Bichop R.H. (Ed.) Mechatronic Systems, Sensors, and Actuators: Fundamentals and Modeling

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21-72 Mechatronic Systems, Sensors, and Actuators

also known as distributors, are distinguished according to the type of mobile element and therefore of

their internal structure, by the number of possible connections with external pipes and by the number

of switching positions.

The mobile element can be a poppet type or a spool type. Poppet valves are indifferent to fluid type

and are not affected by impurities in the fluid, but require high actuating forces as it is not possible to

compensate for the hydraulic forces of the oil pressure. Spool valves permit simultaneous connection to

several ways and different switching schemes and therefore are more common because of their variability.

The number of possible connections is defined by the number of hydraulic connections or ways present

on the external body of the valve. The number of switching positions corresponds to the number of

connection schemes which a valve makes it possible to obtain by means of appropriate movements of

the mobile element.

Figure 21.99 shows the operating scheme of a four-way, two-position spool valve (indicated as 4/2)

connected to a double acting linear actuator. In the first position (Figure 21.99a) the supply is in

communication through output A with the rear chamber of the cylinder, while the front chamber

discharges through port B. In this configuration, the piston effects an advance stroke with the rod coming

out. In the second position, (Figure 21.99b), the result of the movement of the slide valve is that the feed

and discharge conditions of the two chambers are inverted, and therefore, a retract stroke is effected.

A directional valve with several positions is represented symbolically by means of quadrants side by

side depicting the connections made by each position. Figure 21.100, for example, shows some directional

valve symbols in accordance with ISO standards. The central configuration of the three-position valves,

which is normally the rest position, is linked with the geometry of the valve spool and of the associated seats.

Directional valves can be controlled in various ways (Figure 21.100): manually, by applying muscle

power; mechanically, by means of devices such as cams, levers, etc.; hydraulically and pneumatically, by

means of fluids under pressure; and electromagnetically, directly or piloted, depending on whether the

positioning force is generated directly by the electromagnet placed in line with the slide valve, or by

means of a hydraulic fluid, the direction of which is managed by a pilot valve which is smaller than the

main controlled valve.

On–Off Valves

On–off valves are unidirectional valves, which permit the fluid to flow in one direction only. Because they

impede flow in the opposite direction they are also called nonreturn or check valves. On-off valves are

normally placed in the hydraulic circuit between the pump and the actuator so that, when the generator

stops, the fluid contained in the system is not discharged into the reservoir but remains in the piping. This

prevents a waste of energy for subsequent refilling and guarantees positioning of the actuator under load.

Constructively, check valves consist of an actuator, with ball or piston, which in the impeded flow

configuration is maintained in contact against its seat by the thrust of a spring (nonreturn valve), or by

the pressure difference between inlet and outlet (unidirectional valve).

Pressure Regulator Valves

There are essentially two types of pressure regulator valves: pressure limiter valves or relief valves, and

pressure reduction valves.

FIGURE 21.99 Scheme of four-way two-position valve.

SupplyReturn

(b)

(a)

BBAA

SupplyReturn

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Relief valves guarantee correct operation of the system, preventing the pressure from exceeding danger

levels in the system itself. There is always one maximum pressure valve in a hydraulic circuit to discharge

any excess flow not used by the system back towards the reservoir. This is because the generator, or

positive-displacement pump, provides a continuous flow of fluid which, if not absorbed by the user and

in the absence of a relief or maximum pressure valve, would let the pressure in the system increase to

unacceptable values. Pressure limiter valves can be direct-acting or piloted. The first provides the force

of a spring with a fixed preload as the force contrasting the pressure of an obturator or an adjustable

one, which guarantees the maximum opening pressure. The latter replaces the action of the spring with

that of the hydraulic control fluid managed by a pilot valve.

The function of the pressure regulator valves is to maintain a constant pressure valve downstream

from them, independently from variations in the upstream pressure. The regulated pressure value can

be set manually, by means of a pilot signal, or by an electrical analog command. In the latter case, pressure

regulator valves may operate in closed electrical loops, as they have an internal transducer to measure

the controlled pressure.

Flow-rate Regulator Valves

A flow-rate regulator valve makes it possible to control the intensity of the flow of fluid passing through

it. Functionally it operates as a simple restriction, similar to an orifice, with a variable area. The flow

passing through a restriction is a function of the area of passage and of the difference in the pressures

upstream and downstream from the component. The simple restriction is therefore sensitive to the load,

as the flow rate also depends on the pressure drop at its ends, which is established by the other components

in the circuit.

In the case of a pressure-compensated flow regulator valve, the flow rate is found to be maintained

sufficiently constant above a minimum pressure stage (typically 10 bar) as an exclusive function of the

external manual or electrical set-point. In this case, the valve has two restrictions in series, one of which

is fixed and the other automatically variable, so as to maintain the pressure drop constant on the fixed

restriction and guarantee the constancy of the flow rate.

The symbols for flow regulator valves in accordance with ISO standards are given in Figure 21.101.

FIGURE 21.100 Valves symbols.

3 Position, 4 way

open centre

3 Position, 4 way

P port closed

3 Position, 4 way

tandem centre

3 Position, 4 way

closed centre

3 Position, 4 way value,

solenoid operted with

spring center

2 Position, 4 way value

lever operted with detents

2 Position

4 way

2 Position

3 way

2 Position

2 way

Lever

Plunger Roller Hydraulic pilot Pneumatic pilot Solenoid

Foot pedalPush buttonDetentSpring return

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21-74 Mechatronic Systems, Sensors, and Actuators

Proportional Valves and Servovalves

Servovalves began to appear at the end of the 1930s and were mainly used in the military and aeronautical

fields. The first commercial versions appeared in the mid-50s. Servovalves and proportional valves are

widely used today in the civil field, in the aeronautical, aerospace, automotive, and industrial sectors. In

general, they are used for the continuous control of the displacement, speed, and force of a hydraulic

actuator from which high performance is requested in terms of positioning precision, or accuracy in up

and running conditions, and of working frequency bandwidth amplitude, both in open and closed loop

control configurations.

A servovalve or proportional valve is a fluid component capable of producing a controlled output as

a function of an input of electrical type. The device converting the electric signal into an action of the

spool or poppet of the valve is electromagnetic, of the torque motor or proportional solenoid type. The

torque motor converts a small DC current into torque acting on the rotor plate, in bipolar mode.

Proportional solenoids produce a unidirectional force on the mobile armature function of the current

circulating in the winding, with the characteristic of maintaining this force approximately constant within

the cursor work displacement range. The torque motor, with lower current and inductance values, has

shorter response times than the servosolenoid, which operates with notably higher currents, but generates

lower mechanical power outputs. The torque motor, therefore, constitutes the pilot stage usually found

in servovalves, while the servosolenoid used in proportional valves acts directly on the valve spools.

The magnitude directly controlled by the servovalve or proportional valve can be a flow rate or a

pressure difference, depending on the type.

Servovalves and proportional valves are usually distinguished on the basis of the following character-

istics:

•

Input signals

•

Precision

•

Hysteresis

•

Linearity between input and output

•

Dead band

•

Bandwidth

Input signals are characterized by the type of signal and range of variation. Current signals (±10 mA

or 4–20 mA) or voltage ones (0–10 V) are typical. Precision is intended as the difference between the

desired value and the value effectively achieved. It is provided as a percentage of the full scale value.

The hysteresis derives from the different behavior shown by the component with ascending settings and

corresponding points descending. Its value expresses the percentage ratio between the maximum devi-

ation and the full scale value. Linearity by nature is a characteristic that can be assessed over the

entire working range. It can be expressed in an absolute manner as the maximum percentage deviation

of the input/output relation of its linear regression. In general, better linearity is requested in position

control compared with the cases of speed, pressure, or force controls. The dead band determines the

minimum input value at which an output variation is obtained. Unlike the above, bandwidth is a

FIGURE 21.101 Symbols of flow control valves.

Adjustable

restrictor

valve

Pressure

compensated

flow control valve

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Actuators 21-75

characteristic of the dynamic type. This is because it refers to a frequency diagram of the component

and defines the frequency at which the response drops by 3 dB below the low frequency value. Normally,

a bandwidth two to five times greater is required for continuous control valves compared with that

required by the system.

The main differences between servovalves and proportional valves are shown in Table 21.6. Except for

the traditional difference in the electromechanical conversion device, there are overlaps in the static and

dynamic characteristics in many components available on the market.

On the basis of the generically superior static and dynamic characteristics, servovalves are commonly

used in closed loop controls while proportional valves are used in open loop systems.

Servovalves

Two-stage models are very common in the context of servovalves, where a first pilot stage converts a low

power electric signal into a pressure difference capable of acting on the slide valve of the second stage,

usually four-way and symmetrical. Flow rate control servovalves are divided into two categories on the

basis of how they make the electric–hydraulic conversion:

•

Nozzle-flapper

•

Jet-pipe

An example of nozzle flapper servovalves is shown in Figure 21.102. It comprises two stages: the former

consists of a torque motor, the flapper, and a system of nozzles and chokes, while the latter consists

mainly of the spool valve and output ports. The torque motor, constituted by the motor coil, the magnet,

the armature, and the polepiece, is capable of transmitting a torque to the flapper which undergoes an

angular displacement, thereby obstructing one of more calibrated nozzles to a greater degree. This

operation causes a pressure difference at the ends of the spool, thereby causing the latter to move until

the feedback wire, which connects the spool and the flapper, returns the flapper to the central position.

Through the flow metering slot carried out in the bushing, the spool thereby permits communication

between the various ports. The feedback wire is an elastic flexional element that provides the feedback

between the main power stage (spool valve) and the first stage (torque motor).

This type of valve usually requires a greater degree of oil filtration, as nozzle-flappers are more sensitive

to contaminants compared with the jet-pipe system.

Figure 21.103 shows a schematic section of an example of a servovalve of the jet-pipe type. It is

connected to orifice P (supply) of the servovalve by means of a filter and flexible hose. It should be noted

that, unlike the nozzle-flapper valve, it is not necessary to filter the entire incoming oil flow, but only

what is called the control flow (the one going through the jet-pipe); this is certainly an advantage in

terms of economic running and sensitivity to solid contamination. Starting with a standardized input

voltage, the amplifier produces a voltage increase in one torque motor coil and an identical reduction in

TABLE 21.6 Main Typical Differences between Servovalves and Proportional Hydraulic Valves

Servovalve Proportional Valve

Electromechanical

converter

Bidirectional torque motor (0.1 ÷ 0.2 W)

with nozzle-flapper or jet pipe

Unidirectional servosolenoid

(10 ÷ 20 W)

Input current 100 ÷ 200 mA <3 A

Flow rate 2 ÷ 200 l/min (two stage type) with valve

pressure drop = 70 bar

10 ÷ 500 l/min (single stage type)

with valve pressure drop = 10 bar

Hysteresis <3% (<1% with dither) <6% (<2% with electric feedback)

Bandwidth >100 Hz <100 Hz

depending on the amplitude of the input

and of the supply pressure

depending on the amplitude of

the input

Radial clearance of

the spool

m (aerospace) 2 ÷ 6

m (industrial)

Dead band of the spool <5% of the stroke Overlap 10–20% of the stroke, less

if compensated

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21-76 Mechatronic Systems, Sensors, and Actuators

the other. This provokes an imbalance of the forces at the ends of the motor armature, generating a

torque which tends to make the armature itself rotate and the jet-pipe with it. The displacement of the

nozzle involves a different distribution of the control flow between the two pipes below it and, as a result,

a pressure difference is created at the ends of the spool with a consequent net force on it, which causes

its displacement. A spring element connects the spool and the jet-pipe, creating position feedback. The

displacement of the spool and jet-pipe deforms the feedback spring, giving rise to a force proportional

to it, and this makes it possible to balance the torque applied to the jet-pipe and the force generated at

the ends of the spool. In this way, the system finds an equilibrium position, proportional to the input

voltage. The feedback spring also produces centering of the slide valve at rest, making the presence of

centering springs superfluous. Figure 21.104 shows the block diagram of the jet-pipe servovalve compo-

nents with annotations of the physical magnitudes present in Figure 21.103.

FIGURE 21.102 Nozzle-flapper servovalve (Moog).

FIGURE 21.103 Jet-pipe servovalve scheme.

Motor coil

Armature

Flapper

Nozzle

Magnet

Upper polepiece

Feedback wire

Hydraulic

amplifier

filter

Spool

Bushing

Flexure

sleeve

PBTAP

mot

com

AMP

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Actuators 21-77

Proportional Valves

Proportional valves can be subdivided into proportional in flow and proportional in pressure (relief and

pressure reduction) valves. In the first case, the action of the servosolenoid armature (Figure 21.105a)

displaces the main spool of the valve, which is checked by a spring on the valve body.

The characteristics of the force generated by the servosolenoid, along the entire possible stroke of the

spool, is a function of the input current only, as indicated in Figure 21.105b. For all possible values of

the input current, the equilibrium of the magnetic force supplied by the solenoid and of the feedback

forces of the spring is determined by reaching a certain position value.

In cases in which precise positioning of the slide valve is requested, position feedback is introduced.

The photograph of a proportional valve of this type is shown in Figure 21.106. The input signal to the

servosolenoid, sent by the feedback module, is the error compensated by a PID network between the

reference signal and the feedback signal from the position transducer LVDT. The valve’s accuracy and

repeatability is improved by using the position feedback, as the hysteresis errors and those due to friction

between the moving parts are partially compensated.

Flow proportional valves can have two stages. In this case, the outputs of the pilot proportional valve

feed the end chambers of a spool valve of greater size, permitting greater controlled flows to be obtained

while reducing dynamic performance at the same time. An example of a two-stage flow proportional

valve is shown in Figure 21.107.

In pressure regulator proportional valves, the action of the servosolenoid acts on a conical needle in

such a way so as to regulate the pressure in the chamber upstream from the needle itself. Figure 21.108

shows the plan of a pilot operated proportional relief valve.

FIGURE 21.104 Block diagram of a jet-pipe servovalve.

FIGURE 21.105 Proportional servosolenoid: (a) solenoid section scheme, (b) solenoid characteristics

Electric circuit

Jet-pipe hydraulic

amplificator

Jet-pipe

equilibirum

Output

Spool

equilibirum

com

mot

Input

com

d(X

)/dt

Magnetic circuit

d(X

)/dt

Force

Stroke

0.2 A

0.6 A

1.0 A

1.4 A

Spring characteristic

Non–magentic ring

CoilArmature

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21-78 Mechatronic Systems, Sensors, and Actuators

FIGURE 21.106 Flow proportional valve (Bosch Rexroth).

FIGURE 21.107 Double stage flow proportional valve: (1) main spool valve stage, (2) pilot stage, (3) LVDT of the

pilot stage, (4) LVDT of the main stage (Atos).

FIGURE 21.108 Proportional pressure relief valve (Bosch Rexroth).

A P B T

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21.4.4 Modeling of a Hydraulic Servosystem for Position Control

Figure 21.109 shows the scheme of a hydraulic servo system for position control constituted by a double

acting, double ended actuator controlled in closed loop by a four-way servovalve. The x position of the

piston is determined by the equilibrium of the forces acting on it: external force, thrust due to the pressures

and P

acting in the chambers of the ram, friction force, and force of inertia. The pressures P

and

are determined by the oil flows Q

and Q

entering and leaving the chambers. Flow rate Q

represents

the oil leakage flow between the piston and the barrel. The flow proportional valve controls the oil flow

on the basis of the reference signal ref from a compensator G

. The input to the compensator is the error

between the signal V

SET

, corresponding to the desired rod position x

SET

, and the feedback signal V

F/B

corresponding to the effective rod position x measured by a position transducer LVDT.

The actuator is modeled by considering the equations of flow continuity in the chambers and the

dynamic equilibrium equation for the rod. The continuity equation is expressed in a general form:

(21.39)

where

= sum of the flows in volume entering

OUT

= sum of the flows in volume leaving

= density

V = volume

t = time

From the definition of the compressibility modulus of the oil

, P being the pressure in the chamber

considered:

(21.40)

We obtain

(21.41)

The continuity equation for chamber 1 is

(21.42)

FIGURE 21.109 Scheme of a hydraulic servosystem with position control.

OUT

–

V()

---------------

-------

------

+==

-------

------–

------–==

OUT

–

-------

---

------

– A

-----------------------------------

--------

LVD T

ref

–

SET

RET

••

•

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21-80 Mechatronic Systems, Sensors, and Actuators

The continuity equation for chamber 2 is

(21.43)

where

= flow entering chamber 1

= flow leaving chamber 2

= leakage flow between piston and barrel

= thrust section =

= bore diameter

= rod diameter

= volume of the chambers with piston centered = A

L/2

L = stroke

x = piston displacement (x = 0 in centered position)

= dead band volume

The dynamic equilibrium equation of the piston is

(21.44)

where

M = translating mass

= external force

= force of friction =

= coefficient of viscous friction

= force of coulomb friction

Leaks can be modeled as resistances in laminar and steady-state conditions of the following type:

(21.45)

where

R = resistance

Q = flow rate

∆P = pressure difference

In the case of an annular pipe, we get

(21.46)

where

D = seat diameter

h = meatus thickness = (D − d)/2

d = spool diameter

= eccentricity = 2e/(D − h)

e = distance between seat axis and spool axis

= dynamic viscosity

l = meatus length

– A

− A

-------------------------------------

--------

– )

··

–––– 0=

ATT

sign(x

∆P

-------

11.5

+()

---------------------------------------

∆P=

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Actuators 21-81

The dynamic behavior of the electromechanical converter and of the spool valve can be identified with

a linear model of the second order between the reference ref and the slide valve position x

, as indicated

in Figure 21.110, where K

(m/V) is the static gain of the valve,

(rad/s) the natural frequency of the

valve, and

the damping factor of the valve.

The flows regulated by the proportional valves are indicated in detail in the plan in Figure 21.111.

Having defined the areas A

, A

, functions of the spool displacement x

, on the basis of the

geometry, the flows transiting through the valve as a function of the pressures are given by

(21.47)

(21.48)

(21.49)

(21.50)

where P

is the supply pressure, P

is the pressure of the discharge reservoir, and C

is the flow coefficient

of the metering ports.

Therefore we get

(21.51)

(21.52)

The system of equations given above can be linearized in a working neighborhood, defined by the

passage area of the valve A

, load pressure drop P

= P

– P

, and piston position x

. In the hypothesis

FIGURE 21.110 Block diagram of the valve.

FIGURE 21.111 Reference scheme of the flow rates through the proportional valve.

± X

max

± V

ref max

ref

+ 2

s +

ζσ

STT

sign P

–()

---

–=

sign P

–()

---

–=

sign P

–()

---

–=

sign P

–()

---

–=

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