Torque generation model for Diesel Engine

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Torque generation model for Diesel Engine Paolo Falcone, Maria Carmela De Gennaro, Giovanni Fiengo and Luigi Glielmo Dipartimento di Ingegneria Universit`a del Sannio Corso Garibaldi 107, 82100 Benevento, Italy

Stefania Santini Dipartimento di Informatica e Sistemistica Universit`a degli Studi di Napoli Federico II Via Claudio 21, 80125 Napoli, Italy

Abstract— In this paper a combustion model of Direct Injection Diesel engine is proposed to calculate the in-cylinder pressure and a crank-slider mechanism model to calculate instantaneous indicated torque. The crankshaft is modelled as a rigid body. The parameters of both models are identified via non-linear least square optimization algorithm. The data, used for the identification procedure, are purposely obtained through experiments on a diesel turbocharged BMW MD47 1900cc with a dynamic test-bench. Keywords: Automotive, Modeling, Identification. Regular paper.

I. INTRODUCTION Performances and environmental requirements impose advanced control strategies in design of today’s automobiles. Most of these strategies need several variable measurements and although sensors are available, their cost are not suitable for commercial issues. For this reason an estimation of such variables is often preferred to a direct measurement. As an example, non-contact torque sensors, which must be integrated in the crankshaft, are available [1], but they are too expensive for the mass production use. In literature several works on torque estimation are presented. Each work points out a particular aspect of the topic and uses a different approach. Among the others, we want to notice the torque estimation technique based on signal processing method [2]-[3] and on frequency response function [4]-[5], torque estimator using a model based approach [1]-[6] and, finally, a combustion model aimed to diagnosis [7]-[8]. With this work we want to develop a simulator of the whole combustion process of a direct injection diesel engine. This is the first step of a bigger project aimed to realize a torque estimator that must be used on-line on commercial vehicle. In the following, we propose models both of the combustion process and of the crankshaft dynamics in order to mimic the effective torque generation process. The inputs of the proposed model are the injected fuel, aspirated air, injection timing, intake manifold pressure and temperature, load torque. The paper is articulated as follows: in the next section the engine model is presented; the section after the test bed configuration and signal data path are described; in the last section identification results are shown.

Peter Langthaler Mechatronic Department Johannes Kepler University VOEST BG01, Hochofenstraβe 3, A-4020 Linz, Austria

II. DI D IESEL E NGINE M ODEL In the following, we analyze two models for the torque generation: combustion and dynamical crankshaft model. A. Combustion Model The combustion process in a diesel engine is composed by four phases [9]. The first phase is the Ignition delay period, the period of time between the start of fuel injection (SOI) and the start of combustion. Then, during the second phase, called Premixed phase, the mixture of air and fuel, formed during the ignition delay period, burns in few crank angle degrees presenting the highest heat release rate. When the first fuelair mixture is consumed, the third phase starts, Mixingcontrolled combustion phase: new fuel is injected and the heat release rate is controlled by the velocity at which the new air-fuel mixture becomes available for burning. In this phase the heat release rate may reach a second peak, usually lower then the first one. Finally, during the last phase, Late combustion phase, the heat release continues at lower rate into the expansion stroke. In the following, the cylinder pressure (p) is used to represent the combustion evolution. This pressure is computed applying the first law of Thermodynamics to the combustion chamber, considering it an open system with uniform pressure and temperature (see figure 1), as follows dV dU dQn −p + m˙ f hinj = (1) dt dt dt where: dQn /dt is the net heat release flow; p · dV /dt is the variation of energy due to system boundary displacement. Now, considering the gas as ideal, we can write dU dT = mcv , (2) dt dt Moreover we can derive the state equation of the ideal gas, supposing the gas mass constant, as follows dp dV dT + = . p V T

(3)

Substituting (2) and (3) in the equation (1) and neglecting the heat rate related to the enthalpy component (m˙ f hinj ), we obtain:  cv  dV cv dp dQn p = 1+ + V . (4) dt R dt R dt

Finally, using the Mayer relation (R = cp − cv ) in equation (4), we obtain the cylinder pressure as follows dp p dV γ − 1 dQn = −γ + . (5) dt V dt V dt Once obtained the in-cylinder pressure equation, we need to describe how to compute the in-cylinder gas volume (V ), function of the crank angle, and the net heat release (Qn ), function of the injected fuel mass, the fuel-air ratio, the injection angle and pressure and temperature intake manifold. Hence, as regard the in-cylinder gas volume, it is simply obtained multiplying the displacement of the piston from the top dead center (see figure 2) s = r(1 − cos θ) + l(1 − cos β),

(6)

and the piston area, Ap , and adding the clearance volume, Vc , as follows: V = sAp + Vc . (7) On the other side, the net heat release is the difference between the fuel energy released during the combustion, Qch , and the heat transferred through the cylinder walls, Qht , as follows (see figure 3) Qn = Qch − Qht .

(8)

The heat released during the combustion phase is represented by Qch = QLHV · mf,b , (9) The mass of fuel burning (mf,b ) is modelled using two Wiebe functions, for the premixed (Ψp ) and mixed controlled phases (Ψm ) [10], [11]:   dΨp dΨm dmf,b , (10) = mf α + (1 − α) dθ dθ dθ

Fig. 2.

Forces acting on the crankshaft.

where α, the fraction of fuel burning during the premixed phase, is computed as: α=1−a

φb

. c τid,ms

(11)

The Wiebe function is described by the following equation:  ζ dΨj ζj + 1 θ − θig j · =Cj dθ ∆θj ∆θj " (12) ζ +1 #  θ − θig j exp −Cj ∆θj where j = p, m denotes the Wiebe function respectively for the premixed and the mixed controlled phase and θig is the ignition angle, given by θig = θinj + τid + 180◦ .

(13)

The ignition delay (τid ) is computed as function of temperature and pressure in the cylinder, cylinder geometry, crank rotational speed and chemical properties of the fuel,

Fig. 1. Open system boundary for combustion chamber for heat release analysis.

Fig. 3.

Block diagram for cylinder pressure model

Similarly to the previous, the inertia torque is given by

as follows [12]: τid (θ) = (C1 + C2 Sp ) · "   C 6 # 1 1 C4 exp EA − ˜ TC C3 pTC − C5 RT

Tm (θ) = rFm (θ)f(θ) (14)

where pT C and TT C are the estimate pressure and temperature on the Top Dead Center (TC), supposing the combustion will not happen, computed using a polytropic model for the compression process: TTC = Tman rcn−1

pTC = pman rnc .

(15)

The heat transferred through the cylinder walls, Qht , the other component of the equation (8), is modelled neglecting the heat transferred by radiation, as described in the following equation: ˙ ht = hc (Tg − Tw ), Q (16) where Tg is the mean gas temperature, computed with the gas state equation: pVM Tg = . ˜ mR The heat-transfer coefficient is given by [13]: hc = C7 Bmc −1 pmc wmc Tg0.75−1.62mc

(17)

and the gas speed w, as follows [13]: w = C8 Sp + C9

Vd Tr (p − pm ). pr Vr

where Fm is computed according to (see equation (6)): Fm (θ) = Mo¨s (22) ds d2 s ¨s = ω ¨ + 2 ω2 dθ dθ Finally, the friction torque is modelled as a black box model, function of the crankshaft speed, and the load torque is considered an input of the system. Hence, the motion of the crankshaft is computed using the second Newton law for the rotating masses, as follows: Jθ¨ = Ti − Tm − Tl − Tf .

The pressure obtained by the combustion in the cylinders produces the reciprocating motion of the piston. This motion is converted in a rotational one on the crankshaft by a transmission mechanism, constituted by a connecting rod and a crank for each cylinder. The connecting rod has two types of motion, reciprocating and rotating, so we can divide the system in two lumped masses [14]: the reciprocating mass (Mo ), formed by the piston and the connecting rod small end; the rotating mass (Mr ), formed by the connecting rod big end and the crank. The torques acting on the crankshaft are: Ti (θ) is the indicated torque, Tf (θ) is the friction torque, Tm (θ) is the inertia torque, Tl (θ) is the load torque, and ω(θ) is the crank rotational speed. The indicated torque, Ti (θ), is given by the relation

III. T EST BED CONFIGURATION The engine used is a diesel turbocharged BMW MD47 16V, 1900 cc, whose main features are shown in the table I. TABLE I F EATURES OF THE ENGINE Power 100 kW Bore 84 mm

N. Cylinder 4 - 1900cc Stroke 88 mm

Max. Torque 280 Nm at 1750 rpm Compression ratio 19

The acquisition system is divided into three subsystems, as shown in figure 4: • dSPACE is an hardware/software system used in rapid prototyping of automotive control strategies. The maximum rate of sampling data from test bed is 20kHz. The main data obtained from dSPACE are cylinder pressure, engine speed and crank angle. For the acquisition of in-cylinder pressure is used a piezoelectric pressure transducer.

(19)

where Ft (θ) is the component of the pressure force (Fp (θ) = p(θ)Ap ) orthogonal to the crank radius r. By trigonometric computation we can write (see figure 2): Ft (θ) = Fc (θ) sin(θ + β) =

Fp (θ) sin(θ + β) cos β

sin(θ + β) = p(θ)Ap f(θ), = p(θ)Ap cos β

(23)

(18)

B. Dynamic Model for the crankshaft

Ti (θ) = rFt (θ),

(21)

(20) Fig. 4.

Signal data path in engine test bed.

•

•

ECU-ETAS acquisition subsystem. The engine used for the measurements has a BOSCH ECU. With this system measurements of injected fuel, air mass introduced incylinder, injection timing, boost pressure, intake air temperature, engine speed are obtained at a variable sample rate. AVL main acquisition system. From this system measurements of load torque and engine speed are obtained with a fixed rate of acquisition of 10Hz.

The measurements are taken at steady state and transient time. The measurements in transient time consist of intervals of ECE (Economic Commission for Europe) and FTP (Federal Test Procedure) cycles, respectively the European and American standard drive cycles. IV. I DENTIFICATION RESULTS Now we illustrate the identification results. The overall engine identification is divided in two parts: combustion and crankshaft model identifications. The identification of the combustion model is realized with data referring to a transient of 5 seconds of an ECE cycle. The following 5 seconds are used to validate the model. The results are reported in figures 5-6, where is shown respectively a zoom of the cylinder pressure in the identification and validation data set. The parameters of the model are calibrated through an identification algorithm based on least squares technique. Finally, the crankshaft model is identified with static data. The results are shown in figure 7, reporting the crankshaft speed, the instantaneous and mean value, when is applied a load torque of 78N m. The engine is kept constant at 1500rpm.

Fig. 6. Zoom of the simulated and measured cylinder pressure in the validation data set.

Fig. 7. Instantaneous and mean simulated crankshaft speed, at 78 Nm of load torque.

V. C ONCLUSION AND FUTURE ACTIVITY In this work a DI four cylinder inline Diesel engine is modelled. The model is identified using pressure data collected from an engine test bed, equipped with a BMW four cylinder DI Diesel engine (MD47). This model will be the benchmark to develop and test an other model able to estimate the produced torque and, at the same time, simple enough to be implemented on commercial vehicle. Fig. 5. Zoom of the simulated and measured cylinder pressure in the identification data set.

VI. ACKNOWLEDGEMENT Authors would like to thank prof. Luigi Del Re, dr. Gerald Steinmaurer and ing. Christoph Sammer from Mechatronic

Department, Johannes Kepler University, Linz (Austria), and dr. ing. Giuseppe Police of the Istituto Motori of CNR (Italian National Research Council) for helpful discussions. VII. N OMENCLATURE Qn p V U m mf hinj cv T R ˜ R M cp γ r l θ Ap Vc Qch mf,b Qht QLHV

net heat release in-cylinder pressure in-cylinder gas volume gas internal energy gas mass fuel mass fuel enthalpy specific heat at constant volume in-cylinder gas temperature ˜ (R/M ) gas constant universal gas constant molecular weight of the gas specific heat at constant pressure (cp /cv ) assumed constant equal to 1.3 crank radius length of the connecting rod crank angle piston area clearance volume fuel energy released during the combustion mass of fuel burning heat transferred through the cylinder walls fuel low heating value, equal to 42.5 for diesel engine α fraction of the fuel burning during the premixed phase φ fuel-air ratio τid,ms ignition delay [msec] τid ignition delay [deg] θig ignition angle [deg] θinj injection angle despite the top dead center [deg] ∆θp duration of the premixed phase [deg] ∆θm duration of the mixed controlled phase [deg] Sp (2LN ) mean piston speed L stroke N rotational speed of the crankshaft EA (618840/CN + 25) apparent activation energy CN fuel cetane number pT C estimate pressure on the Top Dead Center (TC), supposing the combustion will not happen TT C estimate temperature on the TC, supposing the combustion will not happen Tman temperature in the intake manifold pman pressure in the intake manifold n polytropic exponent assigned rc compression ratio Tg mean gas temperature Tw wall temperature, supposed equal to 650K

hc B w Vd Tr

heat-transfer coefficient cylinder bore gas speed displacement volume in-cylinder gas temperature at the combustion beginning pr in-cylinder gas pressure at the combustion beginning Vr in-cylinder gas volume at the combustion beginning pm motored pressure, that is the in-cylinder pressure supposing the combustion does not happen Mo reciprocating mass Mr rotating mass J crankshaft inertia Ti indicated torque Tf friction torque Tm torque of inertia Tl load torque ω crank rotational speed Fp pressure force Fm force of inertia ζp , ζm , Cp , Cm , C1 .....C7 , a, b and c are parameters to be identified, and mc , C8 and C9 are assigned constants. VIII. REFERENCES [1] Schagerberg S. and McKelvey T. Instantaneous crankshaft torque measurements. modeling and validation. SAE paper (03P-167), 2002. [2] Guezennec Y. Soliman A. Cavalletti M. Lee B., Rizzoni G. and Waters J. Engine control using torque estimation. SAE Technical Papers (SP-1585), 2001. [3] Rizzoni G. A stochastic model for the indicated pressure process and the dynamics of the internal combustion engine. IEEE Transactions on Vehicular Technology, 38(3), 1989. [4] Taraza D. Henein N.A. and Bryzik W. Determination of the gas-pressure torque of a multicylinder engine from measurements of the crankshaft’s speed variation. SAE Technical Papers (980164), 1998. [5] Azzoni P.M. Minelli G. Moro D. Flora R. and Serra G. Indicated and load torque estimation using crankshaft angular velocity measurements. SAE Technical Papers, 1998. [6] Azzoni P.M. Ponti F. Moro D. and Rizzoni G. Engine and load torque estimation with application to electronic throttle control. SAE Technical Papers, (980795), 1998. [7] Shiao Y. and Moskwa J.J. Cylinder pressure and combustion heat release estimation using nonlinear sliding observers. IEEE Transactions on Control System Technology, 3(1), 1995. [8] Haskara I. and Mianzo L. Real-time cylinder pressure and indicated torque estimation via second order sliding

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