a diesel two-stroke linear engine

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A Diesel Two-Stroke Linear Engine

David Houdyschell

Thesis submitted to theCollege of Engineering and Mineral Resources

at West Virginia Universityin partial fulfillment of the requirements

for the degree of

Master of Sciencein

Mechanical Engineering

Nigel N. Clark, Ph. D., ChairChristopher M. Atkinson, Sc. D.

W. Scott Wayne, Ph. D.Ralph Nine, MSME.

Department of Mechanical and Aerospace Engineering

Morgantown, West Virginia



g , W V g



Acknowledgements

I first thank Dr. Nigel Clark for providing me with an opportunity to work with

him, and for being my advisor and friend. His guidance and comments have aided me in

my college career. Next, I thank Dr. Victor Mucino for providing support for me during

the first part of my graduate work. I thank all of my committee members, Dr.

Christopher Atkinson, Dr. Scott Wayne, Mr. Ralph Nine, for their support in my thesis

work.

I give great thanks to Richard Atkinson and Tom McDaniel for their help in the

design and construction of the test engine. Without the support and guidance of these

two individuals the engine would not have progressed to the extent that it has. Justin

Kern, John Anderson, Dustin McIntyre, Dave McKain, Ron Jarrett, and Marcus Gilbert

all deserve thanks for helping, supporting, and encouraging me.

I give my family a thanks for their support of me during this busy time. Last but

not least I thank my fiancé Rayna for her, help, love and support through the duration of

my masters work. Rayna’s support made it much easier to carry on through any



List of Tables

3.1. In-cylinder pressures and pressure force as a function of the slider displacement.

3.2. Simulation constants.

3.3. Test trials mass and bore values.

4.1. Prototype component description.



List of Figures

3.1. The ideal engine model at the beginning of a left to right compression stroke

( s x x −= ).

3.2. The ideal engine model with the pistons at the midpoint position ( 0= x ).

3.3. Pressure volume diagram of limited-pressure cycle.

3.4. Four regions can be seen for the pressure balance due to the limited-pressure

cycle of operation.

3.5. Obtained half stroke can be seen to be a function of the amount of heat input and

the percentage of heat input at constant volume.

3.6. The constant pressure expansion coordinate defines how much heat is input at

constant pressure. It can be seen to be a function of the heat input and φ.

The compression ratio is defined by the geometry of the engine and the achieved

half stroke.

The period of the operating cycle is seen to be the smallest for a Diesel cycle of



3.12. Slider Velocity versus time shows the velocity is near constant for most of the

stroke.

3.13. Work output versus time shows positive work being performed during the

expansion stroke and negative work during the compression stroke. During the

gas exchange operation when the exhaust port is open, work output can be seen to

have offsetting positive and negative work regions.

3.14. In-cylinder pressure versus time.

3.15. In-cylinder pressure versus in-cylinder volume shows a pressure trace of the

idealized model.

4.1. Diesel prototype.

4.2. Dimensional sketch of cylinder assembly.

4.3. Diesel prototype engine control module block diagram.

4.4. Overhead view of engine setup.

4.5. Front view of engine.



Nomenclature

b bore diameter of the engine

sm mass of the piston slider

vC constant volume specific heat

pC constant pressure specific heat

n ratio of specific heatsr compression ratio

m x maximum theoretical half-stroke length of the engine

s x maximum achieved half-stroke length of the engine

epr x right exhaust port closing coordinate

epl x left exhaust port closing coordinate

a x constant pressure expansion end coordinate

x instantaneous piston position

f F friction force required to move the piston

φ percentage of total heat input performed at constant volume

inQ quantity of heat added during one stroke

f



inT intake air temperature

2T air temperature at point 2 in the cycle3T air temperature at point 3 in the cycle

aT air temperature at point a in the cycle



1. Introduction

The present day internal combustion engine has proven to be successful as a

means of producing power. In its current form, the internal combustion engine converts

the linear energy of the pistons to rotational energy by means of a slider-crank

mechanism. Components such as the crankshaft are the cause of much of the friction inthe current internal combustion engine. The use of a linear engine would eliminate this

friction by eliminating the crankshaft and other rotational components and also the

friction on the piston due to side thrust caused by the slider-crank mechanism. This

reduction in friction would greatly improve the efficiency of the engine.

Past studies of free piston engines have shown that they would be useful in

situations where linear power delivery could be used. Researchers have been studying

methods to use linear power delivery. One such method has been for fluid power

delivery either in the form of a hydraulic pump mechanism or an air compressor. Free

piston engines have also seen use as gas generators where a mix of the exhaust gas and



The current research involved an engine consisting of two pistons, connected

solidly by a rod, such that the two pistons reciprocated with precisely the same motion.

The motion of the piston is not mechanically prescribed but is rather a result of the

balance of in-cylinder pressures, inertia forces, friction forces and the applied load.

Idealized modeling of a two-stroke linear engine, assuming a limited pressure cycle of

operation, has yielded a closed form solution for piston motion. A benchtop prototype of

a linear engine was constructed and tested. The prototype was a direct injection, Diesel

fueled compression ignition engine and was tested with varying degrees of success. At

the time of this thesis the engine has cranked and fired briefly. However, sustained

operation has not taken place due to failures in the engine controller upon firing.

There were several reasons as to why the development of this engine went to

compression ignition over spark ignition. First, it could be seen from the past study that

an increase in the compression ratio would reduce the amount of adverse work required

to reverse the piston motion making more work available for generating power. With the

higher compression ratio the piston would act as a gas spring reversing the piston motion.



2. Literature Review

Free piston engines have been investigated for many years. A study of literature

and patents pertaining to this scrutiny has been presented in this chapter.

Achten [5] studied and documented the different types of free piston engines. His

study concentrated on the conceptual differences between the different mechanisms.

Crankless gas generator piston engines were used in the 1950’s. These engines

consisted of opposed pistons that were each directly connected to an air compressor

piston. The mix of compressed air and engine exhaust was then sent to drive a gas

turbine Cleveland Diesel Engine [6]. Frey et al. [7] built and tested a free piston gas

generator turbine set that was sized for an automobile.

Galitello [8] patented a two-stroke cycle, variable compression, free piston

engine. The engine consisted of two directly opposed identical, outward compressing

pistons that were rigidly connected. Power was extracted from a central hydraulic

cylinder or by a linear alternator. The engine was spark ignited and computer controlled.

Th t t l t d th d i d t t f l b ti ti



for the engine vibration. The engine also had oil cooling by means of cooling jackets

around the cylinders.

Widener and Ingram [10] submitted a numerical model of a free piston linear

generator for a hybrid vehicle modeling study. The model addressed the use of a free

piston engine coupled with a linear generator as a potential auxiliary power unit in

hybrid electric vehicles. The feasibility of such a model was analyzed with regards to

power output and efficiency of the unit with reference to conversion of mechanical power

output of the linear engine to electrical power output. The study was conducted on a two-

stroke cycle engine and a reciprocating rig developed to characterize the operation of the

generator.

In the thesis of Goldsborough [11], a numerical simulation of a two-stroke cycle

free piston engine was performed. This study concentrated on the analysis of

homogenous charge compression ignition (HCCI) of hydrogen fuel. The author

calculated the HCCI process to be near constant volume which enable the engine to

operate on a very lean fuel-air charge. The study concluded that charge temperature at



components of a commercially available chainsaw engine. The testing of the engine was

performed under several loading conditions. It was found that under idle conditions the

ignition timing had to be advanced to the point that spark occurred just after port closing

to insure that the piston motion was reversed. This caused a large section of adverse

work to be performed in reversing the piston, and a high coefficient of variance (COV) in

the indicated mean effective pressure (iMEP). In a loaded highly, retarded timing case it

was found that the adverse work was eliminated and the COV (iMEP) was reduced. This

resulted in the engine operating more like a conventional internal combustion engine.

The fundamental modeling of the engine lead to a closed form solution for the piston

motion in dimensionless parameters. The numerical model of the engine then took the

fundamental model and solved it in a dimensional form. The numerical model yielded

theoretical in-cylinder pressure and displacement plots. From the different studies

conducted it was determined that the design of a linear engine should be large bore and

unthrottled, which would suggest a Diesel engine. The results of the research performed

at West Virginia University have been published in several articles. These papers include



3. Fundamental Analysis

3.1 Introduction

The analysis presented below examines an ideal two-stroke engine with two

opposed pistons connected solidly by a link rod and following the air-standard limited-

pressure cycle of operation. A simple case of an idling engine or an engine from which

power is extracted with constant force was examined. The air standard limited-pressure

cycle of operation was assumed so as to provide pressures prevalent within the cylinders

during idling operation of the engine. This created a fundamental analysis, that was

useful in the study of the effects of heat input and the percent of heat input at constantvolume.

It is understood that real systems are far more complex in comparison to the ideal

case assumed in the following analysis and that a numerical analysis, similar to Atkinson

et al. [4], might have to be employed in order to better understand the complex system.

However, the fundamental analysis presented provides a basic understanding of the linear



symmetric strokes and are outward compressing. The engine was assumed to have

instantaneous intake and exhaust blow down at the opening position of the ports and

partial instantaneous heat release at the outermost position with the balance of the heat

release occurring at constant pressure. Being a linear reciprocating engine, the piston

does not encounter a top dead center position or a bottom dead center position, but rather

has an innermost (for the left piston; s x x = ) and outermost position (for the left piston;

s x x −= ). The analysis was carried out in a dimensional form on this idealized engine,

based on the assumption that an idling case of operation was in progress and the only

load encountered was a frictional force. A better understanding of the model can be

gained from the schematic presented in Figure 3.1. The maximum theoretical half stroke

length of the piston is xm, while the maximum actual half stroke length of the piston is x s

as seen in Figure 3.2 . The piston on a left to right stroke traverses from – x s to + x s. A

fundamental analysis was carried out by taking into consideration the heat added during

one cycle, the intake pressures in the two cylinders, the friction force encountered by the

pistons during their motion from the outermost position to the innermost position and the



Link Rod

Cylinder Wall

Pistons

Figure 3.1. The ideal engine model at the beginning of a left to right compressionstroke ( s x x −= ).

s x− s x+ s x− s x+m x− m x+ m x− m x+

x=0 x=0



2. An idling case of operation with only a frictional force being encountered

during the engine operation was assumed.

3. The heat input to the engine was used entirely for the work done to overcome

the friction drag force acting on the piston (no heat loss).

The analysis was carried out on the idealized engine in a numerical form. Given

these assumptions, a numerical solution in velocity versus position, velocity versus time

and position versus time were obtained and are presented.

3.4 Dynamic Model

The model begins with a dynamic analysis of the engine. Consider the case of the

engine in a left to right movement. The force balance of the system is:

( ) ( ) 044 2

222

=−−−dt

xd m F

b x P

b x P s f r l

ππ

where P l is the left in-cylinder pressure, P r is the right in-cylinder pressure, F f is the

frictional force applied to the engine, m s is the mass of the slider, b is the bore of the

engine, t is time, and x is the slider displacement. Both cylinder pressures are a function



3.5 Thermodynamic Model

The thermodynamic analysis of the engine was performed to calculate the values

of the variables that were based on the value of the heat input into the system. The

engine model followed the air-standard limited-pressure cycle. The cycle consists of

adiabatic compression from point 1 to 2, constant volume heat addition from 2 to 3,

constant pressure heat addition from point 3 to a, adiabatic expansion from point a to 4,

and constant volume blowdown from point 4 to 1. A schematic of the cycle can be seen

in Figure 3.3.

2

3 a

4



33 T T

V V aa ==β Equation (3).

Where T 2, T 3, and T a are the average in-cylinder temperatures at the corresponding

points. These two ratios define how much of the heat input occurs at constant volume

and how much occurs at constant pressure. The temperatures in the cylinders during the

cycle can be defined as functions of the slider displacement and the intake temperature

T in and φ the percentage of the heat input that is at constant volume:

1

2

−

−−=

n

sm

epr min x x

x xT T Equation (4).

1

3

−

−−

+=

n

sm

epr m

inv

in

x x

x x

T mC Q

T φ

Equation (5).

( ) 11

−

−−++−=

n

sm

epr min

v

in

p

ina x x

x xT

mC Q

mC Q

T φφ

Equation (6).

where x m is the maximum half stroke, x epr is the right exhaust port closing coordinate, C v

and C p are the specific heats for the working fluid, Q in is the total heat input into the

system, n is the ratio of the specific heats, and m is the mass of the air in the cylinder.



φβ

1= . Equation (10).

φα

−=1

1. Equation (11).

With these definitions of α and β, stroke length, constant pressure expansion length,

frictional force, and compression ratio can be calculated. By substituting equations 4 and

5 into Equation 2, α becomes:

1

1

+

−−

=

−

inv

n

sm

epr min

T C

x x

x x

mQ

φα .

thus x s is solved for:

−−=−1

1

nin

epr mm s

Q

x x x x

φ

. Equation (12).



s f f x F W 2= ,

invoking limited pressure cycle efficiency:

( ) ( ) −+−−−= − 11

111 1 αβα

αβηnr

n

nth

( )( )

( )

( ) −+−−

−−−=

−

111

11

αβααβ

ηn x x

x x nn

epr m

smth

( )( )

( )

( ) −+−−

−−

−=

−

111

12

1

αβααβ

n x x x x

mQ

x F n

n

epr m

smin s f .

The frictional force then becomes

( )( )

( )

( )

s

nn

epr m

smin

f xm

n x x x x

Q

F 2

111

1

1

−+−

−

−−−

=

−

αβααβ

. Equation (15).

3.6 Pressure Balance

During a left to right stroke of the slider the cylinder pressures will be governed

by several equations because of the constant pressure heat addition, the placement of the

port openings and closings, and the scavenging process. Based on the prototype engine,



is open the pressure remains constant. The governing equations for the cylinder pressures

and pressure force F p are listed in Table 3.1.

Displacement

xa xeprr x=0 xepl-xs +x s

A B C D

Expansion Strokein Left Cylinder

Compression Stroke inRight Cylinder

Figure 3.4. Four regions can be seen for the pressure balance due to the limited-pressure cycle of operation.



15

Table 3.1. In-cylinder pressures and pressure force as a function of the slider displacement.

Component A B C D

P l(x) P o ( )( )nm

namo

x x x x P

++ ( )

( )nm

namo

x x x x P

++ P in

P r (x) P in P in( )

( )nm

nepr min

x x

x x P

−− ( )

( )nm

nepr min

x x

x x P

−−

F p(x) ( )4

2b P P ino

π− ( )

( ) 4

2b P

x x

x x P inn

m

namo π

−

++ ( )

( )( )( ) 4

2b

x x

x x P

x x

x x P n

m

nepr min

nm

namo π

+−

−++ ( )

( ) 4

2b

x x

x x P P

nm

nepr min

inπ

−−−



From analysis of Figure 3.4, it can be seen that regime A corresponds to the point

when x ≥ -x s and x < x a, regime B corresponds to the point when x ≥ xa and x < x epr ,

regime C corresponds to the point when x ≥ xepr , and x < x epl , and regime D corresponds

to the point when x ≥ xepl and x ≤ xs. P 0 is the pressure in the cylinder caused by the

constant volume heat addition. P 0 is related to the pressure before the constant volume

heat addition and α by:

20 P P α=

where P 2 is the pressure in the cylinder after the adiabatic compression (P r at x=x s), this

pressure can be found with knowledge of the intake pressure P in by

( )( )n sm

nepr m

in x x

x x P P

−−=2 . Equation (16).

3.7 Numerical Integration

Once all of the above relationships were derived a computer program to solve

Equation 1 for the acceleration was developed. This program first solved the

thermodynamic model for the half stroke x s, the constant pressure expansion end



calculated and the position can be related to the calculated time. The form of the

equations to calculate the time and the velocity are as follows

( ) ( ) ( ) ( )( )( )1

112

1 21

−

−−− −−+−=∆ −

i

iiii

i A

x x Avvt

iEquation (17).

and

( ) ( ) iiii t Avv ∆+= −− 11 . Equation (18).

These equations can be solved with the knowledge of the boundary condition

00 =v . The MATLAB program can be seen in appendix A.

3.8 Results

The analysis provided relationships which made it possible to obtain the velocity,

and position of the piston with respect to time. It also provided the calculation of the

stroke length, time required for one stroke, and the compression ratio for a given value of

heat input into the system. The time required for one stroke was calculated numerically

by integrating the time intervals constituting one stroke. The thermodynamic analysis

ld d l h b h h d h h d k l h



input into the system. These plot can be seen below in Figures 3.5, 3.6, and 3.7

respectively. According to Heywood [17], the typical operating range for a conventional

compression ignition engine with Diesel fuel is 18 to 70. The upper limit to this range

can be seen by the vertical line in Figures 3.5 to 3.10.



Figure 3.6. The constant pressure expansion coordinate defines how much heat isinput at constant pressure. It can be seen to be a function of the heat input and φφ.



Figure 3.7. The compression ratio is defined by the geometry of the engine and theachieved half stroke.

From the numerical integration the stroke time, average frequency, and mid-

stroke slider velocity can be shown relative to the specific heat input and the value of φ.



Figure 3.8. The period of the operating cycle is seen to be the smallest for a Dieselcycle of operation. The cycle period increases as the amount of heat input at

constant volume increases.



Figure 3.9. The average frequency is related directly to the operational period.



Figure 3.10. Slider mid-stroke velocity is seen to increase with an increase to thespecific heat input.

From the numerical analysis it is possible to obtain the relationships for position,

work output, in-cylinder pressure and velocity as a function of time and pressure as a



Table 3.2. Simulation constants .

Parameter Value

mQ in 1000

kg kJ

φ 0.5

xm 0.0355 m

Table 3.3. Test trials mass and bore values.Trial Slider Mass [kg] Cylinder Bore [mm]

1 5 75

2 10 75

3 2.5 75

4 5 53

5 5 106



the stroke. The plot of the work output in time, Figure 3.13, shows positive work output

during the expansion stroke and negative compression work during compression stroke.

Finally, Figures 3.14 and 3.15 show the in-cylinder pressure traces for the simulated

limited pressure cycle.

Motion Reversal



Figure 3.12. Slider Velocity versus time shows the velocity is near constant for mostof the stroke.

Motion Reversal



Figure 3.13. Work output versus time shows positive work being performed duringthe expansion stroke and negative work during the compression stroke. During thegas exchange operation when the exhaust port is open, work output can be seen to

have offsetting positive and negative work regions.

Constant PressureHeat Addition End

Exhaust PortOpened

Motion Reversal

Exhaust Port Closed



Figure 3.14. In-cylinder pressure versus time


Exhaust PortOpened

Exhaust Port Closed



Figure 3.15. In-cylinder pressure versus in-cylinder volume shows a pressure traceof the idealized model.

Exhaust PortOpened

Exhaust Port Closed

Motion Reversal




4. Engine Prototype

4.1 Description

The Diesel prototype of 75 mm bore and 71 mm stroke was sized to use two-

stroke cycle personal watercraft (Kawasaki Jetski 300sx) components to reduce

development time and cost. Cylinder heads were designed and fabricated that allowed

for direct fuel injection and also provided water cooling to the Kawasaki cylinders. The

pistons also were from the Kawasaki engine but were machined to remove the lower

portion of the piston skirt. This was done to prevent the skirt from contacting the bottom

end that was designed to allow the engine to be scavenged by in house compressed air.

The pistons were directly connected by an aluminum rod that had provisions for

mounting the moving portion of the position sensor and the translator magnets for the

linear alternator. A simple I-beam frame provided support for the cylinders, alternator,

and the stationary portion of the position sensor.

A single manually operated valve regulated air pressure to the engine.

L b i ti t th gi li d th gh th i t k i b f i li i t l



Another variable dependent on the stroke was the compression ratio, which had a

theoretical maximum, for this particular engine of approximately 50:1. This wascalculated with the knowledge of exhaust port locations, the dimensions of the cylinder,

clearance volume and assuming that the motion is reversed exactly at the point of contact

when the piston meets the head. The clearance volume was assumed to be the volume in

the head, which allows access to the cylinder for the glow plugs and fuel injectors. A

sketch of the major engine components is shown in Figure 4.1.

Fuel delivery was preformed by a common rail, direct injection system. The fuel

injectors (Bosch part # B 445 110 130) were supplied by a high-pressure pump (Bosch

part # B445 010 035-01) that maintained the common rail at a pressure controlled by the

ECM, usually set to 9,000 psi. The high-pressure pump maintained the pressure through

the use of a pulse width modulated regulator. Supplying the high-pressure pump was a

automotive fuel pump (Master part # E2000) that was regulated at 38 psi. Fuel metering

was pulse width modulated by the ECM and was manually adjusted by means of a

potentiometer for each cylinder. The ECM allowed for the adjustment of the pulse width



32

Figure 4.1. Diesel prototype.



Figure 4.2. Dimensional sketch of cylinder assembly (dimension in mm).

A listing of the parts and description of their geometry and function is given in

Table 4.1 below.

Table 4.1. Prototype Component Description.

Component DescriptionCylinders Kawasaki Jetski 300sx with 75 mm bore



4.2 Engine Electronics

An engine control unit was constructed with the help of Richard Atkinson of WestVirginia University, to operate the alternator as motoring coils and to control injection

timing, fuel injection pulse width, and injection pressure. The controller was modified

several times in the course of testing. The circuit diagram of the configuration at the

point of this thesis can be seen in Appendix C. A block diagram of the ECM has been

shown in Figure 4.3. A linear potentiometer (Micro-Epsilon part # VIP 50-ZA-2-SR-I)

was purchased for use as the position sensor. The common rail pressure regulator

required a linear feedback circuit including a rail pressure transducer (Omega part # PX

605) to control the injection pressure. The position sensor and pressure transducer were

the only input into the ECM.



35

Figure 4.3. Diesel prototype engine control module block diagram.



In order to directly observe the nature of combustion in this novel engine,

piezoelectric in-cylinder pressure transducers [PCB Part #508 and Part #547] were

mounted with direct access to the combustion chamber.

4.3 Prototype Test Platform

The experimental engine was designed and developed in-house with the

assistance of Thomas McDaniel, along with the engine controller with the assistance of

Richard Atkinson. The engine was tested with several updates to the ECU with varying

degrees of success. Figure 4.4 shows an overhead view of the engine setup. Figure 4.5

shows another view of the engine prototype and the dedicated bench of steel plates

weighing approximately 600 lbs., constructed to reduce the severity of vibrations during

early testing. The experimental results and conclusions have been presented in the next

chapter.

Fuel Pump

Engine ControlUnit



In the top left corner of Figure 4.4 the high pressure fuel pump can be seen. In the top

right corner is the ECM. The top middle the intake and lubrication system can be seen.

Along the bottom of Figure 4.4 is the test engine.

Figure 4.5. Front view of the engine.



6. Conclusions and Recommendations

6.1. Conclusions

The Diesel linear engine offers the potential to generate and deliver power with

out the need to convert linear piston motion to rotary crankshaft motion. An idealized

model of a linear engine, consisting of two pistons linked by a solid rod has revealed the

relationship between stroke, compression ratio, heat input, operational frequency and

other parameters. The model shows an increase in the achieved stroke length with an

increase in the amount of heat input. The idealized model deals with over-fueling by

increasing the stroke of the engine to the maximum. It is believed that this is not how the

engine would behave in reality. It is obvious that in the case of over-fueling, incomplete

combustion would occur. Also the effects of varying the bore and the sliding mass on

operating frequency, and power output have been shown for a given heat input. An

increase in cylinder bore or slider mass effect the system by increasing the amount of

time for a stoke.

Th t t h d f l h t i ti i th t ti g f d Th



This could be accomplished in several ways. A method of protecting the cranking driver

transistors from the current generated by the engine firing could be developed. Another

possible solution would be to implement the type of system first utilized on the gasoline

prototype develop at West Virginia University. This system used two automotive starter

pull back solenoids acting on a steel connecting rod to crank the system. This would

allow the cranking circuitry to be separate from the power generation circuitry,

preventing the current problem. This is a less appealing alternative than the previously

mentioned because it involves a redesign of both the ECU and the engine itself to provide

the cranking circuitry, a steel connecting rod and the space needed to locate the solenoids.

Once the cranking problem is solved it is believed that the engine will run and in-cylinder

data can be collected.



REFERENCES

[1] Clark, N., Nandkumar, S., Famouri, P., “Fundamental Analysis of a Linear Two-

Cylinder Internal Combustion Engine,” SAE 982692, 1999.

[2] Clark, N., McDaniel, T., Atkinson, R., Nandkumar, S., Atkinson, C., Petreanu, S.,

Tennant C., Famouri, P., Modeling and Development of a Linear Engine,” ICE-Vol.

30-2 Proceeding of the Spring Technical Conference of the ASME Internal

Combustion Engine Division, Book No. G1074B, 1998.

[3] Clark, N., Nandkumar, S., Atkinson, C., Atkinson, R., McDaniel, T., Petreanu, S.,

Famouri, P., “Operation of a Small Bore Two-Stroke Linear Engine,” ASME 98-

ICE-120, 1998.

[4] Atkinson, C., Petreanu, S., Clark, N., Atkinson, R., McDaniel, T., Nandkumar, S.,

Famouri, P., “Numerical Simulation of a Two-Stroke Linear Engine-Alternator

Combination,” SAE 1999-01-0921, 1999.

[5] Achten, A. J., “A Review of Free Piston Engine Concepts,” International Off-

Highway & Powerplant Congress & Exposition, SAE 941776, 1994.

[6] Cleveland Diesel Engine Division, 1957, “History and Description of the Free

Piston Engine- Gas Turbine Power,” (authors unknown to GM).[7] Frey, D. N., Klotsch, P., Egli, A., “The Automotive Free-Piston-Turbine Engine,”



[11] Goldsborough, S., “A Numerical Investigation of a Two-Stroke Cycle, Hydrogen-

Fueled, Free Piston Internal Combustion Engine,” Thesis, Colorado State

University, 1998

[12] Allais, E., “Free-Piston Engine with Operatively Independent Cam,” U.S. Patent

Application No. 416,959, Application filed September 9, 1982; U.S. Patent No.

4,480,599, Patent issued November 6, 1984.

[13] Deng, Y. A., Deng, K., “Free-Piston Engine without Compressor,” U.S. Patent

Application No. 154,145 (RDG Inventions Corporation), Application filed February

9, 1988; U.S. Patent No. 4,924,956 (RDG Inventions Corporation), Patent Issued

May 15, 1990.

[14] Heintz, R. P., “Free-Piston Engine Pump,” U.S. Patent Application No. 150,390,

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APPENDIX A

Numerical Analysis Program



clear format long;

% input parametersQin=1000;PHI=.5;Pin=101000;Tin=298;Cv=.718;Cp=1.005;

b=.075;xm=.0355;xepr=-.0015;ms=5;

xepl=-xepr;n=Cp/Cv;

Alpha=1/(1-PHI);

Beta=1/PHI;

%calculation of stroke lengthxs=xm-((xm-xepr)/(PHI*Qin/(Cv*Tin*(Alpha-1)))̂ (1/(n-1)));

%calculation of constant volume heat input final pressureP2=Pin*((xm-xepr)^n)/((xm-xs)^n);Po=Alpha*P2;

%calculation of frictional force componentFf=Qin*((1-((xm-xepr)/(xm-xs))̂ (n-1))*((Alpha*(Beta^n)-1)/(Alpha*n*(Beta-1)+Alpha-1)))/2*xs;



elseif (x(i)>=xepr)&(x(i)<xepl) Pl(i)=Po*((xm+xa)^n)/((xm+x(i))^n); Pr(i)=Pin*((xm-xepr)^n)/((xm-x(i))^n);

Fp(i)=(Pl(i)-Pr(i))*(pi*b^2)/4; A(i)=(Fp(i)-Ff)/ms;

else Pl(i)=Pin; Pr(i)=Pin*((xm-xepr)^n)/((xm-x(i))^n); Fp(i)=(Pl(i)-Pr(i))*(pi*b^2)/4; A(i)=(Fp(i)-Ff)/ms;

endend

%initializing time and velocitydt(1)=0;t(1)=0;v(1)=0;v(length(x)+1)=0;

%loop for numerical integrationfor i=2:length(x);

dt(i)=(-v(i-1)+(((v(i-1))^2)-2*A(i-1)*(x(i-1)-x(i)))^.5)/A(i-1); v(i)=v(i-1)+A(i-1)*dt(i); t(i)=t(i-1)+dt(i);

Dtime(i,1)=dt(i); Vel(i,1)=v(i); time(i,1)=t(i); end



APPENDIX B

Numerical Analysis



Trial 2 Output:

Slider Mass [kg] Cylinder Bore [mm]

10 75

Slider position vs time (trial 2)



Slider velocity vs. time, (trial 2).



In-cylinder pressure (left) vs. time, (trial 2).



Trial 3 Output:


2.5 75




Trial 4 Output:


5 53




APPENDIX C

Engine Control Unit Circuit Diagrams



61

Engine controller



62

Injector drivers.



63

Cranking circuit.



Rail pressure control circuit.

a diesel two-stroke linear engine

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