A review of free-piston engine history and applications

A review of free-piston engine history and applications
A review of free-piston engine history and applications

A review of free-piston engine history and applications.?

R.Mikalsen,A.P.Roskilly?

Sir Joseph Swan Institute for Energy Research,Newcastle University,Newcastle upon Tyne,NE17RU,United Kingdom.

Abstract

This document reviews the history of free-piston internal combustion engines,from the air compressors and gas generators used in the mid-20th century through to recent free-piston hydraulic engines and linear electric generators. Unique features of the free-piston engine are presented and their e?ects on engine operation are discussed,along with potential advantages and disadvantages compared to conventional engines.The paper focuses mainly on developed engines where operational data has been reported.Finally,the potential of the free-piston engine is evaluated and the most promising designs identi?ed.

Key words:free-piston,linear engine.

1.Introduction

Extensive use of fossil fuels as an energy source for both sea and land based transport leads to sig-ni?cant amounts of CO2and other pollutants be-ing produced.Much research,particularly within the automotive industry,is being undertaken to de-velop more environmental friendly fuel chains,and the fuel cell vehicle stands out as a promising tech-nology for the future.Although superior in vehi-cle e?ciency,the implementation barriers for such radical technology change are huge,and the com-plete fuel chain(‘well-to-wheel’)e?ciencies are not yet superior to those of conventional technology[1]. Hybrid electric vehicles powered by conventional in-ternal combustion engines have the potential to re-alise large emission reductions within a signi?cantly shorter timescale.

?This is a preprint version.This paper was published as: Applied Thermal Engineering,Volume27,Issues14-15,Oc-tober2007,Pages2339–2352.

?Corresponding author.

Email addresses:rikard@mikalsen.eu(R.Mikalsen), Tony.Roskilly@https://www.360docs.net/doc/107765847.html,(A.P.Roskilly).

After being abandoned in the mid-20th century, free-piston engines are being investigated by a num-ber of research groups worldwide as an alternative to conventional engine-generator sets or for gener-ating hydraulic power in o?-highway vehicles.Po-tential advantages of the free-piston engine include optimised combustion through variable compres-sion ratio,leading to higher part load e?ciency and possible multi-fuel operation,and reduced frictional losses due to a simple design with few moving parts. This document reviews the history of the free-piston engine with emphasis on recent applications, and investigates the potential of free-piston engines as an alternative to conventional technology.It is the result of an extensive background study on the subject and will be followed up by a more detailed design study and the development of a prototype engine.

2.Free-piston engine basics

Due to the breadth of the free-piston term,many engine con?gurations will fall under this category. The free-piston term is most commonly used to dis-

Preprint submitted to Elsevier17February2009

tinguish a linear engine from a rotating crankshaft engine.The piston is‘free’because its motion is not restricted by the position of a rotating crankshaft, as known from conventional engines,but only deter-mined by the interaction between the gas and load forces acting upon it.

This gives the free-piston engine some distinct characteristics,including(a)variable stroke length and(b)the need for active control of piston mo-tion.Other important features of the free-piston en-gine are potential reductions in frictional losses and possibilities to optimise engine operation using the variable compression ratio.

2.1.The original

R.P.Pescara[2]is usually credited with the inven-tion of the free-piston engine with his patent dating from1928,but other vendors,among others Junkers in Germany,were also working on free-piston ma-chinery at this time.Since then,a high number of patents describing free-piston machinery or related to such machinery have been published.1The orig-inal Pescara patent describes a single piston spark ignited air compressor but the patent seeks to pro-tect a large number of applications utilising the free-piston principle.

Pescara started his work on free-piston engines around1922and he developed prototypes with both spark ignition(1925)and diesel combustion(1928). The latter led to the development of the Pescara free-piston air compressor[4].Pescara continued his work on free-piston machinery and also patented a multi-stage free-piston air compressor engine in1941 [5].

2.2.Piston con?guration

Free-piston engines are usually divided into three categories based on the piston/cylinder con?gura-tion.A fourth category,free-piston gas generators, identi?es engines where the load is extracted purely from an exhaust turbine and not from a load device mechanically coupled to the engine.

Below follows a description of the di?erent cate-gories of free-piston

engines.

Fig.1.Single piston hydraulic free-piston engine[6].

2.2.1.Single piston

A single piston free-piston engine is shown in Fig-

ure1.This engine essentially consists of three parts:

a combustion cylinder,a load device,and a rebound

device to store the energy required to compress the next cylinder charge.In the engine shown in the?g-ure the hydraulic cylinder serves as both load and rebound device,whereas in other designs these may be two individual devices,for example an electric generator and a gas?lled bounce chamber.

A simple design with high controllability is the

main strength of the single piston design compared to the other free-piston engine con?gurations.The rebound device may give the opportunity to accu-rately control the amount of energy put into the compression process and thereby regulating the compression ratio and stroke length.

2.2.2.Dual

piston

Fig.2.Hydraulic dual piston free-piston engine[7].

The dual piston(or dual combustion chamber) con?guration,shown in Figure2,has been topic for much of the recent research in free-piston engine technology.A number of dual piston designs have been proposed and a few prototypes have emerged, both with hydraulic and electric power output.The 1For a comprehensive timeline of free-piston engine devel-opments,see Aichlmayr[3].

2

dual piston engine con?guration eliminates the need for a rebound device,as the(at any time)work-ing piston provides the work to drive the compres-sion process in the other cylinder.This allows a sim-ple and more compact device with higher power to weight ratio.

Some problems with the dual piston design have, however,been reported.The control of piston mo-tion,in particular stroke length and compression ra-tio,has proved di?cult.This is due to the fact that the combustion process in one cylinder drives the compression in the other,and small variations in the combustion will have high in?uence on the next com-pression.This is a control challenge if the combus-tion process is to be controlled accurately in order to optimise emissions and/or e?ciency[3,8].Exper-imental work with dual piston engines has reported high sensitivity to load nuances and high cycle-to-cycle variations[9,10].

2.2.

3.Opposed piston

An opposed piston free-piston engine essentially consists of two single piston units with a common combustion chamber.Each piston requires a re-bound device,and a load device may be coupled to one or both of the pistons.Figure3shows an op-posed piston free-piston engine,with a mechanical piston synchronisation mechanism.

Fig.3.Illustration of an opposed piston free-piston engine with piston synchronisation mechanism.

The opposed piston principle was used almost exclusively in the early free-piston engine designs (1930-1960),and mechanical linkages connected the two pistons to ensure symmetric piston motion,as illustrated in the?gure.These engines served suc-cessfully as air compressors and later as gas gener-ators in large-scale plants,often with a number of units feeding a single power turbine.

The main advantage of the opposed piston con-?guration is the perfectly balanced and vibration-free design.This feature is not shared by any of the other free-piston con?gurations,which need al-

ternative means of controlling vibrations.A further advantage of the opposed piston design is reduced heat transfer losses due to the opposed piston cylin-der(elimination of the cylinder head),and this also allows uni?ow scavenging to be used,giving high scavenging e?ciency.

The absolute need for a piston synchronisation mechanism is the most important disadvantage of the opposed piston design.This,together with the need for a dual set of the main components,makes the engine complicated and bulky.Achten[8]consid-ers the opposed piston design and rejects this,and the only modern opposed piston free-piston design reported is the hydraulic engine developed by Hibi and Ito[11].

2.2.4.Gas generators

Free-piston gas generators(or gasi?ers)are free-piston engines feeding hot gas to a power turbine.

The only‘load’for the engine itself is that to su-percharge the intake air,the output work is taken out entirely from the power turbine.Free-piston gas generators were used in some large-scale marine and stationary powerplants in the mid-20th century,and attempts were made to use this principle in auto-motive applications.Figure4illustrates an opposed piston free-piston gas generator

plant.

Fig.4.Illustration of a free-piston gas generator Compared to a conventional gas turbine,the free-piston gas generator has the advantage of high com-pression and pressure ratios.It further di?ers in the way that the work needed to compress the intake air is already extracted from the gas when supplied to the power turbine.Consequently,the gas fed to the turbine holds a lower temperature which reduces the materials requirements and allows the turbine to be placed further away from the combustor without ex-tensive heat transfer losses.

3

The operational characteristics of a free-piston gas generator do not di?er much from those of other free-piston engines of the same con?guration.The opposed piston free-piston gas generator was the topic of much research in the mid-20th century and many reports can be found describing the design and operation of such engines.However,as con-ventional gas turbine technology matured,the free-piston gas generator concept was abandoned.The only reported modern application of this concept is the single piston free-piston gas generator presented by Johansen et al.[12].

3.Free-piston engine unique features

The free-piston engine has a number of unique fea-tures,some give it potential advantages and some represent challenges that must be overcome for the free-piston engine to be a realistic alternative to con-ventional technology.

3.1.Operating principle

The free-piston engine is restricted to the two-stroke operating principle,as a power stroke is re-quired on every cycle.Although two-stroke engines su?er from poorer performance compared to four-strokes,this performance gap is declining and recent years have seen an increased interest in small scale two-stroke engines.

3.2.Piston dynamics and control

In conventional engines,the crank mechanism and ?ywheel serve as both piston motion control and en-ergy storage.The piston motion control ensures suf-?cient compression in one end and su?cient time for scavenging in the other,while the energy stor-age provides energy for the compression of the next charge.In the free-piston engine the motion of the mover at any point in the cycle is determined by the sum of the forces acting upon it.Hence,the interac-tion of these forces must be arranged in a way that ensures the mover motion is within acceptable lim-its for all types of operation if the concept is to be feasible.

For an engine as shown in Figure5a,one can derive the mover motion mathematically using a free-body diagram as shown in Figure5b.The forces working on the mover are:combustion chamber pressure force F C,bounce chamber(rebound)

force

(a)Single piston free-piston engine

con?guration.

Max

F

BDC

(b)Free body diagram of the mover in a single piston free-

piston engine.

Fig.5.Piston dynamics of a single piston free-piston engine.

F R,load force F L.x denotes mover position,TDC N

and BDC N illustrate nominal top dead centre and bottom dead centre positions and ML are the me-chanical limits of the motion.The mover itself will have a mass m p.

Applying Newtons2nd law to the moving mass in Figure5b,the piston motion can be described with

i

F i=m p

d2x

d t2

.(1)

Knowing that the combustion cylinder and the bounce chamber will have characteristics similar to those of a gas spring,it becomes clear that they will produce a bouncing-type motion of the piston.

Adding a load force,this must have appropriate characteristics or be subordinate the other two to ensure a reciprocating motion of the piston.If a re-bound device with other force-position characteris-tics than a bounce chamber is used,such as a hy-draulic cylinder,the operational characteristics will be slightly di?erent but the same principles will ap-ply.

Figure5b further shows the di?erent parts of the engine stroke.Area A shows the piston position range where the compression ratio of the engine is 4

su?cient for fuel autoignition.For the engine to run, engine TDC must be within this area.Area B shows the piston position range where the scavenging ports are open and the burnt gases can be replaced with fresh charge.For the scavenging to be e?cient,the piston needs to spend a su?cient amount of time in this area in every cycle.

These requirements are absolute and for the en-gine to be practical,an engine control system needs to be able to meet these requirements for all types of engine operation.Accurate control of piston motion currently represents one of the biggest challenges for developers of free-piston engines.

3.2.1.Frequency control

For an engine with a gas?lled bounce chamber, the spring-mass nature of the system means that the frequency and stroke length are closely related. The system will operate at its natural frequency, and the pressure in the gas springs(i.e.spring sti?-ness)can only be varied over a limited range.The stroke length is strictly limited by the need for suf-?cient compression and scavenging,hence there will likely be limitations in the frequency control pos-sibilities of the engine.This also limits the power output range of such free-piston engines,which has been noted by a number of authors as a problem with the free-piston design.

For engines with di?erent types of rebound de-vices,very high levels of controllability can be achieved.The best example of this is the Pulse Pause Modulation(PPM)scheme for hydraulic free-piston engines,presented by Achten et al.[13]. The same principle has been employed by several other authors.

The Pulse Pause Modulation frequency control pauses the piston motion at BDC using a control-lable hydraulic cylinder as rebound device.At BDC the piston velocity is zero and the upwards motion will only begin when the rebound device releases the stored energy.The frequency can therefore be con-trolled by applying a pause between the time the piston reaches BDC and the release of compression energy for the next stroke.The frequency can in the-ory be varied down towards zero,there is no min-imum frequency like the idle speed in conventional engines.This is possible because the piston motion in each stroke is not frequency-dependent—the mo-tion pro?le will have the same form regardless of operating frequency.

Another consequence of this is that the frequency

will not largely in?uence the e?ciency of the engine.

A conventional engine may have to operate over a

range of ine?cient speeds or torques and only parts of the operational time on the design conditions.

Both Hibi and Ito[11]and Achten et al.[13]report very good part-load performance for hydraulic free-piston engines using PPM and Achten et al.present

a direct comparison to a conventional engine-pump

showing signi?cantly better part-load performance for the free-piston engine.

Such frequency control also allows frequency changes to take place instantaneously and step wise.Somhorst and Achten[14]report an idle speed of the Innas Free-Piston Engine with auxiliaries of 1Hz(60rpm).An illustration of the principle is shown in Figure6.

0.20.40.60.81

BDC

TDC

P

i

s

t

o

n

p

o

s

i

t

i

o

n

2.5Hz

5Hz

10Hz

20Hz

t[s] Fig.6.The principle of pulse pause modulation frequency control of a single-piston free-piston engine with20Hz max-imum frequency[14].

3.2.2.Starting

The free-piston engine cannot be cranked over several revolutions for starting like conventional en-gines and other methods for starting must therefore be implemented.Starting can be achieved by im-pulsing the piston to give it su?cient energy to reach top dead centre,or by driving the piston back and forth until it reaches su?cient compression.The lat-ter can be achieved if the load device can be run as motor,e.g.with an electric machine or a hydraulic cylinder.If the impulse strategy is used,it is crucial that the engine starts on the?rst stroke and that the engine control system is able to keep the engine running after this.

The mid-1900’s engines mainly used compressed air to aid starting,by rapidly introducing it into the bounce chamber.Achieving combustion on the 5

?rst stroke was not reported to be a problem,be-cause high compression ratios were achievable with this method.More challenging was to immediately control the amount of air in the bounce chamber to achieve su?cient scavenging for stroke number two, since the bounce chamber was now full of high pres-sure starting air.Although some reports indicate that starting was a challenge for the free-piston en-gines,this is never mentioned as a crucial problem. Most linear engine generator concepts use the electric machine in motoring mode to start the engine.Recent single piston and opposed piston hydraulic free-piston engines use stored hydraulic energy to start the engine.Since the rebound de-vices in these engines are hydraulic cylinders,the ?rst stroke is not di?erent from any other stroke and starting represents no problem.

3.2.3.Mis?ring

Mis?ring may represent a problem in the free-piston engine,since it does not have energy storage capable of driving the engine for several revolutions like the?ywheel in a conventional engine.Hence,if the engine fails to build up su?cient compression or if other factors in?uence the injection/ignition and combustion,the engine may stop.The same result may follow from a mistiming in the fuel injection or ignition timing.

Although this has often been mentioned as a po-tential problem in theoretical surveys on free-piston engine feasibility,such problems are not mentioned by any of the reported experimental work on free-piston engines reviewed.

3.3.Free-piston loads

The free-piston engine requires a linear load,and for the overall system to be e?cient the load must provide e?cient energy conversion.The rotating power source,such as internal combustion engines and turbines,has been the de facto standard for many years within electric power generation but also rotating hydraulic and pneumatic machinery are highly developed technologies.A challenge for free-piston engine developers is to?nd linear equivalents of these machines with comparable performance. The mechanical requirements for free-piston en-gine load devices are high since the load is coupled directly to the mover,and the load will be subjected to high acceleration forces.Secondary e?ects from the high accelerations such as cavitation in hydraulic

cylinders must also be considered.Furthermore,the load device may be subjected to heat transfer from the engine cylinders.

Known free-piston engine loads include electric generators,hydraulic pumps and air compressors.

The dynamic properties of these di?er widely.Im-portant factors when determining the feasibility of

a linear load for a free-piston engine are:Moving

mass,physical size,e?ciency and load force pro-?le.The following characteristics are typical for the mentioned load devices:

–Hydraulic pumps typically work against a high

discharge https://www.360docs.net/doc/107765847.html,bined with the incom-

pressible working?uid,this allows a small unit

with very low moving mass.The e?ciency of

such units is generally high and high opera-

tional?exibility has been demonstrated using

electronically controlled hydraulic control sys-

tems with fast-acting valves in free-piston en-

gines.The load force of a hydraulic pump is

approximately constant,due to the constant

discharge pressure.

–Electric generators can be relatively compact

in size but often su?er from a high moving

mass due to magnets or back iron in the mover,

required to supply or direct the power generat-

ing magnetic?ux within the machine.The ef-

?ciency of electric machinery is,however,gen-

erally very high.The load force of a permanent

magnet electric machine coupled to a purely

resistive load will be proportional to the trans-

lator speed,although other designs or the im-

plementation of power electronics may allow

variations on this.

–Air compressors were the original free-piston

load devices but are not necessarily better

suited for this purpose than the other two.

The variable stroke of the free-piston engine

may lead to poor volumetric e?ciency of the

air compressor when operating at varying

load levels.If operating with atmospheric in-

let pressure,a large compressor cylinder is

needed resulting in a large and heavy con-

struction.One advantage is that a stepped

compressor piston can be applied,giving a

compact multi-stage compressor.The load

pro?le of an air compressor is like that of a

gas?lled bounce chamber in the compression

phase and with an approximately constant

load force when the discharge valves are open

towards the end of the stroke.

Figure7illustrates the typical load characteristics 6

of the mentioned free-piston engine

loads.L o a d f o r c e

G a s f o r c e

Fig.7.Characteristics of free-piston engine loads [3].

3.4.Simplicity

The simplicity of the free-piston engine compared to conventional technology is one of the driving forces behind many of the recent free-piston en-gine developments.The elimination of the crank mechanism reduces the number of parts and the complexity of a free-piston engine signi?cantly and this potentially gives a number of advantages:

–Low frictional losses.Fewer moving parts in the free-piston engine give reduced frictional losses.In addition,the absence of a crankshaft eliminates losses due to crankshaft bearing friction,and the purely linear motion leads to very low side loads on the piston.This also reduces the cylinder lubrication requirements.–Reduced manufacturing costs.The reduced number of parts in the free-piston engine results in lower manufacturing costs.

–Compactness.With reduced number of parts,the size and weight of the free-piston engine can be reduced,giving a more compact unit.–Low maintenance costs and increased lifetime.The reduced number of parts and the reduced frictional losses reduce the maintenance costs of the free-piston engine.

3.5.The combustion process

Some reports have indicated that the combustion in free-piston engines bene?ts from the high piston speed around TDC.This leads to higher air veloc-ity and turbulence level in the cylinder,which ben-e?t air-fuel mixing and increase the reaction rate and ?ame speed.The high piston acceleration just after TDC leads to a rapid expansion,and time-dependent chemical reactions,such as NO x forma-tion,are potentially reduced.

Achten et al.[13]present experimental results showing signi?cantly faster combustion in the In-nas Free-Piston Engine compared to conventional engines.Values for ignition delay are found to be comparable to those found in conventional engines.Tikkanen et al.[9]present similar experimental results,and both groups indicate that combustion takes place predominantly in the premixed phase.Fleming and Bayer [15]describe how theoretical thermodynamic analysis of the engine processes had to be drastically changed to achieve good agreement with experimental data,due to long ignition de-lays and high heat release rate in the free-piston en-gine.Baruah [16]reports signi?cant advantages in emissions for a spark ignited free-piston engine over crankshaft engines,particularly for nitric oxides.As a result of the particular operating character-istics,the in-cylinder heat transfer will also di?er between the free-piston engine and conventional en-gines.The rapid power stroke expansion gives less time available for heat transfer from the hot gases to the cylinder wall,but increased in-cylinder gas mo-tion may have the opposite e?ect and increase the heat transfer rate.However,Uludogan et al.[17]in-vestigated the e?ects of increased engine speed on the combustion in a DI diesel engine and found that the advantages of increased fuel-air mixing far out-weigh the disadvantages associated with increased heat transfer.

A particular feature of the free-piston engine is the ability of the combustion process to in?uence the speed of the expansion,due to the direct coupling of the combustion cylinder to the low-inertia moving member.A rapid combustion process and pressure rise may lead to a faster expansion and vice versa.In a conventional engine,the inertia of the crank sys-tem and ?ywheel ensures that the speed of the en-gine stays constant in the time frame of the combus-tion process.This intricate coupling between ther-modynamics and mechanics makes detailed mod-7

elling of the free-piston engine complex,and models developed for conventional engines are therefore not necessarily suitable of modelling free-piston engine processes.

https://www.360docs.net/doc/107765847.html,bustion optimisation

The variable compression ratio in the free-piston engine may allow an optimisation of the combus-tion process not achievable in conventional engines. Given that a su?ciently accurate piston motion con-trol system can be realised,the compression ratio can be regulated during operation to achieve best possible performance in terms of e?ciency or emis-sions.Free-piston engines with compression ratios as high as50:1was reported in the mid-20th cen-tury[18].

3.5.2.Homogeneous charge compression ignition Homogeneous charge compression ignition (HCCI)engines compress a premixed charge until it self-ignites,resulting in very rapid combustion but with poor control of ignition timing.The free-piston engine is well suited for this since the requirements for accurate ignition timing control are lower than in conventional engines.Potential advantages of HCCI include high e?ciencies due to close to con-stant volume combustion and the possibility to burn lean mixtures to reduce gas temperatures and thereby some types of emissions.HCCI operation of free-piston engines has been attempted by among others Aichlmayr[3]and van Blarigan[19].

A quasi-HCCI approach is mentioned by Hibi and Ito[11].Diesel fuel is injected very early in the com-pression process but after the intake and exhaust ports have closed.The fuel does not ignite at in-jection because the temperature and pressure are too low,but distributes more or less evenly within the cylinder and self-ignites when the pressure and temperature reach higher values.Ignition occurs at multiple points around the cylinder and the burning fuel spray with high local temperatures is avoided.

3.5.3.Multi-fuel operation

The nature of the free-piston engine makes it well suited for multi-fuel operation.The variable com-pression ratio combined with modern engine tech-nology,such as variable fuel injection and valve tim-ing,enable the free-piston engine to run satisfacto-rily on a wide range of fuels.

Flynn[20]reports the successful operation of a free-piston engine on a range of di?erent fuels,in-

cluding gasoline,diesel fuel and crude oil,and states that’It seems that these engines do not care whether they get fuel with octane or cetane numbers’.He further states that the engine runs satisfactorily on vegetable and animal oils,with the only noticeable e?ect being the engine power output varying accord-ing to the heat content of the fuel.The same con-clusion is also reached by other authors[21].

3.6.Balancing

The inherent vibration-free design was an often reported advantage of the early opposed piston air compressors and gas generators.These engines,from the earliest air compressor designs in the1930’s to the gas generators developed during1940-1960,all had mechanical linkages synchronising piston mo-tion.Aichlmayr[3]describes the?rst presentation of the Junkers free-piston air compressor at the Leipzig fair in1936,where the excellent dynamic character-istics of the engines were demonstrated by suspend-ing the compressors from the ceiling in a single steel cable and balancing pencils on the running engine’s housing.Underwood[22]states that the smoothness of the General Motors GMR4-4’Hyprex’gas gen-erator was’frequently demonstrated by balancing a nickel on a horizontal machine surface’.

For the single piston and dual piston engine,how-ever,balancing issues need to be addressed when mounting the engine.Vibrations may be cancelled out by running two or more engines in parallel, but this requires accurate control of engine speed.

Another possibility is to apply counterweights,as demonstrated by Braun[23].Disadvantages of coun-terweights are a more complex design,increased engine size and weight and additional friction losses.

Achten[8]states that for the17kW hydraulic free-piston engine considered in his paper,vibrations can be accounted for when mounting the engine and that the acceleration forces will have about the same magnitude as in conventional engines.

3.7.Mechanical requirements

High pressure gradients,resulting from high fuel burn rate,lead to high forces and accelerations and increased mechanical requirements in the free-piston engine.Flynn[20]reported that the major problems in free-piston engines are the mechanical wear and damage,mainly due to high temperatures and pres-sures.

8

Due to the variable stroke of the free-piston en-gine,high peak pressures may be also be experienced during transient operation or from operation of the engine at too high compression ratios.

4.Reported free-piston engine applications Since the free-piston engine was?rst developed around1930a number of di?erent designs have been proposed using the free-piston concept.The major-ity of these were,however,not commercially suc-cessful.This section gives an overview of known free-piston engine developments,with an empha-sis on engines where experimental results or op-erational performance data have been reported.It should be noted that in addition to these a high number of patents describing free-piston machinery exist,where the actual development of the engines has not been reported.

4.1.Free-piston air compressors

The original free-piston con?guration proposed by Pescara was an air compressor,and these ma-chines proved to possess some very attractive fea-tures.Despite the large research e?orts on the free-piston gas generator during1940-1960,the air com-pressor is by many considered to be the only really successful free-piston engine concept.The excellent performance of the air compressors was a strong con-tributor to the later signi?cant research e?orts put into the free-piston gas generator.

These engines were of the opposed piston type, making them vibration-free.Farmer[4]discusses how the interaction between the bounce chamber and the compressor cylinders controls the compres-sion energy delivered to the combustion cylinder and makes the engine essentially self-regulating. Despite its apparent good performance,the free-piston air compressor did not gain widespread com-mercial success.No reports of serious lacks or?aws in the concept explaining this can be found,except that the free-piston air compressor had a narrow output range.Most reports are,in fact,of the oppo-site opinion,such as McMullen and Payne[24]who state that the free-piston air compressor has proved ’reliable and e?cient under all conditions of service’. Beachley and Fronczak[25]evaluate the lack of success of the free-piston air compressor and present some possible factors,including that(a)stationary installations tended to use cheaper electric motors

to drive compressors;(b)demand for variable power output disfavoured the narrow-output free-piston air compressor for portable applications;(c)low fuel prices and a limited market for such applications dis-couraged the development of such unconventional design.

4.1.1.Reported free-piston air compressors

Junkers One of the earliest successful free-piston engine applications was the air compressor devel-oped by German company Junkers in the early 1930’s.The Junkers air compressor was?rst ex-hibited in1936and was used by the German navy during World War2to provide compressed air for launching torpedoes.After the war,US company Worthington continued development on the Junker model with only minor design changes[27].

The Worthington-Junkers air compressor was an opposed piston,diesel-powered unit with multiple compressor stages and no rebound device,as the compressed air left in the clearance volumes in the compressor cylinders provided the work to drive the next compression.This was possible because the compressor had constant power output and the fuel pump was set to deliver a?xed amount of fuel,with on-o?control regulating the delivery of compressed air[4].

A mechanical synchronisation mechanism con-

necting the two pistons ensured vibration-free op-eration.Starting was done with compressed air,by manually moving the pistons to its outer positions, pressurising the compressor cylinders and then re-leasing the pistons.London and Oppenheim[26] report that a compression ratio of40:1was achieved with this method,virtually ensuring ignition and unproblematic starting.

Toutant[27]reports that the unit occupied about 50%of the space required by a conventional electri-cally driven compressor and that this,together with good fuel e?ciency,gave the unit great advantages in submarine installations.

Braun linear engine In a more recent approach, Braun and Schweitzer[23]present a single piston free-piston engine.The load device in the described engine is an air compressor but the authors state that any suitable linear load may be applied.The en-gine operates on a crankcase-scavenged,two-stroke spark ignited cycle and counterweights make the en-gine completely balanced.A compression ignition 9

version of the engine is also reported to have been successfully operated.

Extensive testing of the engine is reported,among this15,000hours of operation without breakdown and40,000consecutive starts without a miss.The authors state that superior fuel economy is possible due to the on/o?control of the compressor,where conventional engine-compressor sets would run idle.

4.2.Free-piston gas generators

In the late1940’s the free-piston gas generator attracted interest for use in large-scale powerplants, and later also for vehicle propulsion.Many variants emerged,and both General Motors and Ford Motor Company had working prototypes aimed for vehicle https://www.360docs.net/doc/107765847.html,rger free-piston gas generators were installed in a number of stationary powerplants and in some marine installations.Much experience in the operation of free-piston machinery is reported in this period.

These engines were typically diesel powered,op-posed piston engines with mechanical synchronisa-tion of the two pistons.The synchronisation mech-anism did,in addition to evening out possible force di?erences,also drive the accessories such as fuel in-jection pump,oil pump and water pump.The start-ing of the engines was,similar to the Junkers air compressor,performed by rapidly introducing com-pressed air into the bounce chambers.

These engines were highly supercharged and operated on higher mean e?ective pressures than conventional diesel engines[26].The most impor-tant advantages of free-piston gas generators were: low fuel quality requirements,vibration-free design, good dynamic response and low turbine material re-quirements due to lower inlet temperatures.London and Oppenheim[26]state that the fuel economy of the free-piston gas generator power plant was com-petitive with conventional diesel engines and80-100%better than conventional gas turbine plants. The speci?c weight was somewhere between the low speci?c weight of the gas turbine and the high speci?c weight of the conventional diesel engine. McMullen and Ramsey[28]claim that the higher free-piston gas generator e?ciency compared to the conventional gas turbine was due to the higher com-pression pressures.They state that free-piston en-gines could achieve an end-of-compression pressure of100times the atmospheric pressure,whereas in the simple type gas turbine this value was around

6.In relation to this,Aichlmayr[3],however,notes

that the gas turbine was in its infancy in the1940’s and that this must be considered when comparing the two plants.

A particular feature of the free-piston gas gener-

ators,giving them an advantage over conventional gas turbines,was the low temperature of the gas sup-plied to the power turbine.This was a result of the work required to compress the inlet air already hav-ing been extracted before the gas was fed to the tur-bine.This allowed the free-piston unit to be placed further away from the power turbine without exten-sive heat losses from the hot gases,a feature that was one of the driving forces behind the development of such engines for automotive use.

Despite some well documented advantages,the free-piston gas generator never became a real com-petitor to either the diesel engine or the gas turbine.

Some of the reasons for the limited success of the free-piston gas generator are:

–High development e?orts were put in to

both conventional diesel engines and gas tur-

bine technology,giving rapid performance

increases.

–The matching of a pulsating-?ow compressor

with a continuous-?ow turbine proved prob-

lematic,giving low part-load e?ciency and

limiting the gas generator to constant power

applications[18,20].

–High failure rates and low lifetime and avail-

ability were reported,related to high pressure

and temperature operation[20].

–The engines did not provide large advantages

in weight or fuel economy compared to con-

ventional engines and could not compete with

the power to weight ratio of the gas turbine.

With the maturing of conventional gas turbine tech-nology,development of the free-piston gas generator was largely abandoned in the early1960’s.[3,18,20]

4.2.1.Reported free-piston gas generator

applications

SIGMA The model GS-34free-piston gas genera-tor manufactured by Soci′e t′e Industrielle G′e n′e rale de M′e canique Appliqu′e e(SIGMA)in France was one of the most successful free-piston engines ever made.The development of the GS-34was?nished in1944,and it was based on Pescaras patents.

The GS-34was an opposed piston,diesel powered unit aimed for large scale applications such as ma-rine and industrial powerplants.The engine had an 10

output power of around1000kW and a setup with multiple engines in parallel,supplying a single tur-bine was frequently used.Huber[29]reports that in October1957,90gas generators with a total run-ning time of about250000hours were in commercial use and more units were on order.

The engines were used in various installations such as stationary plants,the largest one being the Cherbourg power plant consisting of8gas genera-tors feeding one turbine and giving6000kW electric power output.As marine powerplants,free-piston gas generators were installed in21minesweepers of the French Navy.Huber reports favourable re-sults with excellent vessel manoeuvrability using gas generators compared to conventional diesel en-gine propulsion.Other marine installations are also mentioned,in addition to other applications such as locomotives and the powering of pumps and

compressors.

Fig.8.Illustration of the SIGMA GS-34free-piston gas gen-erator[26].(Note that the illustration is simpli?ed for clar-ity.)

Power output1138hp

Weight(approx.)8000kg

Speed613rpm

Cylinder bore0.34m

Bounce chamber bore0.90m

Stroke0.44m

Compressor pressure ratio 5.42

Engine compression ratio8.5

Piston mass503kg

Overall thermal e?ciency34.6%

Table1

SIGMA GS-34design and performance[26].

General Motors General Motors(GM)gained in-terest in the free-piston engine concept after test-ing a number of free-piston engines including the

SIGMA GS-34gas generator in the mid-1950’s.This ultimately led to the development of two free-piston gas generators,the GM-14,which was based on the SIGMA engine,and the GMR4-4’Hyprex’.

A marine powerplant based on six GM-14units

was installed in the GTS William Patterson,a United States Maritime Administration vessel, in the late1950’s but with disappointing results.

Specht[30]evaluates the powerplant and reports

a number of problems during the test period but

also explains how some of them were addressed.

Problems include air pulsation and noise in the machinery room,piston ring breakage,di?culties in matching gas generators with turbines,and high maintenance costs.Reported advantages of the pow-erplant included high manoeuvrability,the possibil-ity of rapid change in power level,easy maintenance of the units with low implications on vessel opera-tion,and high?exibility in operation due to the6 gas generators and2turbines.The fuel economy is reported to have been comparable to conventional technology.Specht concludes that the gas generator plant is unsuitable for scaling up due to the neces-sary increase in number of units,increasing labour costs for maintenance and operation.

The GMR4-4’Hyprex’was a dual(’siamesed’) opposed piston,diesel free-piston engine aimed for automotive applications,and had power output of around185kW at2400rpm.Underwood[22]lists the reasons for the chosen siamesed design,which include a more compact unit and reduced pressure oscillations at the turbine inlet.The engine was in-stalled in a car,the XP-500,for testing,making this the?rst car in the world to be powered by a free-piston engine.Despite optimistic reports from the GM engineers,the Hyprex could not compete with conventional engines and was abandoned[18].

Ford Like General Motors,Ford saw a potential in the free-piston gas generator for automotive appli-cations in the mid1950’s.Frey et al.[31]mention the potential advantages of mounting the gas gener-ator in the front of the vehicle and the power turbine in the rear,thereby eliminating the drive tunnel and achieving better weight distribution(this is also dis-cussed by Underwood of General Motors[22]).

Frey et al.showed analytical models for the design of a free-piston gas generator and they described the development of a150hp,2400rpm unit.They re-port initial development di?culties regarding start-ing,breakage of piston rings,injection pump fail-11

ures and poor combustion,but describe how most of these were addressed by improvements in the design.Noren and Erwin [21]described the development of the Ford model 519free-piston powerplant and the implementation of that in a farm tractor.The authors state that in the tractor,the free-piston powerplant is more compact,has lower weight and provides more freedom in the mounting of the en-gine than a comparable conventional diesel engine.Based on results from the test vehicle they report su-perior torque characteristics for the free-piston gas generator unit over a conventional piston engine,il-lustrated in Figure 9.Where the crankshaft engine torque will decrease at reducing speeds and the en-gine will ?nally stall or a gear shift has to be made,the free-piston unit torque increases at lower speeds.Other reported advantages of the free-piston unit are vibration free operation and low noise.

Turbine engine

Piston engine

Engine rpm

D r a w b a r p u l l

Fig.9.Torque characteristics of the free-piston powerplant compared to a conventional engine [21].

Kv?rner In a more recent approach,the Norwe-gian company Kv?rner ASA designed an 8-cylinder,8MW free-piston gas generator together with Norwegian University of Science and Technology (NTNU)[12].The engine is a single-piston gas gen-erator,illustrated in Figure 10,and experimental results from a one-cylinder test engine is reported.The developers derived a control strategy for pis-ton motion control,controlling TDC,BDC and syn-chronisation of the cylinders in addition to supervi-sory control objectives of load and combustion opti-misation [32].This engine is the only reported mod-ern attempt of building a free-piston gas generator.However,through personal communication with the developers the authors have learnt that this project

was abandoned before completion.The reasons for this are not

known.

Fig.10.Kv?rner KLC free-piston gas generator [12].

4.3.Hydraulic free-piston engines

Many of the modern approaches in free-piston en-gine technology are hydraulic engines,in which the combustion piston is directly coupled to a hydraulic pump cylinder.A number of projects are ongoing,both within academia and in industry.Most of these units are aimed at o?-highway vehicles such as fork-lift trucks and earth-moving machinery and,conse-quently,most developments are of small size (typ-ically 30-50kW).Such vehicles typically have high hydraulic loads from vehicle accessories and propul-sion,and they are commonly powered by a conven-tional diesel engine coupled to a hydraulic pump.Hydraulic free-piston engines may apply a hy-draulically driven rebound device,using part of the produced hydraulic energy to return the piston,or a bounce chamber.A number of prototypes have been developed in recent years and experimental re-sults from these are currently being reported.The reports show generally good fuel economy and very good performance at part load.

4.3.1.Reported hydraulic free-piston engine applications

Toyohashi University Researchers at Toyohashi University of Technology in Japan have been doing

12

research in the?eld of hydraulic free-piston engines for more than20years.They have reported experi-mental results from both single piston[33]and op-posed piston[11]diesel powered free-piston engines. The latter is the latest published work,with re-ported engine hydraulic thermal e?ciency of31%2. The authors state that this value stays practically constant even with very low hydraulic power output. The fuel injection is hydraulically actuated and the fuel is injected very early in the compression process to achieve a combustion process similar to that of a homogenous charge compression ignition engine. Hibi and Ito[11]further present an alternative pis-ton synchronisation method for the opposed piston engine,eliminating the traditional mechanical link-age.The pistons in the hydraulic free-piston engine are synchronised by using a combination of the elec-tronically controlled hydraulic rebound device and a mechanical spring.A small synchronisation error is reported,but this is not large enough to a?ect the performance of the engine.

Innas The Dutch company Innas BV is among the research leaders within free-piston technology today. They have developed a single piston,diesel powered, hydraulic free-piston engine,intended as an alter-native to conventional engine and hydraulic pump systems in o?-highway vehicles[13].The implemen-tation of the engine in a fork lift truck is also de-scribed[34].The developers claim that reduced ex-haust emissions and lower fuel consumption can be achieved with the engine,due to a mechanically less complex design and high operational?exibility. The Innas Free-Piston Engine engine has17kW power output,and indicated e?ciencies of around 50%are reported[14].The construction of the en-gine is shown in Figure11,and it utilises a complex hydraulic control system.The engine uses the pulse pause modulation control principle,described ear-lier in this text.Fuel consumption is reported to be around20%lower than a conventional engine-pump unit and at low loads even50%lower[13].

Innas is currently also involved in a free-piston engine generator project,under a European Union programme.

Technische Universit¨a t Dresden Researchers at the German university Technische Universit¨a t Dres-

2For comparison:a conventional diesel engine with fuel ef-?ciency of35%coupled to a hydraulic pump with e?ciency 85%would give a total(’hydraulic’)e?ciency of30

%.

(a)The working principle of the Innas Free-Piston

Engine.

(b)Photograph of the engine.

Fig.11.The Innas Free-Piston Engine(?gures courtesy of Innas BV;reprinted with permission).

den report the development of a hydraulic free-piston engine with a patented hydraulic control system[6,35].The unit is a single piston engine similar to the Innas Free-Piston Engine,and the en-gine illustrated in Figure1.Unlike the Innas engine, it is controlled with on/o?control.The developers present the implementation of the engine in a hy-draulic circuit and report a hydraulic e?ciency of above30%.

Tampere University Researchers at Tampere Uni-versity of Technology,Finland,describe the design and performance of a dual piston hydraulic free-piston engine prototype,illustrated in Figure2[9].

The engine is diesel powered,utilising electronic con-trol with a common rail injection system.Starting is done with stored hydraulic energy,using the hy-draulic pump to drive the piston.

Test results from the?rst test engine are de-scribed,and show a piston motion di?erent from that of conventional engines and piston acceleration peak values of more than double than those of com-parable crankshaft engines.In comparison to con-ventional engine piston motion,it is observed that maximum piston velocity is lower for the free-piston 13

engine with equal mean piston speeds.The develop-ers state that the relative long periods of the stroke with almost constant piston velocity and the short turn times at the dead centres bene?t the hydraulic pump circuit.Total e?ciency of20%was reported. The developers report cycle-to-cycle variation in stroke for each cylinder of±1%,giving a variation in compression pressure of around±15%.Combustion pressures varying between77-88bar are reported. The authors state that the results from the initial tests were satisfactory as proof-of-concept for the hydraulic dual piston engine but that the control is-sues should be adressed.Recent publications inves-tigating engine control issues include Tikkanen and Vilenius[36].

4.4.Free-piston engine generators

The free-piston engine generator consists of a free-piston engine coupled to a linear electric machine. Such technology is currently being explored by a number of research groups worldwide.The high e?-ciencies of electrical machinery,along with?exibility and controllability,make this an interesting concept.

A driving force behind the interest in free-piston en-gine generators is the automotive industry’s increas-ing interest in hybrid-electric vehicle technology. Free-piston engine generator designs of both sin-gle piston and dual piston types have been reported.

A bounce chamber may be applied in the single pis-ton engine,but the use of the electric machine as rebound device has also been proposed.Implemen-tation of appropriate power electronics may allow the use of the electric machine in motoring mode to aid engine control and for starting.

4.4.1.Reported free-piston engine generator applications

West Virginia University Researchers at Univer-sity of West Virginia describe the development of a spark ignited dual piston engine-generator[37]. They have thoroughly documented their work and ?ndings in a number of publications,both concern-ing linear alternator design,design and operation of the combustion engine and analysis of the com-bined system[10,37–40].An engine prototype is reported to have achieved316W power output at 23.1Hz,with36.5mm bore and50mm maximum stroke.High cycle-to-cycle variations are reported, particularly at low loads.

This group of researchers is the most successful within academia regarding free-piston engine gener-ator research.It is one of very few that have reported the successful development of a running

prototype.

Fig.12.Illustration of the free-piston engine generator pro-totype developed at University of West Virginia[38].

Sandia National Laboratories Van Blarigan[19] presents the design of a dual piston free-piston en-gine generator with40kW electric power output.

The engine employs homogeneous charge compres-sion ignition(HCCI)and is aimed to operate on

a variety of hydrogen-containing fuels.The HCCI

combustion is to achieve faster combustion than that in SI or CI engines,and to burn lean mix-tures at high compression ratios and thereby re-duce NO x emissions formation.Test results from

a compression-expansion machine are presented,

showing close to constant volume combustion with hydrogen,bio-gas and ammonia at equivalence ra-tios of around0.3.

Van Blarigan states that operation on lean mix-tures and with low mean e?ective pressures is possi-ble without e?ciency penalties due to the low fric-tional losses in the free-piston engine.

KTH,Stockholm A research group from Royal In-stitute of Technology(KTH),Stockholm,Sweden, has published a number of articles evaluating di?er-ent electrical machine possibilities for a free-piston engine generator[41,42].They state that?nding an electrical machine ful?lling their requirements is a challenging task but?nd that the permanent magnet,transverse-?ux machine is the most promis-ing candidate.The transverse-?ux machine bene?ts from a low translator mass compared to other per-manent magnet con?gurations but su?ers from a low power factor and high manufacturing costs.The authors state that all the evaluated machines have satisfactory e?ciency but that none of them come close to achieving the speci?c power requirements.

Based on their initial?ndings,the transverse-?ux machine is further investigated and the development 14

of a prototype is reported[43].Based on the pro-totype testing and further design optimisation,it is concluded that the transverse-?ux machine may satisfy the requirements for an electric machine in a free-piston engine generator.

5.Conclusions

The basic design and unique features of the free-piston engine have been discussed.Although several reports have con?rmed that the free-piston engine is a viable concept,more research is required to inves-tigate potential advantages over conventional tech-nology.The area with most uncertainty is clearly that of piston motion control.Most of the poten-tial advantages of the free-piston engine depend on an appropriate control system being realisable.Op-timisation of the combustion process and multi-fuel or HCCI operation require compression ratio con-trol,and elimination of vibrations by running sev-eral units in opposite phases requires accurate con-trol of engine speed.

A review of reported free-piston engine applica-tions presented performance data and operational experience of the most successful free-piston engine developments to date.Both engines developed in the period1930–1960,namely free-piston air com-pressors and gas generators,and more recent ap-proaches of hydraulic and electric free-piston en-gines were reviewed.The most promising technol-ogy at the moment appears to be the hydraulic free-piston engines,with several developments showing favourable performance compared to conventional technology by fully utilising the powers of modern, microprocessor-based,control technology.

Free-piston engine generators are also under in-vestigation by a number of research groups world-wide.The?exibility and controllability of electric machinery,along with increasing interest in tech-nologies such as hybrid-electric vehicles and the all-electric ship concept,are incentives driving the de-velopment of free-piston engine generator technol-ogy,and the performance of such engines is expected to improve signi?cantly in the future. References

[1]Hekkert MP,Hendriks FHJF,Faaij APC,Neelis ML.

Natural gas as an alternative to crude oil in automotive fuel chains well-to-wheel analysis and transition strategy development,Energy Policy,2005:33:579–594.

[2]Pescara RP.Motor compressor apparatus,US Patent

1,657,641,1928.

[3]Aichlmayr HT.Design Considerations,Modeling,and

Analysis of Micro-Homogeneous Charge Compression

Ignition Combustion Free-Piston Engines,PhD Thesis,

University of Minnesota,2002.

[4]Farmer HO.Free-piston compressor-engines,Proc.Inst.

Mech.Eng.,1947:156:253–271.

[5]Pescara RP.Motor compressor of the free piston type,

US Patent2,241,957,1941.

[6]Brunner H,Winger A,Feuser A,Dantlgraber J,

Sch¨a?er R.Thermohydraulische Freikolbenmaschine als

Prim¨a raggregat f¨u r mobilhydraulische Antriebe,4th Intl

Fluid Power Conference,Dresden,2004.

[7]Tikkanen S,Herranen M,Savela R,Vilenius M.

Simulation of a hydraulic free piston engine:A dual

piston case,Proc.Sixth Scandinavian international

conference on?uid power,pp.339–349,1999.

[8]Achten PAJ.A review of free piston engine concepts,

SAE Paper941776,1994.

[9]Tikkanen S,Lammila M,Herranen M,Vilenius,M.First

cycles of the dual hydraulic free piston engine,SAE

Paper2000-01-2546,2000.

[10]Clark N,Nandkumar S,Atkinson C,Atkinson R,

McDaniel T,Petreanu S et al.Operation of a small-

bore two-stroke linear engine,Proc.of the Fall Technical

Conference of the ASME Internal Combustion Engine

Division,1998:31-1:33–40.

[11]Hibi A,Ito T.Fundamental test results of a hydraulic

free piston internal combustion engine,Proc.Inst.Mech.

Eng.,2004:218:1149–1157.

[12]Johansen TA,Egeland O,Johannesen EA,Kvamsdal

R.Dynamics and control of a free-piston diesel engine,

ASME J.Dynamic Systems,Measurement and Control,

2003:125:468–474.

[13]Achten PAJ,van den Oever JPJ,Potma J,Vael GEM.

Horsepower with brains:The design of the Chiron free

piston engine,SAE Paper2000-01-2545,2000.

[14]Somhorst JHE,Achten PAJ.The combustion process

in a DI Diesel hydraulic free piston engine,SAE Paper

960032,1996.

[15]Fleming JD,Bayer RJ.Diesel combustion phenomena

as studied in free piston gasi?ers,SAE Paper630449,

1963.

[16]Baruah PC.A free-piston engine hydraulic pump for an

automotive propulsion system,SAE Paper880658,1988.

[17]Uludogan A,Foster DE,Reitz RD.Modeling the e?ect

of engine speed on the combustion process and emissions

in a DI Diesel engine,SAE Paper962056,1996.

[18]Amann CA.Evaluating alternative internal combustion

engines:1950-1975,Trans.of the ASME–Journal of

Engineering for gas turbines and power,1999:121:540–5.

[19]van Blarigan P.Advanced Internal Combustion

Electrical Generator,Proc2002U.S.DOE Hydrogen

Program Review,NREL/CP-610-32405,2002.

[20]Flynn G Jr.Observations on25,000hours of free-piston-

engine operation,SAE Transactions1957:65:508–515.

[21]Noren OB,Erwin RL.The future of the free-

piston engine in commercial vehicles,SAE Transactions

1958:66:305–314.

[22]Underwood AF.The GMR4-4“HYPREX”engine–

A concept of the free-piston engine for automotive use,

SAE Transactions1957:65:377–391.

15

[23]Braun AT,Schweitzer PH.The Braun linear engine,

SAE paper730185,1973.

[24]McMullen JJ,Payne WG.Performance of free-piston

gas generators,Transactions of the ASME1954:76:1–13.

[25]Beachley NH,Fronczak FJ.Design of a free-piston

engine-pump,SAE Technical Paper921740,1992. [26]London AL,Oppenheim AK.The free-piston engine

development–Present status and design aspects, Transactions of the ASME,1952:74(2):1349–1361. [27]Toutant WT.The Worthington-Junkers free-piston air

compressor,Journal of the American Society of Naval Engineers,1952:64(3):583–594.

[28]McMullen JJ,Ramsey R.The free-piston type of gas

turbine plant and applications,Transactions of the ASME,1954:76:15–29.

[29]Huber R.Present state and future outlook of

the free-piston engine,Transactions of the ASME, 1958:80(8):1779–1790.

[30]Specht DH.Evaluation of free piston-gas turbine marine

propulsion machinery in GTS William Patterson,SAE Paper620280,1962.

[31]Frey DN,Klotsch P,Egli A.The automotive free-piston-

turbine engine,SAE Transactions,1957:65:628–634. [32]Johansen TA,Egeland O,Johannesen EA,Kvamsdal R.

Free-piston diesel engine timing and control–towards electronic cam–and crankshaft,IEEE Trans.Control Systems Technology,2002:10:177–190

[33]Hibi A,Kumagai S.Hydraulic free piston internal

combustion engine–test result,Hydraulic Pneumatic Mechanical Power,1984:30(357):244–9.

[34]Vael GEM,Achten PAJ.The Innas Fork Lift Truck,

Working Under Constant Pressure,Proc. 1.IFK, IFAS/RWTH Aachen,1998.

[35]Brunner H,Dantlgraber J,Feuser A,Fichtl H,Sch¨a?er

R,Winger A.Renaissance einer Kolbenmachine, Antriebstechnik,2005:4:66–70.

[36]Tikkanen S,Vilenius M.Control of a dual hydraulic

free piston engine,Int.J.Vehicle Autonomous Systems, 2006:4(1):3–23.

[37]Clark N,Nandkumar S,Atkinson C,Atkinson R,

McDaniel T,Petreanu,S et al.Modelling and development of a linear engine,ASME Spring Conference,Internal Combustion Engine Division, 1998:30(2):49–57.

[38]Famouri P,Cawthorne WR,Clark N,Nandkumar S,

Atkinson C,Atkinson R et al.Design and testing of a novel linear alternator and engine system for remote electrical power generation,Proc.IEEE Power Engineering Society winter meeting,pp.108–112,1999.

[39]Clark N,Nandkumar S,Atkinson C,Atkinson R,

McDaniel T,Petreanu S et al.Numerical simulation of

a two-stroke linear engine-alternator combination,SAE

Paper1999-01-0921,1999.

[40]Clark N,Nandkumar S,Atkinson C,Atkinson R,

McDaniel T,Petreanu S et al.Fundamental analysis of

a linear two-cylinder internal combustion engine,SAE

Paper982692,1998.

[41]Arshad WM,B¨a ckstr¨o m T,Thelin P,Sadarangani C.

Finding an appropriate electrical machine for a free piston generator,Proc.Intl Battery,Hybrid and Fuelcell Electric Vehicle Symposium and Exhibition,Busan, Korea,2002.

[42]Arshad WM,Thelin P,B¨a ckstr¨o m T,Sadarangani C.

Alternative electrical machine solutions for a free piston

generator,The Sixth Intl Power Engineering Conference

(IPEC2003),Singapore,2003.

[43]Arshad WM,Thelin P,B¨a ckstr¨o m T,Sadarangani

https://www.360docs.net/doc/107765847.html,e of transverse-?ux machines in a free-piston

generator,Proc.IEEE Intl Electric Machines and Drives

Conference(IEMDC),Madison,Wisconsin,USA,2003. 16

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matlab函数用法

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(完整版)matlab函数大全(非常实用)

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