Design and Modeling of Fluid Power Systems
ME 597/ABE 591 - Lecture 2
Dr. Monika Ivantysynova
MAHA Professor Flud Power Systems
MAHA Fluid Power Research Center
Purdue University
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
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Fluid Power System Design
• 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
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Fluid Power System Design
Example
φ
φ
φ
φmax
φmaxmax
Flight
max Flight
during
© Dr. Monika Ivantysynova
M
l
/s
/s
FmaxmaxFlight
Flight
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
MAHA
Learning
Fluid Distance
Properties
Density
Compressibility
Viscosity
Properties of Fluids
Change of density with pressure
Viscosity - temperature behavior
Change of density with temperature
Viscosity - pressure behavior
•Oxidative, hydrolytic and thermal stability
•Foaming (release air without forming emulsions)
•Lubricity (boundary lubricating property)
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•Air/Gas absorption
•Pour Point
•Flash point/ fire point
Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Fluid Properties
Compressibility of a real fluid
Density is defined:
and
Change of fluid volume with pressure and temperature:
Isothermal coefficient of compressibility
dV = -V ⋅ βp ⋅dp
Bulk modulus is defined as reciprocal
of compressibility coefficient
⋅dp
Therefore we can write:
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Fluid Properties
Bulk modulus
Fluid can be compressed isothermally or isentropically (adiabatic process)
Isothermal bulk modulus K
Adiabatic bulk modulus KA
⋅ dp
V1
V
⋅ (p2 - p1)
1
2
V2
p1
p2
p
In practice secant bulk modulus KS is often used!
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Influence of entrapped air
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 pressure
In a simplified way for the change of volume of the
fluid – air mixture dVM we can derive:
For isothermal process follows:
Change of air volume with pressure:
© Dr. Monika Ivantysynova
simplified:
and for the change of fluid volume:
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Influence of entrapped air
(2)
(1) and
Due to VAir << VF we can make the following simplification: VF=V
then
(3)
Substituting Eq. (3) in Eq. (1) and (2) follows:
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.
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Viscosity of a real fluid
y
p1=p2
v
p1
h
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).
v0
p2
x
µ … dynamic viscosity [Pa·s=N·s/m2]
are empirical constants for a given fluid, whereas
Typical values for mineral oil:
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Viscosity of a real fluid
Kinematic viscosity
[m2·s-1] or [cSt]
Kinematic viscosity:
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
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Viscosity-Temperature
Viscosity-temperature diagram
Kinematic viscostiy [mm2/s]
Ordinate: lg lg (ν+0.8)
Abszissa: lg T
Skydrol (Phosphate ester)
Temperature [°C]
© Dr. Monika Ivantysynova
ISO viscosity grade reference temperature
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
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
Water
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
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Water versus Mineral Oil
50% reduction of
pressure loss
Viscosity 30 lower
Viscosity-temperature dependency 14 lower
Specific heat 2.3 higher
5 times higher thermal conductivity
Better coolingability
50% higher bulk modulus
Air –release ability 30times better
but
Higher stiffness
Higher vapor pressure
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Vapor Pressure of Water
Pressure [bar]
Vapor Pressure Water
Water
Vapor
pV H2O=0.1133 bar @ 50°C
Temperature [°C]
pV mineral oil= 0.053Pa = 0.53 µbar @ 50°C
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591
Fluid Properties
Thermal properties
Specific heat c [ J/kg ·K]
Thermal conductivity λ [W/m ·K]
Solubility of gas
Henry’s law
Cavitation
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Design and Modeling of Fluid Power
Systems, ME 597/ABE 591