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.
Author(s): Anders Hedegaard Hansen
Series: Fluid Mechanics and Its Applications, 129
Publisher: Springer
Year: 2023
Language: English
Pages: 260
City: Cham
Preface
Contents
1 Introduction—It's Just a Gear
1.1 Hydrodynamics Versus Hydrostatics
1.1.1 Kinetic Power and Hydrodynamics
1.1.2 Pascal's Principle and Hydrostatics
1.1.3 Three Hydrostatic Systems
1.2 Hydraulic Systems Versus Fluid Power Systems
1.3 Units in Fluid Power Systems
Part I Physics of Fluid
2 Fluid Parameters
2.1 Viscosity
2.1.1 Viscosity Models
2.1.2 Viscous Force Due to Fluid Flow
2.2 Fluid Density and Compressibility
2.2.1 Equation of State for a Fluid
2.2.2 Pressure Dependent Density and Bulk Modulus of Fluid-Air Mixture
2.2.3 Summery
Reference
3 Fluids Mechanics
3.1 Conservation of Mass
3.1.1 Control Volume Approach
3.1.2 Continuity Equation—Differential Form
3.2 Momentum of Fluids–Newton II. Law
3.2.1 Differential Form—Cartesian Coordinates
3.2.2 Momentum Equation of a Fluid
3.2.3 Conservation of Momentum—Control Volume Form
3.3 Euler's Equations of Motion–Inviscid Flow
3.4 Viscous Flow
3.4.1 Navier-Stokes Equations—Incompressible Fluid
4 Flow Through Restriction
4.1 Turbulent or Laminar—Reynolds Number
4.2 Flow in a Pipe
4.2.1 From Navier-Stokes Equation
4.2.2 From Force Balance
4.2.3 Volume Flow
4.2.4 Turbulent Flow in Pipes
4.2.5 Summary of Flow in Pipe
4.3 Flow in Gaps—Leakage Flows
4.3.1 From Force Balance
4.3.2 Volume Flow
4.3.3 Velocity Profile from Naiver-Stokes Equation
4.3.4 Summary on Laminar Flow Between Parallel Plates
4.4 The Orifice Equation
4.4.1 Laminar Versus Turbulent Orifice Flow
Reference
Part II Fluid Power Components
5 Fluid Power Pumps
5.1 Displacement Pumps
5.1.1 Single Piston Pump
5.2 The General Pump Model—Steady State
5.2.1 Ideal Pump Model
5.2.2 Non-ideal Pump Model
5.2.3 Summary on General Pump Model
5.3 Pump Types
5.3.1 Gear Pumps
5.3.2 Vane Pumps
5.3.3 Piston Pumps
5.3.4 Discrete Displacement Pumps
6 Rotary Actuator—Motors
6.1 Motor Models
6.1.1 Ideal Motor Model
6.1.2 Non-ideal Motor Model
7 Linear Actuators—Cylinders
7.1 Differential Cylinder
7.1.1 Modelling
7.1.2 Steady State Model
7.1.3 Summary
7.2 Multi-chamber Cylinder
8 Control Elements—Valves
8.1 General Valve Models
8.2 Directional Valves
8.2.1 Check Valve
8.2.2 On-Off Valves
8.2.3 Directional Spool Valve
8.2.4 Flow Force on Spool Valve
8.2.5 Servo Valves
8.3 Pressure Control Valves
8.3.1 Pressure Relief
8.3.2 Pressure Reduction
8.3.3 Pressure Control
8.4 Flow Control Valves
8.4.1 Throttle Valve
8.4.2 Case Illustration—Throttle Valves
8.4.3 Pressure Compensated Flow Control Valve
8.4.4 Pressure Compensated Flow Control Valve—Bypass
8.5 Pressure Compensated Proportional Valves
References
9 Accumulators
9.1 Piston Accumulator
9.1.1 Mass Loaded Piston Accumulators
9.1.2 Spring Loaded Piston Accumulators
9.1.3 Gas Loaded Piston Accumulators
9.2 Bladder Accumulator
9.3 Diaphragm Accumulator
10 Fluid Power Transmission Lines
10.1 Steady State Transmission Line Model
10.2 Dynamic Transmission Line Model
10.2.1 Lumped Parameter Model
10.3 Fluid Power Pipes and Hoses
10.3.1 Construction of Hoses
Part III Fluid Power Systems
11 Modelling Fluid Power Systems
11.1 Models
11.1.1 Time Domain Model—Non-linear
11.1.2 Reduced Order Model
11.1.3 Linear Model—Time Domain
11.2 Motor-Valve Drive
11.2.1 Time Domain Model
11.2.2 Linear Model
11.3 Cylinder-Valve Drive
11.3.1 Time Domain Model
11.3.2 Linear Model
11.3.3 Reduced Order Time Domain Model—Symmetric Cylinder
11.4 Solving the Model
References
12 Steady State Analysis
12.1 The Algorithm
12.2 Simple Differential Cylinder System
12.3 Complex Differential Cylinder System
13 Frequency Analysis
13.1 Analysis Methods
13.2 Motor-Valve Drive
13.2.1 Transfer Function
13.2.2 Frequency Response
13.2.3 System Understanding—Motor-Valve Drive
13.3 Cylinder-Valve Drive
13.3.1 Transfer Function for the Reduced Order Model
13.3.2 Frequency Response
13.3.3 System Understanding—Cylinder-Valve Drive
14 Control of Fluid Power Systems
14.1 Pressure Feedback
14.2 Flow Feed Forward
14.2.1 Passive
14.2.2 Active
14.3 Valve Compensator
14.4 Valve Dynamics
14.5 Multi-input Systems
14.5.1 SMISMO—System
15 Fluid Power Systems Design
15.1 System Operation
15.2 Operation of Subfunction
15.3 System Architecture—Diagram
15.4 System Pressure Level
15.4.1 Actuator Sizing
15.5 Pump and Primary Mover Sizing
15.6 Fluid
15.7 Fluid Lines
15.8 Control Elements
15.9 Steady State Analysis and Overall Efficiency
15.10 Tank and Cooling
15.11 Filtration
15.12 Procedure for Assembly, Operation and Maintenance
15.13 Estimate Costs
References
Part IV Learning by Doing
16 Exercises
16.1 Fluid Mechanics I
16.1.1 Fluid Compressibility
16.1.2 Fluid Spring
16.1.3 Viscous Force on Rotating Body
16.1.4 Fluid Momentum
16.2 Fluid Mechanics II
16.2.1 Orifice Flow I
16.2.2 Orifice Flow II
16.2.3 Orifice Flow III
16.2.4 Pipe Flow I
16.2.5 Pipe Flow II
16.2.6 Pipe Flow III
16.2.7 Velocity Profile in an Annular Flow
16.3 Pumps, Motors and Cylinders
16.3.1 Pump I
16.3.2 Pump II
16.3.3 Motor I
16.3.4 Cylinder I
16.3.5 Cylinder II
16.3.6 Cylinder III
16.4 Steady State Analysis
16.4.1 System 1—Raising a Differential Cylinder
16.4.2 System 1—Lowering a Differential Cylinder
16.4.3 System 2—Flow Regeneration 1
16.4.4 System 3—Flow Regeneration 2
16.4.5 System 4—Motor Lifting a Load
16.4.6 System 4—Motor Lowering a Load
16.5 System Modelling
16.5.1 System D1—Simple Pump Cylinder Drive
16.5.2 System D2—Hanging Mass
16.6 Analysis of Dynamic Systems
16.6.1 Pilot Chamber I
16.6.2 Pilot Chamber II
16.6.3 Spring Loaded Accumulator
16.6.4 Analysis of System D1
16.6.5 Analysis of System D3—Hanging Mass
16.7 Control of Dynamic Systems
16.7.1 Velocity Control of System D3—Hanging Mass
16.7.2 Position Control of System D3—Hanging Mass
16.7.3 System Manipulation of System D3—Hanging Mass
17 Solutions
17.1 Fluid Mechanics I
17.1.1 Fluid Compressibility
17.1.2 Fluid Spring
17.1.3 Viscous Force on Rotating Body
17.1.4 Fluid Momentum
17.2 Fluid Mechanics II
17.2.1 Orifice Flow I
17.2.2 Orifice Flow II
17.2.3 Orifice Flow III
17.2.4 Pipe Flow I
17.2.5 Pipe Flow II
17.2.6 Pipe Flow III
17.2.7 Velocity Profile in an Annular Flow
17.3 Pumps, Motors and Cylinders
17.3.1 Pump I
17.3.2 Pump II
17.3.3 Motor I
17.3.4 Cylinder I
17.3.5 Cylinder II
17.3.6 Cylinder III
17.4 Steady State Analysis
17.4.1 System 1—Raising a Differential Cylinder
17.4.2 System 1—Lowering a Differential Cylinder
17.4.3 System 2—Flow Regeneration 1
17.4.4 System 3—Flow Regeneration 2
17.4.5 System 4—Motor Lifting the Load
17.4.6 System 4—Motor Lowering the Load
17.5 System Modeling
17.5.1 System D1—Simple Pump Cylinder Drive
17.5.2 System D2—Hanging Mass
17.6 Analysis of Dynamics Systems—Solutions
17.6.1 Pilot Camber I
17.6.2 Pilot Camber II
17.6.3 Spring Loaded Accumulator
17.6.4 Analysis of System D1
17.6.5 Analysis of System D2
17.6.6 System D3—Hanging Mass
