International journal of automotive technology, tập 12, số 2, 2011

International Journal of Automotive Technology, Vol 12, No 2, pp 149−157 (2011) DOI 10.1007/s12239−011−0019−7 Copyright © 2011 KSAE 1229−9138/2011/057−01 COMMON RAIL INJECTION SYSTEM ITERATIVE LEARNING CONTROL BASED PARAMETER CALIBRATION FOR ACCURATE FUEL INJECTION QUANTITY CONTROL F YAN and J WANG * Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio 43210, USA (Received 17 May 2010; Revised July 2010) ABSTRACT−This paper presents an accurate engine fuel injection quantity control technique for high pressure common rail (HPCR) injection systems by an iterative learning control (ILC)-based, on-line calibration method Accurate fuel injection quantity control is of importance in improving engine combustion efficiency and reducing engine-out emissions Current Diesel engine fuel injection quantity control algorithms are either based on pre-calibrated tables or injector models, which may not adequately handle the effects of disturbances from fuel pressure oscillation in HPCR, rail pressure sensor reading inaccuracy, and the injector aging on injection quantity control In this paper, by using an exhaust oxygen fraction dynamic model, an on-line parameter calibration method for accurate fuel injection quantity control was developed based on an enhanced iterative learning control (EILC) technique in conjunction with HPCR injection system A high-fidelity, GT-Power engine model, with parametric uncertainties and measurement disturbances, was utilized to validate such a methodology Through simulations at different engine operating conditions, the effectiveness of the proposed method in rejecting the effects of uncertainties and disturbance on fuel injection quantity control was demonstrated KEY WORDS: Common rail injection system, Iterative learning control, Fuel injection quantity control, Diesel engines NOMENCLATURE k α α ϕ ηv λ K int K exh s ρ ∆P fuel θ(t) A c d ET F cyl d,cyl i F e F F k c ec m m m c e : index of engine cycle : piston surface area effective parameter : piston surface area effective parameter : engine crank angle : engine volumetric efficiency : Stoichiometric oxygen fuel mass ratio for complete combustion : fuel density : pressure difference between common rail and incylinder pressures : uncertainty parameter to be calculated : area of the total outflow section : fuel flow discharge coefficient : in-cylinder charge density during valve overlapping : injection duration : oxygen fractions of the gases in intake manifold at IVC : oxygen fractions of the gases in exhaust manifold at IVC : oxygen fractions of the gases in cylinder at IVC : oxygen fractions of the gases out of cylinder : index of engine cycle ic m ec m ce m ∆m f restV ∆m restB N p p R T T V V W i e i e i e c : mass of gas in the cylinder at IVC : mass of gas in exhaust manifold at IVC : mass of gas from intake manifold to cylinder per cycle : mass of gas from exhaust manifold to cylinder per cycle : mass of gas from cylinder to exhaust manifold per cycle : fuel mass quantity per cylinder per cycle : mass from exhaust manifold to cylinder caused by the volume change : mass from exhaust manifold to cylinder caused by the pressure difference : engine speed (rpm) : pressure in intake manifold : pressure in exhaust manifold : ideal gas constant : temperature in intake manifold : temperature in exhaust manifold : volume of intake manifold : volume of exhaust manifold : mass flow rate through cylinder INTRODUCTION With the consistently-increasing demands on vehicle fuel *Corresponding author e-mail: wang.1381@osu.edu 149 150 F YAN and J WANG economy and pollutions worldwide, precise engine control is becoming imperative for improving engine combustion fuel efficiency and reducing engine-out emissions (Benajes et al., 2010; Wang, 2008b; Seykens et al., 2005; Tsutsumi, et al, 2009; Lee and Huh, 2010) The engine combustion process is mainly determined by the in-cylinder conditions (ICCs) and fuel injection strategies To achieve the desired combustion on a cycle-by-cycle basis, seamless combinations of advanced air-path control techniques and precise fuel injection control are critical (Wang and Chadwell, 2008; Wang 2008a; Wang 2008b) As the control through fuel-path is much faster than that of the air-path and the combustion process is very sensitive to the fuel injection, accurate fueling control is thus necessary (Benajes et al., 2010) High pressure common rail (HPCR) fuel injection systems, typically employed in light- and medium-duty Diesel engines, provide an effective way in fuel injection quantity and injection timing control primarily due to their high rail pressure (Huhtala and Vilenius, 2001; Stumpp and Ricco, 1996) Through HPCR systems, typically, fuel injection per cycle per cylinder can be controlled based on a pre-calibrated table or injector models However, HPCR pressure oscillation, HPCR pressure sensor reading inaccuracy, and the injector aging can all cause fuel injection quantity error (Alzahabi and Schulz, 2008; Baumann and Kiencke, 2006) It is therefore desirable to have some on-line adaptive correction methods for reducing such effects To a large extent, the imprecise of the fuel injection are caused by periodical disturbance (the oscillation effect of HPCR pressure) and quasi-constant inaccuracy (HPCR pressure sensor reading inaccuracy and the injector aging) This type of disturbance can be effectively rejected by iterative learning control (ILC) algorithms (Chien, 1998; Chien, et al, 2007) By combining the information of previous control signal and the feedback error, an updated control law can be generated to reduce the effect of system variations/ uncertainties without exactly knowing the system dynamics (Norrlof and Gunnarsson, 2001; Norrlof, 2004) In this paper, an ILC-based HPCR injection system on-line parameter calibration algorithm is presented To generate the error used in the ILC algorithm, an oxygen mass fraction model, based on the engine breathing process, is introduced An ILC on-line calibration control law can then be devised to reduce the effect of the periodical HPCR pressure disturbance and slowly varying uncertainties (pressure sensor reading inaccuracy and fuel injector parameter uncertainties) The algorithm can help to achieve accurate injection quantity control without additional hardware Such an algorithm can also be applied for injection system on-board fault diagnosis purposes The arrangement of the rest of this paper is as follows In section II, the oxygen mass fraction model is presented Section III describes a fuel injection on-line parameter calibration algorithm based on the enhanced ILC (EILC) method and the convergence criterion In section IV, the validation of the on-line calibration method is shown by applying it to a high-fidelity GT-Power engine model, which is an industrial standard simulation package and is able to simulate the one-dimensional wave dynamics and heat transfer throughout the engine systems Conclusive remarks are provided in the end OXYGEN MASS FRACTION MODEL The aim of this model is to generate a nominal exhaust oxygen mass fraction with respect to the desired fuel injection By comparison between the nominal value and the one measured from a lambda sensor installed in the exhaust manifold of a real engine, a base error can be derived for disturbance rejection purpose in ILC Here a single-input-single-output (SISO) dynamic model is proposed through the engine breathing and gas exchanging process (Yan and Wang, 2010) Respectively, the input is the fuel injection quantity and the output is the exhaust oxygen mass fraction For lean-burn engines such as Diesel engines, the oxygen mass fraction in exhaust gas is considerable The combustion is assumed complete, i.e the fuel injected into the cylinder is completely burned Only the in-cylinder oxygen mass fraction at the crank angle of intake valve closing (IVC), which is before the occurrence of combustion for each cylinder/cycle, is considered as the other state The dynamic models were developed based on the mass conservation and are described by the following difference equations as: mc( k + )Fc( k + 1)= (mc ( k ) + mf( k ))Feo( k ) + m ic ( k ) F i ( k ) + m ec ( k ) F e ( k + ) – m ce ( k ) F eo ( k ) , (1) me(k + 1)Fe( k + 1) = mce(k)(Feo(k) – Fe(k)) + me(k)Fe(k) , (2) where k is the index of engine cycle, mc(k) and are the mass of charge in the cylinder and in the exhaust manifold at the kth IVC, respectively mic(k), mec(k), and mce(k) are the mass of charge from intake manifold to cylinder, from exhaust manifold to cylinder, from cylinder to exhaust during the period right after the kth IVC Fi(k), Fe(k), Fc(k) and Feo(k) are the oxygen fractions of the gases in intake manifold, in exhaust manifold, in cylinder, and out of cylinder after combustion at or right after the kth IVC, respectively mf(k) is the mass of injected fuel after the kth IVC Figure illustrates the evolving process The oxygen fraction of the gas after combustion can be derived by: ( mc( k ) + mf( k ) )Feo( k ) = mc ( k )Fc ( k ) – mf( k )λs, (3) i.e f ( k )λ S , Feo( k ) = -m c ( k -) F c-( -k ) -– m mc ( k ) + mf ( k ) (4) where λs is the stoichiometric oxygen fuel mass ratio for complete combustion COMMON RAIL INJECTION SYSTEM ITERATIVE LEARNING CONTROL BASED PARAMETER C mce λs m m m 151 (16) = – - ⋅ e c+ f Here, we denote mce, mec, mic, mc, me, mf as mce(k), mec(k), mic(k), mc(k) (or mc (k+1)), me(k) (or me (k+1)), mf(k) respectively for simplicity As illustrated above, the oxygen fraction can be described as a discrete linear parameter-varying system with C = ( C C C C C C C )T (17) The system states are: Figure Engine breathing and gas exchanging process from the kth IVC to (k+1)th IVC It is assumed that the mass of inlet gas equals to that of outlet gas for both the cylinder and the exhaust manifold in each cycle (Wang, 2008b; Ammann et al., 2003), i.e., mce( k ) = mic( k) + mec ( k ) + mf( k) (5) So, mc(k + ) = mc(k) + mf(k) + mic(k) + mec(k) – mce( k) = mc(k) , (6) and also me ( k + ) = me ( k ) , (7) x = [ Fc Fe ]T System input is: u = mf F c ( k + ) = C Fc ( k ) + C F e ( k ) + C Fi ( k ) + C m f ( k ) , (8) Fe ( k + ) = C Fc ( k ) + C Fe ( k ) + C mf ( k ) , (9) where, C mce mce mec , m m m m m = – - + - ⋅ c+ f e c+ f (10) mce ⎞ ec ⎛ - ⋅ – , C =m mc ⎝ mem⎠ (11) ic , C =m mc (12) C C C λs mce m m m λs mec mce λs , m m m m m = – - – - ⋅ - ⋅ c( c + f) c c e c+ f (13) (19) System output is: y = Fe (20) With the assumption that the density of in-cylinder charge at IVC is considered the same as the one in intake manifold (Killingsworth et al., 2006; Koehler and Bargende, 2004), and can be approximated, by the ideal gas law, as below: , mc = p i-V IVC RTi (21) me = p -V RT (22) Thus, the resultant dynamic models are given as follows: (18) 6 By the speed-density equation, the mass flow rate into the engine cylinder, Wic, can be calculated as: η v p i V IVC Wic = N 120 RT i (23) Then, the mass into cylinder per cycle, mic, can be generated as: mic = η v p -i-V IVC RTi (24) Here, pi, pe and Ti, Te are pressures and temperatures of intake manifold and exhaust manifold, respectively ηv is the engine volumetric efficiency R is the ideal gas constant In what follows, the mass flow from exhaust manifold to cylinder during intake and exhaust valve overlapping period are derived by using the model developed in (Koehler and Bargende, 2004): mce mc , m m m (14) mec = ( ∆mrestV + ∆mrestB ) mce , me (15) where ∆mrestV and ∆mrestB are the mass flow caused by the = - ⋅ e c+ f = – - (25) 152 F YAN and J WANG volume change and pressure difference, respectively The two terms can be written as: HPCR FUEL INJECTION PARAMETER ON-LINE CALIBRATION ∆mrestV = di ⋅ K1 , (26) dt K , ∆mrestB = SGN( pe – pi )AK 2diABS( pe – pi) ⋅ -dϕ (27) 3.1 Injector Model The predicted exhaust manifold oxygen fraction can be generated by the oxygen fraction model presented in section based on the desired fuel injection amount and the signals measured on the engine Thus, the difference between the predicted exhaust manifold oxygen fraction and the one measured from the engine can be chosen as the base error in the injector model parameter on-line calibration algorithm The HPCR injection mass quantity can be modeled by (Lino et al., 2005, 2007): where EVC dv αKexh2 dϕ , K1 = ∫IVO -⋅ dϕ αKexh2+ αKint2 (28) αK_exh ⋅ αK_int EVC - dϕ , K2 = ∫IVO αK_exh + αK_int (29) mce = mic + mec (30) 2 Here, di is the in-cylinder charge density during valve overlapping, and can be approximated by the intake manifold charge density calculated through ideal gas law ABS(pe-pi) denotes the absolute value of pressure difference between intake manifold and exhaust manifold AK is the piston surface area αKint and αKexh are piston surface area effective parameters ϕ is the crank angle The intake and exhaust manifold signals (including pressures, temperatures, and oxygen fractions) can be obtained by sensors and/or air-path observers (Wang, 2008a; Wang, 2008b) for calculating the predicted exhaust manifold oxygen fraction based on the desired (commanded) fuel injection quantity Such intake and exhaust manifold sensors are available on some new engine platforms As the effectiveness of the method proposed in this paper relies on the accuracy of the exhaust oxygen mass fraction model, the parameters in the model need to be carefully calibrated Figure illustrates the comparison of the foregoing discrete dynamic model with a high-fidelity, one-dimensional computational, GT-Power engine model As it indicates, the dynamic model can well predict the exhaust oxygen fractions in both the steadystate and transient conditions with varying oxygen fractions and engine speed ∆p- , mf = ρfuel ⋅ sgn( ∆P) ⋅ cd cyl ⋅ Acyl ⋅ ET ⋅ -ρfuel , (31) where Acyl is the area of the total outflow section, cd,dyl is the fuel flow discharge coefficient, ET is the injection duration commanded to the injector, and ∆P is the pressure difference between common rail and in-cylinder pressures ρfuel is the fuel density The injection model (31) can be used to generate the injection duration with the information of the desired fuel quantity and the pressure difference between HPCR and cylinder pressures However, the pressure difference reading may not be accurate due to the sensor bias, and the injector parameters may change with injector aging and environmental conditions These uncertainties/variations will affect the actual fuel injection quantity To ensure the injection quantity control accuracy, an uncertainty parameter θ(k) is introduced in the injector model and it will be calibrated on-line Thus, the injection model (31) can be modified as: ∆P- , mf = θ( k ) ⋅ ρfusl ⋅ sgn n( ∆P) ⋅ cd cyl ⋅ Acyl ⋅ ET ⋅ ρfusl , (32) where, the nominal value of θ(k) is 1.0 3.2 ILC and EILC Here, ILC and Enhanced ILC algorithms are briefly reviewed The ILC algorithm in (Chien, 1998; Chien et al., 2007) can be written as: ui ( n ) = ubi ( n ) + ufi( n) (33) where ufi(n) is the feedforward control in the form of: ufi ( n ) = Σij –=mi – 1Gjuj( n) + Σij –=mi – 1Lj( n)ej( n + 1) , (34) and ubi ( n) is the feedback controller in the form of: Figure Comparison of the exhaust manifold oxygen fraction model with a high-fidelity GT-Power engine model zi ( n + ) = p ( zi ( n ) ) + q ( zi ( n ) ) ei ( n ) , (35) ubi ( n) = r ( zi ( n ) ) + s ( zi( n) ) ei( n) (36) COMMON RAIL INJECTION SYSTEM ITERATIVE LEARNING CONTROL BASED PARAMETER Here, e (n) denotes the tracking error between the desired and system outputs at time n in iteration i G and L denote the forgetting factor and learning gain operator In the basic ILC, G is chosen as e (n) is the current tracking error and p, q, r and s are the functions for bounded conditions Essentially, the ILC includes the information from previous control signal (feed-forward) and the feedback signal So, by choosing m = i−1, G = 1, r(·) = 0, and s(·) = K , in (34)~(36), one of the basic controller, Dtype ILC (Chien et al., 2007), can be derived as: i j j j i j p u ( n ) = u ( n ) + Le ( n + ) + k e ( n ) , i–1 i i –1 p (37) i In ILC, the control law includes the control signal and the error signal in the last iteration However, the convergence of the ILC in (37) requires identical initial condition, which may not be satisfied in the highly nonlinear engine systems (Chien, 1998) Thus, in this paper, the enhanced ILC (Chien et al., 2007) is employed to release the identical initial condition requirement The control law is given as: u ( n ) = u ( n ) + Le ( n + 1) + K[ e ( n ) – e ( n) ] i–1 i i–1 (38) i–1 i Here K is the compensation gain and K[e (n)−e (n)] term compensates the state difference between two iterations at time n Thus there is no requirement for the same initial conditions for all iterations as that in normal ILC (Chien, 1998) i i-1 3.3 EILC-based On-line Fuel Injection Parameter Calibration In the EILC algorithm (38), the was chosen by the difference of the oxygen fraction ∆F , and the ∆θ = θ(k)−1 as the u in (38) Each of the iterations contains 10 engine cycles To keep consistent with the EILC algorithm, we use ∆F (z), ∆θ (z), to represent ∆F (z) in i th iteration Thus, the EILC algorithm in (38) can be written as e e,i i e ∆θi( n) = ∆θi – 1( n ) + L ∆Fe i – 1( n + ) + K [∆Fe i( n) – ∆Fe i – 1( n) ] , , , (39) As can be seen from the simulation scheme in Figure 3, the input signal is the desired fuel injection quantity The nominal values of the injector model parameters can be 153 obtained by injector calibration and measurement from the rail pressure sensor By applying the EILC, a compensating value ∆θ can be generated, and it can be used in the injector model to generate the adjusted injection duration signals for delivering accurate injection quantity to the cylinders 3.4 Convergence Criterion and Parameters Selection In EILC, the parameters, L and K used in (39) can be chosen by the following convergence criterion, which is similar to the one for linear time-invariant (LTI) systems as proposed in (Chien et al., 2007) Considering the model generated in Section 3, the actual dynamics of oxygen fraction can be written as: Fc(k + 1) = C1Fc(k) + C2Fe(k) + C3Fi(k) + C4(mf( k) + d(k)) , (40) Fe ( k + ) = C Fc ( k ) + C Fe ( k ) + C7 ( m f ( k ) + d ( k ) ) , (41) where m (k) is the desired injection fuel amount, d(k) is the disturbance caused by fuel pressure oscillation and etc The dynamics of oxygen fraction generated by the comparison model is: Fˆ (k + 1) = C Fˆ (k) + C Fˆ (k) + C Fˆ (k) + C (m ( k) + ∆m ( k) ),(42) f c c e i f f Fˆ e(k + 1) = C5Fˆ c(k) + C6Fˆ e(k) + C7( mf(k) + ∆mf(k)) , (43) where m (k) is the adjusted fuel amount and can be written as: f ∆mf ( k ) =∆θ ( k ) ⋅ ρfuel ⋅ sgn ( ∆P ) ⋅ cd cyl ⋅ Acyl ⋅ ET ∆P- = γ ∆θ ( k ) ⋅ ρfuel , (44) Denote ∆F (k) = F (k) – Fˆ (k ) and ∆F (k) = F (k) – Fˆ (k) Then one can get: e e e c c c ∆Fc( k + ) = C1∆Fc( k ) + C2∆Fe( k ) + C4( d( k ) – ∆mf( k ) ) , (45) ∆Fe( k + ) = C5∆Fc( k ) + C6∆Fe( k ) + C7( d( k ) – ∆mf( k ) ) (46) Here, we denote Figure Block diagram of the fuel injection on-line parameter calibration system 154 F YAN and J WANG φ ( C ) = ⎛⎝ By choosing and satisfying Equation (54), as indicated in ∆F , ( ω ) < , i.e., ∆F will converge The convergence (53), - C1 C2⎞ , C5 C6⎠ e i F , – 1( ω ) ∆ e e i Then a z-form transfer function of the system can be derived as: of ∆F will lead to the correction of fuel injection amount Here we not provide the proof of the detectability It can be easily realized that, in real engineering practice, with the other conditions being the same, the injection fuel amount and exhaust oxygen mass fraction are one-to-one correspondence, i.e., when error of the latter converges to zero, the former can be corrected as well G(C, z ) = H( zI – φ (C))–1T(C) SIMULATION STUDIES T ( C ) = C4 , C7 H = [01] e (47) i.e (48) Fe (z ) = ( d( z) – γ ∆θ (z ) )G( C, z) = d( z )G( C, z ) – γ ∆θ (z )G( C, z ) By taking z-transform of (39), we can get: z = ∆θ – 1(z) + zL∆F ∆θ i ( ) i e, i – ( z) + K[∆F (z) – ∆F e, i e, i – ( z)] (49) As the transfer function G(C,z) depends on the parameter vector C, to distinguish the difference between G in i th and (i−1) th iterations in one expression, we use G and G − , respectively Inserting (49) to (48) and denoting ∆F as ∆F in the th iteration lead to: i i e e,i ∆F ( z ) = d ( z ) G ( z ) – γ ∆θ ( z ) G ( z ) = d ( z ) G ( z ) – γ G ( z ) ∆θ ( z ) (50) –γLzG (z)∆F (γK[G (z)∆F (z) – G (z)∆F (z) ]) e, i i i e, i – i i i i e, i i–1 i e, i – i By rearrangement of (50), one can get + γKG (z))∆F (z) = d(z)G (z) – γG (z)∆θ (z) –(γLzG (z) – γKG (Z))∆F (z) ( i e, i i i i–1 i (51) e, i – i Consequently, by considering Equation(48), one can have: –γG (z)∆θ – 1(z) + d(z)G (z-) γ LzG (z) – γKG (z)F (z)- F – 1(z) = ∆F – 1(z)(1 + γKG (z)) – (1 + γKG (z)) –γG (z)∆θ – 1(z) + dzG (z) = -–(γ G – 1(z)∆θ – 1(z) + d(z)G – 1(z))(1 + γKG (z)-) – γ LzG ( z ) – γ KG ( z ) G (z) - = G -– ( + γ KG ( z ) ) – ( z ) ( + γ KG ( z ) ) γ LzG ( z ) – γ KG ( z ) (52) ( + γ KG ( z ) ) Evaluating (49) on the unit cycle z = e ω leads to: ∆F ( ω ) = ∆F – ( ω ) ω G (ω ) γ Le G ( ω ) – γ KG ( ω ) -, (53) – G – 1(ω )(1 + γKG (ω )) ( + γ KG ( ω ) ) ∆ ∆ e, i i e, i i i e, i i i i i d,cyr fuel -8 cyl i i i i i i i i 4.2 Case 1-Fuel Injection Parameter Uncertainty and Disturbance Rejection 4.2.1 Simulation conditions To evaluate the parameter calibration algorithm, a “real” engine, including injection system, was constructed with the typical parameters: HPCR high-frequency pressure oscillation as shown in Figure (one periodical disturbance was set times of fuel injection frequency to simulate the circumstance of a 8-cylinder engine, i.e 80 Hz with a magnitude of 15 MPa for 1200 rpm engine speed; another low frequency disturbance was added with Hz frequency and 15 MPa magnitude); the fuel flow discharge coefficient c = 0.75; the fuel density ρ = 850 kg/m ; the area of injection section A = 2×10 m Whereas, the parameters of injector model with the uncertainty and variations were i i i i 4.1 Simulation Setup In this section, a high-fidelity, 1-D computational, GTPower engine model is utilized to evaluate the on-line injection quantity correction algorithm GT-Power is an industrial standard computational simulation package and is able to simulate the one-dimensional wave dynamics and heat transfer throughout the engine systems In the GTPower combustion model, the fuel injection quantity was assumed to be precise i i i i j e, i e, i j i i i i i i Thus, the convergence criterion is derived as: ω G (ω ) γ Le G ( ω ) – γ KG ( ω ) -– < 1, ∀ω G (ω )(1 + γKG (ω )) ( + γ KG ( ω ) ) j i i–1 i i i i (54) Figure HPCR pressure variation COMMON RAIL INJECTION SYSTEM ITERATIVE LEARNING CONTROL BASED PARAMETER Figure Error convergence assumed as: HPCR pressure sensor reading p = 150 MPa; the fuel flow charge coefficient cd,cyi = 0.71; the fuel density ρfuel = 870 kg/m ; the area of injection section Acyl = 1.9×10 m Thus, without the active fuel injection system parameter online calibration, the actual fuel injection quantity delivered into GT-Power combustion model will be different from the desired one due to the unknown uncertainties To evaluate the developed injection system parameter on-line calibration algorithm, co-simulations within Matlab/SIMULINK and GTPower were conducted The parameters in the controller were chosen as: L = -1.2, K =-1.2 155 Figure Desired and actual fuel injection quantities during the injection model parameter on-line calibration - 4.2.2 Simulation results The predicted exhaust manifold oxygen fraction, Femodel in Figure 5, was modeled based on the desired injection quantity and measured intake and exhaust manifold signals according to the oxygen mass fraction model in section II The difference between this predicted exhaust manifold oxygen fraction and the measured one is related to the injection quantity error Therefore, such an oxygen fraction difference can provide an error signal in EILC algorithm In the simulation, the uncertainty parameter θ(t) on-line calibration was initiated at the 110 engine cycle As can be th Figure Model uncertainty parameter adjustment seen from Figure 5, the error between the predicted and measured exhaust manifold oxygen fractions was rendered to zero after the algorithm was applied Figure shows that the uncertainty parameter of the injection model, θ(t), was actively calibrated after the EILC-based parameter calibration algorithm was activated Figure shows that the desire fuel injection amount is 20 mg, whereas the actual injection amount before EILC algorithm correction was around 22.3 mg, with oscillation After parameter on-line calibration was started, the actual fuel injection quantity was adjusted to the desired value (20 mg) by updating the uncertainty parameter in the injector model (32) and thus the corresponding injection duration for the injector 4.3 Case 2-Effects of Engine Signal Measurement Inaccuracy 4.3.1 Simulation conditions The proposed on-line parameter calibration method is based on signals (temperature, pressure, and oxygen fraction) measured in intake and exhaust manifolds The accuracies of such measurements will affect the oxygen fraction model Figure HPCR pressure variation 156 F YAN and J WANG Figure Intake manifold oxygen fraction signals and therefore the performance of the on-line parameter calibration To show the effects by inaccurate measurements, another simulation was conducted at a different operation condition (different EGR opening and engine speed, i.e 1800 rpm) with measurement signal uncertainties/noise The parameters in the “real” engine, including injection system, were set as follows: the fuel flow discharge coefficient c = 0.8; the fuel density ρ = 835 kg/m ; the area of injection section A = 1.8×10 m The HPCR pressure is indicated as Figure Comparing to the previous case, two periodical disturbances (one is with a frequency of 60 Hz and a magnitude of 12 MPa; the other is with Hz frequency and a magnitude of 16 MPa) for 1800 rpm engine speed were added to the HPCR pressure The parameters of injector model with the uncertainty and variations were assumed as: HPCR pressure sensor reading p = 150 MPa; the fuel flow charge coefficient c = 0.71; the fuel density ρ = 870 kg/m ; the area of injection section A = 1.9×10 m To be noted, comparing to the sensor pressure reading 150 MPa, the real HPCR pressure d,cyl fuel -8 cyl d,cyl fuel -8 Figure 11 Desired and actual fuel injection quantities during the injection model parameter on-line calibration with measurement inaccuracies has a mean value of 135 MPa, i.e 15 MPa bias value was included To evaluate the influence of inaccurate manifold signals, a measurement uncertainty with a bias value of -0.02 was added to the actual intake manifold oxygen fraction (Figure 9) and a noise signal was added to the exhaust manifold pressure as indicated in Figure 10 4.3.2 Simulation results By the same on-line calibration design method, the simulation result is shown in Figure 11 As it indicates, the inaccurate measurement signals affect the correction of fuel injection quantity to a certain extent This simulation shows that the performance of the proposed method is related to engine measurement signal accuracies cyl Figure 10 Exhaust manifold pressure signals CONCLUSIONS In this paper, a HPCR injection system on-line parameter calibration method based on the EILC algorithm was developed for accurate fuel injection quality control of Diesel engines Such an algorithm can significantly reduce the effects of periodical disturbance and uncertainties (such as the HPCR pressure sensor uncertainty and variations associated with injector aging and fuel properties) on the fuel injection quantity control accuracy Simulations using a high-fidelity GT-Power engine model with added disturbance and uncertainties were utilized to demonstrate the effectiveness of the developed algorithm It was observed that, by the on-line calibration, the actual HPCR fuel injection quantity can be precisely controlled around the desired value However, the effectiveness of the proposed method relies on accurate engine signal measurements as indicated in simulation case COMMON RAIL INJECTION SYSTEM ITERATIVE LEARNING CONTROL BASED PARAMETER REFERENCES Ammann, M., Fekete, N P., Guzella, L and lattfelder, A H G (2003) Model-based control of the VGT and EGR in a turbocharged common-rail diesel engine: Theory and passenger car implementation SAE Paper No 2003-010357 Alzahabi, B and Schulz, K (2008) Analysis of pressure wave dynamics in fuel rail system Int J Multiphysics 2, 3, 223−246 Baumann, J and Kiencke, U (2006) Practical feasibility of measuring pressure waves in common rail injection systems by magneto-elastic sensors SAE Paper No 200601-0891 Benajes, J., Molina, S., Novella, R., Amorim, R., Hamouda, H B H and Hardy, J P (2010) Comparison of 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(2009) HCCI combustion characteristics during operation on DME and methane fuels Int J Automotive Technology 10 , 6, 645−652 Wang, J and Chadwell, C (2008) On the advanced airpath control for multiple and alternative combustion mode engines SAE Paper No 2008-01-1730 Wang, J (2008) Air fraction estimation for multiple combustion mode diesel engines with dual-loop EGR systems Control Engineering Practice 16, 12, 1479−1486 Wang, J (2008a) Hybrid robust air-path control for diesel engines operating conventional and low temperature combustion modes IEEE Trans Control Systems Technology 16, 6, 1138−1151 Wang, J (2008b) Smooth in-cylinder lean-rich combustion switching control for diesel engine exhaust-treatment system regenerations SAE Int J Passenger Cars - Electronic and Electrical Systems 1, 1, 340−348 Yan, F and Wang, J (2010) In-cylinder oxygen mass fraction cycle-by-cycle estimation via a Lyapunov-based observer design Proc American Control Conf., 652−657 Copyright © 2011 KSAE 1229−9138/2011/057−17 International Journal of Automotive Technology, Vol 12, No 2, pp 299−305 (2011) DOI 10.1007/s12239−011−0035−7 VIRTUAL PRODUCT DEVELOPMENT FOR AN AUTOMOTIVE UNIVERSAL JOINT G SUN , W REN and J ZHANG 1, 3) 2)* 2) Wuhan University of Technology, Wuhan 430070, China Huazhong University of Science and Technology, Wuhan 430074, China Wanxiang Group Technical Center, Hangzhou 311215, China 1) 2) 3) (Received 13 May 2009; Revised 25 June 2010) ABSTRACT−Constant velocity universal joints play a very important role in automotive drivelines The traditional development method, based on a physical prototype and experimenting, is time consuming and costly This test-based method does not easily identify rational design clues Therefore, a virtual product development method, which is based on dynamics modeling and simulation, is necessary Virtual prototyping for a universal joint has been developed using the simulation software package MSC.ADAMS Dynamics simulation has been performed to predict and evaluate joint behaviors This virtual product development method has been implemented by the WanXiang Group Co., which is one of the most famous Chinese automotive component manufacturers KEY WORDS : Constant velocity joint, Virtual prototyping, Dynamics simulation, MSC ADAMS INTRODUCTION used to simulate vehicle dynamics Using this method, some factors in universal joint can be modeled more accurately, such as the impact forces and the friction forces between the universal joint physical components Another consideration is that the simulation model can have more direct corresponding relations with the physical components using this method Based on these direct relations, the simulation and optimization results can be used to direct changes in the physical component parameters First, a detailed virtual prototype model of a certain universal joint with its inner components was constructed The impact forces and the friction forces were included in the dynamics model to reflect accurate interactions of the components Second, the simulation was performed so that the behavior of the universal joint could be evaluated Finally, there were some design improvements based on the simulation results The implementation of this virtual prototyping method was supported by Wanxiang Group Co., one of the most famous Chinese automotive component manufacturers The virtual product development approach is used to develop Wanxiang universal joints Automotive universal joints play a very important role in vehicle driveline behaviors However, the traditional development method for the universal joint is empirical design The universal joint design parameters need to be validated by experience, and a number of tests based on the physical prototype must be performed to test its performance This empirical method based on physical prototypes is timeconsuming, and the high-cost process cannot achieve the optimal design Because the simulation method is widely used in full vehicle level performance analysis, it has also become an indispensable methodology for predicting, optimizing and assessing the dynamics performance for universal joints and drivelines (Vedam , 1995; Krishna , 2000) This simulation-based development method can be completed before the physical prototype is built, which can reduce the time and the cost Furthermore, it can provide a clue to a more rational design for the constant velocity joint The simulation method is based on a simplified theoretical model Too much simplification lowers the simulation accuracy A more accurate and subtle simulation method, the virtual prototyping method, can solve this problem effectively The virtual prototyping method is based on a commercial complex numerical simulation software package, such as MSC.ADAMS, which is widely et al * Corresponding author et al VIRTUAL PROTOTYPE MODELING FOR A RZEPPA CONSTANT VELOCITY JOINT A Rzeppa constant velocity joint has the typical structure of a constant velocity universal joint (Miller , 1979) The MSC.ADAMS software package is used to model the prototype virtually The detailed model includes the geometric model and data, the physical data and the impact et al e-mail: renweiqun@tsinghua.org.cn 299 300 G SUN, W REN and J ZHANG The geometry model also includes some clearance data and manufacturing deviations (Dubowaky, 1987) Figure Basic structure of a Rzeppa constant velocity joint forces and friction forces 2.1 Geometry Model and Geometry Data The geometric model of a Rzeppa constant velocity joint was constructed as shown in Figure Part is the outer race that is shaped like a bell and fixed in the input axle Part is the inner race that is shaped like a star and is fixed in the output axle Part is the set of six rolling balls Part is the cage, which separates the six balls The geometric parameters of these parts can be input using the software panel and are parametric Some of the important geometry parameters are summarized in Table Table Some of the geometry parameters Parts Parameter items Diameter of inner contact surface with cage (mm) Theoretical diameter of the rolling ball Outer installation circle (mm) race Radius of ball groove arc (mm) Ball groove offset relative to the input axle (mm) Ball groove contact angle (o) Theoretical diameter of the rolling ball installation circle (mm) Diameter of outer contact surface with Inner cage (mm) race Radius of ball groove arc (mm) Ball groove offset relative to the input axle (mm) Ball groove contact angle (o) Diameter of outer contact surface with outer race (mm) Cage Diameter of inner contact surface with inner race (mm) Cage window width (mm) Quantity Balls Diameter (mm) Data 58.715 52.89 8.255 3.75 2.2 Physical Data and Virtual Prototype Model Based on the geometric model above and the material data, the physical data, including the mass, inertia and the location/ orientation of gravity center, can be obtained, as shown in Table From the geometric model, the geometric data and the physical data, the virtual prototype model for the joint assembly was constructed as shown in Figure 2.3 Constraints of Impact Forces and Friction Forces The virtual prototype model for the mechanical structure needs to include an accurate model of the force constraints to capture the dynamic behavior of the joint and its effect on the driveline performance These force constraints mainly include the impact forces and the friction forces The existing impact forces and friction forces during joint assembly are shown Table Inertia data Outer race Inner race Cage Mass (kg) 1.312 0.445 0.0426 Inertia Ixx 2092 289 25 (kg mm2) Inertia Iyy 1139 43 36 (kg mm2) Inertia Izz 2092 289 25 (kg mm2) Gravity center 0.0,40.0,0.0 0.0,-23.0,0.0 0.0,0.0,0.0 location (mm) Gravity center 0.0,90.0,0.0 0.0,90.0,0.0 0.0,90.0,0.0 orientation (o) 45 52.85 50.755 8.255 3.75 45 58.655 50.823 15.855 15.875 Figure Virtual prototype model of the Rzeppa constant velocity joint assembly VIRTUAL PRODUCT DEVELOPMENT FOR AN AUTOMOTIVE UNIVERSAL JOINT Table Impact and friction force pairs in rzeppa constant velocity joint assembly Force quantity Force items (in pairs) Between ball and outer race Impact Friction Between ball and inner race Impact Friction Between ball and the cage Impact window Friction Impact Between outer race inner surface and cage outer Friction surface Between cage inner surface and inner race outer surface Impact Friction 1 et al FNi = Kδ· ei + C1δ· i + C2δ· iδi (1) is the impact force in normal direction K is the Hertz contact stiffness and are the damping ratios δ is the FNi C Figure Friction coefficient curve penetration depth of the contact point in the normal direction δ· i is the velocity of the contact point in the normal direction ≥ is an exponent factor The impact force expressed by (1) can be modeled in MSC.ADAMS by some impact functions Wherever a vertical impact force exists, a tangential friction force should also exist In the universal joint contact surface, the friction force is the typical Coulomb friction, where the dynamic friction coefficient is a constant value that is less than the static friction coefficient However, this coefficient is applied, and the friction coefficient curve needs to be a smooth, continuous curve to make the numerical calculation converge more easily The friction coefficient curve shown in Figure is used here In the curve above, µ is the static friction coefficient, µ is the dynamic friction coefficient, is the velocity of static friction conversion, and is the velocity of dynamic friction conversion The friction coefficient values shown in Figure can be input into MSC.ADAMS as =0.5 mm/ s, =0.8 mm/s, µ =0.3 and µ =0.1 to model the friction force automatically using the software e in Table In this table, the forces are counted in pairs For example, a pair of forces between the ball and outer ring includes a force acting from the ball to the outer ring and a force reacting from the outer ring to the ball The typical impact forces among the outer race, ball and inner race are shown in Figure The two arrows facing the ball in the figure are the impact forces acting on the ball, and the ellipses that cross the arrows are the stress ellipses (Hills , 1993) For the impact between the ball and outer race, the force acts on the right side of the figure This side is named the positive side The left side of the figure is always loose and has no impact force This side is named the negative side However, in some cases, there are unexpected impact forces on the negative side, which causes abnormal noise The impact force can be modeled as a nonlinear equivalent spring-damper model as below C 301 i Figure Impact force between the ball and outer race and between the ball and inner race s d Vs Vd Vs Vd s d VIRTUAL PROTOTYPE SIMULATION FOR THE JOINT PERFORMANCE EVALUATION The virtual prototype model above can be used for the simulations to evaluate the dynamics of the universal joint The simulation process also requires solving the functions numerically, which can be finished with the software The parameters for the simulation need to be selected carefully to control the simulation process After the numerical solving process, the simulation results can be obtained, which include displacements and clearances, pressure forces, and contact stresses 3.1 Displacements and Clearances From the virtual prototype simulation, the displacement results can be obtained For example, the angular displacement of the input axle (outer race of the joint) is given as the input, which rises constantly from zero to some value The 302 G SUN, W REN and J ZHANG Figure Angular displacement of output axle (inner race) angular displacement of the output axle (inner race of the joint) can be calculated, as shown in Figure In this figure, the angle varies initially, which shows the transient behavior of the joint Later, the curve rises constantly, which shows the constant velocity transmission between the input axle and the output axle The exact angular displacement difference between the input axle (outer race) and the output axle (inner race) is shown as Figure The curve shows a relatively large change at the beginning, which is due to the mating clearance between the outer race and inner race The transient behavior of the joint can also be observed in Figure In Figure 6, the difference is reduced to a constant value with small fluctuation This fluctuation is mostly produced by the clearance variation coming from the manufacturing deviations From the simulation, the clearance between the rolling balls and the outer race or the clearance between the rolling balls and the inner race can also be calculated This kind of clearance can be used to evaluate the uniformity and smoothness of the rotation As shown in Figure 3, the clearance between the rolling ball and the outer race is defined on the negative side (left side in Figure 3) As an example of the clearance calculation result, the clearance between the rolling ball and the outer race is shown in Figure In this figure, the clearance has mostly positive values, which means the joint works well However, at 0.14 s and 0.34 s, there are two negative values, which indicates that the rotations of the two axles have an unexpected difference This difference can induce unexpected contact force and abnormal noise 3.2 Result of Pressure Forces The impact forces between contacting component pairs are defined as in Section 2.3 after the simulation the pressure forces can be obtained Wherever the impact forces defined in Table exist,pressure forces can be calculated For example, the pressure force between the ball and the outer race is shown in Figure In this figure, the solid line curve is the pressure force on the positive side, and the dashed curve is the pressure force on the negative side The pressure force curve on the positive side has positive values, which means that real contact and real impact force exist on the positive side On the negative side, the theoretical ideal value of pressure force is zero However, as shown in Figure 7, there are two negative values of contact clearance, which means that at these two time points, physical contacts that induce positive pressure forces exist These two positive peak values can be observed in the dashed curve in Figure 8; the pressure force values are zero at all other times The negative side’s positive pressure force is analyzed in Section 4.2 in more detail Figure Angular displacement difference between the input and output axles Figure Clearance between the rolling ball and the outer race (on the negative side) Figure Pressure force between the ball and the outer race VIRTUAL PRODUCT DEVELOPMENT FOR AN AUTOMOTIVE UNIVERSAL JOINT Figure Simulation result of contact stresses 3.3 Contact Stress Results The pressure force results in Section 3.2 give the boundary conditions for calculating the contact stresses at the points of contact From the contact pressure force, the contact stress can be calculated using the Hertz contact theory (Hills , 1993) In the software, a user-defined function can be used to define the contact stress in the modeling process After the simulation, the contact stress can be obtained For example, the contact stresses between the ball and the outer/inner race are shown in Figure (The time frame is staggered and different from that in Figure because the step is 0.1 s, which is not consistent with in the steps of 0.05 s in Figure 8.) The solid line is the contact stress between the ball and the outer race, and the dashed curve is the contact stress between the ball and the inner race The contact stress is a criterion for evaluating the fatigue pitting and wear of the universal joint The application of the contact stress result is shown in Section 4.1 in more detail et al DESIGN IMPROVEMENTS USING VIRTUAL PROTOTYPING TOOLS The virtual prototype simulation results shown in Section can be used as evaluating criteria for the universal joint dynamics behaviors This evaluation can be correlated with some physical design problems To solve these problems, some of the design parameters were changed, and then the simulations were performed again The simulation results for the new designs show effective improvement for these problems Some examples are shown in the case studies below 4.1 Case – Outer Race with Early Wear The fatigue test of the universal joint physical prototype shows that the outer race suffers earlier wear than the inner race Then the number of service life cycles of the whole joint is reduced due to the outer race wear Fatigue life has direct relationships with the contact stress, illuminating a thorough study of the contact stress In Section 3.3 and Figure 9, it can be observed that the contact stress between the outer race and the ball has a sharp peak value around 0.22 s This value is even higher than the contact stress 303 Table Geometry parameter changes Data for Data for Parts Parameter items old design new design Diameter of inner contact surface with cage 58.715 58.415 (mm) Outer race Theoretical diameter of the rolling ball installa- 52.89 52.89 tion circle (mm) Diameter of outer contact surface with cage 50.755 50.455 (mm) Inner race Theoretical diameter of the rolling ball installa- 52.85 52.85 tion circle (mm) Diameter of outer contact surface with outer 58.655 58.315 race (mm) Cage Diameter of inner contact surface with inner 50.823 50.523 race (mm) between the ball and the inner race For the joint material, the permitted contact stress between the ball and the outer ring is 4109 MPa, and the permitted contact stress between the ball and the inner ring is 4257 Mpa Thus, if the actual stress of the inner race is slightly higher than that of the outer one, their fatigue lives should be almost the same However, in the result shown in Figure 9, the outer race has a higher peak value than the inner one, which is the main cause of the outer race wearing early Therefore, reducing this peak value and making the outer race value lower than the inner one is an effective way to solve the problem The contact stress value is closely related to the geometric parameters of the components Thus, to improve the design several trials with different geometric values were performed to obtain the optimum values The old design and the new design are compared, and the changes Figure 10 Simulation result of contact stresses for the new design 304 G SUN, W REN and J ZHANG are shown in Table The simulation results with new design parameters are shown in Figure 10 A comparison of Figure 10 and Figure shows that the sharp peak value of outer race contact stress is eliminated With the new parameters, the outer race contact stress shows more mild changes, with the peak value lower than that of the inner race The inner race value increased slightly with the new design parameters, and the outer race value is lower than the inner race curve overall, which causes the outer race and inner race to have almost equal fatigue lives To validate the result above, a rig test for the physical prototype is performed, as shown in Figure 11 In this test, the input axle torque is 456 Nm, and the rotating speed is 450 rpm The angle between the input axle and the output axle varies from degrees to 6.5 degrees at Hz for 177 seconds and from 11.5 degrees to 15 degrees with at Hz for seconds The cycle above is 180 seconds, and the whole test was 300 hours For the old design with the results shown in Figure 9, the outer race had fatigue pitting and wear However, for the new design with the result shown in Figure 10, both the outer race and the inner race did not have fatigue pitting and wear The fatigue test on Figure 11 Fatigue test rig for the constant velocity joint Table Tolerance parameter changes Mating Parts Tolerance for Tolerance for old design new design Outer race-cage Outer race +0.03 +0.05 (with contact) 0 Cage -0.03 -0.03 -0.06 -0.08 Cage-inner race Cage +0.046 +0.06 (with contact) 0 Inner race -0.03 -0.03 -0.06 -0.08 Outer-inner race Outer race +0.03 +0.025 (mating with0 out contact) Inner race -0.01 -0.01 -0.04 -0.035 Figure 12 Simulation result of pressure force for the new design the physical prototype with the new design parameters verified the outer race anti-wear performance improvement 4.2 Case – Outer Race Abnormal Noise As analyzed in Section 3.1, there are two time points with negative clearance between the rolling ball and the outer race in negative side, as shown in Figure The negative clearance means that physical contact exists at these two time points, which can induce positive pressure forces, as analyzed in Section 3.2 and shown as a dashed curve in Figure As mentioned in Section 2.3, the impact force on the negative side is usually zero Thus, the unexpected positive pressure at these two points can cause abnormal noise The abnormal noise phenomenon can be observed in the physical prototype test of the universal joint The pressure force is closely related to the tolerance parameters between mating surfaces Thus, the tolerance parameters were varied in several trials to achieve the optimal parameters The old design and the new design are compared, and the changes are shown in Table The simulation result with new design parameters is shown in Figure 12 A comparison of Figure 12 and Figure shows that the positive value of pressure force in the negative side is eliminated With the rational changed tolerance value in the new design, all of the pressure force on the negative side is zero Thus, the unexpected impact on the negative side is eliminated, and the abnormal noise is reduced The test on the physical prototype with the new design parameters verified that the abnormal noise was eliminated CONCLUSIONS (1) A virtual product development method based on MSC.ADAMS was used for constant velocity universal joint development The virtual prototype model for a certain universal joint was constructed based on the geometric data and physical data; in particular, there VIRTUAL PRODUCT DEVELOPMENT FOR AN AUTOMOTIVE UNIVERSAL JOINT were some special considerations included, such as compression forces and friction forces, that made the model more efficient (2) A virtual prototype of the universal joint was simulated to evaluate the dynamic behaviors, and simulations with design parameter changes were performed to solve the problems of early wear in the outer race and abnormal noise in the outer race ACKNOWLEDGEMENTS−This paper is partially sponsored by the Chinese National Science Funding (60674067), which is greatly appreciated REFERENCES Dubowaky, S., Deck, J F and Costello, H (1987) The dynamic modeling of flexible spatial machine system 305 with clearance connections J Mechanisms Transmissions and Automation in Design 109, 1, 87−94 Hills, D A., Nowell, D and Sackfield, A (1993) Mechanics of Elastic Contacts Butterworth- Heinemann UK Krishna, V., Naganathan, N G., Phaduis, R and Dukkipati, R V (2000) Analysis of driveline load in an automotive powertrain with multiple Cardan joints Proc IMechE, Part D: J Automobile Engineering 214, 5, 509−522 Miller, F F., Holzinger, D W and Wagner, E R (1979) Universal Joint and Drive Shaft Design Manual (3.2.8 Rzeppa Universal Joint) SAE-AE-7, 145−150 Vedam, K., Naganathan, N G., Szadkowski, A and Prange, E (1995) Analysis of an automotive driveline with Cardan universal joints SAE Paper No 950895, 371−379 Copyright © 2011 KSAE 1229−9138/2011/057−18 International Journal of Automotive Technology, Vol 12, No 2, pp 307−314 (2011) DOI 10.1007/s12239−011−0036−6 DEVELOPMENT OF A LOW-NOISE COOLING FAN FOR AN ALTERNATOR USING NUMERICAL AND DOE METHODS 1) 2)* W KIM , W.-H JEON 3) 4) 4) , N HUR , J.-J HYUN , C.-K LIM 4) and S.-H LEE Graduate School of Sogang University, Seoul 121-742, Korea CEDIC Co., LTD., 1202 ACE Highend Tower 3, 371-50 Gasan-dong, Geumcheon-gu, Seoul 153-787, Korea Mechanical Engineering, Sogang University, Seoul 121-742, Korea Korea Delphi Automotive Company, Buk-ri, Nongong-eup, Dalseong-gun, Daegu 711-712, Korea 1) 2) 3) 4) (Received 29 July 2009; Revised 12 July 2010) ABSTRACT−An alternator, which converts mechanical rotational energy into electrical energy, is an important component of a vehicle Alternators operate over a broad range of rotational speeds, typically from 3,000 RPM to 18,000 RPM, which demands a cooling fan producing sufficient airflow, ideally with a minimum of noise In the current study, an optimized alternator-cooling fan was developed through a linked DOE(Design OF Experiment) process and numerical analysis The SC/ Tetra and FlowNoise S/W programs were used to calculate flow rates and noise levels, respectively, for the newly developed fan Compared with original model, the numerical results predicted a dBA noise reduction; the measured reduction was dBA KEY WORDS : Fan, Noise, Alternator, CFD, DOE equation, as in the FW-H equation, the Lowson equation and the Curle equation (Lighthill, 1952; Ffowcs and Hawking, 1955; Curle, 1955) The source term in this method may be applied with various theoretical or numerical methods Jeon and Lee (1997) have developed a method for estimating the noise of centrifugal fan Other methods for estimating noise have been developed and applied with the impeller blades while calculating the unsteady-state flow field using the CFD method with the noise source term of the CAA method or with the surface-pressure data of the stationary area (Jeon and Lee, 1997; Jeon and Lee, 1999; Kim , 2006; Liu , 2006; Lee , 2007) The factors that can influence both the performance and the noise of centrifugal fan include the outer diameter, width of the fan, the inlet/outlet angles of the blades, the chord length and the number of blades However, in the case of the alternator-cooling fan, the effect of the outer diameter of the fan is limited Hence, in this study the blade inlet/outlet angle, chord length and number of blades were selected as the main design factors We used the Taguchi analysis for the optimization method, which has been frequently used in the design of experiment (DOE) component of various statistical methods (Roy, 2001) Using these four design factors for the alternator-cooling fan, we designed nine cooling fans by arranging the factors a four-factor/three-level L9 Taguchi table and performed unsteady-state CFD analysis and CAA analysis for each We used the program for the CFD analysis, and then checked the propensity of each factor according to the INTRODUCTION An automobile alternator converts the mechanical rotational energy of the engine into electrical energy, and is generally operated by connecting it to the engine with a belt A common automobile engine operates at a low speed of 800 RPM at idle up to a high speed of 6,000 RPM under conditions in which the rotational speed changes suddenly according to the driving situation Thus, the design of the cooling fan of an alternator is complicated due to the frequent changes in both operating range and conditions A cooling fan must provide an appropriate flow rate over the entire operating range, and the noise it produces can be an important design factor Thus, the design of an optimal alternator cooling fan must consider both the flow rate and noise To satisfy the flow rate and static-pressure requirements, centrifugal fans have commonly been designed using CFD The tonal noise in the blade-passing frequency (BPF) and noise in the harmonic frequency are normally the main causes of centrifugal fan noise The tonal noise in the BPF is attributable to the interactions between the rotating impeller and the nonrotating structure (Morfey, 1970; Chen and Wu, 1999) The computational acoustic analogy (CAA) method is a way of estimating the noise; here, the source term is applied by discretizing the nonhomogeneous solution of the Lighthill * Corresponding author et al al et al SC/Tetra e-mail: whjeon@cedic.biz 307 et 308 W KIM et al Taguchi method ALTERNATOR AND CENTRIFUGAL FAN The external appearance and a cutaway diagram of the alternator used in this study are shown in Figure As this alternator is a structure with a number of cooling holes on the outside, it differs from the structure of common centrifugal fans in which the inlets and outlets are well designed There are two centrifugal fans inside this alternator Fan cools the generator coil and rotor; Fan is intended to cool the electrical parts controlling the generation of electricity Likewise, a common generator has two cooling fans and we also developed the cooling fan for the electrical parts for the latter A special feature of the inside of this alternator is that the unsteady-state CFD analysis cannot be easily performed because the distance between the rotor and stator is very small, as low as 0.5 mm This structure is additionally problematic because a grille and irregularly arranged electric parts are positioned in front of the entry of the cooling fan, and the parts also influence the noise and flow performance of the fan The main design parameters of the centrifugal fan are shown in Figure In this study, we selected the inlet angle, outlet angle, chord length and number of blades as the major design factors, as the outer diameter and width of the fan were fixed The fan blades were designed according to the basics of pump design (Eck, 1972) NUMERICAL FLUID AND NOISE ANALYSIS METHOD 3.1 Navier-stokes Equation of a Moving Object and Twoequation k-ε Turbulence Model The ALE (Arbitrary Lagrangian Eulerian) method can be used to calculate the flow field of a moving object like a fan using CFD This method is applied to a fixed-coordinate Navier-Stokes equation, which is derived as follows ∂(u v ) (1) ∂x i – i - = i u ∂p ∂ ∂u ∂ ρ -u - -∂ -( u -– -v ) ρ - = + µ -+ ∂x ∂x ∂x ∂t ∂x i j j i (2) i j i j j where u is the velocity of incompressible flow and v is the velocity of the moving grid A turbulence model is usually used because it is difficult to calculate turbulence flow directly, as this often becomes computationally prohibitive If the Navier-Stokes Equations (1) and (2) are rearranged so that the time-fluctuating velocity is divided into two terms, i.e., the time-averaged velocity and a fluctuating component, the Reynolds stress ( ρ u u ), which is the turbulent stress, and six unknown terms are derived for the viscous term The equations in these six unknown terms are not solvable due to the closure problem, i.e., the number of unknown terms greater than the number of equations In this model, the turbulent eddyviscosity coefficient µ , the turbulent energy k and the viscous dissipation rate ε are defined as follows because viscous stress is proportional to the deformation rate of the velocity ∂u ∂u ⎞ (3) ρ u u µ ⎛⎝ ρkδ ∂x ∂x ⎠ – i j t – k Figure External and internal views of the alternator µ i j = -2 t = = t i j j i – -3 + ij ( u + u2 + u ) 2 (4) 2 C ρ kε t (5) - The turbulence model is a method to solve for these terms using other equations and so obtain the constants via empirical or theoretical methods The two-equation k-ε turbulence model is commonly used in industrial applications because the convergence of the k-ε turbulence model is among the more stable and rapid of the various RANS (Reynolds-averaged Navier-Stokes) turbulence models The transport equations for k and ε of the k-ε turbulence model are derived as follows ∂ ρ -k ∂ ( u -– -v ) -ρ -k- ∂ ⎛ -µ - -∂ -k ⎞ + = +G ∂t ∂x ∂x ⎝ σ ∂x ⎠ i i t i Figure Geometry and terminology of a centrifugal fan impeller i ∂ ( u – v ) ρε ∂ ρε + - = ∂x ∂t i i i k i s + Gr – ρε (6) DEVELOPMENT OF A LOW-NOISE COOLING FAN FOR AN ALTERNATOR ∂ ⎛ µt ∂ε ⎞ ∂ x i ⎝ σ φ ∂ x i⎠ - Gs - = + C1εk (Gs GT)( - + 1+ C3Rf) C2ρεk – ∂ u ∂ u j⎞ ∂ u i µt ⎛⎝ i ∂ xj ∂ xi ⎠ ∂ xj + (9) i GT (10) GS GT The constant terms in the above equations are empirically determined in the case of the standard ε model, while they determined theoretically by Fourier analysis in the RNG ε model The accuracy of the RNG ε model is usually better than that of the standard ε model Rf = – -+ k- k- k- k- 3.2 Unsteady-State Calculation of a Fan Flow Field using CFD In this study, SC/Tetra Ver 6, a commercial CFD code, was used in combination with an MPI parallel library in a Linux cluster SC/Tetra's discretization method uses a node-based FVM for space, an implicit method for time, a second-order MUSCL algorithm for advection and a sliding-interface scheme for interpolation between rotating and stationary parts to describe the variable rotation of a fan SC/Tetra can handle hybrid grids consist of hexa, tetra, prism and pyramid The RNG ε model was selected from the RANS turbulence models The LES turbulence model was not adequate for this study because the computational expense of LES is much higher than for the RNG ε model In this case, the noise of an axial flow fan is mainly due to the effect of the periodic rotation of fan blades, and the noise generated by turbulence is relatively small (Liu, 2006) k- k- 3.3 Prediction Method for Aeroacoustic Noise Neise previously showed that the dipole resulting from the unsteady force fluctuation was the dominant source of fan noise (Neise, 1992) The predominant source of the dipole in a centrifugal fan is the rotating impeller Therefore, the sound field generated by the forces of the impeller and diffuser blades was considered in this study Equation (11) represents the inhomogeneous wave equation following Ffowcs-Williams and Hawkings, which can be derived from the basic fluid dynamic equations using generalized functions 2 ∂ ⎞ ⎛ ∂ ⎝ a2o ∂ t2 ∂ x2i ⎠ p - - – ∂ [ ρ v δ ( f ) ∇f ] ∂t n ' = - ∂ ∂ [ n p δ ( f ) ∇f ] [ T H(f)] ∂ xi ∂ xj ij ∂xi i – - + where, p = sound pressure [Pa] ρ = air density [kg/m3] i = surface normal ' n T i j ij o ij f - - t = speed of sound [m/s] = normal surface velocity [m/s] = static pressure [Pa] ij = ρ u u + P – a ρδ = Lighthill tensor [Pa] δ( ) = Dirac delta distribution H( ) = Heaviside distribution ao p (8) GT giβµt σµt ∂∂xT = (7) 309 (11) f The first, second and third terms in the right-hand side of Equation (11) represent the monopole, dipole and quadruple, respectively Only the dipole term in Equation (11) was considered in this study; here, the force was modeled as a point force as described earlier Thus, Equation (11) can be simplified to Equation (12): x –y F -∂ M- ⎫ -⎧ ∂ F- + (12) P' = 4π a r (1 – M ) ⎨⎩ ∂t – M ∂t ⎬⎭ i i i o i r r r This formula indicates that the acoustic pressure due to the moving point force can be calculated using the time variation of the force and acceleration Here, o is the speed of sound, i is the force and r is the distance between the observer and source, where and are the positions of the observer and source, respectively r is defined as follows: Mr ( x i r yi ) M i (13) By applying this equation to each blade element, we can predict the acoustic pressure in the free field The effects of the scattering, reflection and refraction of a casing on the sound field was not considered in this analysis Therefore, only the behavior of the noise source and its radiation to the free field were calculated in this study a F x y M – = - 3.4 Linkage Method between CFD and CAA The linkage method between CFD and CAA was constructed as a separate process in this study Pressure data for each surface mesh and each time step were written to a neutral data file during CFD calculations The CAA code then read stored data from the neutral file and analyzed it using the Ffwocs-William and Hawkings equations NUMERICAL SIMULATION OF THE VARYING FLOW FIELD 4.1 Numerical Method A CAD draft of the detailed geometric data for a centrifugal alternator shown in Figure was prepared for the CFD analysis for improved accuracy Figure shows the base grid size of the alternator surface, which was set to 1.5 mm; finer grid sizes were used for complexly shaped parts For the numerical simulation, the computational domain size was selected as seven times the size of the alternator, which was positioned in the domain similarly to actual experimental setup, as shown Figure (a); the sliding interface between rotating and stationary parts is shown in Figure (b) The 310 W KIM et al Figure Surface mesh of the alternator and fan Figure Boundary conditions gauge pressure conditions are given at the boundary condition of the computational domain For the boundary condition of the centrifugal fan, only the rotational speed is given; it was analyzed for the test conditions of 3,000 RPM, 10,000 RPM and 18,000 RPM A sliding mesh with 240 cycles per rotation was used for the unsteady-state simulation of the centrifugal fan For example, when the rotational speed is 10,000 RPM, the time interval becomes 0.000025 seconds In the view of the total computational time, it is not easy to maintain an unsteady-state simulation CFL number, which ideally should be equal to The simulation grid of the alternator is shown in Figure Because the operating range of the alternator reaches up to 18,000 RPM, the size of the simulation mesh is quite important Therefore, a fine computational grid of 0.75 mm was constructed in the flow zone of the fan, and the thickness of the prism layer was reduced to 0.04 mm because the narrow space between the rotor and stator causes the calculations to diverge easily The number of computational grids configured in this way could reach as many as 20 million The threedimensional unsteady-state flow simulation of the centrifugal fan was performed using the commercial CFD program SC/ Tetra, which has the ability to simulate the Navier-Strokes equation within unstructured grids by applying node-based finite-volume methods The unstructured grids simulated on SC/Tetra include prism, pyramid, hexa and tetra grids The unsteady-state simulation of the centrifugal fan was performed using a sliding-mesh scheme and the RNG k-ε turbulence model The RANS equation was used, as it is difficult to perform calculation down to small-scale eddies However, Figure Computational grids the RANS model allows us obtain the pressure-field and velocity-field data, which can then be used to estimate the dipole source quite accurately within a commercially available computational time and capacity For the mathematical model of the unsteady-state numerical simulation of the centrifugal fan, the logarithmic law was used together with the RNG k-ε turbulence model; also employed were the first-order implicit method for the time scheme, the SIMPLEC for the pressure-term correction and the second-order MUSCL method for the convection scheme 4.2 Numerical Analysis Results of the Old Fan To validate the feasibility and accuracy of the simulation method, we first analyzed the old fan, i.e., the one currently available on the market for this alternator During unsteady-state simulation, approximately four cycles were required to reach periodic convergence, and the surface-pressure data were obtained for noise simulation in the fifth cycle The old fan has the blade-curvature change common to backward-blade type centrifugal fans Figure shows the pressure distribution at the rotor surface and the vertical section pressure and velocity distributions The higher pressure at the central rotor surface than on the blade may be due to smaller distance between the rotor and stator, in which the cooling flow is continuously induced by the slanted blade of Fan It can be seen from the DEVELOPMENT OF A LOW-NOISE COOLING FAN FOR AN ALTERNATOR Figure Surface pressure of the rotor and pressure and velocity in the vertical cross-section pressure-distribution diagram in Figure (b) that the pressure distribution is not uniform due to the asymmetry of the entry part of Fan Figure (c) also shows the flow directions of each fan Figure shows the pressure distribution over the surface of the impeller of Fan and the absolute and relative velocities Figure 7(a) shows that the pressure-difference between suction and pressure side on the leading edge of the blade is quite large This pressure difference causes noise and reduces the performance of the fan Figure (b) shows the state when the speed at the exit interferes with the exit grille From the relative velocity shown in Figure 7(c), it can be seen that a secondary flow occurs, largely due to the blade-tracing flow within the space between the blades This flow could be a cause of performance degradation and noise increase Figure shows the noise spectrum of a centrifugal fan 311 Figure Pressure contour of the fan and absolute and relative velocities in horizontal section Figure Sound-spectrum graphs of centrifugal fan noise simulated by linking CFD and CAA In the case of the old fan, the spectrum shows traditional turbofan noise characteristics: 312 W KIM et al Figure Comparison of sound-spectrum levels tonal noise (BPF) and broadband noise Figure compares the results of noise calculations and actual measurements, where the position of the observer microphone is inclined 45o from the axis and 0.3 m from the end of the alternator Although the results were quite satisfactory at low velocity, the error increased at higher velocity This could be due to transmission loss, which was not considered in the current study However, the overall levels and trends were relatively well matched Table L9 DOE table NO β1 [o] L1 25 L2 25 L3 25 L4 30 L5 30 L6 30 L7 35 L8 35 L9 35 β2 [o] 50 55 60 50 55 60 50 55 60 Z [EA] 10 13 10 13 13 10 CL [mm] 21.5 18.0 14.5 14.5 21.5 18.0 18.0 14.5 21.5 DESIGN OF CENTRIFUGAL FAN 5.1 Design of Major Factors Regarding the selection of the inlet and outlet angles, the major design parameters for a centrifugal fan, the default values may be chosen by the velocity triangle and Euler equation while considering the system flow and the rotating velocity of the fan (Stepanoff, 1957) However, the actual flow of a fan differs from the theoretical values because the blades are made in dimensional shape Therefore, the selected values before/after the inlet/outlet angle calculated theoretically by considering the correspondence of the chord length and the inlet diameter; resonance from the motor was also considered in the selection of blade number The design factors and their ranges, as shown in Tables and 2, were 25o−30o for the inlet angle, 50o−60o for the outlet angle, 8, 10 and 13 for the number of blades and 14.5 mm−21.5 mm for the chord length Figure 10 shows the designed fan parameters and shape Applying the process above described, nine different Table Design factors and range of levels Level Factor o o 25 30 35o Inlet angle (β1) Outlet angle (β2) 50o 55o 60o No of blades (Z) 10 13 Chord length (CL) 21.5 mm 18.0 mm 14.5 mm Figure 10 Fans designed with L9 DOE table centrifugal fans were designed and simulated for flow and noise at 10,000 RPM The results obtained are shown in Figure 11 Comparing the results of the new designs with the old fan, the L5 fan is the only one that simultaneously achieved higher performance and lower noise characteristics, with a noise level decreased by dBA from the old design Thus, the optimized result of the Taguchi analysis is L5, with an inlet angle of 30o, an outlet angle of 55o, 13 blades and a chord length of 21.5 mm The results of a Taguchi analysis of the flow and noise simulation are shown in Figure 12, where yellow circles indicate the design factors simultaneously satisfying flow rate and noise level Although the inlet angle did not influence the flow rate, it should be set to an optimum value to reach a low noise level The safe value should been selected by focusing either on flow rate or noise level, as the flow and noise showed the same tendencies with respect to the outlet angle As the number of blades was DEVELOPMENT OF A LOW-NOISE COOLING FAN FOR AN ALTERNATOR Figure 11 Numerical results of noise and flow of newly designed fans 313 Figure 13 Shape of the optimum fan Figure 14 Numerical results for the optimum fan optimum blade are shown in Figure 14; here, the flow rate was increased by 2.7% and the noise level was decreased by dBA in comparison with the old fan Figure 12 Taguchi analysis results of flow rate and noise increased, the flow rate also increased and the noise level tended to decrease Therefore, it was worth attempting to increase the number of blades further Although the chord length had the identical tendency, the selection was focused on the flow rate because the flow-rate increase was larger 5.2 Uneven Pitch Design of the Centrifugal Fan The noise level after execution of the first DOE was decreased by dBA at the same flow rate Because the results of the Taguchi analysis showed that the flow and noise were both improved with an increase in the number of blades, the optimum fan was designed as shown in Figure 13 The pitched-blade configuration was employed to reach a better flow rate, and the number of blades was increased to 16 to reduce the tonal noise and to avoid resonance The results of the flow-rate and noise simulations of the 5.3 Comparison between an Old Fan and New Fans The sound-spectrum of simulation of the newly designed fans was compared with that of the old fan, and the results are presented in Figure 15 The SPL of the old fan was high throughout the entire area This result seems to show a serious secondary flow between the blades due to flow separation on the leading edge The overall noise level of the L5 fan is dBA higher than the optimal fan because the noise level of the first BPF is higher than the optimum fan In the case of the optimum fan, the noise spectrum is not Figure 15 Sound spectra of old, L5 and optimum fans 314 W KIM et al smoothly along with the blades, thus decreasing the noise level The flow lines of the optimum fan are improved over those of the L5 fan, especially in the space between blades CONCLUSIONS We applied linked CFD and CAA analysis methods to the numerical design process of a centrifugal fan New fans were designed using the L9 DOE method, a Taguchi analysis, to optimize design The optimum design resulted in a new fan design showing a 3% increase in flow rate and dBA decrease in noise level at the same flow rate This result indicates that the simulated results were well estimated These results for fan design also suggest that, in the absence of test measurements, this type of development is most feasible using linked CFD and CAA analyses REFERENCES Figure 16 Impeller surface pressure and streamlines clear enough in other frequency 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