International journal of automotive technology, tập 11, số 1, 2010

Figure 14 shows that with an increase of exhaust gastemperature, the pressure drop within the cyclone decreases,and for a particular temperature, as the flow rate increases,the pressure

International Journal of Automotive Technology , Vol 11, No 1, pp 1 − 10 (2010)

1

IMPROVED THEORETICAL MODELING OF A CYCLONE SEPARATOR

AS A DIESEL SOOT PARTICULATE EMISSION ARRESTER

P K BOSE 1)* , K ROY 2) , N MUKHOPADHYA 3) and R K CHAKRABORTY 4)

1)Department of Mechanical Engineering, Jadavpur University, Kolkata 700032, India

2)Department of Mechanical Engineering, Central Calcutta Polytechnic, Kolkata 700014, India

3)Department of Mechanical Engineering, Jalpaiguri Government Engineering College, Jalpaiguri 735102, India

4)Department of Mechanical Engineering, Jadavpur University, Kolkata 700032, India

(Received 3 July 2007; Revised 10 December 2008)

ABSTRACT− Particulate matter is considered to be the most harmful pollutant emitted into air from diesel engine exhaust, and its reduction is one of the most challenging problems in modern society Several after-treatment retrofit programs have been proposed to control such emission, but to date, they suffer from high engineering complexity, high cost, thermal cracking, and increased back pressure, which in turn deteriorates diesel engine combustion performance This paper proposes a solution for controlling diesel soot particulate emissions by an improved theoretical model for calculating the overall collection efficiency of a cyclone The model considers the combined effect of collection efficiencies of both outer and inner vortices by introducing a particle distribution function to account for the non-uniform distribution of soot particles across the turbulent vortex section and by including the Cunningham correction factor for molecular slip of the particles The cut size diameter model has also been modified and proposed by introducing the Cunningham correction factor for molecular slip of the separated soot particles under investigation The results show good agreements with the existing theoretical and experimental studies of cyclones and diesel particulate filter flow characteristics of other applications.

KEY WORDS : Diesel soot particulate emission, Particulate filter, Cyclone separator, Cunningham correction factor

NOMENCLATURE

A : inlet cross sectional area of cyclone flow [m2]

H : inlet height of the cyclone [m]

B : inlet width of the cyclone [m]

D 1 : outer diameter of the cyclone [m]

D 2 : diameter of the vortex finder [m]

D d : diameter of the dust exit [m]

D p50 : cut size diameter of the particle [µm]

D p50m : modified cut size diameter of the particle [µm]

d p : diameter of soot particle [µm]

F C : centrifugal force [N]

F D : drag force acting on the particle [N]

L 1 : length of the cylindrical portion of the cyclone [m]

L 2 : length of the conical portion of the cyclone [m]

L i : inner vortex length [m]

L o : outer vortex length [m]

V θ : tangential velocity of the exhaust gas and particle

T : exhaust gas temperature in K

N θ : number of particles remain in the outer vortex at

an angle of turn θ

N 0 : number of particles at the inlet of cyclone, at θ=0

P ref : reference pressure [pa]

∆ P : pressure drop across cyclone [pa]

Q : volume flow rate [m3/sec]

r 1 : vortex finder or Inner radius of cyclone flow [m]

r 2 : outer radius of cyclone flow [m]

t : temperature of the exhaust gas [oC]

ρ c : density of the exhaust gas [kg/m3]

ρ p : density of the particle [kg/ m3]

η o : collection efficiency of outer vortex

η i : collection efficiency of inner vortex

η overall : overall collection efficiency of the cyclone

µ : dynamic viscosity of the gas [kg/m-sec]

θ : angle of turn in traversing the cyclone [rad]

θ i : angle of turn of the inner vortex [rad]

θ o : angle of turn of the outer vortex [rad]

R gas : characteristic gas constant of the exhaust gas

[N-m/kg/ok]

R u : universal gas constant, in N-m/kmolk

C p : concentration of the particles per unit area

C p(r 1,θ) : concentration of particles at inner radius r 1 & at

an angular position θ

C p(r 2,θ) : concentration of particles at outer radius r 2 & at

*Corresponding author. e-mail: pkb32@yahoo.com

2 P K BOSE, K ROY, N MUKHOPADHYA and R K CHAKRABORTY

an angular position θ

: mean value of particle concentration at outer vortex

: mean value of particle concentration at inner vortex

C * : cunningham correction factor

λ : mean free path of the gas molecules [µm]

: mean molecular velocity

M : molecular weight [kg/kmol]

m : mass of the soot particles

T in : inlet temperature [K]

1 INTRODUCTION

The diesel engine is one of the most reliable, durable, and

economical power plants extensively used to transport

goods, services, and people The engine emits a significant

level of particulate matter (PM), which is considered to be

most harmful pollutant in the air The particulate matter is

associated with carcinogenic compounds such as PAH

(poly-nuclear aromatic hydrocarbons), nitro-PAH, and

sulfates, and due to its extreme diameter range of 0.05 to

1.0 µm (Kittelson, 1998; Oh et al., 2002),such emissions

can easily enter the human respiratory system Therefore,

concern over the quality of air and, in particular, the

implications for human health have led to continued

tightening of particulate matter emission limits Hence, to

achieve the existing particulate emission target, several

after-treatment retrofit programs are being implemented

Many solutions proposed to date suffer from high structural

complexity, thermal cracking, cost, and increased

back-pressure, which, in turn, deteriorates diesel engine

com-bustion performance On the other hand, a cyclone separator

has tremendous potential to be applied to cheaper, easily

fabricable diesel particulate filters(DPF) that are not subject

to thermal failure in the exhaust gas operating temperature

range Many studies of cyclone separators in other industries

are already available in the literature, but very few

theoretical and experimental studies have been reported

(Mukhopadhya et al., 2006; Crane and Wisby, 2000) with

cyclone separators as a diesel engine exhaust gas

after-treatment device Experimental studies shows that soot

particles of 0.5 µm and higher in diameter can be

effec-tively eliminated by a cyclone separator (Mayer et al.,

1998) This paper presents a computer-aided improved

analytical approach for controlling diesel soot particulate

emissions by a cyclone separator with low back pressure,

reasonably high particulate collection efficiencies and reduced

regeneration problems The analysis of fluid flow and

particle motion in a cyclone is very complicated The

primary flow has been studied previously (Shepherd and

Lapple, 1939; Stairmand, 1951) The aerodynamics inside

the cyclone create a complex two-phase, three-dimensional,

turbulent swirling flow with a confined outer free vortex

(irrotational flow) and a low-pressure, highly turbulent

inner forced vortex (solid body rotation) The transfer of

fluid from the outer vortex to the inner vortex apparently

begins below the bottom of the exit tube and continues

down into the cone along the natural length of the vortex of

a cyclone (Alexander, 1949) Shepherd and Lapple cluded that the radius marking the outer limit of the innervortex and the inner limit of the outer vortex was roughlyequal to the exit duct radius The length of the inner vortexcore is also referred to as the cyclone effective length,which does not necessarily reach the bottom of the cyclone,(Leith and Metha, 1973) Particle collection in the cyclone

con-is due to the induced inertia force resulting in radialmigration of particles suspended in the swirling gas to thewalls and down the conical section to the dust outlet andthe gas exits through the vortex finder Flow near thecyclone wall is assumed to be laminar, although it isusually somewhat turbulent

In an earlier such work on the modeling of a cyclone, itwas assumed that the soot particles are uniformly distribut-

ed within the cyclone turbulent flow field both in the outerand the inner vortex However, that was a strong assump-tion, leading to conservative results Therefore, to make theanalysis more physically realistic, this paper proposes animproved analytical approach to calculate the overall collec-tion efficiency of a cyclone by considering a particle dis-tribution function due to non-uniform distribution of sootparticles across the cyclone turbulent flow field Because ofthe extreme size of the soot particles, a molecular slipcorrection factor (Crawford, 1976; Strauss, 1975) has beenintroduced The cut section diameter model (Mukhopadhya

et al., 2006; Lapple, 1951) has been modified by ing the molecular slip correction factor for the calculation

introduc-of actual viscous drag introduc-of the soot particles under gation The back-pressure of this system is found to bewithin the recommended limit and less than that of othermethods of particulate filtration Studies of earlier and pre-sent work through computer-aided graphical analysis havebeen presented, compared, and discussed

investi-2 FORMULATION OF THE MODEL

, C=Constant n=0.5, (Shepherd and Lapple, 1939)

or n=0.4-0.8 for the outer vortex (Cortes and Gil, 2007)

IMPROVED THEORETICAL MODELING OF A CYCLONE SEPARATOR AS A DIESEL SOOT PARTICULATE 3

n=(−) 1, for the inner vortex (First, 1950)

(1)(Alexander, 1949)

For a cyclone with the outer free vortex [Vθ=C/r] having

turbulent swirling flow and with a particle distribution

func-tion and effective turn angle made by the gas in traversing

the cyclone, as proposed by Crawford, the collection

effici-ency is:

for 0 <θ<θ 1,

where the effective turn angle made by the gas in traversing

the cyclone is:

(Crawford, 1976) or

(Mukhopadhya et al., 2006)

The angle of turn under laminar flow, at which the

effici-ency is unity, is given by:

The tangential velocity in the annular section of the

cyclone can be determined by the following equation

(Crawford, 1976; Ter Linden, 1949; Leith and Licht, 1972)

(Crawford, 1976)2.1 Collection Efficiency Model Over the Outer Vortex

For the proposed mathematical model of collection

effici-ency of diesel soot particles with cyclone flow in the outer

vortex of both the cylindrical and the conical parts, the

effect of the boundary layer and secondary circulation inthe flow due to the presence of side walls are neglected.Furthermore, the effects of particle-gas interaction, inter-action between particles, particle-wall interaction, and gravi-tational force on exhaust two-phase flows are also ignored.The following assumptions were made for formulatingthe model:

(1) Laminar particle motion in the radial direction.(2) Exhaust gas flow rate in the cyclone is constant, i.e.,steady flow

(3) The flow of the exhaust gas is turbulent in nature.(4) Soot particle distribution across the cyclone vortex cross-section is non-uniform

(5) Distribution of the particles across the cyclone vortexsection is linear

(6) Soot particles begin sequestering at the outer wall mediately as the exhaust gas enters the cyclone.(7) Cyclone separator flow field is 2-D axi-symmetric (8) Stokes’ law can be applied to the movement of theparticles relative to the gas stream

im-(9) Buoyancy effect is neglected

(10) The tangential velocity of particles is constant andindependent of position

The effect of strong turbulent swirling flow at any givenangle θ will lead to a transfer of gas between the outer andinner vortex, which is important for particle separation Alaminar sub-layer forms adjacent to the outer edge of thecyclone, such that all particles entering it are captured From Figure 3, the distance a particle travels in thedirection ‘θ’ or ‘dθ’ of angular distance, within the thinlaminar layer ‘dr’ over a time interval ‘dt’ becomes:

V θ 2 dt=r 2 dθ

By substituting dt, the thickness of the captured zone whereparticle removal occurs is:

(2)After entering the cyclone, the soot particles are subjected

to a strong centrifugal force, leading to non-uniform bution of the particles across the cross-section of outervortex Therefore, a general particle distribution functionwas used in the analysis of collection efficiency, set in

distri-n=1− 1 0.67D ( – 20.14) t 273⎝⎛ -+283 ⎠⎞0.3

η collection =1 exp – ( ) − ρp Qd p θ

18µHr 2 ( r 2 – r 1 )lnr 2

r 1

- 1 θ

2θ -1 +

Figure 3 Turbulent cyclone flow

4 P K BOSE, K ROY, N MUKHOPADHYA and R K CHAKRABORTY

terms of particle concentration, and was defined as the

number of particles per unit area (Crawford, 1976)

Let C p(r,θ) be the number of particles per unit area

(particle concentration) at a radius ‘r’ and at a angle of turn

‘θ’ of the exhaust gas, and let ‘dr’ be the radial thickness

(captured zone) of unit depth within the cross-section of the

outer vortex Then, the total number of particles ‘N θ’ at the

same co-ordinate from the inner radius r 1 to the outer radius

r 2 of cyclone can be written as:

If C p (r 2,θ) is the particle concentration at the outer radius

‘r 2’ of the cyclone, then the fractional diminution of soot

particles over the angle ‘θ’ in the outer vortex is:

(3)

Substituting ‘dr’ into equation (3) we obtain:

(4)

The mean value of particle concentration between radius r 1

and r 2 over an angle ‘θ’ is:

Substituting into equation (4):

Integrating the above equation gives:

Evaluating this constant of integration at the inlet, θ=0,where ‘N 0’ is the total numbers of particles and at θ=θ o(actual angle of turn of the exhaust gas at the outer vortex):

(5)Substituting equation (5) into the collection efficiency (η o)

of the outer vortex at a angle of turn θ=θ o is expressed as:

(6)The rate of flow in the cyclone is:

Q=

A generalized expression for tangential velocity is:

(7)Next, the expression for radial velocity considering theCunningham correction factor ‘C *’ (Strauss, 1975) due tomolecular slip of very small soot particles under investi-gation, acting to decrease resistance to particle motion, can

be written as:

(8)where:

and

(9)Subsequently, substituting equations (7), (8), and (9) intoequation (6), the collection efficiency of the outer vortexbecomes:

-θo

∫Cp ( r 2 ,θ )

C p ( ) θ o -dθ

1 n – -[ r 21 n– – r 11 n– ] C= Q 1 n( – )

H r [ 21 n– – r 11 n– ] -

V θ2= Q 1 n( – )

Hr 2n[ r 21 n– – r 11 n– ] -

V r2= C*ρp ( 1 n – ) 2 Q 2 d p 18µH 2 r 22n 1+[ r 21 n– – r 11 n–]2 -

C * =1+2 λd

p 1.257 0.400e–0.55dp /λ

IMPROVED THEORETICAL MODELING OF A CYCLONE SEPARATOR AS A DIESEL SOOT PARTICULATE 5

Assuming the particle distribution function is linear, as shown

in Figure 5, therefore, the mean particle concentration is:

(11)

As the particles gas turn from the inlet along with the

exhaust, the particle concentration at the inner radius is

reduced, and if this angle of turn ‘θ’ is less than the angle

of turn at which the efficiency is unity under laminar flow

‘θ 1’(Crawford, 1976), then:

(12)Using equations (11) and (12), we obtain:

(13)Therefore, the modified collection efficiency of the outer

vortex, considering the Cunningham correction factor by

substituting equation (13) into equation (10), becomes:

(14)

At 0 < θ o < θ 1

where:

and

The modified angle of turn at laminar flow, at which the

efficiency is unity (η=1), considering the Cunningham

correction factor due to molecular slip of the particles,

becomes:

2.2 Collection Efficiency Model Over the Inner Vortex

The assumptions are:

(1) The exhaust gas flow rate Q is constant

(2) The inner radius of the inner forced vortex (i.e., a solid

body rotation) is neglected

(3) Soot particle distribution over the inner vortex section is non-uniform

cross-(4) Maximum tangential velocity occurs at a radius of halfthe diameter of the vortex finder (Stairmand, 1951).(5) The particle distribution profile is linear from the center

to the radius of the inner vortex

(6) Stokes’ law can be applied to the movement of theparticles relative to the gas stream

(7) Buoyancy effect is neglected

(8) The tangential velocity of particles at the inner vortex isconstant and independent of position

Similarly, for the inner vortex, if the inner radius=0 andthe outer radius=r 1, then:

(15)

As for the forced vortex, the angle of turn ‘θ s’ at which theefficiency is unity is infinitely large; therefore, the ratiobetween the two angle of turn (i.e., θ i/θ s) is vanishinglysmall and is neglected

Considering the above, the modified version of thecollection efficiency for the inner vortex is:

(16)for 0 <θ i<θ s,where and

(Mukhopadhya et al., 2006)

2.3 Overall Collection Efficiency Model Let N o be the number of soot particles that have enteredinto the outer vortex with the diesel exhaust gas through theinlet duct If η o is the collection efficiency of the outervortex, then N 0(1−η o) is the numbers of particles that enterthe inner vortex Thus, the number of particles that will becollected from the inner vortex is N 0(1−η o)η i, where ‘η i’ isthe collection efficiency of the inner vortex of cyclone.Therefore, the total numbers of particles that will becaptured by the cyclone is

Then, the modified overall collection efficiency of thecyclone separator becomes:

(17)2.4 Pressure Drop Model of the Cyclone

In a cyclone, the back pressure affects the diesel engine

C p ( ) θ o =Cp ( r 1 ,θ ) C + p ( r 2 ,θ )

2 -

η i =1−exp ( )ρ− p Qd p2( 1 n – )C * × θ i

18µH r ( 11 n– ) r ( )r 1 1n -

θ i =2πL i H -

L i = L { i – ( H L + 3 ) }+ r ( 2 – r 1 )L 2

r 2 D d 2 -–

N 0 { η o + 1 η ( – o )η i }

η overall collection = η [ o + η i – η o η i ] 100 ×Figure 5 Linear particle distribution function

6 P K BOSE, K ROY, N MUKHOPADHYA and R K CHAKRABORTY

combustion performance; hence, the objective is to

maxi-mize the particle collection efficiency and minimaxi-mize the

pressure drop for a better cyclone separator

A theoretical pressure drop model by Caplan is given

below:

(18)where:

(Crawford, M., 1976)

and ‘f’ is given in terms of ‘n,’ for n=0.5, f=2.125

2.5 Modified Cut Size Diameter Model

The expression for drag force that acts on a spherical diesel

soot particle in the radial inward direction in cyclone flow

may be determined by Stokes’ law:

(19)The radial force responsible for radial acceleration of a soot

particle with mass ‘m,’ equal to the centrifugal force on the

soot particle may be determined as:

(20)When F C>F D, the particle to be collected moves towards

the cyclone wall When F C<F D, the particle will move to

the inner vortex of the cyclone At terminal velocity of theparticle, F C= (−) F D

Therefore, the force balance differential equation becomes:

(21)The Cunningham correction factor ‘C *’ is included in thedrag force to account for the effect of molecular slip,resulting in lower drag force for very small soot particlesunder investigation

(22)

At terminal velocity, the modified force balance differentialequation incorporating the Cunningham slip correctionfactor becomes:

(23)The solution of the above particle force balance differentialequation gives the particle radial trajectory, which is thecritical path in the radial direction and is a function ofparticle diameter (smaller particles having larger radialtrajectories and vise-versa)

Therefore, the modified cut size diameter can be pressed as:

F D = 3πµd ( p /C * ) dr⎝ ⎠⎛ ⎞ -dt

d 2 r

dt 2 -−r dθ⎝⎛ -dt⎠⎞2 = −( ) 18µ/d( pρpC* ) dr⎝ ⎠⎛ ⎞ -dt

d p,50m = 9µB2H

C * ρ p Qθ m -

Table 1 Diesel engine exhausts flow parameters

Allowable pressure drop <300 mbar, 30000 (pa)

<400 mbar, 40000 (pa) Dementhon and Martin (1997),Luders et al (1999)

Diesel particulate diameter ≤(0.1-1) µm, <1 mm Khalil and Levendis (1992)

d p,50m = 9µB2H

C * ρ p Qθ m

- θ m =2π L1 + r { ( 2 – r 1 )L 2 / r ( 2 – D d /2 ) }

H -

IMPROVED THEORETICAL MODELING OF A CYCLONE SEPARATOR AS A DIESEL SOOT PARTICULATE 72.6 Exhaust Gas Viscosity and Density Model

(Mukhopadhyay, N et al., 2006)

(26)

3 RESULTS AND DISCUSSION

Figure 6 shows that with a decrease of cyclone diameter,

the overall collection efficiency increases As the cyclone

diameter decreases, the centrifugal force on the particles

increases, leading to the increase of overall collection

efficiency of the cyclone, and vise-versa The graphical

trend analysis matches with the trends described by Davis

and Cornwell (1998) and the theoretical work of

Mukhopadhya et al (2006)

Figure 7 shows that with an increase of overall collection

efficiency, the pressure drop of the cyclone increases Back

pressure affects the combustion performance of the diesel

engine, and the study shows that the pressure drop is within

the accepted range (Dementhon and Martin, 1997)

speci-fied in Table I, giving reasonably higher collection

effici-ency The graphical trend analysis matches the theoretical

work of Mukhopadhya et al (2006) and experimental work

of Richard Bloom (1995) with ceramic fiber wound DPF.Figure 8 shows that as the diameter of the cycloneincreases, the pressure drop across the cyclone separatordecreases, and vise-versa Here, with an increase of thecyclone diameter, the centrifugal force on the particles de-creases; hence, particulate collection efficiency also decreases,which results in a gradual pressure drop across the cyclone.This graphical trend analysis matches the conclusionsdrawn by Davis and Cornwell (1998) and by the theoreticalwork of Mukhopadhya et al (2006)

Figure 9 shows that the pressure drop across the cycloneincreases with an increase of exhaust flow rate Theoreticalpredictions show satisfactory results in comparison withthe experimental work of Cutler and Merkel (2000) with acordierite ceramic DPF filter and with the theoretical work

of Mukhopadhya et al (2006) The pressure drop is withinthe allowable limit of the diesel engine performance (Luders

Figure 8 Variation of pressure drop with cyclone diameter

Figure 9 Variation of pressure drop with flow rate

Figure 10 Variation of overall collection efficiency withAED

8 P K BOSE, K ROY, N MUKHOPADHYA and R K CHAKRABORTY

Figure 10 shows that the overall collection efficiency

increases with an increase in aerodynamic equivalent soot

particle diameter (AED) of diesel particulate emission As

the diameter of the particles increases, the mass of the

particles increases, and as a result, centrifugal force also

increases; hence, the collection efficiency increases Similar

trends were observed in the theoretical work of Dietz

(1981) and Mukhopadhya et al (2006) and in the

experimental work of Wheeldon and Burnard (1987) on a

cyclone with a PFBC unit

Figure 11 shows that the overall collection efficiency

increases with the increase of normalized particle size ratio

The predicted results of the modified cut size diameter

(dp50m) model produce matching trends similar to those of

the work of Lapple (1951), of the experimental work of

Wheeldon and Burnard (1987) with a PFBC unit, and of

the theoretical work of Mukhopadhya et al (2006)

Figure 12 shows that with the increase of exhaust gas

flow rate, the cut size diameter of the soot particles to be

separated is decreased As the flow rate increases, the finer

particle will be subjected to increasing centrifugal force,leading to greater degree of separation, resulting in a de-crease of cut size diameter of the particle The predictedresults of the modified cut size diameter (dp50m) modelproduce trends similar to those of the works of Lapple(1951) and Mothes and Loffler (1988)

Figure 13 shows that with an increase of the exhaust gastemperature, the cut size diameter of the particle increases.The rise of the temperature increases the viscosity of thefluid, which results the increase of drag resistance on thesoot particles This leads to the increase in cut size dia-meter The graphical trend analysis matches the model ofMothes and Loffler (1988) and the experimental results atvarious temperatures of Bohnet (1995)

Figure 14 shows that with an increase of exhaust gastemperature, the pressure drop within the cyclone decreases,and for a particular temperature, as the flow rate increases,the pressure drop across the cyclone separator also increases.This graphical trend matches the pressure drop model ofCaplan (1968) and the theoretical work of Mukhopadhya et

al (2006)

Figure 15 shows that as the temperature of the exhaustgas increases, the collection efficiency of the cyclonedecreases A temperature rise increases the fluid viscosityand decreases the exhaust density (Suresh et al., 2000),leading to a decrease of the vortex component (Dietz,1981) The net result is a decrease in the overall collectionefficiency of the cyclone The graphical trend matches the

Figure 11 Variation of overall collection efficiency with

particle size ratio

Figure 12 Variation of cut size diameter with flow rate

Figure 13 Variation of cut size diameter with temperature

Figure 14 Variation of pressure drop with temperature

Figure 15 Variation of overall collection efficiency withtemperature

IMPROVED THEORETICAL MODELING OF A CYCLONE SEPARATOR AS A DIESEL SOOT PARTICULATE 9

theoretical work of Mukhopadhya et al (2006) and the

analysis of the mathematical model presented in this study

(Crawford, 1976)

Figure 16 shows that at a particular flow rate, as the size

of the cyclone increases, the centrifugal force on the particles

decreases; hence, the particulate collection efficiency

de-creases, resulting in a gradual decrease of pressure drop

across the cyclone The model shows a similar trend as that

of the theoretical work of Mukhopadhya et al (2006) and

of the experimental work of Cutler and Merkel (2000)

4 CONCLUSIONS

(1) The collection efficiencies of both the outer and the

inner vortex have been separately modified and presented

by considering a particle distribution function and the

Cunningham molecular slip correction factor of the

soot particulates under investigation

(2) The modified overall collection efficiency model of a

cyclone separator as a diesel soot particulate arrestor

has been shown

(3) This study demonstrates that the collection efficiency of

the soot particulates will be improved by the above

modifications

(4) The cut section diameter model has been modified by

introducing the Cunningham correction factor

(5) The developed back pressure is below the diesel engine

operational limit

(6) The proposed analytical model of the cyclone separator

shows the same graphical trend as the existing

theoretical and experimental work with a ceramic fiber

wound diesel particulate filter (DPF)

(7) Variations of overall collection efficiency and pressure

drop with cyclone diameter predict the optimum size of

the device; thus, the optimum performance of a cyclone

separator can be ascertained

(8) Graphical trends show good agreement with the

existing published work and with cyclone separators

used in other industries

(9) In summary, the present studies show that the cyclone

separator is a good non-contact type filtration device

for arresting diesel soot particulates emitted from diesel

engine exhaust, operating at a low pressure drop and

with low cost Thus, by optimizing the design of a

cyclone separator, harmful soot particles can be

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International Journal of Automotive Technology , Vol 11, No 1, pp 11 − 17 (2010)

(Received 15 October 2008; Revised 19 August 2009)

ABSTRACT− We investigated the effects of the fuel injection timing - both for early and late injection - in conjunction with the throttle opening ratio on the fuel-air mixing characteristics, engine power, combustion stability and emission characteristics of a DI CNG spark engine and control system that had been modified and designed according to the author’s original idea We verified that the combustion characteristics were affected by the fuel injection timing and that the engine conditions were affected by the throttle opening ratios and the rpm The combustion characteristics were greatly improved for

a complete open throttle ratio with an early injection timing and for a partial throttle ratio with a late injection timing The combustion duration was governed by the duration of flame propagation in late injection timing scenarios and by the duration

of early flame development in cases of early injection timing As the result, the combustion duration is shortened, the lean limit

is improved, the air-fuel mixing conditions are controlled, and the emissions are reduced through control of the fuel injection timing and vary according to ratio of the throttle opening.

KEY WORDS : Direct injection, CNG, Stratified charge, Injection timing, Throttle opening ratio

1 INTRODUCTION

Compared with light oils, natural gas, which contains methane

as the main ingredient, is easy to obtain as both an energy

resource and a fuel supply Furthermore, it is convenient

and safe to use as a fuel It also results in lower emissions

of SO2 and PM, with reductions of 20~30% in CO2

emissions compared with light oils

In recent years, most CNG engines have used the PFI

(port fuel injection) method, in which fuel is injected into

the intake port (Tanaka et al., 2007; Park et al., 2007) The

DI CNG engine, however, has various advantages over the

PFI engine, such as an increase of about 10 percent in

generated power compared with gasoline engines resulting

from its greater volumetric efficiency, an improvement in

the fuel consumption rate, and the use of a super-lean

mixture to drive the engine The DI CNG engine can also

avoid low burning speeds that result from problems with

the engine control response (Goto and Sato, 2001; Kang et

al., 2007; Chung et al., 2007)

In order to obtain higher efficiency and ultra-lean

burn-ing in the DI CNG engine, we must obtain more

infor-mation about the characteristics of the combustion process

and output power The present study thus addresses some

of these issues; in particular, it seeks to clarify how the

timing of the fuel injection, in relation to either the intakestroke or the compression stroke and the throttle openingratio (TOR) of the intake port, affects the mixing of the fueland air This study finds that knowledge of the timing ofthe injection and the TOR are required to improve enginepower and reduce emissions These two parameters impactcombustion by influencing the air-fuel mixing process, theignition, the mass fraction burned, the duration of com-bustion, and the formation of emissions in a DI CNG engine

2 EXPERIMENTAL DEVICES AND METHODS

Table 1 presents information on the test engine Here, asingle DI diesel engine has been modified into a CNGengine that can use CNG as a fuel Furthermore, a commer-cial ignition system, injector, and cooling system controllerwere added to the engine

The eddy-current engine dynamometer, which can trol the torque and the rpm of an engine, was connected inseries with the crankshaft An electronic control system,designed in accordance with prior research of the author,was used to control the timing of the injection of fuel, theduration of injection and the ignition system The ignitiontiming was controlled with the maximum brake torqueunder all the engine conditions The encoded signal fromthe encoder, installed on the crankshaft, was used to controleach part of the system The air-fuel ratio was determined

con-*Corresponding author. e-mail: hajy@dau.ac.kr

12 J Y HA, J S PARK and J H KANG

by an oxygen sensor installed in the exhaust pipe that

measured the concentration of oxygen in the exhaust gases

The components of the exhaust gases were analyzed using

an exhaust-gas analyzer (EXSA-1500, Horiba Co.) The

sampling pipe of the exhaust-gas analyzer was situated in

the exhaust pipe between the exhaust valve and the

three-way catalytic converter The cylinder pressure at each cycle

and data on the concentrations of the exhaust gases were

acquired using LabVIEW with a control program designed

during the author’s prior research

To control the TOR in relation to variations in the engine

load and rpm, an acceleration pedal that could manually

control the throttle valve was installed An air-flow meter

(Series 8000 MP/NH, Eldridge Products Inc.) was also

installed at the upper end of the intake manifold to measure

air intake The fuel-flow meter (9500 Flow meter, Thermal

Instrument Co.) was set between the pressure regulator and

the site where the fuel injector measured the amount of

decompressed CNG that was injected into the cylinder

The optimal value of the compression ratio (ε=13) of the

test engine was determined based upon prior research The

compression ratio was adjusted throughout the thickness of

the gasket (Kim et al., 2003, Chung et al., 2007) A piston

containing a toroidal cavity was used for stratified charging

of the air-fuel mixture

The injector driver, which was designed in accordance

with the author's prior research, maintained a peak voltage

for 2.5 ms from the commencement of the injection The

solenoid voltage continuously switches on and off not only

to reduce the consumption of electric energy but also to

reduce the generation of heat in the injector, which

increases with the duration of the injection (Kang et al.,

2007)

Figure 1 shows the CNG fuel supply system that was

used in the present study The pressure of the CNG, which

charged to a high pressure of 22 MPa, decreased to 6 MPa

through the use of two pressure regulators- the CNG, it issupplied to the injector

For safety reasons, the following valves were installedbetween the CNG tanks and the injector: a manual shut-offvalve in the high pressure lines; a high-pressure solenoidvalve that automatically shuts off fuel when the enginestops; and an anti-overflow valve, which operates when thefuel line is broken

A surge tank, with a volume of 200 cc was installedbefore the inlet of the injector to decrease the pulsation ofthe fuel pressure and to increase the repeatability of theamount of fuel that is injected at each cycle The CNG fuelconsists of CH4 (86.8%), C2H6 (8.2%), C3H8 (3.9%), and C+(1.0%)

Table 2 presents information on the injection timingunder all of the experimental conditions

3 RESULTS AND DISCUSSION

In the case of the DI CNG engine, we can realize a greaterefficiency compared to the PFI engine due to the non-intakethrottle loss In this case, however, a mixture that exceedsthe lean limit can exist locally and lead to an emission ofTHC and other species (Goto and Sato, 2001) The presentstudy discusses the above-mentioned issues and clarifieshow the throttle opening ratio and fuel injection timing(FIT) affect combustion in a DI CNG engine

Table 1 Specifications of equipment for the test engine

Type of engine Single-cylinder 4stroke cycle

Valves and piston 2 valves, toroidal

Ignition Commercial spark ignition system

Fuel supply Direct injection into cylinder

Injector Injector for GDI (Single hole, swirl type)

Injection pressure (MPa) 6

Intake valve open/close

Exhaust valve open/close (oCA) BTDC20/ABDC44BBDC44/ATDC20

Figure 1 CNG fuel supply system in the experimentalapparatus

Table 2 Injection timing table

rpmTOR λ

1.0 110oBTDC 150oBTDC 170oBTDC 270oBTDC1.2 80oBTDC 110oBTDC 140oBTDC 250oBTDC1.4 70oBTDC 90oBTDC 120oBTDC 240oBTDC

EFFECTS OF THE THROTTLE OPENING RATIO AND THE INJECTION TIMING OF CNG ON THE COMBUSTION 13

3.1 Effects of Fuel Injection Timing (FIT)

Figure 2 shows the P-θ diagram and the rate of heat release

in relation to the excess air ratios at a throttle opening ratio

(TOR) of 25% and 1700 rpm The pressure diagram and

the rate of heat release were obtained from data that were

sampled over 100 cycles and were calculated at each crank

angle using the ensemble average method

The excess air ratio (λ) varies between 1.0 and 2.4 and λ

cannot exceed 2.4 under normal operation of the engine In

accordance with the excess air ratio, the timing of the fuel

injection is varied from 60o BTDC to 80o BTDC and the

timing is delayed with an increasing λ Under the delayed

injection (80o BTDC), the fuel is injected into the cylinder

during a compression stroke The problems with regard to

decreases in Pmax and the combustion duration are thus

compounded as the excess air ratio increases In the figure,

Pmax decreases and the combustion duration increases as the

excess air ratio, λ, increases These phenomena become

relatively dull under conditions of late injection

Figure 3 shows the variation in the imep with the

injec-tion timing for various excess air ratios (i.e., various values

of λ) As the excess air ratio increases, the injection timing

corresponding to the maximum value of the imep is

delay-ed by several degrees The injection timing corresponding

to the maximum value of the imep for a λ of 1.4 is 90o

BTDC In particular, the value of the imep decreases under

either especially advanced or especially delayed injection

timings

On the one hand, in the cases of λ=1.0 and λ=1.2, the

imep takes on the mean value range for a wide crank angle

(170o-120o BTDC and 140o-90o BTDC, respectively) Thus,

a wide range of injection timings is possible On the other

hand, as λ increases, the range of injection timings thatcorrespond to a relatively high imep narrows, and the imepvaries greatly across different injection timings

Figure 4 presents the behavior of the coefficient of cyclevariation of the imep (COVimep) and the indicated thermalefficiency (η i) with variations in the excess air ratio and thefuel injection timing

At λ=1.0 and an injection timing of 170o-110o BTDC,the COVimep is very stable, ranging over 2~3% For λ=1.2,the COVimep is relatively high: in the range of 3~7%.Further, for λ=1.4, the COVimep is higher than when λ=1.0,except for with an injection timing of 90o BTDC TheCOVimep is greater for injection timings that are eitheradvanced or delayed in relation to the optimal injection

Figure 2 Variation in the cylinder pressure and the rate of

heat release with the excess air ratio

Figure 3 Variation in the imep with injection timing ateach excess air ratio

Figure 4 Coefficient of cycle variation of the imep and theindicated thermal efficiencies as a function of the injectiontiming at each excess air ratio

14 J Y HA, J S PARK and J H KANG

timing This is because of the condition of the air-fuel

mixture (i.e., whether or not it is lean), the mixed state, and

the shape of the combustion chamber both at the moment

of ignition and during the duration of flame propagation

Hence, these phenomena need to be clarified with a visible

combustion chamber

Even if the COVimep is somewhat high (7.5%) at λ=2.2,

the imep itself is lower; hence, the engine is able to run

quietly because the variation in the imep is not very large

The appropriate fuel injection timing for normal operation

of the engine is, however, limited to a BTDC of 60o As

Figure 4 shows, the range in fuel injection timings that

yield a lower COVimep narrows when the air-fuel mixture is

lean

The indicated thermal efficiencies are highest at BTDCs

of 150o, 110o, or 90o, depending upon λ For each value of

λ, the thermal efficiency is the highest at the timing that

maximizes the imep The behavior of the thermal

effici-ency is similar to that of the COVimep As λ increases, both

the imep and COVimep are very sensitive to the injection

timing This implies that the timing of the fuel injection

seriously affects the air-fuel mixing process, the ignition,

and the flame propagation Further, the thermal efficiency

decreases as the COVimep increases, owing to a poor fuel

consumption rate On the other hand, although the range of

variation in the thermal efficiency, for each value of the

injection timing, is on the rise as λ increases, the maximum

values of the thermal efficiency are almost the same as

those for a lean mixture These maxima are attained at

different BTDC values, and depend on the value of λ The

invariance of the maximum thermal efficiency is due to a

decrease in the cooling loss that results from the lower

combustion temperature and improved combustion

The thermal efficiency is generally relatively high,

rang-ing from a minimum of about 28% to a maximum of about

45% The relatively high values persist because the fuel

flow-meter that gauges the amount of injected fuel is only

for methane, which constitutes 86.8% of the CNG; the

flow-meter cannot measure other constituents such as C2H6

and C3H8

3.2 Influence of the Throttle Opening Ratio

The relationship between the imep and excess air ratio is

shown in Figure 5 for TORs of 25%, 50%, and 100%

Owing to differences in the amount of fuel supplied and the

amount of air in each cycle, the imep decreases with an

increase in the excess air ratio for each TOR value

The slope of the imep vs λ curve yields values of 0.17,

0.29 and 0.53 for TORs of 25%, 50%, and 100% (full

throttle), respectively This means that as the TOR

de-creases, the rate of reduction in power decreases along with

an increasing excess air ratio We can confirm this

phen-omenon from the observation that if λ increases, ηi either

increases or stays nearly the same However, in the case of

a full throttle, the slope is not consistent around the lean-air

limit because the timing of the injection is delayed from

λ=1.3 to λ=1.6 for 100% TOR

For insight into the characteristics of combustion in a DICNG engine under normal driving conditions, the massfraction burned is shown in Figure 6 for throttle conditions

of 25%, 50%, and 100% The mass fraction burned curvesare obtained from the measured cylinder pressure dataversus crank-angle records using equation for χb Thisbehaves in a similar manner to the speed of flame propa-gation, and is very useful for understanding both flamepropagation and combustion characteristics in a cylinder.The rate of the mass fraction burned (χ b) can be expressed

as follows:

Θs: Crank angle at the start of combustion

Θ e: Crank angle at the end of combustionFrom the curve of the mass fraction burned, we canascertain the combustion characteristics relating to the

Figure 5 Imep with the excess air ratio at each TOR andinjection timing

Figure 6 Mass fraction burned as a function of the bustion duration at each throttle opening ratio and excessair ratio

com-EFFECTS OF THE THROTTLE OPENING RATIO AND THE INJECTION TIMING OF CNG ON THE COMBUSTION 15

structure of the stratified air-fuel mixture and the lower

burning speed under a late injection of fuel Under 1700

rpm, the injection timings for both (i) excess air ratios of

λ=1.0 or 1.2 and 100% TOR and (ii) λ=1.0 and 50% TOR,

are just before the end of the intake stroke, i.e., BTDCs of

170o-140o (the end of the intake stroke is set at 136o BTDC)

For other values of λ, the injection timing occurs after the

start of the compression stroke (130o-60o BTDC), which

corresponds to a late injection

When the fuel is injected into the cylinder during the

intake stroke, the combustion characteristics exhibit similar

trends to the case of PFI under near-stoichiometric

condi-tions for λ=1.0 or 1.2 and 100% TOR(Catania et al., 2004)

However, under other conditions where the fuel is injected

during the compression stroke, the slope of the mass

frac-tion burned increases with λ, which is exactly the opposite

of what happens under an early injection To clarify these

phenomena in detail, Figure 7 shows the results for the

combustion duration as a function of the excess air ratio

and TOR

For 1700 rpm and TORs of 25% and 50%, Figure 7

breaks down the combustion duration into three parts: the

duration of early flame development (0~10%); the duration

of rapid burning (10~90%); and the duration of

after-burn-ing (90~100%) These definitions are most commonly used

to characterize the energy-release aspects of combustion

With regard to TORs of 25% and 50%, every injection

timing corresponds to late injection (fuel is injected into the

cylinder during the compression stroke), except when

λ=1.0 and the TOR is 50%, in which case the FIT is 150o

BTDC

The variation in the combustion duration with the excess

air ratio shows the same trend under both levels of TOR

The combustion duration for stoichiometric conditions (λ=

1.0) is longer than that for λ=2.2 The intermediate values

of λ yield shorter combustion durations compared with the

extreme values This finding is at odds with that for the

premixed combustion, wherein the combustion duration

increases with λ In other words, the combustion

charac-teristics when the air and fuel are mixed and injected late

contrast with those characteristics that are obtained whenthe air and fuel are premixed (and the injection is early)

In spite of the wide range of variation in λ (from 1.0 to2.2), the largest variation, across the two levels of TOR, inthe combustion duration does not exceed 13o CA (whichrepresents 24% of the combustion duration) An analysis ofthe combustion durations reveals that the variation in theduration of early flame development is 4o CA (24%) at allexcess air ratios and both TOR levels However, the range

of the rapid burning duration is 12-19o CA and 13-23o CA,respectively, for 25% and 50% TOR, i.e., 37-43% Thismeans that under late injection, the combustion duration isinfluenced more by the duration of the rapid burning than

by the duration of the early flame development From theseresults, we infer that the combustion duration is largelygoverned by the fuel injection timing As the TOR lowers,the combustion duration is shortened

Figure 8 shows how the engine rpm and λ affect thecombustion duration at 100% TOR Injection timings are170-140o BTDC at λ=1.0, 1.2 and 1700 rpm and 270-240oBTDC (early injection) at all values of λ and 2000 rpm Inthe case of early injection, premixing is possible becausefuel is injected into the cylinder during the intake stroke.The combustion durations in Figure 8 are similar to thosefor the case of ordinary pre-mixed combustion, except that

at 1700 rpm, the leaner condition of the excess air ratio,rather than a ratio of λ=1.3, exhibits the combustioncharacteristics of a late injection These findings regardingleaner mixtures suggest that the mechanism by which airand fuel mix differs from that occurring when air and fuelare pre-mixed We believe this phenomenon reflects astratified charge of the air-fuel mix

Figure 8 shows the differences in the combustion teristics between early and late injection, including thevariations in the three components of the combustionduration at each excess air ratio In the case of 1700 rpmand λ=1.2, the fuel injection commences during the intakestroke but continues through to the compression stroke.The difference between the maximum and minimum values

charac-of the combustion duration is 4o CA (7%) The durations of

Figure 7 Combustion duration as a function of the excess

air ratio and TOR Figure 8 Combustion duration as a function of the excessair ratio at 1700 and 2000 rpm

16 J Y HA, J S PARK and J H KANG

early flame development and rapid burning are 2.5o CA

(12.1%) and 2.5o CA (10.8%), respectively On the other

hand, for λ=1.3~1.6 and late injection timing, the

differ-ence between the maximum and the minimum values of the

combustion duration, the duration of the initial flame

development, and the duration of rapid burning are 7.5o CA

(14.7%), 1o CA (6.2%), and 4o CA (19.5%), respectively In

the case of 2000 rpm, each excess air ratio (λ=1.0~1.4)

corresponds to early injection The difference between the

maximum and minimum values of the combustion duration,

the duration of the initial flame development, and the

duration of rapid burning are 22o CA (27%), 8o CA (29%),

and 8o CA (24.6%), respectively

According to these results, the late injection has a greater

effect upon the rapid burning duration than on the other

durations Under an early injection, the duration of the

early flame development increases with λ The duration of

the initial flame propagation has a larger variation under

early injection because there is more time for the air and

fuel to mix when compared with the late injection As a

result, the mixture is more homogeneous, which in turn can

lead to variation in the burning speed along with variation

in the excess air ratio The duration of the initial flame

development is less affected by the air-fuel ratio under the

late injection because the fuel that is injected in the vicinity

of the spark plug does not have time to mix well with the

air, much like a stratified charge The air-fuel mix can be

partially stoichiometric These results are similar to those

reported by Kim, who studied the air-fuel mixing process

with the planar laser-induced fluorescence (PLIF) technique

using an optical access engine (Kim and Samimy, 1999)

Figure 9 indicates the thermal efficiency and the cyclevariations of the imep in relation to the excess air ratio atconditions of 25% and 100% TOR for 1700 rpm, and100% TOR for 2000 rpm Under the 100% TOR, 2000 rpmconditions, with early injection, the range of λ is quitenarrow, varying from the stoichiometric conditions (λ=1.0)

up to λ=1.4 The thermal efficiency increases with the fuel ratio up to λ=1.2 and then rapidly decreases Thethermal efficiency and COV vary widely At 1700 rpm and

air-a TOR of either 25% or 100% (air-and air-an eair-arly injectioncorresponding to λ=1.0, 1.2), a wider lean-limit and greaterthermal efficiency result compared with the 100% TORand early injection conditions The indicated thermal effici-ency and COVimep fluctuate less over a wide range of air-fuel ratios and also exhibit improved results compared tothe case of early injection

The results of this study for conditions of 2000 rpm andearly injection are similar to the results for the CNG enginewith PFI at the same compression ratio (ε=13) (Kim et al.,2003)

In other words, the two engine conditions have similarlean-limits (λ=1.3) and combustion characteristics In parti-cular, the cycle variation under PFI is similar to that shownfor 2000 rpm and 100% TOR, as shown in Figure 9 Thisimplies that the mixtures resulting from the early injection

in a DI engine and in a PFI engine are both homogeneous.The thermal efficiency at λ=1.0 and 25% TOR is lowerthan for other conditions because the partially rich mixture,which is injected into a cavity and formed during the com-pression stroke, burns incompletely We can examine thesephenomena using the results based on the cycle variationand emissions concentrations The cycle variations rapidlyincrease up to 6% under early injection, 2000 rpm, and

λ=1.4 However, the values are generally lower for lateinjection and 1700 rpm In particular, Figure 4 clarifieswhy the cycle variations increase under the lean conditions

of 25% TOR

Figure 10 shows the variations in the CO, THC, and NOx

concentrations for excess air ratios at 1700 rpm and TORs

of 25%, 50%, and 100% In general, under 25% TOR, theconcentration of CO decreases as the excess air ratioincreases Meanwhile, the CO concentration is higheraround λ=1.0 (FIT=110o) for the same reasons as discussedwith regard to Figure 9 The CO concentration under 50%TOR and λ=1.0 (FIT=150o) is relatively lower than that for25% TOR; the former corresponds to an early injection,while the latter corresponds to a late injection However,there is a reverse in the trend of the CO concentrations atlow values of λ for 100% TOR: the CO concentrationincreases from 600 to 900 ppm over the excess air ratios,

λ=1.0~1.4, before slowly decreasing above λ=1.4 When

λ=1.2, 100% TOR, and 1700 rpm, the fuel is injected intothe cylinder during valve overlap, i.e., when both the intakeand exhaust valves are open Therefore, the trend in the COconcentration is opposite that for 25% TOR but similar tothat for 50% TOR

Figure 9 Indicated thermal efficiencies and cycle

vari-ations for various excess air ratios and TORs

EFFECTS OF THE THROTTLE OPENING RATIO AND THE INJECTION TIMING OF CNG ON THE COMBUSTION 17

The stratified charge in the cavity during the

compre-ssion stroke is a cause of the higher THC concentration

around λ=1.0~1.2 (FIT of 110o~80o) and 25% TOR The

reason for this is that, under such conditions, a reach

mixture is partially formed in the cavity and causes lower

combustion efficiency, as is stated above in Figure 9

Methane, which is the main ingredient in the CNG, has a

higher lean-limit of 5.6% Therefore, it exists beyond the

flame propagation for lean mixtures over λ=1.8, and causes

a high concentration of THC

The concentration of the NOx, which is generally

affect-ed by the flame temperature and the level of Pmax,

de-creases under low loads and lean mixtures In particular,

the concentration of the NOx is relatively high at λ=1.0,

1.2, and 50% and 100% TOR, wherein the amount of

injected fuel increases because every imep is greater under

a high release rate and a homogeneous mixture

4 CONCLUSIONS

The present study investigated how fuel injection timing,

particularly early injection and late injection in conjunction

with the throttle opening ratio, affects the fuel-air mixing

characteristics, engine power, combustion stability, and

emission characteristics of a DI CNG spark engine The

key findings are summarized below

(1) For any throttle opening ratio and rpm, the combustion

characteristics are largely dependent upon variations in

the injection timing That is, the indicated thermal

effi-ciency, combustion duration, and lean limit can be

improved by varying the timing Further, under every

set of operating conditions, there is an appropriate

injection timing that leads to reduced emissions

(2) As the excess air ratio increases, the optimal fuel tion timing is delayed towards TDC for a late injectionfor the throttle opening ratio and rpm values specifiedfor the engine in this study The combustion duration isgreatly affected not only by the excess air ratio but also

injec-by the fuel injection timing and the flow conditions ofthe air-fuel mixture in the cylinder

(3) Late injection, in which fuel is injected during the pression stroke, is tremendously advantageous under alower throttle opening ratio, and can reduce the com-bustion duration and enlarge the lean limit

com-(4) In the present study, the entire combustion duration islargely governed by the duration of early flame develop-ment (29%) under an early injection conditions, and bythe duration of rapid burning (38~43%) under a lateinjection conditions, respectively

(5) The concentrations of THC and CO are mainly affected

by the injection timing, while the concentration of the

NOx is affected by the excess air ratio

REFERENCES

Catania, A E., Misul, D., Spessa, E and Vassallo, A.(2004) Analysis of combustion parameters and theirrelation to operating variables and exhaust emissions in

an upgraded multi-valve bi-fuel CNG SI engine SAE Paper No. 2004-01-0983

Chung, S S., Ha, J Y., Park, J S., Kim, K J and Yeom, J

K (2007) Comparison of the combustion characteristicsbetween S.I engine and R.I engine Int J Automotive Technology 8, 1, 19−25

Goto, Y and Sato, Y (2001) Combustion improvementand exhaust emissions characteristics in a direct injec-tion natural gas engine by throttling and EGR Trans Japan Society Mechanical Engineers(Ser B) 67, 659,

227−233

Kang, J H., Lee, J S., Park, J S and Ha, J Y (2007) Theeffect of fuel injection timing on combustion and powercharacteristics in a DI CNG engine Trans Korean Society Automotive Engineers 15, 1, 193−200

Kim, J H and Samimy, M (1999) Effects of injectiontiming on mixture preparation in a DI CNG engine. Fall Conf Proc., Korean Society of Automotive Engineers,

169−176

Kim, J Y., Kang, J H and Ha, J Y (2003) Performancecharacteristics of CNG engine at various compressionratio Fall Conf Proc., 1, Korean Society of Automotive Engineers, 3−7

Park, J S., Ha, J Y., Yeom, J K., Lee, J S., Lee, C J., andChung, S S (2007) Radical ignition technique in aconstant volume chamber Int J Automotive Technology

8, 3, 269−274

Tanaka, H., Sato, Y., Ito, S., Nakai, S and Wakabayashi, T.(2007) Effect of fuel/air mixing on the performance of anatural gas engine Trans Japan Society Mechanical Engineers(Ser B) 38, 3, 49−54

Figure 10 Effects of the injection timing on emissions at

each excess air ratio

International Journal of Automotive Technology , Vol 11, No 1, pp 19 − 26 (2010)

19

SIMULATION OF HCCI COMBUSTION WITH SPATIAL

INHOMOGENEITIES VIA A LOCALLY DETERMINISTIC APPROACH

Y J LEE * and K Y HUH

Mechanical Engineering Department, Pohang University of Science and Technology, Gyeongbuk 790-784, Korea

(Received 24 November 2008; Revised 14 June 2009)

ABSTRACT− There has been recent interest in a new engine type, Homogeneous Charge Compression Ignition (HCCI), to combine the advantages of SI and CI engines In this paper, a locally deterministic approach is employed to consider spatial inhomogeneities using the KIVA-CHEMKIN package Validation is performed for two experimental HCCI engines fueled, respectively, by hydrogen and n-heptane The full mechanism for hydrogen and a skeletal mechanism for n-heptane are used for combustion chemistry Differences in the reaction flow paths are shown at ignition and the heat release reaction stages of the two fuels Results show good agreement between measured and calculated pressures for different initial mixture temperatures with estimated residual fractions A parametric study is performed in both engines to consider the influences of the physical parameters wall temperature, swirl ratio and global equivalence ratio The ignition time of n-heptane is shown to

be relatively insensitive to variations in these parametric due to its two-stage ignition behavior.

KEY WORDS : HCCI Engine, Ignition delay, KIVA, Combustion chemistry, Two-stage igntion

1 INTRODUCTION

In the worldwide automotive industry, increasingly strict

regulations have been imposed as a result of intensifying

environmental concerns regarding atmospheric pollution

Spark Ignition (SI) engines have efficient post-processing

measures to handle emissions, but suffer from a low

part-load efficiency Compression Ignition (CI) engines have

attractive thermal efficiencies with low CO2 emission, and

there are current efforts to simultaneously reduce NOX and

particulate matter (PM) There has been recent interest in

developing a new engine type to combine the advantages

of SI and CI engines (Johnsson, 2007; Aleiferis et al.,

2007): a Homogeneous Charge Compression Ignition (HCCI)

engine One major difference of HCCI engines is that

chemistry plays a dominant role in the ignition and

com-bustion processes, while turbulence is the controlling

para-meter that determines the reaction rate in conventional

engines There have been intensive research efforts to

ad-dress excessive heat release rates at ignition and to generate

an efficient control strategy over a wide operation range of

engine loads and speeds for the HCCI engine

To successfully develop a commercially viable engine, it

is crucial to have a proper simulation model for various

complexities of HCCI combustion Several multi-zone models

(Ognik and Golovitchev, 2002; Fiveland and Assanis, 2002)

and multi-dimensional CFD models (Kong et al., 2001)

that represent the heat release and emissions of an HCCI

engine have been proposed Hessel et al. (2008) mented a multi-zone model in KIVA3V to calculate detai-led combustion chemistry with an improved wall heattransfer model (Han and Reitz, 1995) Bikas (2001) investi-gated the HCCI combustion process with a single zonemodel and a reduced chemical mechanism He applied theRepresentative Interactive Flamelet (RIF) model for spatialinhomogeneities and compared the results with 0-D simu-lation Kong et al. (2003) presented a model to combineCFD calculation with a detailed kinetic mechanism forHCCI combustion The CHEMKIN was called at eachcomputational cell in KIVA3V to resolve spatial inhomo-geneities The locally deterministic method is similar to theapproach in Kong and Reitz (2003) with no explicitconsideration of turbulent fluctuations in the mean reactionrate In this paper, validation is performed for the two testHCCI engines in the literature that are fueled by hydrogenand n-heptane, respectively A parametric study is perform-

imple-ed in both engines to consider the influences of the physicalparameters such as wall temperature, swirl ratio and globalequivalence ratio

2 DIFFERENT REGIMES AND MODELING OF HCCI COMBUSTION

Two different modes of HCCI combustion have beenidentified (Sankaran et al., 2005); one is sequential auto-ignition according to a local mixture condition, and theother is premixed flame propagation with a strong spatialgradient and consequent diffusive transport In the former,

*Corresponding author. e-mail: trotbs@postech.ac.kr

20 Y J LEE and K Y HUH

the flame structure may or may not be influenced by

turbulent mixing or the scalar dissipation rate, according to

the level of turbulence Weak spatial inhomogeneities may

result from gradients of either the fuel/air mixture

com-position or enthalpy with convective heat transfer on the

wall Premixed flame propagation may be dominant when

the local chemistry of a cold mixture is slower than

diffu-sive transport from neighboring hot products A typical

example is premixed flame propagation in a conventional

SI engine Otherwise, the sequential autoignition mode is

applied with relatively weak scalar spatial gradients The

criterion for the sequential autoignition mode may be given

as

The diffusive time scale is given in the laminar or

tur-bulent regime in the above It is necessary to consider the

effect of turbulent fluctuations on the mean reaction rate in

the turbulent regime This requires estimating both the

conditional flame structure and the local probability

den-sity function in general In the laminar regime or with a

negligible fluctuation effect in a nearly homogeneous

mix-ture, it may be modeled in terms of the mean scalars with

the locally deterministic approach Criteria for the validity

of the locally deterministic approach may, therefore, be

given as

where ε and ε h represent appropriate small numbers ξ and

ξ h are the mixture fractions based on fuel mass fraction and

enthalpy, respectively It has been verified that the two test

engines correspond to the HCCI mode of sequential

auto-ignition, in which the locally deterministic approach remains

valid

3 TEST ENGINES AND OPERATING

CONDITIONS

Experiments are conducted for the two test engines: a CFR

engine and TD100 Table 1 lists the specifications of the

TD100 engine fueled by hydrogen (Stenlaas et al., 2004)

There are four different cases with intake gas temperatures

of 109oC, 111oC, 114oC and 117oC Other simulation tions are fixed at 1200 RPM with a compression ratio of 17and equivalence ratio of 0.22

condi-Table 2 presents the specifications of the CFR enginefueled by n-heptane (Machrafi et al., 2005) Three differentcases include intake gas temperatures of 45oC, 60oC and

70oC Other simulation conditions are fixed at 600 RPMwith a compression ratio of 10.2 and equivalence ratio of0.4 The diesel fuel is represented by n-heptane with asimilar cetane number in the following simulations

4 COMPARISON OF MEASURED AND CALCULATED PRESSURE TRACES

Validation is performed for the locally deterministic proach by the KIVA3V and CHEMKIN package by com-paring to HCCI engine data in literature An axisymmetric2-D mesh is composed of 400 cells with no mean variation

ap-in the azimuthal direction

A sensitivity study is performed with respect to the gridsize in Figure 1, which shows negligible dependence on thenumber of grids greater than 400 in both engines Thedetailed chemical kinetic mechanism of hydrogen involves

26 reversible elementary reactions among 10 species Areduced chemical kinetic mechanism is employed to avoid

an excessive computational burden in handling the full

τ c <<τ d τ d =τ l = D

S L2 τ d =τ t

Engine connecting rod to crank radius ratio 3.26

Table 1 Specifications of the TD100 engine

Intake valve close (CAD) −167o Figure 1 Pressure traces for sensitivity with respect to the

grid size in the hydrogen HCCI engine

SIMULATION OF HCCI COMBUSTION WITH SPATIAL INHOMOGENEITIES VIA A LOCALLY APPROACH 21

kinetic mechanism of n-heptane The reduced mechanism

of n-heptane is composed of 114 reversible elementary

reactions among 44 species (Liu et al., 2004)

The residual gas fraction (x r) in the TD100 engine is

estimated approximately as 10% according to, (Heywood,

1988)

(3)The residual gas is represented as a mixture of N2, H2O

and O2 Figure 1 shows a comparison of measured and

calculated pressure traces for different initial gas

temper-atures at the beginning of the compression stroke Good

agreement is achieved for all cases in terms of the ignition

times and the peak pressures Results show that the

dis-crepancy in the rates of pressure rise after ignition is

influ-enced by the heat transfer on the cylinder wall Relevant

parameters that determine the heat transfer coefficient may

include the temperature difference between the cylinder

gas and wall and the flow conditions, swirl ratio and

turbu-lent intensity The wall temperature is adjusted between

424 and 450 K as the intake gas temperature varies from

109oC to 117oC It is tuned to match the measured pressures

because no such data were provided in the reference

(Stenlass et al., 2004) It is shown in Figure 2(b) that the

peak heat release rate tends to decrease as the ignition time

is delayed for a lower initial temperature The initial gas

temperature is a major factor to determine the ignition timeand the amount of fuel mixture that satisfy the autoignitioncondition

Figure 3 shows the mean temperature distributions ing compression and ignition in the cylinder It corresponds

dur-to the initial intake temperature of 117oC Note that themaximum temperature occurs in the central region near theaxis, while there are lower peripheral temperatures due toconvective heat loss on the wall There is a difference ofabout 40oC between the central region and the wall bound-ary layer before a significant chemical reaction Combus-tion proceeds in the mode of sequential autoignition with-out any strong spatial gradients or propagation of a pre-mixed flame in Figure 3 The mixture goes through ignition

as the corresponding local temperature increases because

of adiabatic compression by the neighboring expandingmixture The rate of pressure rise after ignition is, there-fore, closely related to the initial intake temperature, themean temperature gradient due to wall heat transfer and themixture composition including residual gas fraction inFigure 2

The residual gas fraction in the CFR engine was

estimat-ed as 6% and also modelestimat-ed as a mixture of CO2, H2O, N2and O2 Figure 4 presents validation of the mechanism of n-heptane in diesel HCCI combustion There is good agree-ment for the initial charge temperatures in the range bet-ween 318 K and 343 K However, there is some discre-pancy in the ignition time or the ignition delay at the initialstage of ignition in the cool flame region In Figure 4, it isobvious that n-heptane goes through two-stage ignition:one in the cool flame region and the other during majorheat release The first minor peak results from the coolflame chemistry in Figure 4(b) It is characterized by aNegative Temperature Coefficient (NTC), which involves

a decreasing reaction rate with increasing temperature atconstant pressure (Serinyel et al., 2007) The NTC involvesthe formation of unstable intermediate species from fuel,which may proceed in either chain branching or steadystate reactions There were some previous works on the

-Figure 2 Measured and calculated pressure traces (a) and

the heat release rates (b) for the hydrogen HCCI engine

Figure 3 Mean temperature distributions during ssion and ignition in the cylinder for the hydrogen HCCIengine (magnified twice in the axial direction)

compre-22 Y J LEE and K Y HUH

NTC of n-heptane in a rapid compression machine, e.g.,

Minetti et al. (1995) There is room for further

improve-ment in the reduced n-heptane mechanism to better

repre-sent autoignition in the cool flame region

Figure 5 presents the mean temperature distributions

during the ignition and the main heat release phases in a

cylinder They correspond to an initial intake temperature

of 70oC, while the wall temperature is set equal to 450oC

The wall temperature is initially higher than the mean

mixture temperature so that ignition occurs in the boundarylayer (Glassman, 1996) A cool flame is initiated at thecylinder wall and subsequently propagates to the center ofthe cylinder (Figure 5)

The diagram in Figure 6 shows dominant reaction paths

in the low temperature, cool flame and main ignition phases

of the two-stage ignition of n-heptane It is a temporallyintegrated global reaction path for a homogeneous mixtureconstructed with CHEMKIN Heat release in the coolflame region is primarily associated with the production of

H2O and CO at 800 K-900 K (Kongsereeparp and Checkel,2007) H2O is mainly produced by reactions (4) and (5),while CO is produced by reactions (6) and (7) The hydro-peroxide radical, H2O2, is produced by decomposition of

HO2 through reaction (8) and the collision of HO2 and

CH2O according to reaction (9) At the time of main tion, H2O2 is rapidly decomposed through reaction (10) togenerate a pool of OH radicals that subsequently parti-cipate in producing CO2 and H2O with major heat releaseaccording to reactions (5), (11) and (12) (Westbrook,2000)

Figure 4 Measured and calculated pressure traces (a) and

the heat release rates (b) for the n-heptane HCCI engine

Figure 5 Mean temperature distributions during

compre-ssion and ignition in the cylinder for the n-heptane HCCI

engine

Figure 6 Reaction path diagram in the cool flame regionfor oxidation of n-heptane

SIMULATION OF HCCI COMBUSTION WITH SPATIAL INHOMOGENEITIES VIA A LOCALLY APPROACH 23

5 PARAMETRIC STUDY WITH RESPECT TO

WALL TEMPERATURE, SWIRL RATIO AND

EQUIVALENCE RATIO

5.1. HCCI Engine Fueled by Hydrogen

The ignition time is one of the important control parameters

when operating an HCCI engine Figure 7 shows pressures

and heat release rates of the hydrogen HCCI engine for

wall temperatures between 465 K and 590 K It is obvious

that ignition occurs earlier with a higher wall temperature,

although it does not have as much influence as the intake

temperature in Figure 2 The duration of heat release is not

affected by the wall temperature, while the initial intake

temperature affects both ignition time and heat release

duration in Figure 2

Figure 8 shows the results of the parametric study with

respect to the initial swirl ratio between 0.3 and 2.8 There

is significant delay in the ignition time with a longer

dura-tion of heat release at a higher swirl ratio The effect of the

swirl ratio may be interpreted in terms of heat transfer on

the wall and the resulting mean temperature and its

gradi-ent A higher swirl ratio leads to a lower peak temperature

Figure 7 Pressures (a) and heat release rates (b) of the

hydrogen HCCI engine for different cylinder wall

24 Y J LEE and K Y HUH

and a thicker thermal boundary layer as shown in Figure

8(b)

A higher swirl ratio involves a higher turbulent intensity

and a higher convective heat transfer coefficient and,

con-sequently, a larger fraction of fuel trapped in the wall

boundary layer

In Figure 9, the equivalence ratio has the most

signifi-cant effect on ignition time, peak pressure and heat release

rate A shorter ignition delay at a higher equivalence ratio

is simply due to the faster increase of temperature with a

higher fuel fraction in the mixture The duration of heat

release remains approximately the same because the mean

temperature is independent of the global equivalence ratio

before ignition It is obvious that combustion is complete

with a heat release less than about 5 degrees CA for all

cases in Figure 9(b)

5.2 HCCI Engine Fueled by n-heptane

Figure 10 shows a similar trend as Figure 5, while it

involves a wider range of wall temperatures between 450 K

and 700 K Ignition is advanced while the duration of heat

release remains approximately constant as the wall

temper-ature increases There are notable double peaks of

two-stage ignition in the heat release rates in Figure 10(b) It is

obvious that the ignition delay of n-heptane is less sensitive

to the temperature than that of hydrogen This is a result of

the two-stage ignition behavior of n-heptane, in which thefirst ignition due to cool flame chemistry occurs at a cylin-der mean temperature of about 800 K The main ignitionfollows as the temperature increases with contributionsfrom both cool flame chemistry and compression by thepiston

Negligible influence of the swirl ratio is shown for the heptane HCCI engine in Figure 11 On the other hand thehydrogen HCCI engine showed appreciable dependence onthe swirl ratio in Figure 7 It may be explained in terms ofthe same phenomenon of two-stage ignition in Figure 10.The first ignition or the cool flame chemistry does notdepend on the temperature distribution or the level of themean temperature in the cylinder The swirl ratio deter-mines turbulent intensity, which in turn determines the heattransfer and the temperature distribution in the wall bound-ary layer Cool flame chemistry is affected by the walltemperature, but is not significantly affected by the distri-bution profile from any given wall temperature, according

n-to Figures 10 and 11

In Figure 12 the ignition time is not significantly

affect-ed by the equivalence ratio, while the rate of pressure riseand the peak pressure show approximately proportionalvariation with the equivalence ratio The main heat releasetiming tends to be delayed at a lower equivalence ratio due

to lower heat release from the first ignition phase This isagain quite different from the behavior of the hydrogen

Figure 10 Pressures (a) and heat release rates (b) of the

n-heptane HCCI engine for different cylinder wall

temper-atures

Figure 11 Pressures (a) and heat release rates (b) of the heptane HCCI engine for different swirl ratios

n-SIMULATION OF HCCI COMBUSTION WITH SPATIAL INHOMOGENEITIES VIA A LOCALLY APPROACH 25

HCCI engine in which both the ignition time and the

duration of heat release show strong dependence on the

equivalence ratio in Figure 9

6 CONCLUSION

In this paper, a simulation is performed to validate the

locally deterministic approach for the hydrogen and diesel

HCCI engines with detailed and skeletal mechanisms of

hydrogen and n-heptane

(1) Results show good agreement between measured and

calculated pressure traces in both engines The locally

deterministic approach can handle HCCI combustion

in the sequential autoignition mode with a smooth

mean temperature distribution, but not the effect of

turbulent fluctuations with strong spatial gradients The

diesel chemistry is well represented by that of

n-heptane with a similar cetane number

(2) At ignition, the rate of pressure rise is reduced by the

temperature gradient due to turbulence and heat

trans-fer on the wall Ignition occurs at the center of the

cylinder in the hydrogen HCCI engine, while cool

flames are initiated in the wall boundary layer in the

n-heptane HCCI engine This is a result of the two-stage

ignition behavior of n-heptane and a wall temperature

that is initially higher than the gas temperature

(3) Hydroperoxide, H2O2, is generated and accumulated

during the first ignition phase by the cool flame stry of n-heptane At the second phase, or main ignitiontime, it subsequently gets decomposed rapidly into OHradicals, which contribute to major heat release reac-tions Further improvement may be required in thereduced n-heptane mechanism to reproduce the igni-tion time more accurately

chemi-(4) Parametric investigation is performed on ignition timeand heat release rate with respect to wall temperature,swirl ratio and equivalence ratio The single stage igni-tion of hydrogen shows dependence on wall temper-ature and swirl ratio, which determine the mean temper-ature distribution due to convective heat loss on thewall On the other hand the two stage ignition of n-heptane is partly supported by heat release in the coolflame region and shows only minor dependence onthose parameters

ACKNOWLEDGEMENT− This research was supported by the Korea Institute of Machinery & Materials (KIMM) project,

‘Investigation and validity of HCCI engine simulational model (4.0002492)’ The author would like to thank their support and helpful comments on this paper.

REFERENCES

Aleiferis, P G., Charalambides, A G., Hardalupas, Y., Taylor,

A M K P and Urata, Y (2007) Axial fuel stratification

of a homogeneous charge compression ignition (HCCI)engine Int J Vehicle Design 44, 1/2, 41−61

Bikas, G (2001) Kinetic Mechanism for Hydrocarbon Ignition Dissertation RWTH Aachen

Fiveland, S and Assanis, D (2001) A quasi-dimensionalHCCI model for performance and emission studies 9th Int Conf Num Comb. No MS052

Glassman, I (1996) Combustion Academic Press 3rd Edn

81−88

Han, Z and Reitz, R D (1995) Turbulence modeling ofinternal combustion engines using RNG k-e model

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Hessel, R P., Foster, D E., Steeper, R R., Aceves, S M.and Flowers, D L (2008) Pathline analysis of full-cyclefour-stroke HCCI engine combustion using CFD andmulti-zone modeling SAE Paper No 2008-01-0048.Heywood, J B (1988) Internal Combustion Engine Fund- amentals McGraw-Hill Int Edn 169−172

Johnsson, B (2007) Homogeneous Charge CompressionIgnition: The future of IC engines? Int J Vehicle Design

44, 1/2, 1−19

Kong, S., Marriot, C., Reitz, R and Christensen, M (2001).Modeling and experiments of HCCI engine combustionusing detailed chemical kinetics with multidimensionalCFD Comb Sci and Tech., 27, 31−43

Kong, S C and Reitz, R D (2003) Numerical study ofpremixed HCCI engine combustion and its sensitivity tocomputational mesh and model uncertainties Comb.

Figure 12 Pressures (a) and heat release rates (b) of the

n-heptane HCCI engine for different equivalence ratios

26 Y J LEE and K Y HUH

Theory Modeling, 7, 417−433

Kongsereeparp, P and Checkel, M D (2007) Intake

ignition mechanism of n-heptane/air mixture in an HCCI

combustion engine Spring Technical Meeting Comb.

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Liu, S., Hewson, J C., Chen, J H and Pitsch, H (2004)

Effects of strain rate on high-pressure nonpremixed

n-heptane autoigniton in counterflow Comb Flame, 137,

320−339

Machrafi, H., Lombaert, K., Cavadias, S and Guibert, P

(2005) Reduced chemical reaction mechanism:

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autoigni-tion process of n-heptane in internal combusautoigni-tion engines

SAE Paper No 2005-24-035

Minetti, R., Carlier, M., Ribaucour, M., Therssen, E and

Sochte, L R (1995) A rapid compression machine

investigation of n-heptane: measurements and modeling

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Ognik, R and Golovitchev, V (2002) Gasoline HCCImodeling: An engine cycle simulation cod with a multi-zone combustion model SAE Paper No. 2002-01-1745.Sankaran, R., Im, H G., Hawkes, E R and Chen, J H.(2005) The effects non-uniform temperature distribution

on the ignition of a lean homogeneous hydrogen-airmixture Proc Comb Institute, 30, 875−882

Serinyel, Z., Moyne, L L and Guibert, P (2007) geneous charge compression ignition as an alternativecombustion mode for the future of internal combustionengines Int J Vehicle Design 44, 1/2,20−40

Homo-Stenlaas, O., Christensen, M., Egnell, R and Johansson, B.(2004) Hydrogen as homogeneous charge compressionignition engine fuel SAE Paper No. 2004-01-1976.Westbrook, C K (2000) Chemical kinetics of hydrocarbonignition in practical combustion system Prec Comb Institute, 28, 1563−1577

International Journal of Automotive Technology , Vol 11, No 1, pp 27 − 32 (2010)

27

HIERARCHICAL MODELING OF SEMI-ACTIVE CONTROL OF A FULL MOTORCYCLE SUSPENSION WITH SIX DEGREES OF FREEDOMS

L WU * and W.-J ZHANG

Department of Physics and Electromechanical Engineering, Sanming University,

Sanming 365004, Fujian Province, China

(Received 19 March 2008; Revised 13 December 2008)

ABSTRACT− Hierarchical control is a new control framework in the vehicle vibration control field In this paper, a hierarchical modeling method is presented to form a different motorcycle model, compared to the traditional model with six degrees of freedoms (DOF), so as to construct hierarchical modeling control The whole control framework is composed of

a central control, two local controls and two uncontrollable parts The front and rear wheel systems of a motorcycle are all dealt with by using two independent local 2-DOF systems The driver and engine act as uncontrollable passive parts The central control is composed of an algorithm made up of some dynamic equations that harmonize local relations The vertical and pitch accelerations of the suspension center are treated as central control objects With the help of Linear Quadratic Gaussian (LQG) algorithms adopted by two local controls, respectively, and Matlab software, some results of the simulation show that hierarchical modeling control requires less CPU time, reduces respond time and improves ride quality

KEY WORDS : Hierarchical modeling method, Motorcycle suspension, Semi-active control, Six degree of freedoms, Simulation

1 INTRODUCTION

The motorcycle is an important transportation facility in

our society Because of its simple structure, relative to a

car, a passive vibration system, composed of springs and

hydraulic dampers, is widely applied However, the passive

suspension system cannot meet demands due to its

un-adjusted essentiality on different types of road In recent

decades, with the development of new materials and

advanced technologies, a semi-active control system, based

on the magneto-rheological (MR) damper, has emerged

and is receiving more attention in the motorcycle vibration

control field (Ericksen, 2003; Hitchcock et al., 2002)

In traditional vibration control design, a motorcycle

sus-pension system was modeled as a whole body (Cho, 2005)

If vibration of a motorcycle could be controlled precisely,

the model would fully and clearly describe the body;

with-out requiring control strategies independent to the body

model, such as fuzzy and neural networks control However,

it is necessary to adopt a machine model with sophisticated

control strategies, and one that has been field-tested Hence,

when a motorcycle model is fully and precisely calculated,

which requires several DOF, a heavy online calculating

load is needed, reducing the control response speed Thus,

we seek a solution to this problem by using a new control

framework with sophisticated control strategies

The idea of hierarchical control has been applied in

many fields, such as internet frameworks, power systemcontrol, etc for a long time (Shankaran et al., 2006; Chen

et al., 2004) In the vehicle vibration control field, Hagopianand Gaudiller (1999) introduced hierarchical ideas intoactive control fields of a half vehicle suspension Becausethe selection of independent variants means that there is nocoupling in equilibrium conditions, a central control wasproposed to take into account the pitch and gap between thebody and ground in their method Since a traditionalmathematical model was employed, the method still requir-

ed the same online calculating load, and did not solve theproblem of response lag Recently, the author proposed ahierarchical modeling method to construct new models ofmotorcycles with 4- and 5-DOF, so as to frame hierarchicalmodeling control (Wu and Chen, 2006a, 2006b, 2007; Wu

et al., 2006) In this method, the important aspects werehow to treat a continuous sprung-mass as two parts of afront and rear concentrated sprung-masses An algorithm

of the central control was formulated However, model ofthe motorcycle suspension with 5-DOF has more complexity,compared to current models Hence, an easy acceptedmathematical model to realize hierarchical modeling control

is necessary

In this paper, a hierarchical modeling control is putforward Here, the vertical and pitch accelerations of thesprung-mass center are adopted as central objects, toharmonize front and rear local motions By simplifying the6-DOF motorcycle model, the online CPU time is decreas-

ed dramatically Compared with the traditional case, the

*Corresponding author. e-mail: smuwl@126.com

28 L WU and W.-J ZHANG

results showed both the accuracy and advantages of the

method

2 HIERARCHICAL MODELING

A traditional full motorcycle dynamic model is presented

in Figure 1 This motorcycle model has 6-DOF, represented

by z uf, z ur, z c, θ c, z p and z g, respectively These are the

vertical motion of the front axle, vertical motion of the rear

axle, vertical motion of the motorcycle body, pitch motion

of the motorcycle body, vertical motion of the driver and

vertical motion of the engine, respectively Here, the

natural vibration of the engine can be measured in advance

Motorcycle behavior is expressed by vertical and pitch

motions, in terms of acceleration, velocity and movement,

for various motorcycle components This system is made

up of the following parameters: m g, m p, m c, m uf and m ur,

which represent the masses of the engine, driver,

motor-cycle body (sprung-mass), front and rear wheel

(unsprung-mass), respectively; c η f and c η r are the damping coefficients

of the front and rear wheel system; k mf and k mr are the

stiffness coefficients of the front and rear wheel systems; k uf

and k ur are the tire stiffness coefficients of the front and rear

wheel systems; F mf and F mr are the semi-active control

forces of the front and rear wheel systems; k g and c g are the

stiffness and damping coefficients between the engine and

suspension, respectively; k p and c p are the stiffness and

damping coefficients between the driver and suspension,

respectively; l f, l r, l g and l p are the distances from front axle,

rear axle, engine and driver to the sprung-mass center,

respectively Finally, z efand z er are the front and rear road

excitations

According to the traditional 6-DOF model, a series of

dynamic equilibrium equations can be written Therefore,

if some modern control strategies, excluding fuzzy and

neural networks algorithms, were used to control vibration

based on the traditional motorcycle model, some matrix

products, which have twelve rows and columns, would be

involved in the operating process of the state space

How-ever, if a hierarchical modeling control method is applied,

see Figure 2, a whole motorcycle suspension could betreated as two independent 2-DOF suspensions, according

to its control viewpoint Hence, some matrix products,which only have four rows and columns, will be required.Due to parallel reduction, the advantages of the hierarchicalmodeling control would undoubtedly emerge Thus, it willeffectively shorten computing time, quicken response speedand increase sampling frequency, which indirectly improvesthe handling properties and ride comfort of a motorcycle

To realize the control mode, a continuous sprung-massshould be considered as two concentrated sprung-massesfor the front and rear parts Thus, an algorithm should beconstructed so as to transform a motorcycle model with 6-DOF into two quarter suspensions with 2-DOF Using thismodel, force analysis of the whole sprung-mass, separatedfrom motorcycle model, must be executed first Figure 3 isthe force diagram of the sprung-mass F f, F r, F g and F p areconcentrated forces of the front, rear, engine and driversupports, respectively Thus, two dynamic equilibrium equa-tions for the force and moment of the sprung-mass centercan be written as follows

(1)(2)The analysis is used to transform the center motion intofront and rear motions, so the relationship between thevertical motions of the sides of the sprung-mass and thecenter vertical motion should be taken into account.Assuming z cf and z cr are front and rear vertical motions,respectively, then we have

(3)(4)

Figure 1 Traditional motorcycle dynamic model

Figure 2 Hierarchical modeling control framework

Figure 3 Force diagram of sprung-mass

HIERARCHICAL MODELING OF SEMI-ACTIVE CONTROL OF A FULL MOTORCYCLE SUSPENSION 29

Substituting equations (3) and (4) into equation (1),

respectively, and connecting equation (2), we get

(5)(6)Where m cf=m c l r/l, m cr=m c l f/l, I ce=I c − m c l f l r and l=l f+l r

The results derived above indicate that the sprung-mass

could be simplified into a rigid rod with two concentrated

masses at both ends, and it is subject to the influences of

the engine and driver Equations (5) and (6) can act as the

force and moment dynamic balance equations,

respective-ly The key of the hierarchical modeling method, how to

distribute the sprung-mass, has now been settled As

men-tioned above, a motorcycle suspension can be treated as a

combination of two independent 2-DOF suspensions If l f

equals l r, a motorcycle suspension can be decomposed into

front and rear 2-DOF suspensions This is the concept of

mass partition coefficients, which is referenced by many

books on automobile theory (Yu, 2000)

Due to the demand for the predicted values of

suspen-sion center motion during hierarchical control, the

concent-rated forces of the front and rear suspensions, calculated

using equations (1) and (2), are obtained as follows

(7)(8)Where

(9)(10)Without restriction of the rear sprung-mass, the concent-

rated mass of the front suspension m cf would move from the

original position z cf to a new position z f, and generate a

displacement ∆ z f Similarly, without restriction of the front

sprung-mass, the concentrated mass of the rear

suspension would move from the original position z cr to

a new position z r, and generate a displacementn ∆ z r

Suppose ∆ z f=z cf − z f and ∆ z r=z r − z cr, we get

(11)(12)After substitution, we obtain

(13)(14)

By changing the suspension sprung-mass, its

unsprung-mass m uf(m ur) would be moved from the original position z uf

(z ur) to a new position ( ), and generate a displacement

∆ z uf (∆ z ur) For example, the dynamic balanced equations ofthe front suspension about two positions are

(15)(16)Since, , we can write a new equation relat-ing the displacements of the front sprung- and unsprung-mass

(17)Thus, we can obtain ∆ z uf after ∆ z f was calculated so as toget z uf or In the same way, because ∆ z ur= − z ur, theunsprung-mass displacement ∆ z ur of the rear suspensioncan be obtained

(18)All mathematical equations deduced above are adopted

to construct the central control algorithm We can pose a whole suspension into two quarter suspensions with2-DOF in the presence of the algorithm and establish ahierarchical modeling control The detailed computing pro-cess of the hierarchical modeling method for a motorcyclesuspension is as follows

decom-(1) The predicted values of and , by virtue of roadexcitation, should be determined first The given range

of and will statistically not exceed 99.7 percent

of the limited values σ s and σ p, respectively We require

(19)Where σ s and σ p are the limited values of the body verticaland pitch accelerations, respectively, and can be pre-estimated

(20)(21)(2) The acting forces, F p and F g, can be calculate usingequations (9) and (10), z c, and engine excitation.(3) The predicted values of , , F f and F r can becalculated by equations (3), (4), (7) and (8) Thepredicted values of ∆ z f and ∆ z r can be derived fromequations (13) and (14) Thus, the front and rearpredicted values of the decomposed sprung-massaccelerations and can be determined

(4) Consider and as known values, and set up a DOF state space The state vector is Z i as follows

2-(22)The output vector is Ψ i

(23)The state differential and output equations are as follows

··f z··r

30 L WU and W.-J ZHANG

(25)Where the subscript i denotes the front or rear suspension

According to the output equation and optimal control

strategy, the actual control force F mi can be determined The

true values of and are subsequently obtained

(5) The true variables of , , F f, F r and F p are

deter-mined according to the reverse procedure The true

values of and can then be calculated

3 NUMERICAL SIMULATION

In this paper, the semi-active damper is the

magneto-rheological damper shown in Figure 4 It was designed for

motorcycles Figure 5 shows some velocity vs force curves

Figure 6 shows an approximate shaded curve surface of

current vs velocity, and force of the MRF damper based on

experimental data

A motorcycle suspension with 6-DOF is simulated for

traditional and hierarchical semi-active control The LQG

module in Matlab is employed for the front and rearsuspensions The suspension parameters are as follows

(1) The front and rear suspension deflections are limited to

±0.03 m,which is the piston travel of MRF damper.The front and rear tire deformations are restricted to

±0.02 m.

(2) MRF damper output force changes from 200 Nto 1000

N.

(3) Excitation of engine is z g=0.01 sin(100π t)

Matlab6.5 was used to program and simulate the system

in a computer with a 1.0 GHz CPU and 256 M memory.Under semi-active control, the weights of the front suspen-sion are 1000, 100000 and 0.0048, and 200, 100000 and 0for the rear Some results are presented in Figure 7 to 11.Road excitation under the front and rear wheels in thetime domain are shown in Figure 7 and acted as simulation

Figure 4 Magneto-rheological damper

Figure 5 Velocity-force graph under different current of

the MRF damper

Figure 6 Velocity-force-current graph of the MRF damper

HIERARCHICAL MODELING OF SEMI-ACTIVE CONTROL OF A FULL MOTORCYCLE SUSPENSION 31

input After employment of the hierarchical modeling method,

less computer time is required because front and rear

suspension calculated can be performed simultaneously

Figure 8 shows CPU times for 100 cycles of the

hierar-chical modeling and traditional methods, under the same

conditions The total time of 100 cycles, using the

hierar-chical modeling method, is 0.637 seconds, and 1.156 seconds

for the traditional method Therefore, a single cycle time

for the former is 0.0637 seconds, and 0.1156 seconds for

the latter We note that the value is reduced by 44.9% in the

case of the hierarchical modeling method when compared

with the traditional method The results show that the

control response speed has increased With an accelerated

response speed, the sampling time could be diminished to

some extent and road excitation can be fully and clearly

described Thus, the control performance of the motorcycle

system can be improved

Figure 9 and Figure 10 show the vertical acceleration of

the seat and sprung-mass Figure 11 gives the pitch

accele-ration of the sprung-mass By reducing the sampling time,

the acceleration in the time domain under hierarchicalsemi-active control is less than that under traditional semi-active control It can be seen that the hierarchical modelingcontrol method can decrease body acceleration to someextent

From the simulation results above, it can be seen thatsemi-active control based on the hierarchical modelingmethod given in this paper provides better performancethan the one under traditional semi-active control

4 CONCLUSION

The purpose of this paper is to present a hierarchical ing method, which can translate a motorcycle suspensionsystem with 6-DOF into two quarter suspension systemswithout special conditions As a result of decompositionand simplification of a motorcycle suspension, the controlresponse speed is increased, thereby decreasing the per-mitted sampling time Thus, road excitation can be betterdescribed, and ride comfort of a semi-active motorcyclesuspension can be improved If the method is extended tomulti-wheel vehicles, the complexity of the vehicle modelcould be simplified, and the excessive workload resultingfrom more degrees of freedom would be avoided Thus, thehierarchical modeling method is an effective technique forsolving vehicle vibration problems

model-ACKNOWLEDGEMENT− I would like to thank the partly financial support provided by the item of Talented Youth Foundation of Fujian Province (No 2007F3090), of Science and Technology Project of the Education Department of Fujian Province (JA08239), of Science and Technology Project of

Figure 7 Displacement of the C grade road

Figure 8 CPU online calculation time

Figure 9 Vertical accelerations of the driver seat

Figure 10 Vertical accelerations of the suspension center

Figure 11 Pitch accelerations of the suspension center

32 L WU and W.-J ZHANG

Sanming City (No 2007-G-6) and of Sanming University

(HX200804).

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Chen, Z., Yan, W., Xu, G and Wang, G (2004) Hierarchical

control theory and its application to power system

auto-mation Proc IEEE Int Conf., 2, 643−646

Cho, B K., Ryu, G and Song, S J (2005) Control strategy

of an active suspension for a half car model with

pre-view information Int J Automotive Technology 6, 3,

243−249

Ericksen, E O and Gordaninejad, F (2003) A

magneto-rheological fluid shock absorber for an off-road motorcycle

Int J Vehicle Design, 33, 139−152

Hagopian, J D and Gaudiller, L (1999) Hierarchical

con-trol of hydraulic active suspensions of a fast all-terrain

military vehicle J Sound and Vibration, 222, 723−752

Hitchcock, G H., Gordaninejad, F and Wang, X (2002) A

new by-pass, fail-safe, magneto-rheological fluid damper

Proc SPIE Conf Smart Materials and Structures, 1,1−

7

Shankaran, N., Koutsoukos, X D., Schmidt, D C., Xue, Y

and Lu, C Y (2006) Hierarchical control of multipleresources in distributed real-time and embedded systems

Proc 18th Euromicro Conf Real-Time Systems IEEE Computer Society, 151−160

Wu, L and Chen, H (2006a) Complex stochastic wheelbasepreview control and simulation of a semi-active motor-cycle suspension based on hierarchical modeling method

Int J Automotive Technology 7, 6, 749−756

Wu, L and Chen, H (2006b) Hierarchical preview controland simulation of vehicle suspension Trans Chinese Society for Agricultural Machinery, 4, 12−17

Wu, L and Chen, H (2007) A HIL simulation experimentdesign based on a hierarchical modeling method Int J Vehicle Autonomous System, 1/2, 158−169

Wu, L., Chen, H and Chen, L (2006) Hierarchical previewcontrol and simulation of semi-active motorcycle suspen-sion Chinese J System Simulation, 6, 2239-2243-2246

Yu, Z (2000) Automobile Theory Mechanical ing Publishing Group China

Engineer-Zhang, Y (2003) Time domain model of road irregularitiessimulated using the harmony superposition method Trans Chinese Society of Agricultural Engineering, 6, 32−35

International Journal of Automotive Technology , Vol 11, No 1, pp 33 − 40 (2010)

33

ROBUST CONTROL FOR 4WS VEHICLES CONSIDERING A VARYING

TIRE-ROAD FRICTION COEFFICIENT

G.-D YIN * , N CHEN, J.-X WANG and J.-S CHEN

School of Mechanical Engineering, Southeast University, Nanjing 210096, China

(Received 23 May 2008; Revised 17 December 2008)

ABSTRACT− A µ -synthesis for four-wheel steering (4WS) problems is proposed Applying this method, model uncertainties can be taken into consideration, and a µ -synthesis robust controller is designed with optimized weighting functions to attenuate the external disturbances In addition, an optimal controller is designed using the well-known optimal control theory Two different versions of control laws are considered here In evaluations of vehicle performance with the robust controller, the proposed controller performs adequately with different maneuvers (i.e., J-turn and Fishhook) and on different road conditions (i.e., icy, wet, and dry) The numerical simulation shows that the designed µ -synthesis robust controller can improve the performance of a closed-loop 4WS vehicle, and this controller has good maneuverability, sufficiently robust stability, and good performance robustness against serious disturbances

KEY WORDS : Four-wheel steering, Optimal control, Robust control, µ -synthesis

1 INTRODUCTION

Many researchers in the last decade have reported that the

four-wheel steering (4WS) technique is one of the most

effective methods of active chassis control, and can

consi-derably enhance vehicle stability and maneuverability A

large number of studies have been done on various control

strategies for 4WS vehicles since the first 4WS system was

reported (Young and Kim., 1995; El Hajjaji et al., 2005)

It is well known that vehicle maneuvering containing

various uncertainties is a highly nonlinear and complex

dynamic process The parameters of a vehicle are subject to

a vast range of uncertainties such as external disturbances,

unmodeled dynamics, road roughness, wind gusts, load

fluctuations, and braking/accelerating forces This raises a

serious robust stability problem for 4WS vehicle control

Namely, the vehicle controller has to successfully cope

with these uncertainties to maintain maneuvering stability

and to insure that system performance is not excessively

deteriorated

Modern robust control theory provides a powerful tool

to increase robust stability and improve the performance of

4WS vehicle control against significant uncertainties

Typi-cal robust control theory includes H 2/ synthesis (You

and Chai, 1999; Lv et al., 2004) However, synthesis by the

standard method is relatively conservative since a

system perturbation cannot be carefully distinguished with

this theory, which considers only the boundary of the

un-modeled dynamics Among various approaches, the design

of robust control problems can be further enhanced by µ

-analysis (Packard and Doyle, 1993) Recent advances in µsynthesis have made it possible to analyze and design acontroller to deal with a dynamic system with strong un-certainties (Gao et al., 1995)

-This paper presents the design issues of robust trollers for 4WS vehicles under a yaw rate tracking archi-tecture by using µ-synthesis with a D-K iteration algorithm(Balas et al., 2001) This approach is employed to improvevehicle performance with regard to its robustness andlateral motion stability when faced with a given class ofuncertainties The vehicle yaw rate is chosen as the onlyfeedback signal to avoid the practical difficulty of measur-ing the CG sideslip angle of the vehicle In addition, aLinear Quadratic Regulator (LQR) controller (Zhou andDoyle, 1996), as an optimal regulator, is designed to mini-mize the sideslip angle Evaluations of vehicle performancedetermined that the proposed controller performs adequate-

con-ly with different maneuvers (i.e., J-turn and Fishhook) and

on different road conditions (i.e., icy, wet, and dry) Consequently, the designed µ-synthesis controller provides

a good robustness that ensures stability against parametricperturbations (such as varying cornering stiffness withdifferent road conditions) and rejects external disturbances(such as side wind) The numerical simulation results showthat the 4WS vehicle equipped with the proposed controllerprovides better maneuverability and driving safety Thewhole control system has fine dynamic characteristics andbetter stability robustness and performance robustness

34 G.-D YIN, N CHEN, J.-X WANG and J.-S CHEN

4WS vehicle is assumed to be a symmetric rigid body of

mass m resting on four wheels moving forward at a

constant speed v In this model, the coordinate frame is

fixed on the vehicle body in the center of gravity, denoted

as CG Only lateral and yaw motions are considered, which

are described by the sideslip angle β and the yaw rate r,

respectively

(1)(2)where I z denotes the yaw moment of inertia about its mass

center z-axis, L fand L r are the distances from the CG to the

front and rear axles, δ f and δ r are the steering angles of the

front and rear wheels, and F f and F rare the lateral forces of

the front and rear wheels Because δ f and δ r are generally

small,

The slip angles of front and rear tires are represented by

α fand α r If β is small and v varies slowly, α fand α r will

be given by

(4)

In general, lateral tire force is a non-linear function of

slip angle As long as the tire slip angle is small, a linear

relationship between tire force and slip angle can be

justified Within the linear region, nonlinear tire

characteri-stics can be approximated as

F f=µ K f α f and F r=µ K r α r (5)

where

,,

µ is the adhesion coefficient between road surface and the

tire ranging from 0.8 (dry road) to 0.25 (icy road), the

cornering stiffness of the front (rear) tire is denoted by K f

(K r), K fn and K rn are normalized cornering stiffnesses, and

K cf and K cr are cornering stiffness coefficients

Thus, the system equations of this model that govern the

sideslip angle and the yaw rate are written as follows

(6)

In addition, the lateral acceleration α y at the CG is obtained

by the yaw rate and the vehicle sideslip angle with thefollowing relation:

(7)Referring to Equation (6) and (7), we obtain the state-spacedescribing the system dynamics as

(8)where the state vector , control input vector

The matrices A, B, C,and D in equation (8) are given as

The key parameters of the vehicle and the tires used inthis paper are summarized in Table 1

- µ L – K f f + L r K r

mv 2 - 1

µ L – K f f + L r K r

I z

- – L µ f 2K f + L r 2K r

I z v -B=

K f mv

- – µ – Klf f + l r K r

mv -D=

µ K f m

- µ K r m -

Figure 1 Half-vehicle dynamic model

Table 1 Parameters of the vehicle and the tires

ROBUST CONTROL FOR 4WS VEHICLES CONSIDERING A VARYING TIRE-ROAD FRICTION COEFFICIENT 35

It is known that the linear vehicle model in Equation (8)

contains plant uncertainties due to cornering stiffness, which

depends on the tire characteristics and tire-road contact

conditions Thus, the coefficients in the vehicle model are

generally not fixed A robust controller has to be designed

for an uncertain vehicle model

3 ROBUST CONTROL DESIGN AND ANALYSIS

3.1 Robust Control Design and Analysis Using a µ

-Ap-proach

In vehicle control system design, it is necessary to consider

changes in vehicle model parameters due to varying road

conditions In order to provide robustness against changes

in the parameters, a linear feedback controller K is

design-ed by applying µ-synthesis

To consider the uncertainty in the vehicle running

environment by µ-synthesis, we identified a nominal plant

model for designing the controller It is well known that the

adhesion coefficient µ in the state-space realization matrices

(A, B, C, D) is taken as a constant; that is to say, the

controller design is related to a constant µ at that moment,

but in practice, the adhesion coefficient always varies within

a range, tracking uncertainties from the set of all possible

system variations It is always necessary to design different

controller parameters corresponding to different adhesion

coefficients and to perform real-time switching of the

controller parameters in response to the current cornering

stiffness However, changes in the controller parameters

are not smooth; thus, it is desired to have a controller

parameter designed for only one adhesion coefficient that

will also work well for a certain constant range

As shown in Figure 2, the closed-loop system includes

the feedback structure of the model G and controller K and

elements associated with the uncertainty models and

per-formance objectives In the diagram, u is the control input,

which denotes the rear wheel angle Since the estimation of

the sideslip angle is difficult but the yaw rate is easier to

measure in practice, the yaw rate is chosen as the only

feedback signal to determine the control of the system

Measurement noise is designated by n In the figure, the

front wheel angle δ fis considered as the external

distur-bance signal w The value z represents the performanceoutput, which is the sideslip angle, which is usually mini-mized to approach zero in the four-wheel steering controlsystem

In this system, the desired yaw rate Gf - r is selected as(Nagai et al., 1997; An et al., 2008)

(9)where Gf - r corresponds to a yaw rate of vehicle response,which is agile and without much overshoot

To deal with system perturbation, the weighting function

is a key issue in the µ-synthesis design process Theweighting matrices, which characterize the input/outputsignals of the control system, have to be formulatedappropriately Since the robust controller has to provide adesired degree of stability and performance robustness, it isnecessary to translate the design specifications into fre-quency-dependent weighting functions

The parametric uncertainties of the mass, velocity, andadhesion coefficient are represented by the ∆ f block, whoseinput and output are y f and u f Moreover, the transferfunction ∆ f block is stable and norm-bounded, The unmodeled dynamics are represented by W r and Äm It

is assumed that the transfer function W r is known and that itreflects the uncertainty in the model The transfer function

∆ m is assumed to be stable and unknown with the normcondition

The high-pass frequency weightings can be described as

(10)

At any frequency ω, the magnitude of can beinterpreted as the percentage of model uncertainty at thatfrequency Therefore, this particular weight implies that themodel error can potentially be about 35% at low frequencyand up to 100% at high frequency

The weighting function W p represents the performanceoutputs, which are related to the components of z Sub-sequently, the performance weighting function is used todefine design specification The inverse of the performanceweight indicates the fraction of the external disturbances to

be rejected at the output, i.e., the amount of steady statetracking due to external input to allow W p(jω) for the side-slip angle are the weights specifying system performance.The upper bound on is the weight for thetolerable maximum angle β; the weight is assumed to beconstant over all frequencies and is set to

(11)The corresponding steady-state control error is less than0.01/0.5=2%

The input of the perturbation is denoted as e, and d is itsoutput The weighting function W nrepresents the impact ofthe different frequency domain in terms of sensor noise n

36 G.-D YIN, N CHEN, J.-X WANG and J.-S CHEN

To account for the inability to sense system outputs without

noise, all measurement signals will always be corrupted by

frequency-dependent noise The noise-varying frequency

should be suppressed In this study, the noise occurs at a

high frequency Therefore, it has to be weighted by

high-pass characteristics The weighting W n(s) is given by

(12)where the upper bound of represents the

maximal expected noise gain

Necessary and sufficient conditions for robust stability

and robust performance can be formulated in terms of the

structured singular value denoted as µ (Packard and Doyle,

1993; Zhou and Doyle, 1996) At this point, the design

setup in Figure 2 should be formalized as a standard design

problem In order to analyze the performance and

robust-ness requirements, the closed-loop system, which is illustrated

in Figure 3, is expressed by using the feedback effect u=Ky

It should be noted that the system P consists of

recogni-zing three pairs of input/output variables The complete

vehicle model for the control system is described by

(13)

(14)

The system P augmented with weighting functions can

be re-partitioned as described in Equation (13) For the

problem, the controller K can be combined with P via a

lower linear fractional transformation (LFT) to yield the

transfer function matrix M:

(16)Moreover, the upper LFT connects w and , which isobtained by combining Equation (14) with Equation (16)and expressed as

(17)where is the upper LFT The robust performance

of the closed-loop system with nominal plant perturbation

∆ m, is a fictitious uncertainty block with input e and output

d This block is applied to incorporate the performanceobjective of the weighted output sensitivity transfer func-tion into the µ-framework

Subsequently, the structured singular value (SSV) (µ) of

a complex matrix M is defined with respect to a blockstructure ∆ as follows:

(20)unless no makes I-M∆ singular, in which case,

Thus, is the ‘size’ of the smallestperturbation ∆, measured by its maximum singular value,which makes det(I-M∆)=0 It has been shown that thecomputation of µ is an NP hard problem However, tightupper and lower bounds for µ may be effectively computedfor the perturbation sets

At present, no direct method is practical for synthesizing

a µ optimal controller; however, the D-K iteration thatcombines µ-analysis with µ-synthesis yields good results.For a constant matrix M and an uncertainty structure ∆, the

ROBUST CONTROL FOR 4WS VEHICLES CONSIDERING A VARYING TIRE-ROAD FRICTION COEFFICIENT 37

upper bound of µ ∆(M) is an optimally scaled maximum

singular value:

(21)where D ∆ is the set of matrices with the property that

D∆=∆D for every ,

Using this upper bound, the optimization is reformulated

as

(22)where D ω is selected from the set of scaling D indepen-

dently of every ω The optimization problem can be solved

in an iterative way using K and D, called D-K iteration It is

performed with a two-parameter minimization in a

sequen-tial way, first minimizing over K with D ω fixed, then

mini-mizing pointwise over D ω with K fixed, etc., although the

joint optimization of D and K is not convex and global

convergence is not guaranteed

3.2 Optimal Control Design

The goal of linear quadratic optimization control is to seek

an optimization controller signal u(t) that minimizes the

following performance index J with reference to the system

described by Equation (8):

(23)Here, the state that weighting coefficient , and the

input weighting coefficient R>0 (A,B) is assumed to be

controllable, and (A,C) is assumed to be observable The

control input u that minimizes Equation (23) is ,

where K op is called an optimal feedback coefficient matrix

given by K op=R −1 B T P Here, P, which is a positive definite

matrix, is the solution of the following Riccati matrix

equation:

(24)Therefore, to regulate the dynamics of the vehicle model,

the controller may attempt to minimize the sideslip angle to

improve the vehicle handling stability performance By trial

and error, Q and R take the following values:

4 NUMERICAL SIMULATION RESULTS

4.1 Comparison of Robust and Optimal Control Simulation

In this section, the dynamic performances of both versions

of the controller will be compared in order to validate the

approximation put forward In what follows, the 4WS

robust controllers are evaluated in the time domain using

µ-Toolbox (Balas et al., 2001) As shown in the µ design

procedure with the D-K iteration, a robust controller is

synthesized and designed for the 4WS vehicle at a velocity

of 30 m/s The results of the iterations are summarized inTable 2

To achieve the desired performance and to deal with theuncertainty for the considered vehicle, a set of frequency-dependent weightings have to be included; thus, the order

of the generalized 4WS control system is increased, ing in a high-order controller It is difficult to implement ahigh-order controller because the controller is normally ill-conditioned By adopting a balanced model reduction via atruncation method (Safonov and Chiang, 1989), the 14-order controller obtained by the above iteration can bereduced to a 3-order controller In reality, the controller has

result-to be discretized because it is implemented by a digitalcomputer By using bilinear transformation, a continuousreduced-order controller K(s) can be discretized as

J = ∫0∞( x T Qx+u T Ru )dt

Q 0 ≥ u= K – op x

Table 2 Summary of D-K iteration

38 G.-D YIN, N CHEN, J.-X WANG and J.-S CHEN

where T is the sampling time interval; that is, T=1/1024 sec

in our simulation

Figure 4 illustrates the simulation results of the transient

response to the steering wheel angle input, which changes

from 0 to 35 deg (gear ratio=15) Thus, the given front

wheel steering angle δ f is 0.04 rad, approximately equivalent

to 2.29 deg

Results obtained from the computer simulation indicate

that the vehicle with the robust controller has superior

performance compared to one with the optimal control

Figure 4(a) illustrates that the steady state values of the

yaw rate of two controllers are almost equal to that of the

desired yaw rate However, the yaw rate response of the

robust controller is more rapid than that of the optimal

controller, and the peak value of the robust controller is

lower than that of the optimal controller This means that

lower sensitivity of the steering system is achieved at high

speed with the robust controller Furthermore, Figure 4(b)

indicates that reduction in the vehicle sideslip angle is an

important safety criterion, which could certainly be further

reduced in the robust controlled vehicle Figure 4(c) shows

the turning of the rear steering angle as control input is

maintained as the front steering angle

Overall, the comparison of robust and optimal controls

for improving vehicle performance shows that the robust

controller can certainly improve vehicle handling

compar-ed to the performance of the optimal controller The

following simulation was performed to further validate the

superiority of the robust controller

4.2 µ Robust Control Simulation

From the evaluation of the performance of vehicles with

the robust controller, the proposed controller performs

ade-quately with different maneuvers and on different road

conditions (dry road µ=0.8, wet road µ=0.4, icy road µ=

0.25) The primary maneuvers are variations of J-turn and

fishhook maneuvers The J-turn maneuver simulates vehicle

behavior under sudden turns onto a sharp ramp In this

maneuver, at the start, the vehicle is moving in a straight

line Because the front wheel steering angle is commonly

proportional to the steering wheel angle controlled by driver,

the front wheel steering angle is taken as the input signal

At time 0 s, the driver turns the steering wheel from 0 to 0.6rad (the front wheel steering angle changing by 0.04 rad)within 0.5 s Figure 5(a) shows the front wheel steeringangle as a function of time The fishhook maneuver attempts

to induce two-wheel lift-off by suddenly making a drasticturn and then turning back even further in the oppositedirection As shown in Figure 5(b), the driver turns thesteering wheel from 0 to approximately 0.12 rad during thefirst 0.5 s After maintaining the steering angle for 0.5 s, thedriver turns the steering wheel in the opposite direction to

Figure 4(c) Rear angle response for robust and optimal

control laws

Figure 5(a) J-turn maneuver

Figure 5(b) Fishhook maneuver

Figure 6 Sideslip angle response under the J-turn ver

maneu-ROBUST CONTROL FOR 4WS VEHICLES CONSIDERING A VARYING TIRE-ROAD FRICTION COEFFICIENT 39

0.6 rad within 2 s and maintains it at that position for the

remainder of the maneuver

Figure 6 through Figure 9 show the time responses of the

vehicle with yaw rate and sideslip angle under J-turn and

Fishhook maneuvers, respectively In Figure 6 and Figure

7, the sideslip angle steady state gain under dry road

condi-tions is approximately zero It can be seen that the sideslip

angle steady state gain is less than zero under wet and icy

road conditions, which shows that the sideslip and running

directions are opposite of each other when the vehicle runs

at low adhesion coefficients Moreover, the same trends are

seen with the running direction under the two different

maneuvers

As shown in Figure 8 and Figure 9, the yaw rate gainsare equal to the desired yaw rate gain at steady state forboth maneuvers It can be seen that the settling process israpid; during the transient response, every yaw rate has littleovershoot under different road conditions, which provesthat the designed robust controller is not sensitive to systemdisturbance

From Figure 6 through Figure 9, we determine that thelateral acceleration has a maximum peak value when µ=0.25, and the peak values do not exceed 0.4 g It is alsoshown that the 4WS vehicle equipped with the µ-synthesiscontroller maintains good lateral acceleration while respond-ing to rather serious system perturbations

5 CONCLUSIONS

In this paper, a robust µ-method has been applied to a wheel steering system design Since a vehicle runs ondifferent road conditions, vehicle system uncertainty alwaysexists and must be dealt with carefully The proposed con-troller performs adequately with different maneuvers (i.e.,J-turn and Fishhook) and on different road conditions (i.e.,icy, wet, and dry) A µ-synthesis robust controller withoptimized weighting functions for the considered structureuncertainties is chosen to resist the disturbances Therefore,the 4WS vehicle with a µ-synthesis robust controller hasgood maneuverability, sufficiently robust stability, and goodperformance robustness against serious disturbance.ACKNOWLEDGEMENT−This work was supported by National Natural Science Foundation of China Fund (No 50975047), Southeast University Technology Foundation (No KJ2009346).

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Figure 7 Sideslip angle response under the Fishhook

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Figure 8 Yaw rate response under the J-turn maneuver

Figure 9 Yaw rate response under the Fishhook maneuver

40 G.-D YIN, N CHEN, J.-X WANG and J.-S CHEN

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