HYDRAULIC POWER SYSTEM ANALYSIS © 2006 by Taylor & Francis Group, LLC HYDRAULIC POWER SYSTEM ANALYSIS Arthur Akers Iowa State University Ames, Iowa, U.S.A Max Gassman Iowa State University Ames, Iowa, U.S.A Richard Smith Iowa State University Ames, Iowa, U.S.A Boca Raton London New York A CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa plc © 2006 by Taylor & Francis Group, LLC Published in 2006 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2006 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S Government works Printed in the United States of America on acid-free paper 10 International Standard Book Number-10: 0-8247-9956-9 (Hardcover) International Standard Book Number-13: 978-0-8247-9956-4 (Hardcover) This book contains information obtained from authentic and highly regarded sources Reprinted material is quoted with permission, and sources are indicated A wide variety of references are listed Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data Catalog record is available from the Library of Congress Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com Taylor & Francis Group is the Academic Division of Informa plc © 2006 by Taylor & Francis Group, LLC and the CRC Press Web site at http://www.crcpress.com Preface The text introduces and reinforces key principles, concepts, and methods of analysis of the performance of fluid power components and systems The physical configuration of individual components is presented and this information is supplemented with material relating to dynamic analysis The principles of analysis have been demonstrated with a comprehensive range of worked examples and with suitable exercises for the student to follow in order to acquire considerable command of fluid power system design details Some of the ways are shown where fluid power can be used to advantage in engineering systems Fluid power may often provide a way to transmit power that, for certain levels of power and other circumstances, may be superior to other mechanical or electrical techniques The text has been written primarily for mechanical, aerospace or agricultural engineering seniors or for graduate students undertaking research to extend the limits of fluid power technology The text should also be helpful for engineers working on design or research projects in manufacturing facilities who require knowledge of computer simulation of the dynamic performance of fluid power components and systems We now take the opportunity to express our appreciation for the efforts of all who brought this text to fruition We acknowledge gratefully the advice provided by the prepublication reviewers: Richard Burton, University of Saskatchewan, and several others Our consultations with Brian Steward of the Agricultural and Biosystems Engineering Department of ISU have provided us with excellent and original ideas to help us with our text We wish to thank the publisher for their trust in us This text was started under the guidance of Steve Sidore and John Corrigan of Marcel Dekker The content of the text owes much to these two individuals whose knowledge of the fluid power field was extensive After Marcel Dekker was assimilated by Taylor & Francis, our editors there were Jessica Vakili and Jay Margolis We would like to thank Jessica for her help and patience as deadlines were agreed upon and missed We should also like to thank Jay © 2006 by Taylor & Francis Group, LLC PREFACE for his painstaking attention to detail and his ability to find errors that we had overlooked even after countless readings of the text Producing a book is not a trivial task, but is somewhat simplified by the availability of computers and the programs that run on them This text was produced using LATEX Any author using LATEX owes a huge debt of gratitude to the many members of the TEX Users Group who maintain and enhance LATEX Production of this text was very much facilitated by several packages developed by the many people associated with TUG Lastly we owe a debt of gratitude to our wives, namely Marcia L Akers, and Gail E Gassman Without their care, their help, encouragement and patience, this work could never have been completed A Akers M P Gassman R J Smith Ames, Iowa © 2006 by Taylor & Francis Group, LLC Chapter Synopsis Chapter gives a description of how fluid power is used, a brief history of fluid power activities to the present, some projections for future applications, and some advantages of using fluid power for mechanical power transmission Chapter outlines details of the U.S Customary and (the more modern) S.I Systems of units Conversion between these two systems is discussed, and the worked examples switch randomly between the two systems throughout the text The physical properties of fluids described are oil density, viscosity, bulk modulus, specific heat and thermal conductivity Values of these properties are usually required to design the components of fluid power systems Chapter outlines procedures for steady state modeling In this text, steady state is defined somewhat freely as a condition where a system may change state with time The changes with respect to time, however, are sufficiently slow that algebraic equations rather than time dependent differential equations may be used for the problem solution Sources of the mathematical equations used are given where the principles described are conservation of flow and of energy The main part of the chapter deals with conversion of pressure energy into heat energy in various forms of fluid flow in pump and motor systems A model of a flow regulator valve is presented showing how preliminary estimates of valve opening and flow can be made using steady state analysis The chapter also includes an example of using an accumulator in a system to reduce pump size and energy use Chapter gives the development of analytical methods for determining the dynamic behavior of fluid power systems In order to this, Newton’s Second Law of motion is invoked together with the phenomenon of pressure change as a function of volume change affected by fluid bulk modulus © 2006 by Taylor & Francis Group, LLC CHAPTER SYNOPSIS Thus it is shown that the dynamic performance of fluid power components and systems can be described by sets of ordinary differential equations with displacements, velocities, and pressures as the state variables A servovalve controlled actuator and the same system with positional feedback are presented as worked examples As noted in the text, there are numerous pieces of software and programs in the technical literature that may be used to solve these sets of equations numerically Chapter gives a brief review of the Laplace transform method of solving linear ordinary differential equations The material is presented as a precursor to discussion of stability, the spring-mass-damper, and the concept of a time constant The Laplace transform approach also gives an opportunity to introduce the block diagram, which is often a very helpful intermediate step between a physical system and its representation as a set of differential equations The chapter also discusses the consolidation of block diagrams and the concept of a transfer function Chapter shows how the consolidated transfer function developed in Chapter may be used to predict the steady state response of a linear system to a constant sinusoidal input excitation The chapter then discusses ways of using frequency response for establishing an appropriate level of controller gain in a feedback system Although there are a number of procedures to select feedback gain to produce a stable system, the procedure using frequency response is felt to be particularly applicable to fluid power systems The hydromechanical servo examined in Chapter is revisited and controller gain is determined using the frequency response method The text also indicates how frequency response diagrams can be generated from a mathematical model of the system and indicates that the diagrams may also be generated experimentally Chapter deals with valves, the purpose of which is to modulate flow rate, direction of flow, flow sequence, and to control pressure The text is provided with many figures showing how these tasks are accomplished The spool valve is commonly used for proportional control Modulation of large spool valves by solenoids and torque motors may be difficult because of the flow forces developed by fluid momentum changes in the valve Expressions for the magnitude of these flow forces are developed Linearization of the characteristics of spool valves is developed because these expressions are required when mathematical models of valves are used in the analysis of automatic control systems © 2006 by Taylor & Francis Group, LLC CHAPTER SYNOPSIS Chapter outlines the design details of pumps and motors There are hydrodynamic pumps which generate rotation of the fluid This rotational kinetic energy is transformed into pressure Such pumps are seldom used in fluid power applications for which constant outlet pressure is required The pumps usually employed are known as positive displacement or hydrostatic pumps There are seven types described in the text and it is demonstrated which type is optimum for certain applications Motoring action may be achieved by pumping oil through a hydrostatic unit In some instances the geometry of a pumps differs little from that of a motor Such a situation may not always be valid It is possible to obtain values of efficiencies from manufacturers’ catalogs for different speeds and pressures so that a correct choice can be made for each application Chapter deals with axial piston pumps, which are the type most frequently used where precision and high volumetric efficiency are required The type of axial pump described is the swash plate design and pressure transition during pump rotation is analyzed It is demonstrated how the pressure variation is affected by the geometry of the fluid outlet and it is shown how a suitable compromise between controlling pressure rise and maintaining volumetric efficiency may be achieved The chapter ends with a discussion of the variation of torque and flow rate associated with multiple piston pumps Chapter 10 discusses the operation of hydrostatic transmissions A conceptual design for a mechanical hoist is presented that has a gearbox and a progressive action clutch that enables the speed to be varied economically and smoothly It is suggested that such design would not be suitable for a hoist because of the intermittent nature of the power transmission The example was used to show the need for a stepless transmission Other stepless transmissions using sheaves or electric motors are briefly described in the text The usual components of a hydrostatic transmission are a variable displacement pump and a fixed displacement motor A typical plot of motor torque and motor speed shows that the transmission can be limited for torque at low output speeds and by power at high output speeds A typical performance envelope is presented The design of a hydrostatic transmission to drive a research soil bin is described The analysis is presented and a block diagram of the governing equations is given The pressure and velocity of the bin have been presented The velocity profile was shown to be greatly affected by the value of bulk modulus chosen © 2006 by Taylor & Francis Group, LLC CHAPTER SYNOPSIS Chapter 11 describes a pressure regulating valve, an essential device in a hydraulic system because the supply pump is a positive displacement device (see Chapter 8) Without such a valve, the pressure would increase until damage and failure of machine parts would occur Dynamic operation of the valve is described and the governing equations of motion are developed Providing a solution to the challenging problem of valve spool damping is also discussed Chapter 12 extends the model given in the previous chapter An actuator and load are added and the equations of motion of the dynamic behavior of the complete system are developed Computer simulation is a tool that allows the geometry of the various parts to be modified to satisfy the particular needs of the system Chapter 13 presents√flow division using a modification of Ohm’s law for electrical resistance, ∆p = RQ Expressions for consolidating series and parallel sets of resistances are presented for this law Worked examples are presented of increasing complexity, culminating in the dynamic analysis of a flow regulator valve √ The limiting case of steady flow was presented by Esposito [1] The ∆p = RQ law approach was considerably expanded by Gassman [4-6] to solve problems with time variable flow conditions and orifice areas The general problem of the dynamic analysis of a flow regulator valve entails bifurcated flow with multiple varying resistances The solution is achieved by an iterative procedure that automatically updates the varying resistances, while concurrently solving the dynamic equations in displacement, velocity, and pressure using a conventional differential equation solver The authors believe that this is the first appearance of the solution in the technical literature Chapter 14 shows that positive displacement pump design employs pistons, vanes or gear teeth that cause the oil flow to pulsate The resulting pressure waves in the fluid stream cause vibration noise at frequencies related to the rate of pumping or pump rotation It is shown that the analogy between electrical and fluid circuit resistance introduced in Chapter 13 may be extended for the properties of capacitance and inductance Fluid circuit expressions for inductance are developed for plug flow and laminar flow in a circular pipe An example is given of applying the electrical/fluid analogy to noise reduction for a tractor hydraulic pump Reference numbers in this discussion of Chapter 13 refer to the references at the end of that chapter © 2006 by Taylor & Francis Group, LLC Programs INTRODUCTION A CD of programs accompanies this text It is the authors’ belief that a new comer to fluid power analysis should start by writing equations, solve those equations with a general purpose programming language, and display the results in the form of tables and graphs Only when the reader has become experienced with the formulation of equations and discovered that the analysis of systems requires assumptions and simplifications, should he/she graduate to more complex application packages that often conceal these factors R is a very good general purpose calcuThe spreadsheet program Excel lating program that allows easy plotting of results Many users are familiar with the cability of placing formulae in cells Although this is useful capability, its utility becomes limited as the complexity of the task increases R can record macros from a series of key Many users know that Excel R into a strokes or mouse clicks These actions are translated by Excel R (hereafter VB) subroutine that can be called Visual Basic for Applications by the user It will be seen that VB may be used to write quite complex programs R programs that are being provided here The major reason for the Excel is that many people who have a computer also have this program installed Initially, the reader can try out analysis of fluid power systems without R or needing to invest in other mathematical programs such as Mathcad R R MATLAB It is not suggested that Excel replaces such mathematical programs for serious design work, but a student can use the program to gain familiarity with analytical concepts covered in the text before moving on to the more powerful tools This text cannot pretend to be a manual exploring all the capabilities of VB It is hoped, however, that the material presented in the readme.pdf file in the root directory of the disk will allow the reader to start writing VB programs © 2006 by Taylor & Francis Group, LLC ... command of fluid power system design details Some of the ways are shown where fluid power can be used to advantage in engineering systems Fluid power may often provide a way to transmit power that,... 1.1 WHAT IS FLUID POWER? 1.2 A BRIEF HISTORY OF FLUID POWER 1.3 FLUID POWER APPLICATIONS, PRESENT AND FUTURE 1.4 ADVANTAGES OF USING FLUID POWER SYSTEMS ... how fluid power is used, a brief history of fluid power activities to the present, some projections for future applications, and some advantages of using fluid power for mechanical power transmission