Fit) 16 14 12 10 8
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Fig. 11 (top graph) shows the results for 6-step commutation, showing KV (x) profiles for the 6 possible combinations of coil energization. If we energize LG coils with a single automotive 12-volt battery, a steady-state current of about 25Amps will flow in the coils. The bottom graph of Fig. 11 shows how much force will be generated by the 6 possible combinations. Switching positions for 6-step commutation are then determined from either graph by tracing the maximum possible force profiles throughout the stroke and identifying the positions where one profile crosses another; these crossing points are then the required switching positions. Corresponding profiles for square-wave commutation are shown in Fig. 12, while Fig. 13 presents the final switching matrix for both directions, for both 6-step and square-wave commutation. With all phases energized in square-wave commutation, current levels are expected to be 33% higher than that of 6-step. However, the force graphs show that square-wave commutation could generate only about 13% more force, as the resultant KV (x) profiles do not increase in magnitude proportionately with the additional energized phase, due to flux cancellation.
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D. Simulation and Experimental Validation The electrical and mechanical subsystem models are combined to form an integrated LG model, implemented on Matlab Simulink. The toolbox SimPower Systems is used for the electrical modeling. Fig. 14 shows the complete simulation program. The electrical circuit and its components – DC bus supply, MOSFET transistors, resistors, inductors, back emf generation and various metering utilize SimPower Systems
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building blocks, while electromagnetic models of KV and KF (represented by 9th-order polynomial functions) employ standard Simulink blocks. Primary motivation for simulation is twofold: 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 safety reasons and hardware limitation, some field experiments are not possible and this is where simulation is beneficial. Experimentation for LG takes place in the LG laboratory at Universiti Teknologi PETRONAS. Both data acquisition and controls are implemented on a common hardware and software platform: National Instruments’ PXI embedded controller running LabView Real-Time software. Fig. 15 shows a block diagram of the experimental set-up. Measured parameters are compression-expansion pressure of the engine cylinders, linear position of the translator assembly and various branch and phase currents of the electrical circuit. Model validation and refinement are carried out extensively, first against field experiments using low DC bus voltage in motionless coil energization tests, generated emf tests and single-stroke motoring tests without compression (Fig. 16). Further model refinement and analysis are implemented with both singlestroke and cyclic tests to validate the compression model, ensure a reliable integrated LG model and understand LG system behavior under different external excitation [1].
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Phase C
Phase A
-31.00
2 -5.375
-18.125
-35
-30
-25
-20
-15
-5
Phase C
-8 -10
Displacement (mm)
Phase A Phase B Phase C Simulated Phase A Simulated Phase B Simulated Phase C
0
5
10
-2
-4
Fig. 14. LG electrical model on Matlab Simulink
-10
-2
-6
4.25
0 -40
Phase A Phase B Phase C Simulated Phase A Simulated Phase B Simulated Phase C
-4 -6 -8
Displacement (mm)
-10
Fig. 16. Simulation and experimental results for model validation, refinement and system analysis using low DC bus voltage
IV. LG STARTING INVESTIGATION
Fig. 15. Block diagram of experimental setup for LG starting investigation
The final objective is to investigate viability of a certain starting strategy for LG, which consists of applying motoring force of low but sufficient magnitude to reciprocate the piston assembly in small amplitudes initially, using rectangular current commutation and open-loop control. Over time, its amplitude and speed are expected to grow - due to mechanical resonance - to achieve the final required stroke length (69mm), speed (3-5 Hz cyclic frequency) and compression pressure (about 7-9 bars) for combustion to occur. Numerous field
430
0
10
20
30
40
-40
-30
-20
-10
-20 Displacement (mm)
Displacement & Current Chart: Experimental Data LEFT-RIGHT_1-STROKE_MAX_6-STEP_IBAT 40
30
60
30
20
0
0
-10
-20
-20
-40 Displacement Current (IBAT)
-30
1.00
1.10 1.20 Time (s)
1.30
1.40
1.50
-60 -80 1.60
D is p la c e m e n t (m m )
10
0.90
30
LEFT-RIGHT_1-STROKE_MAX_SQUARE-WAVE_IBAT
80 60 40 20
0
0
-10
-20
-20
-40 Displacement Current (IBAT)
-30 -40 0.50
0.60
0.70
0.80 0.90
1.00 1.10 Time (s)
1.20 1.30
1.40
0.8 0.6 0.4 0.2
0 -10-40 -35 -30 -25 -20 -15 -10 -5 0 -20 -30
0.0 5 10 15 20 25 30 35 40 -0.2 -0.4 -0.6 Current (IBAT) Velocity
-0.8 -1.0 -1.2
Displacement (mm)
Experimental Velocity vs Displacement Chart
Experimental Pressure (Right Cylinder) vs Displacement
Comparison of 6-Step and Square-Wave Commutation: Cyclic Motion 1.2
Comparison of 6-Step and Square-Wave Commutation: Cyclic Motion
1.0
6-Step Velocity (Test 1)
0.8
Square-Wave Velocity (Test 3)
5.0
0.4 0.2 0.0 -40 -35 -30 -25 -20 -15 -10 -5 -0.2 0
5
10 15 20 25 30 35 40
-0.4 -0.6 -0.8 -1.0
-80 1.50
4.5
6-Step Pressure (Test 1)
4.0
Square-Wave Pressure (Test 3)
3.5
0.6
-60
1.2 80 70 1.0 60 0.8 50 0.6 40 30 0.4 20 0.2 10 0.0 0 -10-40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 -0.2 -20 -0.4 -30 -40 -0.6 -50 -0.8 C urrent (IBAT) -60 -1.0 Velocity -70 -80 -1.2 Displacement (mm)
Velocity (m/s)
1.2 1.0
-40 -50 -60
40
10
Velocity vs Displacement Chart CYCLIC_MOTION-LTD_SQUARE_IBAT: Stroke 1 (Left to Right)
30 20 10
-70 -80
20
40 Current (Am ps)
Displacem ent (m m )
20
0.80
20
Displacement & Current Chart: Experimental Data 80
0.70
10
-20 Displacement (mm)
40
-40 0.60
0 -10
Velocity (m /s)
0 -10
Velocity vs Displacement Chart CYCLIC_MOTION-LTD_6-STEP_IBAT: Stroke 2 (Left to Right)
Velocity (m/s)
10
C u rre n t (A m p s )
-10
Current (Amps)
20
0 -20
80 70 60 50 40
30
10
Experimental DC Bus Current (IBAT) and
Experimental DC Bus Current (IBAT) and
50
Current (Amps)
Current (Amps)
20
5 10 15 20 25 30 35 40
Fig. 18. Experimental comparison of velocity and pressure profiles between 6step and square-wave commutation in single-stroke tests
40
30
0
-0.50 Displacement (mm)
60
40
-30
0.00 -0.25
Current (Amps)
50
-40
0.25
-1.2 Displacement (mm)
P ressure (b ar)
Square-Wave Commutation 6-Step Commutation
Square-Wave Velocity (Test 3)
0.50
-40 -35 -30 -25 -20 -15 -10 -5
5.0 6-Step Pressure (Test 2) 4.5 Square-Wave Pressure (Test 3) 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -40 -35 -30 -25 -20 -15 -10 -0.5 -5 0 5 10 15 20 25 30 35 40 Displacement (mm)
6-Step Velocity (Test 2)
0.75
70
Square-Wave Commutation 6-Step Commutation
Experimental Pressure vs Displacement Chart Comparison of 6-Step and Square-Wave Commutation: Single Stroke (Left to Right), Maximum Stroke
1.00
DC Bus (IBAT) Current vs Displacement Comparison Between 6-Step and Square-Wave Commutation Right to Left Motion: Experimental Data
DC Bus (IBAT) Current vs Displacement Comparison Between 6-Step and Square-Wave Commutation Left to Right Motion: Experimental Data 70 60
Experimental Velocity vs Displacement Chart Comparison of 6-Step and Square-Wave Commutation: Single Stroke (Left to Right), Max Stroke
P re s s u re (b a r )
A. Performance Comparison: 6-Step vs. Square-Wave Fig. 17 shows experimental graphs of DC bus current versus displacement (top) and current charts versus time (bottom) for single-stroke motoring tests using low DC bus voltage. The different switching positions for 6-step and square-wave can be observed. The characteristic saw-toothed or triangle-shaped current profiles are due to the inductive lag and back emf effects of rectangular commutation switching. Current levels never reach the maximum possible steady-state values – only about 20% to 60% of the maximum levels. They are lower in the middle sections than at the ends due to the back emf effect: higher velocity at the center suppresses the injected current more than it does at the ends. Indeed, these are key features of rectangular current commutation: with simple and direct energization of motor coils from a fixed DC source and without current control, the graphs represent typical current profiles arising from the interaction of current, speed and back emf. Fig. 18 shows experimental pressure profiles (right) and velocity profiles (left) of the right engine cylinder in singlestroke motoring. It shows almost the same peak pressures but occurring at different positions using 6-step and square-wave. Beyond these points, pressure decreases relatively slowly, due to air leakage around piston rings. Although motor force is still present, the much larger compression force renders such a low speed of motion that much air gets to leak through. The jerks in the upward and downward pressure slopes are due to either a switching event or the translator reaching end of stroke. Pressure traces in the upward slope appear overlapped while velocity profiles exhibit little difference between the two switching techniques.
Fig. 19 shows experimental profiles of cyclic motoring tests at low DC bus voltage. When the translator is bouncing off the air spring of the left cylinder to move towards the right, current levels are much lower compared to when the translator reaches the right end of the stroke, since speed is higher on the left side than on the right. Higher speed leads to higher back emf, which in turn leads to lower effective current. The speed is high on the left side due to additional energy from the air spring of the left engine cylinder as the translator bounces off the left cylinder to move towards the right. The speed is low on the right side due to the drain of energy in compressing the right cylinder, to be stored in the right cylinder’s air spring. Vertical spikes at both ends of the current profiles are due to inductive voltage spikes arising from transistor switch-off of the previous cycle. Due to the higher overall velocity of square-wave, the current level even dips below zero due to excessive back emf, which is not seen on the 6-step graph. Pressure leakage through the piston rings is clearly seen from the difference in the upward (compression) stroke and downward (expansion) stroke of the pressure profiles; without air leakage - these pressure curves would overlap.
V e lo c ity (m /s )
experimentation and simulation using the integrated and validated LG model are performed [1] and the following is a summary of the experimental and simulation results.
3.0 2.5 2.0 1.5 1.0 0.5
0.0 -40 -35 -30 -25 -20 -15 -10 -5 -0.5 0
5
10 15 20 25 30 35 40
-1.0 Displacement (mm)
Fig. 19. Experimental comparison of current, velocity and pressure profiles between 6-step and square-wave commutation in cyclic motoring
Fig. 17. Experimental comparison of current and displacement profiles between 6-step and square-wave commutation in single-stroke tests
431
Experimental Pressure vs Displacement Chart
Right Pressure vs Displacement Chart
Comparison of 6-Step and Square-Wave Commutation: Single Stroke (Left to Right), Maximum Stroke, 4 Batteries
Experimental Comparison of 6-Step and Square-Wave Commutation: Cyclic Motion, 4 Batteries
6.0 6-Step Pressure (Test 2)
5.5
Square-Wave Pressure (Test 1)
5.0
Square-Wave Commutation
4.5
P ressu re (bar)
Pressure (bar)
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 -40 -35 -30 -25 -20 -15 -10
0.0 -5-0.5 0
6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 0 -40 -35 -30 -25 -20 -15 -10 -5 -1.0 6-Step Commutation
5
10
Displacement (mm)
15
20
25
30
35
40
5
10 15 20 25 30 35 40
Displacement (mm)
Fig. 20. Experimental comparison of pressure profiles between 6-step and square-wave commutation using higher DC bus voltage
Right Pressure vs Displacement (Final Simulation Data) Experiment vs Simulation Comparison: Cyclic Motion, 6-Step Commutation, Offset Ehxaust Port of 0.5mm
4.5 4.0 3.5 P re s s u re (b a r)
3.0
5.0
Experimental Pressure (Test 1)
Experimental Pressure (Test 1)
Simulation Pressure (Leakage: 0.00000055)
Simulation Pressure (Leakage: 0.00000041)
2.0 1.5 1.0
0.0 -40 -35 -30 -25 -20 -15 -10 -5 -0.5 0
5
10 15 20 25 30 35 40
3.0
1.0 0.5
0.0 -40 -35 -30 -25 -20 -15 -10 -5 -0.5 0
5
10 15 20 25 30 35 40
-1.0 Displacement (mm)
DC Bus Current (IBAT) vs Displacement
Velocity & Displacement vs Time Comparison of Experimental and Final Simulation Data
60
2.0
50
1.6
40
1.2
30
0.8
20 10 5 10 15 20 25 30 35 40
V e lo c ity (m /s )
C u rre n t (A m p s )
3.5
1.5
Comparison of Experimental and Final Simulation Data
Experimental Current
4.0
2.0
-1.0 Displacement (mm)
0 -40 -35 -30 -25 -20 -15 -10 -5-10 0
4.5
2.5
P re s s u re (b a r)
2.5
0.5
40 30 20 10
0.4 0.0 -0.4 -0.8
-20
0 .000 .005 .010 .015 .020 .025 .030 .035 .040 .045 .050 .055 .060 .065 .070
Experimental Velocity Simulation Velocity Experimental Displacement
-1.6
-40 Displacement (mm)
-10
Time (s)
-1.2
Simulation Current (Friction Magnitude = 230 N, Friction -30 Factor = 2, Inductance = 1.9 mH, KV = 1.1, KF = 0.9)
-20 -30
Simulation Displacement
-2.0
-40
Fig. 21. Final simulation profiles of pressure, current, velocity and displacement after model validation and refinement Simulation DC Bus Current (IBAT), Motoring Force,
Simulation DC Bus Current (IBAT), Motoring Force,
Cogging and Friction vs Displacement
Cogging and Friction vs Displacement
Final Simulation Parameters: 2 Batteries, 22mm Motoring Cutoff
Final Simulation Parameters: 3 Batteries, 15mm Motoring Cutoff
1100
60
1100
50
900
50
900
40
700
40
700
30
500
30
500
-20 0 5 0 5 0 5 0 -30 -40 -50 Displacement (mm)
-100 -300
Current Motoring Force Cogging Friction Net Force
-500
300
10
100
0
F o rc e (N )
-10 -4 -3 -3 -2 -2 -1 -1 -5 0 5 10 15 20 25 30 35 40
F o rc e (N )
100
0
-60
20
300
10
C u rre n t (A m p s )
60
20 C u rre n t (A m p s )
B. Final Motoring Simulation and Experimentation Following experimental validation and refinement of the individual models, final simulation runs of LG starting are implemented. Fig. 21 presents experimental and simulated profiles of pressure, current and displacement for motoring at low DC bus voltage. The graphs show good correspondence between experimental and simulation results. Through simulation, graphs of Fig. 22 are obtained for parameters which cannot otherwise be measured experimentally: motoring force, cogging force and friction. The two graphs show that with more batteries (higher DC bus voltage level), the resultant DC bus current, motoring force and friction profiles increase accordingly, as these parameters are interrelated (higher DC bus voltage means more current; motoring force is a direct result of current; more motoring force means higher speed and higher speed leads to higher friction levels.) However, apart from the much higher values at the left and right ends, the net force profiles seem just to oscillate about zero in the middle sections of the stroke. This relates well to the fact that the resultant velocity profile is quite uniform (Fig. 21), which in turn infers very little acceleration or deceleration, which finally means very little net effective force is involved in the middle sections. The initial net force profile just after energization (left end of stroke) shows correspondingly higher values with higher DC bus; otherwise, the net force does not seem to be much different throughout the stroke.
Left Pressure vs Displacement (Final Simulation Data) Experiment vs Simulation Comparison: Cyclic Motion, 6-Step Commutation, Offset Ehxaust Port of 0.5mm 5.0
D is p la c e m e n t (m m )
Pressure trace in the upward stroke shows an overlap between the two commutation techniques; thus, even with the higher motoring velocity of square-wave commutation, the resultant compression profile is no different from that of 6-step commutation. In the downward stroke, pressure even becomes negative before the exhaust port re-opens (at around -10mm), due to excessive air leakage. Even when motoring with higher DC bus voltage (48 VDC), although current levels of squarewave are higher than 6-step commutation (33% ideally), there is little difference in the resultant pressure curves. Fig. 20 shows experimental pressure profiles for both single-stroke and cyclic motoring at higher DC bus. Only very minor gain in the upward pressure trace is observed; square-wave profile does seem slightly ‘tighter’, indicating less air leakage during the bounce process. Nonetheless, the difference is so insignificant that it can be concluded that there is no conceivable advantage of square-wave commutation over 6-step commutation.
-100
-10 -4 -3 -3 -2 -2 -1 -1 -5 0 5 10 15 20 25 30 35 40 -300 -20 0 5 0 5 0 5 0 -500
-30
-700
-40
-900
-50
-1100
-60
Displacement (mm)
Current Motoring Force Cogging Friction Net Force
-700 -900 -1100
Fig. 22. Final simulation profiles of current, motoring force, cogging, friction and net force
Fig. 23 compares experimental and simulated pressure profiles of cyclic motoring for several levels of DC bus voltage. Wave-shapes of the simulated pressure profiles match reasonably well with experimental profiles although the exact simulation values are generally lower. Albeit the quantitative inaccuracy, the integrated LG model is acceptable for a qualitative assessment of the proposed starting strategy, not for quantitative prediction of operating parameters. Yet, neither field experimentation nor simulation proves the resonating strategy to work, as the cyclic amplitude does not seem to grow with time. A qualitative analysis provides an insight: the additional energy from using higher DC bus can do the following three things: 1) increase the cyclic amplitude, 2) increase the translator velocity and 3) increase the air spring’s effectiveness of the engine cylinders (higher motoring force leads to higher velocity and thus less pressure leakage). Since translator velocity clearly increased with using higher DC bus and so does the air-spring performance (indicated by the increasingly ‘tighter’ inward and outward pressure curves), little energy is left to also increase the amplitude.
432
P r e s s u r e (b a r )
[1]
Fig. 23. Comparison of experimental and simulation pressure profiles for cyclic motoring with 6-step commutation
However, increasing the DC bus voltage further (up to 72 Volts) still fails to produce a growing amplitude - the extra energy continues to be used to improve the compressionexpansion process to become closer to ideal. With even more energy (84 Volts onwards), the amplitudes start to increase. However, for each DC bus voltage level, the peak amplitude is reached right after the first cycle, signifying absence of a growing-amplitude, resonating system but steady-state operation (Fig. 24). Thus, at each DC bus level, there is a steady-state value for motoring force, current, velocity and amplitude. All these parameters find an equilibrium point against each other due to their interdependency (so that mathematically, the dynamic differential equation of LG is solved), giving rise to a fixed cyclic amplitude and a steadystate operation right after the first cycle. The resonating strategy has been shown to work in mechanical simulation due to using a constant-magnitude motor force, which is theoretically achievable by sinusoidal current commutation and closed-loop current control. On the other hand, motoring with open-loop rectangular commutation results in not only a greatly varying and highly-rippled motoring force, but also force that is directly affected by translator velocity, due to the back emf effect. This would be a primary motivation for having a closed-loop current or force control as a more effective method for LG starting, necessitating sinusoidal commutation of current. Nevertheless, the required amplitude for starting can still be achieved with rectangular current commutation - right after the first cycle using a DC bus voltage of 144 Volts (provided by 12 batteries) (Fig. 24). The resultant cyclic speed and compression pressure of the engine cylinders however, exceed the required values for starting, as they represent equilibrium values of a steady-state operation and as such, cannot be regulated without an active, closed-loop control system.
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. [2] 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. [3] Aichlmayr, H.T., “Design Considerations, Modeling and Analysis of Micro-Homogeneous Charge Compression Ignition Combustion FreePiston Engines,” Ph.D. Thesis, University of Minnesota, 2002. [4] 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. [5] Nandkumar, S., “Two-Stroke Linear Engine,” Master’s Thesis, West Virginia University, Morgontown, 1998. [6] 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. [7] Arshad, W.M., “A Low-Leakage Linear Transverse-Flux Machine for a Free-Piston Generator,” Ph.D. Thesis, Royal Institute of Technology, Stockholm, 2003. [8] 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. [9] 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. [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.
V. CONCLUSION This paper investigates viability of a proposed starting strategy for a free-piston linear engine-generator (LG) by field experimentation and simulation. However, results show that motoring the LG with rectangular current commutation and open-loop control does not produce cycles of increasing amplitude but steady-state operation after the very first cycle,
433
Right Pressure & Displacement vs Time
Displacement vs Time
Final Integrated Simulation Data: Cyclic Motion, 6-Step Commutation, 12 Batteries
Final Integrated Simulation Comparison: Cyclic Motion, 6-Step Commutation; 10, 11 and 12 Batteries
20 40 18 35 16 30 14 25 12 10 20 8 15 6 10 4 5 2 0 0 -5 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .10 .11 .12 -2 -4 -10 -6 -15 -8 -10 -20 -12 -25 -14 -30 -16 -35 Displacement -18 -40 -20 Pressure Time (s)
P re s s u re (b a r)
P re s s u re (b a r)
REFERENCES
D is p la c e m e n t (m m )
6.0 5.5 5.0 3 Batteries 4.5 4 Batteries 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 0 5 10 15 20 25 30 35 40 -40 -35 -30 -25 -20 -15 -10 -5 -1.0 Displacement (mm) 2 Batteries
40 35 30 25 20 15 10 5 0 -5 .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 .10 .11 .12 .13 .14 -10 -15 -20 -25 -30 -35 Displacement (10 Batteries) Displacement (11 Batteries) -40 Time (s) Displacement (12 Batteries)
Current & Velocity vs Time
Velocity vs Displacement Chart
Final Integrated Simulation Data: Cyclic Motion, 6-Step Commutation, 12 Batteries
Final Integrated Simulation Comparison: Cyclic Motion, 6-Step Commutation; 10, 11 and 12 Batteries
160 140 120 100 80 60 40 20 0 -20 -40.00 -60 -80 -100 -120 -140 -160
6
6
5
5
4
4
3
3
2
2
1 0
.01 .02 .03 .04 .05 .06 .07 .08 .09 .10 .11 .12 -1 -2
Current Velocity
1
0 -40 -35 -30 -25 -20 -15 -10 -5 -1 0 -3
-4
-4
-6
5 10 15 20 25 30 35 40
-2
-3 -5 Time (s)
V e lo c ity (m /s )
6.0 5.5 5.0 3 Batteries 4.5 4 Batteries 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 0 5 10 15 20 25 30 35 40 -40 -35 -30 -25 -20 -15 -10 -5 -1.0 Displacement (mm) 2 Batteries
so that at every DC bus voltage level, certain fixed cyclic amplitude, speed and compression pressure will result. Thus, using sufficiently high DC bus voltage, the LG can be reciprocated at the required amplitude for starting but the resultant compression pressure and cyclic speed are much higher than required.
V e lo c ity (m /s )
Simulation Comparison of 2, 3 and 4 Batteries: Cyclic Motion, 6-Step Commutation
D is p la c e m e n t (m m )
Right Pressure vs Displacement Chart
D is p la c e m e n t (m m )
Right Pressure vs Displacement Chart Experimental Comparison of 2, 3 and 4 Batteries: Cyclic Motion, 6-Step Commutation
-5 -6 Displacement (mm)
Velocity (10 Batteries) Velocity (11 Batteries) Velocity (12 Batteries)
Fig. 24. Results of final simulation tests with up to 144-Volt DC bus voltage
