Lecture 6 - College of Engineering, Purdue University

Design and Modeling of Fluid Power Systems ME 597/ABE 591 - Lecture 6 Dr. Monika Ivantysynova MAHA Professor Fluid Power Systems MAHA Fluid Power Research Center Purdue University

Content Steady state characteristics, measurement and modeling Volumetric and torque efficiency Measurement of steady state characteristics Determination of derived displacement volume Measurement based steady state models Aim:

Application of basic equations for calculation of performance data of pumps Performance test circuit design Basic knowledge about the generation of steady state models

© Dr. Monika Ivantysynova

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Design and Modeling of Fluid Power Systems, ME 597/ABE 591

Losses - displacement machines Axial piston machine – swash plate design A

B

Volumetric Losses

C

D

B C

F G

I

Torque Losses A B C D E G H J E

F

G


H

J

I 3


Pump Efficiency Volumetric efficiency:

p2, Qe

where Vi …. represents the derived displacement volume

Te , n p1

Torque efficiency (hydraulic-mechanical efficiency):

Total efficiency:

The derived displacement volume can only be determined by measurement © Dr. Monika Ivantysynova

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Volumetric Efficiency of a Pump Volumetric efficiency

v

Qe = α ⋅ Vmax ⋅ n - Qs

Vi ⋅ nmin = Qs [Pa·s]

Dynamic viscosity of fluid: © Dr. Monika Ivantysynova

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7


Volumetric Efficiency of a Pump Volumetric efficiency


Variable displacement pump

Typical values of dynamic viscosity used in displacement machines: 0.0435 Pa ⋅ s ÷ 0.0087 Pa ⋅ s with: Kinematic viscosity

[cSt, mm2/s]

and

μ=ν⋅ρ

ν = 10mm2 ⋅s-1 ÷ 50 mm2 ⋅s-1 with ρ = 870kg ⋅ m-3 © Dr. Monika Ivantysynova

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Torque Efficiency of a Pump

η

Ts = TSμ + TSρ + TSp + TSc = Cμ ⋅ μ ⋅ n + Cρ ⋅ ρ ⋅ n2 + Cp ⋅ Δp +TSc


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9


Total Efficiency of a Pump


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10


Steady State Characteristics

v = 20cSt


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Example Lecture 2 The displacement pump with a displacement volume of V=100 cm3/rev is driven by an electric motor at 1800 rpm. At steady state conditions the pressure difference across the pump is Δp= 380 bar. Determine the effective flow rate at the pump outlet Qe and the power required to drive this pump. Assume the following values for efficiency: p2 Qe - volumetric efficiency ηv=0.87 n - torque efficiency ηhm=0.95 The effective volume flow rate: p1 The effective torque yields:

The power required to drive the pump:


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Steady State Measurement The aim of steady state measurements is determination of steady state characteristics of pumps. Losses and their dependency on operating parameters Efficiency and its dependency on operating parameters Effective torque Te and effective volumetric Flow rate Qe in the whole parameter range Parameters to be measured: Temperatures θ1, θ2 θSe , © Dr. Monika Ivantysynova

p2, Qe QSi

Te , n QSe

p1

Under stable conditions, all parameters remain constant, including temperatures !

Inlet pressure p1

Outlet pressure p2

Torque Te

Shaft speed n

Volume flow rate at pump outlet Qe=Q2 11

14


Steady State Characteristics Vi derived displacement volume to be determined during measurements QS must be calculated using measurement results


Measured value

TS must be calculated using measurement results

Pin = Pout + PS = Δp ⋅ Qe + Ps = Te ⋅ 2 ⋅ π ⋅ n PS must be calculated using measurement results © Dr. Monika Ivantysynova

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Derived displacement volume Vi Measurement of effective volume flow rate at pump outlet under defined conditions

Δ

Qe

Qe

Δ

Vi=Qe/n

Δ

measured values 0

0

Δ

Vi required for determination of losses and volumetric and torque efficiency © Dr. Monika Ivantysynova

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Test Circuit Measured Values: Inlet pressure p1 Torque T Shaft speed n Outlet pressure p2 Temperature θ1, θ2 θSe ISO 4409 Volume flow rate at pump outlet Q2 Temperature θ1 must remain constant during measurements Pressure relief valve θ2

θ1

θSe Additional measured values:

T, n EM

Flow meter

Case flow rate QSe Pressure case line pSe © Dr. Monika Ivantysynova

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Steady State Measurement θ3 In case that Q2 is measured in low pressure line, the measured Q3 value must be corrected with respect to p2 and θ2

θ1

with K … bulk modulus ßθ …thermal volumetric expansion coefficient

3

θ2

θSe

T

K=2·109 Pa ßθ=0.65·10-3 K-1


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Steady State Measurement Measurement in pumping and motoring mode

θB

θL

θA

QA

QA θA pA θB pB QB

θL pL QL

Less temperature problems, because only a small amount of volume flow is throttled in pressure relief valve © Dr. Monika Ivantysynova

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T

n


Steady State Measurement ISO measurement accuracy classes Table 1: Permissible systematic errors of measuring instruments as determined during calibration Permissible systematic errors for classes of measurement accuracy

Parameter of measuring instrument

A

B

C

Rotational frequency [%]

± 0.5

± 1.0

± 2.0

Torque [%]

± 0.5

± 1.0

± 2.0

Volume flow rate [%]

± 0.5

± 1.5

± 2.5

Pressure below 2 bar gauge [bar]

± 0.01

± 0.03

± 0.05

Pressure greater than or equal to 2 bar gauge [%]

± 0.5

± 1.5

± 2.5

Temperature [°C]

± 0.5

± 1.0

± 2.0

Permissible temperature variation Accuracy class Temperature variation [K] © Dr. Monika Ivantysynova

A

B

C

±1.0

±2.0

±4.0

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Pressure Measurement The different types of pressure differ only with respect to their reference point.

Absolute pressure pabs

pamb=p0

Atmospheric pressure pamb

pg=pmeasured-pamb

0

t [s]

Direct measuring pressure instruments Indirect measuring pressure instruments Electrical pressure sensors © Dr. Monika Ivantysynova

pg

pabs 1 pamb

Gauge pressure pg

p [Pa]

Differential pressure Δp

p1

Fluctuation of pamb ~ ±5% p2 Δp

Types of pressure

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Using a liquid column Using the effect of a pressure acting on a material or on bodies of a certain shape Design and Modeling of Fluid Power Systems, ME 597/ABE 591

Electrical Pressure Sensors


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Flow Measurement Flow measuring instrument is defined as device which measures the flow rate of a fluid. Displacement of a spring loaded floated element

Pressure difference across an orifice

D