Simulation and experimental research of hydraulic pressure and intake valve lift on a fully hydraulic variable valve system for a spark-ignition engine

Abstract

A fully hydraulic variable valve system based on spark-ignition engine BJ486EQ is introduced in this article, which can provide fully variable valve lifts, valve timing, and valve opening duration. A simulation model of fully hydraulic variable valve system is established, which is verified through experimental intake valve lift and hydraulic pressure. It is found that pressure fluctuation in hydraulic system of fully hydraulic variable valve system becomes greater with the increase in engine speed, which even leads to “lift distortion.” The cam profile of fully hydraulic variable valve system and the structure of the throttling valve which is used to reduce valve seating speed are optimized by simulation. The lift distortion and rebound do not occur in the optimized fully hydraulic variable valve system, which is indicated by the results of simulation and experiments when the engine speed is 5000 r/min, and valve seating characteristics become stable and soft.

Keywords

Fully hydraulic variable valve system simulation and modeling intake valve lift pressure fluctuation lift distortion

Introduction

Fully variable valve technology (FVVT) can achieve continuous variation of the maximum valve lift, valve opening duration, and valve timing.^1,2 Pumping loss is the main issue of the spark-ignition (SI) engine because of the traditional throttle-based load control, which makes low efficiency of SI engines. Early intake valve closing (EIVC) can be adopted in FVVT to control the amount of airflow sucked into the cylinder so that the throttle can be removed. Thus, the unthrottled SI engine can greatly reduce the pumping loss through regulating quantity of intake air. Therefore, FVVT has significant meanings to energy conservation.^3–5

The current variable valve technologies are mainly mechanical,⁶ electromagnetic,⁷ and electro-hydraulic.⁸ Valvetronic from BMW^9,10 is a mechanical variable valve mechanism. Many researchers have developed different kinds of designs of which some are used in commercial cars. This technology can control loads without the throttling valve and reduce the pumping loss.^11,12 However, most of them cannot provide fully variable valve timing, and too many parts are involved in the valve movement, which makes the mechanism too complex, and mechanical energy loss is big under high speeds.¹³ The electromagnetic variable valve mechanism^14,15 is mainly controlled by a solenoid valve. The main problems of this mechanism are the low response speed of electromagnet which limits the mechanism’s maximum speed and precisely controllable valve movement and hysteresis.¹⁶

A new electro-hydraulic fully variable valve mechanism from Fiat named UniAir⁸ has been published recently. It can operate at the speed of 8000 r/min. A solenoid valve is used as the controlling switch that determines the motion of the valve. It relies on high-frequency solenoid to realize fully variable valve lift and timing. Actually, high-frequency solenoid is mostly adopted by the electro-hydraulic variable valve system.¹⁷ However, some factors make it difficult to control the movement of the valve accurately, such as pressure fluctuation, compressibility of high-pressure liquid, and the response speed of the solenoid valve, so the valve seating speed is high. Furthermore, the system is very complex with high cost.

A new innovative fully hydraulic variable valve system (FHVVS) is introduced in this article. The main innovation of FHVVS is that a mechanical oil relieving valve is adopted to replace the high-frequency solenoid valve as the control switch to control the valve lift and opening duration. The oil relieving valve consists of couples of precise components which have advantages of fast response, reliable operation, and low cost. First, FHVVS is simulated by the simulation software to study dynamic characteristics of the intake valve, and the hydraulic pressure of FHVVS and lifts of the intake valve are measured in a cylinder head of a multi-cylinder SI engine equipped with FHVVS. Second, comparative analysis of experimental and simulating results at different intake valve lifts validates the accuracy of the simulation model. Then, pressure fluctuation of the high-pressure system is studied through the combination of simulation and experiments. Finally, the throttling valve of FHVVS is optimized to improve the high-speed dynamic performance of FHVVS and reduce the valve seating speed.

The structure and working principle of FHVVS

The structure and working principle of intake valve driving mechanism

As shown in Figure 1, FHVVS includes an intake cam, a hydraulic tappet, a hydraulic piston, an oil relieving valve, and an intake valve. The hydraulic tappet driven by the intake cam produces high-pressure oil and then it flows into hydraulic piston chamber to drive the hydraulic piston and drive the intake valve open. When the intake valve rises to a certain position, oil relieving valve opens, and the intake valve seats under the force of intake valve spring. The high-pressure system consists of hydraulic tappet chamber, hydraulic piston chamber, and connecting oil passages. High-pressure oil from the oil relieving valve flows into the low-pressure system when the oil relieving valve opens. The low-pressure system of FHVVS is connected with the lubricating system of the SI engine to provide oil.

Figure 1.

Sketch of the intake valve driving mechanism.

The structure and working principle of oil relieving valve

Oil relieving valve is composed of a couple of the valve spool and the valve sleeve. The three-dimensional structure of the oil relieving valve is shown in Figure 2. There is a center hole and a radial hole B which connect with the low-pressure system in the valve spool. There is a radial hole A and a circular groove which connect permanently with the high-pressure system in the valve sleeve. One oil relieving valve can control two cylinders.

Figure 2.

Three-dimensional structure of the oil relieving valve.

Working principle of the oil relieving valve is as follows: the valve spool rotates synchronously with the cam. If the hole B and the hole A are not connected, the oil relieving valve is at the closing state, and the intake valve rises as the intake cam rotates. If the hole B turns to the position where it connects with the hole A, the oil relieving valve is at the opening state to let high-pressure oil flow into the low-pressure system, and the intake valve goes down under the force of the intake valve spring. The intake valve lift and the intake valve opening duration can be changed along with the different position of the radial hole A. Oil relieving angle is the crank angle when the radial holes A and B connect.

Working principle of the throttling valve

In FHVVS, the throttling valve consists of a couple of a hydraulic piston and a hydraulic piston sleeve, as shown in Figure 3. Hydraulic oil in the hydraulic piston chamber flows out through throttle holes and the throttle groove in the hydraulic piston sleeve when the intake valve falls back. As the intake valve lift gradually decreases, the effective throttling area of the throttle hole reduces rapidly. When the intake valve drops to a certain lift (2 mm for FHVVS), hydraulic oil can only flow out through the throttle groove, but not throttle holes. The effective flow area of the throttle groove is gradually reduced along with decrease in the intake valve lifts. Thus, volume of the hydraulic oil that flows out of the hydraulic piston chamber reduces, so that the valve seating speed reduces to ensure the smooth intake valve seating.

Figure 3.

Three-dimensional structure of the throttling valve.

Simulation and validation experiments of FHVVS

Theoretical basis of the simulation modeling

The system needs to be analyzed theoretically in order to establish the simulation model of FHVVS, describe the dynamic characteristics of the whole system, and determine the parameters of the simulation model. Hydraulic piston and the intake valve assembly are taken as the object, and force on the intake valve from gas in the cylinder is neglected. Figure 4 is the force analysis diagram of hydraulic piston and the intake valve assembly. As can be seen from Figure 4, hydraulic pressure from hydraulic piston chamber $F_{p}$ , intake valve spring force $F_{s}$ , and damping force $F_{d}$ which consists of the damping force between hydraulic piston and hydraulic piston sleeve and the damping force between intake valve and valve guide rod act together on the hydraulic piston and the intake valve assembly, according to Newton’s law

m_{j 1} \frac{d^{2} H_{v}}{d t^{2}} + F_{d} + F_{s} - F_{p} = 0

(1)

where $m_{j 1}$ is the equivalent mass of the hydraulic piston and the intake valve assembly; $H_{v}$ is the intake valve lift; damping force $F_{d} = b (d H_{v} / d H_{v})$ , b is the damping coefficient; intake valve spring force $F_{s} = K_{1} \cdot H_{v} + F_{0}$ , $F_{0}$ is the preload of the intake valve spring, $K_{1}$ is the stiffness of the intake valve spring; hydraulic force $F_{p} = P_{v} \cdot A_{v}$ , $P_{v}$ is the hydraulic pressure acting on the hydraulic piston, $A_{v}$ is the cross-sectional area of the hydraulic piston $A_{v} = π D_{1}^{2} / 4$ , and $D_{1}$ is the diameter of the hydraulic piston.

Figure 4.

Force analysis diagram of hydraulic piston and the intake valve assembly.

Based on the continuity equation of fluid, the differential equation of the pressure of the hydraulic tappet chamber $P_{t}$

β \cdot V_{t} \cdot \frac{d P_{t}}{dt} - Q_{tv} - Q_{to} + Q_{ti} - A_{t} \cdot \frac{d H_{t}}{dt} = 0

(2)

where $β$ is the coefficient of fluid compressibility which is a constant; $P_{t}$ is the pressure of the hydraulic tappet chamber; $A_{t}$ is the cross-sectional area of the hydraulic tappet chamber $A_{t} = π D_{2}^{2} / 4$ , $D_{2}$ is the diameter of the hydraulic tappet; $H_{t}$ is the lift of the hydraulic tappet which is determined by the intake cam profile; $V_{t}$ is the instantaneous volume of the hydraulic tappet chamber $V_{t} = V_{t 0} - A_{t} \cdot H_{2}$ , $V_{t 0}$ is the volume of the hydraulic tappet when the lift is 0 mm; $Q_{tv}$ is the flow volume of hydraulic oil from the hydraulic tappet chamber to the hydraulic piston chamber; $Q_{to}$ is the flow volume of hydraulic oil which flows out of the hydraulic tappet chamber through the oil relieving valve; and $Q_{ti}$ is the flow volume of hydraulic oil which flows into hydraulic tappet chamber through the check valve. All these can be calculated from equation (3)

Q = (μ \cdot s) \cdot \sqrt{\frac{2 | Δ P |}{ρ}}

(3)

where $(μ \cdot s)$ is the effective flow area, $Δ P$ is the pressure difference, and $ρ$ is the density of the hydraulic oil.

In the same way, according to the continuity equation of the fluid, differential equation of pressure $P_{v}$ is shown as follows

β \cdot V_{v} \cdot \frac{d P_{v}}{dt} + Q_{tv} + A_{v} \cdot \frac{d H_{v}}{dt} = 0

(4)

where $V_{v}$ is the volume of the hydraulic piston chamber, $V_{v} = V_{v 0} + A_{v} \cdot H_{v}$ , $V_{v 0}$ is the volume of hydraulic piston chamber when the intake valve lift is 0 mm.

Ordinary differential equations of variables $H_{v}$ , $P_{t}$ , and $P_{v}$ consist of equations (1), (2), and (4) together, which can be calculated. The dynamic characteristics of the intake valve lift along with the crank angle $H_{v} (φ)$ , the pressure fluctuation in the hydraulic piston chamber $P_{v} (φ)$ , and in the tappet chamber $P_{t} (φ)$ can be obtained through the mathematical transformation as the crank angle $φ = 6 nt$ , where $n$ is the engine speed.

The simulation model of FHVVS is shown in Figure 5. The simulation model consists of four parts: cam driving subsystem, hydraulic transmission subsystem, intake valve assembly subsystem, and controlling subsystem. Signals from cam driving subsystem are input into controlling subsystem to make hydraulic subsystem open the intake valve. The step of the simulation is set to be 0.01 ms. The model only discusses two intake valves in one cylinder because the high-pressure oil generated by a hydraulic tappet in the FHVVS can drive two intake valves and the movement state of each intake valve is independent.

Figure 5.

Diagram of FHVVS model.

Introduction of the validation experiment

The SI engine BJ486EQ with dual overhead camshafts is selected to be the experimental prototype, each cylinder of which has four valves and rated power is 95 kW and rated speed is 5000 r/min. Main parameters of experimental prototype are shown in Table 1. FHVVS is mounted on the cylinder head of the prototype which is shown in Figure 6. In order to maintain versatility of the cylinder head of the original engine, both the intake and exhaust cams are combined on the exhaust camshaft. Each intake cam controls two intake valves of the corresponding cylinder through hydraulic pressure. The intake cam and exhaust cams of the first cylinder are marked in Figure 6. The oil relieving valve is, respectively, installed in the front case and the rear case. A synchronous gear is arranged in the middle of the camshaft, and the valve spool of the oil relieving valve is driven by the gear driving unit to synchronously rotate with the camshaft. A stepping motor that is mounted on the cylinder head cover drives the motor shaft in order to make the gear sector and the valve sleeve gear shown in Figure 2 mesh to adjust the oil relieving angle of the oil relieving valve. As can be seen from Figure 6, FHVVS is less than the size of the original cylinder head in the direction of the width and the length, which uttermost maintains compactness and the overall structure of the cylinder head.

Table 1.

Main parameters of the original engine BJ486EQV4.

Item (unit)	Parameter
Number of cylinders	4
Rated power (kW)	95
Rated speed (r/min)	5000
Bore (mm)	86
Stroke (mm)	86
Standard IVO (°CA BTDC)	21
Standard IVC (°CA ABDC)	−180 to 100
Standard EVO (°CA BBDC)	36
Standard EVC (°CA ATDC)	14
Maximum lift of intake valve (mm)	0 to 8.5
Maximum lift of exhaust valve (mm)	9

Figure 6.

Installation of FHVVS on the cylinder head.

Lifts of the intake valve and pressure of the high-pressure system are measured in the motored test bench which mainly comprises an engine cylinder head, a frequency transducer, a motor and measuring equipment, and a hydraulic pump station. The schematic diagram of the test bench is shown in Figure 7.

Figure 7.

Interconnection between the test rigs for FHVVS.

The camshaft of the valve train is driven by the electric motor through transmission. The speed of the motor that is the half of engine speed is controlled by a frequency converter which can continuously adjust the speed of the electric motor within 0–3000 r/min. The hydraulic oil with suitable temperature and pressure in the FHVVS is provided by the hydraulic pump station that replaces the lubrication system of the original SI engine to ensure the cycle operation of the system, and it also provides lubricant oil for the camshaft and other moving parts in the experiment.

Intake valve lift signals, high-pressure signals, CDM (crank angle degree marker) signals, and TDC (top dead center) signals were collected in the experiment. The original signals were transmitted to a computer through high-speed data acquisition board in real time. Data were collected and processed by the computer. The main instruments are shown in Table 2.

Table 2.

Experimental equipment.

Name of equipment	Model	Manufacturer
Laser displacement sensor	LK-H087	Keyence
Motor	YVP132M-4	Shanghai Haiguang
Frequency transducer	FM8-RB10	Shanghai Ribo
Pressure sensor	QC42X	AVL
Charge amplifier	5018A	Kistler

Results and discussion

Validation of simulation results and experimental results

For the validation of the simulation model, lifts with different oil relieving angles are achieved through the simulation and experiments on the motored test bench when the engine speed is 3000 r/min, which are shown in Figure 8. As can be seen from Figure 8, lift curves of simulation and experiment have the consistent trend and nearly the same shape. The maximum intake valve lift and the intake valve opening duration increase along with the increase in the oil relieving angle when the intake valve lift is less than the maximum designed lift at the same speed. The intake valve opening duration will continue to increase, while the maximum intake valve lift remains unchanged with the increase in the oil relieving angle when the intake valve lift reaches the maximum designed value. In conclusion, FHVVS can achieve continuously variable maximum intake valve lift and fully variable intake valve opening duration at a variety of speeds by adjusting the oil relieving angle.

Figure 8.

Experimental and simulating intake valve lifts at 3000 r/min.

Intake valve lift and pressure of the hydraulic tappet chamber are shown in Figure 9 when the engine speed is 3000 r/min and the oil relieving angle is 100°CA ATDC. As can be seen from Figure 9, the simulation and experimental results of the hydraulic tappet chamber’s pressure and intake valve lift have basically consistent wave period and amplitude. The pressure of the hydraulic tappet chamber fluctuates periodically and the intake valve lift mainly depends on the intake cam profile when the crank angle is below the oil relieving angle. Hydraulic tappet chamber’s pressure decreases rapidly and the intake valve seats quickly after the lift under the function of inertia force when the crank angle is over the oil relieving angle.

Figure 9.

Pressure of tappet chamber and intake valve lift at 3000 r/min.

Analysis of pressure fluctuation

In order to further analyze the dynamic characteristics of the intake valve of FHVVS, with the damping force neglected, equation of the acceleration of the intake valve $J$ which can be obtained from the differential equation (1) is shown as follows

\frac{d^{2} H_{v}}{d t^{2}} = \frac{1}{m_{j 1}} (P_{v} A_{v} - K_{1} H_{v} - F_{0})

(5)

where $F_{0}$ is the preload of the intake valve spring which is a constant value; force $K_{1} H_{v}$ linearly changes with the intake valve lift. As a result, characteristic of acceleration of the intake valve depends on the characteristic of the pressure of hydraulic piston chamber $P_{v}$ . Because the space of the hydraulic piston chamber is too small, it is not convenient to measure the pressure $P_{v}$ directly while it can be calculated by simulation. The pressure of the hydraulic tappet chamber $P_{t}$ and the acceleration $J$ of the intake valve are measured when the speed is 3000 r/min and the oil relieving angle is 100°CA ATDC, which are shown in Figure 10. The pressure of the hydraulic piston chamber $P_{v}$ is simulated under the same condition, which is also shown in Figure 10.

Figure 10.

Experimental and simulating pressure fluctuation and acceleration of the intake valve.

As can be seen from Figure 10, when the crank angle is less than the oil relieving angle 100°CA ATDC, pressure of the hydraulic tappet chamber $P_{t}$ and pressure of the hydraulic piston chamber $P_{v}$ fluctuate periodically with the same characteristic during the intake valve opening process. When the crank angle is over the oil relieving angle, high-pressure system begins relieving oil so that pressure of the hydraulic tappet chamber $P_{t}$ and pressure of piston chamber $P_{v}$ decrease rapidly. Since the throttling valve begins to throttle, pressure of piston chamber $P_{v}$ rises sharply and acceleration of the intake valve $J$ increases greatly when the crank angle is 155°CA ATDC, which makes the speed of intake valve reduce quickly, and ultimately the intake valve seats smoothly. The pressures $P_{t}$ and $P_{v}$ gradually reduce to the pressure of the low-pressure system after the seat of the intake valve.

Figure 10 indicates that periods of the intake valve acceleration $J$ and the piston chamber pressure $P_{v}$ are basically the same, and each of pressure’s peak corresponds to the peak of the acceleration. Therefore, in order to ensure the stability of the system, it is necessary to reduce the pressure fluctuation of the system to ensure the smooth operation.

Pressure of the hydraulic tappet chamber at different speeds is shown in Figure 11 when the oil relieving angle is 125°CA ATDC. As can be seen from Figure 11, the pressure fluctuation in the high-pressure system is stronger and the peak increases, while the trough decreases as speed increases. The lowest pressure A occurs in the first trough when the engine speed is 5000 r/min. Obviously, as the speed increases, the value of the lowest pressure decreases further and is even below the pressure of the low-pressure system $P_{0}$ , which makes FHVVS out of control. If pressure of the high-pressure system is lower than pressure of the low-pressure hydraulic P₀ in the opening process of intake valve, the actual intake valve lift will be greater than the lift determined by the cam profile on theory, which means that distortion of intake valve lift occurs. Under this situation, hydraulic oil cannot be discharged in time, which makes movement characteristics of the intake valve uncontrollable. Change of the oil relieving angle cannot alter the intake valve movement, and then the phenomenon “out of control” appears for the time being. Obviously, the pressure value of the trough will be lower as the engine speed increases, which makes the uncontrollable range of the valve movement bigger. Therefore, the lift distortion is not allowed to appear in FHVVS within the working engine speed.

Figure 11.

Pressure fluctuation of hydraulic tappet chamber at different engine speeds.

Optimization of the intake cam profile

Cam is the power source of intake valve movement and also the vibration source in FHVVS. Therefore, it is the fundamental problem to design a reasonable intake cam profile to decrease the pressure fluctuation in the hydraulic system. Thus, the optimum cam profile is selected from many different cam profile schemes by simulation to prevent the phenomenon of “lift distortion” to occur at high speed. Figure 12 shows the theoretical intake valve lift and acceleration determined by intake cam profile of FHVVS and prototype. It can be seen that compared with the prototype, the theoretical intake lift and acceleration determined by the intake cam profile of FHVVS have the following characteristics:

The maximum theoretical intake valve acceleration of FHVVS is set at the beginning of the working section, and its value is reduced properly.

The AB segment in the curve of FHVVS that is between the positive intake valve acceleration and the negative intake valve acceleration becomes very flat.

Figure 12.

Lift and acceleration of intake valve on theory.

Experiments on FHVVS under the high speed are carried out in order to analyze the dynamic performance. Figures 13 and 14, respectively, show lift and acceleration of the intake valve when the oil relieving angle is 43°, 123°CA ATDC at the speed of 5000 r/min. As can be seen from figures, lift curves of FHVVS are smooth and the intake valve seating is soft, which illustrates the steady performance of FHVVS at the rated speed of 5000 r/min.

Figure 13.

Intake valve lifts at 5000 r/min with different oil relieving angles.

Figure 14.

Intake valve accelerations at 5000 r/min with different oil relieving angles.

In Figure 14, the maximum negative acceleration $J_{max}$ is obtained according to the force of intake valve spring and pressure of the low-pressure system $P_{0}$ . In equation (5), when $P_{v} = P_{0}$ , the maximum negative acceleration of the theory $J_{\max}$ is as follows

J_{max} = \frac{1}{m_{j 1}} (A_{v} P_{0} - K_{1} H_{v} - F_{0})

(6)

The phenomenon of “lift distortion” occurs if the pressure of the high-pressure system is lower than that of the low-pressure system $P_{0}$ , which means that the actual acceleration of the intake valve is less than the theoretical maximum negative acceleration $J_{\max}$ . Figure 14 shows that the intake valve acceleration does not exceed the theoretical maximum negative acceleration $J_{\max}$ , which indicates that the phenomenon of “lift distortion” does not occur in FHVVS at 5000 r/min. FHVVS with the intake cam profile has stable operation within the maximum speed of 5000 r/min.

Optimization of the throttling valve

In the seating stage of the intake valve, flow of hydraulic oil through the throttling valve is supposed to be controlled to adjust the valve seating speed and buffer impact of intake valve seating. An optimal structure of the throttling valve is obtained through the simulation to ensure the smooth seating of the intake valve.

Two different schemes of throttling valves are shown in Figure 15(a). Throttling area reduces rapidly as the intake valve lift decreases. $S_{0}$ is the minimum throttling area as the intake valve is 0 mm. The minimum throttling area $S_{0}$ and the length of the throttling stage determine the throttling effect together. Compared with scheme 1, scheme 2 has a smaller minimum throttling area. Through simulating lifts and valve seating speeds of different schemes shown in Figure 15(b), the engine speed is 5000 r/min and oil relieving angle is 55°CA ATDC. The results of simulation shows that the valve seating speed of scheme 1 $V_{1}$ is 0.4 m/s, and the height of the intake valve rebound is 0.45 mm. The valve seating speed of scheme 2 $V_{2}$ is 0.25 m/s, and there is no significant intake valve rebound. Simulating results also indicate that if the throttling area $S_{0}$ is too small, it will take too long time to make the intake valve seat. Therefore, scheme 2 is selected to be the reasonable designed structure of the throttling valve.

Figure 15.

Effects of different schemes of the throttling valve on intake valve seating process: (a) throttling area of different throttling valves and (b) intake valve lifts and speeds.

The intake valve lift and speed obtained from experiments are shown in Figure 16 when the engine speed is 5000 r/min and the oil relieving angle is 55°CA ATDC. The valve seating speed is 0.21 m/s for FHVVS, and there is no significant rebound phenomenon. The intake valve seats softly.

Figure 16.

Experimental intake valve lift and speed at intake valve seating stage at 5000 r/min.

Conclusion

One new FVVT called FHVVS has been introduced in this study. Simulation and experiments have been performed in this article to study pressure fluctuation and high-speed dynamic characteristics of FHVVS. Some conclusions are listed as follows:

FHVVS is innovative to use oil relieving valve as an oil control switch. Simulation model and experiments have proved that FHVVS can achieve fully variable valve lift and duration.

With the increase in the engine speed, the pressure fluctuation in FHVVS becomes stronger. Once pressure in the high-pressure system is lower than that of the low-pressure system $P_{0}$ during the intake valve opening stage, lift distortion will occur to make the intake valve movement out of control temporarily, which should be avoided for FHVVS.

The intake cam profile of FHVVS is optimized by simulation and experiments which show that it is more appropriate for FHVVS that the intake cam profile has smooth acceleration curve and its maximum intake valve acceleration point on theory is set at the initial stage. The optimized cam profile makes intake valve movements stable at the speed of 5000 r/min, and there is no lift distortion.

The valve seating speed of FHVVS is controlled by a throttling valve the structure of which is optimized through simulation and experiment. Proper minimum throttling area $S_{0}$ and the length of the throttling stage ensure the smooth seating of the intake valve. As for FHVVS, there is no obvious “rebound” phenomenon and it has stable valve seating.

Footnotes

Handling Editor: Jose Antonio Tenreiro Machado

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by National Natural Science Foundation of China (51375265) and the National Key Basic Research Plan (2013CB228404).

References

Ashhab

Stefanopoulou

Cook

et al . Camless engine control for a robust unthrottling valved operation. SAE Paper 1998-98-1031, 1998, https://www.sae.org/publications/technical-papers/content/981031/

Turner

JWG

Bassett

Pearson

et al . New operating strategies afforded by fully variable valve trains. SAE Paper 2004-01-1386, 2004, https://www.sae.org/publications/technical-papers/content/2004-01-1386/

Wang

Zhang

Wang

et al . Effect of throttling valve-free load control strategies on a SI engine performance. J Transactions of CSICE 2009; 27: 224–230.

Boretti

. Use of variable valve actuation to control the load in a direct injection, turbocharged, spark-ignition engine. SAE Paper 2010-01-2225, 2010, https://www.sae.org/publications/technical-papers/content/2010-01-2225/

Pischinger

Salber

van der Staay

et al . Benefits of the electromechanical valve train in vehicle operation. SAE Paper 2000-01-1223, 2000, https://www.sae.org/publications/technical-papers/content/2000-01-1223/

Cairns

Zhao

Todd

et al . A study of mechanical variable valve operation with gasoline–alcohol fuels in a spark ignition engine. J Fuel 2013; 106: 802–813.

Park

Kim

Rhee

et al . A study on the design of electromagnetic valve actuator for VVT engine. J Mech Sci Tech 2003; 17: 357–369.

Wong

Tam

. Modeling and simulation of a dual-mode electrohydraulic fully variable valve train for four-stroke engines. Int J Automot Tech 2008; 9: 509–521.

Bokulich

. BMW returns to formula one with V10. J Automot Eng Int 2000; 3: 42.

10.

Bösl-Flierl

Flierl

Hannibal

et al . Variable valve lift device for the lift adjustment of gas-exchange valves of an internal combustion engine. Patent 7895981, USA, 2011.

11.

Flierl

Kausch

Kairies

et al . Potential of a mechanical fully-variable valve train: results of simulated and actual engine operation for the new univalve system. SAE Paper 2005-01-0768, 2005, https://www.sae.org/publications/technical-papers/content/2005-01-0768/

12.

Pierik

Burkhard

. Design and development of a mechanical variable valve actuation system. SAE Paper 2000-01-1221, 2000, https://www.sae.org/publications/technical-papers/content/2000-01-1221/

13.

Maas

Neukirchner

Dingel

et al . Potential of an innovative fully variable valvetrain. SAE Paper 2004-01-1393, 2004, https://www.sae.org/publications/technical-papers/content/2004-01-1393/

14.

Theobald

Lequesne

Henry

. Control of engine load via electromagnetic valve actuators. Technical Paper, SAE, Troy, MI, 1994.

15.

Cope

Wright

. Electromagnetic fully flexible valve actuator. SAE Paper 2006-01-0044, 2006, https://www.sae.org/publications/technical-papers/content/2006-01-0044/

16.

Giglio

Iorio

Police

et al . Analysis of advantages and of problems of electromechanical valve actuators. SAE Paper 2002-01-1105, 2002, https://www.sae.org/publications/technical-papers/content/2002-01-1105/

17.

Allen

Law

. Production electro-hydraulic variable valve-train for a new generation of IC engines. SAE Paper 2002-01-1109, 2002, https://www.sae.org/publications/technical-papers/content/2002-01-1109/