Hydraulic Power System Analysis

381 Pages·2006·7.02 MB·English

by  Arthur Akers

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 9 8 7 6 5 4 3 2 1
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 and the CRC Press Web site at
is the Academic Division of Informa plc. http://www.crcpress.com
© 2006 by Taylor & Francis Group, LLC
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.
Someofthewaysareshownwherefluidpowercanbeusedtoadvantage
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 agri-
cultural 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 manufactur-
ingfacilitieswhorequireknowledgeofcomputersimulationofthedynamic
performance of fluid power components and systems.
Wenowtaketheopportunitytoexpressourappreciationfortheefforts
of all who brought this text to fruition. We acknowledge gratefully the ad-
vice provided by the prepublication reviewers: Richard Burton, University
ofSaskatchewan,andseveralothers. OurconsultationswithBrianSteward
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.
Lastlyweoweadebtofgratitudetoourwives,namelyMarciaL.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 1 gives a description of how fluid power is used, a brief history
of fluid power activities to the present, some projections for future appli-
cations, and some advantages of using fluid power for mechanical power
transmission.
Chapter 2 outlines details of the U.S. Customary and (the more mod-
ern) S.I. Systems of units. Conversion between these two systems is dis-
cussed,andtheworkedexamplesswitchrandomlybetweenthetwosystems
throughoutthetext. Thephysicalpropertiesoffluidsdescribedareoilden-
sity,viscosity,bulkmodulus,specificheatandthermalconductivity. Values
of these properties are usually required to design the components of fluid
power systems.
Chapter 3 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 dif-
ferential equations may be used for the problem solution.
Sources of the mathematical equations used are given where the princi-
plesdescribedare conservationofflowandofenergy. Themainpartofthe
chapterdealswithconversionofpressureenergyintoheatenergyinvarious
formsoffluidflowinpumpandmotorsystems. Amodelofaflowregulator
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 4 gives the development of analytical methods for determining
thedynamicbehavioroffluidpowersystems. Inordertodothis,Newton’s
Second Law of motion is invoked together with the phenomenon of pres-
sure 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
andsystemscanbedescribedbysetsofordinarydifferentialequationswith
displacements,velocities,andpressuresasthestatevariables. Aservovalve
controlled actuator and the same system with positional feedback are pre-
sentedasworkedexamples. Asnotedinthetext,therearenumerouspieces
of software and programs in the technical literature that may be used to
solve these sets of equations numerically.
Chapter 5 gives a brief review of the Laplace transform method of solving
linearordinarydifferentialequations. Thematerialispresentedasaprecur-
sor 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
stepbetweenaphysicalsystemanditsrepresentationasasetofdifferential
equations. The chapter also discusses the consolidation of block diagrams
and the concept of a transfer function.
Chapter 6 shows how the consolidated transfer function developed in
Chapter 5 may be used to predict the steady state response of a linear sys-
tem 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 pro-
cedures to select feedback gain to produce a stable system, the procedure
using frequency response is felt to be particularly applicable to fluid power
systems.
ThehydromechanicalservoexaminedinChapter 4isrevisitedandcon-
troller 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 7 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.
Thespoolvalveiscommonlyusedforproportionalcontrol. Modulation
of large spool valves by solenoids and torque motors may be difficult be-
causeoftheflowforcesdevelopedbyfluidmomentumchangesinthevalve.
Expressions for the magnitude of these flow forces are developed. Lin-
earization 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 8 outlines the design details of pumps and motors. There are
hydrodynamic pumps which generate rotation of the fluid. This rotational
kineticenergyistransformedintopressure. Suchpumpsareseldomusedin
fluidpowerapplicationsforwhichconstantoutletpressureisrequired. The
pumpsusuallyemployedareknownaspositivedisplacementorhydrostatic
pumps.
Thereareseventypesdescribedinthetextanditisdemonstratedwhich
typeisoptimumforcertainapplications. Motoringactionmaybeachieved
bypumpingoilthroughahydrostaticunit. Insomeinstancesthegeometry
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’ cata-
logsfordifferentspeedsandpressuressothatacorrectchoicecanbemade
for each application.
Chapter 9 deals with axial piston pumps, which are the type most fre-
quently 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 multi-
ple piston pumps.
Chapter 10 discusses the operation of hydrostatic transmissions. A con-
ceptualdesignforamechanicalhoistispresentedthathasagearboxanda
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
hoistbecauseoftheintermittentnatureofthepowertransmission. Theex-
amplewasusedtoshowtheneedforasteplesstransmission. Otherstepless
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 trans-
mission can be limited for torque at low output speeds and by power at
high output speeds. A typical performance envelope is presented. The de-
sign 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 mod-
ulus chosen.
© 2006 by Taylor & Francis Group, LLC
CHAPTER SYNOPSIS
Chapter 11 describes a pressure regulating valve, an essential device in a
hydraulicsystembecausethesupplypumpisapositivedisplacementdevice
(see Chapter 8). Without such a valve, the pressure would increase until
damage and failure of machine parts would occur. Dynamic operation of
thevalveisdescribedandthegoverningequationsofmotionaredeveloped.
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 par-
ticular 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]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
generalproblemofthedynamicanalysisofaflowregulatorvalveentailsbi-
furcatedflowwithmultiplevaryingresistances. Thesolutionisachievedby
an iterative procedure that automatically updates the varying resistances,
whileconcurrentlysolvingthedynamicequationsindisplacement,velocity,
and pressure using a conventional differential equation solver. The authors
believe that this is the first appearance of the solution in the technical lit-
erature.
Chapter14showsthatpositivedisplacementpumpdesignemployspistons,
vanes or gear teeth that cause the oil flow to pulsate. The resulting pres-
sure 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 be-
tween electrical and fluid circuit resistance introduced in Chapter 13 may
beextendedforthepropertiesofcapacitanceandinductance. Fluidcircuit
expressions for inductance are developed for plug flow and laminar flow in
acircularpipe. Anexampleisgivenofapplyingtheelectrical/fluidanalogy
to noise reduction for a tractor hydraulic pump.
1ReferencenumbersinthisdiscussionofChapter13refertothereferencesattheend
ofthatchapter.
© 2006 by Taylor & Francis Group, LLC
Programs
INTRODUCTION
ACDofprogramsaccompaniesthistext. Itistheauthors’beliefthata
new comer to fluid power analysis should start by writing equations, solve
thoseequationswithageneralpurposeprogramminglanguage,anddisplay
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.
The spreadsheet program Excel(cid:13)R is avery goodgeneral purpose calcu-
latingprogramthatallowseasyplottingofresults. Manyusersarefamiliar
with the cability of placing formulae in cells. Although this is useful capa-
bility, its utility becomes limited as the complexity of the task increases.
Many users know that Excel(cid:13)R can record macros from a series of key
strokes or mouse clicks. These actions are translated by Excel(cid:13)R into a
VisualBasicforApplications(cid:13)R (hereafterVB)subroutinethatcanbecalled
by the user. It will be seen that VB may be used to write quite complex
programs.
ThemajorreasonfortheExcel(cid:13)R programsthatarebeingprovidedhere
isthatmanypeoplewhohaveacomputeralsohavethisprograminstalled.
Initially, the reader can try out analysis of fluid power systems without
needing to invest in other mathematical programs such as Mathcad(cid:13)R or
MATLAB(cid:13)R. It is not suggested that Excel(cid:13)R 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