Fast on-line identi?cation of instantaneous mechanical losses in internal combustion engines
F.Cruz-Perago
′n a,?,J.M.Palomar a ,F.A.D?′az a ,F.J.Jime ′nez-Espadafor b a Departamento de Ingenier?
′a Meca ′nica y Minera,Universidad de Jae ′n,Paraje Las Lagunillas s/n,Edi?cio A3,23071Jae ′n,Spain b
Departamento de Ingenier?
′a Energe ′tica,Universidad de Sevilla,Camino de los Descubrimientos s/n,Isla de la Cartuja,41092Sevilla,Spain a r t i c l e i n f o
Article history:
Received 8May 2008Received in revised form 12June 2009
Accepted 19June 2009
Available online 2July 2009Keywords:
Mechanical losses Engine
Multi-cylinder Identi?cation
a b s t r a c t
A fast and easy procedure to evaluate instantaneous mechanical losses in internal combustion engines (appropriate to any multi-cylinder engine)has been developed.First,a performance measurement procedure to obtain losses in one cycle is conducted.Subsequently,they must be proportionally divided into all cylinders,even considering those with no combustion.Finally,a non-linear identi?cation procedure is applied to determine the coef?cients of the P –o method for each cylinder.The methodology has been applied to a single-cylinder compression ignition engine,and to a three-cylinder spark ignition engine.The ?rst engine allows the procedure to be validated by comparing results with those obtained using other established methodology.The second engine makes it possible to analyze the robustness of the method when it is applied to a multi-cylinder engine.
&2009Elsevier Ltd.All rights reserved.
1.Introduction
Dynamic models in internal combustion engines have been applied to design,optimization or diagnosis [1–4],using geometric and dynamic engine characteristics.An important feature associated to the engine dynamics corresponds to mechanical losses.Their instantaneous evaluation at each condition can be applied to several engine tasks.Such examples are identifying mechanical malfunctions in mechanical elements (such as rings or bearings)and their degradation during the engine-operating time,or materials optimization to reduce the effect of mechanical losses.These potential applications can be quite attractive in power plants installations.
The most important component corresponds to friction,mainly associated to the piston assembly [5,6].Loss determination is quite complex,due to the combination of several physical mechanisms combined at different locations into the engine.In general form,there exist four types of methods to determine them [6].First,performance measurement implies that the overall engine performance may evaluate friction.Power indicators are widely used in the engine ?eld [7],throughout the net indicated mean effective pressure (Nimep)and break mean effective pressure (Bmep),to obtain the friction mean effective pressure (Fmep).Other methods use correlation functions [5].On the other hand,motoring methods involve rotating the engine with a motoring dynamometer and recording the required torque to maintain a constant speed.As ?ring does not exist,gas pressure contribution is not considered.Finally,direct friction measurement is a more accurate method to ?nd these losses [8,9],although their major drawbacks are related to device accuracy and cost.
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journal homepage:https://www.doczj.com/doc/0a5691359.html,/locate/jnlabr/ymssp
Mechanical Systems and Signal Processing
0888-3270/$-see front matter &2009Elsevier Ltd.All rights reserved.
doi:10.1016/j.ymssp.2009.06.009
?Corresponding author.Tel.:+31953212367;fax:+31953212870.
E-mail addresses:fcruz@ujaen.es (F.Cruz-Perago
′n),fcojjea@https://www.doczj.com/doc/0a5691359.html,.es (F.J.Jime ′nez-Espadafor).Mechanical Systems and Signal Processing 24(2010)267–280
A particularly cheap methodology consists of measuring the instantaneous angular velocity in the ?ywheel and
predicting the instantaneous mechanical loss torque.In this sense,Rezeka and Henein [10]were pioneers in introducing a model based on six components,weighted by certain proportionally coef?cients a l (l ?1à6).These terms were obtained by a linear regression ?tting.It is a very effective starting point for other later contributions [11–13].Nevertheless,the linear identi?cation presents certain drawbacks depending on the application:?rst,considering a ?exible crankshaft,even for single-cylinder engines,it is not easy to discriminate the instantaneous speed pro?les associated to the different degrees of freedom.Second,for multi-cylinder engines,overlapping between torque pro?les associated to the different cylinders makes it dif?cult to evaluate those coef?cients.Finally,pressure acts as an unknown quantity when the inverse problem is applied;that is,pressure pro?le is determined from angular speed measurements by an indirect method [14,15].In these conditions,a non-linear identi?cation procedure is required.
The goal of the present research is to develop a general,fast,and practical methodology to characterize overall and instantaneous mechanical losses in engine-load systems for use in time (or angle)domain modelling with any assumptions
Nomenclature CIE
compression ignition engine
SIE spark ignition engine
Nimep net indicated mean effective pressure (MPa,bar)
Nimep k net indicated mean effective pressure in cylinder k (MPa,bar)
Bmep break mean effective pressure (MPa,bar)
Bmep m break mean effective pressure for motored engine (MPa,bar)
Fmep friction mean effective pressure (MPa,bar)Fmep m friction mean effective pressure for motored engine (MPa,bar)
Fmep k friction mean effective pressure in cylinder k (MPa,bar)
n mean angular speed (rad/s or rpm)
P k i
gas pressure pro?le into each cylinder k
a
instantaneous angular acceleration along a cycle (s à2)
o
instantaneous angular speed along a cycle (s à1)
y rotating angle (rad,deg)
y o
initial crank angle of the cycle (deg)J mass moments of inertia (kg m 2)K stiffness coef?cient (N m/rad)D damping coef?cient (N m s)
F ?component l of the mechanical losses model a l
proportionally coef?cient associated to each F ?(dimensionless)
m
dynamic viscosity of the lubricant (kg/m s)c linear piston speed (m/s)e ring thickness (m)D bore (m)
R crank radius (m)
L FP length piston skirt (m)
g a thickness of the oil layer in the piston skirt (m)n o number of oil rings
n c number of compression rings N V number of valves
P e ring elastic pressure (Pa)L s valve spring stiffness (N/m)
R 2
coef?cient of determination (dimensionless)C k
objective function in the identi?cation proce-dure for cylinder k
T LM
mean load torque (N m)
T L instantaneous load torque (N m)T iM mean engine indicated torque (N m)
T i instantaneous engine indicated torque (N m)T k a instantaneous reciprocating torque associated to each crank section k (N m)
T fM mean engine mechanical losses (N m)
T k fM mean engine mechanical losses for cylinder k (N m)
T ’fM mean engine mechanical losses for ?ring cylinders (N m)
T f instantaneous engine mechanical losses torque (N m)
T k f instantaneous torque losses for a cylinder k of the engine (N m)
T f 1ring viscous lubrication friction component of T f k (N m).
T f 2ring mixed lubrication friction component of T f k (N m).
T f 3piston skirt friction component of T f k (N m)T f 4valve train friction component of T f k (N m)T f 5auxiliaries and unloaded bearing friction com-ponent of T f k (N m)
T f 6loaded bearing friction component of T f k (N m)T fM,ml mean mechanical torque losses for one cylin-der with motored engine (N m)
T iM engine mean indicated torque (N m)
T ’iM engine mean indicated torque considering ?ring cylinders (N m)
T k i instantaneous indicated torque for cylinder k (N m)
T iM k mean indicated torque for cylinder k (N m)T iM,ml
mean indicated torque for cylinder with motored engine (N m)
Sub-index
j ?1,2,y ,z crankshaft throws F ?ywheel f mechanical losses C coupling D damper L load I inertia i indicated
F.Cruz-Perago
′n et al./Mechanical Systems and Signal Processing 24(2010)267–280268
in the driveline.A validation procedure has been applied to a single-cylinder compression ignition engine(CIE)and a three-cylinder spark ignition engine(SIE).A systematic engine test set with different operating conditions was carried out in each of those engines,obtaining the torque and in-cylinder pressure waveforms,as well as the instantaneous angular speed in a speci?c location of the system driveline.For each operating condition,the procedure starts accounting for performance measurements,comparing them with other correlations.Different methodologies have been evaluated,adopting?nally an iterative procedure in order to assure coef?cient determination in any operating condition and for any kind of multi-cylinder engine.
2.Materials and methods
2.1.Experimental engine test bed set-up and pre-processing
To put into practice the methodology,different analyses were conducted using two different engines(see Table1).The laboratory rig(see Fig.1and characteristics in Table1)included an electric dynamometer attached to the engine for testing.
A pressure transducer was mounted in each cylinder,passing the signal through a charge ampli?er.A magnetic pulse sensor placed in the?ywheel was employed to indicate the angular position with time,to subsequently obtain the instantaneous angular speed and acceleration[1].Measurements were done in the time domain with a multi-channel data acquisition system of1MHz sampling frequency(NICOLET420).
Then,a signal proportional to the angular position?uctuation y F referred to a constant cyclic angular speed was?rst obtained.The instantaneous angular speed o F(t)and acceleration a F(t)at this location were subsequently calculated using Eq.(1),taking into account the mean angular speed n.The number of teeth in the?ywheel establishes the cycle limits,with their corresponding time and angle.Thus,the engine motored method serves to identify the top dead centre(TDC)with a very low error[16].
o FetT?ntd y FetT;a FetT?d o FetT
?
d2y FetT
dt
(1)
Table1
Main characteristics of whole system lab rig for analyzed engines.
Characteristics Deutz dieter lkrs—a single-cylinder CIE Maruti800three-cylinder SIE
Stroke(mm)100.072.0
Bore(mm)85.068.5
Maximum torque(N m)34(at2400rpm)61.7(at3000rpm)
Compression ratio17.5:19:1
Maximum power(kW)9.5(at3000rpm)33(at6000rpm)
Pulse sensor Peper+Fuchs,NJO8-4,5-N,max.frequency10k Hz
Pulse per revolution(No.of?ywheel teeth)14896
Pressure transducer Kistler6061B piezoelectric cooled Kistler6117B piezoelectric in spark plug
ACQUISITION
AND DATA
PROCESSING
Fig.1.Basic scheme of a lab rig.
F.Cruz-Perago′n et al./Mechanical Systems and Signal Processing24(2010)267–280269
2.2.Performance measurements
Global results during steady-state tests (pressure,load,mean speed)must be evaluated in order to establish an
energetic equilibrium in the whole cycle with the proposed approach [7].The Nimep and Bmep can be experimentally obtained,and the Fmep inferred,as Eq.(2)shows.These indicators are directly related to the mean associated torques (with subscript M ),such as load T LM ,whole indicated torque T iM ,and mechanical friction losses torque T fM ,described as follows:
Fmep ?Nimep àBmep T fM ?T iM àT LM
(2)
2.3.Instantaneous dynamic model
With the dynamic and geometric engine characteristics,next to both measured pressure pro?le P k i into each cylinder k and at the load T L along the cycle duration time (or angle),a torque balance equation can be applied to determine the angular speed along a cycle for different degrees of freedom o l [1,2].For a ?exible behaviour,one following set of equations appears for a z -cylinder engine [4]:
a D ?
d o D ?D D eo D ào 1T
D
a 1?d o 1dt ?T 1i àT 1f àT 1
a àK 1ey 1ày 2TàD 1eo 1ào 2TtD D eo D ào 1T
J 1
a 2?d o 2?T z i àT z f àT z
a tK z à1ey z à1ày z TtD z à1eo z à1ào 1TàK z ey z ày F TàD z eo z ào F T
2a 3?d o z dt ?T 3i àT 3f àT 3
a tK 2ey 2ày 3TtD 2eo 2ào 3TàK 3ey 3ày 4TàD 3eo 3ào 4T
J 3......a z ?d o 3dt ?T 3i àT 3f àT 3
a tK 2ey 2ày 3TtD 2eo 2ào 3TàK 3ey 3ày 4TàD 3eo 3ào 4T
J z
a F ?d o F ?K z ey z ày F TtD z eo z ào F TàK C ey F ày L TàD C eo F ào L T
F
a L ?d o L dt ?K C ey F ày L TtD C eo F ào L TàT L
J L
o l et T?n td y l et T
dt
8l ?D ;1;2;...;z ;F ;C ;L T
(3)
where T k i ,T k a ,and Tf
k
correspond to the instantaneous values of indicated torque,variable reciprocating torque,and absolute value of mechanical losses torque in the crank section k associated to each engine cylinder along the cycle.Additionally,mass moments of inertia,stiffness,and damping of different components are denoted by J ,K,and D respectively.Sub-indexes l ?1,2,y ,z refer to crankshaft throws,F corresponds to ?ywheel,C to coupling,D to damper,and L to load.Solving Eq.(3)by the Runge–Kutta method [17]provides the instantaneous angular speed from known quantities,such as indicated pressures,and dynamic and geometric properties.This procedure is called the direct problem.
2.3.1.Instantaneous mechanical losses torque sub-model
Different sub-models can evaluate the torque of mechanical losses T f [5],from the simplest and constant approaches that depend on speed (n )and pressures (throughout mean indicators,as Bmep)to others that analyze them instantaneously [10–13].The most important contribution to the mechanical losses comes from the ring friction.The ring assembly lubrication mode is assumed as hydrodynamics but around the top and bottom dead centre (TDC and BDC),where the oil ?lm breaks down,there nearly exists a dry contact between ring and liner surfaces [18,19].On the other hand,the gas pressure also has a high in?uence in the ring friction effect.Rezeka and Henein [10]model the mechanical losses by means of a very effective procedure.It establishes a sub-model divided into six components F ?(l ?1,y ,6),each one weighted by a certain dimensionless proportionally coef?cient a l ,giving an absolute value of torque losses T k f for a cylinder k of the engine,as Eq.(4)denotes.The ?rst three terms are related to the piston assembly friction,and the rest to the
F.Cruz-Perago
′n et al./Mechanical Systems and Signal Processing 24(2010)267–280270
crankcase assembly friction.
T k f1?a k
1
?m ceP etP k iTe 0:5Den ot0:4n cTR
siney ktb kT
b
k
?a k
1
F k
f1
T k f2?a k
2
p Dn ceP etP k
i
Tee1àsin y k
TR
siney ktb kT
cos b k
?a k
2
F k
f2
8y k2?270 ;450
T k f3?a k
3
m c
a
DL FP R
siney ktb kT
b
k
?a k
3
F k
f3
T k f4?a k
4
N v L s R
siney ktb kT
cos b k
1
???????o
k
p?a k
4
F k
f4
T k f5?a k
5
mo k?a k
5
F k
f5
T k f6?a k
6
p
4
D2r c P k
i
cos y k
1
???????o
k
p?a k6F k f6
T k
f
?S6l?1ea k l F k flT(4) where T f1denotes the ring viscous lubrication friction,according to the mean mode of lubrication between ring and liner, which is hydrodynamic;T f2corresponds to the ring mixed lubrication friction;T f3is the piston skirt friction component, where viscous friction exists;T f4denotes the valve train friction,where both boundary and mixed lubrication modes appear,mainly in the cam/tappet interface,and at the rocker arm/fulcrum contact;T f5represents the auxiliaries and unloaded bearing friction,which includes many elements with rotational movement,such as fuel pump,oil pump,electric generator,and so on;T f6corresponds to the loaded bearing friction,where a great load is transmitted by the crankshaft,due to the high pressures into the cylinder.Both lubrication modes also appear,depending on the oil viscosity,speed,and pressures.The dynamic viscosity m(kg/m s)of the lubricant has been adjusted using a?tting function,depending on pressure and temperature,as done by other researchers[13].The linear piston speed is denoted by c(m/s),the ring thickness is e(m),D(m)corresponds to the bore,R(m)is the crank radius,L FP(m)corresponds to the length skirt,and g a (m)is the thickness of the oil layer in it.Additionally,n o corresponds to the number of oil rings,n c is the number of compression rings,and the number of valves is denoted by N v.Finally,the ring elastic pressure P e(N/m2)and the valve spring stiffness L s(N/m)have been calculated following the procedures given in literature[20].
When proportional coef?cients a l are well known,the direct problem can be easily solved,such as in Eq.(3),and the angular speed pro?le can be obtained(system results).The reality is that they must be identi?ed for each engine-operating condition.In this case,the P–o method takes the instantaneous angular speed o F(y),as well as the pressure pro?le P i(y),in order to evaluate those coef?cients.For p data,each datum corresponds to a certain angle y p,and for a single-cylinder engine,Eq.(5)shows a very fast way to determine those six terms by a linear regression technique,in order to minimize the error estimation[10]:
a?
a1
a2
...
a6
2
66
66
4
3
77
77
5
?eF t FTà1F t T F;F?
F f1;1F f2;1áááF f6;1
F f1;2F f2;2áááF f6;2
...
F f1;p F f2;páááF f6;p
2
66
66
64
3
77
77
75;T F?
T f;1
T f;2
...
T f;p
2
66
66
64
3
77
77
75(5)
3.Preliminary results:justi?cation of the integrated validation into the model
3.1.Initial global results
The procedure starts by carrying out different steady-state tests with varying loads and speeds,including idle conditions.At this point,the obtained data of the Fmep and T fM for both engines correspond to unique solutions in Eq.(2), assuring an energetic equilibrium.
Results for the whole tests set is shown in Figs.2and3,where they have been compared with results form other investigations[5,7,21–28].A good agreement can be observed between approaches and real values in the single-cylinder engine(see Fig.2).Discrepancies presented in Fig.3could be because other research approaches were obtained from the motoring method.
3.2.Initial results applying the P–o method with linear identi?cation
For the single-cylinder engine,the six coef?cients a l are unknown,and they must be identi?ed for each operating condition of the engine,as Eq.(5)indicates.Initially,the instantaneous load torque has been assumed as constant along the cycle,since the electrical device does not generate signi?cant effects over the system response[4].Nevertheless,if an instantaneous load torque is measured,Eq.(3)would provide more accurate results.Fig.4shows an example of the
F.Cruz-Perago′n et al./Mechanical Systems and Signal Processing24(2010)267–280271
evaluated mechanical loss torques associated to the single-cylinder engine in one full load condition (2600rpm and 27N m).It demonstrates the strong loss dependency on the pressure around TDC ?ring.It can be observed that friction terms of the model are the most relevant.
The next step is to evaluate possible ?tting equations for different operating conditions associated to coef?cient values.In this way,Fig.5includes results of these terms for all the tested conditions.Graphics show the best test parameter (angular speed or load)that presents minimal dispersion.The coef?cient of determination R 2(that is,the proportion of variability in a data set that is accounted for by a statistical model)[29]is also shown.
If a good correlation is achieved,relations can be incorporated to the model of Eq.(4)for a direct evaluation of instantaneous angular speed,such as in Eq.(3).Nevertheless,a high dispersion in the results can be observed,with a low value of R 2.This makes us to suspect the existence of high partial correlations between some of those parameters,which prevents an unique combination of values for each condition.This supports the fact that it is not possible to infer a ?tting function for each coef?cient according to the operating conditions and forces us to determine the coef?cients by an identi?cation procedure for every test.
Results presented in Fig.5have been initially obtained from the o P –o 4method.Subsequently,results have been obtained again using the proposed improved method,showing similar results.If a low dispersion is observed in Fig.5,then several accurate ?tting functions would be provided for these terms according to the operating conditions (mean angular speed and load).Then,it would be necessary only to incorporate those functions to the model in Eqs.(3)and (4).Nevertheless,this is not the case.The reality is the existence of a high dispersion of these six coef?cients (see Fig.5).Because of this,these coef?cients must be identi?ed at each new evaluated engine-operating condition,according to the proposed method in the manuscript.
0102030150020002500
3000
20406080100M E A N A
N
G U L A R S P E E D (r p m
)L O A
D T O R
Q U E (N
m )
M e c h a n i c a l L o s s (% o f N I m e p )
1400
1600
1800
2000
2200
240026002800
0102030405060708090
100MEAN ANGULAR SPEED (rpm)
M e c h a n i c a l L o s s (% o f N I m e p )
5
10
15
20
25
30
20
30405060708090100LOAD TORQUE (Nm)
M e c h a n i c a l L o s s (% o f N I m e p )
Fig.2.Performance measurement of mechanical losses for a single-cylinder CIE:(a,b)Percentage of Fmep with respect to Nimep for a set of conditions (?tting functions included by continuous lines)and (c)comparison with other correlations.
F.Cruz-Perago
′n et al./Mechanical Systems and Signal Processing 24(2010)267–280272
3.3.Limits of the linear method
When the whole procedure is applied to a multi-cylinder engine,it is not possible to directly discriminate the individual contribution of each cylinder [6],due to overlapping between the different cylinders pro?les.Then,Eq.(5)is not useful because non-unique solutions can be obtained.A ?rst approach could be distributing the mean torque losses T fM between cylinders.On the other hand,for ?exible crankshaft and driveline considerations (even for single-cylinder engines),there are several applications where an iterating procedure must be established,such as the indirect determination of in-cylinder pressure pro?le from the angular speed measurement [2,14,15].Thus,the solution can be obtained by solving Eqs.(3)and (4)employing an iterative procedure that considers a proportional distribution of mean losses between cylinders.
Nevertheless,there exists a possible drawback:if the cylinder k presents a behaviour without combustion,its individual Nimep k is negative,and thus it is impossible to apply the loss distribution previously mentioned.For this reason,the engine motoring method is applied,measuring a Bmep m (n )(Bmep for motored engine at a certain mean angular speed n )and the corresponding Nimep m (n )(Nimep for motored engine)to obtain the contribution of Fmep m (n )(Fmep for motored engine at speed n ).The individual contribution of one motored cylinder will be the z part of that value (for a three-cylinder engine,z is equal to three).Fig.6shows the experimental results of the motored method applied to the three-cylinder SIE.
2000
2500
3000350040004500500055006000
15
202530354045505560
65MEAN ANGULAR SPEED (rpm)
M e c h a n i c a l L o s s (% o f N I m e p )
2000
2500
3000350040004500500055006000
010
20
30
40
50
60
70
MEAN ANGULAR SPEED (rpm)
M e c h a n i c a l L o s s (% o f N I m e p
)
10
2030405060
1020304050607080LOAD TORQUE (Nm)
M e c h a n i c a l L o s s e s (% o f N I m e p
)
Fig.3.Performance measurement of mechanical losses for a three-cylinder SIE:(a,b)Percentage of Fmep with respect to Nimep for a set of conditions (?tting functions included by continuous lines)and (c)comparison with other correlations.
F.Cruz-Perago
′n et al./Mechanical Systems and Signal Processing 24(2010)267–280273
3.4.Proposed iterative procedure
The proposed non-linear method can be observed in Fig.7.After the instantaneous speed and pressures pro?les,the load torque is measured.
The procedure starts by establishing a constant angular speed along the cycle,for all the degrees of freedom y l of the engine.The sharing procedure (see Fig.7b)evaluates the associated indicated torques (T i (y k )k ,T k iM ,and T iM )from pressures pro?les,obtaining the T fM value.If motored cylinders exist,their mean individual contributions T iM,m l and T fM,ml must be
subtracted from T iM and T fM in order to obtain the ?nal T 0iM and T 0
fM for only ?ring cylinders.This last value is then divided into different individual mean loss torques T k fM associated to the ?ring cylinder k ,as Eq.(6)shows (where y o in rad is the
?100
0100200300400500
1234567P r e s s u r e (M P a )
?100
100
200
300
400
500
263
264265266267268269270I n s t a n t a n e o u s a n g u l a r s p e e d (r a d /s )
Flywheel angle (degrees)
?100
100
200
300
400
500
10
20304050607080Flywheel angle (degrees)
M e c h a n i c a l l o s s t o r q u e (N m
)
Fig.4.Instantaneous mechanical losses in a single-cylinder CIE at 2600rpm and 27N m,as a result of applying the linear P –o method:(a)input
(pressure)and response (angular speed)of the engine system and (b)mechanical loss torque along the cycle.
F.Cruz-Perago
′n et al./Mechanical Systems and Signal Processing 24(2010)267–280274
1600
1800
2000
2200
2400
2600
0.15
0.20.25
0.30.350.40.450.50.55MEAN ANGULAR SPEED (rpm)
0510152025
0.15
0.20.250.30.350.40.450.50.55
LOAD TORQUE (Nm)
1600
1800
2000220024002600
0.25
0.30.350.40.450.50.55
MEAN ANGULAR SPEED (rpm)1600
1800
2000220024002600
00.020.04
0.060.080.10.12
MEAN ANGULAR SPEED (rpm)
5
10
15
20
25
0.25
0.3
0.350.4
0.450.50.55
LOAD TORQUE (Nm)
5
10
15
20
25
00.002
0.0040.0060.0080.010.0120.0140.0160.0180.02LOAD TORQUE (Nm)
Fig.5.Coef?cients of the mechanical losses after the whole set test for the single-cylinder CIE:(a)ring viscous lubrication friction (R 2?0.3245);(b)ring mixed lubrication friction (R 2?0.4355);(c)piston skirt friction (R 2?0.1959);(d)valve train friction (R 2?0.0252);(e)auxiliaries and unloaded bearing friction (R 2?0.0079)and (f)loaded bearing friction (R 2?0.2914).
F.Cruz-Perago
′n et al./Mechanical Systems and Signal Processing 24(2010)267–280275
initial crank angle of the cycle).
T iM ?X
k
T k iM where
T k iM
?1
4p
Z
y 0t4p y 0
T k i ey k Td y k
T 0iM ?T iM àN ml T iM ;ml à
á;T 0fM ?T fM àN ml T iM ;ml
à
áT k fM
?T 0fm T k iM =T 0
iM
efiring cylinder T(6)
The next step consists of a non-linear parameter identi?cation procedure [30],where an objective function c k must be
de?ned for 4p rad of engine cycle duration (Four stroke engine),as seen in Eq.(7).At this point,the six loss coef?cients per cylinder in the vector a k can be obtained:
c k eˉa k T?X l
Z y 0t4p y 0
T k
fl ey k Td y k !,4p ()àT k fM
"#2
x (7)
Eq.(3)is then solved in order to determine the modeled instantaneous angular speed for each degree of freedom.The
previously explained procedure is repeated until the speed pro?le converges to an invariant shape in the measurement point,in this case,the ?ywheel (see Fig.7a).4.Final result validation of the iterative procedure 4.1.Single-cylinder approach
In order to guarantee the effectiveness of the proposed method,it has been applied ?rst to this engine for idle conditions.In this case,the mean loss torque is equal to the mean value of the indicated torque.The instantaneous loss torque (absolute value)can be easily obtained by subtracting the instantaneous inertia torque from the instantaneous indicated https://www.doczj.com/doc/0a5691359.html,paring the experimental method with the new procedure,instantaneous torque error is very low (relative errors below 0.1%),as illustrated in Fig.8.
As a result of applying the procedure to all the loaded tested conditions,results of coef?cients a l are quite similar to the linear P –o method presented in Fig.5.As previously mentioned,no reliable correlations can be achieved because of high dispersion in the data.Thus,it demonstrates once again that coef?cients must be identi?ed for each new operating condition evaluated during the engine performance.4.2.Three-cylinder SIE
The application of the proposed method in the SIE provides results such as those presented in Fig.9,for a condition tested near the maximum power,with 37.5%losses with respect to Nimep (see Fig.3c).
100020003000400050006000
2
4681012MEAN ANGULAR SPEED (rpm)
M e c h a n i c a l L o s s e s (k W )
Fig.6.Mechanical losses from the motoring method applied to the three-cylinder SIE.
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F.Cruz-Perago′n et al./Mechanical Systems and Signal Processing24(2010)267–280277
Fig.7.Proposed algorithm to evaluate mechanical losses:(a)main procedure and(b)sharing procedure.
All the test sets(see Fig.3)have been evaluated,showing very low values in the objective function,that is,both measured and modelled angular speed pro?les are very close,with tendencies similar to those in Fig.9.As an example of diagnosis application of this method,it can be observed that cylinder1shows the worst mechanical behaviour because of
the deterioration of the rings;its pressure pro?le reaches a maximum value lower than those of others,with less friction losses associated (around the TDC ?ring).On the other hand,cylinder 2has the associated elements in very good conditions (higher pressures and friction losses).
Then,a new attempt to obtain reliable correlations has been carried out by means of regression curves to the
coef?cients a k l for all the cylinders and operating conditions.Table 2shows the resulting R 2
coef?cients.As for the single-cylinder engine,a high dispersion in the coef?cients can also be observed,and thus no reliable correlated function exists.This demonstrates again the necessity of identifying those coef?cients every time at each new evaluated operative condition.Because of the low computation time required for the proposed method,it can be applied to a device incorporated to the engine,making it possible to evaluate these losses on line.
?100
0100200300400500
12345P r e s s u r e (M P a )
?1000
100
200
300400500
160
161162163164165I n s t a n t a n e o u s a n g u l a r s p e e d (r a d /s )
Flywheel angle (degrees)
?100
100200300400
500
?15
?10
?5
5x 10?3
Flywheel angle (degrees)
T o r q u e l o s s e s
e r r o r (N m )
Fig.8.Results for an idle condition (1570rpm)in the single-cylinder CIE:(a)input (pressure)and model output (instantaneous angular speed)and (b)torque balance error pro?le between the proposed method and P –o method.
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5.Conclusions
Conventional methods applied to the evaluated engines show tendencies in the same way as in the literature reviewed,validating the presented experimental procedure.Nevertheless,for non-linear identi?cation procedures in combustion
0100200300400500600700
2468
P r e s s u r e (M P a )
0100
200300400500600700
562
564566568570I n s t a n t a n e o u s a n g u l a r
s p e e d (r a d /s )
Flywheel angle (degrees)
100
200300400500600700
510152025303540
45Flywheel angle (degrees)
M e c h a n i c a l l o s s t o r q u e (N m )
Fig.9.Results for three-cylinder SIE at 5400rpm and 49N m (27.7kW):(a)input (pressures)and system response (angular speed at ?ywheel)and (b)instantaneous mechanical losses.
Table 2
R 2coef?cients of regression curves for losses terms a l .Coef?cient
R 2approach depending on maximum pressure in cylinder R 2approach depending on mean angular speed a 10.41090.0796a 20.35890.0996a 30.50.1406a 40.20130.3768a 50.50180.1427a 6
0.1606
0.1926
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engines (such as direct problems considering driveline without assumptions or diagnosis via indirect methods)the original
P –o method is not valid to establish the mechanical loss coef?cients.
For this reason,a practical,fast,and reliable method to estimate losses and the associated coef?cients has been proposed,for any kind of engine and any number of cylinders.The iterative procedure establishes an energetic equilibrium in the engine system,which makes it possible to correctly solve the torque balance equation system.
For all the evaluated situations using both methods (original and proposed),the high level of dispersion in the coef?cients does not make it possible to achieve an accurate relation of mechanical losses with the engine operative conditions (load and mean speed).Thus,generation of loss coef?cients per each running steady-state condition is required.In this case,an on-line evaluation incorporating a speci?c equipment and software is proposed,to obtain accurate results fast.One major application of the method could be power plant diagnosis,in which engine conditions are maintained constant over time (although load changes depending on the electric network load,their sampling rate is much higher than that considered during one-cycle analysis).
Finally,if an instantaneous torque meter device is installed between the dynamometer and the engine,results can be more accurate,and thus transient engine conditions (between two engine steady-state conditions)can be evaluated with a high level of accuracy.References
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