** DESIGNERS' HANDBOOK FOR ELECTROHYDRAULIC SERVO
AND**

PROPORTIONAL SYSTEMS

__TABLE OF CONTENTS__

(1)
PHYSICS OF HYDRAULIC FLUID POWER

UNITS
OF MEASURE

ARBITRARY
UNITS AND SYSTEMS OF MEASURE

Time

Length

Mass
and Force

DERIVED
UNITS OF MEASURE FOR HYDRAULICS

Area

Volume

Velocity

Acceleration

Flow

Pressure

Angle

Angular
velocity

Angular
acceleration

Torque

Mass
Moment of Inertia

Work

Energy

Power

FLUID
PROPERTIES

Density

Specific
weight

Specific
gravity

Viscosity

Absolute
viscosity

Kinematic
viscosity

SAYBOLT
UNIVERSAL SECONDS

The
affect of temperature on viscosity

Bulk
Modulus

Fluid
statics

Pressure
exerted by a column of fluid

Atmospheric
pressure and absolute pressure

Vacuum
pressure

Vapor
pressure

Cavitation

HYDRAULIC
CYLINDER PERFORMANCE CALCULATIONS

Output
force

Cylinder
Area Notation

Speed
and Flow

Hydraulic
cylinder Work and Power

FLUID
DYNAMICS

Flow
through an orifice

Accounting
for energy losses using dimensionless coefficients

Expressing
orifice resistance in terms of Kv "Holes"

Flow
and pressure loss through a tube

General
steady-state, steady-flow energy equation

Conservation
of mass

D'Arcy
pressure drop equation

THE
MOODY DIAGRAM

Solving
for pressure drop through pipe, tubing, and hose

Hagen-Poiselle
law for laminar flow

Colebrook
Equation (for turbulent flow)

CIRCUIT
FLOW AND PRESSURE DROP

Flow
through orifices in series

Flow
through orifices in parallel

Flow
through 90 and 45 degree elbows

PRESSURE
LOSS COEFFICIENT FOR PIPE ELBOWS

Flow
through reductions and expansions

Sudden
contraction in flow path

Flow
path expansion

Laminar
flow through paths in Series

Turbulent
flow through paths in series

Generalized
flow through paths in series

Flow
Q, is known, calculate DP

Pressure
loss observations

Introduction
to Power Sources

Introduction
to 4-way spool valves

(2) PHYSICS
OF MECHANICAL LOADS

FIVE
DESIGN TIME DECISIONS

NEWTON'S
LAWS

ONE
DIMENSIONAL MOTION

FOUR
COMPONENTS OF FORCE

Forces
That Oppose Acceleration

Forces
That Oppose Velocity

Friction

Forces
That Oppose Position

Pendulous
Effects

Spring
Force

Energy
Storage in a Spring

Constant
Load Forces

COMBINING
FORCES ON A FREE BODY

FORCE
WAVESHAPES

LINEARIZED
VISCOUS COEFFICIENT

ROTATIONAL
MOTION VIS-À-VIS LINEAR

(TRANSLATIONAL)
MOTION

TABLE
I COMPARISON OF LINEAR AND ROTATIONAL MOTION PARAMETERS AND VARIABLES

(3)
MECHANICAL TRANSFORMATION DEVICES

REFLECTING
LOADS THROUGH THE TRANSFORMER

OTHER
MECHANICAL TRANSFORMING DEVICES

Power
and Performance Considerations in the Conveyor-Elevator

Inertia
at the Shaft of the Conveyor

Non-Accumulating
Conveyors

Belts
and Pulleys

(4)
NON-LINEAR TRIANGULAR LOAD TRANSFORMATION

EQUIVALENT
MASS

MASS
POLAR MOMENT OF INERTIA

PARALLEL
AXIS THEOREM

SPRING-INERTIA
RESONANCE METHOD OF DETERMINING INERTIA EMPIRICALLY

PENDULOUS
RESONANCE METHOD OF DETERMINING INERTIA EMPIRICALLY

IN-POSITION
LOAD HOLDING FORCE

LOAD
RESONANCE

(5) HYDRAULIC CIRCUIT ANALYSIS FUNDAMENTALS

INCH-POUND-SECOND
SYSTEM - AN EDITORIAL COMMENTARY

CONSISTENT
UNITS EMI

UNITS
PREFIXES EMG

TEMPERATURE
AND TEMPERATURE SCALES

PRESSURE
AND FLOW

FLUID
COMPRESSIBILITY

KIRCHOFF'S
LAWS APPLY TO HYDRAULIC CIRCUITS

PRESSURE-FLOW
CHARACTERISTICS OF ORIFICES

Laminar
Fluid Flow

Figure
2 - Laminar Pressure-flow relationships for common geometric passages,
based upon the Hagen-Poiseuille Law.

THE
"KNIFE-EDGED" ORIFICE AND TURBULENT FLOW

COMBINING
ORIFICES

PRESSURE
DROP

HYDRAULIC
AND MECHANICAL POWER

CONVERSION
OF FLOW UNITS

(6) FLUIDS
AND CONDITIONING SUBSYSTEMS

FILTERS

Beta
Ratio

RESERVOIRS

HEAT
EXCHANGERS

FLUIDS

Viscosity

Bulk
Modulus

Hydraulic
Capacitance

ACCUMULATORS

Adiabatic
Case

Adiabatic
Hydraulic Capacitance

Iso-Thermal
Case

Accumulator
Placement in the Circuit

MATERIAL
PROPERTIES

PLUMBING

Table
I - PROPERTIES OF MATERIALS

Table
2 - SERVO VALVE FOOTPRINT CHART

Figure
4 - Summary Chart for Viscosity

Table
3 - WALTHER FORMULA COEFFICIENTS

(7)
HYDRAULIC PUMPS AND MOTORS

MATH
MODELS OF IDEAL ENERGY CONVERTERS

SYMBOLS,
IDEAL MACHINES AND PRACTICAL MACHINES

POSITIVE
FLOW AND PRESSURE SOURCES

FIXED
DISPLACEMENT MOTOR CHARACTERISTICS

Table
1 - PUMP AND MOTOR NOMENCLATURE

Table
2 - PUMP AND MOTOR NOMENCLATURE - SUBSCRIPTS

A
LOOK INSIDE A HYDRAULIC MOTOR

SIMPLIFIED
LINEARIZED HYDRAULIC PUMP

TWO
PORT MODELS

INTRODUCTION
TO PRIME MOVER MODELING

MORE
ABOUT CASE DRAIN FLOW AND PRESSURE

LIMITATIONS
IN THE LINEAR MODELS

LOW
SPEED COGGING EFFECTS

(8)
APPLICATION METHODS FOR PRESSURE COMPENSATED PUMPS

ABOUT
PRESSURE COMPENSATED PUMPS AND

CONSTANT
PRESSURE SOURCE

PRESSURE
COMPENSATED PUMP AND MOTOR DATA

ABOUT
CONSTANT PRESSURE AND

ALMOST
CONSTANT PRESSURE SOURCES

AN
ADJUSTABLE CONSTANT PRESSURE SOURCE

BLACK
BOX MODEL FOR CALCULATING INPUT,

OUTPUT
AND INTERNAL PERFORMANCE

SOME
APPLICATION CONSIDERATIONS

RELIEF
VALVE AS PRESSURE REGULATOR

PRESSURE
COMPENSATED MOTORS OVERVIEW

SPEED-TORQUE
CHARACTERISTICS

(9) SERVO
AND PROPORTIONAL VALVE CONSTRUCTION

INTRODUCTION

BASICS
OF VALVE SYMBOLOGY

Pressure
Control Valves

Flow
Control Valves

CONSTRUCTION
DETAILS OF SOME SERVO/PROPORTIONAL VALVES

(10) VALVE
TESTING AND CHARACTERISTICS

ZERO-LAPPED
PROPORTIONAL VALVE

NULLING
THE VALVE

ANALYZING
TEST RESULTS

Flow
Gain

Linearity

Pressure
Gain, Port

Pressure
Gain

Servo
Valve Null Characteristics

Null
Sensitivity Tests

Valve
Coefficient

(11)
CYLINDERS

CYLINDER
CLASSIFICATIONS

POWERED
AND RETURN END AREAS AND CYLINDER RATIO

MECHANICAL
OUTPUT POWER

STALL
FORCE

CYLINDER
DYNAMIC CONSIDERATIONS

Hydraulic
Capacitance of the Double Acting Cylinder

Hydraulic
Cylinder Circuits with Valve Losses

EXAMPLE
PROBLEMS

CYLINDER
DIMENSIONAL DATA - INCH BASED

CYLINDER
DIMENSIONAL DATA - mm BASED

(12)
CYLINDER LOAD HOLDING AND FORCE BALANCE

(13) VALVE
CONTROL OF CYLINDER MOTION

FORCE-VELOCITY
OPERATING ENVELOPE

PROPER
SIZING OF THE HYDRAULIC SERVO SYSTEM

Cylinder
Ratio Conundrum

SCENARIO
#1 -Two Points on the Operating Envelope

Situation
#1 - Supply pressure is specified

Situation
#2 - Cylinder area is specified

Situation
#3 - Valve coefficient is specified

SCENARIO
#2 - One Point on the Operating Envelope

Situation
#1 - Cylinder and valve are specified

Situation
#2 - Cylinder and pressure are specified

Situation
#3 - Pressure and valve are specified

SCENARIO
#3 - All Hydraulic Parameters are specified

Situation
#1 - Solve for force

Situation
#2 - Solve for velocity

OPTIMAL
SIZING OF THE HYDRAULIC SYSTEM

Situation
#1 - Supply pressure is specified

Situation
#2 - Cylinder area is specified

Situation
#3 - Valve coefficient is specified

VALVE
SHOPPING

DESIGNING
FOR RETRACTING CONDITIONS

MAXIMUM
OVER-RUNNING LOAD WITHOUT CAVITATION

MAXIMUM
PRESSURE ON THE DECELERATING END

ISSUES
INVOLVING MAXIMUM ACCEL AND DECEL

NON-SYMMETRICAL
VALVES

TABLE
1 - OPTIMAL AND SUB-OPTIMAL DESIGNS COMPARED

UNDER
IDEAL AND PRACTICAL SCENARIOS

TEST
METHOD A - EQUAL FLOWS

TEST
METHOD B - EQUAL PRESSURE DROPS

FORWARD-TO-REVERSE
SYMMETRY

(14)
HYDRAULIC POWER UNIT FOR MOTION CONTROL

RETURN
LINE TRANSIENT TEST

PUMP
RESPONSE TEST DATA

THE
PULSE WIDTH MODULATION METHOD OF PRESSURE CONTROL

ACCUMULATOR
SIZE

(15) DYNAMIC SIMULATION OF A PRESSURE COMPENSATED PUMP

MODELING
PUMP DYNAMIC CHARACTERISTICS

PRELIMINARY
CALCULATIONS FOR THE PUMP DYNAMIC MODEL

STATE
EQUATIONS FOR THE SYSTEM

Pump
Response to a Flow Step

PUMP
STEADY-STATE CHARACTERISTICS

SET
UP CONDITIONS FOR THE FLYING CUT OFF SIMULATION

CAVEAT
REGARDING THE LINEAR SIMULATION

Load
Flow Profile

DEMAND
FLOW PROFILE SYNTHESIS

Line-By-Line
Explanation of the Corner Point Profile Chart

FLOW
PROFILES FOR THE SIMULATION

RESULTS
OF THE DYNAMIC SIMULATION

0.045
Second Pump Simulation Data

Evaluation
of Simulation Results - 0.045 Second Pump

0.225
Second Pump Simulation Data

Evaluation
of Simulation Results - 0.225 Second Pump

STATISTICAL
SUMMARY OF THE SIMULATION

CONCLUSIONS

ACCUMULATOR
SIZING TO ACHIEVE A PRESSURE VARIATION GOAL

INTEGRATED
DEMAND FLOW

A
NOTE OF CLARIFICATION

LINEAR
SIMULATION TO VERIFY THE ACCUMULATOR SIZE

(16)
PHYSICS OF MOTION CONTROL AND FLOW PROFILES

THE
MOTION CONTROL SYSTEM

MOTION
CONTROL DEFINED

THE
MATHEMATICAL APPROACH

Acceleration,
velocity and position are not independent

THE
GEOMETRIC APPROACH

Scenario
1 - Cycle Time, Distance and ΔT Intervals are Specified

Scenario
2 - Only Total Time and Distance Are Specified

Scenario
3 - Cycle Time and ΔX Intervals are Specified

Scenario
4 - Cycle Time, Distance and Accelerations are Specified

Other
Scenarios

FLOW
PROFILES

SELECTION
OF ACCELERATION & DECELERATION TIME

(17) CLOSED
LOOP BANDWIDTH NEEDED FOR SPECIFIED ACCURACY

MOVING
NULL DIAGRAM

Consequences
of the Overlapped Valve

Dead
Band Compensation

Closed
Loop Gain

STEAD
STATE POSITIONING ERROR

TOTAL
DISTURBANCE CURRENT

Disturbance
Current Contributors Explained

Simplifying
Rule of Thumb for Disturbance Current

FOLLOWING
ERROR AT STEADY STATE SPEED

FREQUENCY
RESPONSE CONSIDERATIONS

HYDROMECHANICAL
RESONANT FREQUENCY

HYDROMECHANICAL
DAMPING RATIO

Valve
Leakage Resistance

FREQUENCY
SEPARATION RATIO

Outline
for Using Separation Ratio in the Servo Loop Design Process

SEPARATION
RATIO GRAPH

SECOND
ORDER RESPONSES

DESIGNERS'
AIDS REGARDING RESONANCE AND DAMPING

ESTIMATING
DAMPING RATIO, ζm, FROM FRICTION FEATURES

Table
1 - CANONICAL QUADRATIC FORMS

FOR
SECOND ORDER SYSTEMS

(18) LINEAR
MODEL OF THE HYDROMECHANICAL VALVE-CONTROLLED CYLINDER SYSTEM

DISCUSSION
ON LINEAR VERSUS NON-LINEAR SYSTEMS

GENERAL
COMMENTARY ON LINEARITIES AND NON-LINEARITIES

DEVELOPING
THE LINEARIZED MODEL

Modeling
the Valve

Simplified
servovalve Model

DERIVATION
OF A TWO-SOURCE, ASYMMETRICAL LINEAR VALVE MODEL

Valve
Leakage Resistance

Summary
of the Linear Model

Symmetrical
Load Valve Model

DYNAMIC
MODEL OF THE HYDROMECHANICAL SYSTEM

Making
a Block Diagram of the Hydromechanical System

Sketching
the State Variable Diagram

When
There is Leakage Across The Piston

(19)
COMBINING THE VALVE DYNAMIC MODEL WITH THE HYDROMECHANICAL DYNAMIC MODEL

Background

Valve
Time Delay

DEVELOPING
A VALVE DYNAMIC MODEL

Simplified
Approximation for Finding Valve Transfer Function

Rigorous
Method for Finding Valve Transfer Function

The
Transfer Function

Commentary
on the Frequency Response For Model Synthesis

Scaling
the Transfer Function

Obtain
A Block Diagram from A Transfer Function

Combining
the Valve, Amplifier And Hydromechanical Circuits

Summary
of the Valve-Controlled Cylinder Electrohydraulic State Variable Diagram

Inputs
to the Valve-Controlled Cylinder System

A-Matrix
Elements (The algebraic quantities were defined earlier)

(20)
OPTIMAL SIZING AND SPEED CONTROL OF HYDRAULIC MOTORS

OPTIMAL
SIZING

EXAMPLE
OPTIMAL DESIGN PROBLEM

FOR
MOTOR SPEED CONTROL

CLOSED
LOOP SPEED CONTROL

SPEED
GAIN OF THE ELECTROHYDRAULIC SYSTEM

(21)
ELECTRICITY AND ELECTRICAL MEASUREMENTS

MOVING
CHARGES AND ELECTRICAL CURRENT

VOLTAGE

Absolute
zero pressure and absolute zero voltage

OHM'S
LAW AND RESISTANCE

Table
1 - Standard and Preferred Resistances for

Carbon
Based Resistors

Table
2 - Standard and Preferred Resistances for Carbon

Based
Resistors - Megohm ranges

Table
3 - Resistor Color Codes for Carbon-Based resistors

Table
4 - Typical resistance values for equipment that is

encountered
daily

RESISTOR
TYPES

FIVE
AND SIX BAND RESISTORS

OTHER
RESISTOR MARKINGS

BASIC
CURRENT AND VOLTAGE RELATIONSHIPS

AC
VOLTAGE

Voltage
measurement

Intrusiveness

DC
current measurement

USING
THE OHMMETER

KIRCHOFF'S
LAW

CAPACITANCE
AND CAPACITORS

CAPACITOR
TYPES

SELF-HEALING

CAPACITOR
SPECIFICATIONS

CAPACITOR
MARKINGS

CHARGE
AND ENERGY STORAGE

ELECTRIC
FIELD

USING
CAPACITORS

INDUCTANCE

SUMMARY
OF INDUCTANCE

TRANSFORMERS

DIODES
AND RECTIFIERS

(22) COMMON ELECTRONIC DEVICES FOR ELECTROHYDRAULICS

DIODES,
RECTIFIERS, AND POWER SUPPLIES

CONVERSION
FUNCTION

HEATING
VALVES

Reducing
Supply Voltage for Electronics GU4

VOLTAGE
REGULATOR CHARACTERISTICS

CIRCUIT
COMMON, GROUND AND MOTHER EARTH

AMPLIFIERS

A
"Hydraulic Transistor" Circuit

Integrated
Circuits and Operational Amplifiers

PRACTICAL
OPERATIONAL AMPLIFIER CIRCUITS

Basic
Inverting Amplifier

Basic
Non-Inverting Amplifier

Inverting
Summing Amplifier

ZERO,
OFFSET AND BIAS

ADJUSTABLE
GAIN OP-AMP CIRCUITS

Variable
Input Resistance

Variable
Feedback Resistance

Output
Potentiometer

MAKING
CONNECTIONS TO THE SERVO/PROPORTIONAL

AMPLIFIER

ANALOG
INTEGRATION AND DIFFERENTIATION

SERVO
AMPLIFIER

PULSE
WIDTH MODULATION

POTENTIOMETER

DEAD
BAND ELIMINATOR

LIMIT
ADJUSTMENTS

ASYMMETRICAL
GAIN ADJUSTMENT

RAMP
CONTROLS

PHASE
SENSITIVE DEMODULATOR

PROPORTIONAL
VALVE AMPLIFIER

4-TO-20
MILLIAMP CURRENT LOOP

IMPEDANCE
MATCHING AND LOADING ERRORS

Thevenin
Impedance, Output Impedance, Source Impedance

Norton's
Theorem

LOADING
ERRORS

ZEROING,
SCALING AND PHASING THE POSITIONAL SERVO LOOP

CHARGE
AMPLIFIERS

ELECTRONIC
COUNTER

NOISE
CONTROL

GENERAL
RULES FOR CONTROLLING NOISE

PARASITIC
CAPACITANCE AND ELECTROSTATIC INTERFERENCE

ELECTROSTATIC
SHIELDING

GROUND
LOOPS - CAUSE AND CONTROL

DIFFERENTIAL
SIGNAL TRANSMISSION

OPTO-ISOLATION

ELECTROMAGNETIC
INTERFERENCE

RADIO-FREQUENCY
INTERFERENCE

ELECTROMAGNETIC
COMPATIBILITY

(23)SPECIAL
TOPICS ON MOBILE
ELECTRICAL SYSTEMS

VEHICLE
ELECTRICAL SYSTEMS

BATTERIES

CHECKING
BATTERY CHARGE

BATTERY
CHEMISTRY

THERMAL
EFFECTS

ELECTRICAL
TESTS

BATTERY
DETERIORATION AND AGING

DRY-CHARGED
BATTERIES

BATTERY
SERVICE

MAINTENANCE-FREE
BATTERIES

BATTERY
SAFETY

VEHICLE
GROUND CIRCUITS

ALTERNATOR
AND CHARGING SYSTEMS

JOYSTICKS

(24)
OVERVIEW OF ELECTROHYDRAULIC MOTION CONTROL

INTRODUCTION

ELEMENTS
OF MOTION CONTROL TECHNOLOGY

BACKGROUND

CONSTANT
PRESSURE SUPPLY

CONVENTIONAL
HYDRAULIC CIRCUITS

EFFECTIVE
MOTION CONTROL

MOTION
CONTROL DEFINED

PROFILES

ACHIEVING
TRUE MOTION CONTROL

MOTION
CONTROLLERS

OPERATING
ENVELOPE

POSITIONAL
SERVOMECHANISM -- THE ULTIMATE SOLUTION

MOTION
CONTROL SYSTEM DESIGN

SUMMARY
CONCEPTS IN MOTION CONTROL

USING
TEST DATA

DESIGN
METHODOLOGY

ADVANTAGES
OF MOTION CONTROL TECHNOLOGY

(25) BLOCK DIAGRAMS AND TRANSFER FUNCTIONS

BLOCK
DIAGRAMS

BLOCK
DIAGRAM MANIPULATION

TRANSFER
FUNCTIONS

SOURCES
OF TRANSFER FUNCTIONS

NATURAL
FREQUENCY AND DAMPING RATIO

SOME
FEATURES OF TRANSFER FUNCTIONS

HIGHER
ORDER SYSTEMS USING IDAS

FREQUENCY
RESPONSE GRAPH CALCULATED

FROM
THE TRANSFER FUNCTION

GRAPHICAL
DATA PRESENTATION

STEP
RESPONSE OF SYSTEM

TRANSFER
FUNCTIONS AND FREQUENCY RESPONSE

SECOND
ORDER SYSTEMS

SUMMARY
OF FEATURES OF TRANSFER FUNCTIONS

Table
1: Selected Laplace Transform Pairs

(26)
INTEGRAL CONTROL AND THE POSITIONAL SERVOMECHANISM

CHARACTERISTICS
OF INTEGRATORS

CHARACTERISTICS
OF DIFFERENTIATORS

PROPORTIONAL,
INTEGRAL AND DERIVATIVE CONTROL

FEEDFORWARD

AN
EXPANSION OF THE FEEDFORWARD PROCESS

INTEGRAL
CONTROL -- THE CONCEPT APPLIED

TO
ELECTROHYDRAULIC SERVO SYSTEMS

INTEGRAL
CONTROL AS A CONCEPT

INTEGRAL
CONTROL AS A REALITY

TUNING
THE PID CONTROLLER

SOME
PRACTICAL ASPECTS OF INTEGRAL CONTROL

INTEGRAL
CONTROL IN THE DIGITAL MOTION CONTROLLER

SUMMARY
OF INTEGRAL CONTROL

(27)
DYNAMIC TESTING OF A MOTION CONTROL SYSTEM

INTRODUCTION
AND PURPOSE

DESCRIPTION
OF THE TESTED SYSTEM

PROFILE
CONSTRUCTION

SERVO
LOOP TUNING BEFORE TESTING

SYSTEM
OPERATION

TEST
RESULTS

TEST
1 -- SUPPLY PRESSURE VARIATIONS

TEST
1 -- ERROR

TEST
1 -- EXTENSION VS RETRACTION ERROR

MORE
ABOUT THE FOLLOWING ERROR

TEST
1 -- CYLINDER PRESSURES

VELOCITY
ERROR

TEST
2 RESULTS

TEST
2 -- ERROR RESPONSE

TEST
2 -- SUPPLY PRESSURE AND SPEED

TEST
2 -- CYLINDER PRESSURES

CONCLUSIONS
AND RECOMMENDATIONS

EQUIPMENT
LIST

(28) TORQUE
CELL PROFILE TESTS

HYDROMECHANICAL
RESONANCE TEST DATA

DESIGN
METHODOLOGY - ELECTROHYDRAULIC MOTION CONTROL