Dr. Monika IvantysynovaMAHA Professor Flud Power Systems

Design and Modeling of Fluid Power SystemsME 597/ABE 591 - Lecture 2

MAHA Fluid Power Research CenterPurdue University

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 5912

Contents

1. Introduction and overview of components, circuit and system design methods

2. Fluid properties, modeling of transmission lines, impedance model of lines

3. Displacement machines design principles

4. Steady state characteristics, measurement methods and modeling

5. Gap flow models

6. Flow and pressure pulsation

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 5913

• Choose max operating pressure• Size the hydraulic motor• Calculate flow requirement• Select type of control, in case of valve control select type

and size of control valve• Select pump size based on flow requirement and speed

of prime mover• Calculate required line diameter• Add additional components like pressure relief valve,

logic elements, filter, reservoir, accumulators

Fluid Power System Design

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 5914

Fluid Power System DesignExample

maxmax Flight

max Flight

φφmax

φmax Flight

Ml

Fmax Flight

/s/s

during

φ

φ

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 5915

MAHA Distance LearningFluid Properties

Properties of Fluids

CompressibilityDensity Viscosity

Change of density with pressure

Change of density with temperature

Viscosity - temperature behavior

Viscosity - pressure behavior

•Oxidative, hydrolytic and thermal stability•Foaming (release air without forming emulsions)•Lubricity (boundary lubricating property)

•Air/Gas absorption•Pour Point•Flash point/ fire point

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 5916

17

Compressibility of a real fluid

Density is defined:

Change of fluid volume with pressure and temperature:

Isothermal coefficient of compressibility

Bulk modulus is defined as reciprocalof compressibility coefficient

Therefore we can write:

and

Fluid Properties

dV = -V ⋅ βp ⋅dp

⋅dp

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 5917

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Bulk modulus

1

2

V

pp1 p2

V1

V2

In practice secant bulk modulus KS is often used!

Fluid can be compressed isothermally or isentropically (adiabatic process)

Isothermal bulk modulus K Adiabatic bulk modulus KA

Fluid Properties

⋅ dp

⋅ (p2 - p1)

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 5918

Due to entrapped air the compressibility of the fluid (fluid-air mixture) changes.

For the bulk modulus of fluid – air mixture K* can be derived: p0 … atmospheric pressureIn a simplified way for the change of volume of thefluid – air mixture dVM we can derive:

For isothermal process follows: simplified:

and for the change of fluid volume:Change of air volume with pressure:

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Influence of entrapped air

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 5919

Influence of entrapped air

Due to VAir << VF we can make the following simplification: VF=V

then

(1) and (2)

Substituting Eq. (3) in Eq. (1) and (2) follows:

(3)

Example: Calculate how the bulk modulus of the fluid – air mixture with 0.5% undissolved air at p = 100 bar=107 Pa is changed. The bulk modulus of the fluid is K=2·109Pa.

20

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 59110

Viscosity of a real fluid

x

hp1 p2

p1=p2 v0y

The viscosity of a fluid is the measure of its resistance to flow or of its internal friction.According to Newton’s law the shearing stress between adjacent layers of a viscous fluid is proportional to the rate of shear in the direction perpendicular to the fluid motion (flow direction).

v

µ … dynamic viscosity [Pa·s=N·s/m2]

are empirical constants for a given fluid, whereas

Typical values for mineral oil:

23

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 59111

Viscosity of a real fluidKinematic viscosity

Kinematic viscosity: [m2·s-1] or [cSt]

ISO Viscosity Grades for mineral oils (ISO 3448)

ISO VG 10 mean value at 40°C 10 mm2·s-1 , (cSt)

ISO VG 22 22 mm2·s-1

ISO VG 32 32 mm2·s-1

ISO VG 46 46 mm2·s-1

ISO VG 100 100 mm2·s-1

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 59112

Viscosity-Temperature

Viscosity-temperature diagram

Kin

emat

ic v

isco

stiy

[mm

2 /s]

ISO viscosity grade reference temperature

Ordinate: lg lg (ν+0.8)

Abszissa: lg T

Skydrol (Phosphate ester)

Temperature [°C]

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 59113

Types of Hydraulic Fluids

Petroleum based fluids (mineral oils) usually with additives to-prevent oxidation and corrosion HL-reduce foaming -improve lubricity HLP-increase viscosity index HV

Fire resistant fluids - oil – water emulsions (20% H2O) - HFA - water in oil emulsion (about 40% H2O) - HFB- Polymer solutions with H2O - HFC - water free synthetic fluids ( Phosphate ester) - HFD

Biodegradable fluids-Vegetable oil base HTG-Polyglycol base HPG-Synthetic ester HE

Water

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 59114

Water versus Mineral Oil

Viscosity 30 lower

5 times higher thermal conductivity

Viscosity-temperature dependency 14 lower

Specific heat 2.3 higher

50% higher bulk modulus

Air –release ability 30times better

Higher vapor pressure

50% reduction of pressure loss

Better cooling-ability

Higher stiffness

but

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 59115

Vapor Pressure of Water

Water

Vapor

Pres

sure

[bar

]

Temperature [°C]

Vapor Pressure Water

pV H2O=0.1133 bar @ 50°C

pV mineral oil= 0.053Pa = 0.53 µbar @ 50°C

© Dr. Monika Ivantysynova Design and Modeling of Fluid PowerSystems, ME 597/ABE 59116

Fluid Properties

Thermal properties Specific heat c [ J/kg ·K]

Thermal conductivity λ [W/m ·K]

Solubility of gas Henry’s law

Cavitation