I , AVANCERAD NIVÅ EXAMENSARBETE FARKOSTTEKNIK 300 HP
,
STOCKHOLM SVERIGE 2015
Design of Virtual Crank Angle Sensor based on Torque
Estimation
TOBIAS ROSWALL
KTH KUNGLIGA TEKNISKA HÖGSKOLAN SKOLAN FÖR ELEKTRO- OCH SYSTEMTEKNIK
Declaration of Authorship
I, Tobias Rosvall, declare that this thesis titled, ’Design of Virtual Crank Angle Sensor based on Torque Estimation’ and the work presented in it are my own. I confirm that:
This work was done wholly or mainly while in candidature for a Masters degree at KTH, Kungliga Tekniska H¨ogskolan.
Where any part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution, this has been clearly stated.
Where I have consulted the published work of others, this is always clearly at- tributed.
Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work.
I have acknowledged all main sources of help.
Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.
Signed:
Date:
i
”Make your theory as simple as possible, but no simpler ”
- Albert Einstein (1879 - 1955)
Abstract
The topic of thesis is estimation of the crank angle based on pulse signals from an induction sensor placed on the flywheel. The engine management system performs many calculations in the crank angle domain which means that a good accuracy is needed for this measurement. To estimate the crank angle degree the torque balance on the crankshaft based on Newtons 2nd law is used. The resulting acceleration is integrated to give engine speed and crank angle. This approach is made for two crankshaft models, the rigid crankshaft approach and the lumped mass model. The latter can capture the torsional effects of the crankshaft twisting and bending due to torques acting on it. This is then compared to a linear extrapolation of the engine speed which is the chosen method today. To validate results experiments was performed where data for 36 stationary operating points was gathered. The results indicate that using a torque based model and predicting torsion improves the accuracy of the crank angle measurement especially for higher engine speeds. The rigid crankshaft approach does not give enough improvement of the accuracy to warrant further work.
Sammanfattning
Detta examensarbete handlar om att ta fram en metod f¨or att uppskatta vevvinkel fr˚an pulser fr˚an en induktionssensor placerad p˚a sv¨anghjulet. Motorns styrsystem utf¨or m˚anga ber¨akningar med vevvinkeln som bas och d¨arf¨or kr¨avs h¨og noggrannhet. Den valda metoden ¨ar att anv¨anda momentbalans p˚a vevaxeln baserat p˚a Newtons andra lag. Accelerationen som f˚as fr˚an denna ekvation integreras sedan f¨or att ge motorvarv- tal och vevvinkel. Denna metod g¨ors f¨or tv˚a fall av vevaxel modell. En stel vevaxel och en fler-mass modell som anv¨ands f¨or att f¨orutsp˚a f¨orvridningar i axeln. Detta j¨amf¨ors sedan med en linj¨ar extrapolation av hastigheten vilket ¨ar tillv¨agag˚angs¨attet idag. F¨or att kunna validera modellerna samlades data in i experiment som utf¨ordes f¨or 36 sta- tion¨ara arbetspunkter. Resultaten visar p˚a att en momentmodell som ¨aven f¨orutsp˚ar f¨orvridningar ger en f¨orb¨attrad uppskattning av vevvinkeln. Den stela vevaxel modellen ger inte tillr¨ackligt f¨orb¨attrad prestanda f¨or att vara v¨ard fortsatt arbete.
Acknowledgements
First of all I would like to thank Ola Stenl˚a˚as for his supervision of this thesis. Mikael Nordin, Soheil Salehpour and Stephan Zentner for their guidance. I would like to thank my fellow theses workers at the department Domenico Crecenzo, Christian Rugland, Mikael Gustafsson, Mathias Brischetto, Maryam Shojaee and Tobias Johansson. Finally I would like to thank my supervisor at KTH Jonas M˚artensson.
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Abbreviations
BDC Bottom Dead Centre
BMEP Brake Mean Effective Pressure CAD Crank Angle Degree
CI Compression Ignited Disp Displacement
DOF Degrees Of Freedom ECU Electronic Control Unit EVC Exhaust Valve Closing EVO Exhaust Valve Opening
FMEP Friction Mean Effective Pressure HPP High Pressure Pump
HR Heat Release
HRP Heat Release Pressure
IMEP Indicated Mean Effective Pressure IVC Inlet Valve Closing
IVO Inlet Valve Opening MEP Mean Effective Pressure PS Pressure Sensor
RPM Revolutions Per Minute SISO Single Input Single Output SOC Start Of Combustion SOI Start Of Injection TDC Top Dead Centre
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Symbols
Variable Quantity Unit of measure
A torsion state matrix C/J and K/J
Ap cylinder cross section area cm2
B torsion input matrix 1/J
C torsion output matrix [-]
Cd damping Nm/rad/s
Ci damping element of matrix Cd Nm/rad/s
D torsion feedthrough matrix [-]
J moment of inertia kg/m2
K spring constant Nm/∆θ
Ki spring constant of element in matrix K Nm/∆θ
l connecting rod length m
mA, mB weight kg
p In-cylinder pressure bar
PM echanical Power Watt
pg net cylinder pressure bar
p0 crankcase pressure bar
r crank radius m
RM S error Root Mean Square error [-]
RP M engine speed at flywheel Rev./min
T torque(subscript indicates from the source) Nm
t time s
VD displaced engine volume m3
Vd displaced cylinder volume m3
u gear ratio [−]
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w input torsion state space Nm
X torsion state vector rad and rad/s
ω angular frequency rad/s
θ crank angle degree rad or degrees
θ˙ crankshaft angular speed rad/s
θ¨ crankshaft angular acceleration rad/s2
θpuls angle of pulses at flywheel rad or degrees
η efficiency [−]
Chapter 1
Introduction
1.1 Background
The need for more accurate engine control is increasing continuously as more require- ments on emissions and fuel efficiency are appearing. This is needed to have a sustain- able transportation fleet for the future. The argument for better engine control could be made from an economic perspective. With an ever increasing competition in a global- ized world, the engine control is one way to make vehicles more efficient and thus more attractive to customers.
To achieve better efficiency for Compression Ignited (diesel) engines the common rail fuel injection system was introduced. This type of fuel injection is briefly described by Eriksson and Nielsen [1]. The common rail fuel system is an accumulator system where the fuel is kept in a high pressure accumulator, the common rail, and the injection is controlled by opening and closing of the injectors. The pressure is built up by a high pressure pump which is driven by gears on the flywheel side of the engine, (see figure 1.1). The injectors are seen above the cylinder next to the valves. This set up allows for better fuel injection control of each cylinder than using the camshaft. The fuel injection is then controlled by an ECU (Electric Control Unit). The timing of when to inject fuel is determined by the crank-angle-degree (CAD). The injection timing is of crucial importance to control the efficiency and emissions, so finding an accurate model for the CAD is a necessary condition for an accurate control. This is the subject of this paper.
The CAD is measured on the flywheel using a 60-2 hole configuration which gives an angular resolution of the measurements of 360/60=6 degrees. More detailed measure- ments of the CAD is needed for the ECU to meet the growing demands on accuracy.
One way to improve accuracy would be to increase the number of holes which would give
1
Chapter 1. Introduction 2
a higher angular resolution. However this approach is not practical due to sensor prob- lems, such as sensor noise seen in Leteinturier and Benning [2]. Other problems might involve overloading the ECU. The solution is then to use modelling of the crankshaft dynamics to fill the “gaps” and increase the frequency resolution.
Figure 1.1: An overview of an inline 6 - cylinder engine
The suggested approach will be to find a grey-box model for the net torque on the crankshaft and from this estimate the acceleration and in turn estimate the CAD from the acceleration. This has the advantage of being more robust to changes of the engine parameters, since it is based on natural laws rather than on identifying a model solely based on measurement data. The model will mainly use pulse signals from the sensor at the flywheel. Depending on how the cylinder pressure is accquired other sensor that are used might involve, cylinder pressure sensor, manifold pressure, fuel injected etc.
By using previous errors in the estimation and possibly signals from other sensors the aim is also to use a feedback approach that can calibrate the model to minimize future errors.
Chapter 1. Introduction 3
1.2 Internal Combustion Engine basics
An internal combustion engine (ICE) is defined as an engine where mechanical work is extracted from the burning of a fuel and oxidant inside the engine, see Heywood [3].
There are two main types of ICE engines. The spark ignited engine (SI) often referred to as the Otto engine from its inventor1. And the compression ignited engine (CI) often called the Diesel engine from its inventor. These engine names are not to be confused with the fuel used. The ideal Diesel and Otto working cycles are not followed perfectly in each respective engine. This is due to real world implementation problems.
There are two different stroke set ups for an ICE engine, the two-stroke engine and the four-stroke engine. The four-stroke engine is the most commonly used for truck and car applications. The four-stroke cycle is mainly described by two positions of the cylinder.
The Top Dead Center (TDC) and the Bottom Dead Centre (BDC) positions represent the piston at its top position, where the volume of the piston in the cylinder is at its minimum. And the pistons bottom position where the volume is at its maximum. The four-stroke cycle is the following,
• Intake stroke, the piston starts at TDC and ends at BDC. This stroke is used to draw a fresh air/fuel (or just air) mixture into the cylinder. The inlet valve is open during this stroke.
• Compression stroke, The gas in the cylinder is compressed by the mechanical work from the piston, from BDC to TDC.
• Power stroke, the gas mixture is ignited and the piston is forced down by the increasing pressure, forcing the crankshaft to rotate. As the piston draws closer to BDC the exhaust valve is opened.
• Exhaust stroke, in this stroke the remaining gases are swept out of the cylinder by the pressure gradient as well as the piston. When the piston reaches TDC the cycle is complete and starts again.
This is just the basic principles of the strokes. The actual positions for the inlet valve close (IVC), inlet valve open (IVO), exhaust valve opening (EVO) and exhaust valve closing (EVC) can occur at overlapping positions with each other and with the strokes.
It can also vary from engine to engine.
• IVC, the closing of the inlet valve is usually made around 30 − 60◦ after BDC where the compression stroke has started. This is to exploit ram effect phenomena which increases the amount of gas in the cylinder [1].
1Otto patented in 1863 and Diesel in 1893.
Chapter 1. Introduction 4
• IVO, this occurs around 10 − 25◦ before TDC. It should be opened such that the pressure in the cylinder does not dip early in the intake stroke.
• EVO, this is done around 50 − 60◦ before BDC. This event starts the blow-down which is where the combustion gases expand into the exhaust manifold. The timing of EVO is made so that the cylinder pressure reduces to the exhaust manifold pressure as fast as possible.
• EVC, the exhaust is closed off around 8−20◦ after TDC. This timing will influence the amount of residual gases or the amount of burned gases that are blown into the exhaust depending on speed and load.
More detailed information about strokes and working cycles can be found in e.g. [3,1].
To achieve a good efficiency of the engine one can notice that it is very important to have accurate estimations of the TDC and BDC positions. It is in relation to these positions where the most important work of the engine control systems are done. When defining a coordinate system for the crankshaft of the engine, the angular position of TDC at cylinder one is often defined as zero. The angular coordinate for cylinders 1 to 6 are phased with this as reference according to the firing order.
1.3 Related work
There are more thesis work done in parallel to this thesis that investigates the combustion parameters based on pressure measurements and another that deals with using the CAD acceleration to find a pressure estimation. Some collaborations will be made within this group especially concerning the experiments which will be performed together.
There are different approaches for finding the CAD. Most commonly measurements on the flywheel are used for estimation of angle and angular velocity of the crankshaft.
The sensor used is often a sensor employing the induction principle [4]. This effect is the current created in a conductor moving through a magnetic field. Induction can be exploited by measuring the current spike from a shift in geometry of the measured object. One can conclude that an event has occurred based on this current spike. The shift in geometry usually consists of teeth or holes on the flywheel. The Induction sensor have the advantage of being robust to dirt, this would be a problem if e.g. an optical sensor would have been used.
There are many different types of flywheel tooth/hole configurations. Some of these are mentioned by Junmin Wang and Jayant V. Sarlashkar in an article published in SAE [5].
One of these configurations is the 60-2 configuration, see figure1.2and 1.1. This means
Chapter 1. Introduction 5
that there are 60 equally spaced teeth/holes on the flywheel with two consecutive teeth missing. This gives 60-2=58 teeth that are available for measurement. The reason for the missing teeth are to have a reference point of where each revolution of the crankshaft starts. Other approaches than this are available, some of which are also mentioned by Wang and Sarlashkar [5]. These may for example involve an extra wide tooth instead of the two missing teeth.
There has been work performed on the subject of estimation of engine parameters based on CAD measurements, some examples are presented here. The subject of this thesis is an application of some of these methods. Especially concerning the estimation of torque contributions.
A paper by Stefan Schagerberg and Tomas McKelvey [6] use the torque balancing equa- tion to estimate torque based on CAD signals, the torque balance based on Newtons 2nd law for the crankshaft can be written as
J (θ)¨θ = Tgas+ Tmass+ Tf ric+ Tload. (1.1)
Several different models are suggested with different assumptions on crankshaft dynamics and inertia complexity. One assumption is that the moment of inertia for the crank- slider mechanism (piston and connecting rod) is constant. This approximation results in a maximum error of 0.1 % when using the exact expression for the moment of inertia
Rotational direction TDC, is placed on a hole
Induction sensor
Figure 1.2: A 60-2 teeth flywheel
Chapter 1. Introduction 6
compared to the average value, relative to the inertia for the whole crankshaft including the flywheel [6]. This approach has the advantage of being easier to compute which would be of interest for real time applications. In this paper three different approaches for the crankshaft dynamics are used, the rigid body, lumped mass and cylinder condesation model. The rigid body approach is to assume that the crankshaft is infinetely stiff and thus will not be deformed by the torques acting on it. The lumped mass model tries to capture the dynamic aspects by introducing a setup of dampers, springs and inertias.
The cylinder condesation is when the cylinders are condensed to one big mass. This is a combination of the lumped mass model and the rigid body approach.
Finding the friction term Tf ric in (1.1) can be especially hard since friction is a com- plicated phenomena to model accurately. Most commonly experiments are used to find an estimation of the friction. Some theory on friction is available in Heywood [3]. The main contributors to engine friction in this model are (excluding auxiliary systems):
• Pumping work. The work generated by the exchange of gas in the cylinder. More precisely the intake and exhaust of gasses.
• Rubbing friction work. The work that is generated by the relative motion of com- ponents in the engine.
The pumping work can be said to be a result of the pressure difference to force different fluids and gases in the engine through flow restrictions. This would for example involve the ventilation of gases in the cylinder. The work is eventually dissipated in turbulent mixing processes. The work required to do this is proportional to the dynamic pressure i.e. proportional to ρv2.
The lubricated friction can be separated into three cases, boundary, hydrodynamic and mixed friction. Boundary friction is charecterized by that the lubricant film is not enough to separate the two moving surfaces. Hydrodynamic friction is the opposite case.
Under boundary friction the friction is more or less not dependent on speed. When the friction is hydrodynamic the friction is proportional to the speed. This gives a relation that can be approximated by
Wtf = C1+ C2N + C3N2 (1.2)
N is here the rotational speed of the crankshaft. C1is the coefficient describing boundary friction, C2 is the coefficient related to hydrodynamic friction and finally C3 is related to the turbulence dissipation. Other losses that might be considered as friction are the
Chapter 1. Introduction 7
efficiency losses of gears and belt drives. According to Maskinelement [7, 15 p.277] the efficiency of a belt drive is usually between η = 95 − 97%. The gear to gear efficiency is often approximated as 98% [7]. The total friction in (1.2) is most commonly found through experiments, for instance measuring torque on the engine during motoring con- ditions i.e. no fuel injection.
A physical model is not the only way of modelling the crankshaft speed and torque.
By making a linear black-box model of the torque signal, as suggested in an article by Mikael Thor; Ingemar Andersson and Tomas McKelvey from Chalmers University of Technology [8], one can estimate the angular acceleration of the crankshaft from Equation (1.1). The advantage of using a black-box model over a physical model is that it will most likely be less computationally heavy. The downside is that the black-box model will have to be adapted to a very large set of data to capture the aspects of the torque at many different working points (load and speed). It will be more sensitive to changes in the engine and re-calibrating the model could be very time consuming.
Using a grey-box model is also a common approach. An example of this is found in a Licentiate Thesis at Link¨oping University, Nickmehr [9]. This is a good example of the combined physical and system identification theory that can be used for an engine model.
In this thesis an alternative formulation of the lumped mass model for the crankshaft dynamics is used compared to the lumped mass model used in [6]. The advantage is that this formulation uses a reduced amount of states.
Another grey box approach is made by Indrahil Brahma, Mike C. Sharp and Tim R.
Frazier [10]. In this paper the approach is to use a thermodynamic model of the engine as a whole to find some physical knowledge. This is done by setting up a control volume around the engine and then applying the first law of Thermodynamics. After this is done some parts of the equation are simplified. Then a least square fitting of parameters on the model is performed on measured data.
Instead of using a torque-based model it is possible to take a numerical approach to the problem. This is done by Wang and Sarlashkar [5] where an algorithm that predicts the coming angle and period to the next tooth/hole by taking into account previously measured periods and angles. These simple models have the advantage of being very computationally cheap compared to the more complex physical models. The drawbacks being that they are less robust to change in operating conditions. A next step in this numerical approach would be to make a Kalman estimator of the states to eliminate measurement noise as well. An approach of this kind is made by Bo-Chiuan Chen, Yuh- Yih Wu and Feng-Chi Hsieh [11]. In this approach a state-space model is developed from a kinematic based model for the speed and acceleration. A Kalman filter is then
Chapter 1. Introduction 8
designed to give a better estimate of the measurements. In this method the acceleration is used as an input to the system.
1.4 Problem Description
The topic of this thesis will be to find a torque-based model for estimating the crank- angle degree (CAD) based on measurements on the fly-wheel. The crank-angle degree is measured every 6 degrees today. The torque-model will be used to extrapolate the coming crank-angle degrees for an improved angular resolution. The torque model itself will be based on a combination of estimated models of the different torque components and physical models for other components. The estimated parts of the torque equation might be found using black-box modelling. These torque components will then be used to estimate the speed and angle of the crankshaft by kinematic formulas i.e. integration.
Deliveries The end result will consist of a MATLAB/SIMULINK implemented model for extrapolating the CAD. A tolerance analysis will be made with respect to tolerances of the sensor system and mechanical installation this analysis will also investigate the models ability to handle disturbances from external sources. Then a validation study will be made on the model to see how accurate it predicts the behaviour of the crankshaft compared to measured data which will be gathered in a test-cell, see Chapter 3. The model will be compared to the model that is used by most ECUs today to see the potential gains of having a more complex model. Furthermore a study on how plausible this model is will be done, with a focus on the computational effort for the model.
1.5 Delimitations
• Some simplifications have to be made for the model to work. The first assumption is that the pulses from the CAD sensor are assumed to have a delay in crank angles specified in an internal Scania specification.
• The mechanical tolerances are found from the crankshaft through the flywheel to the sensors. This tolerance will be included in the tolerance analysis of the model and possible ways to adjust for this will be investigated.
• The torque balancing equation is quiet complex when considering the physical equations for each part of the net-torque combined with a variable moment of inertia for the cranks-slider (pistons). Therefore a variable moment of inertia for the crank-slider mechanism will not be considered.
Chapter 1. Introduction 9
• The models for the torque contributions will be based on previous work and mea- surements. Some models may be derived but the main focus will be on modelling the whole system rather than very detailed physical modelling of each component.
• The torsion of the crankshaft will be found using a model that is currently in use at Scania.
• This thesis will serve as a basis for future work on CAD estimation, and therefore hardware constraints on model complexity that exists today will not be taken into account. These constraints will instead be seen as soft constraints or a desired goal. The model will be implemented in MATLAB/SIMULINK.
Chapter 2
Model
2.1 Model
The model that will be used in this thesis for estimation of the crank angle is based on the torque balancing equation (1.1). The model for each torque contribution is described in Chapter 2.3. There are two versions of the model, one with a rigid crankshaft and one with a lumped mass model. This is an introduction for the model and it is made for one cylinder on the crankshaft,
θ =¨ Tgas+ Tf ric+ Tmass+ Tload+ Tmodel errors
J (θ) . (2.1)
Rigid-body crankshaft approach. The acceleration of the crankshaft is converted to crank angle and engine speed through integration. In a discrete time domain this corresponds to the kinematic formulas used in [11]. The initial speed, for instance when the engine is starting, is calculated using the difference in time between the first two pulses on the flywheel.
θ˙i+1= ¨θi∆ti+ ˙θi θi+1= ˙θ∆ti+ ¨θi∆t2i
2 + θi. (2.2)
Dynamic crankshaft approach. Note that when using a dynamic crankshaft model the output of the state-space equations is the engine speed at the flywheel and this signal thus only have to be integrated once, see [9] and the section on crankshaft dynamics.
10
Chapter 2. Model 11
θi+1= ˙θi∆ti+ θi. (2.3)
In (2.2) and (2.3) ∆ti is the time between the samples from the ECU i.e. the simulation step time. Note that this is not the sample time of the measurements taken from the flywheel. θ is the CAD and ˙θ is the angular velocity of the crankshaft.
If the rigid-body system is re-written into state-space form with x = [θ ˙θ]T and with the acceleration as input we get (2.4).
˙ xi+1=
"
1 ∆ti
0 1
# xi+
"
∆t2i/2
∆ti
#
θ¨i (2.4)
We define Γ as
"
1 ∆ti
0 1
#
and Φ as
"
∆t2i/2
∆ti
# .
If several cylinders are used the x vector will expand by the number of cylinders. Since this model is for a rigid crankshaft every cylinder will have the same speed and thus x ∈ RN cyl+1×1. Each θ in x will also have the appropriate phase shift based on ignition order. This is 120◦ degrees for a 6 - cylinder engine.
The measurements from the flywheel will enter the model every 6◦. With the exception of the two consecutive missing holes which are used as a synchronisation of the revolutions.
Because of the integrating nature of the model, errors in the torque models will grow with each integration as the model is being simulated. CAD is reset on every pulse from the flywheel so the error does not grow large over time. One way to make sure that the engine speed estimation error does not tend to ∞ as time tends to ∞ is to use the linear extrapolation of the speed seen in (2.5). This could be done by measuring the time between two consecutive pulses, Tpuls, to find the average engine speed over this interval. θpuls= (0 : 6 : 360) is the crank angle for each pulse. This would give,
RP Mpuls,i= θpuls,i(T−θpuls,i−1
puls)
RP M (θpuls,i) = RP Mpuls,i. (2.5)
The engine speed is then calculated using (2.1) between the pulses from the flywheel.
This will cause the engine speed estimation of the linear extrapolation and the torque model approach to be similar.
Chapter 2. Model 12
2.2 Simplifications
The simplifications that were made in the modelling are presented here:
1. A constant inertia for the piston-crank configuration is considered in the first term of the mass torque, Tm1 seen in2.1. This means that the first term can be considered as a normal inertia and can thus be moved to the total inertia for the engine J . The average moment of inertia for the piston-connecting rod becomes,
J¯A= mA
2 r2
This approximation results in a small error compared to a varying inertia, see [6].
This means that the remaining mass torque is completely described by the second term. The complete inertia of the crankshaft becomes J = Jeng+ ¯JA+ mBr2. 2. The piston-crank mechanism is made as a statically equivalent model as described
by [12,6]. This is done to simplify calculations.
3. The crankcase pressure, p0, is ignored to simplify the calculations of the gas torque.
This approximation does not impact the result much since the crankcase pressure is small compared to the in-cylinder pressure. For instance in a typical automotive engine the difference between the crankcase pressure and the intake manifold is between 0.01-0.66 Bar [13]. Considering that the in-cylinder pressure is in the order of 100’s of Bars the crankcase pressure can be ignored. Experimental values gathered in test cell are of the same magnitude.
4. The pressure during the intake stroke is assumed to be the inlet manifold pressure.
The pressure during the exhaust stroke is assumed to be the exhaust manifold pressure. This is made to simplify pumping work calculations, Eriksson and Nielsen [1]. Pumping work is typically rather small for a Diesel engine because of the lack of a throttle Heywood [3].
5. The friction components are calculated from the M EP (Mean Effective Pressure) estimations seen in an internal Scania report. It is assumed that the average torque over an engine cycle is detailed enough for the model. It is also assumed that the friction contribution for each cylinder is uniform.
6. The auxiliary units AC, alternator, water pump and the hydraulic pump are seen as static components and their torque are approximated as constant over an engine cycle w.r.t the equations for each component. The speed of the engine can still vary which means that the torque will fluctuate from the components that depend on speed.
Chapter 2. Model 13
7. Where a physical model is hard to find and where a black-box model is hard to identify, for instance because of multiple inputs, a look-up table is used based on experimental data. This is not an optimal approach and thus leaves opportunities for improvement of the model.
8. The crankshaft dynamics are limited to simple angle displacements. That means that variations in acceleration and speed over the crankshaft are ignored for sim- plicity. A method for the full lumped mass model approach is suggested in 5 and is based on a lumped mass model described in1.
2.3 Torque Models
The modelling approach for each component in the torque balancing equation (1.1) is described below.
The gas torque The model is made according to [6,3]. Tgasis the pressure generated torque from the combustion of fuel in the cylinder. This torque is the driving force of the engine during the combustion stroke. The gas torque is derived from the pressure difference in the cylinder pressure and the piston area combined with the lever arm of the crank slider mechanism, it then becomes
pg(θ) = p(θ) − p0 Tgas(θ) = pg(θ)Apds
dθ. (2.6)
Sometimes it is called combustion torque. pg(θ) is the net gas cylinder pressure, p(θ) is the in-cylinder pressure, p0 is the pressure on the outside of the cylinder (from the crankcase). The torque produced is a product of the cylinder cross section area, Ap and the change of the lever-arm due to the geometry of the crank-slider configuration, ds
dθ, Figure 2.1. The piston motion equations can be found in [3] or [1]. The crank angle θ for the crankshaft is defined to be zero for TDC at cylinder 1. The gas torque could be positive or negative depending on the in-cylinder pressure and the direction of movement of the piston. During the exhaust and intake strokes, i.e. doing the gas exchange, the cylinder is performing what is called pumping work. Torque generated from pumping is sometimes taken care of in the friction torque term which is described in Tf ric.
The pressure in the cylinder p(θ) is seen as an input to the system. Different approaches of finding the cylinder pressure are used in this thesis. The optimal approach would be to
Chapter 2. Model 14
measure the cylinder pressure directly. There are problems with this approach however.
Mostly concerning the pressure sensor itself which is expensive and has a relatively low durability. An alternative approach is instead to use a model of the heat release which can then be solved for the cylinder pressure. The heat release model is not implemented in this thesis but the resulting cylinder pressure is used.
The mass torque Tmass, is the torque generated by the reciprocating masses seen in 2.1. Tmass is quiet complex since it involves a complicated geometry in the form of the crank slider mechanism of the piston and connecting rod. The torque originates from the acceleration of these masses. These forces are a type of d’Alembert Force or more commonly called inertial forces. These are forces that come into existence by using a non-inertial frame to describe the equations of motion. An inertial frame is defined by it being under acceleration such as being in a circular motion, see [14]. To simplify these expressions a Statically Equivalent Model is often used [6]. This approach has the same total mass as the original system and it has the same centre of gravity. What it lacks is the exact moment of inertia of the original system. However this does not influence the result in any meaningful way [6] . The crank-slider is then approximated by two
l
B r
A
Crankshaft Piston Head / TDC
s
Figure 2.1: Crank-slider mechanism
Chapter 2. Model 15
point masses, one rotating and one oscillating as seen in fig2.1, the approach is seen in Automotive Control Systems, Uwe Kiencke [12].
The torque can be found in different ways, for example it may be found using the Kinetic energy of the two point masses [12, p. 184]. This approach gives the total mass torque as
Tm(θ) = −(JA(θ) + mBr2)¨θ − 12dJA(θ) dθ θ˙2 Tm(θ) = Tm1(θ, ¨θ) + Tm2(θ, ˙θ).
(2.7)
The first part of the mass torque is modelled as a constant inertia. This leaves the second part which can be written in the s coordinate of the cylinder as,
Tm2(θ, ˙θ) = −mA
d2s dθ2
ds dθ
θ˙2. (2.8)
The friction torque This is made according to internal Scania reports. The models that are discussed are M EP models that have been validated against experiments. Most models for the F M EP are quadratic or linear in engine speed, this coincides well with the model suggested by Heywood [3]. To calculate the average torque during a cycle from the mean effective pressure one can do as follows,
T ≈ M EP ∗ V
2π ∗ 2 . (2.9)
Where V is the total swept cylinder volume and the denominator comes from the fact that it takes two full revolutions of the crankshaft in a four stroke engine to complete a cycle. The friction mean effect pressure is denoted as F M EP . The friction coefficients consist of; Crank train, Piston group, Valve train, Belt drive. The pumping torque is also described here, this torque consist of one part expressing pressure difference losses called throttling and one part expressing valve pumping losses.
The F M EP relations which describe the friction are all functions of engine speed.
• Crank train, consists of the main bearing, torsional damper, cam shaft bearing, sealing and the transmission.
• Piston group. The piston group is the ring package; top, first ring and second ring land; skirt and the big and small end bearings.
Chapter 2. Model 16
• Valve train. All the friction components that include the valve set up are the cam/roller contact, roller tappet, pushrods, rocker arm, valve bridge pin and the valve guide.
• The pumping torque is described by the intake and exhaust pressures. Which of the intake and the exhaust manifold pressure is relevant depend on the stroke.
This looks similar to the expression for the gas torque.
Tpumping(θ) =
Pintake/exhaust
Ap
ds
dθ (2.10)
Flow losses through the valves are ignored because of the complexity of the calcu- lations. This could be a potential improvement of the model. The blow-down is modelled by a linear decrease in pressure until it reaches exhaust pressure. This also gives room for improvements. Note that the pumping torque is not modelled when the cylinder pressure is measured since the complete pressure curve is mea- sured.
The friction for the valve train, piston group and crank train depend on the oil temperature.
The load torque The load is the torque generated from the auxiliary units on the engine as well as the actual load on the engine from the transmission. The different power requirements for the auxiliary systems in a typical engine can be seen in Heywood [3, 13, p. 740]. The water pump, oil pump and generator typically makes up 20% of the motored torque [3].
The demanded torque at the is seen as an input to the system and is assumed to be a constant for each operating point. The other components involve the alternator, AC, water pump, oil pump, fuel pump (both HPP and low pressure), fan and compressor.
Note that components that are driven on the transmission/flywheel side of the engine suffer efficiency losses due to being driven by gears. These components include the oil pump, air(brake) compressor, hydraulic pump, fuel pump and the camshaft. The losses in the belt drive are approximated as constant.
The gear to gear efficiency is assumed to be 98% according to [7]. Since many compo- nents have a middle gear, the total efficiency instead is 0.98 × n where n is the amount of gear connections for each component. The oil pump is directly connected to the crankshaft and thus n=1 for this component. For the fuel pump, compressor, camshaft and hydraulic pump there is a middle gear so n=2. This means that the oil pump will get the efficiency 98% whereas the other component will have the efficiency 0.982 = 0.9604, 96.04%.
Chapter 2. Model 17
The torque of the oil pump and fuel pump both depend on the pressure, mass flow and speed of the pump. The oil pump also depend on temperature and pressure gradient over the pump. This makes these components hard to model. The fuel pump torque is modelled using a look-up table based on an internal on an internal Scania presentation, the fuel pump is a piston pump and the torque for this component will therefore exhibit an oscillating behaviour, for this purpose a more detailed model is available for one operating point based on experimental data. This is ignored and a static model is made for this component. The oil pump is modelled with a combination of look-up tables and M EP modelling. The look-up tables are made for the pressure and efficiencies of the oil pump based on temperature and rpm. The M EP model is taken from an internal Scania report.
The alternator is modelled as a static torque contribution, Talt = U I
ηωalt
. (2.11)
The relation is based on a balance of mechanical power and electrical power of the alternator. The efficiency, η, of the alternator is a function which varies with speed and load. U is the voltage requirement from the alternator and I is the current requirement.
The current can vary depending on the driving case of the truck. For example if the battery is being charged and which electrical systems in the engine are active.
The torque from the AC compressor is estimated constant when engaged and constant when it is unloaded. The values are found in an internal Scania document. The infor- mation was gathered from a mail conversation.
The fan torque is calculated according to a report on fans from Scania. The fan is a major part of the parasite friction on the engine.
The water pump torque is estimated from internal Scania models. There are three cali- bration groups in this sheet that describes the torque losses for the pump. A regression is made on the correct calibration group data using a 2nd order polynomial.
The torque for the brake compressor can be separated into two cases, either the com- pressor is loaded or unloaded. When it is unloaded the friction torque is found using internal Scania models. The reason for the two different approaches is that two brake compressors are currently in use at Scania. Both behave similarly when loaded but the unloading mechanism differs between them. The first and most common approach is that the compressor uses an expansion chamber to reduce losses when unloaded. This is also evaluated in terms of M EP and is subsequently an average torque contribution over an engine cycle. The other version of compressor is made with a clutch and is has less losses. The losses are almost constant with respect to engine speed.
Chapter 2. Model 18
The torque for the hydraulic pump, which is used to power the steering servo, is gathered from measured data. The load case that is considered in this thesis is nominal drive where no steering is done. For this case the pressure is 3-5 bars and the torque is then gathered from a Scania internal data sheet. The pressure and torque requirements are higher when steering is done at lower speeds.
Model Errors TM odel Errors is the torque that is not captured in the other torque models. This error is found by measuring the BM EP , i.e. the mean effective pressure of torque on the dynamometer and estimating IM EP which is the mean effective pressure of gas and pumping torque. The total losses in the engine i.e. F M EP is then,
F M EPmeasured= IM EP − BM EP. (2.12) The torque estimation error then becomes,
F M EPerror= F M EPmeasured− F M EPestimated. (2.13) F M EPestimated is the sum of all torque model F M EP s. The average torque error can then be found by using (2.9).
2.4 Crankshaft Dynamics Model
The crankshaft is not a completely rigid body. This means that it will flex and bend due to the different strokes of the pistons. Methods with a varying degree of complexity exist to describe the torsional behaviour the crankshaft. The torsion effect plays a big part in the estimation of CAD along the crankshaft especially when considering the accuracy needed for the next generation of control systems. The effect of the torsion is more prominent at certain engine speeds. This is due to the resonance frequencies of the crankshaft.
To capture the dynamic behaviour of the crankshaft a lumped mass model is often used.
This involves separating the engine into several masses, each with its own inertia J . These masses are then connected using dampers and spring elements. An example can be seen in fig 2.2. When using this approach the Torque Balancing Equation becomes
J(θ)¨θ + Cdθ + Kθ = T˙ gas+ Tf ric+ Tmass+ Tload. (2.14)
Chapter 2. Model 19
The Matrices K and Cd in (2.14) are the spring and damping coefficients respectively.
the postion of a spring or damper is called an element. These coefficients might be found for instance using structural mechanics. The lumped mass model for the crankshaft will have 9 DOF. There are 6 cylinders, each cylinder has its own inertia J3−9. The flywheel has its own inertia which is also the largest J9. The free end (belt drive) and torsional damper will also be modelled as separate inertias. The position where an inertia exists is called a node. Since the friction torque sometimes is approximated by viscous damping this contribution may be set to zero, depending on the application. In this thesis the lumped mass model parameters are found via a Scania torsion program.
Where the loads(torques) affect the crankshaft is also important to implement correctly.
Each component of the torque will therefore be a vector such that it only affects the correct inertia node. The approach is similar for each torque component. The gas torque is placed on each cylinder as well as the mean value of the friction relating the movement of the pistons. The oil and fuel pumps are positioned at the flywheel node together with the air compressor and hydraulic pump. The fan is placed at the free edge. The waterpump is also placed at the free end with the AC and alternator.
Lumped-Mass Model Equation (2.14) can for each node be written as for i=1,
Jiθ = C¨ i+1,i( ˙θi+1− ˙θi) + Ki+1,i(θi+1− θi), (2.15) for i=[2,...,8],
Jiθ = C¨ i+1,i( ˙θi+3− ˙θi+1) + Ki+1,i(θi+1− θi) − Ciθ˙i
−Ci,i−1( ˙θi− ˙θi−1) − Ki,i−1(θi− θi−1) + Ttot,i. (2.16)
Figure 2.2: Crankshaft dynamical model, 8 DOF, 5-cyl engine, seen in [6]
Chapter 2. Model 20
for i=9,
Jiθ = −C¨ i,i−1( ˙θi− ˙θi−1) + Ki+1,i(θi− θi−1) − Tload. (2.17)
To model the 9-DOF lumped mass model, (2.15),(2.16),(2.17), a state-space formulation is used. This is found by using the strategy implemented in Nickmehr [9]. The states are defined as the speed of each node and the angular displacement between the nodes, θi−(i−1)= θi− θi−1. Introducing these states give the state vector,
X = [ ˙θ1, ˙θ2, θ2−1, ˙θ3, θ3−2, ˙θ4, θ4−3, ˙θ5, θ5−4, (2.18) θ˙6, θ6−5, ˙θ7, θ7−6, ˙θ8, θ8−7, ˙θ9, θ9−8]T (2.19)
The input w(t, θ, ˙θ) is defined as the load on the crankshaft for each node in the form of each external torque component seen in (2.14). This will have the dimension w ∈ R9×1. For instance w9 will mean the load on the flywheel, w8will be the load on cylinder 6 and so forth. The resulting state space matrices A, B have the dimensions, A ∈ R17×17, B ∈ R17×9 . For this reason A and B can be found in the appendix. The output matrix C has the dimension C ∈ R17×17, so that each displacement and the speed at the flywheel can be calculated. The feedthrough matrix D has the same dimension as B but is made up entirely of zeros. The complete state-space becomes
X = AX + Bw(t, θ, ˙˙ θ)
Y = CX + Dw(t, θ, ˙θ). (2.20)
Rigid-Body Crankshaft A second approach to model the dynamic behaviour of the crankshaft in this thesis is to make a rigid body multi-cylinder model as made in [6].
This assumes that the crankshaft and connected parts are rigid. This is the most simple method. The resulting torque and CAD is then a strict summation of each cylinder contribution. The torque balancing equation then becomes,
Tnet=PNc
i=0(Tgas(i) + Tmass(i) + Tf ric(i) + Tload(i))
θ =¨ TnetJ . (2.21)
This is possible since the body is assumed to be rigid and therefore the phase shift from cylinder to cylinder always remain the same, 120o for a 6 cylinder engine. Nc is the number of cylinders.
Chapter 2. Model 21
2.5 Model Summary
2.5.1 Rigid-body Crankshaft approach
When the crankshaft is assumed to be a rigid body each torque component can be summed over the crankshaft. Each component then has the phase 120 degrees from each other for a 6 cylinder engine. The equations then are on the form seen in (2.21) ¨θ is then used to calculate speed and CAD according to,
xi+1= Γxi+ Φ ¨θi (2.22)
Γ, Φ are here expanded from Γ, Φ in (2.4) to suite the dimension of x i.e. the number of cylinders. The measurements from the flywheel are taken as the the current CAD at the flywheel each 6 degrees. The crankshaft speed is reset each revolution to compensate for torque model errors.
2.5.2 Lumped mass model
The crankshaft dynamics are modelled using a 9-DOF lumped mass model described by the state-space formulation in (2.20). The output of the state-space equations are taken as the speed at the flywheel and the displacements between each node. The speed at the flywheel is then integrated using (2.3). The pulses enter on the flywheel node each 6◦ degrees.
When the crank angle on the flywheel has been estimated the appropriate phase and displacement is added to each cylinder. In this way the crank angle for the cylinders also get an explicit influence of the pulse input. If the state-space had been made such that the crank angle is calculated directly the pulses would only affect the flywheel. The crank angle for a cylinder can be calculated using the simple relation,
θn= θf lywheel−
9
X
n=4
θn−(n−1)+ phasen. (2.23)
Here n is the number of the node and phasen is the phase of each node which is decided by the firing order (1-5-3-6-2-4). θf lywheel is the crank angle on the flywheel.
Chapter 2. Model 22
2.6 Induction CAD measurements
The crank-angle degree is today, as previously mentioned, measured using an Induction sensor [4]. Induction works by magnetic force acting on a current-carrying conductor.
When a conductor travels through a magnetic field it experiences a force that is per- pendicular to the magnetic field. This causes electrons to move in the conductor thus causing a current which is measured by the sensor. The CAD is measured on the fly- wheel but another sensor is often used as well. This is called the camshaft sensor. The camshaft sensor is used to measure the camshaft position 1.
With a higher speed on the flywheel a larger current will be measured. This means that the trigger level of the sensor will have to be adjusted to the rpm of the engine to trigger at the same ”relative” level of voltage. To solve this problem trigger curves exist that basically raises the trigger level linearly compared to the rpm. Another thing that influences the trigger level is the distance to the flywheel. Depending on the installation of the sensors, differences in the level of current induced might exist between engines.
Also the eccentricity of the flywheel plays a part in the distance between the sensor and the flywheel.
The measured voltage is not symmetric. It doesn’t rise as fast as it falls. The angle is triggered on the falling edge since it is the closest to the centre of the hole.
For the measurements on current engines with the common rail fuel system two sensors are used, one on the flywheel and one on the camshaft. One reason for this is to have redundant CAD sensors in case of failure since the CAD is an important measurement for the ECU. The required measurement area is 40-3500 RPM. Since the CAD is mea- sured every six degrees on the flywheel in the 60-2 pattern set up the sensor will have to manage frequencies of up to 3500*360/(60*6) = 3500 Hz.
2.7 SIMULINK model
The SIMULINK implemented model is separated into subsystems. One subsystem makes the matrix calculations described in (2.22). An other subsystem calculates each torque component from friction auxiliaries etc. Each torque contribution is calculated using a MATLAB function block.
1The camshaft is used to lift and close the valves. This is done at half the speed to give a correct phasing of the strokes. It was previously used to control the fuel injection
Chapter 2. Model 23
The model has many signals, most are ECU internal signals. Here an overview of the signals required for the model is found.
Inputs:
• Demanded torque. This is a signal of how much torque that is demanded from the engine at the flywheel.
• Rail pressure. The pressure in the common rail is required to calculate the fuel pump torque.
• Massflow of fuel through fuel pump. This signal is also used to calculate the fuel pump torque.
• Oil temperature. The oil temperature is used to adjust the friction of the engine as well as calculate the torque requirements of the oil pump.
• Cylinder pressure. This is either measured by a sensor or estimated by a model.
A heat release model is used in this thesis used to estimate the cylinder pressures.
• Manifold pressures. The intake and exhaust pressures are used to calculate the pumping work of the engine.
• The injected fuel amount is primarily used in the heat release model.
Outputs:
• CAD. The crank angle degree is the main output of the model.
• Angular velocity. The angular velocity of the crankshaft is also an important output of the system.
• Acceleration. The acceleration of the crankshaft is a signal which is also available for output.
Chapter 2. Model 24
Sensor signals Inputs
Torque Models
Estimation CAD, engine
speed Crank Angle
Engine Speed
Pressure, Pulses,
Etc. Net torque
Sensor signals
Figure 2.3: Overview of the Simulink Scheme. The sensor signals are described in the list of inputs and outputs.
Chapter 3
Experiments
To validate the models experiments have been performed. This has been done on a 6 - cylinder inline Scania engine. These experiments have been used for validation and tuning of the models described in chapter2. The experiments have been performed alongside Domenico Crescenzo, Mikael Gustafsson, Tobias Johansson, Christian Rug- land, Maryam Shojaee and which all are thesis workers on the same department at Scania. The engine specific data is presented here.
Engine DL6
Type EURO VI,
Firing sequence 1-5-3-6-2-4 each 120o Displaced Engine Volume 12,74 dm3
3.1 Experimental Setup
An overview of the experimental set up can be seen in figure 3.1. There are two main groups of measured data sets. One group is continuously sampled with a high frequency and the other is averaged data. The continuously sampled signals are CAD based and most are sampled every 0.1◦ CAD, these measurements are listed below.
• In cylinder pressure. This is measured on the 1st and 6th cylinders.
• Crank angle encoder. The CAD is measured using an optical sensor every
0.5 degrees. This means that there are 60 times more pulses than the measurements on the flywheel of a normal engine. These measurements are then interpolated to yield a
resolution of 0.1 degrees.
25
Chapter 3. Experiments 26
• Intake/Exhaust pressure.
• Rail pressure. This signal is sampled in the time domain with a frequency of 50 kHz.
• Knock sensors. These sensors are mounted on the exhaust side of the cylinder block. Two are mounted on the engine, one on cylinder 1 and one on cylinder 6.
• RPM. estimated using the time stamp of each CAD signal pulse.
This list includes the measurements which are averaged over one or several engine cycles.
• Intake/Exhaust temperatures.
• Brake torque. The produced torque from the engine is measured as an average over an engine cycle. This is measured through the dynamometer which is a large and complicated breaking system.
• NOx sensor. This sensor primarily measures the NOx but can also measure the oxygen level in the exhaust gases. This is then used to calculate Lambda (air/fuel equivalence ratio). λ is defined as the ratio between the amount of fuel injected and the air in the cylinder normalized by the stoichiometric ait/fuel ratio for the combustion.
• Oil temperature. Temperatures in the oil are measured on several positions on the engine e.g. oil sump, piston gallery and temperature differences over auxiliary components.
1 2 3 4 5 6
Crank angle encoder
Charge amplifier
In-cylinder pressure sensor
(Kistler 7061B) In-cylinder
pressure sensor (AVL GU24D) Knock sensor
Knock sensor
Cylinders
Amplifier
ECU internal
signals
Mean variables
&
recorders Test cell system
(PUMA) High frequency sampling
and processing system (Indicom) Rail pressure
sensor
Analysis Pressure pegging
Figure 3.1: Setup of Test Cell, compliments of Tobias Johansson
Chapter 3. Experiments 27
Load [%]
Speed [RPM]
0 25 75 100
50
800 1000 1200 1600 1900 2000
Figure 3.2: Stationary operating points
Some signals are model based and are calculated in the ECU. These signals are available and can be saved alongside the other data sets. These are listed below.
• Estimated fuel injected.
• SOI.
• SOC.
• Amount of fuel injected in main and pilot injections.
3.2 Experimental procedure
The test were divided into stationary operating points, dynamic ramps.
Stationary operating points A total of 36 operating points will be tested. Each operating point is defined by an engine speed and an engine load. Each load is tested for each speed.
The operating points can be seen in figure, 3.2. The experiment will be conducted so that one starts in a high load and speed. Then the speed is decremented from the highest
Chapter 3. Experiments 28
to the lowest speed. Then the load case is decremented one step and the speed is varied as before. This is then repeated until all operating points in3.2 have been tested.
For each operating point the engine is stabilized when the exhaust gases have reached a steady state temperature. After this the measurements are performed on approximately 50 engine cycles. This process takes around 5 min.
Dynamic ramps The ramps are performed in speed and in load. The ramp is performed by ramping either the load or speed from a fixed operating point. Each ramp is repeated three times. The tests cases are,
• Constant load, ramp in speed. This is made for a constant load of 50%, 75% and 100%. The starting speed is 1200 and the slope of the ramp is 40 RP M/s over 5 seconds.
• Constant speed, ramp in load. The speed is kept constant at 800, 1200, 1500 RPM.
The load is ramped with 100 N m/s over 5 seconds. The starting load is 50%.
Adjusted SOI During these tests the engine load 75% is kept constant. The tests are made for two engine speeds, 1200 RPM and 1900 RPM. For these two cases the fuel injection timing is changed between 0, ±2, ±10 CAD.
Chapter 4
Results and Discussion
The results are presented for the pressure sensor model (PS), the heat release pressure model (HRP), the rigid crankshaft torque model which is also based on the pressure sensor. These are compared with the linear extrapolation of speed from the pulses of the flywheel (2.5).
4.1 Validation of Accuracy
The accuracy of the suggested model is validated through experimental data aqcuired in experiments , see Chapter 3for details. The data is used to validate the crank angle and engine speed estimations as well as the torque-submodels accuracy.
The importance of having an accurate measure of the crank angle is displayed in the other theses in the CLCC group. See Johansson [15] and Rugland [16] for argumentation of this fact.
4.1.1 Torque Estimations
The torque loss models in Chapter 2 are validated using measurement data. The total F M EP of the engine is estimated for each stationary operating point. The correspond- ing model F M EP is used to find the torque estimation error for each operating point, see the section on model errors in Chapter2. By taking the average value of the torque variations in the error over an engine cycle some information is lost. The fast error dynamics is assumed to be captured in the engine speed and CAD estimation errors.
There is a lot of variation in the torque estimation model error over the engine speed and load range but a trend of increasing error at lower speeds can still be seen. Figure
29
Chapter 4. Results and Discussion 30
RPM
800 1000 1200 1400 1600 1800 2000
Relative error %
Relative Torque estimation error as function of speed 100%
75%
50%
25%
0%
Motored
RPM
800 1000 1200 1400 1600 1800 2000
Relative error %
Relative Torque estimation error as function of speed
100%
75%
50%
25%
Figure 4.1: Comparison of relative Torque loss model accuracy. It is done both for the estimated losses error normalized by the measured losses, TF M EP err.
TF M EP measured
seen in the left plot. In the right plot the errors are instead normalized with the demanded
torque. TF M EP err.
TDem.T q. .
4.1 show the tendency of the model to have especially low performance at low engine speeds i.e. ≤ 1200 rpm. It can be noted that this also corresponds to when the engine produces the most torque. Even if the largest errors are considered as outliers the overall performance of the models produce quiet poor results. Note that the relative error is in relation to the measured losses on the engine. In relation to the demanded torque the error is still small. In conclusion the accuracy of the torque models for auxilliary units and friction is low.
The fuel pump is perhaps the one auxilliary unit which demands the most torque to run especially for high loads. For this reason a more accurate model is investigated for two operating points to see if it yields better results. This fuel pump model includes the strokes of the pistons and has been taken from an internal Scania document. The results for the operating point with and without this improved model for the operating point 100% load, 2000 RPM and 50% load, 1000 RPM are shown in 4.2. Note that this is engine speed without using the linear extrapolation each six degrees to amplify differences. For the high load and high engine speed the difference in engine speed is not noticeable. For the lower RPM and load however there is a difference which can easily be seen. This suggests that the fuel pump might be a contributing reason to why the engine loss models produce so poor results at lower RPMs.
Another aspect of the torque that might be considered to have some inaccuracies is the HRP model. To validate how accurate this model is over the operating points a similar approach as for the engine losses. In Figure4.3 the pressure of the HRP pressure trace is compared to the pressure from the pressure sensor. It can be noted that during the gas exchange the difference is small and will therefore not have a large impact on the torque. However near TDC the estimation is a bit off and this will cause the estimation of the torque generated from the cylinders to be off. This will lead to a drift in the
Chapter 4. Results and Discussion 31
CAD
RPM
Accurate FP model FP model
CAD
RPM
RPM With and without accurate fuel pump model Accurate FP model FP model
Figure 4.2: Comparison of engine speed estimation with and without an accurate fuel pump model. Left is for the operating point 2000 RPM 100% load and the right is the operating point 50% load and 1000 RPM. Red is with the more accurate fuel pump
model. Blue is with the simpler fuel pump model.
engine speed as mentioned before. The HRP model is however not calibrated for the specific engine setup used to acquire test cell data.
CAD
0 100 200 300 400 500 600 700 800
Bars
0 50 100 150 200
250 Comparison of Pressure sensor and HRP model
PS HRP
Figure 4.3: Comparison between the pressure sensor, PS, and the heat release mod- elled pressure, HRP. Operating point 100% load 1200 RPM. Note: HRP model was not
calibrated to test engine.
4.1.2 Torsion-model
The lumped mass torsion model described in2.4is compared to a internal Scania torsion simulation program, this will be refered to as the ”torsion simulation program”. Since torsion is such a complicated phenomena lots of time and effort could be spent on evaluating the torsion model in terms of accuracy for each cylinder and operating point and the accuracy of the speed prediction for each node. The torsion estimation is displayed for the operating points 100%, 25% load and 1000, 2000 RPM, these are seen
