A Dynamic Model of an Electropneumatic Valve Actuator for Internal Combustion Engines Jia Ma Delphi Powertrain Systems, This paper presents a detailed model of a novel electropneumatic valve actuator for both Auburn Hill, MI 48326 engine intake and exhaust valves. The valve actuator’s main function is to provide vari- e-mail: [email protected] able valve timing and variable lift capabilities in an internal combustion engine. The pneumatic actuation is used to open the valve and the hydraulic latch mechanism is used to hold the valve open and to reduce valve seating velocity. This combination of pneu- Guoming G. Zhu matic and hydraulic mechanisms allows the system to operate under low pressure with an e-mail: [email protected] energy saving mode. It extracts the full pneumatic energy to open the valve and use the hydraulic latch that consumes almost no energy to hold the valve open. A system dynam- Harold Schock ics analysis is provided and followed by mathematical modeling. This dynamic model is e-mail: [email protected] based on Newton’s law, mass conservation, and thermodynamic principles. The air com- pressibility and liquid compressibility in the hydraulic latch are modeled, and the dis- Michigan State University, continuous nonlinearity of the compressible flow due to choking is carefully considered. East Lansing, MI 48824 Provision is made for the nonlinear motion of the mechanical components due to the physical constraints. Validation experiments were performed on a Ford 4.6 l four-valve V8 engine head with different air supply pressures and different solenoid pulse inputs. The simulation responses agreed with the experimental results at different engine speeds and supply air pressures. ͓DOI: 10.1115/1.4000816͔

Keywords: automotive systems, powertrain systems, camless valve actuation, hydraulic and pneumatic system model

͑ ͒ 1 Introduction of carbon monoxide CO and NOx emissions was obtained. Urata et al. ͓5͔ also showed that the operational range of a homoge- In a camless valvetrain, the motion of each valve is controlled neously charged compression ignition ͑HCCI͒ engine can be ex- by an independent actuator. There is no camshaft or other mecha- panded to both high and low load ranges through the adoption of nisms coupling the valve to the crankshaft as in a conventional VVT and VVL. The advantages of VVT and VVL engines lead to valvetrain. This provides the possibility to control the valve combustion optimization over a broad engine operational range. events, i.e., timing, lift, and duration, independent of crankshaft For example, Trask et al. ͓6͔ developed the VVT and VVL opti- rotational angle. Various studies have shown that an engine with mization methodologies for an I4 2.0 l camless ZETEC engine at variable valve actuation reduces pumping losses, adjusts the various operational conditions including cold starts, cylinder de- cycle-to-cycle internal residual gas recirculation ͑RGR͒, and re- ͑ ͒ activation, full load, idle, and transient operations. duces nitrogen oxide NOx emissions with improved perfor- Three primary types of camless valve actuators are electromag- mance over a wide operating range. netic, hydraulic, and pneumatic actuators. Sugimoto et al. ͓7͔, A significant amount of research has been contributed to dem- Theobald et al. ͓8͔, and Pischinger and Kreuter ͓9͔ presented the ͑ ͒ onstrate the advantage of variable valve actuation VVA over the results of electromagnetic actuators. A hydraulic actuator was dis- traditional cam-based valvetrain for both gasoline and diesel en- cussed in Ref. ͓10͔. A pneumatic actuator incorporated with a gines. The investigation of intake valve timing control of a spark permanent magnet control latch was presented in Ref. ͓11͔. The ͑ ͒ ͓ ͔ ignited SI engine was conducted in Ref. 1 . It was found that at advantages and disadvantages of a pneumatic actuator over a hy- low and partial load conditions, engine pumping loss was reduced draulic actuator were addressed in Ref. ͓12͔, where a pneumatic by 20–80% due to throttless operation. Fuel consumption was valve actuator with a physical motion stopper was presented and improved up to 10% at idle. Through simulation and experiments, the simulations of the valve actuation system were shown. Imple- Negurescu et al. ͓2͔ showed that SI engine efficiency can be im- mentation of various camless valve actuators was studied in ͓13͔. proved up to 29% due to variable valve timing ͑VVT͒, compared In order to provide an insight to the pneumatic actuator design with a classic throttled engine. The engine torque output was also and its control requirements, mathematical modeling was per- improved by up to 8% at low speed with wide open throttle. formed to the engine and its various actuation systems. A variable Research carried out in Ref. ͓3͔ demonstrated how VVT and valve timing engine was modeled in Ref. ͓14͔, along with its variable valve lift ͑VVL͒ affect the partial load fuel economy of a engine control strategy. Tessler et al. ͓15͔ analyzed and modeled light-duty diesel engine. In this study, the indicated and brake- the dynamics of a pneumatic system consisting of a double-acting specific fuel consumptions were improved up to 6% and 19%, or single-acting cylinder and servo valve. A mathematical model respectively. The operation of an Otto–Atkinson cycle engine by of a pneumatic force actuator was presented in Ref. ͓16͔. late intake valve closing to have a larger expansion ratio than In this article, an electropneumatic valve actuator ͑EPVA͒ is compression ratio was studied in Ref. ͓4͔. A significant reduction employed to replace the traditional camshaft in an internal com- bustion engine. The EPVA is capable of varying valve lift, timing, and opening duration as desired in a variable valve timing engine. Contributed by the Dynamic Systems Division of ASME for publication in the Different from the pneumatic valve discussed in Ref. ͓12͔, the JOURNAL OF DYNAMIC SYSTEMS,MEASUREMENT, AND CONTROL. Manuscript received November 15, 2008; final manuscript received November 20, 2009; published online EPVA is designed to extract the maximum work from the air flow February 3, 2010. Assoc. Editor: Bin Yao. by incorporating a hydraulic latch mechanism to hold valve open

Journal of Dynamic Systems, Measurement, and Control MARCH 2010, Vol. 132 / 021007-1 Copyright © 2010 by ASME

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms Fig. 1 System dynamics at the air charging stage Fig. 2 System dynamics at the expansion and dwell stage

and to reduce the power consumption; a hydraulic damper mecha- nism is also enabled to produce a desirable slow and smooth seat- now charges the cylinder, the actuator piston starts moving down ing velocity when the valve returns to its seat. It has been shown and opens the poppet valve. Although the right side of the outlet that less than 4 kW power was required at 6000 rpm to run a 16 port valve is subject to the high pressure air, it remains closed due valve 2 l turbocharged four-cylinder engine ͓17͔. This is well in to the area difference between the two sides of the port valve. The line with the electromagnetic valve systems and well below the on and off valve S1 is deactivated at the moment when solenoid 1 hydraulic ones. Nonlinear mathematical model was developed in is energized. This only allows the oil to flow down through the this paper to help establish the design and control criteria and to check valve parallel to S1 and prevents the oil from returning to be used as a base to develop a control oriented model required for the reservoir. Note that the oil supply pressure is the same as the model-based control strategy development. air supply pressure. This paper is organized as follows. System dynamics is de- 2.2 Expansion and Dwell Stage. In the expansion and dwell scribed in Sec. 2, and a mathematical model is developed compo- stage as shown in Fig. 2, both solenoids 1 and 2 are energized. nent by component in Sec. 3. The experimental validation of the The time delay between the activation of two solenoids is usually developed model is provided in Sec. 4. Finally, conclusions are chosen between 2 ms and 5 ms depending on the desired valve lift drawn in Sec. 5. height. The spool valve 2 is pushed slightly to the left so that the 2 System Dynamics high pressure air can be sent to the left of the inlet port valve through the same spool valve. The on and off valve S2 is closed at The EPVA consists of two solenoids, two spool valves, two port the same time when solenoid 2 is energized to prevent the high valves, an actuator piston, an actuator cylinder, and a hydraulic pressure air from escaping to the atmosphere through the first latch-damper system. An actuator piston pushes the back of the spool valve. The inlet port valve is closed mainly due to the spring engine poppet valve stem, causing the valve to open. Solenoid- force applied on the inlet port valve, which cuts off the air supply controlled spool valves are used to control the flow of the air that to the piston cylinder. Meanwhile, solenoid 1 remains energized; enters and exits the actuator cylinder. In order to reduce the en- therefore, the outlet port valve remains closed. The air that was ergy consumption, EPVA uses a hydraulic latch, which allows the drawn into the actuator cylinder during the previous ͑air charging͒ actuator to extract the full expansion work out of the air that is stage is able to expand completely. The actuator piston and poppet drawn into the actuator cylinder. Meanwhile, the actuator is still valve both reach their maximum displacement. The high pressure ͑ ͒ ͑ capable of holding the valve open over the desired opening dura- oil dark gray trapped in the hydraulic latch on and off valve S2 tion. A hydraulic damping mechanism is added to provide a soft remains closed͒ balances the valve spring force and keeps the seating velocity for the valve. According to the events taking poppet valve open at its maximum lift height. This is called the place in the actuator cylinder, the system dynamics are divided energy saving mode. It allows the system to extract the full ex- into three stages: air charging, expansion and dwell, and air dis- pansion work from the air, which has entered the cylinder without charging stages. Figure 6 illustrates three stages over the valve lift losing the capability of varying the valve open duration. profile. 2.3 Air Discharging Stage. In the air discharging stage, the 2.1 Air Charging Stage. Figure 1 depicts the system dynam- air leaves the actuator cylinder and the valve returns to its seat. As ics when the actuator cylinder is operated at the air charging stage. displayed in Fig. 3, both solenoids are de-energized. Conse- The light gray color represents the high pressure ͑supply pressure͒ air, the white color represents the low pressure ͑atmospheric pres- sure͒ air, and the dark gray color represents the oil in the hydraulic latch damper. S1 and S2 are two on and off valves controlled by solenoids 1 and 2 through their mechanical linkages to the corre- sponding spool valves 1 and 2, respectively. Each controlled on and off valve is parallel to a check valve, see Fig. 1. When a solenoid is energized, its corresponding on and off valve is closed, and when the solenoid is deactivated, the on and off valve is tune on to allow two-way flow. An energized solenoid is shown in black while a de-energized one is transparent. During the charging stage, solenoid 1 is energized pushing the spool valve 1 slightly to the right. As a result, the high pressure air is sent to two locations, the left of the outlet port valve and the right of the inlet port valve. The left side of the inlet port valve is subject to the low pressure. Therefore, the high pressure air closes the outlet port valve and opens the inlet port valve. The supply air Fig. 3 System dynamics at the air discharging stage

021007-2 / Vol. 132, MARCH 2010 Transactions of the ASME

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms constant. The difference between the cylinder pressure and the supply pressure decreases as the pressure in the cylinder chamber builds up over time. The air then becomes unchoked and flows through the inlet with decreasing pressure. The flow exiting the outlet switches between a choked and an unchoked pattern as well for the same reason. This discontinuous nonlinearity of the flow has to be taken into consideration in the actuator piston model. As shown in Fig. 4, considering the control volume above the actuator piston in the cylinder chamber including the inlet and outlet, the first law of thermodynamics can be written as Eץ v2 v2 Q˙ − W˙ + m˙ ͩh + i ͪ − m˙ ͩh + e ͪ = ͑1͒ tץ i i 2 e e 2

where Q˙ and W˙ are the heat transfer rates into the control volume and the work rate delivered by the control volume to the actuator piston, respectively; m˙ i and m˙ e are the mass flow rates entering ˙ ˙ and exiting the control volume; hi and he are the enthalpies of the tץ/Eץ ,gas entering and exiting the cylinder chamber; and finally is the rate of change of the control volume total energy. The rate of the work done W˙ on the actuator piston by the control volume is ˙ ͑ ͒ W = ApPpy˙ 2

where Ap is the area of the actuator piston, Pp is the pressure of the control volume ͑the pressure applied on the actuator piston͒, and y˙ is the velocity of the actuator piston movement. Fig. 4 Actuator piston model The supply air entering the cylinder chamber from the inlet can be viewed as a gas from a reservoir. The gas in the reservoir has zero velocity; therefore, its enthalpy is the stagnation enthalpy of h quently, both on and off valves, S1 and S2, are activated. the inlet supply air in. Modeling the air leaving the cylinder Both air and the oil flows are able to travel in two directions. chamber is simplified by considering the case that the pressure is Since both solenoids are off, the springs inside the two spool balanced and the dynamics during the pressure balancing is ig- valves return the spools to their original positions. The high pres- nored. In this case, the air leaving the cylinder chamber from the sure air is then sent to both sides of the inlet port valve. The port outlet can be viewed as a gas leaving a reservoir, which is the valve remains closed mainly due to the spring force. Meanwhile, control volume inside the chamber. Hence, the enthalpy of the air the low pressure air is applied on both sides of the outlet port leaving the chamber can be represented by the stagnation enthalpy valve. Since the oil in the hydraulic latch is now able to flow back of the air in the actuator cylinder hp: up to its reservoir, the actuator piston returns to its rest position v2 due to the valve spring force. The spring force pushes the actuator i ͑ ͒ hi + = hin = CpTin 3 piston as well as the poppet valve back and the volume of the air 2 in the actuator cylinder is then reduced. This results in an increase in the air pressure in the actuator cylinder and an increase in the v2 h + e = h = C T ͑4͒ air pressure at the right side of the outlet port valve. Therefore, the e 2 p p p outlet port valve is pushed open, the air in the actuator cylinder is able to discharge, and its pressure decreases immediately. The Treating air as an ideal gas leads to poppet valve continues on its return course. The hydraulic damper P = ␳ RT ͑5͒ activates when the poppet valve moves close to its seat. Due to the p p p decreasing flow area where the oil leaves the passage, the velocity Replacing Tp in Eq. ͑4͒ by Pp /R␳p results in of the valve is reduced greatly, providing a smooth return. v2 C P h + e = p p ͑6͒ e ␳ 3 Mathematical Modeling 2 R p The purpose of this section is to derive governing equations of where Tin and Cp are the temperature of the air at the inlet, which the individual components of the pneumatic-hydraulic valve ac- equals to the ambient temperature Tatm=295 K, and the specific tuator, which consists of the actuator piston, the hydraulic latch heat of the air at constant pressure, respectively; R and ␳p are the damper, the inlet and outlet port valves, two solenoids, and two gas constants of the air and the density of the air in the cylinder spool valves, as displayed in Fig. 1. These equations were used to chamber above the actuator piston; and Pp and Tp are the pressure model the behavior of the valve under different sets of operating and temperature of the air in the cylinder chamber above the ac- conditions. tuator piston. 3.1 Actuator Piston. In this subsection, energy conservation, In order to derive the equations for the mass flow rate when the mass conservation, and Newton’s second law were used to deter- air flow enters the inlet or leaves the outlet, two cases are consid- mine the following variables: the rate change of the gas pressure ered, and they are choked and unchoked gas flows. The proof of ͓ ͔ ˙ the derivation of the mass flow equation is shown in Ref. 15 . inside of the cylinder chamber Pp, the rate change of the gas The following are the two main assumptions: ͑a͒ the gas flow in ␳˙ ¨ density p, and the acceleration of the actuator piston y, see Fig. 4. ͑ ˙ ͒ ͑ ͒ A sudden reduction in pressure occurs at the inlet port when it the valve actuator is adiabatic Q=0 and b the flow is isentropic opens. This causes the air flow to expand in an explosive fashion. everywhere except across normal shock waves. Also a term pro- The flow is choked and the pressure at the port is assumed to be portional to W˙ is subtracted from the total power that is delivered

Journal of Dynamic Systems, Measurement, and Control MARCH 2010, Vol. 132 / 021007-3

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms ͓ ͔ to the actuator piston to compensate the heat loss 16 . 1 k3P3 P˙ = ͫC A ͑w͒P ␥ ͱk3RT − C A ͑z͒␥ ͱ p ͬ The flow pattern at the inlet depends on the cylinder pressure p din in supply in in dout out out ␳ Apy p Pp and the supply pressure Psupply. Applying the compressible flow equation yields the expression for the mass flow rate at inlet P y˙ ␣ p ͑ ͒ ˙ − pk 18 mi as follows: y k where C and C are the flow discharge coefficients at the inlet ˙ ␥ ͱ ͑ ͒ din dout mi = in PsupplyAin 7 and outlet, respectively; ␣ is multiplied by the rate change of RTin p ˙ Ͼ work W as it is assumed that part of the work is dissipated as heat For the unchoked case, where Pp 0.53Psupply based on the re- ␣ sults from Refs. ͓15,16͔, loss from the system. Parameter p is chosen to be between 0 and 1 depending on the actual heat loss during the process. This for- / / / ͓ ͔ 2 P k+1 2k P 1−k k 1 2 mulation is studied in Ref. 16 . ␥ ͱ ͩ p ͪ ͫͩ p ͪ ͬ ͑ ͒ in = −1 8 Applying the law of mass conservation to the control volume k −1 Psupply Psupply above the actuator piston in the cylinder results in Յ and for the choked case, where Pp 0.53Psupply, ͑␳ ␳ ͒͑͒ m˙ i − m˙ e = Ap py˙ + ˙ py 19 ␥ = 0.58 ͑9͒ in Replacing m˙ i and m˙ e by Eqs. ͑7͒ and ͑11͒ leads to the expression / for ␳˙ , Note that k=Cp Cv is the specific heat ratio, where Cv is the p specific heat of air at constant volume. A is the area of the inlet. in 1 k Since the port valves open and close at a very fast rate, the effec- ␳˙ = ͫC A ͑w͒P ␥ ͱ − C A ͑z͒␥ ͱkP ␳ ͬ p A y din in supply in RT dout out out p p tive flow area Ain is approximated by p in ␳ ␲r2, w Ͼ 0 py˙ ͭ 1 ͮ ͑ ͒ − ͑20͒ Ain = , 10 y 0, w =0 Now the acceleration of the actuator piston y¨ can be obtained by where r is the inner radius of the inlet port valve and w is the 1 applying Newton’s second law, see below: displacement of the inlet port valve, see Fig. 7. The mass flow rate ͑ ␦ ͒ ͑ ͒ m˙ e equation can be derived as follows: My¨ + Cfy˙ + Kp y + p = ApPp + AcapPoil − Ap − Acap Patm

ͱ k M = M + M + 1 M + M ͑21͒ ␥ ͑ ͒ piston valve spring cap m˙ e = out PpAout 11 3 RTp where Mpiston, Mvalve, Mspring, and Mcap are the mass of the actua- Ͼ For the unchoked case, where Pout 0.53Pp, tor piston, intake valve, valve spring ͑the effective spring mass equals one-third of the total spring mass, see Ref. ͓18͔͒, and the 2 P ͑k+1͒/2k P ͑1−k͒/k 1/2 ␥ ͱ ͩ outͪ ͫͩ outͪ ͬ ͑ ͒ cap on the top of the valve stem; Acap is the area of the cap on the out = −1 12 ␲ 2 ␲ 2 k −1 Pp Pp top of the actuator piston stem; Ap = rp − roil is the actuator pis- Յ ton area, where rp and roil are the radius of the actuator piston and and for the choked case, where Pout 0.53Pp, oil passage; Cf is the damping coefficient approximating the en- ␥ ͑ ͒ ergy dissipation due to the friction; and finally K and ␦ are the out = 0.58 13 p p stiffness and preload of the valve spring. Here, Aout is the area of the outlet. It follows the same expression Rearranging Eq. ͑21͒ results in as Ain except that it is dependent on z. The Aout expression can be 1 approximated as follows: ͓ ͑ ͒ ͑ ␦ ͔͒ y¨ = ApPp + AoilPoil − Ap + Aoil Patm − Cfy˙ − Kp y + p ␲ 2 Ͼ M r2, z 0 A = ͭ ͮ ͑14͒ ͑22͒ out 0, z =0 Note that for exhaust valves, there is an additional force Fp due to where r2 is the outer radius of the outlet port valve and z is the in-cylinder pressure: displacement of the outlet port valve, see Fig. 8. ͑ ͒ The rate change of the total energy of the control volume is the Fp = AexhPcyl 23 summation of the rate change of the internal energy, the kinetic where Aexh is the area of the exhaust valve and Pcyl is the in- energy and the potential energy. The kinetic and potential energies cylinder pressure. Incorporating F into Eq. ͑22͒, the acceleration of the control volume are negligible. Hence, the rate change of the p of the actuator piston y¨ becomes total energy is approximated as the rate of change of the internal energy, that is, 1 ͓ ͑ ͒ ͑ ␦ ͔͒ y¨ = ApPp + AoilPoil − Fp − Ap + Aoil Patm − Cfy˙ − Kp y + p U d Mץ Eץ = = ͑mC T ͒͑15͒ t dt v p ͑24͒ץ tץ

where m is the mass of air inside the control volume and Cv is the 3.2 Hydraulic Latch and Damper. Another mechanism that specific heat of air at a constant volume. The expression for m˙ is has a direct impact on the dynamics of the actuator piston is the ␳ ͑ ͒ hydraulic latch damper. The compressibility of the fluid in the m˙ = pApy˙ 16 hydraulic latch is considered and the mechanism of adjusting the Expanding Eq. ͑15͒ and using Eqs. ͑16͒ and ͑5͒ result in valve seating velocity is modeled in detail. Figure 5 illustrates the hydraulic latch function. The oil sits on E A Cץ p v ͑ ˙ ͒͑͒ the top of the actuator piston stem with the same supply pressure = Ppy˙ + Ppy 17 / .t R as the air pressure. Fluid enters or exits through area Aoilin Aoiloutץ When the air, drawn in during the air charging stage, is fully ˙ The expression for Pp can be derived by substituting Eqs. ͑2͒, ͑3͒, expanded in the actuator cylinder, the actuator piston reaches to its ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ ͑ ͒ 6 , 7 , 11 , and 17 into Eq. 1 . That is, maximum displacement. The on and off valve S1 is closed due to

021007-4 / Vol. 132, MARCH 2010 Transactions of the ASME

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms Fig. 5 Hydraulic latch/damper model

activating solenoid 1 to prevent the oil from returning, recalling lenoid 1 is turned on at the beginning of air charging stage and system dynamics at the air charge, expansion and dwell stages. turned off at the end of expansion and dwell stage. Solenoid 2 is The pressurized oil is trapped in the passage and keeps the actua- turned on before expansion and dwell stage. Solenoid 2 operates tor piston at the maximum displacement until solenoid 1 is turned at the same frequency and duty cycle as these of solenoid 1 with off, see Sec. 2.3. Hence, this hydraulic latch provides a holding a time delay. Both inlet and outlet are closed during the overlap of force to keep the valve opening. Another function of this mecha- solenoids 1 and 2. The oil is modeled as an incompressible flow at nism is to provide a low seating velocity for the valve. When the air charge and discharge stages due to relatively low oil pressure, actuator piston approaches the original position, the cap on the top while in the dwelling region, it is modeled as a slightly compress- of the stem will partially block the exit area A. The actuator piston ible flow under high oil pressure. The slight compressibility is encounters a large resistant force due to the reduced flow area, what causes the volume change of the oil in the passage, hence the which decreases the air flow velocity tremendously. The resistant swing on the top of the valve lift profile. force increases as the exit area reduces. Apply the incompressible flow model at air charging stage to Figure 6 shows a valve lift profile along with the solenoid ac- calculate the flow rate through the oil passage as follows: tion chart. The solenoid itself has about 2–3 ms electromagnetic delay upon activation. These delays were not shown in this chart. P − P As was explained earlier, one valve cycle consists of three stages: q = C A ͱ supply oil = A y˙ ͑25͒ oil doilin oilin ␳ capoil air charging, expansion and dwell, and air discharging stage. So- oil

Fig. 6 Valve lift profile with the solenoid action chart

Journal of Dynamic Systems, Measurement, and Control MARCH 2010, Vol. 132 / 021007-5

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms Fig. 7 Inlet port valve model Fig. 8 Outlet port valve model

Therefore, the pressure of the oil at air charging stage is air flow from the spool valve with pressure PcupR and the supply A y˙ 2 ͩ cap ͪ ␳ ͑ ͒ pressure Psupply. Pressure PcupR alternates between atmosphere and Poil = Psupply − oil 26 supply pressure, which is regulated by the spool valve. CdoilinAoilin The port valve remains closed when PcupR equals Psupply due to where qoil and Cdoilin are the volumetric flow rate of the fluid and the spring force and the valve opens when PcupR decreases to the the discharge coefficient as the fluid enters the passage, respec- atmosphere pressure. The supply air is treated as a stagnant flow ␳ tively; Aoilin and oil are the area where the fluid enters the passage with constant pressure. The equation of motion can be obtained ͑ ͒ it will be calculated later and the density of the fluid; Psupply and using Newton’s second law: Poil are the supply and oil pressures, where Psupply= Poil. ͑ ͒ ͑ ͒ Apply the compressible flow model at expansion and dwell mcRw¨ + CcRw˙ + KcRw = Psupply − PcupR AcR 32 c stages to derive the oil pressure. The state equation PV =K where 0ՅwՅw and A =␲r2. r is the outer radius of the =const is used here by choosing c large enough to represent the max cR 2 2 inlet and outlet port valve ͑see Fig. 4͒. Variables mcR and CcR are high level of incompressibility: the mass of the inlet port valve and the damping coefficient com- c c ͑ ͒ PoillockV = PiVi 27 pensating for the friction loss of the valve, and KcR is the spring constant. Parameters w, w˙ , and w¨ are the displacement, the veloc- Note that Eq. ͑27͒ is true only for an isothermal process. Substi- ity, and the acceleration of the inlet port valve; and w is the tuting V=A y and V =A y into Eq. ͑27͒ to obtain max cap i cap i maximum distance, which the inlet port valve is allowed to travel. P yc The discontinuous nonlinearity in the port valve dynamics caused P = i i ͑28͒ ͑ ͒ oillock yc by this physical limitation was considered. Rearranging Eq. 32 leads the expression for w¨ , where Poillock is the pressure of the oil at the expansion and dwell ͑ ͒ 1 lock stages, yi is the maximum valve displacement, Vi is the ͑ ͒͑͒ w¨ = AinletPsupply − PcupRAcR − CcRw˙ − KcRw 33 volume of the fluid at yi, and Pi is the oil pressure Poil at yi. mcR Similarly, the equation of motion at air charging stage was ob- tained using the incompressible flow model as follows: 3.4 Outlet Port Valve. The outlet port valve functions in a similar way to the inlet port valve, except that the air that pushes P − P q = C A ͱ oil supply = A y˙ ͑29͒ the port valve open is with the actuator cylinder pressure. The oil d_oilout oilout ␳ cap oil pressure in the actuator cylinder is unsteady; thus, the flow dy- Rearranging Eq. ͑29͒ results in namic behavior is modeled. The modeling process is similar to the actuator piston. The control volume used here is shown in Fig. 8. A y˙ 2 Applying conservation of energy as shown in Eq. ͑1͒, we evalu- P = P + ͩ cap ͪ ␳ ͑30͒ ͒ / 2 ͑ ͒ / 2 ͑ ץ/ ץ ˙ oil supply oil Cd_oiloutAoilout ate W, E t, hi + vi 2 , m˙ i, he + ve 2 , and m˙ e as follows: where Cd_oilout is the discharge coefficient as the fluid exits the ˙ ␲ 2 ͑ ͒ W = AcLPoutz˙ and AcL = r2 34 passage and Aoilout is the area where the fluid exits the passage Aoilin=Aoilout=A, where where Pout is the pressure on the outlet port valve in the control volume. Then, ␲ 2 ͑ ͒ Յ 2 rpass + Aoil − Acap , y p1 U d A Cץ Eץ 2 A = y ͑31͒ ͑ ͒ cL v ͑ ˙ ͒͑͒ Ά ␲ ͑ ͒ Ͼ · = = mCvTout = Pouty˙ + Pouty 35 ץ ץ A − A , y p + ͪ ͩ 2 2 oil cap 1 t t dt R where z is the displacement of the outlet port valve, Tout is the gas The variables rpass, Aoil, Acap, and p1 are shown in Fig. 6. The seating velocity is greatly reduced when the stem enters the area temperature in the control volume, and Pout is the gas pressure in Ͻ the control volume. The ideal gas law, Eq. ͑5͒, is used to derive where y p1. By adjusting p1 during the hydraulic latch design ͑ ͒ process, the slope of the response can be altered by adjusting the Eq. 35 . Treating the air flow from the actuator cylinder as stag- Ͻ nant flow leads to timing of entering the region where y p1. v2 C P 3.3 Inlet Port Valve. As illustrated in Fig. 7, the inlet port h + i = h = C T = p p ͑36͒ i p p p ␳ valve is modeled as a mass-spring-damper system driven by the 2 pR

021007-6 / Vol. 132, MARCH 2010 Transactions of the ASME

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms Fig. 9 Spool valve model

k m˙ − m˙ = A ͑␳ z˙ + ␳ z͒͑47͒ ␥ ͱ ␥ ͱ ␳ ͑ ͒ i e cL out out m˙ i = inL PpAout = Aout inL k pPp 37 RTp Substituting m˙ i using Eq. ͑37͒ and m˙ e using Eq. ͑42͒ into the equation above, ␳˙ can be written as below: where Aout is the inlet area of the control volume. Similar to the out ͑ ͒ evaluation of Ain in Eq. 14 , the equivalent Aout can be approxi- 1 ␳ ͓ ͑ ͒␥ ͱ ␳ ͑ ͒␥ ͱ ␳ ͔ mated by the following equation: ˙ out = CdinLAout z inL k pPp − CdoutLAL z outL kPout out AcLz ␲r2, z Ͼ 0 A = ͭ 2 ͮ ͑38͒ ␳ z˙ out 0, z =0 − out ͑48͒ z Similar to the actuator piston modeling in Sec. 3.1, for the un- Finally, Newton’s second law yields the equation of motion for choked case, where P Ͼ0.53Pp, out the outlet port valve, 2 P ͑k+1͒/2k P ͑1−k͒/k 1/2 ␥ ͱ ͩ outͪ ͫͩ outͪ ͬ ͑ ͒ ͑ ͒ inL = −1 39 mcLz¨ + CcLz˙ + KcLz = PoutAoutlet − PcupLAcL 49 k −1 Pp Pp Յ Յ ␲ 2 ␲ 2 Յ where 0 z zmax, Aoutlet= r1, and AcL= r2. Parameters mcL and and for the choked case where Pout 0.53Pp, CcL are the masses of the outlet port valve and the damping coef- ␥ ͑ ͒ inL = 0.58 40 ficient compensating for the friction loss of the valve, respec- Treating ambient air as stagnant flow results in tively, and KcL is the spring constant. Parameters z, z˙, and z¨ are the displacement, the velocity, and the acceleration of the outlet port v2 valve, and z is the maximum distance, which the outlet port h + e = h = C T ͑41͒ max e 2 atm p atm valve is allowed to travel. The discontinuous nonlinearity in the port valve dynamics was considered in the simulation. Rearrang- k ing Eq. ͑49͒ to obtain an expression for z¨ results in ␥ ͱ ␥ ͱ ␳ ͑ ͒ m˙ e = outL PoutAL = AL outL k outPout 42 RT 1 out ͑ ͒͑͒ z¨ = AoutletPout − PcupLAcL − CcLz˙ − KcLz 50 where Tout is the temperature of the gas in the control volume, Pout mcL ␳ is the inlet air pressure of the control volume, out is the density in All the discharge coefficients that are involved in the flow equa- the control volume, and AL is the outlet area of the control volume tions were determined numerically and experimentally. and also a function of geometry and the displacement of the outlet port valve, where 3.5 Spool Valve. The armature of the solenoid pushes the stem of the spool valve with the magnetic force F when the A =2␲r z ͑43͒ s L 1 solenoid is energized and a precompressed spring returns the Ͼ If Patm 0.53Pout, for the unchoked case, spool valve when the solenoid is de-energized. The spool valve is pressure balanced at two ends, as shown in 2 P ͑k+1͒/2k P ͑1−k͒/k 1/2 ␥ ͱ ͩ atmͪ ͫͩ atmͪ ͬ ͑ ͒ Fig. 9. The spool valve equation of motion is outL = −1 44 k −1 Pout Pout m x¨ + C x˙ + K ͑x + ␦ ͒ = F ,0Ͻ x Ͻ x ͑51͒ Յ spool s s s s 0 and if Pout 0.53Pp, for the choked case where mspool is the mass of the spool valve, Cs is the damping ␥ = 0.58 ͑45͒ outL coefficient used to model the frictional loss, and Ks and ␦s are the Here, the gas was assumed ideal and the nonlinearity of the flow stiffness and preload of the spring, respectively. was considered in Eqs. ͑39͒, ͑40͒, ͑44͒, and ͑45͒. One can obtain 3.6 Solenoid Model. A solenoid can be modeled as a resis- ˙ ͑ ͒ ͑ ͒ Pout in the following form by substituting Eqs. 34 – 45 into Eq. tance and inductance ͑RL͒ circuit, as shown in Fig. 10. Note that ˙ ˙ ͑1͒ and letting Q=␣LW as it was treated in the actuator piston when a peak and hold drive circuit is used, Vin becomes a function model. Then of time when the solenoid is activated. The relationship between the current i in the coil and the magnetic force F on the armature k s 1 Pp is assumed to take the following form: P˙ = ͫC A ͑z͒P ␥ kP ͱ out A z dinL out p inL p ␳ cL p bi2 ͑ ͒ Fs = L 52 P z˙ x − C A ͑z͒␥ RkT ͱk␳ P ͬ − ␣ k out ͑46͒ 1+ doutL L outL atm out out L z a

where ␣L is a number between 0 and 1 depending on heat loss, where x is the displacement of solenoid actuator, see Fig. 10. and CdinL and CdoutL are the discharge coefficients. Applying mass Coefficients a and b are chosen by curve fitting the empirical data conservation law to the control volume results in provided by the manufacture.

Journal of Dynamic Systems, Measurement, and Control MARCH 2010, Vol. 132 / 021007-7

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms 4 Simulations and Experiments 4.1 Experiment Setup. A Ford 4.6 l four-valve V8 engine head was used for the valve test. The camshaft was removed from the intake valve side and an EPVA was installed above one of the intake valves. A Micro-Epsilon point range laser sensor was used to measure the intake valve displacement. The laser sensor was mounted on an angle such that the laser beam from the emitter of the laser sensor would be perpendicular to the surface of the end of the valve stem. A dSPACE PCI board was used for both control and data acquisition. A low side switch drive circuit, made from two insulated gate bipolar transistors ͑IGBTs͒, was used as a driver circuit for both solenoids. Two STP2416-015 small push- pull solenoids were used to drive two spool valves in the EPVA. The experiments were conducted under the combinations of ͑ Fig. 10 Solenoid model various control parameters, where two supply pressures 30 psi and 40 psi͒ were used; three solenoid periods, 100 ms, 40 ms, and 24 ms, ͑corresponding to engine speed at 1200 rpm, 3000 rpm, and 5000 rpm͒ were selected and two solenoid duty cycles ͑30% and 25%͒ were applied. The delay between the first and second Table 1 Test matrix solenoids was selected to be 3 ms and 5 ms. Table 1 lists all 18 experiments conducted. The valve responses Psupply Period Duty Delay Test No. ͑psi͒ ͑ms͒ ͑%͒ ͑ms͒ were compared with the simulation responses in Sec. 4.2. The EPVA is aimed to tailor the engine intake flow without throttling. 1 30 100 30 3 Therefore, in the experiments and simulations, the engine intake 2 30 100 30 5 manifold pressure is considered to be close to the atmospheric 33040303 pressure. No pressure loads are included on the valve head ͑Fp 43040305͒ 53024303=0 . In future studies where the exhaust valve dynamics are in- 63024305vestigated, the valve will have to open against a high engine cyl- 7 40 100 30 3 inder pressure. This model can be expended to perform the ex- 8 40 100 30 5 haust valve simulation, see Eq. ͑24͒. 9 40 100 25 3 10 40 100 25 5 4.2 Simulation Results. The equations of motion derived 11 40 40 30 3 previously were written in state space form and programed in 12 40 40 30 5 MATLAB/SIMULINK. The simulations were performed under the 13 40 40 25 3 same parameter sets as these used in experiments. Eighteen ex- 14 40 40 25 5 15 40 24 30 3 perimental and simulation responses of the valve displacement are 16 40 24 30 5 presented in Figs. 11–13 for all 18 tests. The dashed lines repre- 17 40 24 25 3 sent the experimental responses and the solid lines represent the 18 40 24 25 5 simulation responses.

Fig. 11 Plots with 30 psi supply pressure and 30% duty cycle

021007-8 / Vol. 132, MARCH 2010 Transactions of the ASME

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms Fig. 12 Plots with 40 psi supply pressure and 30% duty cycle

Figure 11 compares the experimental and simulation responses hydraulic latch is utilized to hold the valve open. The slight com- with 30 psi supply pressure. The top two graphs of Fig. 11 display pressibility of the oil in the hydraulic latch causes a few oscilla- the responses of 30% solenoid duty cycle at 100 ms period with 3 tions of the valve responses. The hydraulic damper is engaged ms ͑test 1͒ and5ms͑test 2͒ delay between two solenoids. Note when the valve is roughly 1 mm away from its seat ͑which can be that the 100 ms solenoid period corresponds to the engine speed at adjusted by adjusting the actuator piston stem clearance͒, where 1200 rpm. The response with 5 ms delay ͑test 2͒ had about 6 ms the slope of the response is largely decreased. The valve ap- rising time, and the response with 3 ms delay ͑test 1͒ had about 5 proaches to the original position gradually afterwards. ms rising time. The maximum valve lift height was 6 mm for the The responses in the middle two graphs of Fig. 11 were ob- response with 5 ms delay ͑test 2͒ and 3.8 mm for the response tained under the same operating conditions as those on the top with 3 ms delay ͑test 1͒. The swing motion on the top of the graphs except that the solenoid period was reduced to 40 ms ͑cor- profile indicates that the valve is in the dwell stage when the responding to 3000 rpm͒. The rising times of the responses with 5

Fig. 13 Plots with 40 psi supply pressure and 25% duty cycle

Journal of Dynamic Systems, Measurement, and Control MARCH 2010, Vol. 132 / 021007-9

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms ms ͑test 4͒ and3ms͑test 3͒ delay between two solenoids were 6 Acknowledgment ms and 5 ms. As the solenoid period was reduced, the dwell stage The authors gratefully acknowledge the support for this work was shorter. The maximum valve lift height was 6 mm for the from the U.S. Department of Energy, National Energy Technology response with 5 ms delay ͑test 4͒ and 4 mm for the response with Laboratory, Energy Efficiency and Renewable Energy Division, 3 ms delay ͑test 3͒. Samuel Taylor, Project Manager. The authors also like to ac- The solenoid period was further reduced to 24 ms ͑correspond- knowledge the support from Urban Carlson, Anders Hoglund, and ing to 5000 rpm͒. The responses ͑tests 5 and 6͒ are shown in the Mats Hedman of Cargine Engineering. This work was completed bottom two graphs of Fig. 11. In this case, the maximum valve lift during the Ph.D. study of J. Ma at Michigan State University. was 5 mm and the rising time was 6 ms for the response with 5 ms delay between two solenoids ͑test 6͒; the maximum valve lift was 4 mm and the rising time was 5 ms for the response with 3 ms delay ͑test 5͒. The maximum valve lift height in the 5 ms delay References case was decreased from 6 mm to 5 mm. This happened because ͓1͔ Lenz, H. P., Wichart, K., and Gruden, D., 1988, “Variable Valve Timing—A Possibility to Control Engine Load Without Throttle,” SAE Paper No. 880388. the solenoid was de-energized before the actuator piston can fully ͓2͔ Negurescu, N., Pana, C., Popa, M. G., and Racovitza, A., 2001, “Variable expand to its maximum displacement; the valve started returning Valve—Control Systems for Spark Ignition Engine,” SAE Paper No. 2001-01- before it reached its maximum lift. Moreover, the valve never 0671. entered the dwelling region in these two cases. The solenoid pe- ͓3͔ Lancefield, T., 2003, “The Influence of Variable Valve Actuation on the Part Load Fuel Economy of a Modern Light-Duty Diesel Engine,” SAE Paper No. riod was so short that the valve entered the air discharging stage 2003-01-0028. immediately after the air charging stage. Hence, the swing motion ͓4͔ Boggs, D. L., Hilbert, H. S., and Schechter, M. M., 1995, “The Otto-Atkinson disappeared on the top of the profile. Cycle Engine-Fuel Economy and Emissions Results and Hardware Design,” The experiment and simulation responses at 40 psi supply pres- SAE Paper No. 950089. ͓5͔ Urata, Y., Awasaka, M., Takanashi, J., Kakinuma, T., Hakozaki, T., and Ume- sure with 30% and 25% solenoid duty cycles are presented in Fig. moto, A., 2004, “A Study of Gasoline-Fuelled HCCI Engine Equipped With an 12 and 13, respectively. The rising time of the valve varied from 4 Electromagnetic Valve Train,” SAE Paper No. 2004-01-1898. ms to 6 ms. The maximum valve lift was around 8 mm for the ͓6͔ Trask, N. R., Hammoud, M., Haghgooie, M., Megli, T. W., and Dai, W., 2003, responses with 5 ms delay and 6 mm for the response with 3 ms “Optimization Techniques and Results for the Operating Modes of a Camless Engine,” SAE Paper No. 2003-01-0033. delay in this case. ͓7͔ Sugimoto, C., Sakai, H., Umemoto, A., Shimizu, Y., and Ozawa, H., 2004, As expected, the valve lift height could be controlled by regu- “Study on Variable Valve Timing System Using Electromagnetic Mechanism,” lating the supply pressure and/or varying the delay between two SAE Paper No. 2004-01-1869. solenoids, and the valve open duration could be controlled by ͓8͔ Theobald, M. A., Lequesne, B., and Henry, R. R., 1994, “Control of Engine Load Via Electromagnetic Operating Actuator,” SAE Paper No. 940816. controlling the activation duration of the solenoid. The mathemati- ͓9͔ Pischinger, F., and Kreuter, R. P., 1984, “Electromagnetically Operating Ac- cal model was able to capture the dynamics of the EPVA closely. tuator,” U.S. Patent No. 4,455,543. ͓10͔ Lenz, H. P., Geringer, B., and Smetana, G., 1989, “Initial Test Results of an 5 Conclusions Electro-Hydraulic Variable Valve Actuation System on a Firing Engine,” SAE Paper No. 890678. This article presented a dynamic model for an EPVA. This ͓11͔ Richeson, W. E., and Erickson, F. L., 1989, “Pneumatic Actuator With Perma- model is a key element for developing control strategies of the nent Magnet Control Valve Latching,” U.S. Patent No. 4,852,528. ͓ ͔ EPVA for an internal combustion engine. Two solenoids and two 12 Watson, J. P., and Wakeman, R. J., 2005, “Simulation of a Pneumatic Valve Actuation System for Internal Combustion Engine,” SAE Paper No. 2005-01- spool valves, a single-acting cylinder, an inlet port valve, an outlet 0771. port valve, a hydraulic latch-damper, and an intake valve with its ͓13͔ Turner, J. W. G., Bassett, M. D., Pearson, R. J., Pitcher, G., and Douglas, K. J., valve spring are included in this model. The mathematical model 2004, “New Operating Strategies Afforded by Fully Variable Valve Trains,” employs Newton’s law, mass conservation, and principle of ther- SAE Paper No. 2004-01-1386. ͓14͔ Bobrow, J. E., and McDonell, B. W., “Modeling and Control of a Variable modynamics. The nonlinearity of the flow, incompressibility, and Valve Timing Engine,” Proceedings of the 2000 American Control Conference, compressibility of the hydraulic fluid and the nonlinearity of the Chicago, IL, Jun. motion due to the physical constraint was carefully considered in ͓15͔ Tressler, J. M., Clement, T., Kazerooni, H., and Lim, M., 2002, “Dynamic Behavior of Pneumatic Systems for Lower Extremity Extenders,” Proceedings the modeling process. The model was implemented in MATLAB/ of the 2002 IEEE International Conference on Robotics & Automation, Wash- SIMULINK under different combinations of operation conditions. ington, DC, May. Validation experiments were performed on a Ford 4.6 l four-valve ͓16͔ Richer, E., and Hurmuzlu, Y., 2000, “A High Performance Pneumatic Force V8 engine head with various air supply pressures, solenoid peri- Actuator System: Part I—Nonlinear Mathematical Model,” ASME J. Dyn. ods, solenoid duty cycles, and time delay between two solenoids. Syst., Meas., Control, 122, pp. 416–425. ͓17͔ 2009, http://www.cargine.com/tech2.html The numerical simulation results were compared and showed ex- ͓18͔ Thomson, W. T., 1998, Theory of Vibration With Applications, 5th ed., cellent agreement with the experimental data. Prentice-Hall, Upper Saddle River, NJ.

021007-10 / Vol. 132, MARCH 2010 Transactions of the ASME

Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 04/02/2015 Terms of Use: http://asme.org/terms