Oil-Hydraulic Servo System, Design and Analysis

(1)

NII-Electronic Library Service Mmto:ns or SiGxx:

INeT:TvTs or TrctNoLoGy

Vor.

IS,

Ne. 1,19s4

OiFHydraulic

Servo

System,

Design

and

Analysis

Sadao

ISHIHARA'

Preface

This

paper

is

a part of the manuscript

for

the symposium

held

by

The

Scientists

&

Engineers

Society

in

Republic

of

China

on

Nov.

23,

1982.

1.

Introduction

Some

fundamentals

which

have

much concerns to the following _paragraphs are

ex-plained

here.

1.1 Types

of

Servo

System

and

Stationary

Error

Type

of servo system

is

classified by a number _of

lfs

in

_open

loop

transfer

function.

For

example,

if

the transfer

function

can

be

written

in

following

form,

n

is

called the

type number.

K

G(S)=

s.(1+Ts) , n=O, 1,2, etc..

Stationary

error

has

a close relation to the type number, and is_given

in

Table

1.1. In

oil-hydraulic servo system, type 1

is

most _popular,

because

hydraulic

_actuator

is

essentially an

integrating

unit.

1.2 Stability

Stability

is

an

important

factor

for

a servo system, and issometimes inconsistentto

the stationary error which is_mentioned _above.

Integration

improves

accuracy,

but

on the contrary, it_contains a _phase lag of 90

degree,

so

it

has

_tendency _to reduce stability.

There

are many ways to

judge

stability, such as

Routh,

Hurwitz,

and Nyquist. But

in

thispaper,

Bode

plot

is

used

for

a _practical _purpose.

Phase

margin and _gain margin

are shown

in

Fig.

1.1. There

are rnany ways to increase stability, such as _phase lead network, rate feedback,

and so on.

1.3 Nichols

Chart

Open

loop

data

and closed

data

can

be

changed reciprocally to each other

by

Nichols

chart as shown

in

Fig.

1.2.

2. Semi-Automatic

Blade

Centrol

Deviee ef Motorgrader 2.1

General

Descriptien

Motorgrader

is

a

kind

of _construction machinery, which main _purpose are road finish,

ground surface finish,snow-removing, etc..

Operation

is

a

little

cornplicated, and

it

is

diMcult

for

an unskilled operator.

Motor-grader equipped with _{semi-automatic}

blade

control

device

is

shown

in

Fig.

2.1. This

device

is

composed of control

box,

_solenoid _valve _and

inelinometer.

_By _this _device, _operation

*

_diutII:\"

_tyN

₁₉₈₃_49A ₆ _Hectt

(2)

Shonan Institute of Technology

NII-Electronic Library Service ShonanInstitute ofTechnology

ie

ecI#

]k\a

ff

M

18

#

ag

1e , -.-.･ ,.･..

rt. t /.t tt . it .

t

-becomes

easier, and accuracy of road

finish

is

improved

very much.

2.2 Blade

Control

Device

Hydraulic

eircuit

is

_giVen

in

Fig.

2.2,

vvhere

O

control

lever-

of

lefti

cy]inder,

@

left

cylinder,

@

control

lever

of right cylinder,

@

right cylinder,

e

blade,

@

inclinometer,

¢ control

box,

e

solenoid valve,

@

flow

control valve.

The

blade tiltingangle iscontrolled automatically at a _preset value by this

device,

so that ]evellingoperation can easily

be

accomplished

by

the

left

blade

control

lever

only.

An

operator needs only to watch and control the blade height of leftend.

It

makes not only

blade

conyrol easier,

but

also

improves

finishing

accuracy two times cornpared to

ordinary manual operation.

Considering

cost and maintenance, solenoid vatve

is

used, so the control

is

essentially

ON-OFF

control.

To

avoid a bad effect of

ON-OFF

control,

PWM

(Pulse

WidthModula-tion)

is

applied, and the system can

be

considered approximately equivalent to proportional

control.

2.3 Analysis

ef the

System

Block

diagram

is

given

in

Fig.

2.3. Symbols

are as

follows.

c:

input

angle of control

box,

Sinx1oo%

{V)

e:

output angle of

inclinometer,

Sinx1oo%

(V)

e: error signal, e=c-0

(V)

K,: gain of

OP

amp,

PWM

i:

current to solenoid valve

Q:

flow

rate of solenoid valve

(cm3i's)

pt]

cylinder stroke

(crn)

A:

cylinder area

(cm2)

T: time

lag

of solenoid valve

(s)

K2: gain of

blade

(radlcm)

e:

blade

angle

(rad)

K5:

gain of

inclinometer,

Sinx100%

(V!rad)

Characteristics

of

PWM

and

ON-OFF

control rnay not be _easy to be understood.

So

it

is

better

to

be

transformed equivalently

into

more understandable

form.

Principle

of

Pwu

is

shoWn

in

Fig.

2.4.

Error

signal

(e)

decreaseS

with the time

(t).

Hacksaw

wave, which period

is

T

and

maximurn

height

is

eM

is

super-imposed on the error signal.

During

_e

is

_greater than e..,

solenoid

is

continuously

ON,

and _pulse width tw.

is

equal t'o

T,

tw.=T.

When the error signal across the

hacksaw

wave, where error signal

is

e., _pulse width

tw.

becomes

Txe./e,..

That

is,

for each _period of

T,

pulse Width

(tw.)

is

proportional to

error

(en)･

Mean

flow

rate

Q

is

as

follows.

Q=Qtw./T==(QfeM)e.

Kl'

=Q/eM

is

equivalent gain of

PWM

and

ON-OFF.

Equivalent

block

diagram

isshown

in

Fig.

2.5.

There still remains a non-linear

func-tion,of saturation,

but

it

is

more easier to be under:stood than the .former.

2.4 Result

Indicial

response

is

_given

in

Fig. 2.6.

Curve

presents

lst

order lag, and the most

effective

factor

is

time cpnstant of

inclinometeg.

_.(T). _..,.... . .

Test

result

is

_given

in

Fig. 2.7. By the help of this

device,

accuracy of road

finish

(3)

NII-Electronic Library Service

Oil-Hb,drauiicServo

System,

Design and Analysis

is

improved

satisfactory.two

timescompared with a ordinary manual operation,and _the _test_result

is

3. Synchre

Servo

3.1 General

Description

This

is

a rernote control system which will control automatically _the _angular motion

of a

heavy

load

in

response to the synchro signal

from

a controller.

Schematic

is

_shown

in

Fig.

3.1. The

centroller sends a comrnand signal by _two _speeds _synchro, coarse signal of1speed

and

fine

signal of

18

speed.

Two

signals are

interchanged

at

6 degree

of _coarse _signal.

Synchro

differential

motor

(5DM)

drives

a stroke control assmbly composed of _pilot

valve and cylinder and speed error corrector.

The

cylinder controls the variable

displacement

_purnp, _and

hydraulic

motor

drives

the

]oad, and then angle of load

is

fed

back

to switching relay and differentialmotor.

This

system

has

only one

integrating

unit of hydraulic motor, and

is

type

1

servo.

In

general, as

it

is

explained

before,

type

1

servo

has

a stationary error at constant speed,

but

in

thiscase, speed error corrector eliminates the above _error.

Hydraulic

circuit

is

shown

in

Fig.

3.2.

3.2 Analysis

of the

System

(1)

Diferential

synchro torque motor

e,:

command signal

from

fine synchro

5Gl

e,:

feedback

signaHrom

fine

synchro

5G3

0t: error angle, e'==ei-e,

(1)

e: rotation of rotor

J:

moment of inertiaof rotor

'D: _viscous

drag

_coeMcient _of _rotor

T:

torque of rotor shaft

k,:

torque coeMcient of rotor shaft

u: _position of error corrector _piston

d:

distance

between

torque motQr shaft and error corrector

piston

le,i:spring coeMcient of torque motor spring

Equation

of motion

T=k,(e,-e)+le,,("--d･e)d

ld2o,r'dtt+Dde,fdt=k,(e'-e)+k,,(u-d･e)d

Transfer

function are shown

in

Fig.

3.3 (a),

(b).

(2)

Pilot valve and aylinder x:

displacement

of _pilot_piston

y: displacement of _pilot_piston sleeve z:

displacernent

of

_power

_piston a: length _of link

b:

length

of Iink

c: length of torque motor arm '

kh:

valve cylinder coeMcient

-kn

is

obtained frorn _the following equation. ,

(rad)(rad)(rad)(rad)O.OO08

(kgf･cm-s2)

O.3 (kgf･cm･s･rad-t)

(kgf･cm)

1.2

_{(kgf･cm･rad-i)}

(crn)

8(cm)O.3

(kgf･cmLi)

(2)

(3)

(cm)

1 (cm)

5.1 (cm)

6.4 (cm)

2.5 (cm)

'

510 (s-i)

-3-NII-Electronic

(4)

NII-Electronic Library Service ShonanInstitute ofTechnology Nff-* rk#rept eg188 ij1 e

h,=XV

P-EiA

A:

P:

F:

a: g: at: r:

R:

&:

Thus

2+-2-

×

le2Rxe'

'

effectiye area of cylinder supply pressure

ayerage

load

of power piston

flow

coeficient of pilotpiston

gravity acceleration

equivalent width of circular _port

specific weight of oil

resistance of pipe

line

(neglected)

input

amplitude

k-aa'

V

2,g

(4)

6.9 (cm2)

10.5 _(kgf･cm'2)

16 (kgf)

O.8980

(cm-s"2)

1.46 (cm)

O.88

×

107S

(kgf}cm"3)

(cm>

x==ce y=(a/b)z

d2!dt=k,(x-y)==kh(ce-az!b)

(5)

<6)

(7)

Transferfunction

becomes as follows.

Z(s>e(s) bcta

3.1 b1+

ale, S1+O.oo25

s

(8)

(3)

speed

error corrector

i:

length of error corrector lever

l:

distance

of error corrector piston

from

error corrector

lever

hinge

k,2:

spring coeMcient of error correction spring

M':

mass of error corrector

piston

D':

viscous

drag

coethcient of error corrector _piston

Equation of rnotion Mt(d2u/dt2)+D'(dut'dt)=k,,(de-u)+k,2(l21i"U)

2 (cm)

5.3 (cm)

1.2 (kgf･cm-i)

2

×

10Jli

(kgf･cmJ'･s2)

O.45 (kgf･cmJi･s2)

(9)

Transfer

functions are shown

in

Fig.

3.3 (c),

(d).

(4)

Tbrque motor _and strcke control assembly

Block

diagram

is

build

up

from

Fig.

3.3

and equation

(8>,

and isshown

in

Fig.

3.4 (a).

This

contains a positive

feedback

of

lst

order lag, and isapproximately transformed into

(b).

Positive

feedback

of lstorder lag isexplained

in

Fig.

3.5. If

KH

is

equal to 1,itwill be

phase

lead

network with integral.

In

this application,

it

changes a type

1

servo

into

type

2

with _phase

lead,

so

it

im-proves system performance as long as itisstable.

Mechanical

meaning isexplained in

Fig.

3.6. Number

in

circle

is

same as Fig. 3.4. An error angle

(1)

makes the retation angle

(2),

and then _piston movement

(3)

and error corrector lever movement

(3')

follow.

These

(5)

Oil-Hlv,drauiicServo

System,

Design and Analysis

make _piston rnovement

(6)

by

spring

forces

(4)

and

(5).

Spring

force

(7)

is

fedback

posi-tively to the torque motor shaft.

Even

an error angle

diminishes,

spring

force

(7)

keeps

the rotation angle

(2),

so that the system can work without constant speed error.

(5)

HZydrosratic

transmission

Q.:

flow

rate of variable

displacement

_pump

(cm3-s-i)

S.:

flow

coeMcient of

PV

540 _{(cm3･s-i･cm-i)}

Q.:

flow

rate of

fixed

displacement

motor

(cmB･s-i)

ei:

flow rate _of leakage

(cm3･sLi)

Q,:

fiow

rate

by

compression of oil

(cm3.sui)

d.:

displacernent

of motor per radian

O.8 (cmS)

O:

rotation angle of motor

<rad)

1':

equivalent moment of

inertia

on motor shaft

O.oo5

(kgf･cm･srr2)

P:

working

hydraulic

_pressure

(kgf･cm-2)

L:

leakage

flow

coeMcient

O.15 (cm5･s-i･kgf-i)

As

the purnp and motor are assernbled

integra]ly

in

one casing, oil passages are very

short, and oil compression can

be

neglected.

Q,=O

Q.:=:S.･z=Q.+Qt

(10)

Q,.

=

d.

dd9tr

(11)

1,

d20

P=

(12)

dm dt2

Q,-L･P-f,'.`

d,"',e,

(i3)

Then

dip

,

Ll,

d2p

Spa=dmdtTd.

dt2

(14)

Transfer

function

is

as

follows.

¢

(S)u

Sp/dm _- 675

Z(S) Us(1+

dL.J.L'

s) -s(1+O,Ol s)

<15)

(6)

Total

system

Gear ratio from

hydraulic

motor to finesynchro isO.05.

Block diagram of total system ismade from equation

_(1),

Fig. 3.3,Fig.

3.4

and

equa-tion

_(15),

and

it

is

shown

in

Fig.

3.7. Bode

plot

is

shown

in

Fig.

3.8.

3.3 Experiment

(1)

,FVequenay resPonce

System

is

tested

in

closed

loop

condition,

frequency

and arnplitude of sinusoidal

input

are changed. Measurement

is

done

by

_{potentiorneter} and osciliograph.

An

example

is

shown in Fig. 3.9.

(6)

-5-Shonan Institute of Technology

in

e,(s)

It

is

(3)

,.

Static

3.4

The

This

and they are

4. 30oo

ton 4.1

GeneraE

This

sure vessel condition

1

3

5

7

9

11 Slide

13

15 Test

17

4.2

(1)

(3)

.

(5)

(7)

(9)

(11>

(13)

(15)

(17)

(19)

re

st

=*

)c4re

et ca 18

#

ng

Closed

1oop

data

are _changed _to open

loop

data

by

Fig.

3.8,

Table

3.1

and

Table

3.2. (2)

indicial

response

Indicial

response

is

as

follows.

20.6(1+O.3s)

le

Nicholschart,andthey

are .glven

(16)

s[20.6{1+O,3 s)+s2I(-ig6ri)2+2xO.4 ×

(

lg6

)+1)(1+O.oo25

s)](1+O.Ol s)

approximately changed

into

time

function.

e,(t)=1+1.36

e-3i26' sin

(3.59

t-O.832)

(17)

Experimental

record isshown

in

Fig.

3.10

and

Table

3.3. Static

accuracy

acguracy

is

given

in

Table

3.4.

Conclusion

most significant

feature

of this system

is

the speed error corrector.

system

is

very stable, and phase margin

is

60 degree

_and

_gain

_margin

is

20dB,

proper values

for

a seryo system.

Fatigue

Tester

Description

machine

is

a special

big

fatigue

tester to test a thick plate

for

boiler

and

of neuclear _plant.

It

can testthe

full

size test _piece under

low

cycle

fatlgue

(Fig.

4.1).

Frame,

cylinder side

2 Frame,

shaft side

Cylinder

piston

4 Column

Large

shaft

6 Nut

Spherical

washer

8 Spherical

washer

Locking

washer

10 Rotating

device

base

12 Rolling

ball

Rotating

device

14 Shaft

support

piece

16 Piston

connection

Hydraulic

cylinder

18 Intensifier

Specification

is

shown

in

Table

4.1. Hydraulic

Cireuit

and

Centrol

Sehematie

Hydraulic

circuit and control schematic

is

shown in

Fig.

4.2.

Pressure

transducer

(2)

Bridge

circuit

Arnplifier

(4)

Differential

transformer

Amplifier

(6)

Amplifier

Differential

transformer

(8)

Bridge

circuit

Amplifier

(10)

Servo

amplifier

Program

controller

(12)

Funetion

_generator

(14)

Hydraulic

cylinder

Arbitrary

function

generator

Servo'valve

･

(16)

Flow

control valve

Accumulator

(18)

Intensifier

Solenoide

valve

(20)

Pilot

operated valve

(7)

Oii-H),draulicServo

System,

Design and- Analysis

(21)

Pilot

operated valve '

(22)

Solenoid

valve .

(23)

Solenoid

valve

(24)

Throttle valve

(25)

Trottle

valve

(26)

Unload

vale

(27)

Relief

valve

(28)

Zero

_voltage

detector

(29)

Accelometer

(30)

Acceleration

sensor

Two

kinds

of control are available, one isa

displacement

control, and the other

is

a

load

control, and they are selected

by

switch

Sl.

In

displacement

control,

displacement

of both top and bottom _sides _of _the _test_piece

are

detected

by

differential

transformers, and signals are sent to a bridge _circuit and

am-plifier,and their mean value isfed back to the servo amplifier.

In

load

control,

pressure

at

both

sides of the cylinder are _picked up by the _pressure

transducer, and their difference is fed back to the servo amplifier,

because

_Ioad _force _is

proportinal to the

_pressure

difference

of both sides of the _piston.

In

the fatigue tester,ifthe btoken surfaces' of the test _piece are

_pushed

against each

other, their surfaces will

be

damaged

and not

good

for

electronic microscope

inspection.

In

this machine, the broken _pieces are separated imediately after breakage.

The

acceleration sensor _pick up shock of

breakage,

and the accelometer _actuates _the

solenoid valve

<22).

Oil in the left side of the cylinder

(14)

_goes through the solenoid

valve

(22)

_and _the _throttlevalve･･(24), and enters

in･the

tank.

So

the _piston moves

left-ward, and the broken test _pieces are separated at once.

Wave

form

of

input

signal

is

selected by the switch

S2.

Sinusoidal or triangular wave

comes from the function _generator of

low

frequency

type, and arbitrary repeated wave

form

comes

from

the arbitrary

function

_generator.

4.3 Hydraulic Systera . ..,.

Specification

is

shown

in

Table

4.2. High

pressure of 5ookgflcm!

is

used

in

this system to make

large

force

of _quick

response.

The

intensifier

makes

high

_pressure

from

mediumpressure of

175kgfXcm2.

It

works automatically by combination of two limit switches, the amplifier

(6),

the solenoid

valve

(19),

the pilotoperated valve

(20)

_and

four

_check _valves.

The

accumulator

is

also a kind of

intensifier,

and

it

supplies

high

_pressure only when

the

intensifier

ehanges

its

moving

direction.

To

control

large

hydraulic

_power, combination of the servo valve and the large

flow

control valve is

dsed.

Minor

loop, which iscomposed _of fiow_control valve, _the

differential

transformer

(4),

the amplifier

<5),

the servo amplifier

(10),

and the servo valve, makes

flow

control very stable.

4.4 Control

Circuit

(1)

Block

diagram

Block

diagrams

of two control systems are shown

in

Fig.

4.3 and

Fig.

4.4. Definition

of symbolsare as

follow,

e:

input

signal to the system

(V)

e,:

input

sigrial to the minor

loop

(V)

i.:

input

current to the servo valve

(mA)

x.: _spool

displacement

of servo valve

(cm>

eqr:spool

displacement

of

flow

control valve

(cm>

y:

displacement

of

_piston

<cm)

R:

load

pressure of _piston

(kgf!cm2)

Standard

premise condition of

design

is

_as

follows,

(8)

reecI* rt#reut eg18 8 or1 -e

Test

piece:

2,OOOmm

length,

1,OOOmm

width,

1oomm

thickness

Spring

coeMcient of frame: 5.13× 106kgf/cm

(2)

TVansfer

.ftenction

of

mtijor comPonents and _synthesis

of

the

_system

(a)

Amplifier

of

displacement

control

Kl=54

(1)

(b)

Servo

amplifier

G. This

amplifier contains phase

lead

network to

irnprove

performance.

Kiai(TDs+1)

Ga(S)=

(2)

ai71Ds+1

Where,

KL=850,

cr,r-O.1,

T.=O.Ol19

(c)

Servo

valve

XL(S)

-

kv'tov2

(3)

Gn(S)

:

4(s)

- s2+2C.to.s+to.2

Where,

to.=1oo radls,

C.=O.7,

le.==O.oo133

cm!mA

(d)

Flow

control valve

Xf<S)

-

lef..f2

Gi(s)=

(4)

XL(s)

-(1+T,s)(s2+er,bl,s+to,2)

Where,

Tlt:=O.77s,

tof=

960rad/s,

gf==O.033,

kf=535

(e)

Hydraulic

cylinder

(displacement

control)

lectoc2

(5)

G,(s)

=

(1+TLS)<S2+2C;e(veS+cve2)

Where,

to.==38rad/s,

Tl,==10s,

C,=O.O06,

k.=2.0

(f)

Differential

transforrner

Kli==1.66Vfcm

(6)

(g)

Differential

transformer

Kl=O.333Vfcm

(7)

(h)

Minor loop

Closed

loop

plot of rninor loop

is

shown

in

Fig.

4.5. (i)

Bode plot of

displacement

control system

Bode

plot

is

shown

in

Fig.

4.6. Gain

margin

is

about

5dB,

and _phase margin

is

90 degree.

(j)

Amplifier

G,

To

increase

stability at

high

frequency,

G,

has

_galn adjusment

by

low

pass

filter.

G,(s)

=

(1

+3

.

2,,

),

(s)

Where,

tot=5radfs

(k)

Hydraulic

cylinder

G.'(s)

k.t(S2+?12

>toc2

Gc'(S)=(i+TL;)(s'W+'2c,6,s+w.2)

(9)

Where, k,'=1,OOO

(kgflcm2)/cm,

to,=17.6radls, w.=38radfs,

T,=10s,

C,=O.O06

(9)

Oil-H),draulicServo

S},stem,

Design and Analysis

(1)

Bode

plot of

load

control system

Systern

can be adjusted

in

many _points of electric circuit.

A

typical characteristics

is

shown

in

Fig.

4.7. (m)

Accuracy

of wave

form

Wave

form

is

pretty good as shown

in

Fig.

4.8,

Strain

of test _piece

is

also recorded

for

a _purpose of material tester,

but

it

is

not explained before, because it

is

eutside of

this servo system.

4.5

Conclusion

This

high pressure oil-hydraulic servo system satisfies the specification of the

fatigue

tester,and

it

works very _good.

Good

control _performances are obtained

by

the

help

of phase

lead

network, minor

loop,

low

_pass

filter,

and so on.

References

1) Sadao Ishihara: Analysis of a Hydraulic Servomechnism. Autornatic Control. Vol. 8, No.4, 1961.

2) Sadao Ishihara: Operating Force of Axial Plunger Pump. Measurement and Automatic Centrol,

Vo]. 1, No. 7, 1962,

3) Sadao Ishiharaancl I$ao Sugioka: Study on the ControlForce of a RodlessType VariableDelivery

Axial Plunger Pump.

Journal

of

J.S.M.E,,

Vol. 29, No. 198, 1963.

4) Sadao Ishihara: Multistroke RadialPistonMotor.

Journal

of J.S.M.E.,Vol. 74,No. 628,1972.

5) Tornoo Ishihara, Sadao Ishiharaand Takeshi Takagi: Designof FluidPowerTransrnission.

SHA, 1967.

6) Sadao Ishiharaand Kazuo Uehara: Energy Saying in Hydraulic System of Hydraulic Excavator.

Journalof

J.S.M.E.,

No. 780-1,1978.

7) Sadao Ishihara: Applicationof Oil-hydraulicsand Pneumatics inConstructionMachinery.

Journal

of Hydraulics and Pneurnatics Society,Vol. 3,No. 1,1972.

8) Sadao Ishihara and Mutsuo Shino: Application of ReliabilityTheory on Oil-Hydraulics,(1).Journal

of H.P.S,,Vol. 8, No. 3, 1977. Sadao Ishihara and Satoru Sasano: Application of Reliability

Theory on Oil-Hydraulics,

(2).

Journal

of H.P.S.,Vol.8,No. 4, 1977. Sadao Ishiharaand Hiroshi

Shirnamura: Application of ReliabilityTheory on Oil-Hydraulics,_(3).

Journal

of H,P.S., Vol. 8,

No. 5, 1977.

9) Ryuji Itoand Sadao Ishihara: Applicationof Hydraulic and Pneumatic Servomechanism on

struction Machinery. Journalof H,P.S., Vol. 9,No. 3, 1978.

10) Sadao Ishihara: PistonPumps and Motors, Theory and Practice. OHM-SHA. 1979.

(10)

NII-Electronic Library Service Shonan 工nstitute of _Teohnology

相模工業大学紀要　第 18 巻　第 1 号

Tables

　and 　

Figures

Table　1，1．　 Stationary　error 　of　unity 　feedback　syste 皿

Kind　of　stationary 　error

Constant　_position Constant　speed Constant　acceleration

Type　of　serve lnput　（’）

　r_（_t_）　　0 ’ ） ’ （ 7 0 t r（t_）　0

去

・_・

」

；2 t 　　　 K Type　OG_（s｝＝　　　 1十 Ts 　 ro1 十K oo QQ 　　　 K

T

夕pel 　G（s｝＝　　　 s（1＋ Ts） 0 彑 K ○ ○ 　　　 K Type　2G_（s_）＝　　　　　　　 s2_（1＋Ts） 0 0 彑　　 40 　　 20 霞 ε ．E 　　O8 　 −20 　 −−40 　　　 ω _l 　　Fig 。1。1．

1

B’

111

1

phase 　　　　鹽 ma 「91n

総

o

1

；｝c’ _川

li

它

1

　　．gam，出・・幽

L

… 幽 _易

1ll

_田 c 呂 2010 　α

ilI1i

I

ω ωユ一₁₀₀ 　　　驚．−₁₄₀₈ 　　　 ζ 　　　　憎_一 180 暢　　　　＄　　　　−₂₂₀ 2 　　　氏一₂₆₀

Phase　rnargin 　and 　gain　margln ．

「

一 10 畄

(11)

Oit-ll),draulicServoSystem, Designand tAnatvsis

40 30 20

disg

losEg-. oo.ENo-10 -20 -30 -270 M=O.25dB g=-1' -t .5

age11.si.

H-2' ' 5e .b."ts5dSxp 'LO tloe 1dBx"2aB - t--...-" .t.-- L '' 2:l--'u5B -20' 30' tt ..-. -x / -4dB.-...-8dBNt-]ouB ' ff0e

H

. ut....].t ...-...t..t..-.t.r . --270'-24e' -15Q'-120d t"'--90 -180' A{](;rJ'a,)I=,--1edB_{ZCCiill}=--90'} --15dBu2oaB ...--L tt '

{"'L==1i,iSB

1-l'-2suB"-3ouB

' -240 -210 -180 -150 -12e

}'haseof open loop

(deg.)

Fig.1.2.Nicholschart.

-90 AI:9:

-60 -30

Gainef cleSed loop

(dB)

Pha'seof closed loop

(deg.)

o Controll)ox

Solenoid

valve

o

A-s>

Nv

ri''

co)o Inclinometev Fig.2J.Motorgrader.

(12)

相模工業大学紀要　第 18 巻　第 1 号

　　　山

Fig ．2．2．Blade　_control 　device．

Inpntanglec （V） ÷ Error e （V｝ OP　amp ． i（A） So】enoid va ］ve

Q

（cm3 ／s）」 κ1 fPWM Cylinder y（cm _） Bla（】e Q ε 一 E 　　　eON −OFF e−「sAs Kz θ_（rad _） Inc］inometer θ’_｛V〕 K31 十Ts

Fig．2．3，　 Block　diagram　of　blade　control 　device．

一 ₁₂ − 一

(13)

NII-Electronic Library Service Oit-H),draulicServoS)'stem,Designand Analysis k --o esk=k tnm 'ase trxi9-es di=s )dim"Pvttu di=e -v"=lr

g--pt

6

gokkooj Time t Fig.T2.4.2'r3TPrinciple4TofPWM. ime t Timet cCV) e(V)ProportienalSaturation Kl-Qe,u Q(cm:ls) _y(cm) e(rad) Q(? E,eLr e 'T-g.As K, e･(v,) _K,1r7-s

Fig.2.5.Equivalentblockdiagrarn ofblade control device.

(i'1'[L,,.i

[I==

--.

OlFig.

2.6234. Indicialt(sec)response.

(14)

相模工業大学紀要　第 18 巻　第 1 号　　　　mm 　　　　　±30 い O J：台．9　±

20

田ε

羹

±1。 123456k ・

！

b

．、 Con 七roU ，er Coarse 呂yllchro genera 七〇r 弸 Y

：

ー

盆

1　Speed 　signa1 Fig．2。7。　 Vehicle　speed ．_．

1

』_． Test　result ， _，　　Machine

　　　CoarBe 　synchro motor

Fiコユesynehro gener ユ七〇r 183peed

5M

signal ヒ L 　一 Response 一 signal 　ノ！，！ _「6 0 ＿　＿　＿！ Fin6 庵 1Coarse 　l 　l 　I 　　　 ’ 5Dr・1 ．丶　、　b 7 「聖 8 　 @1 　 i Coarse ＿fi 　rel

3peed 　eでror 　correc 七

vFine 　reSPQn3e sig

1 iFig ．

DL

　　　　　C 〔）

arse

_re3ponse 　si alSchematic 　of　synchro　se o．工 o 一 Ele ｵc へ Hydr lj ．cMec ica1 一14 一 N工工一Eleotronio 　Library 　

(15)

Oil-HZydra"licServoSystem,Design and Analysis

"STowS-cbqtwe}

･._..･;Nt . tt s t HtGH PRESSURE REUEtVALYE, xy-W LUt9!9mR GONSTANT OISPLncEMENr

ZERO TO 27eO R.P.U.FILTER

ELEMENr ]i''i' ･fR:l-.=-REPLENtSHIua CH[CKVALYES

---t-=""-/'Li=qm-t`

1

Ecec"E"rJET"R" DITHERsH Rooigliz timaAULR2UttE MLAeua orsuLACtmettT ERROR t'' SLDE eLDCKpmttt3 FILTERHOU51NG PR!5REGU PVMP SHAFT) M･ER,(l

IEkl.lv

CORREeTOR PtSTON plsTON

X

: v rr LNTAKE TORQUEMOTORSPRiNG

Ail--

ORtFteE"-iii

L

/

PrLOT PtSTON ADJUSTMENTTCROUMOTORSbSJIFTc -LC'tt?u COHRECTOR LEY[Ht t:TmosE aNtReASCEX LYd Fig. 3.2.Hydraulic diagram.

ERftC"l

ffljilSPRVtG

ECTOR clrcult e' +atleEnE"sd ht "jS,.Ds-Cts+hsld2)e iila) eJ+ ao6e u+(dir+2iaKigS)+i 2 '1'oi'que motoril.b'i e'9 _O.06 @e _3.1 z@ +'riJ,)52xO.4(ii")+1 1+O.O025s m 2.4 a-g.6[L ,.O,CD3.2

o

2-1+O,3s ot ez +"d +!s2t 1 Mts'+Dls+(hpt+hs2)u '[cltt e+ _a67u 2,4+1+O.3s z3,2 d/

(a)

Blockd]agram e' O,61(1+C.3s) Z slGif)'-2so.4(et)+il"+o.oo2ss) Fig.3.3. Em'-v ('oi'i'eetov

Transfer functionof conponents.

/'b'/ 'Fransferfunction ,t1Fig. 3.4.Strokecontrol ass'y. + Fig.3.5. +KH1+TsPositive .-tK" ±-LE.L(1T}.-ttC"±[lst.") d+Ts-KH Ts (KH=d)

feedbackof lstorder lag.

pK6

e

Fig.

3.6.q

[]6

/P

..,.i-6-t-vEg ,-"Mechanical 'meanmg.

(16)

　相模工業大学紀要 a61Cl＋O．3S）　　　　Z 第 18 巻　第 1 号） 1 （ nO “ aUqE ） a （ e「 5_〔_（

th

），卜2属aヰ_く_歯_〕＋1_｝く1＋aoO25s〕

Stroke　control　as5 ’y

9 ₆₇₅ φ

5 （1＋0．015 ）

　（b）e’＋

　　　　 Total　system

Fig ．3．7．　 Total　system ．

　　4Q 密 2。 ε ．E む ¢ ．　 o

　　　

　　　　　 −20 　　　　 Hydrostatic transm鳳ssm

轡

Gear　_ratio θ・＋　一 20，6（零＋ O．35｝ θ。 52_脚 2 ・2・α・_{愉）}・1｝（1・α 。。蕊51〔1… 。1S〕　　　 1　　　 10 　　　　　　　 ω _こr・cレ5ec ］

　 Fig 。3．8．　Bode　plot　of　total　system ．

Input

　

　　　　　　　　 Output 　　　　

　

　　　 1　畳　 l　l　l　l　l　 1　 1　 5　 1　 1　｝　l　I　 l

　　　Fig ．3。9．　Frequency　response ．

　　　 − 16 一（．蚕DO 唱）姦 7 ［ uり gD に ‘ 山

誥

欄欄燗噸鱒 ’ 100 I　I N工工一Eleotronio _Library

(17)

NII-Electronic Library Service Oit-H),draulic Table3.1. Servo

_S}'stem,

Frequency Design response and Analysis (amplitude3.3deg.) Frequency tu

(rad,is)

Closedloop Open1oop

Gain Lil4'[(dB) Phase _F(deg) Gain

_IGI

_(dB) Phase e(deg)

O.98 1,94 2,68 5.559.5112.5515.00 o. L L o.-L-3.-5. 835957525251 o -4. -12. -44. -71. -85.-111. 446o3o 20.5 15.0 11.0 2,9-2.0-4.8-7,5 -180-158=14e-117-119-119.5-135 Table32.Frequencyresponse(amplitude 6,54deg,) Frequency w

(rad,･'s)

Closedloop Openloop

Gain

_IMI(dB)

Phase _y(deg) Gain

_[Gl

(dB) Phase e(deg)

O,95 2.02 4.62 5.609.2412.30 o. L L-o.-2.-5. 2505581459 o -6. -29. -41, -74-106 9518 31 14.2 6.5 3.0-2,95-7.8 -1eo-128-123-110-115-131 Fig.3.10. Ilrl n 111 /: ₁₁ _1: _[9 _:E _W _:,E_CE Transient reeponse rl [.t:.1:/ ,(angle ill! tl { gt･r diff.1.11 deg.)

(18)

reecx*J<\rest

Table 3.3. In

ag

18 dicial

ig

mlg

response Angledifferrence(deg.) Lll 2.22 3.33 4.44 5.55

Ratioof evershoot O.186 O.106 O.14 O.14 O.153

Time ofovershoot(sec.) O.38 O.47 O.45 O.47 O.5

Settlingtirne(sec.) 1.2 1.3 1.3 1.3 1.6

Table 3.4. Staticaccuracy(Spec. 1')

Controllerangle <deg.) o 1 2 3 2 1 o

Errorangle of1oad o, ot O.3, O.6, O.6, O.4, ot

17 ID

L2,eoe

1

(ll)@@

' 8,3000 !5 14

"

82 ; 5 22ooA ' io,-if) .-i.-;1-."ets-A'/ eutpt! oom.cu1 : '.7 sl8iutM-･oo

_fo"j9

/ g '/ -=L.--u2oeDooopN/t 6 lo -G " , l' ]･ ' ttt..ltt.ttt-lt;1' Fig.4.1. Table 4.1. ..i ., d' ., J. Generalview Specification of of i.t. -/ .3000t 3ooet t-t...-t.. Fatigue Fatigue - ..- .-.t Tester. tester ..-, .- ..-1 .tt

Oscillatingload maximum tensien

maximum compression

'

maximum totalarnplitude

Wave form

sinusoidal, triangle,trapezoid and

Cyclespeed '

1-60cfrnin

Maximum stroke Static:200mm, I)ynamic: 30rnm

Programing Repeat many stepB ef fiuctuating

Maximum test _piece Length

Width Thickness 3000t 1000t 3000t arbitrary lead 3000rnrn 15oomrn 2oo mm

(19)

-18-NII-Electronic Library Service

Oil−Hydraulic　Servo_跏5’8脚，　Design　and 　Analysis

醐

Fig ．4，2．　 Hydraulick　circuit 　and 　control 　schematic ．

一 19 一

(20)

eec r# Jk\re st

ag

18 g

ca

1 e

Table4.2.Specification ofhydraulicsystem

Superchargeunit Pumpdelivery=902llm,pressure=5kgf/cm2

MainPumpunit type of _pump: axial piston, No. of pump=4ea.

total flow rate=848 l,tmin,_{pressure--175} kgffcrn2

electric motor: 150kWx2ea.

Intensifier primary: 175 kgffcm!

secondary: 5ookgflcm2,230 t/'min.

Highpressureaccumulatorpressure=5oo kgf/cm2,capacity=61. Maincylinder pressure=5ookgflcmE, rod diameter=750 mm, streke=2oo mm piston diameter=1,170 mm effective area=6,330crn2

Flowcontrolvalve pressure=5oo kgflcm2,rnax. flow rate=2301i'min. Servovalve current= ±30rnA, pressure=140 kgflcm2

flow rate=4011min.

Input AmplifierInput to

Fig.4.3.Block

Serve

diagram

Servu Flow contrel

DTFof

displacementcontrolsystem,

HydraulicPiston

Fig.4.4.Blockdiagram of load controlsystem.

(21)

-mo-NII-Electronic Library Service

Oit-H]ydrauticServoSystem,Designand Analysis

rc, o-2t'eAe'= --4t''t:E=v F6t'Lh-BC･ -10C･ --12Ci -14i/.

i'Gain

,I, - t-- -1-Ij 1't-L45 tsOtO J04Uu ･- .-se oo to J w<raa!s) loop _plot

F-v･ sooecol,eeo,oou o-20-40-60-80-100-12e-t40-160 of rninor loop. -ISO-200-220-240 ,oooto,oeo nthov.J--]-.-=uteco"sm Fig.4.5.Closed ¢

:･E.v,v･-d[-ec-6:'1ee

Gain] jo]v'El d[ o-20-no 2L. tt PhEiscT eosoleo12e l60 240 ec 6:･ -lao--1BO-2Da-220 ec･.Ll u[Tuv/..-t-teltltL --26e 1o.to.o.rl;t]csUVU3V.[,UILft)70U/-L]bCe,CMO Fig.4.6.Bodeplot (d/(_radls) of displacementcontrol system. -...tz,sedLtmomg=-

(22)

相模工業大学紀要　第 18 巻　第 1 号剛_冒〉三 δ τ 123 一一一．：．−IGain1 ．．一 _Calcしllat °・‘E叩 erim L4 ，　　1 　． Phase ．　　　． _喝 o 「　卜一．．

1

． i 『「_｝． _， _一啣一 1．冖7−−．．｝ゴ − ．．．一一一 0．Q5　　0、I　　O，し一　　　　　　．5 5　　 0 Fi言_「4。7・　　　　　　　　　　　　　o　　勃　　　　　　　一2。　毛　　　　　　　v＿t 　　　 −40 　　　ゆ　　　　　　　一50 _毟　　　　　　　一80　炉　　　　　　｛　　　 −loe 　　　　　　　　　　　　　　　　　　　　　　　　　−120 　　　　　　　　　　　　　　　　　　　　　　　　　啣140 　　　 −r60 　　　 −【80 　　　　−200 　　　　　　　　　ω _（rad ／s）