J. Cent. South Univ. (2014) 21: 3098−3106 DOI: 10.1007/s11771-014-2281-0

Waveforms analysis and optimization of new electro-hydraulic excitation technology

HAN Dong(韩冬), GONG Guo-fang(龚国芳), YANG Hua-yong(杨华勇),

LIU Yi(刘毅), LIAO Xiang-ping(廖湘平)

State Key Laboratory of Fluid Power Transmission and Control (Zhejiang University), Hangzhou 310027, China

© Central South University Press and Springer-Verlag Berlin Heidelberg 2014

Abstract: A new electro-hydraulic exciter that consists of rotary valve and micro-displacement double-functioned hydraulic cylinder was proposed to realize different kinds of waveforms. Calculated fluid dynamics (CFD) simulation of rotary valve orifice reveals that orifice exists the two-throttle phenomenon. According to the finding, the revised flow area model was established. Vibration waveforms analysis was carried out by means of mathematic model and the related experiments were validated. Furthermore, as a new analysis indicator, saturation percentage was introduced first. The experimental results indicate that the revised flow area model is more accurate compared to the original one, and vibration waveforms can be optimized through suitable spool parameters and the revised cylinder structure. Key words: rotary valve; micro-displacement double-functioned hydraulic cylinder; two-throttle phenomenon; revised flow area model; saturation; drift motion

1 Introduction

Electro-hydraulic exciter is a kind of device that applies cyclic roads on object and motivates it to have certain vibration [1]. For its high power density, high thrust and adaptive load, electro-hydraulic exciter is widely used in earthquake simulation [2−3], railway maintenance [4] and construction machinery areas [5].

For current electro-hydraulic exciter, servo valve is mainly used. Because of slide valve spool’s structural limits, waveforms distortion is severe and vibration frequency is only limited in the low range, generally less than 20 Hz. For the reason, many researchers have designed new structures to overcome the limits. CUI et al [6−7] proposed a high-pressure rotary servo valve. RUAN et al [8−9] designed a 2D digital valve to improve vibration frequency. Other progresses include LEONARD’s rotary servo valve [10] and HOCHREIN’s rotary valve with special gear teeth structure [11]. On the other hand, researchers have made some progress in vibration waveforms. WEI [12] got the approximate analytical solution of waveform distortion of ultralow frequency standard vibrator. Current research is mainly focused on vibration waveform analysis. While related research on vibration waveform optimization is few

overseas, and less in China. In this work, new electro-hydraulic exciter

composed of rotary valve [13] and micro-displacement double-functioned hydraulic cylinder [14] is proposed, based on the new designed tamping device with hydraulic excitation and independent clamping movement [15−19]. Considering two-throttle principle concluded in CFD simulation, the revised flow area model of rotary valve orifice is founded and related experiments are validated. In addition, as a new preferable indicator, saturation percentage is first presented to analyze vibration waveforms. Suitable spool parameters and special revised cylinder structure are selected to optimize vibration waveforms. 2 Characteristics and work principle of new

electro-hydraulic exciter

As shown in Fig. 1, new electro-hydraulic exciter is made up primarily of rotary valve and micro- displacement double-functioned hydraulic cylinder. In the new designed tamping device [15], the load that shifting yoke drives the lower-damping arm to swing through the rotary shaft is replaced by the load that cylinder body drives the mass to reciprocate on the linear guide rail. The rotary spool which is driven by step

Foundation item: Project(51275499) supported by the National Natural Science Foundation of China; Project(2013CB035404) supported by the National

Basic Research Program (“973” Program) of China; Project(51221004) supported by the Science Fund for Creative Research Groups, National Natural Science Foundation of China

Received date: 2013−05−06; Accepted date: 2013−10−12 Corresponding author: GONG Guo-fang, Professor, PhD; Tel: +86−571−87952500; E-mail: gfgong@zju.edu.cn

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motor has two shoulders with the same structure. There are some rectangle grooves on the shoulder, and also the same numbers of corresponding rectangle windows in the sleeve. The hydraulic cylinder is driven by the rotary valve. As the piston is fixed with moving body, the main oil channel is designed in the piston rod, check valve lying at the end of main channel. Besides, with the requirement of micro-displacement, some unique limit holes linked to main channel are applied not only to achieve automatic displacement limit but also to avoid collision between piston and end cap.

When the step motor impels spool to an specific angle, oil flows from port P to port A, through the main channel, through the right check valve, then through the right check valve and the right limit holes. At the same time, oil flows through left limit holes, through main channel, then from port B to port T. In this case, the cylinder body moves right and gets the outer load to vibrate right. When the step motor impels spool to another angle, similar with the above mentioned, oil flows from port P to port B and from port A to port T. In this case, the cylinder body moves left and gets the outer load to vibrate left. With the change of step motor’s

speed, the frequency of rotary spool changes leading to the change of cylinder’s working frequency. 3 CFD simulation of orifice

Figure 2 presents the structure of spool and sleeve. Four same rectangle grooves are distributed evenly on each side of every shoulder. Every groove’s central angle is 22.5° and central angle of two neighbor grooves is 90°. Figure 3 shows the flow field model of inlet orifice. Because of its complex, flexible unstructured mesh is adopted. Figure 4 illustrates the inlet orifice with about 120000 tetrahedron meshes.

Before the dynamic simulation, boundary conditions and initial conditions are set as follows. Assuming that oil is regarded as incompressible and its gravity is negligible. Oil density is 889 kg/m3 and kinematic viscosity is about 4×10−5 m2/s. The boundary conditions of inlet and outlet are both pressure boundary condition. Considering the dramatic changes in flow field, k-ζ turbulent model is adopted.

Assuming that it is zero opening when the angular displacement is at θ=0°, Fig. 5 shows inlet orifice’s

Fig. 1 Schematic diagram of new electro-hydraulic exciter

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Fig. 2 Structure of spool and sleeve

Fig. 3 Flow field model of inlet orifice

Fig. 4 Flow field model of inlet orifice with meshes

pressure distribution under different angular displacements at θ=12°, 22.5° and 33°. In Figs. 5(a) and (b), when the angular displacement is at θ=12°, the opening is also at 12° with a bigger tendency. Pressure drop is mainly concentrated on A1 and A2 surfaces. In Figs. 5(c) and (d), when the angular displacement is at

Fig. 5 Pressure distribution of inlet orifice (Unit: 106 MPa): (a) Pressure distribution in z plane, θ=12°; (b) Pressure distribution in x

plane, θ=12°; (c) Pressure distribution in z plane, θ=22.5°; (d) Pressure distribution in x plane, θ=22.5°; (e) Pressure distribution in z

plane, θ=33°; (f) Pressure distribution in x plane, θ=33°

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θ=22.5°, the opening is largest at 22.5°. Pressure drop is also concentrated on A1 and A2 surfaces, but in less extent than that in Figs. 5(a) and (b). In Figs. 5(e) and (f), when the angular displacement is at θ=33°, the opening is at 12° with a smaller tendency. Pressure drop is also concentrated on A1 and A2 surfaces in equal extent compared with Figs. 5(a) and (b). According to the above analysis, conclusion can be made that pressure drop is mainly concentrated on A1 and A2 surfaces. With a rise of orifice opening, unchangeable A1 and bigger A2 made the pressure distribution change. As consequence, pressure drop is less concentrated. Therefore, the rotary valve orifice exists the two-throttle phenomenon. 4 Theoretical model 4.1 Original flow area model of orifice

As every groove’s central angle is relatively small, the previous original flow area model of orifice is simplified as the corresponding expansion form between grooves and windows shown in Fig. 6. The grooves and windows are both matched and symmetrical, also in accord with zero lap structure. Thus, the previous original flow area model of orifice is listed as

v

v v'v

v v

v v

π (4 1)π4 , ,

2 8

(4 1)π (4 2)ππ 4 , ,

8 8

(4 2)π (4 3)π4 π , ,

8 8

(4 3)π ( 1)π4 2π , ,

8 2

n nx r

n nx r x r

Sn n

x r x r

n nx r x r

(1)

where xv is the axial width of orifice, r is the radius of spool and n is the number of turns, n=0,1,2….

Fig. 6 Corresponding form between grooves and windows

4.2 Revised flow area model of orifice

According to the above dynamic simulation, the two-throttle phenomenon happened in the orifice. Therefore, compared to the previous original flow area model, the revised flow area model of orifice is established based on the two throttles phenomenon. Combined with conduction relationship shown in Fig. 2 and geometrical relationship shown in Fig. 3, flow area of A1 surface doesn’t vary with the spool rotation and can be written as

22

1 vπ π π π

sin cos 2 sin16 16 16 16ir

S r rz (2)

where zv is the radial length of orifice.

Flow area of A2 surface varies periodically with the spool rotation. So, it can be described as

v

vv

2

π (4 1)π, ,

2 8

π (4 1)π (4 2)π, ,

4 8 8( 1, 4)

(4 2)π (4 3)π0, ,

8 8

(4 3)π ( 1)π0, ,

8 2

i

n nx r

x r n nx r

S in n

n n

(3)

2v

v

vv

π (4 1)π0, ,

2 8

(4 1)π (4 2)π0, ,

8 8( 2,3)

π (4 2)π (4 3)π, ,

4 8 8

(4 3)π ( 1)π, ,

2 8 2

i

n n

n n

S ix r n n

x r

x r n nx r

(4)

Taking the two-throttle phenomenon into account, the revised flow area of orifice is calculated in accordance with series connection between A1 surface and A2 surface. So, the relation among pressure drop of orifice pi, pressure drop of A1 surface p1i and pressure drop of A2 surface p2i is given as

1 2i i ip p p (5)

The flow equation through the orifice is shown as

d 2i i iq C S p (6) where Cd is flow rate coefficient, is oil density.

The flow equation through A1 surface is shown as

1 d 1 12i i iq C S p (7)

The flow equation through A2 surface is shown as

2 d 2 22i i iq C S p (8)

Because of series connection between A1 surface and A2 surface, qi=q1i=q2i. Thus, based on the above analysis equations, the flow area of all orifices is calculated as

v

2 21 2

4

1 1i i

S

S S

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2 22 v2v

2 22v2

vv

22

v

4,

1 1

( )π π π πsin cos 2 sin

16 16 16 16

π (4 1)π ,

2 8

4,

1 1

ππ π π πsin cos 2 sin

416 16 16 16

(4 1)π (4 2)π ,

8 8

4

1

π π π πsin cos 2 sin

16 16 16 1

x rrr rz

n n

x rr x rr rz

n n

rr rz

2 2

vv

2 22v2

vv

,1

π

46

(4 2)π (4 3)π ,

8 8

4,

1 1

ππ π π πsin cos 2 sin

216 16 16 16

(4 3)π ( 1)π ,

8 2

x rx r

n n

x rr x rr rz

n n

(9)

Figure 7 shows the flow area curve of original model and revised model under 40 Hz. It can be seen that the flow area curve of original model is linear, whose peak reaches 144 mm2. However, the flow area curve of revised model is non linear and its peak reaches 96 mm2, which is about 2/3 of that in original model.

Fig. 7 Flow area of original model and revised model

4.3 Electro-hydraulic exciter model

The flow equation of rotary valve is calculated as

s L B Ad v

L

s L A Bd v

,

π (2 1)π ,

2 4

,

(2 1)π ( 1)π ,

4 2

p p p pC S

n n

qp p p p

C S

n n

(10)

where ps is the supply pressure, pL is the load pressure, pA and pB are pressure drops of limit holes in cylinder’s two chambers, respectively.

Figure 8 describes the flow area change of limit holes. First, oil flows into the inlet chamber through check valve. Then, limit holes in the inlet chamber open. The flow area of inlet limit holes enlarges with the increase of cylinder displacement. At the same time, the flow area of outlet limit holes minifies. Therefore, the total flow area of inlet chamber is equal to flow area of inlet limit holes plus flow area of inlet check valve, which is expressed as

For 0≤yp≤L/2,

2p2

in

2π 1arccos 1

4 4

ydA L

L

2p p p

1( 2 )

2L y Ly y (11)

For L/2≤yp≤L,

2 2p2

in

2π 1 πarccos 1 +

4 4 4

yL dA L

L

2p p p

1(2 )

2y L Ly y (12)

Fig. 8 Flow area change of limit holes

The total flow area of outlet chamber is equal to

flow area of outlet limit holes, which is expressed as For 0≤yp≤L/2,

2

p2out

2π 1arccos 1

4 4

yLA L

L

2p p p

1( 2 )

2L y Ly y (13)

For L/2≤yp≤L,

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p2 2out p p p

21 1arccos 1 (2 )

4 2

yA L y L Ly y

L

(14)

where yp is the displacement of rod, L is the diameter of limit holes and d is the diameter of check valve.

The continuity equation of inlet chamber is written as

p 0 p p AA p ip L ep A

e

d ( ) d

d dAy V A y p

q A C p C pt t

(15)

The continuity equation of outlet chamber is written

as p 0 p p B

B p ip L ep Be

d ( ) d

d dBy V A y p

q A C p C pt t

(16)

where Ap is the effective area of rod, Cip and Cep are internal and external leakage coefficient, respectively, pA and pB are pressure of two chambers, VA0 and VB0 are initial volume of two chambers, e is effective bulk modulus of oil.

Considering that the outer load of system can be equivalent to the mass-spring-damp model, regardless of arbitrary force, the force equilibrium equation of cylinder is expressed as

2p p

p L p p p p2

d d

dd

y yA p m B K y

tt (17)

where mp is equivalent mass, Bp is equivalent viscous damping coefficient, Kp is equivalent stiffness of spring. 5 Waveforms analysis and optimization 5.1 Waveforms experiment

The electro-hydraulic exciter diagram is illustrated in Fig. 9. In this system, relief valve is used to control the supply pressure. Accumulator can absorb the pressure fluctuation under high frequency. In addition, some manometers and flowmeters are mounted to measure the local pressure and flux. With Labview software, the industrial control computer sends out command signals to stepper driver. After receiving command signals, the stepper driver controls step motor to rotate, thus driving spool to rotate. As a result, the rotating spool realizes the piston’s periodic reciprocating movement. Related movement parameters are acquired by the ICP sensor and their curves are finally displayed on the screen of computer. Figure 10 shows the picture of electro- hydraulic exciter. Related main parameters of the hydraulic system are listed in Table 1.

Figure 11 shows the theoretical and experimental waveforms at xv=6 mm and f=40 Hz. It can be seen that there is drift motion of the piston. That is to say, because of asymmetrical flow, errors of manufacturing and assembling, external disturbance and so on, the piston is asymmetrical around the middle point and drifts towards

Fig. 9 Diagram of hydraulic system: 1−Tank; 2−Filter;

3−Variable displacement pump; 4−Relief valve; 5−Check valve;

6−Globe valve; 7−Flowmeter; 8−Manometer; 9−Accumulator;

10−Rotary valve; 11−Step motor; 12−Micro displacement

cylinder; 13−Mass; 14−ICP sensor; 15−Data acquisition card;

16−Industrial control computer; 17−Stepper driver.

Fig. 10 Picture of electro-hydraulic exciter

Table 1 Main parameters of hydraulic system

Parameter Value

r/m 0.0155

zv/m 0.005

e/Pa 8×108

Cd 0.62

VA0/L 1.44

ps/Pa 8×106

f/Hz 20−40

xv/m 0.006

mp/kg 42

Ap/mm2 4040

VB0/L 1.44

/(kg·m−3) 870

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Fig. 11 Waveforms at xv=6 mm, f=40 Hz

one side. The drift motion seriously affects the waveform quality. Besides, compared with theoretical result in original model, the diagram proves that the theoretical result in revised model and the experimental result basically tally regardless of drift motion. Therefore, it comes to the conclusion that the revised flow area model of orifice is more accurate compared to the original one.

Figure 12 illustrates waveforms with different working frequencies at xv=6 mm. The waveforms are all asymmetrical in a cycle, which is due to the drift motion of cylinder. What’s more, amplitudes decrease with the increase of working frequencies. When working frequency exceeds the critical valve, it is an approximate triangular wave without saturation. However, below the critical valve, it is an approximate trapezoidal wave with saturation.

Fig. 12 Waveforms with different working frequencies at xv=

6 mm

Figure 13 presents waveforms with different axial

lengths of orifice at f=30 Hz. Waveforms have larger amplitudes and steeper slopes with the increase of axial lengths of orifice, which is because flow rate increases through orifices per unit time. When axial length of

orifice exceeds the critical valve, it is an approximate trapezoidal wave with saturation. However, below the critical valve, it is an approximate sine wave without saturation.

Fig. 13 Waveforms with different axial lengths of orifice at

f=30 Hz.

In order to measure the extent of waveform

saturation, saturation is proposed that is equal to the percentage of saturation span in a cycle. Figure 14 shows the waveform saturations with different working frequencies and different axial lengths of orifice. The theoretical result in revised model basically agrees with the experimental result. In addition, axial length decrease of orifice or working frequency decreases leads to the increase of saturation. Saturation is nonlinearly related to axial length of orifice and the nonlinearity decreases with the increase of working frequency.

Fig. 14 Waveform saturations with different working

frequencies and different axial lengths of orifice

5.2 Revised cylinder structure

In order to solve the drift motion, a revised cylinder structure is designed, as shown in Fig. 15. Compared with the original one, there are two internal leakage channels. One is in the side wall of body and the other is

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in the piston. Not only the two internal leakage channels are connected, but also the opening is controlled by the displacement of piston. What’s more, the renewable damping hole and the check valve are both designed in the first internal leakage channel, so as to adjust internal leakage flow and direction. With the revised cylinder structure, waveforms with different damping hole diameters are displayed in Fig. 16. It can be seen that with the increase of damping hole diameters, the drift motion first decreases, and then increases. For the cylinder, 2 mm damping hole is most suitable to avoid the drift motion.

Fig. 15 Original and revised cylinder structures: (a) Original

cylinder structure; (b) Revised cylinder structure

Fig. 16 Waveforms with different damping hole diameters in

revised cylinder.

6 Conclusions

1) With unique characteristics and new principle, the electro-hydraulic exciter composed of rotary valve and micro-displacement double-functioned hydraulic cylinder is proposed, so as to realize different kinds of waveforms.

2) Dynamic simulation of rotary valve orifice is conducted and pressure distribution with different openings shows that the orifice exists two throttles phenomenon. Original flow area model and revised model by taking the simulation result into account are both established and related experiments prove that the revised model is more accurate.

3) Certain amplitude and slope of approximate triangular wave, sine wave and trapezoidal wave can be achieved by adjusting suitable working frequency and axial length of orifice. Axial length increase of orifice or working frequency decrease can lead to saturation increase. Besides, working frequency increase reduces the nonlinearity between saturation and axial length of orifice.

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(Edited by DENG Lü-xiang)