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1 Copyright © 2018 by ASME

Proceedings of the 2018 Bath/ASME Symposium on Fluid Power and Motion Control

FPMC 2018

September 12-14, 2018, University of Bath, Bath, United Kingdom

FPMC2018-8864

A NOVEL PIEZOELECTRIC DOUBLE-FLAPPER SERVOVALVE PILOT STAGE:

OPERATING PRINCIPLE AND PERFORMANCE PREDICTION

ABSTRACT

This paper proposes a novel architecture for the pilot stage of

electro-hydraulic two-stage servovalves that does not need a

quiescent flow and a torque motor as well as a flexure tube to

operate. The architecture consists of two small piezoelectric

valves, coupled with two fixed orifices, which allow variation of

the differential pressure at the main stage spool extremities in

order to move it with high response speed and accuracy. Each

piezoelectric valve is actuated by a piezoelectric ring bender,

which exhibits much greater displacement than a stack actuator

of the same mass, and greater force than a rectangular bender.

The concept is intended to reduce the influence of piezoelectric

hysteresis. In order to assess the validity of the proposed

configuration and its controller in terms of spool positioning

accuracy and dynamic response, detailed simulations are

performed by using the software Simscape Fluids. At 50%

amplitude the -90 bandwidth is about 150Hz.

Keywords: Servovalve, Piezoelectric, Ring bender, Simscape

NOMENCLATURE

A

Spool end area [mm2]

Aleak

Leakage area [mm2]

Ar

Restricted area [mm2]

Ar,0

Restricted area fixed orifice [mm2]

b

Width of the slots [mm]

C

Damping coefficient of the main spool [Ns/m]

Caprb

Capacitance of the ring bender [nF]

CD

Discharge coefficient of the main valve

CD,0

Discharge coefficient of the fixed orifice

CD,P

Discharge coefficient of the piezovalve

Crb

Damping coefficient of the ring bender [Ns/m]

Cstop

Damping coefficient hard stop [Ns/m]

D

Main spool diameter [mm]

Dint

Diameter of the hydraulic chamber [mm]

d

Diameter of the piezo valve orifice [mm]

E

Bulk modulus [N/m2]

E0

Pure liquid bulk modulus [N/m2]

e

Error

Fb,rb

Blocking force [N]

Fflow

Flow force [N]

Imax

Maximum current [A]

Ka

Gain of the amplifier

Kd,v

Max. blocking force over max. voltage [N/V]

KI

Integral gain

Kp

Proportional gain

Krb

Spring stiffness of the ring bender [N/m]

Ks

Additional spring stiffness [N/m]

Kstop

Stiffness hard stop [N/m]

Lint

Length of the hydraulic chamber [mm]

M

Main spool mass [kg]

m

Ring bender mass [kg]

n

Hysteresis non-linear term [V]

p

Pressure [N/m2]

pa

Ambient pressure [N/m2]

Q

Flow rate through the main valve[m3/s]

qc

Flow rate through the hydraulic chamber [m3/s]

Paolo Tamburrano

Department of Mechanics, Mathematics and

Management (DMMM), Polytechnic University of

Bari, Via Orabona 4, 70125, Bari, Italy

Riccardo Amirante

Department of Mechanics, Mathematics and

Management (DMMM), Polytechnic University of

Bari, Via Orabona 4, 70125, Bari, Italy

Elia Distaso

Department of Mechanics, Mathematics and

Management (DMMM), Polytechnic University

of Bari, Via Orabona 4, 70125, Bari, Italy

Andrew R. Plummer

Centre for Power Transmission and Motion

Control (PTMC), Department of Mechanical

Engineering, University of Bath, Claverton

Down, BA2 7AY, Bath, UK

2 Copyright © 2018 by ASME

q0

Flow rate through the fixed orifice [m3/s]

qs

Flow rate through the external chamber[m3/s]

qv

Flow rate through the piezo valve[m3/s]

Recr

Critical Reynolds number

t

Time [s]

u

Control output [V]

Vamp

Voltage from the amplifier [V]

Vc

Control Voltage [V]

Vcham

Oil volume in the hydraulic chamber [mm3]

Vdead

Dead volume [mm3]

Vleft

Oil volume in the left spool chamber [mm3]

Vo

Volume of the hydraulic chamber [mm3]

Vright

Oil volume in the right spool chamber [mm3]

X

Main spool displacement [mm]

x

Ring bender displacement [mm]

x0

Pre-compression of the additional spring [mm]

α

Parameter for the hysteresis formula

β

Parameter for the hysteresis formula

γ

Ratio of the specific heats

δ

Parameter for the hysteresis formula

ε

Relative gas content at atmospheric pressure

θ

Flow angle [rad]

ξ

Damping factor of the amplifier

Fluid kinematic viscosity [m2/s]

ρg0

Gas density at ambient pressure [kg/m3]

ρl

Actual density of the oil [kg/m3]

ρl0

Density of the oil at ambient pressure [kg/m3]

ωn

Natural frequency of the amplifier [rad/s]

INTRODUCTION

Electro-hydraulic two-stage servovalves adopt a hydraulic

amplification system serving as a pilot stage to move a main-

stage fluid-metering spool; the amplification system is usually a

flapper nozzle, a deflector jet or a jet pipe [1]. These valves are

widely used in aerospace and industrial sectors because of their

reliability and high performance in terms of step response speed

and frequency response [2]. However, they present a few

disadvantages that are still unsolved at the state of the art. One

of these disadvantages is the necessity for the pilot stage to have

a quiescent flow rate to work; although small compared to the

flow rate through the main stage, this internal leakage causes

power consumption [3]. Another disadvantage is given by the

electromagnetic torque motor assembly, which is necessary to

generate the hydraulic amplification, because it is composed of

a large number of mechanical and electrical parts that penalize

simplicity, set-up, and manufacturing costs [4]. Among these

parts, the most critical one is the flexure tube. The flexure tube

is a key component in the operation of a two-stage servovalve,

since it acts as a seal between the torque motor and the hydraulic

section of the valve. However, the presence of this component

increases the complexity of the valve, costs and duration of

manufacture because it needs to be manufactured very accurately

to ensure the stiffness required [5].

The use of piezoelectric actuators can be instrumental in

removing both the torque motor and the flexure tube from a

servovalve design, thus reducing complexity and manufacturing

costs. A piezoelectric actuator produces mechanical strain and

actuation force when a voltage is applied. A piezoelectric

actuator can provide very fast response times, but the drawbacks

are the high hysteresis (which can be as high as 20% of the

maximum displacement), the high dependence on temperature

variations, and creep. Common commercially available

piezoelectric actuators are the stack-type, amplified stacks,

rectangular benders and ring benders, as shown in Fig.1.

A stack actuator provides very high forces but low

displacement. To overcome this issue, amplification systems are

adopted to increase the displacement of a stack actuator but

producing lower forces. As an alternative to amplified stack

actuators, bimorph rectangular benders use a bending

deformation to exhibit high displacement but with very low

actuation forces. Finally, a ring bender is a flat annular disc

which deforms in a concave or convex fashion depending on the

polarity of the applied voltage. A ring bender exhibits greater

displacement than a stack actuator of the same mass, and an

increase in stiffness in comparison to similar size rectangular

bimorph type actuators.

(a) (b) (c) (d)

Figure 1. Piezo-stack actuator (a); amplified piezo-stack

actuator (b); bimorph actuator (c); ring bender actuator (d)

All these typologies of piezo-actuators have been used in the

literature as actuators for novel concepts of servovalves.

A stack actuator was used in [6] to control the flapper in a nozzle-

flapper pilot stage. In [7], four poppet valves as variable

restrictors were proportionally driven by a piezoelectric stack for

the actuation of a main stage valve.

In [8] and [9], a piezoelectric valve was directly actuated by

an amplified piezo stack actuator, with a lever element being

used to amplify the motion of the piezoelectric stack.

In [10], a commercially available stack actuator with a

flexure amplification system was used in place of a torque motor

to move a flapper in a flapper nozzle pilot stage.

In [11], [12] and [13], a piezoelectric bimorph actuator was

used to actuate the flapper in place of a torque motor in a two-

stage nozzle–flapper servovalve.

Sangiah et al. [5] used a bimorph piezoelectric actuator for

the control of the first stage of a deflector jet valve.

Bertin et al. [14] developed a pilot stage of a nozzle flapper

valve by using ring bender actuators.

In [3], [15] and [16], the first stage of a two stage servovalve

was realized by employing a four-way three-position small spool

controlled by a piezoeletric ring bender. The flow through the

small spool was capable of controlling a larger spool of the main

stage valve. The servovalve body was constructed using additive

manufacture (AM). This can provide significant benefits in

3 Copyright © 2018 by ASME

weight and manufacturing labour cost, as well as providing

additional design freedom.

In [7], a pilot operated piezo valve developed by

Hagemeister is described. The valve uses two adjustable

restrictors to change the pressure at the extremities of a main

stage spool. The pilot stage uses a flapper-nozzle system with a

piezoelectric bender realising the variable orifice. Since the

benders are only capable of very small forces, the bending

elements are equipped with compensating pistons for pressure

compensation.

DEVELOPMENT OF THE VALVE CONCEPT

The architecture proposed in this paper is shown in Fig. 2

and is based on the use of two small piezo valves which have the

task of changing the pressure at the extremities of a main spool.

The piezo valves are two way two position (2/2) valves which

are both actuated by a piezoelectric actuator. Each valve is

hydraulically connected both to one of the extremities of a main

spool and to one of two fixed orifices, which in turn are

connected with the high pressure port P. The main spool can be

a typical main spool of a four way three position (4/3) main stage

valve. The sliding spool is moved directly by opening the left

piezovalve or the right piezovalve depending on the required

hydraulic connections (P-A and B-T, or P-B and A-T).This

architecture can provide the following advantages compared to a

typical two stage valve:

The two piezo valves are normally closed, therefore ideally

there is no internal flow through the small piezo valves when

they are closed, which results in a notable reduction of the

internal leakage through the system.

The implementation of small piezo valves has the potential

to improve the response time of the main stage, because of

the high dynamics of piezo-actuators, the low inertia of the

components of the small piezo valves and the possibility of

using control systems that act on both piezovalves

simultaneously.

The need for a torque motor pilot stage with its associated

disadvantages is also avoided.

Figure 2. Architecture proposed

A piezoelectric actuator exhibits mechanical strain and/or

actuation force in response to an applied voltage. For a given

input voltage, the higher the mechanical strain, the lower the

actuation force exerted by the piezo-material. Fig. 3 shows the

relationship among displacement, force and voltage. The

maximum actuation force, called the blocking force, is obtained

at null strain.

For this specific application, the piezoelectric actuator that

best fits the displacement and force requirement is the ring

bender (see Fig. 1d). Table 1 reports the characteristics of the

ring benders produced by the manufacturer Noliac [17], showing

that different models are available according to the force and

displacement required. Note that all piezoelectric actuators

driven by voltage amplifiers exhibit hysteresis, typically of up to

20%. The presence of hysteresis can cause errors in the control

of the opening degrees of the piezo valves; it can also cause the

piezo valves to remain slightly open in the case of zero voltage

applied to the ring bender. These effects will be translated to the

main stage spool, causing errors in the spool positioning. For

these reasons, it is important to take measures to compensate for

hysteresis.

Figure 3. Displacement-Force-Voltage relationship for a

piezoelectric actuator

Figure 4. Possible designs for the piezo valves

P

T

A

B

P

P

T

T

Piezo

actuator

Piezo

actuator

Force

Displacement

Voltage

Blocking

Force

Free

stroke

0

4 Copyright © 2018 by ASME

The piezo valve can be designed either as a spool valve (see

fig.4a) or as a poppet valve (see fig.4b to 4e). Among possible

designs for the poppet valve type, the architectures shown in Fig.

4b, 4c, and 4d provide pressure compensation. The architecture

shown in Fig. 4a is very similar to that shown in Fig. 4d, apart

from the fact that the latter presents a mechanical stop for the

inner spool. The mechanical stop present in a poppet valve can

help to reduce the effect of hysteresis, as the ring bender can be

provided with a negative voltage to come back into a closed

position, thus avoiding internal leakage. Instead, in the case of

no mechanical stop (fig. 4a), hysteresis can be compensated by

providing the spool with a significant overlap, which must be as

high as 20 % of the spool travel.

Table 1. Characteristics of the ring benders produced by the

manufacturer Noliac

Product

type

Length /

outer

diameter

Width /

inner

diameter

Height

Operating

voltage,

max.

Free

stroke,

max.

Blocking

force,

max.

CMBR02

20 mm

4 mm

1.25

mm

200 V

± 28

µm

16 N

CMBR03

20 mm

4 mm

1.8 mm

200 V

± 20

µm

22 N

CMBR04

30 mm

6 mm

0.7 mm

200 V

± 108

µm

11 N

CMBR05

30 mm

6 mm

1.25

mm

200 V

± 70

µm

29 N

CMBR07

40 mm

8 mm

0.7 mm

200 V

± 185

µm

13 N

CMBR08

40 mm

8 mm

1.25

mm

200 V

± 115

µm

39 N

In the following, the nozzle-flapper type architecture of Fig.

4(e) is selected as the design to be investigated, by virtue of its

highest simplicity of construction. To provide null adjustment,

the ring bender is provided with an additional spring, as shown

in Fig.5, but there is no pressure compensation (i.e. the null will

shift with supply pressure changes).

The effects of cavitation can negatively affect the

performance of the nozzles and they can be evaluated by means

of numerical investigations [18].

Figure 5. Selected architecture of piezovalve with additional

spring for null adjustment

NUMERICAL MODEL

Fig. 6 shows the implementation of the two selected nozzle-

flapper piezo valves into a two stage valve design. In order to

analyze the feasibility of the proposed architecture, a simulation

model was developed using Simscape Fluids, which provides

component libraries for simulating fluid systems including

hydraulic pumps, valves, actuators, pipelines, and heat

exchangers [19]. The dynamic system was solved by computing

its states at successive time steps over a specified time span. The

time step was taken equal to 10-6 s, in order to increase the

accuracy. In the developed model, port A and port B of the main

valve are hydraulically connected, port P is connected to a pump

providing a constant pressure pp, whereas port T is connected to

a tank having constant pressure pT. The developed model is very

accurate, since it accounts for real phenomena such as fluid

viscosity, compressibility effects and presence of air within the

hydraulic oil.

Figure 6. Schematization of the main stage spool connected

with the two piezovalves

Main spool model

Assuming that the main spool (having mass M) moves to

the right with a displacement denoted by X, the following

equations were applied to analytically study the main stage

valve. The overall actuation force acting on the main spool is to

be calculated as the product of the pressure difference between

the left and right control chambers (pl-pr) and the spool area A.

The overall actuation force is counteracted by the flow forces in

the control chambers (FflowPB, FflowAT), the damping force (C)

and the inertia force ():

(1)

The damping coefficient C allows the fluid viscosity to be

taken into account. The flow rates qs,l and qs,r flowing through the

external chambers of the main spool are calculated as follows:

T

B

p

p

Spool

pl

P

T

A

pr

q

s,l

qs,r

p

p

q

o,l

q

o,r

Q

Q

T

T

P

X

5 Copyright © 2018 by ASME

(2a)

(2b)

where Vleft and Vright are the oil volumes present in the left and

right external chambers of the main spool, which can be

calculated as a function of the dead volume, Vdead, the spool

position, X, and the spool surface A:

(3a)

(3b)

In equations 2, ρl0 is the oil density at ambient pressure and

ρl is the actual density of the oil, calculated as follows:

(4)

where accounts for the quantity of air present in the oil, E0 is

the bulk modulus at atmospheric conditions, while and are

the gauge pressure of the oil and the atmospheric pressure; γ is

the ratio of the specific heat at constant pressure to the specific

heat at constant volume, with ρg0 denoting the gas density at

atmospheric pressure.

Each metering chamber of the main spool is approximated

by an orifice with variable area, applying the following

equations:

(5)

(6)

(7)

where Q is the flow rate through the main spool, is the

discharge coefficient, is the pressure drop across the metering

section, is the restricted area, b is the width of the slots;

denotes the minimum pressure for turbulent flow, is the

critical Reynolds number and is the fluid kinematic viscosity,

is the leakage area, which can be calculated as the product

of the spool perimeter and the clearance between the spool and

the bushing.

The flow forces must be taken into account for a precise

analysis of the spool dynamics; their value is usually very high

and cannot be neglected. Because of this, numerical and

experimental investigations are present in the literature to reduce

the flow forces [20] [21]. The flow force in each metering section

was calculated by using the equation:

where θ is the flow angle, which is calculated by using the

relation [22]:

) (9)

The position of the main spool is measured by an ideal

translational motion sensor, which does not account for inertia,

friction, delays and energy consumption.

Piezovalve model

Two hydraulic chambers are considered in order to evaluate

the effects of the fluid compressibility in the lines connecting the

piezovalves with the main stage:

(10)

(11)

where is the geometrical volume of the chamber (equal to the

product of an internal diameter Dint and an overall internal length

Lint), is the oil volume in the chamber at the gauge

pressure p, with denoting the flow rate through the chamber.

If the pressure in the chamber reaches the cavitation limit, the

above equations are enhanced by representing the fluid in the

chamber as a mixture of liquid and a small amount of entrained,

non-dissolved gas, and by calculating the mixture bulk modulus

as:

(12)

In this way it is possible to introduce an approximate model of

cavitation, which takes place in a chamber if the pressure drops

below the fluid vapor saturation level. In fact, the bulk modulus

of a mixture decreases at p→pa, thus considerably slowing down

further pressure change. At high pressure, p>>pa, a small

amount of non-dissolved gas has practically no effect on the

system behavior.

Each piezovalve is simulated as an orifice with variable area

through the following equations:

(13)

(14)

(15)

where CD,p denotes the discharge coefficient of the piezo valves,

is the flow rate through the piezovalve, d is the diameter of

the orifice, x is the ring bender position, is the fluid kinematic

viscosity, is the pressure drop across the piezovalve.

The position x of the ring bender is determined according to the

actuation force and the resistant forces acting on the ring bender

(having the mass denoted by m), as follows:

(16)

where denotes the blocking force exerted by the ring bender

having a stiffness denoted by . The additional spring has

6 Copyright © 2018 by ASME

stiffness denoted by and pre-compression denoted by x0; is

the damping coefficient of the ring bender which allows taking

into account the effects of viscosity upon the piezo valve

performance. Considering that the flow exiting the piezo valve

can be assumed radial, the flow forces acting on the left and on

the right ring bender (Fflow,pl and Fflow,pr) are calculated as follows:

(17)

(18)

The ring bender stroke is limited by two stops that restrict

its motion between upper and lower bounds. Each stop is

represented as a spring and damper. A force Fstop acts on the ring

bender when the maximum or minimum displacement is

reached:

for x (19a)

for

x (19b)

where and are the spring stiffness and damping of the

stop, with and denoting the maximum and minimum

displacement of the ring bender.

The flow through the fixed orifices is calculated as follows:

(20a)

(20b)

(21)

where CD,0 denotes the discharge coefficient of the two fixed

orifices, and denotes the orifice area.

Piezoelectric hysteresis was considered by implementing

the Bouc-Wen hysteresis model, described and used in [15]. The

Bouc-Wen model is represented by equation 22, where is the

hysteresis nonlinear term:

(22)

where α, β and δ are tuning parameters used to match the

hysteresis model to experimental data (the values from [15] are

used), and Vamp is the output voltage from the amplifier. The

hysteresis non-linear term allows the blocking force to be

expressed as a function of the output voltage from the amplifier

as follows: = (23)

where Kd,v is the ring bender maximum blocking force divided

by the maximum operating voltage.

The amplifier was simulated by using a second order

transfer function:

(24)

where Vc is the control voltage that is supplied to the amplifier,

and is the gain of the amplifier. In addition, to model the

current limit, the rate of change of voltage is limited according

to the following equation:

(25)

where Caprb is the capacitance of the piezoelectric ring bender.

Controller model

The control voltages to the left and to the right ring bender,

Vc,l and Vc,r, were obtained as follows:

= (26a)

= (26b)

where ul and ur are the control output, while off is an offset

introduced to cope with hysteresis; ul and ur are obtained through

a Propotional-Integral (PI) controller. The control output from

the PI controller is calculated through a proportional-integral

action employing a clamping anti-wind up method:

for e(t)≥0 (27a)

for e(t)≤0 (27b)

where e(t) is the error between the actual spool position and the

demand.

PARAMETERS VALUES

The blocking force can be adjusted by changing the voltage

applied to the ring bender, from -100 Volt to 100 Volt, and the

range values for the blocking force depend on the selected ring

bender. In this analysis, the ring bender CMBR08 (see Table 1),

having a maximum blocking force of ±39 N, is used.

Simulations were performed using the values for the operating

parameters as reported in Table 2.

The parameters of the main stage were assumed in order to

consider the simulation of a medium-size valve having a main

stage spool characterized by a diameter of 7 mm and mass of 20

g. The width of the slots of the bushing were assumed equal to

10 mm, namely about one half of the spool perimeter. A very

small value for the leakage area was considered, since in

servovalves the clearance between spool and bushing is usually

very small (lower than 3µm [1]). The dead volume, Vdead, was

7 Copyright © 2018 by ASME

calculated as the product of the main spool lateral surface and

the double of the maximum spool displacement (assumed equal

to 1 mm).

Table 2. Parameters assumed for the simulations

Component

Parameter

Symbol

Value

Main Valve

Main spool lateral surface

38.5 mm2

Main spool diameter

D

7 mm

Discharge coefficient

CD

0.7

Width of the slots

b

10 mm

Leakage area

1e-9 m2

Main spool mass

M

20 g

Dead volume

Vdead

77 mm2

Damping coefficient

C

10 Ns/m

Piezo valves

Diameter of the orifice

d

1 mm

Discharge coefficient

CD,p

0.7

Maximum displacement of

the ring bender

xmax

0.115 mm

Minimum displacement of

the ring bender

xmin

0 mm

Mass

m

6 g

Damping coefficient

Crb

412 Ns/m

Ring bender stiffness

krb

340000 N/m

Additional spring stiffness

Ks

340000 N/m

Pre-compression

additional spring

X0

0.06 mm

Stop damping coefficient

150 Ns/m

Stop stiffness

106 N/m

Fixed orifices

Restricted area

Ar,0

0.08 mm2

Discharge coefficient

CD,0

0.7

Hydraulic

chambers 1 & 2

Diameter

Dint

3 mm

Length

Lint

40 mm

PI parameters

Proportional gain

12

Integral gain

700

Offset

off

1 V

Saturation limits

ul,max

ur,max

6V

Pump

Pressure

pP

210 bar

Reservoir

Pressure

pT

1 bar

Oil

Density

ρl0

966 kg/m3

Relative gas content

ε

0.005

Amplifier

Natural frequency

ωn

12000 rad/s

Damping factor

ξ

0.8

Maximum current

Imax

1A

Ring bender capacitance

2x1740 nF

Gain of the amplifier

20

The dimensions of the additional chambers (Dint, Lint) were

calculated by estimating a possible hydraulic volume comprised

between the piezovalves and the fixed orifices (note that the

overall hydraulic volume at the left and right of the main spool

is given by the sum of the dead volume and the volume of the

additional chamber). The parameters of the ring bender and

amplifier are the same as those reported in a previous paper [3].

With regard to the stiffness of the additional spring, it was

assumed equal to that of the ring bender. The pre-compression of

the additional spring was calculated by equating the maximum

flow force acting on the ring bender with the pre-compression

force. The resulting pre-compression is then increased by 20%

to account for the hysteresis of the ring bender:

(28)

In this way, the additional spring is capable of keeping the

piezovalve closed in case of a null voltage applied to the ring

bender.

The results of the simulations, analyzed in the following

section, have been obtained for the fixed parameters reported in

Table 2. Future investigations will deal with the numerical

optimization of the main parameters, such as the area of the fixed

orifices, the diameter of the orifice of the piezo valves and the

PID parameters, in order to obtain the maximum response speed

of the valve.

RESULTS

The effectiveness of the proposed valve architecture has

been studied using step responses for the position of the main

spool. Fig. 7a, 7b, 7c and 7d show the time history of four step

tests, for step sizes of 0.1 mm, 0.4mm, 0.7mm and 1 mm,

respectively.

Similarly, Fig. 8a, Fig 8b, Fig. 8c and Fig. 8d show the time

history of the ring bender positions for steps of 0.1mm, 0.4mm,

0.7mm, and 1mm respectively. Table 3 reports the flow rate and

response times achieved for the four step tests.

The response rate is given by the rising time interval

required to reach 90% of the imposed set point. The valve

responds rapidly, with the response time increasing with

increasing step amplitude. Very small overshoots are seen.To

reach the desired target position, the right piezovalve is opened,

while the left piezovalve is maintained closed. The opposite

happens in the case of a negative step (i.e. the main spool moving

from the right to the left). The right piezovalve reaches its

maximum opening for the steps of 0.4mm, 0.7mm and 1mm, and

just remains open longer for the larger steps. When the set point

has been reached, the right piezo valve is maintained slightly

opened in order to have a pressure difference at the spool

extremities that is capable of counteracting the flow forces. It is

noteworthy that, thanks to the proposed control strategy, both

ring benders come back to the zero position when X=0mm in

spite of hysteresis. This is a notable result, as this ensures that no

internal leakage is present in the small piezo valves.

8 Copyright © 2018 by ASME

(a)

(b)

(c)

(d)

Figure 7. Main spool position vs time; (a): step=0.1mm,

(b): step=0.4mm, (c): step=0.7mm, (d): step=1mm.

(a)

(b)

(c)

(d)

Figure 8. Ring bender position vs time;

(a): step=0.1mm, (b): step=0.4mm, (c): step=0.7mm, (d):

step=1mm.

Table 3. Results of the step tests

Step test

X=0.1mm

X=0.4mm

X=0.7mm

X=1mm

Flow rate

6 l/min

25 l/min

43 l/min

62 l/min

Time to reach 90% of

the output

1.11 ms

2.73 ms

4.45 ms

6.2ms

9 Copyright © 2018 by ASME

The frequency analysis has been performed using a step-sine

signal. Figure 9 shows the time history of the main spool position

predicted for an amplitude of X=1mm and an input frequency of

50 Hz (Fig.9a) and 100 Hz (Fig. 9b). Figure 10 shows the

corresponding ring bender positions.

(a)

(b)

Figure 9. Frequency response: main spool position vs time; (a):

amplitude=1mm, frequency=50 Hz; (b): amplitude=1mm,

frequency=100 Hz.

(a)

(b)

Figure 10. Frequency response: ring bender position vs time;

(a): amplitude=1mm, frequency=50 Hz; (b): amplitude=1mm,

frequency=100 Hz.

(a)

(b)

Figure 11. Bode Plot: magnitude diagram (a) and phase

diagram (b)

As visible in both graphs of Fig.9a and 9b, the response to

a high frequency sinusoidal input is more like a triangle wave,

with an amplitude that decreases with increasing frequency. This

is because at these amplitudes and frequencies, the ring bender

valves are saturating, i.e. reaching their maximum opening.

The Bode Plot has also been plotted for an amplitude of 1

mm, 0.5 mm and 0.1 mm, as shown in Fig. 11.

When the amplitude is 1 mm, the phase shift is around -90

deg for a frequency of 100 Hz; when the amplitude is 0.5mm, the

phase shift is about -90 deg for 150 Hz frequency; when the

amplitude is 0.1mm, the phase shift is about -90 deg for 275 Hz

frequency.

These results confirm the effectiveness of the proposed

valve architecture: the main spool displacement reaches the set

point in a very short time and with negligible overshoot. The

dynamic characteristics of the system are also very good, with

the frequency response being comparable to that of conventional

two stage servovalves. The main advantage is the lack of internal

leakage in the small piezo valves, which will result in a more

energy efficiency for the system compared to conventional two

stage servovalves.

-8

-6

-4

-2

0

2

4

6

8

10 100

Amplitude (db)

Frequency-Hertz

500

Magnitude plot

1 mm amplitude 0.5 mm amplitude

0.1 mm amplitude

-120

-100

-80

-60

-40

-20

0

10 100

Phase-degrees

Frequency-Hertz

500

Phase plot

1 mm amplitude 0.5 mm amplitude

0.1 mm amplitude

10 Copyright © 2018 by ASME

CONCLUSIONS

This paper has presented a novel architecture for

servovalves that is based on the use of two small piezovalves

capable of changing the pressure at the extremities of a main

stage spool. Each piezovalve is actuated by a piezoelectric ring

bender, which can provide a good level of force and

displacement. The main advantage of this architecture is the

reduction of internal leakage, which results in power savings. A

SimScape model was developed to study this architecture. Both

step tests and frequency analysis have been carried out. It has

been shown that the response time is very fast, with negligible

overshoots being registered. When the spool position amplitude

is 1 mm, which is its maximum design value, the phase shift is

around -90 deg for a frequency of 100 Hz. Also, when the

amplitude is 50%, the phase shift is about -90 deg at 150 Hz

frequency.

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