Indian Journal of Engineering & Materials Sciences Vol. 16, February 2009, pp. 7-13 Inestigation on the characteristics of a new high frequency three-way proportional pressure reducing ale in ariable ale system of automobile engine Jin-rong Liu a, Bo Jin a*, Ying-jun Xie a, Ying Chen a & Zhen-tao Weng b a The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang Uniersity, Hangzhou 310027, China b Ningbo HOYEA Machinery Manufacture Co., Ltd, Ningbo 315131, China Receied 21 April 2008; accepted 6 January 2009 In this study, a new high frequency three way proportional pressure-reducing ale has been deeloped. By reducing the turns of the coil and using a high speed amplifier, the responding time of the proportional solenoid is reduced to less than 1 ms. The steady and dynamic analyses show that the output pressure is proportional to the coil and the dynamic bandwidth can be increased by increasing the coil. An experimental system is built up and results well agreed with the theoretical and simulation analyses. The bandwidth of the ale is about 130 Hz at -3dB, which can meet the demand of automobile engine with maximum speed of 3000 rpm. Keywords: High frequency, Proportional pressure reducing ale, Variable ale, Proportional amplifier, Simulation The conentional mechanism of ale in automobile engine is drien by cam. This method is difficult to meet the demand for high dynamic quality, economical efficiency and enironment protection. Some research showed that by using ariable ale techniques, engine performance can be improed 1. There are three kinds of ariable ale systems including cam system, electromagnetic system and electro-hydraulic system 2. Because the adjustable range of cam system is restricted within narrow limits, electromagnetic system and electro-hydraulic system are showing its potential features in industry application. In electro-hydraulic system, there is no cam 3 ; hence the opening and closing processes of the ale are controlled by a high-speed electromagnetic ale. The response time and the flow rate are two contradictory parameters for a high-speed electromagnetic ale. Many high speed ales hae been deeloped for the control of fuel injection 4-7. Because the ariable ale system requires larger flow rate, usually sero ales are employed in the system 8-10. Due to the high cost of sero ales, therefore many lower cost, high speed and large flow rate ales are deeloped 11-13. In this study, a low cost, high frequency proportional pressure-reducing ale was deeloped. First, we introduce the schematic diagram of electrohydraulic ariable ale system and working principle *For correspondence (E-mail: bjin@zju.edu.cn) of the ale. Then, based on the mathematical model, we analyze the steady-state and dynamic performance of the ale. Finally, we carry out experiments to erify both the analysis and the desired performances of the ale. Structure and Working Principle In this paper, a newly deeloped pressure-reducing proportional ale with low cost and high frequency is employed in the ariable ale system show in Fig. 1. Figure 1 shows the schematic diagram of electrohydraulic ariable ale system. It is easy to see that the opening process of ale in the engine is proportional to the output pressure of the pressure reducing ale. The working principle of the pressure reducing ale is shown in Fig. 2. This is a three way proportional pressure reducing ale without return spring. The force generated proportional electromagnet is balanced by the hydraulic force acted on the left side of the spool. Hence, the output pressure P c can be controlled by the of the electromagnet. The maximum working stroke of the ale spool is 0.6 mm, which is beneficial to obtain good performance in dynamic response. Steady State Analysis of the Vale In order to analyze the effect of the input on the steady-state and dynamic performance, the mathematical model of the ale was built 14-16.
8 INDIAN J. ENG. MATER. SCI., FEBRUARY 2009 Fig.1 Schematic diagram of electro-hydraulic ariable ale system (1-tank; 2-proportional relief ale; 3-hydraulic pump; 4- proportional pressure-reducing ale; 5-motor; 6-single-rod hydraulic cylinder; 7-return spring; 8-ale) (2) and (3), the relationship between output pressure and solenoid can be expressed as following: K F = i f c I A A (4) P Equation (4) indicates that the output pressure of ale is proportional to the and has a deadband because of friction. Fig. 2 Working principle of the ale In steady state, the position of engine ale remains unchanged, hence Q L =0, the input flow from hydraulic power source is used to compensate the leakage: C wx 2( Ps Pc ) = K P (1) ρ d c c The force balance equation for ale spool can be expressed as following: Fm Pc A Ff K f X = 0 (2) The force output of the solenoid can be expressed as: Fm = KiI K y X (3) Because the leakage of the ale is ery small, from Eq. (1), it can be obtained: X =0, combine with Eqs Dynamic Model of the Vale The motion equation of the spool can be expressed as: 2 d X dx m 0 2 c F M B P A dt dt = (5) The force output of the solenoid can be expressed as: F m KI = e τ s + 1 ts (6) The continuity equation of chamber V c can be expressed as: V dp dx Q Q Q C P = A (7) 1 2 where c c L ip c βe dt dt Q L =0 (8) CdW ( X U ) 2( Ps Pc ) / ρ U < X max Q1 = 0 - X max U (9)
LIU et al.: PROPORTIONAL PRESSURE REDUCING VALVE 9 Fig. 3 Circuit diagram of the amplifier CdW ( U X ) 2 Pc / ρ X max < U Q2 = 0 U max (10) Combine Eqs (5) ~ (7), the dynamic model of the ale can be obtained. Design of Solenoid and its Amplifier The requirements for the solenoid mainly contain two aspects: (i) it should output enough force to oercome the hydraulic force and (ii) it should hae fast-response. The time constant of the solenoid is L τ = (11) R 2 N L = (12) r απ N( D + d) R = (13) 2q By putting Eqs (12) and (13) into Eq. (11), we can obtain: 2qN τ = απ r( D + d) (14) Equation (14) indicates that decreasing N can reduce time constant. Fig. 4 Dynamic response of the To meet both force and response requirements for the solenoid, smaller turns and larger must be used. In this case, N = 100 and I = 8 A. To make the solenoid act as quick as possible, a feedback PWM amplifier was employed, whose schematic diagram is shown as Fig. 3. The operating principle of the proportional amplifier is as follows: (i) the in the solenoid is detected and fedback to compare with the input signal; (ii) if the is smaller than desired, the comparators will turn T1 and T2 on, so the solenoid is charged, the begin to increase and (iii) if the is greater than desired, the comparators will turn T1 and T2 off, the is discharged from the feedback resistance R f, the diode D2, the power supply E, the ground and the diode D1. Hence, the in the solenoid can be controlled in the loop. By choosing smaller turns, larger s and the use of PWM amplifier, the time constant of the solenoid can be reduced significantly. Figure 4
10 INDIAN J. ENG. MATER. SCI., FEBRUARY 2009 Fig. 5 Simulation model Fig. 6 Simulation result of the pressure of port A with different Table 1 Simulation parameters Parameter Value N 100 X 0.6 mm P s 6 MPa L 1.2 mh R 1.2 Ω I 8.7 A M 0.09 kg U 12 V B 100 N(m/s) 8 mm D shows the dynamic response of the in the solenoid, the time constant is less than 1 ms. Digital Simulation of the Vale A digital simulation model has been build up using AMESim, the model is shown in Fig. 5 and the simulation parameters are defined in Table 1. Figure 6 shows the relationship between output pressure and input in steady state, it shows Fig. 7 Simulation results of step response of the ale with different that the output pressure is proportional to the input and has a small dead-band, the results agree well with the results of Eq. (3). Figure 7 shows the simulation results of step response under the different conditions of I is 4 A, 6 A and 8 A.
LIU et al.: PROPORTIONAL PRESSURE REDUCING VALVE 11 From these figures, the following conclusions can be drawn: (i) there is a delay time between the input signal and the output pressure, which is because of the oerlap of the ale spool; (ii) the delay time will decrease with the increases of the input. Because the oerlap is a constant alue, when the increases the force output will increase, the spool can moe faster to oercome the oerlap, and the oershot increase too. In the real application, the delay time can be compensated by software ; and (iii) the output pressure is a little bit lack of damping, this is because the load is cut off (Q L =0). In real application, the damping will increase significantly. From Fig. 8, we can come to the following conclusions: (i) the cut-off frequency at -3db increases with the increase of input. This phenomenon coincides with Fig. 6, i.e., the larger force moes the spool quicker, hence increase the dynamic response. In real applications, this character will help increase the dynamic response of engine ale; (ii) the oershot of pressure increases with the increase of ; and (iii) the system s damping is low, because the shut off of load. Experimental System An experiment system is employed to testify the pressure reducing ale. The block diagram of the experimental bench is shown in Fig. 9. The experimental bench consists of a lowfrequency signal generator, a proportional relief ale, the PWM amplifier, a pump, a motor, and the proportional pressure-reducing ale to be tested, a pressure transducer and an oscilloscope. The output pressure is measured by the pressure transducer. The oscilloscope is used to display and store the signals. Results and Discussion The steady state and dynamic experiment results are shown in Figs10-12. These experimental results coincide with the theoretical analyses and digital simulation. The output pressure has a dead-band and a hysteresis less than 3%. The dynamic response will increase when the input increases. Fig.8 Simulation results of frequency responding with different Conclusions In this paper, a high-frequency three-port proportional pressure-reducing ale is deeloped, whose features are studied by the means of theoretical analysis, digital simulation and experiments. The following conclusions may be drawn from this study: Fig. 9 Block diagram of the experimental bench (1-oil filter; 2-proportional relief ale; 3-motor; 4-pump; 5-tank; 6-low frequency signal generator; 7-amplifier; 8-proportional pressurereducing ale; 9-pressure transducer; 10-pressure gauge; 11- oscilloscope) Fig. 10 Experimental result of output pressure with different
12 INDIAN J. ENG. MATER. SCI., FEBRUARY 2009 Fig. 12 Experimental result of frequency response with different () The cut-off frequency is about 130 Hz with a 8 A input. It can meet the demand for automobile engine with maximum speed of 3000 rpm. (i) Digital simulation results agree well with the experimental results, which alidates the mathematical model. Consequently, the model can be used for optimizing the ale performance in the future. Acknowledgement This paper is supported by the Nature Science Foundation of Zhejiang Proince, China. Project Number: Z106543 Fig. 11 Experimental results of step response with different (i) The output pressure is proportional to the input. Hence, the engine ale lift can be changed by arying the input. (ii) The output pressure has a small hysteresis less than 3%. (iii) The ale is lack of damping with the cut off of the load. (i) The dynamic response speed increases with increase in input, which can help the engine ale act faster with large input. Nomenclature P c = pressure of port A I = input X = spool displacement F m = solenoid force K i = -force gain K y = displacement-force gain Q L = load flow K c = leakage coefficient C d = flow coefficient w = port width P s = system pressure K f = steady flow force stiffness A = orifice area F f = friction force K = the gain N = number of turns L = coil inductance R = coil resistance τ = time constant r = the reluctance D = outer diameter of the coil d = internal diameter of the coil q = sectional area of the wire
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