Description

Book Synopsis

This book covers some of the fundamental topics in fluid power technology, presenting detailed derivations of formulas that form the basis of the theory. It shows the reader how to properly (i) design basic fluid power systems, (ii) construct lumped parameter models of simple fluid power systems, (iii) perform frequency analysis of fluid power components and systems, and (iv) develop controllers for fluid power systems. The book mainly focusses on mathematical modelling and analysis of fluid power components and systems i.e. practical issues such as working principles and construction of components are not covered in depth. The text is organized in four main parts: I Physics of Fluid, II Fluid Power Components, III Fluid Power Systems and IV Learning by Doing.




Table of Contents
1 Introduction 11.1 Hydro-statics and hydro-dynamics . . . . . . . . . . . . . . . . 11.1.1 Pascals law . . . . . . . . . . . . . . . . . . . . . . . . . 1I Physics of Fluid 32 Fluid parameters 52.1 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Force due to shear velocity field . . . . . . . . . . . . . . 62.1.2 ViscosityModels . . . . . . . . . . . . . . . . . . . . . . 82.2 Fluid Compressibility and Density . . . . . . . . . . . . . . . . 112.2.1 Equation of State for a Fluid . . . . . . . . . . . . . . . 112.2.2 Pressure dependent density and stiffness of Fluid-air mixture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Fluids Mechanics 193.1 Conservation ofMass . . . . . . . . . . . . . . . . . . . . . . . . 193.1.1 Control Volume Approach . . . . . . . . . . . . . . . . . 193.1.2 Continuity Equation - Differential form . . . . . . . . . 223.2 Momentum of Fluids - Newton II. Law . . . . . . . . . . . . . . 253.2.1 Differential Form- Cartesian Coordinates . . . . . . . . 253.2.2 MomentumEquation of a Fluid . . . . . . . . . . . . . . 293.2.3 Conservation of Momentum - Control Volume Form . . 303.3 Inviscid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4 Viscous Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.1 Incompressible fluid . . . . . . . . . . . . . . . . . . . . 334 Flow Through Restriction 374.1 Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Flow in a tube . . . . . . . . . . . . . . . . . . . . . . . . . . . 37vvi CONTENTS4.2.1 FromNaiver-Stokes equation . . . . . . . . . . . . . . . 384.2.2 Fromforce balance . . . . . . . . . . . . . . . . . . . . . 404.2.3 Turbulent Flow in Pipes . . . . . . . . . . . . . . . . . . 424.2.4 Summary on Flow in Tubes . . . . . . . . . . . . . . . . 434.3 Flow in Gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.1 FromForce Balance . . . . . . . . . . . . . . . . . . . . 444.3.2 Velocity Profile fromNaiver-Stokes Equation . . . . . . 464.3.3 Summary on flow between parallel plates . . . . . . . . 484.4 The Orifice Equation . . . . . . . . . . . . . . . . . . . . . . . . 504.4.1 Laminar versus turbulent orifice flow . . . . . . . . . . . 52II Fluid Power Components 555 Fluid Power Pumps 575.1 Displacement Pumps . . . . . . . . . . . . . . . . . . . . . . . . 575.1.1 Data Sheet Units . . . . . . . . . . . . . . . . . . . . . . 575.1.2 Single Piston Pump . . . . . . . . . . . . . . . . . . . . 585.2 The General PumpModel - steady state . . . . . . . . . . . . . 585.2.1 Ideal PumpModel . . . . . . . . . . . . . . . . . . . . . 595.2.2 Non-ideal PumpModel . . . . . . . . . . . . . . . . . . 605.2.3 Summary on General PumpModel . . . . . . . . . . . . 625.3 Pump Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.3.1 Gear pumps . . . . . . . . . . . . . . . . . . . . . . . . . 645.3.2 Vane Pumps . . . . . . . . . . . . . . . . . . . . . . . . 655.3.3 Piston Pumps . . . . . . . . . . . . . . . . . . . . . . . . 675.3.4 Discrete Displacement pumps . . . . . . . . . . . . . . . 686 Rotary Actuator* 716.1 MotorModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.1.1 IdealMotorModel . . . . . . . . . . . . . . . . . . . . . 716.1.2 Non-idealMotorModel . . . . . . . . . . . . . . . . . . 727 Linear Actuators- Fluid Power Cylinders 757.1 Differential Cylinder . . . . . . . . . . . . . . . . . . . . . . . . 767.1.1 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 767.1.2 Steady StateModel . . . . . . . . . . . . . . . . . . . . 797.1.3 Summery . . . . . . . . . . . . . . . . . . . . . . . . . . 817.2 Multi-Chamber Cylinder . . . . . . . . . . . . . . . . . . . . . . 82CONTENTS vii8 Control Elements - Valves 838.1 General ValveModels . . . . . . . . . . . . . . . . . . . . . . . 838.2 Directional Valves . . . . . . . . . . . . . . . . . . . . . . . . . 848.2.1 Check Valve . . . . . . . . . . . . . . . . . . . . . . . . . 848.2.2 On-Off Valves . . . . . . . . . . . . . . . . . . . . . . . . 858.2.3 Directional Spool Valve . . . . . . . . . . . . . . . . . . 858.2.4 Flow Force on Spool Valve . . . . . . . . . . . . . . . . 898.2.5 Servo valves . . . . . . . . . . . . . . . . . . . . . . . . . 918.2.6 Direct Drive Servo Valves -Moog D633 . . . . . . . . . 928.3 Pressure control Valves . . . . . . . . . . . . . . . . . . . . . . . 958.3.1 Pressure relief . . . . . . . . . . . . . . . . . . . . . . . . 958.3.2 Pressure Reduction . . . . . . . . . . . . . . . . . . . . . 988.3.3 Pressure Control . . . . . . . . . . . . . . . . . . . . . . 1008.4 Flow Control Valves . . . . . . . . . . . . . . . . . . . . . . . . 1028.4.1 Throttle Valve . . . . . . . . . . . . . . . . . . . . . . . 1028.4.2 Pressure Compensated Flow Control Valve . . . . . . . 1058.4.3 Pressure Compensated Flow Control Valve - By Pass . . 1088.5 Pressure Compensated Proportional Valves . . . . . . . . . . . 1129 Accumulators 1159.1 Piston Accumulator . . . . . . . . . . . . . . . . . . . . . . . . 1159.1.1 Mass Loaded Piston Accumulators . . . . . . . . . . . . 1169.1.2 Spring Loaded Piston Accumulators . . . . . . . . . . . 1179.1.3 Gas loaded piston Accumulators . . . . . . . . . . . . . 1179.2 Bladder Accumulator . . . . . . . . . . . . . . . . . . . . . . . . 1189.3 DiaphragmAccumulator . . . . . . . . . . . . . . . . . . . . . . 11910 Pipes and Hoses 12110.1 Fluid Power Pipes . . . . . . . . . . . . . . . . . . . . . . . . . 12210.2 Fluid Power Hoses . . . . . . . . . . . . . . . . . . . . . . . . . 12210.2.1 Construction . . . . . . . . . . . . . . . . . . . . . . . . 12310.3 Steady State Transmission LineModel . . . . . . . . . . . . . . 12310.4 Dynamic Transmission LineModel . . . . . . . . . . . . . . . . 12310.4.1 Lumped ParameterModel . . . . . . . . . . . . . . . . . 123III Fluid Power Systems 12711 System Design 12911.1 Synthesis of Fluid Power Systems . . . . . . . . . . . . . . . . . 12911.1.1 System Operation . . . . . . . . . . . . . . . . . . . . . 13011.1.2 Operation of Sub Function . . . . . . . . . . . . . . . . 13011.1.3 System Architecture - Diagram . . . . . . . . . . . . . . 131viii CONTENTS11.1.4 System Pressure Level . . . . . . . . . . . . . . . . . . . 13111.1.5 Actuator sizing . . . . . . . . . . . . . . . . . . . . . . . 13211.1.6 Pump and PrimaryMover Sizing . . . . . . . . . . . . . 13211.1.7 Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13311.1.8 Fluid Lines . . . . . . . . . . . . . . . . . . . . . . . . . 13411.1.9 Control Elements . . . . . . . . . . . . . . . . . . . . . . 13611.1.10Steady state analysis - overall efficiency . . . . . . . . . 13611.1.11Tank and cooling . . . . . . . . . . . . . . . . . . . . . . 13611.1.12 Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . 13711.2 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . 14011.2.1 Simple differential cylinder system . . . . . . . . . . . . 14011.2.2 Differential Cylinder System. . . . . . . . . . . . . . . . 14512 Modelling and Analysis 14912.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15012.1.1 LinearModel . . . . . . . . . . . . . . . . . . . . . . . . 15012.1.2 Frequency analysis . . . . . . . . . . . . . . . . . . . . . 15212.2 Symmetric Cylinder Valve Drive . . . . . . . . . . . . . . . . . 15412.2.1 Time DomainModel . . . . . . . . . . . . . . . . . . . . 15412.2.2 Reduced OrderModel . . . . . . . . . . . . . . . . . . . 15612.2.3 Linear Reduced OrderModel . . . . . . . . . . . . . . . 16012.2.4 Linear model . . . . . . . . . . . . . . . . . . . . . . . . 16212.2.5 Transfer Function for the Reduced Order Model . . . . 16512.2.6 Results of Full System . . . . . . . . . . . . . . . . . . . 17212.3 Fixed Displacement Motor Valve drive . . . . . . . . . . . . . . 17312.3.1 Time DomainModel . . . . . . . . . . . . . . . . . . . . 17412.3.2 Reduced OrderModel . . . . . . . . . . . . . . . . . . . 17512.3.3 Reduced Order Linear and Laplace Domain Model . . . 17612.3.4 Linear model . . . . . . . . . . . . . . . . . . . . . . . . 176IV Controlof Fluid Power Systems 17913 Controller Design and System Manipulations 18113.1 Pressure feedback . . . . . . . . . . . . . . . . . . . . . . . . . . 18213.2 Flow Feed Forward . . . . . . . . . . . . . . . . . . . . . . . . . 18313.2.1 Passive . . . . . . . . . . . . . . . . . . . . . . . . . . . 18413.2.2 Active . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18513.3 Valve Compensator . . . . . . . . . . . . . . . . . . . . . . . . . 18613.4 Valve Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 18713.5 Multi-Input Systems . . . . . . . . . . . . . . . . . . . . . . . . 18713.5.1 SMISMO - System . . . . . . . . . . . . . . . . . . . . . 188CONTENTS ix14 Reference generation 19114.1 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19114.1.1 Maximumpower transfer . . . . . . . . . . . . . . . . . 19114.1.2 Power request . . . . . . . . . . . . . . . . . . . . . . . . 19214.2 Input versus state requirement . . . . . . . . . . . . . . . . . . 19214.3 Polynomial position reference . . . . . . . . . . . . . . . . . . . 193V Exercises and Solutions 19515 Problem Solving 19715.1 FluidMechanics I . . . . . . . . . . . . . . . . . . . . . . . . . . 19815.1.1 Fluid Compressibility . . . . . . . . . . . . . . . . . . . 19815.1.2 Fluid Spring . . . . . . . . . . . . . . . . . . . . . . . . 19815.1.3 Viscous force on rotating body . . . . . . . . . . . . . . 19915.1.4 FluidMomentum . . . . . . . . . . . . . . . . . . . . . . 19915.2 FluidMechanics II . . . . . . . . . . . . . . . . . . . . . . . . . 20115.2.1 Orifice flow I . . . . . . . . . . . . . . . . . . . . . . . . 20115.2.2 Orifice flow II . . . . . . . . . . . . . . . . . . . . . . . . 20115.2.3 Pipe flow I . . . . . . . . . . . . . . . . . . . . . . . . . 20215.2.4 Pipe flow II . . . . . . . . . . . . . . . . . . . . . . . . . 20215.2.5 Pipe flow III . . . . . . . . . . . . . . . . . . . . . . . . 20315.2.6 Velocity profile in an annular flow . . . . . . . . . . . . 20315.3 Pumps,Motors and Cylinders . . . . . . . . . . . . . . . . . . . 20415.3.1 Pump I . . . . . . . . . . . . . . . . . . . . . . . . . . . 20415.3.2 Pump II . . . . . . . . . . . . . . . . . . . . . . . . . . . 20415.3.3 Motor I . . . . . . . . . . . . . . . . . . . . . . . . . . . 20415.3.4 Cylinder I . . . . . . . . . . . . . . . . . . . . . . . . . . 20415.3.5 Cylinder II . . . . . . . . . . . . . . . . . . . . . . . . . 20515.3.6 Cylinder III . . . . . . . . . . . . . . . . . . . . . . . . . 20615.3.7 Volumetric Pump Efficiency - VLE* . . . . . . . . . . . 20715.3.8 Pump Efficiency map - VLE* . . . . . . . . . . . . . . . 20715.3.9 Constant Pressure Pump - VLE* . . . . . . . . . . . . . 20715.3.10Hydrostatic Transmission - VLE* . . . . . . . . . . . . . 20715.3.11Valve cylinder drive - VLE* . . . . . . . . . . . . . . . . 20815.4 Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20915.4.1 Pressure relief valve I . . . . . . . . . . . . . . . . . . . 20915.4.2 Valve flow . . . . . . . . . . . . . . . . . . . . . . . . . . 20915.5 Steady State SystemAnalysis . . . . . . . . . . . . . . . . . . . 21015.5.1 System 1, raising the piston . . . . . . . . . . . . . . . . 21015.5.2 System 1, lowering the piston . . . . . . . . . . . . . . . 21115.5.3 System 2 - with flow control valve . . . . . . . . . . . . 21215.5.4 System 3 -Motor lifting the load . . . . . . . . . . . . . 213x CONTENTS15.5.5 System 3 -Motor lowering the load . . . . . . . . . . . . 21315.5.6 System 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 21515.6 System Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 21615.6.1 Workshop system flow control valves - Steady state . . . 21615.6.2 Dynamic model of Workshop system - Servo valves . . . 21715.7 System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 21815.7.1 Pilot Chamber I . . . . . . . . . . . . . . . . . . . . . . 21815.7.2 Pilot Chamber II . . . . . . . . . . . . . . . . . . . . . . 21815.7.3 Pressure relief valve . . . . . . . . . . . . . . . . . . . . 21915.7.4 System analysis - Differential cylinder and servo valve . 21915.8 System Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 22015.8.1 Position and velocity control of differential cylinder . . . 22015.8.2 System manipulation by pressure feedback . . . . . . . . 22015.9 System Power Limits and Input Reference . . . . . . . . . . . . 22115.9.1 Maximum load pressure, flow diagram . . . . . . . . . . 22115.9.2 Position input trajectory . . . . . . . . . . . . . . . . . . 22115.9.3 Simulation of position trajectory . . . . . . . . . . . . . 22115.10System design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22216 Solution 23516.1 FluidMechanics I . . . . . . . . . . . . . . . . . . . . . . . . . . 23616.1.1 Fluid Compressibility . . . . . . . . . . . . . . . . . . . 23616.1.2 Fluid Spring . . . . . . . . . . . . . . . . . . . . . . . . 23616.1.3 Viscous force on rotating body . . . . . . . . . . . . . . 23816.1.4 FluidMomentum . . . . . . . . . . . . . . . . . . . . . . 23816.2 FluidMechanics II . . . . . . . . . . . . . . . . . . . . . . . . . 24016.2.1 Orifice Flow I . . . . . . . . . . . . . . . . . . . . . . . . 24016.2.2 Orifice Flow II . . . . . . . . . . . . . . . . . . . . . . . 24016.2.3 Pipe Flow I . . . . . . . . . . . . . . . . . . . . . . . . . 24216.2.4 Pipe Flow II . . . . . . . . . . . . . . . . . . . . . . . . 24216.2.5 Pipe Flow III . . . . . . . . . . . . . . . . . . . . . . . . 24216.2.6 Velocity profile in an annular flow . . . . . . . . . . . . 24316.3 Pumps,Motors and Cylinders . . . . . . . . . . . . . . . . . . . 24516.3.1 Pump I . . . . . . . . . . . . . . . . . . . . . . . . . . . 24516.3.2 Pump II . . . . . . . . . . . . . . . . . . . . . . . . . . . 24516.3.3 Motor I . . . . . . . . . . . . . . . . . . . . . . . . . . . 24616.3.4 Cylinder I . . . . . . . . . . . . . . . . . . . . . . . . . . 24616.3.5 Cylinder II . . . . . . . . . . . . . . . . . . . . . . . . . 24716.3.6 Cylinder III . . . . . . . . . . . . . . . . . . . . . . . . . 24816.4 Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25116.4.1 Pressure relief valve I . . . . . . . . . . . . . . . . . . . 25116.5 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . 25216.5.1 System 1, raising the piston . . . . . . . . . . . . . . . . 252CONTENTS xi16.5.2 System 1, lowering the piston . . . . . . . . . . . . . . . 25216.5.3 System 2 - with flow control valve . . . . . . . . . . . . 25316.5.4 System 3 -Motor lifting the load . . . . . . . . . . . . . 25516.5.5 System 3 -Motor lowering the load . . . . . . . . . . . . 25616.5.6 System 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 25616.6 Dynamic Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 25716.6.1 Steady State analysis ofWorkshop System. . . . . . . . 25716.6.2 DynamicModel ofWorkshop System. . . . . . . . . . . 26116.7 Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 26316.7.1 Pilot Chamber I . . . . . . . . . . . . . . . . . . . . . . 26316.7.2 Pilot Chamber II . . . . . . . . . . . . . . . . . . . . . . 26416.7.3 Pressure Relief Valve . . . . . . . . . . . . . . . . . . . . 26516.7.4 System analysis -Workshop System . . . . . . . . . . . 265

Fluid Power Systems: A Lecture Note in Modelling,

    Product form

    £85.49

    Includes FREE delivery

    RRP £89.99 – you save £4.50 (5%)

    Order before 4pm today for delivery by Fri 26 Jun 2026.

    A Hardback by Anders Hedegaard Hansen

    1 in stock

      Trusted by thousands of customers. See 2,385+ Customer Reviews

      View other formats and editions of Fluid Power Systems: A Lecture Note in Modelling, by Anders Hedegaard Hansen

      Publisher: Springer International Publishing AG
      Publication Date: 11/02/2023
      ISBN13: 9783031150883, 978-3031150883
      ISBN10: 3031150880
      Also in:
      Technology, Engineering & Agriculture Engineering: Mechanics of fluids

      Description

      Book Synopsis

      This book covers some of the fundamental topics in fluid power technology, presenting detailed derivations of formulas that form the basis of the theory. It shows the reader how to properly (i) design basic fluid power systems, (ii) construct lumped parameter models of simple fluid power systems, (iii) perform frequency analysis of fluid power components and systems, and (iv) develop controllers for fluid power systems. The book mainly focusses on mathematical modelling and analysis of fluid power components and systems i.e. practical issues such as working principles and construction of components are not covered in depth. The text is organized in four main parts: I Physics of Fluid, II Fluid Power Components, III Fluid Power Systems and IV Learning by Doing.




      Table of Contents
      1 Introduction 11.1 Hydro-statics and hydro-dynamics . . . . . . . . . . . . . . . . 11.1.1 Pascals law . . . . . . . . . . . . . . . . . . . . . . . . . 1I Physics of Fluid 32 Fluid parameters 52.1 Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Force due to shear velocity field . . . . . . . . . . . . . . 62.1.2 ViscosityModels . . . . . . . . . . . . . . . . . . . . . . 82.2 Fluid Compressibility and Density . . . . . . . . . . . . . . . . 112.2.1 Equation of State for a Fluid . . . . . . . . . . . . . . . 112.2.2 Pressure dependent density and stiffness of Fluid-air mixture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Fluids Mechanics 193.1 Conservation ofMass . . . . . . . . . . . . . . . . . . . . . . . . 193.1.1 Control Volume Approach . . . . . . . . . . . . . . . . . 193.1.2 Continuity Equation - Differential form . . . . . . . . . 223.2 Momentum of Fluids - Newton II. Law . . . . . . . . . . . . . . 253.2.1 Differential Form- Cartesian Coordinates . . . . . . . . 253.2.2 MomentumEquation of a Fluid . . . . . . . . . . . . . . 293.2.3 Conservation of Momentum - Control Volume Form . . 303.3 Inviscid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4 Viscous Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.1 Incompressible fluid . . . . . . . . . . . . . . . . . . . . 334 Flow Through Restriction 374.1 Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Flow in a tube . . . . . . . . . . . . . . . . . . . . . . . . . . . 37vvi CONTENTS4.2.1 FromNaiver-Stokes equation . . . . . . . . . . . . . . . 384.2.2 Fromforce balance . . . . . . . . . . . . . . . . . . . . . 404.2.3 Turbulent Flow in Pipes . . . . . . . . . . . . . . . . . . 424.2.4 Summary on Flow in Tubes . . . . . . . . . . . . . . . . 434.3 Flow in Gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.3.1 FromForce Balance . . . . . . . . . . . . . . . . . . . . 444.3.2 Velocity Profile fromNaiver-Stokes Equation . . . . . . 464.3.3 Summary on flow between parallel plates . . . . . . . . 484.4 The Orifice Equation . . . . . . . . . . . . . . . . . . . . . . . . 504.4.1 Laminar versus turbulent orifice flow . . . . . . . . . . . 52II Fluid Power Components 555 Fluid Power Pumps 575.1 Displacement Pumps . . . . . . . . . . . . . . . . . . . . . . . . 575.1.1 Data Sheet Units . . . . . . . . . . . . . . . . . . . . . . 575.1.2 Single Piston Pump . . . . . . . . . . . . . . . . . . . . 585.2 The General PumpModel - steady state . . . . . . . . . . . . . 585.2.1 Ideal PumpModel . . . . . . . . . . . . . . . . . . . . . 595.2.2 Non-ideal PumpModel . . . . . . . . . . . . . . . . . . 605.2.3 Summary on General PumpModel . . . . . . . . . . . . 625.3 Pump Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.3.1 Gear pumps . . . . . . . . . . . . . . . . . . . . . . . . . 645.3.2 Vane Pumps . . . . . . . . . . . . . . . . . . . . . . . . 655.3.3 Piston Pumps . . . . . . . . . . . . . . . . . . . . . . . . 675.3.4 Discrete Displacement pumps . . . . . . . . . . . . . . . 686 Rotary Actuator* 716.1 MotorModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.1.1 IdealMotorModel . . . . . . . . . . . . . . . . . . . . . 716.1.2 Non-idealMotorModel . . . . . . . . . . . . . . . . . . 727 Linear Actuators- Fluid Power Cylinders 757.1 Differential Cylinder . . . . . . . . . . . . . . . . . . . . . . . . 767.1.1 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 767.1.2 Steady StateModel . . . . . . . . . . . . . . . . . . . . 797.1.3 Summery . . . . . . . . . . . . . . . . . . . . . . . . . . 817.2 Multi-Chamber Cylinder . . . . . . . . . . . . . . . . . . . . . . 82CONTENTS vii8 Control Elements - Valves 838.1 General ValveModels . . . . . . . . . . . . . . . . . . . . . . . 838.2 Directional Valves . . . . . . . . . . . . . . . . . . . . . . . . . 848.2.1 Check Valve . . . . . . . . . . . . . . . . . . . . . . . . . 848.2.2 On-Off Valves . . . . . . . . . . . . . . . . . . . . . . . . 858.2.3 Directional Spool Valve . . . . . . . . . . . . . . . . . . 858.2.4 Flow Force on Spool Valve . . . . . . . . . . . . . . . . 898.2.5 Servo valves . . . . . . . . . . . . . . . . . . . . . . . . . 918.2.6 Direct Drive Servo Valves -Moog D633 . . . . . . . . . 928.3 Pressure control Valves . . . . . . . . . . . . . . . . . . . . . . . 958.3.1 Pressure relief . . . . . . . . . . . . . . . . . . . . . . . . 958.3.2 Pressure Reduction . . . . . . . . . . . . . . . . . . . . . 988.3.3 Pressure Control . . . . . . . . . . . . . . . . . . . . . . 1008.4 Flow Control Valves . . . . . . . . . . . . . . . . . . . . . . . . 1028.4.1 Throttle Valve . . . . . . . . . . . . . . . . . . . . . . . 1028.4.2 Pressure Compensated Flow Control Valve . . . . . . . 1058.4.3 Pressure Compensated Flow Control Valve - By Pass . . 1088.5 Pressure Compensated Proportional Valves . . . . . . . . . . . 1129 Accumulators 1159.1 Piston Accumulator . . . . . . . . . . . . . . . . . . . . . . . . 1159.1.1 Mass Loaded Piston Accumulators . . . . . . . . . . . . 1169.1.2 Spring Loaded Piston Accumulators . . . . . . . . . . . 1179.1.3 Gas loaded piston Accumulators . . . . . . . . . . . . . 1179.2 Bladder Accumulator . . . . . . . . . . . . . . . . . . . . . . . . 1189.3 DiaphragmAccumulator . . . . . . . . . . . . . . . . . . . . . . 11910 Pipes and Hoses 12110.1 Fluid Power Pipes . . . . . . . . . . . . . . . . . . . . . . . . . 12210.2 Fluid Power Hoses . . . . . . . . . . . . . . . . . . . . . . . . . 12210.2.1 Construction . . . . . . . . . . . . . . . . . . . . . . . . 12310.3 Steady State Transmission LineModel . . . . . . . . . . . . . . 12310.4 Dynamic Transmission LineModel . . . . . . . . . . . . . . . . 12310.4.1 Lumped ParameterModel . . . . . . . . . . . . . . . . . 123III Fluid Power Systems 12711 System Design 12911.1 Synthesis of Fluid Power Systems . . . . . . . . . . . . . . . . . 12911.1.1 System Operation . . . . . . . . . . . . . . . . . . . . . 13011.1.2 Operation of Sub Function . . . . . . . . . . . . . . . . 13011.1.3 System Architecture - Diagram . . . . . . . . . . . . . . 131viii CONTENTS11.1.4 System Pressure Level . . . . . . . . . . . . . . . . . . . 13111.1.5 Actuator sizing . . . . . . . . . . . . . . . . . . . . . . . 13211.1.6 Pump and PrimaryMover Sizing . . . . . . . . . . . . . 13211.1.7 Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13311.1.8 Fluid Lines . . . . . . . . . . . . . . . . . . . . . . . . . 13411.1.9 Control Elements . . . . . . . . . . . . . . . . . . . . . . 13611.1.10Steady state analysis - overall efficiency . . . . . . . . . 13611.1.11Tank and cooling . . . . . . . . . . . . . . . . . . . . . . 13611.1.12 Filtration . . . . . . . . . . . . . . . . . . . . . . . . . . 13711.2 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . 14011.2.1 Simple differential cylinder system . . . . . . . . . . . . 14011.2.2 Differential Cylinder System. . . . . . . . . . . . . . . . 14512 Modelling and Analysis 14912.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15012.1.1 LinearModel . . . . . . . . . . . . . . . . . . . . . . . . 15012.1.2 Frequency analysis . . . . . . . . . . . . . . . . . . . . . 15212.2 Symmetric Cylinder Valve Drive . . . . . . . . . . . . . . . . . 15412.2.1 Time DomainModel . . . . . . . . . . . . . . . . . . . . 15412.2.2 Reduced OrderModel . . . . . . . . . . . . . . . . . . . 15612.2.3 Linear Reduced OrderModel . . . . . . . . . . . . . . . 16012.2.4 Linear model . . . . . . . . . . . . . . . . . . . . . . . . 16212.2.5 Transfer Function for the Reduced Order Model . . . . 16512.2.6 Results of Full System . . . . . . . . . . . . . . . . . . . 17212.3 Fixed Displacement Motor Valve drive . . . . . . . . . . . . . . 17312.3.1 Time DomainModel . . . . . . . . . . . . . . . . . . . . 17412.3.2 Reduced OrderModel . . . . . . . . . . . . . . . . . . . 17512.3.3 Reduced Order Linear and Laplace Domain Model . . . 17612.3.4 Linear model . . . . . . . . . . . . . . . . . . . . . . . . 176IV Controlof Fluid Power Systems 17913 Controller Design and System Manipulations 18113.1 Pressure feedback . . . . . . . . . . . . . . . . . . . . . . . . . . 18213.2 Flow Feed Forward . . . . . . . . . . . . . . . . . . . . . . . . . 18313.2.1 Passive . . . . . . . . . . . . . . . . . . . . . . . . . . . 18413.2.2 Active . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18513.3 Valve Compensator . . . . . . . . . . . . . . . . . . . . . . . . . 18613.4 Valve Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 18713.5 Multi-Input Systems . . . . . . . . . . . . . . . . . . . . . . . . 18713.5.1 SMISMO - System . . . . . . . . . . . . . . . . . . . . . 188CONTENTS ix14 Reference generation 19114.1 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19114.1.1 Maximumpower transfer . . . . . . . . . . . . . . . . . 19114.1.2 Power request . . . . . . . . . . . . . . . . . . . . . . . . 19214.2 Input versus state requirement . . . . . . . . . . . . . . . . . . 19214.3 Polynomial position reference . . . . . . . . . . . . . . . . . . . 193V Exercises and Solutions 19515 Problem Solving 19715.1 FluidMechanics I . . . . . . . . . . . . . . . . . . . . . . . . . . 19815.1.1 Fluid Compressibility . . . . . . . . . . . . . . . . . . . 19815.1.2 Fluid Spring . . . . . . . . . . . . . . . . . . . . . . . . 19815.1.3 Viscous force on rotating body . . . . . . . . . . . . . . 19915.1.4 FluidMomentum . . . . . . . . . . . . . . . . . . . . . . 19915.2 FluidMechanics II . . . . . . . . . . . . . . . . . . . . . . . . . 20115.2.1 Orifice flow I . . . . . . . . . . . . . . . . . . . . . . . . 20115.2.2 Orifice flow II . . . . . . . . . . . . . . . . . . . . . . . . 20115.2.3 Pipe flow I . . . . . . . . . . . . . . . . . . . . . . . . . 20215.2.4 Pipe flow II . . . . . . . . . . . . . . . . . . . . . . . . . 20215.2.5 Pipe flow III . . . . . . . . . . . . . . . . . . . . . . . . 20315.2.6 Velocity profile in an annular flow . . . . . . . . . . . . 20315.3 Pumps,Motors and Cylinders . . . . . . . . . . . . . . . . . . . 20415.3.1 Pump I . . . . . . . . . . . . . . . . . . . . . . . . . . . 20415.3.2 Pump II . . . . . . . . . . . . . . . . . . . . . . . . . . . 20415.3.3 Motor I . . . . . . . . . . . . . . . . . . . . . . . . . . . 20415.3.4 Cylinder I . . . . . . . . . . . . . . . . . . . . . . . . . . 20415.3.5 Cylinder II . . . . . . . . . . . . . . . . . . . . . . . . . 20515.3.6 Cylinder III . . . . . . . . . . . . . . . . . . . . . . . . . 20615.3.7 Volumetric Pump Efficiency - VLE* . . . . . . . . . . . 20715.3.8 Pump Efficiency map - VLE* . . . . . . . . . . . . . . . 20715.3.9 Constant Pressure Pump - VLE* . . . . . . . . . . . . . 20715.3.10Hydrostatic Transmission - VLE* . . . . . . . . . . . . . 20715.3.11Valve cylinder drive - VLE* . . . . . . . . . . . . . . . . 20815.4 Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20915.4.1 Pressure relief valve I . . . . . . . . . . . . . . . . . . . 20915.4.2 Valve flow . . . . . . . . . . . . . . . . . . . . . . . . . . 20915.5 Steady State SystemAnalysis . . . . . . . . . . . . . . . . . . . 21015.5.1 System 1, raising the piston . . . . . . . . . . . . . . . . 21015.5.2 System 1, lowering the piston . . . . . . . . . . . . . . . 21115.5.3 System 2 - with flow control valve . . . . . . . . . . . . 21215.5.4 System 3 -Motor lifting the load . . . . . . . . . . . . . 213x CONTENTS15.5.5 System 3 -Motor lowering the load . . . . . . . . . . . . 21315.5.6 System 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 21515.6 System Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 21615.6.1 Workshop system flow control valves - Steady state . . . 21615.6.2 Dynamic model of Workshop system - Servo valves . . . 21715.7 System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 21815.7.1 Pilot Chamber I . . . . . . . . . . . . . . . . . . . . . . 21815.7.2 Pilot Chamber II . . . . . . . . . . . . . . . . . . . . . . 21815.7.3 Pressure relief valve . . . . . . . . . . . . . . . . . . . . 21915.7.4 System analysis - Differential cylinder and servo valve . 21915.8 System Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 22015.8.1 Position and velocity control of differential cylinder . . . 22015.8.2 System manipulation by pressure feedback . . . . . . . . 22015.9 System Power Limits and Input Reference . . . . . . . . . . . . 22115.9.1 Maximum load pressure, flow diagram . . . . . . . . . . 22115.9.2 Position input trajectory . . . . . . . . . . . . . . . . . . 22115.9.3 Simulation of position trajectory . . . . . . . . . . . . . 22115.10System design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22216 Solution 23516.1 FluidMechanics I . . . . . . . . . . . . . . . . . . . . . . . . . . 23616.1.1 Fluid Compressibility . . . . . . . . . . . . . . . . . . . 23616.1.2 Fluid Spring . . . . . . . . . . . . . . . . . . . . . . . . 23616.1.3 Viscous force on rotating body . . . . . . . . . . . . . . 23816.1.4 FluidMomentum . . . . . . . . . . . . . . . . . . . . . . 23816.2 FluidMechanics II . . . . . . . . . . . . . . . . . . . . . . . . . 24016.2.1 Orifice Flow I . . . . . . . . . . . . . . . . . . . . . . . . 24016.2.2 Orifice Flow II . . . . . . . . . . . . . . . . . . . . . . . 24016.2.3 Pipe Flow I . . . . . . . . . . . . . . . . . . . . . . . . . 24216.2.4 Pipe Flow II . . . . . . . . . . . . . . . . . . . . . . . . 24216.2.5 Pipe Flow III . . . . . . . . . . . . . . . . . . . . . . . . 24216.2.6 Velocity profile in an annular flow . . . . . . . . . . . . 24316.3 Pumps,Motors and Cylinders . . . . . . . . . . . . . . . . . . . 24516.3.1 Pump I . . . . . . . . . . . . . . . . . . . . . . . . . . . 24516.3.2 Pump II . . . . . . . . . . . . . . . . . . . . . . . . . . . 24516.3.3 Motor I . . . . . . . . . . . . . . . . . . . . . . . . . . . 24616.3.4 Cylinder I . . . . . . . . . . . . . . . . . . . . . . . . . . 24616.3.5 Cylinder II . . . . . . . . . . . . . . . . . . . . . . . . . 24716.3.6 Cylinder III . . . . . . . . . . . . . . . . . . . . . . . . . 24816.4 Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25116.4.1 Pressure relief valve I . . . . . . . . . . . . . . . . . . . 25116.5 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . . 25216.5.1 System 1, raising the piston . . . . . . . . . . . . . . . . 252CONTENTS xi16.5.2 System 1, lowering the piston . . . . . . . . . . . . . . . 25216.5.3 System 2 - with flow control valve . . . . . . . . . . . . 25316.5.4 System 3 -Motor lifting the load . . . . . . . . . . . . . 25516.5.5 System 3 -Motor lowering the load . . . . . . . . . . . . 25616.5.6 System 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 25616.6 Dynamic Modelling . . . . . . . . . . . . . . . . . . . . . . . . . 25716.6.1 Steady State analysis ofWorkshop System. . . . . . . . 25716.6.2 DynamicModel ofWorkshop System. . . . . . . . . . . 26116.7 Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 26316.7.1 Pilot Chamber I . . . . . . . . . . . . . . . . . . . . . . 26316.7.2 Pilot Chamber II . . . . . . . . . . . . . . . . . . . . . . 26416.7.3 Pressure Relief Valve . . . . . . . . . . . . . . . . . . . . 26516.7.4 System analysis -Workshop System . . . . . . . . . . . 265

      Recently viewed products

      © 2026 Book Curl

        • American Express
        • Apple Pay
        • Diners Club
        • Discover
        • Google Pay
        • Maestro
        • Mastercard
        • PayPal
        • Shop Pay
        • Union Pay
        • Visa

        Login

        Forgot your password?

        Don't have an account yet?
        Create account