Hydraulic Systems Volume 7

Modeling and Simulation

for Application Engineers

Dr. Medhat Kamel Bahr Khalil, Ph.D, CFPHS, CFPAI.

Director of Professional Education and Research Development,
Applied Technology Center, Milwaukee School of Engineering,
Milwaukee, WI, USA.

CompuDraulic LLC
www.CompuDraulic.com
 CompuDraulic LLC
Hydraulic Systems Volume 7

Modeling and Simulation for Application Engineers

ISBN: 978-0-9977634-3-0

Printed in the United States of America

First Published by June 2020
Revised by --

All rights reserved for CompuDraulic LLC.

3850 Scenic Way, Franksville, WI, 53126 USA.
www.compudraulic.com

No part of this book may be reproduced or utilized in any form or by any means, electronic or
physical, including photocopying and microfilming, without written permission from
CompuDraulic LLC at the address above.

Disclaimer

It is always advisable to review the relevant standards and the recommendations from the
system manufacturer. However, the content of this book provides guidelines based on the
author's experience.

Any portion of information presented in this book might not be suitable for some applications
due to various reasons. Since errors can occur in circuits, tables, and text, the author/publisher
assumes no liability for the safe and/or satisfactory operation of any system designed based on
the information in this book.

The author/publisher does not endorse or recommend any brand name product by including
such brand name products in this book. Conversely the author/publisher does not disapprove
any brand name product not included in this book. The publisher obtained data from catalogs,
literatures, and material from hydraulic components and systems manufacturers based on
their permissions. The author/publisher welcomes additional data from other sources for
future editions. This disclaimer is applicable for the workbook (if available) for this textbook.
 1 HSV7: Modeling and Simulation for Application Engineers
Table of Contents

Hydraulic Systems Volume 7

Modeling and Simulations for Application Engineers

PREFACE, 9

ACKNOWLEDGEMENT, 10

ABOUT THE BOOK, 11

ABOUT THE AUTHOR, 14

Chapter 1: Introduction to Physical Systems Modeling and Simulation, 155

1.1- Importance of Physical Systems Modeling and Simulation
1.2- History of Physical Systems Modeling and Simulation
1.3- Product Development Cycle
1.4- Physical Systems Identification
1.4.1- Linear versus Nonlinear Systems
1.4.2- Static versus Dynamic Systems
1.4.3- Digital versus Analog Systems
1.4.4- Distributed versus Lumped Systems
1.4.5- Design Parameters and Assumptions
1.5- Physical Systems Mathematical Modeling
1.6- Physical Systems Modeling in t-Domain using Differential Equations
1.6.1- Classifications of Differential Equations
1.6.1.1- Ordinary versus Partial Differential Equations
1.6.1.2- Linear versus Nonlinear Differential Equations
1.6.1.3- Homogeneous versus Non-Homogeneous Differential Equations
1.6.1.4- First Order versus Second Order Differential Equations
1.6.2- Mathematical Solution in t-Domain for a Physical System Response
1.7- Physical Systems Modeling in s-Domain using Laplace Transform
1.7.1- Laplace Transform
1.7.2- Block Diagram Algebra
1.7.3- Transfer Function
1.8- t-Domain versus s-Domain Physical Systems Modeling
1.9- Development of Simulation Models for Physical Systems
1.9.1- Processor-Time Simulation
1.9.2- Real-Time Simulation
1.9.3- Hardware-in-the-Loop Simulation
1.10- Physical Systems Performance Simulation
1.11- Physical Systems Performance Analysis
1.11.1- Impulse Response
1.11.2- Step Response
 2 HSV7: Modeling and Simulation for Application Engineers
Table of Contents

1.11.3- Ramp Response

1.11.4- Frequency Response
1.12- Challenges of Physical Systems Modeling and Simulation
1.12.1- Challenges in Physical System Identification
1.12.2- Challenges in Mathematical Model Development
1.12.3- Challenges in Simulation Model Development
1.12.4- Challenges in Performance Simulation
1.12.5- Challenges in Performance Analysis
1.13- Basic Elements of Physical Systems
1.14- Effort and Flow Variables of Physical Systems
1.15- Power Calculation for Physical Systems
1.16- Mathematical Representation of Inductive Elements
1.17- Mathematical Representation of Resistive Elements
1.18- Mathematical Representation of Capacitive Elements

Chapter 2: Modeling and Simulation of First-Order Dynamic Systems, 53

2.1- First-Order Physical System Identification
2.2- First-Order System Mathematical Modeling
2.2.1- First-Order System Mathematical Model in t-domain
2.2.2- First-Order System Mathematical Model in s-domain
2.2.3- First-Order System Normalized Transfer Function
2.3- Simulation Model Development of First-Order Systems
2.4- Performance Simulation of First-Order Systems
2.5- Step Response Analysis of First-Order Systems
2.5.1- Identification of First-Order Systems Based on Step Response
2.5.2- Effect of Design Parameters on First-Order System Step Response
2.5.2.1-Effect of Time Constant
2.5.2.2-Effect of Friction Coefficient
2.6- First-Order System Modeling Based on Step Response
2.7- Frequency Response Analysis of First-Order Systems
2.7.1- Identification of First-Order Systems Based on Frequency Response
2.7.2- Effect of Design Parameters on First-Order System Frequency Response
2.7.2.1- Effect of Time Constant
2.7.2.2- Effect of Exciting Frequency
2.8- First-Order System Modeling Based on Frequency Response

Chapter 3: Modeling and Simulation of Second-Order Dynamic Systems, 82

3.1- Second-Order Physical System Identification
3.2- Second-Order System Mathematical Modeling
3.2.1- Second-Order System Mathematical Model in t-domain
3.2.3- Second-Order System Normalized Transfer Function
3.3- Simulation Model Development of Second-Order Systems
3.4- Performance Simulation of Second-Order Systems
 3 HSV7: Modeling and Simulation for Application Engineers
Table of Contents

3.5- Step Response Analysis of Second-Order Systems

3.5.1- Identification of Second-Order System Based on Step Response
3.5.2- Effect of Design Parameters on Second-Order System Step Response
3.5.2.1- Effect of Moving Mass
3.5.2.2- Effect of Friction Coefficient
3.5.2.3- Effect of Spring Constant
3.5.2.4- Effect of Natural Frequency
3.5.2.5- Effect of Damping Ratio
3.5.2.6- Difference between 1st Order and Overdamped 2nd Order Step Response
3.5.2.7- Effect of Damping Ratio as Presented on s-Plane
3.6- Second-Order System Modeling Based on Step Response
3.7- Frequency Response Analysis of Second-Order Systems
3.7.1- Identification of Second-Order Systems Based on Frequency Response
3.7.2- Effect of Design Parameters on Second-Order System Frequency Response
3.7.2.1- Effect of Damping Ratio
3.7.2.2- Effect of Exciting Frequency
3.7.3- Stability Analysis Based on Bode Plot

Chapter 4: Modeling Approaches for Hyd. Components and Systems, 122

4.1- Modeling Approaches for Component Developers
4.1.1- Basic Purposes of Modeling for Component Developers
4.1.2- Features of Modeling for Component Developers
4.2- Modeling Approaches for Application Engineers
4.2.1- Basic Purposes of Modeling for Application Engineers
4.2.2- Features of Modeling for Application Engineers
4.3- Lumped Modeling Approach for Application Engineers
4.3.1- Introduction to Lumped Modeling Approach
4.3.2- Lumped Model Structure for Hydraulic Components
4.3.3- Lumped Model Structure for Open Circuits
4.3.4- Lumped Model Structure for Closed Circuits
4.3.5- Simulating the Static Characteristics of a Hyd. Component in a Lumped Model
4.3.6- Simulating the Dynamic Characteristics of a Hyd. Component in a Lumped Model
4.3.7- Example of Lumped Modeling

Chapter 5: Modeling of Fluid Properties, 140

5.1- Introduction to Fluid Properties Modeling
5.2- Modeling of Hydraulic Fluid Bulk Modulus
5.2.1- Definition and Mathematical Expression of Bulk Modulus
5.2.2- Case Study 1 for Modeling of Bulk Modulus
5.2.2.1- Effect of Temperature and Pressure on Bulk Modulus
5.2.2.2- Effect of Entrained Air on Bulk Modulus
5.2.2.3- Structure of Lumped Model for Case Study 1
5.3- Modeling of Hydraulic Fluid Density and Specific Gravity
5.3.1- Definitions and Mathematical Expression of Density
 4 HSV7: Modeling and Simulation for Application Engineers
Table of Contents

5.3.2- Definitions and Mathematical Expression of Specific Weight

5.3.3- Definitions and Mathematical Expression of Specific Gravity
5.3.4- Case Studies for Modeling of Density and Specific Gravity
5.3.4.1- Case Study 2 based on Effect of Temperature and Pressure on Density
5.3.4.2- Structure of Lumped Model for Case Study 2
5.3.4.3- Case Study 3 based on Density as Function of other Properties
5.3.4.4- Structure of Lumped Model for Case Study 3
5.3.4.5- Case Study 4 based on Effect of Temp. and Pressure on Specific Gravity
5.3.4.6- Structure of Lumped Model for Case Study 4
5.4- Modeling of Hydraulic Fluid Viscosity
5.4.1- Definitions and Mathematical Expression of Viscosity
5.4.2- Case Study 5 for Modeling of Viscosity Based on Effect of Temp. and Pressure
5.5- Lumped Model for Hydraulic Fluid Properties

Chapter 6: Modeling of Hydraulic Transmission Lines, 163

6.1- Modeling of Seamless Hydraulic Transmission Lines
6.1.1- Modeling Pressure Losses due to Line Resistivity
6.1.2- Modeling Pressure Losses due to Line Inductance
6.1.3- Modeling Inlet Pressure of Transmission Line
6.1.4- Case Studies for Modeling a Hydraulic Transmission Line
6.1.4.1- Case Study 1: Steady State Condition
6.1.4.2- Case Study 2: Surge Inlet Flow
6.1.4.3- Case Study 3: Surge Outlet Pressure
6.2- Modeling of Hydraulic Fittings
6.3- Modeling of Hydraulic Orifices
6.4- Modeling Hydraulic Transmission Line Assembly

Chapter 7: Modeling of Hydraulic Pumps, 183

7.1- Lumped Model Structure of a Unidirectional Hydraulic Pump
7.2- Lumped Model Structure of a Bidirectional Hydraulic Pump
7.3- Modeling Fixed Displacement Pumps
7.4- Model #01 for an Ideal Fixed Displacement Pump
7.4.1- Model Features and Assumptions
7.4.2- Pump Theoretical Flow Rate
7.4.3- Theoretical Torque Acting on the Pump Drive Shaft
7.4.4- Model Structure
7.4.5- Simulation Model
7.5- Model #02A for a Fixed Displacement Pump Running at Constant Operating Conditions
Based on Given Test Values
7.5.1- Model Features and Assumptions
7.5.2- Pump Actual Flow and Volumetric Efficiency
7.5.3- Pump Input Power and Overall Efficiency
7.5.4- Pump Mechanical Efficiency
7.5.5- Pump Actual Torque
5 HSV7: Modeling and Simulation for Application Engineers
Table of Contents

7.5.6- Simulation Model

7.5.7- Model Validation
7.6- Model #02B for a Fixed Displacement Pump Running at Constant Operating Conditions
Based on Given Efficiency Values
7.6.1- Model Features and Assumptions
7.6.2- Simulation Model
7.7- Model #03A for a Fixed Displacement Pump Running at Variable Operating Conditions
Based on Given Test Data
7.7.1- Model Features and Assumptions
7.7.2- Mathematical Model
7.7.3- Simulation Model
7.7.4- Model Validation
7.8- Model #03B for a Fixed Displacement Pump Running at Variable Operating Conditions
Based on Given Efficiency Curves
7.8.1- Model Features and Assumptions
7.8.2- Simulation Model
7.8.3- Model Validation
7.9- Modeling Variable Displacement Pumps
7.10- Lumped Modeling of Pressure-Compensated Pumps
7.10.1- Characteristics of Pressure-Compensated Pumps
7.10.2- Model #04A for Pressure-Compensated Pumps Based on Given Test Data
7.10.2.1- Model Features and Assumptions
7.10.2.2- Mathematical Model
7.10.2.3- Simulation Model
7.10.2.4- Model Validation
7.10.3- Model #04B for Pressure-Compensated Pumps Based on Given Efficiency Curves
7.10.3.1- Model Features and Assumptions
7.10.2.2- Simulation Model
7.10.2.3- Model Validation
7.10.4- Simplified Model #04C for Pressure-Compensated Pumps
7.10.4.1- Case Study
7.10.4.2- Model Features and Assumptions
7.10.4.3- Simulation Model
7.10.4.4- Model Validation
7.11- Lumped Modeling of Displacement-Controlled Pumps
7.11.1- Characteristics of Displacement-Controlled Pumps
7.11.2- Simplified Model #05A for Displacement-Controlled Pumps
7.11.2.1- Model Features and Assumptions
7.11.2.2- Simulation Model
7.11.2.3- Model Validation
7.11.3- Model #05B for Displacement-Controlled Pumps Based on Given Eff. Curves
7.11.3.1- Model Features and Assumptions
7.11.3.2- Simulation Model
7.11.3.3- Model Validation
 6 HSV7: Modeling and Simulation for Application Engineers
Table of Contents

7.12- Lumped Modeling of Torque-Limited Pumps

7.12.1- Characteristics of Torque-Limited Pumps
7.12.1.1- Electro-Hydraulic Constant-Power Pumps
7.12.1.2- Hydro-Mechanical Constant-Power Pumps
7.12.1.3- Modeling Approaches for Torque-Limited Pumps
7.12.2- Simplified Model #06A for Torque-Limited Pumps
7.12.2.1- Model Features and Assumptions
7.12.2.2- Simulation Model
7.12.2.3- Model Validation
7.12.3- Model #06B for Torque-Limited Pumps Based on Given Efficiency Curves
7.12.3.1- Model Features and Assumptions
7.12.3.2- Simulation Model
7.12.3.3- Model Validation

Chapter 8: Modeling of Hydraulic Motors, 240

8.1- Lumped Model Structure of a Unidirectional Hydraulic Motor
8.2- Lumped Model Structure of a Bidirectional Hydraulic Motor
8.3- Modeling Fixed displacement Motors
8.4- Model #01 for an Ideal Fixed Displacement Motor
8.4.1- Model Features and Assumptions
8.4.2- Motor Theoretical RPM
8.4.3- Moto Torque Calculation
8.4.4- Theoretical Differential Pressure Across the Motor
8.4.5- Simulation Model
8.4.6- Model Validation
8.5- Model #02A for a Fixed Displacement Motor Running at Constant Operating Conditions
Based on Given Test Values
8.5.1- Model Features and Assumptions
8.5.2- Motor Actual Speed and Volumetric Efficiency
8.5.3- Motor Actual Torque and Mechanical Efficiency
8.5.4- Motor Overall Efficiency and Power
8.5.5- Simulation Model
8.5.6- Model Validation
8.6- Model #02B for a Fixed Displacement Motor Running at Constant Operating Conditions
Based on Given Efficiency Values
8.7- Model #03A for a Fixed Displacement Motor Running at Variable Operating Conditions
Based on Given Test Data
8.7.1- Model Features and Assumptions
8.7.2- Mathematical Model
8.7.3- Simulation Model
8.7.4- Model Validation
8.8- Model #03B for a Fixed Displacement Motor Running at Variable Operating Conditions
Based on Given Efficiency Curves
8.8.1- Model Features and Assumptions
 7 HSV7: Modeling and Simulation for Application Engineers
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8.8.2- Simulation Model

8.8.3- Model Validation
8.9- Modeling Variable Displacement Motors
8.10- Model #04 for Variable Displacement Motors
8.10.1- Model Features and Assumptions
8.10.2- Simulation Model
8.10.3- Model Validation
8.11- Simplified Model #05 for Valve-Controlled Fixed-Displacement Bidirectional Hyd. Motor
8.11.1- Case Study
8.12.2- Model Features and Assumptions
8.11.3- Simulation Model
8.11.4- Model Validation

Chapter 9: Modeling of Hydraulic Cylinders, 276

9.1- Lumped Model Structure of a Double-Acting Hydraulic Cylinder
9.2- Lumped Model #01 for Hydraulic Cylinder
9.2.1- Mathematical Model
9.2.1.1- Cylinder Effective Areas
9.2.1.2- Cylinder Inlet Pressure
9.2.1.3- Cylinder Internal Leakage
9.2.1.4- Cylinder Speed
9.2.1.5- Cylinder Outlet Flow
9.2.1.6- Cylinder Force
9.2.2- Simulation Model
9.2.3- Model Validation
9.3- Modeling Cylinder Drifting due to Oil Bulk Modulus
9.4- Modeling of Pressure Increase due to Thermal Expansion

Chapter 10: Modeling of Hydraulic Valves, 293

10.1- Introduction to Hydraulic Valve Modeling
10.2- Lumped Model #01 for Pressure Relief Valve Based on Linear Characteristics
10.2.1- Mathematical Model
10.2.2- Simulation Model
10.2.3- Model Validation
10.3- Lumped Model #02 for Pressure Relief Vale Based on Nonlinear Characteristics
10.4- Lumped Model #03 for Flow Control Valves
10.4.1- Model Structure and Assumptions
10.4.2- Mathematical and Simulation Model
10.4.3- Model Validation
10.5- Lumped Model #04 for Check Valves
10.5.1- Mathematical and Simulation Model
10.5.2- Model Validation
10.5.3- Validating the Models for Check Valve and PRV together
10.6- Lumped Model #06 for Continuous Directional Control Valves
 8 HSV7: Modeling and Simulation for Application Engineers
Table of Contents

10.6.1- Model Structure and Assumptions

10.6.2- Developing Static Characteristics (Flow Gain) of a Continuous Valve
10.6.3- Developing Dynamic Characteristics of a Continuous Valve
10.6.4- Mathematical Model Based on the Flow Gain
10.6.5- Model Validation

Chapter 11: Modeling of Hydraulic Control Systems, 317

11.1-Modeling Electro-Hydraulic Cylinder Position Control System
11.1.1- Simulation Model
11.1.2- System Performance Simulation
11.1.2.1- Step Response
11.1.2.2- Harmonic Response
11.1.3- Model Validation
11.1.4- Effect of Cylinder Leakage
11.1.5- Effect of Proportional Gain
11.2-Modeling Energy Saving Loading System
11.3-Modeling Electro-Hydraulic Motor Speed Control System
11.3.1- Simulation Model
11.3.2- System Performance Simulation
11.3.2.1- Step Response
11.3.2.2- Harmonic Response
11.3.3- Model Validation
11.3.4- Using the Model for System Design

APPENDIXES, 333

APPENDIX A: LIST OF FIGURES, 333

APPENDIX B: LIST OF TABLES, 341

APPENDIX C: LIST OF MODELS AND SOFTWARE, 344

APPENDIX D: LIST OF REFERENCES, xx

INDEX, 353
 9 HSV7: Modeling and Simulation for Application Engineers
Preface

PREFACE
Modeling and simulation techniques are essential tools for dynamic systems design and
production. This book introduces an overview of common mathematical modeling techniques
in t-domain and s-domain, various types of physical systems, and challenges of modeling them.

This book is targeting industry professionals who oversee modeling machine at large rather
than modeling a single component. This book is also a great resource for mechanical
engineering graduate students for their research work.

The book adopted lumped modeling technique, using Matlab-Simulink, to model discrete
hydraulic components that can be recharacterized and used repeatedly in system models. The
book isn’t intended to present a model for every hydraulic component, it rather applies the
lumped modeling concept on hydraulic fluids, transmission lines, pumps, motors, cylinders,
pressure relief valves, flow control valves, proportional valves, and servo valves. This book
uses the component lumped models to assemble an electrohydraulic cylinder position control
system and an electrohydraulic motor speed control as case studies.

More than 60 models are presented. This book provides a comprehensive explanation on how
these models are structured, validated, and used for analyzing system performance. These
models are available to download when you purchase the book.

The author is working hard to finish his goal of supporting fluid power professional education
by developing the following series of volumes and relevant software:

Hydraulic Systems Volume 1: Introduction to Hydraulics for Industry Professionals.

Hydraulic Systems Volume 2: Electro-Hydraulic Components and Systems.
Hydraulic Systems Volume 3: Hydraulic Fluids and Contamination Control.
Hydraulic Systems Volume 4: Hydraulic Fluids Conditioning. Under Development (UD)
Hydraulic Systems Volume 5: Safety and Maintenance. UD
Hydraulic Systems Volume 6: Troubleshooting and Failure Analysis. UD
Hydraulic Systems Volume 7: Modeling and Simulation for Application Engineers.
Hydraulic Systems Volume 8: Design Strategies of Hydraulic Systems. UD
Hydraulic Systems Volume 9: Design Strategies of Electro-Hydraulic Systems. UD
Hydraulic Systems Volume 10: Hydraulic Components Modeling and Simulation. UD

Dr. Medhat Kamel Bahr Khalil

10 HSV7: Modeling and Simulation for Application Engineers
Acknowledgment

ACKNOWLEDGEMENT
This book was written during the hardship of Covid-19 Virus.

All praise is to Allah who granted me the knowledge, resources and health to finish this work

To the soul of my parents who taught me the values of ISLAM

To my wife who offered me all the best she can to make this work complete

To my family: wife, sons, daughters in law, and grandson “Adam”

To my best teachers and supervisors

The author also thanks the following gentlemen for their effective support in developing this
book:
Kamara Sheku, Dean of Applied Researches at Milwaukee School of Engineering.
Tom Wanke, CFPE, Director of Fluid Power Industrial Consortium and Industry
Relations at Milwaukee School of Engineering.
 11 HSV7: Modeling and Simulation for Application Engineers
About the Book

ABOUT THE BOOK

Book Description:
This book is targeting system design engineers who oversee hydraulic control system design
whether for industrial or mobile applications. This book introduces conceptual methodology to
build lumped models for hydraulic components and assemble them to form a system. This
book is also a great resource for mechanical engineering graduate students for their research
work. The book presents models for hydraulic fluids, transmission lines, pumps, motors,
cylinders, pressure relief valves, flow control valves, proportional valves, and servo valves.

This book is colored and has the size of standard A4. The book is associated with a separate
colored workbook. The workbook contains printed power point slides, chapter reviews and
assignments. This book is the seventh in a series that the author plans to publish to offer
complete and comprehensive teaching references for the fluid power industry. The book
contains a total of eleven chapters distributed over 320 pages with very demonstrative figures
and tables. The contents of the book are brand non-biased and intends to introduce the latest
technologies related to the subject of the book.

Book Objectives:
Chapter 1: Introduction to Physical Systems Modeling and Simulation
Modeling and simulation are essential tools in today’s system design process. This chapter
introduces the subject matter overviewing, the importance, historic background, and the
challenges in physical systems modeling and simulation. The chapter also provides a brief
overview of the common techniques used for mathematical modeling of physical systems in t-
domain and s-domain. The chapter also presents the typical forcing functions used to simulate
physical systems performance analysis under various load conditions or commands.

Chapter 2: Modeling and Simulation of First-Order Dynamic Systems

In this chapter, methods and theories presented in Chapter 1 are applied to First-Order
dynamic systems. The chapter presents mathematical modeling for first-order systems in t-
domain and s-domain. This chapter also presents the response of first-order systems to the
typical forcing functions including, step, ramp, and harmonic inputs. The chapter discusses the
measured characteristics of first-order step response and how to develop the transfer function
of the system based on existing dynamic characteristics.

Chapter 3: Modeling and Simulation of Second-Order Dynamic Systems

In this chapter, methods and theories presented in Chapter 1 are applied for Second-Order
dynamic system. The chapter presents mathematical modeling for second-order systems in t-
domain and s-domain. This chapter also presents the response of second-order systems to the
 12 HSV7: Modeling and Simulation for Application Engineers
About the Book

typical forcing functions including, step, ramp, and harmonic inputs. The chapter discusses
measured characteristics of second-order step response and how to develop the transfer
function of the system based on existing dynamic characteristics.

Chapter 4: Modeling Approaches for Hydraulic Components and Systems

This chapter explores the different approaches when modeling a hydraulic component versus
modeling a hydraulic system at large. The chapter presents the basic idea and the structure of
lumped modeling, an adopted modeling approach for application engineers.

Chapter 5: Modeling of Fluid Properties

This chapter presents different techniques to model hydraulic fluid properties based on
available information. Properties considered in this chapter are bulk modulus, density, specific
gravity and viscosity. In modeling such properties, effects of working temperature and
pressure are considered. Case studies are presented, and Matlab-Simulink models were built
and validated based on given information.

Chapter 6: Modeling of Hydraulic Transmission Lines

This chapter presents modeling transmission lines, fittings and orifices. Model for a
transmission line considers compressible fluid so that effect of line capacitance can be
investigated. Developed models were validated based on other software.

Chapter 7: Modeling of Hydraulic Pumps

This chapter presents the lumped modeling concept as applied for fixed and variable
displacement pumps. This chapter considers situations where a pump works under a constant
or variable pressure and driving speed. Models for pressure-compensated, displacement-
controlled, and torque-limited pumps are developed.

Chapter 8: Modeling of Hydraulic Motors

This chapter presents the lumped modeling concept as applied for fixed and variable
displacement motors. This chapter considers situations where a motor works under a constant
or variable torque and inlet flow. Models for two-position control, proportional control, and
torque-limited motors are developed.

Chapter 9: Modeling of Hydraulic Cylinders

This chapter presents the lumped modeling concept as applied for double-acting hydraulic
cylinders. This chapter considers situations where a cylinder works under a constant or
variable external load and inlet flow. Calculations for cylinder slowing due to leakage, cylinder
drift due to oil compressibility, and pressure increase due to thermal expansion are presented.

Chapter 10: Modeling of Hydraulic Valves

This chapter presents the lumped modeling concept as applied for hydraulic valves. This
chapter considers modeling at least one pressure control valve, one flow control valve, and one
 13 HSV7: Modeling and Simulation for Application Engineers
About the Book

directional control valves. Models for electro-hydraulic proportional and servo valves are also
developed.

Chapter 11: Modeling of Hydraulic Control Systems

This chapter utilizes the lumped component models previously built to build system models. In
this chapter, there is no additional math models to be developed. This chapter assembles
system models from component models. After validating system models, they can be used as
reference models for purposes of system design or investigating effects of operating conditions
on system performance. This chapter presents models for electrohydraulic cylinder position
control, electrohydraulic motor speed control, and hydraulic loading system.

Book Statistics:
The table shown below contains interesting statistical data about the textbook:

Chapter # Pages Figures Models Equations Tables Lines Words Characters

Chapter 1 38 19 0 12 5 390 8218 46847

Chapter2 29 27 9 16 0 192 4044 23057

Chapter 3 45 36 13 27 0 245 5172 29484

Chapter 4 13 7 0 2 0 131 2757 15720

Chapter 5 23 19 5 20 3 189 3990 22749
Chapter 6 20 20 4 15 0 119 2520 14369

Chapter 7 57 68 12 7 0 344 7244 41292

Chapter 8 36 41 7 6 0 234 4926 28080

Chapter 9 17 18 1 12 1 130 2752 15691

Chapter 10 24 28 6 7 0 157 3323 18946

Chapter 11 16 21 5 0 0 98 2074 11826

Other 39 0 0 0 0 0 0 0

Total 357 304 62 124 9 2229 47020 268061

 14 HSV7: Modeling and Simulation for Application Engineers
About the Author

ABOUT THE AUTHOR

Medhat Khalil, Ph.D. is Director of Professional Education & Research
Development at the Applied Technology Center, Milwaukee School of
Engineering, Milwaukee, WI, USA. Medhat has consistently been working on
his academic development through the years, starting from bachelor’s and
master’s Degrees in Mechanical Engineering in Cairo Egypt and proceeding
with his Ph.D. in Mechanical Engineering and Post-Doctoral Industrial
Research Fellowship at Concordia University in Montreal, Quebec, Canada. He
has been certified and is a member of many institutions such as: Certified
Fluid Power Hydraulic Specialist (CFPHS) by the International Fluid Power Society (IFPS); Certified
Fluid Power Accredited Instructor (CFPAI) by the International Fluid Power Society (IFPS); Member of
Center for Compact and Efficient Fluid Power Engineering Research Center (CCEFP); Listed Fluid
Power Consultant by the National Fluid Power Association (NFPA); and Listed Professional Instructor
by the American Society of Mechanical Engineers (ASME). Medhat has balanced academic and
industrial experience. Medhat has a vast working experience in the field of Mechanical Engineering and
more specifically hydraulics, having developed and taught fluid power system training courses for
industry professionals, being
quite aware of the technological
developments in the field of fluid
power and motion control and the
production program of the
leading fluid power companies. In
addition, Medhat had worked for
several world-wide recognized
industrial organizations such as
Rexroth in Egypt and CAE in
Canada. Medhat had designed
several hydraulic systems and
developed several analytical and
educational software. Medhat also has considerable experience in modeling and simulation of dynamic
systems using Matlab-Simulink.
 Index

A C
Algebraic Loops, 39 Capacitance, 41
Amplifier, 318 Capacitive, 41
Amplitude, 37 Characteristic Equation, 26
Amplitude Ratio, 37 Characteristics, 19
Angular Displacement, 43 Check Valve, 303
Angular Speed, 43 Closed-Center, 307
Closed-Loop, 318, 327
Coefficient of Fluid Friction, 165
Coefficient of Thermal Expansion, 292

B
Complex Plane, 23, 28
Conditions, 27
Constant, 68
Constant Block, 59
Bandwidth, 38
Constant-Power, 232
Binary, 21
continuous value, 21
Bode Plot, 37, 76, 120
Control, 319
Bond, 23
Control Unit, 233
Bulk Modulus, 142
Correction Factors, 145
Cracking, 208
Cracking Pressure, 295
Critical Pressure, 295

353
354

Index

Cubical Thermal Expansion Coefficient, Electrical Charge, 43

153 Electrical Current, 43
Cut-off, 208 Electrical Inductance, 41
Cycle Time, 94 Electrical Inductor, 41
Cylinder Drift, 291 Error Signal, 319
Cylinder Position Control, 318

D F
Feedback, 319
Damping Coefficient, 41 Feedback Signal, 319
Damping Ratio, 85, 87, 94 Final Value Theorem, 56, 85
Dead Zone, 307 Finite Elements, 22
Decibel, 37 First Order, 26
Delay Time, 94 First-Order, 54
Density, 149 Flow, 306
Differential Equations, 23-24, 39 Flow Control, 300
Differential Pressure, 43, 306 Flow Control Valves, 294
Digital, 21 Flow Gain, 306
Directional Control Valves, 294 Flow Variable, 43
Discharge Coefficient, 179 Flow-Pressure Sensitivity, 306
Discrete, 21 Fluid Bulk Modulus, 41
Dissipated Energy, 49 Fluid Flow, 43
Distributed, 22 Fluid Flow Resistivity, 41
Domain, 23-24, 28 Fluid Volume, 43
Dynamic, 20 Following Error, 36
Dynamic (Absolute) Viscosity, 157 Force, 43
Forcing Function, 26
Frequency Response, 37
Friction Coefficient, 48

E
Frictional Losses, 167
Function, 23

Effort, 43
Electric, 233
Electric Resistivity, 41
Electrical Capacitance, 41
Electrical Capacitor, 41
355

Index

G K
Gain Curve, 37 Kinematic (Relative) Viscosity, 157
GOTO Block, 59 Kinetic Energy, 47
Graph, 23

L
H
Laplace Transform, 23, 28
Hardware, 34 Linear, 19
Heat, 43 Linear Differential Equation,, 25
Heat Flow, 43 Linear Displacement, 43
Heat Shield, 41 Linear Speed, 43
Heat Sink, 41 Linear Spring, 41
Hertz, 37 Liner Damper, 41
Higher Order, 26 Load Force, 277
Homogeneous, 26 Load Torque, 241
Homogeneous DE, 27 Local Losses, 175
Loop, 34
Lumped, 22, 130

I
Imaginary, 23, 28 M
Impulse Response, 36
Inductive, 41 Mass Moment of Inertia, 41
Initial, 27 Matrix, 23
Internal or External, 245, 280 Mechanical Efficiency, 191, 251
Inverse Laplace Transform, 28 Modeling and Simulation, 17
Irreversible, 130 Modulus of Elasticity, 142, 146
Moody Diagram, 166
Motor Speed Control, 327
Multidimensional, 137
356

Index

Potential Energy, 51

N Pressure, 208
Pressure Control Valves, 294
Pressure Relief Valve, 295
Natural Frequency, 87, 94 Pressure-Compensated Pumps, 208
Negative-Feedback, 318, 327 Proportional, 309
Nominal, 306
Nominal (Rated) input signal, 306
Nonlinear, 19
Nonlinear Differential Equation,, 25
Normalized Transfer Function, 57, 72,
86
R
Radians, 37
Ramp, 36
Ramp Input, 66, 93
O Rated, 306
Ratio, 37
Real, 17, 23, 28
Off Pressure, 295 Reference, 319
Ordinary Differential Equation, 24 Resistive, 41
Overall Efficiency, 191, 251 Resistivity Factor, 48
Overflow, 39 Response, 36
Overlapped, 307 Resultant, 43
Override Zone, 208, 295 Resultant Torque, 43
Overshoot, 94 Reversible, 130
Reynolds's Number, 165
Rise Time, 94
Roots, 27

P Rotational Damper, 41
Rotational Mass, 41

Partial Differential Equation, 24

Passive or Active, 245, 280

S
Peak Time, 94
Percentage Overshoot, 94
Phase Angle, 38
Phase Curve, 38 Sampling Rate, 40
Phase Lag, 37-38 Sampling Time, 60, 64, 91
Positive (Resistive) or Negative Second Order, 26
(Assistive), 245, 280 Second-Order, 83
357

Index

Servo, 309 Transient Response, 36

Settling, 68 Translational Mass, 41
Settling Time, 68, 72, 94
Shear Rate, 157
Shear Stress, 157

U
Signal, 319
Sinusoidal Input, 67, 93
Space, 23
Specific Gravity, 150
Undamped Natural Frequency, 85
Specific Weight, 149
Spring Constant, 50, 142
Spring Stiffness, 41
State, 23
State Error, 36
Static, 19-20
V
Steady, 36
Steady Sate (Forced) Response, 27 validation, 18
Steady State Value, 94 Variable, 43
Step Input, 65, 92 Viscosity, 157
Step Response, 36 Voltage Difference, 43
Subsystem, 60, 87 Volumetric Efficiency, 191, 250
System Linearization, 25
System Stability, 36

Z
T Zero-Lapped, 307

Temperature Difference, 43
Thermal Capacitance, 41
Thermal Resistivity, 41
Thermal Resistor, 41
Time, 17, 24, 68
Time Constant, 56
Torsion Spring, 41
Transfer, 23
Transfer Function, 28, 31
Transfer Functions, 39
Transient (Free) Response, 27