for the model adaptation, the model predicts the valve response sufficiently accurately. Keywords: solenoid valve modelling, model validation, simulation-based ...
Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering http://pii.sagepub.com/
Modelling and validation of a fast switching valve intended for combustion engine valve trains J Pohl, M Sethson, P Krus and J-O Palmberg Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 2002 216: 105 DOI: 10.1243/0959651021541462 The online version of this article can be found at: http://pii.sagepub.com/content/216/2/105
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105
Modelling and validation of a fast switching valve intended for combustion engine valve trains J Pohl*, M Sethson, P Krus and J-O Palmberg Fluid and Mechanical Engineering Systems, Linko¨ping University, Linko¨ping, Sweden
Abstract: In recent years much research has been done in the area of variable-valve actuation in order to improve the eYciency of combustion engines. Currently, a number of diVerent concepts for variable-valve actuation are under development or at a prototype stage. Hydraulic actuation has been an obvious candidate, but the lack of suYciently fast switching valves with appropriate owrates has been the major shortcoming. Design of such highly dynamic systems requires accurate models of the actual included components. In this paper a model of a fast 2/2 switching valve is presented, where both the magnetic path as well as the spool assembly are modelled. The model presented here is primarily aimed at system simulations; therefore it has to be kept simple with the number of parameters low. Some of the parameters are often hard to obtain, especially when it comes to magnetic material properties. In this study, an optimization strategy has been utilized in order to parameterize the model against measured data. However, even for major deviations from the operational point used for the model adaptation, the model predicts the valve response suYciently accurately. Keywords: solenoid valve modelling, model validation, simulation-based optimization, twomicrophone method
NOTATION a Aä A, B, C, D b l B C q D p F H i k s l L, L 0 L l m N p q r
sonic velocity (m/s) air gap area (m2) four-pole elements viscous friction coeYcient (N s/m) magnetic ux density ( V s/m2) discharge coeYcient pump displacement (m3) various forces (N ) magnetic eld intensity (A/m) current (A) mechanical spring stiVness (N/m) length (m) inductance (H ) position-dependent inductance (H/m) spool mass ( kg) number of turns pressure (Pa) oil ow (m3/s) pipe radius (m)
The MS was received on 15 November 2000 and was accepted after revision for publication on 11 October 2001. * Corresponding author: Fluid and Mechanical Engineering Systems, Linko¨ping University, S-581 83 Linko¨ping, Sweden. I08100 © IMechE 2002
R t T w V s x xÇ Z
resistance (¿) time (s) time constant (s) area gradient (m) supply voltage ( V ) valve position (m) valve speed (m/s) impedance ( N s/m5)
á â e è í 0 r ö ö
constant compression modulus (Pa) oil viscosity (N s/m2) permeability mass density of uid (kg /m3) jet angle rotational frequency (rad/s)
1
INTRODUCTION
One of the main goals in today’s combustion engine design is to decrease the engine’s overall fuel consumption. The eYciency of the combustion engine is governed by mechanical, combustion and volumetric eYciency, while all three are inuenced by the gas exchange process. Proc Instn Mech Engrs Vol 216 Part I: J Systems and Control Engineering
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J POHL, M SETHSON, P KRUS AND J-O PALMBERG
In today’s car engines, one or several camshafts act on the intake and exhaust valves commonly to accoplish gas exchange. The valve openings and closings, as well as the valve lifts for such systems, are xed and unchangeable. The valve timing and lift that are optimal for an engine’s top-end performance, high lift and long overlap between the intake and exhaust events are diVerent from those required for fuel economy at part load [1]. Fully variable-valve actuation means that the valve events and lifts for both intake and exhaust valves can be varied independently and that valves can even be deactivated. This constitutes the most exible valve actuation system conceivable. When the valve events (valve opening and closing) can be chosen dependent on the point of operation, variable-valve actuation bridges the gap between idle stability and full-throttle torque. Today numerous variable-valve train systems are under development or at a prototype stage. These systems fall into three diVerent categories, namely camshaft-based add-on systems with at least two cam lobes per valve, electromechanical systems with electro-
Fig. 1
magnetic actuators [2] and thirdly electrohydraulic valve train systems. The valve train system presented here consists of a hydraulic piston which is mounted directly on to the engine’s valve stem. In Fig. 1 there is one system for the inlet valves and one for the outlet valves. As inlet and exhaust valves usually open against diVerent cylinder pressures, the inlet and exhaust valve trains may not be fully identical in terms of component sizing. In order to be able to dimension these systems properly, a good knowledge of the load proles for inlet and exhaust valve actuation is necessary. It is opportune to study the valve train systems together with an engine model as the valve opening, i.e. valve lift, duration and timing in turn strongly inuence the cylinder pressure. This engine model should be as simple as possible, since it is the cylinder pressure that is mainly of interest and not the temperature or emissions (see reference [3] for further references). The valve train system works as follows. The oil ow is controlled by a hydraulic main stage working as a ow amplier since the ow capacity of the solenoid valves
Schematic of an electrohydraulic valve train system. The high- and low-pressure switching valves are operated to initiate the down- and upwards strokes respectively. (From reference [3])
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I08100 © IMechE 2002
MODELLING AND VALIDATION OF A FAST SWITCHING VALVE
is itself not suYcient. This main stage can be omitted if fast switching valves with suYcient ow capacity are developed in the future. In this respect, the valve train system presented constitutes a very exible solution. A valve opening is initiated by the high-pressure solenoid valve, so that the main stage is switched to its lower position. In this manner, the A and B ports of the hydraulic piston will be connected and oil can ow from the high-pressure side through the lower piston chamber into the upper piston chamber. As a consequence, the engine valve moves downwards. After approximately half the stroke length the piston cuts the oil supply from the high-pressure side and a connection to the low-pressure side is established (see Fig. 1). Due to the valve’s inertia, the valve will continue its downwards journey until the kinetic energy has been used to draw oil from the low-pressure side into the upper piston chamber. During the entire downwards stroke, oil from the highpressure side ows through the check valve. The advantage with this type of valve train system is that due to the check valve the hydraulic piston remains in the extended position regardless of the stage of the solenoid valves. In this manner, the engine valve’s movement is only initiated by the solenoid valve, which may be activated for longer than the actual engine valve stroke. Thus the closing characteristic of the solenoid valve is not a critical parameter. Closure of the valve is initiated by the low-pressure switching valve, which makes the main stage move into the upper position. The B port is connected to the tank while the C port is connected to the supply pressure; the engine valve is closed. At an early design stage it is common industrial practice to build a prototype of the entire system in order to gain information for the subsequent concept selection procedure. This can be both costly and time consuming. Hydraulic valve trains are diYcult to evaluate analytically due to their highly dynamic nature. Using an approach called simulation driven experiments [3], it is possible to identify components that might jeopardize a proper system function early in the concept evaluation phase. These components are then studied in separate tests and simulation models are made and validated against measurements. This results in a number of minor prototypes instead of one single prototype system. In this manner both design cycle time and development cost are reduced, but on the other hand an accurate component model that has been validated by measurements is needed. This paper focuses on modelling of a 2/2 switching valve that could be used in electrohydraulic valve trains. A drawing of this valve can be seen in Fig. 2. A model of a solenoid valve is indispensable not only for the development of control strategies but also when it comes to system design. The model must therefore handle accurately the mechanical components in the valve as well as uid ow characteristics. I08100 © IMechE 2002
Fig. 2
107
Drawing of the 2/2 switching valve used in this study. The valve was originally designed by FWM (Feinmechanische Werke Mainz). (By courtesy of Mannesmann Rexroth AG, Germany)
The solenoid of such an electrohydraulic valve represents an electromechanical interface, where the electric current is transformed into a magneto-motive force acting on a spool. Modelling of the elctromagnetic conversion process is often regarded as the major obstacle as it is highly non-linear and very much dependent on the ferromagnetic material used. Several authors have treated modelling of solenoid valves. Vaughan and Gamble [4 ] present a model that requires measured or given model parameters. Each energy conversion process is described by a set of equations whose parameters are obtained by curve-tting techniques. The result is a very accurate model with a comparatively large amount of parameters. Such a high degree of accuracy is surely required to predict the static and dynamic characteristics of proportional valves, but may be unnecessary for a 2/2 switching valve. In Sethson and Vaughan [5] a similar approach was presented, using a mathematical model for the hysteresis eVects. That model still required parameters to be tted to measurements. Both Gamble and Sethson showed the diYculties in modelling the hysteresis eVect in the magnetic path. In this paper a comparatively simple valve model with a restricted amount of model parameters is proposed. Great attention was paid to the fact that all parameters have a physical meaning and therefore can be measured directly or can be obtained from material data sheets. As this model is mainly intended for use in dynamic simulation systems, a lumped modelling approach was preferred to the nite element based approaches. As a consequence, the ne tuning of model parameters is indispensable. Such a ne tuning can preferably be done using optimization. In order to validate the valve model, the oil ow in the measurement pipe was calculated with the help of the two-microphone method [6 ]. This method relies on a description of a measurement pipe in the frequency domain and calculates the oil ow at both ends of the pipe from the corresponding pressure signals. The pressures can be obtained using dynamic pressure sensors at Proc Instn Mech Engrs Vol 216 Part I: J Systems and Control Engineering
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the ends of the pipe. In this manner, the simulated oil ow could then be compared with the ow estimated by the two-microphone method.
2
was taken as a model parameter. Figure 5 shows the simplest model of a solenoid, which is an inductor in series with a resistor. The voltage over the coil with inductance L and resistance R can then be written as [4] di dL V =V +V =iR +L +i s R L dt dt
THE VALVE MODEL
The valve model can be separated into two distinct parts, namely the solenoid itself with its electromagnetic equations and the mechanical part, consisting of a spring– mass system. The uid ow properties are accurately described by the orice equation for turbulent ow. That will be presented in the following equation sets. Figure 3 shows the principle of the model, from input voltage to output ow. The intermediate state variables are also included.
(1)
In equation (1) the time dependency of the inductance is included. This is necessary, as the coil in the solenoid moves under operation, which will change the inductance. Here the inductance is modelled as a linear function of the coil displacement: L =L +L x 0 1 dL =L xÇ 1 dt (2)
2.1 Solenoid model The solenoid model has to handle the transformation of an applied input voltage to an electromagnetic force on the spool of the valve, covering all the intermediate system states. Material properties such as hysteresis and saturation have been shown to be important in solenoid modelling (see references [4] and [5]). However, treatment of these material properties in lumped solenoid models is a problem, which is often circumvented by introducing an energy storing and an energy dissipating part of the inductor current (see reference [7]). In this way the material behaviour is captured by a rather simple equation set, which still has a large number of parameters to identify. Identication is often done under xed air gap operation; i.e. the spool is xed in certain positions and measurements of the magnetic characteristics are performed without any movement of the spool. Unfortunately, it was not possible to implement this scheme in the present project for practical reasons (see Fig. 2). In this work the hysteresis model of Tellinen [8] is used. This model constitutes a set of diVerential equations with the actual materials hysteresis loop used as a parameterized input data set. As this data set was unknown for the spool material used, the saturation eld strength (the width of the hysteresis loop) (see Fig. 4)
Fig. 3
Principle of the model outline for the switching valve with intermediate state variables
The state variable x represents the coil displacement. Using the current i, the magnetic eld strength H can be calculated as H=
N i l
(3)
The coil is represented by the number of turns, N, and its magnetic path length, l. The magnetic ux density B can be obtained from the hysteresis model [8] and some material data [9]. In the hysteresis model the state of the magnetization and its derivatives is taken into account:
C
D
C
D
B (H )b dB dB h+ (H ) í hÕ =í + 0 B (H )B (H ) dH 0 dH h+ hÕ for dH>0 bB (H ) dB dB h+ hÕ (H ) í =í + 0 B (H )B (H ) dH 0 dH hÕ h+ for dH
