*This book is very light on derivations and theory. Instead, it presents hundreds of applicable formulas that relate to the successful application of servo and proportional valves. Theoretical* *discussions are supplanted with scores of completely worked example problems in order to illustrate how the formulas are to be used. It is a necessary reference handbook for any engineer or technician who intends to successfully use servo and proportional valve technology. It should prove useful as a classroom text* *for applied technology.*

This is the fourth edition of this book, which was originally published under the title of * Introduction to Design of Electrohydraulic Circuits Using Servo and Proportional Technology*. Enough was added in third edition that the change in title was felt to be justified, but the title will remain for this edition.

This book supplements a lecture series on the design of electrohydraulic circuits and systems. In this context, systems design consists of the selection, matching and interconnection of a variety of components from a variety of technologies in order that the system performs to a given set of specifications. Normally, a reasonably complete treatment of the subject requires about two semesters of college level effort, however, an overview can be gained in two or three full days, if diligence is the rule of the day. I hope the reader will realize that this work represents only an introduction to a subject that many of us have spent a career trying to master, and at times, when attempting to get a particularly troublesome system up and running, we have all wondered if we have gotten very far.

This book is **not** heavy on theory. Quite the contrary. It is intended to be a concise summary of the technology, and derivations for the most part and theory have been replaced by a number of completely solved example problems that are scattered throughout the book. About half the theory, should the reader wish to pursue it, will be found in another of my books, *Design of Electrohydraulic Systems for Industrial Motion Control Systems*, second edition, 1995. The other half of the theoretical background is contained in scores of file folders of unpublished chapters in my office.

There have been several attempts to offer a way of looking at hydraulic circuits which somewhat parallels my own electrical engineering education. The first is that constant pressure systems and valve control cannot be approached from the point of view of the conventional hydraulic circuit that uses positive displacement pump control. Prior exposure to conventional hydraulic circuit design can be both helpful and a hindrance. All too often, we fall into the trap of thinking that positive displacement pump control is a first principle from which all other principles flow. Quite the contrary. For example, we learn that in constant pressure valve control, single rod end cylinders extend faster than they retract, a reality in the classroom that is at once frustrating, but at times, entertaining.

Second, an analytical schematic is introduced because the traditional industrial symbol set is inadequate for conveying concepts. The symbols must be used in different, unconventional ways. I found it necessary to create, for example, orifices that convey the difference between turbulent and laminar flow regimes.

Third, it is essential to distinguish between ideal components, especially in pumps and motors, and practical components. The concept of an ideal component is a great teaching tool, because it forms a clear idea of what we would like to achieve with our components, the ideal, and then we proceed from there to explain with more complex models, how real components behave. But by using symbology that distinguishes the difference, the reader should be very certain of the nature of the model that is at hand. Clearly, we all use both real and ideal models, but methods for distinguishing the two have never been adopted. For clarity, I feel it essential that readers know the kind of device that is being dealt with at the point of discussion. The distinctions between real and ideal are clear. Therefore, the concept of ideal and practical components is introduced.

Next, significant emphasis is placed on the pressure metering characteristics of valves. Conventional hydraulic training does not usually take up the issue, and yet, it is impossible to understand servo and proportional valves without understanding the way that the pressure metering characteristics interact with the actuator and load. When pressure metering concepts are mastered, it is a short step to understand why there are errors in servo mechanisms, how they can be contained, and why we design systems around the error containment process. The statement, "The load stops because the force on the actuator comes into balance. Therefore, the flow stops, not the other way around" makes sense. And, of course, it is true.

And then, once the errors are understood, one of the most profound realities is, that it is possible to relate them to the frequency response, or, bandwidth of the system and the components. It then leads to another major gremlin lurking in every feedback control system, that of instability, or sustained oscillations. It is necessary that the system designer contain the errors in order to achieve the necessary performance, however, the system cannot be allowed to go unstable. If the student cum reader will master pressure metering of proportional and servo valves, then all the rest flows naturally from it.

I have found through the years of teaching this subject that if the theory is to be covered, then it must be done so in detail, and a book that is heavy with theory will tend to bury the reader in analytical chaff, when interest may consist only of an overview. For this reason, the theory has been reduced, and the end results presented, with examples. That is, the book uses the principle that the student learns by doing. There are scores of fully worked example problems. These should be studied in detail and will help in understanding the concepts, plus, it will help in defining the various elements of a given equation or formula and it will help to focus attention on the most important part of learning, where do you look for the information you need to solve the problem? The number of worked example problems has more than tripled from the second edition to this.

Several chapters were added in the third edition. Two of them are devoted to the *pressure compensated pump*, which is a vital part of the electrohydraulic motion control servo system. Constant pressure is a necessity, and the pressure compensated pump is the means to that end, along with a flow-augmenting accumulator. The first of the two chapter deals with modelling and applying the pressure compensated pump. The second added chapter is a summary of the results of simulating the dynamic response of the pump and various sized accumulators. The objective is to come away with a sensible procedure for estimating the size of the accumulator in order to achieve a specified dynamic pressure regulation target.

The third edition also added a chapter on *block diagrams* and *transfer functions*. Although the theory behind transfer functions, generally is beyond the scope of the technical level of this book, I felt it was needed in order to be a complete reference for both engineers and technicians who are forced to deal with feedback control systems. The chapter can be safely ignored by those who wish to do so, but it is there for those interested.

Eighteen new, fully worked example problems were added to the chapter on *cylinders*. Anyone interested in understanding how valves control the motion of cylinders is urged to master these problems before proceeding. The chapter on *Valve Control of Cylinder Motion* will be easier to deal with.

Lastly, discussions of electricity and electronics was expanded for the third edition. A few more items of interest o mobile equipment users have been included, such as joysticks. In the aim of decreasing dependence on the standard temperature-viscosity charts, a chart of **Walther coefficients for more than 500 commercial hydraulic fluids have been added.** Viscosity can be calculated directly from a knowledge of the fluid and temperature.

This fourth edition is the result of your continuing requests for a more complete handbook. Toward that end, the first chapter is completely new and provides a more fundamental approach to the Physics of Hydraulics, and of course, is replete with fully worked example problems. There was a call for more insight into analysis of loads that are encountered in the application of hydraulic fluid power. The call was answered by adding three chapters devoted to that subject, but the approach is one of meeting the needs of motion control, more than an exhaustive dissertation on statics, dynamics and kinematics. Again, there are several worked problems in each chapter.

And there was a call for more explanations regarding the ever-present and ever-expanding electronic gadgets that motivate and control all the wonderful electrohydraulic machines. The electronic subjects have more than doubled, and even includes a section devoted to special topics about electronics for mobile hydraulics.

Yes, electrohydraulic system design using servo and proportional valve technology is an analytical and, at times, a challenging process, however, successful implementation is rewarding and satisfying all by itself. The future will see more of this stuff put to good use, not less. There is a future for anyone who sets out to master the technology. So, review the contents with the idea that you are embarking an exciting technological adventure. It is not an end, only a beginning. Good luck!

Jack L Johnson, BSEE, PE

East Troy, Wis.

**Table of Contents**

**Chapter 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° 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 is Known, Calculate ∆P; Pressure Loss Observations; Introduction to Power Sources; Introduction to 4-Way Spool Valves;

**Chapter 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 Wave shapes; Linearized Viscous Coefficient; Rotational Motion compared to Linear (Translational) Motion; Comparison of Linear and Rotational Motion Parameters and Variables

**Chapter 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

**Chapter 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

**Chapter 5 — Hydraulic Circuit analysis Fundamentals**

Inch-Pound-Second System: a 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; The Knife-Edged Orifice and Turbulent Flow; Combining Orifices; Pressure Drop; Hydraulic and Mechanical Power; Conversion of Flow Units

**Chapter 6 — Fluid 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; Properties of Materials; Servovalve Footprint Chart; Walther formula Coefficients

**Chapter 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; Pump and Motor Nomenclature; 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

**Chapter 8 —Application Methods for Pressure Compensated Pumps**

Pressure Compensated Pumps and Constant Pressure Sources; Pressure Compensated Pump and Motor Data; 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

**Chapter 9 — Servo and Proportional Valve Construction**

Introduction; Basics of Valve Symbology; Pressure Control Valves; Flow Control Valves; Construction Details of Some Servo/Proportional Valves

**Chapter 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

**Chapter 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

**Chapter 12 — Cylinder Load Holding and Force Balance**

**Chapter 13 — Valve Control of Cylinder Motion**

Force-Velocity Operating Envelope; Proper Sizing of The Hydraulic Servo System; Cylinder Ratio Conundrum: Two Points on The Operating Envelope; Supply Pressure is Specified; Cylinder Area is Specified; Valve Coefficient is Specified; One Point on The Operating Envelope; Cylinder and Valve are Specified; Cylinder and Pressure are Specified; Pressure and Valve are Specified; All Hydraulic Parameters are Specified; Solve for Force; Solve for Velocity; Optimal Sizing of the Hydraulic System: Supply Pressure is Specified; Cylinder Area is Specified; Valve Coefficient is Specified.

Shopping for a Valve; Designing for Retracting Conditions; Maximum Over-Running Load Without Cavitation; Maximum Pressure on The Decelerating End; Issues Involving Maximum Acceleration and Deceleration; Non-Symmetrical Valves; Optimal and Sub-Optimal Designs Compared Under Ideal and Practical Scenarios: Equal Flows, Equal Pressure Drops. Forward-to-Reverse Symmetry

**Chapter 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

**Chapter 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; Linear Simulation to Verify the Accumulator Size

**Chapter 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: With Cycle Time, Distance and ∆T Intervals Specified; With Only Total Time and Distance Specified; With Cycle Time and ∆X Intervals Specified; With Cycle Time, Distance and Accelerations Specified; Other Scenarios; Flow Profiles; Selection of Acceleration and Deceleration Time

**Chapter 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, ?M, From Friction Features; Canonical Quadratic forms for Second Order Systems

**Chapter 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

**Chapter 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; Matrix Elements

**Chapter 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

**Chapter 21 — Electricity and Electrical Measurements**

Moving Charges and Electrical Current; Voltage; Absolute Zero Pressure and Absolute Zero Voltage; Ohm's Law and Resistance; Standard and Preferred Resistances for; Carbon Based Resistors; Standard and Preferred Resistances for Carbon; Based Resistors – MΩ Ranges; Resistor Color Codes for Carbon-Based Resistors; 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;

**Chapter 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 mA 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

**Chapter 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;

**Chapter 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

**Chapter 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 software; 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; Selected Laplace Transform Pairs

**Chapter 26 — Integral Control and The Positional Servo Mechanism**

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

**Chapter 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; Supply Pressure Variations; Extension Vs Retraction Error; More About The Following Error; Test 1 -- Cylinder Pressures; Velocity Error; Error Response; Supply Pressure and Speed; Cylinder Pressures; Conclusions and Recommendations; Equipment List

**Chapter 28 — Torque Cell Profile Tests **Hydromechanical Resonance Test Data; Design Methodology: Electrohydraulic Motion Control; Additional Related Reading and References