IEEE Electrification Magazine - December 2014 - 31

powertrain component, can be controlled to emulate the
fan that would be a load torque applied to the fan shaft.
The reference torque can be obtained by given fan maps
of specific model and corresponding flight conditions.
The closed-loop torque-control algorithm for the emulator will be developed and tested through a simulation
model in MATLAB/Simulink prior to implementation in
the test rig.

1.35

Pressure Ratio

1.3

Modeling of Fan Map
Complete fan maps are either based on fan rig test results or
are predicted by a special computer program. A fan map is
important, since it is an integral part of predicting the performance of a gas turbine engine, both at design and off-design
conditions. However, these maps are difficult to use in a computer simulation due to their steep gradients and multiple
independent variables. Thus, beta maps were developed as a
technique to reduce conventional component characteristic
maps into a number of simpler maps. More maps are
required for the beta format because they take the variables
from a conventional map and split them into maps that contain only one dependent variable as a function of one independent variable used in generally corrected speed.
Figure 8 shows fan maps used in the simulation, which
can generate an equivalent power level of a Boeing 787 GEnx
fan at high speeds. This fan has the dependent variable
pressure ratio (Pexit/Pinlet) on the ordinate and the first independent variable, corrected mass flow, on the abscissa. The
second independent variable, corrected speed, is shown as
lines of constant corrected speed that extend from surge to
choked conditions. Using the beta-line technique, two sets
of data can be obtained. One set of data would be the pressure ratio as a function of corrected speed. This collection of
data would provide one beta line on the fan pressure ratio
on the beta map. The second set of data would be the corresponding corrected mass flow as a function of corrected
speed. The corrected mass flow data would also provide one

1,300
1,250
1,200
Flow

1,150
1,100

1.25
1.2
1.15
1.1
1.05
1
900 950 1,000 1,050 1,100 1,150 1,200 1,250 1,300
Mass Flow
100% Engine Speed
95% Engine Speed
90% Engine Speed

beta line on the fan corrected mass flow on the beta map. By
collecting data for a number of pressure ratios and corrected
mass flow beta lines as a function of corrected speed, a
mass flow beta map versus speed and a pressure ratio beta
map versus speed can be obtained from the original fan
maps. Figure 9 shows the airflow beta map and pressure
ratio beta map necessary for the computer simulation.
These two beta maps have been implemented into the simulation code as lookup tables.
Figure 10 shows a proposed block diagram for the
motor-fan drive system. First, engine speed and beta coordinates go to the lookup table blocks to predict the values

Linear Beta Lines

1.45

9
8
7
6
5
4
3
2
1
0

1.4
1.35
1.3
1.25
1.2

1,050

1.15

1,000

1.1

950

1.05

900
0.75

85% Engine Speed
80% Engine Speed
75% Engine Speed

Figure 8. Fan maps at high speed used in the simulation.

0
1
2
3
4
5
6
7
8
9

Linear Beta Lines

Fan Maps

1.4

0.8

0.85
0.9
Engine Speed
(a)

0.95

1

1
0.75

0.8

0.85
0.9
Engine Speed
(b)

0.95

1

Figure 9. linear beta lines: (a) flow versus engine speed and (b) pressure ratio versus engine speed.
IEEE Electrific ation Magazine / d ec em be r 2 0 1 4

31



Table of Contents for the Digital Edition of IEEE Electrification Magazine - December 2014

IEEE Electrification Magazine - December 2014 - Cover1
IEEE Electrification Magazine - December 2014 - Cover2
IEEE Electrification Magazine - December 2014 - 1
IEEE Electrification Magazine - December 2014 - 2
IEEE Electrification Magazine - December 2014 - 3
IEEE Electrification Magazine - December 2014 - 4
IEEE Electrification Magazine - December 2014 - 5
IEEE Electrification Magazine - December 2014 - 6
IEEE Electrification Magazine - December 2014 - 7
IEEE Electrification Magazine - December 2014 - 8
IEEE Electrification Magazine - December 2014 - 9
IEEE Electrification Magazine - December 2014 - 10
IEEE Electrification Magazine - December 2014 - 11
IEEE Electrification Magazine - December 2014 - 12
IEEE Electrification Magazine - December 2014 - 13
IEEE Electrification Magazine - December 2014 - 14
IEEE Electrification Magazine - December 2014 - 15
IEEE Electrification Magazine - December 2014 - 16
IEEE Electrification Magazine - December 2014 - 17
IEEE Electrification Magazine - December 2014 - 18
IEEE Electrification Magazine - December 2014 - 19
IEEE Electrification Magazine - December 2014 - 20
IEEE Electrification Magazine - December 2014 - 21
IEEE Electrification Magazine - December 2014 - 22
IEEE Electrification Magazine - December 2014 - 23
IEEE Electrification Magazine - December 2014 - 24
IEEE Electrification Magazine - December 2014 - 25
IEEE Electrification Magazine - December 2014 - 26
IEEE Electrification Magazine - December 2014 - 27
IEEE Electrification Magazine - December 2014 - 28
IEEE Electrification Magazine - December 2014 - 29
IEEE Electrification Magazine - December 2014 - 30
IEEE Electrification Magazine - December 2014 - 31
IEEE Electrification Magazine - December 2014 - 32
IEEE Electrification Magazine - December 2014 - 33
IEEE Electrification Magazine - December 2014 - 34
IEEE Electrification Magazine - December 2014 - 35
IEEE Electrification Magazine - December 2014 - 36
IEEE Electrification Magazine - December 2014 - 37
IEEE Electrification Magazine - December 2014 - 38
IEEE Electrification Magazine - December 2014 - 39
IEEE Electrification Magazine - December 2014 - 40
IEEE Electrification Magazine - December 2014 - 41
IEEE Electrification Magazine - December 2014 - 42
IEEE Electrification Magazine - December 2014 - 43
IEEE Electrification Magazine - December 2014 - 44
IEEE Electrification Magazine - December 2014 - 45
IEEE Electrification Magazine - December 2014 - 46
IEEE Electrification Magazine - December 2014 - 47
IEEE Electrification Magazine - December 2014 - 48
IEEE Electrification Magazine - December 2014 - Cover3
IEEE Electrification Magazine - December 2014 - Cover4
https://www.nxtbook.com/nxtbooks/pes/electrification_december2022
https://www.nxtbook.com/nxtbooks/pes/electrification_september2022
https://www.nxtbook.com/nxtbooks/pes/electrification_june2022
https://www.nxtbook.com/nxtbooks/pes/electrification_march2022
https://www.nxtbook.com/nxtbooks/pes/electrification_december2021
https://www.nxtbook.com/nxtbooks/pes/electrification_september2021
https://www.nxtbook.com/nxtbooks/pes/electrification_june2021
https://www.nxtbook.com/nxtbooks/pes/electrification_march2021
https://www.nxtbook.com/nxtbooks/pes/electrification_december2020
https://www.nxtbook.com/nxtbooks/pes/electrification_september2020
https://www.nxtbook.com/nxtbooks/pes/electrification_june2020
https://www.nxtbook.com/nxtbooks/pes/electrification_march2020
https://www.nxtbook.com/nxtbooks/pes/electrification_december2019
https://www.nxtbook.com/nxtbooks/pes/electrification_september2019
https://www.nxtbook.com/nxtbooks/pes/electrification_june2019
https://www.nxtbook.com/nxtbooks/pes/electrification_march2019
https://www.nxtbook.com/nxtbooks/pes/electrification_december2018
https://www.nxtbook.com/nxtbooks/pes/electrification_september2018
https://www.nxtbook.com/nxtbooks/pes/electrification_june2018
https://www.nxtbook.com/nxtbooks/pes/electrification_december2017
https://www.nxtbook.com/nxtbooks/pes/electrification_september2017
https://www.nxtbook.com/nxtbooks/pes/electrification_march2018
https://www.nxtbook.com/nxtbooks/pes/electrification_june2017
https://www.nxtbook.com/nxtbooks/pes/electrification_march2017
https://www.nxtbook.com/nxtbooks/pes/electrification_june2016
https://www.nxtbook.com/nxtbooks/pes/electrification_december2016
https://www.nxtbook.com/nxtbooks/pes/electrification_september2016
https://www.nxtbook.com/nxtbooks/pes/electrification_december2015
https://www.nxtbook.com/nxtbooks/pes/electrification_march2016
https://www.nxtbook.com/nxtbooks/pes/electrification_march2015
https://www.nxtbook.com/nxtbooks/pes/electrification_june2015
https://www.nxtbook.com/nxtbooks/pes/electrification_september2015
https://www.nxtbook.com/nxtbooks/pes/electrification_march2014
https://www.nxtbook.com/nxtbooks/pes/electrification_june2014
https://www.nxtbook.com/nxtbooks/pes/electrification_september2014
https://www.nxtbook.com/nxtbooks/pes/electrification_december2014
https://www.nxtbook.com/nxtbooks/pes/electrification_december2013
https://www.nxtbook.com/nxtbooks/pes/electrification_september2013
https://www.nxtbookmedia.com