Golak Karol, Lindstedt Paweł: Analysis of the quality assessment of the jet engines rotational speed signal from set value and noise. Analiza oceny jakości przebiegu prędkości obrotowej silnika odrzutowego od wartości zadanej i sygnału zakłócenia.

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ANALYSIS OF THE QUALITY ASSESSMENT OF THE

JET ENGINES ROTATIONAL SPEED SIGNAL FROM

SET VALUE AND NOISE

ANALIZA OCENY JAKOŚCI PRZEBIEGU PRĘDKOŚCI

OBROTOWEJ SILNIKA ODRZUTOWEGO OD

WARTOŚCI ZADANEJ I SYGNAŁU ZAKŁÓCENIA

Golak Karol

1

, Lindstedt Paweł

2

1

Bialystok Technical University, Faculty of Mechanical Engineering

2

Air Force Institute of Technology

e-mail: 1karolgolak@gmail.com; 2 p.lindstedt@pb.edu.pl

Abstract:Turbojet engine is a complex technical object. It fulfils an important role in the civil and military aviation. Its undesired operation can lead to tragic accidents. Hence the large role takes the proper preparation for work and adequate regulation. The correctness of the engine work is tested periodically during ground tests. During the ground tests the responses to set engine control lever (DSS) shift is examined, thus means that the engine is examined from the "set point". During ground testing is not possible to reflect the impact of changing conditions during engine operation in flight so the engine is not tested on the noise signal. It turns out that it is the properties of the noise signal often have a decisive effect on the engine operation correctness and by that on the safety of the flight. Hence there is a need to develop methods to assess the state of the engine control signal from noise on the basis of standard ground test from the set point (delivered by the DSS).

Keywords: diagnostics, reliability, control, jet engine

Streszczenie: Turbinowy silnik odrzutowy jest złożonym obiektem technicznym. Spełnia

on ważną rolę w lotnictwie cywilnym i wojskowym. Jego nieprawidłowe działanie może prowadzić do tragicznych wypadków. Stąd dużej roli nabierają ich prawidłowe przygotowanie do pracy i odpowiednia regulacja. Poprawność pracy silnika jest testowana podczas okresowo przeprowadzanych prób naziemnych. Bada się jego odpowiedzi na zadane przesunięcie dźwignią sterowania silnikiem (DSS) zatem silnik badany jest od “wartości zadanej”. W trakcie prób naziemnych nie ma możliwości odzwierciedlenia wpływu zmiennych warunków panujących podczas pracy silnika w trakcie lotu zatem silnik nie jest badany od sygnału zakłóceń. Okazuje się, że to właśnie właściwości od sygnału zakłóceń niejednokrotnie mają decydujący wpływ na poprawność pracy silnika a przez to na bezpieczeństwo lotu. Stąd pojawiła się potrzeba opracowania metody oceny stanu regulacji silnika od sygnału zakłóceń na podstawie standardowych badań podczas prób naziemnych od wartości zadanej (DSS).

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1. Introduction

Simplified diagram of the air jet engine control system (UAR) can be reduced to the standard automatic control scheme like it has been shown in Fig. 1:[3, 4, 5, 6]

Fig. 1. Simplified turbo jet engine control system,

where: GR – controller transfer function, GO –object transfer function, w – set value (setting

by the engine control lever), z – input signal (noise), y – output signal (rotational speed), e=w-y – controller input signal (control error), u – controller output signal (command signal)

During engine ground tests set value “w” can be easily delivered by the engine control lever, but the introduction of noise signal "z" to the system, e.g. by partially covering the air intake is difficult and dangerous, and therefore prohibited. In addition, a noise signal "z" during ground tests is low-power and constant, so therefore the study of UAR from "z" was dropped and focused solely on the study from "w" [3, 4, 5].

However, during the flight noise signal "z" generated by such phenomena as the firing of rockets, turbulence, side gusts, tight turn, etc. takes on high power as well as the importance and impact on the engine operation, sometimes leading to undesirable changes in the speed and even the flameout. It is also known that improving the quality of the engine from the "w" causes deterioration of the motor from the "z" [1, 9, 10].

2. Description of control system of the K-15

Functional diagram of the air jet engine (K-15) control system was shown on fig. 2. Based on the functional diagram (fig. 2) the block diagram of the jet engine control system was made. [3]

It is worth noting that the jet engine parameters change with the change of flight parameters (eg height). It is possible to calculate THW and kHW - which are the time constant and the gain of the jet engine at a certain height H, based on the engine T and k during ground tests and dependencies [1]:

0 H HW

p

k

p





(1) 0 0 H HW H T T T T p p   (2)

Where: p0 and pH it is pressure on ground level and height H

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Fig. 2. Functional diagram of the fuel-control system EUP-150S for the engine K-15; A- starting and acceleration control valve; C – proportion needle of starting and acceleration system; D – nozzle controlling deceleration; DSS - engine control lever;

E – electro-hydraulic valve; Max – valve limiting max fuel flow rate; Min - valve limiting min fuel flow rate; N – centrifugal transmitter of the rotational speed signal;

P - comparison valve (coupling the main and control fuel system); Q - nozzle for measuring the volumetric flow rate of the fuel; Reg – hydromechanical controller of the rotational speed; Stop - valve shutoff the fuel flow to the injectors; T - main plunger

pump; U - fuel release valve; W- supporting pump; Z - fuel tank; pc2 - air pressure from the compressor; ṁpal – mass flow rate of fuel in the main supply line; ṁb - mass

flow rate of fuel in the line of control; I0 – an electrical signal controlling electrohydraulic valve. Own figure based on [1] and [8]

Below in table 1 values taken by the parameters THW i kHW on the height H=10000 m above sea level for T0=288,15 K, TH= 223,15 K, p0=100000 Pa, pH= 26000 Pa was shown.

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Table 1. Values of the object parameters T and k for heights H0=0 m and

H=10000 m.

H

0=0 m, T0=288,15 K, p0=10000 Pa

k=0,5

T=1,5

H=10000 m, T

H= 223.15 K, pH= 26000 Pa kHw=0,16 THw=6,80

Fig. 3. Block diagram of the jet engine control system [4, 5]

For the assumed parameters of the object shown in table 1 simulations have been carried out on the engine response from the set value "w" and the noise "z" during the ground tests and during the work on height H for set constant changes of engine parameters Δk=0,1 and ΔT=1 resulting primarily from special cases on the fly[4].

Fig 4. The impact of object’s parameters changes k and T on the response waveforms during ground tests

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Fig 5. The impact of object’s parameters changes on the response waveforms on height H=10000 m with occurring changes of the Δk and ΔT from special cases on the fly.

Fig 6. The impact of controller parameter “kr” changes on the response waveforms on height H=0 m.

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Fig 7. The impact of controller parameter “Ti” changes on the response waveforms on height H=0 m.

Summary of quality indicators H (overshoot) and tr (regulation time)

H for input

functions "w" and "z" are shown in Table 2

Table 1. Values of quality indicators for different input functions where H is overshoot and tr is the regulation time.

figure Parameter changing step response from „w” step response from „z”

k T kr Ti H H/ Hopt tr tr/tropt H H/ Hopt tr tr/tropt

4 0,4 0,5 66 100 1,71 0,45 0,62 0,60 2,19 1,02 0,66 1 0,5 1,5 66 100 3,80 1 1,03 1 2,14 1 0,66 1 0,6 2,5 66 100 5,40 1,42 1,09 1,06 2,11 0,98 1 1,51 5 0,06 5,8 66 100 55,96 1,15 7,53 0,76 0,63 0,65 8,62 1,21 0,16 6,8 66 100 48,75 1 9,89 1 0,96 1 7,14 1 0,26 7,8 66 100 43,40 0,89 6,57 0,66 1,14 1,19 5,71 0,80 6 0,5 1,5 56 100 1,37 0,36 0,73 0,71 2,18 1,02 0,79 1,20 0,5 1,5 66 100 3,80 1 1,03 1 2,14 1 0,66 1 0,5 1,5 76 100 6,92 1,82 0,97 0,94 2,11 0,98 0,94 1,42 7 0,5 1,5 66 1 28,94 7,60 2,50 2,43 2,13 0,99 2,13 3,23 0,5 1,5 66 100 3,80 1 1,03 1 2,14 1 0,66 1 0,5 1,5 66 199 3,66 0,96 1,01 0,98 2,14 1,01 0,66 1

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The table 2 shows that the engine in flight is more sensitive to Δk and ΔT changes. Signals "y" and "w" occurring in the block diagram of the automatic control of a jet engine turbine (Fig. 1) are recorded during the standard ground tests, so that makes possible to calculate the relationship between them. [4, 5] What remains unknown is the relationship between "y" and "z", which is an important relationship for aircraft in flight. Therefore is searched the possibility of carry out such tests on the ground (the input signal is "w"), to get not only y=f(w) but also y=f(z).

3. A comprehensive aircraft engine research model from “w” and “z”

To study work quality of the jet engine from "z" using the sample of "w", is necessary to carry out the identification of transfer functions of the automatic control system components (fig. 1). Here's how to identify [4, 5].

Identification of the object from the "w" (the assumption that z=0) where the input signal is "u", the output is "y":

OW Y G

U

 (3)

Identification of the controller from the "w" (the assumption that z=0) where the input signal is „w-y” or „1-y”, the output is "u".

1 RW U U G W Y Y     (4)

Identification of the object from the "z" (the assumption that w=0) where the input signal is to „z-u” or „1-u”, the output is "y".

1 OZ Y Y G Z U U     (5)

Identification of the controller from the "z" (the assumption that w=0) where the input signal is „y”, the output is "u".

RZ U G

Y

 (6)

From the analysis of the fig. 1 the transfer functions HW (for z=0) and HZ (for w=0) can be obtained as shown below:

1

OW RW W OW RW

G

H

G





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1

OZ Z OZ RZ

G

H

G G





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Comparing the HW and HZ it is concluded that as a result of multiplication of the transfer function obtained during the engine ground tests by the inverse transfer function from the same tests it is possible to obtain transfer function HZW in the same form as HZ but resulting without the need for test from "z".

1

OW RW OW ZW OW RW RW OW RW

G

H

G









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In addition, it is stated that the transfer functions HZW and HW are determined based on the same signals, which are: "y", "u" and "w".

With relations between HZW and HW can be found links between HZW and HZ. In accordance with the principles of automation system components transfer functions GOW, GOZ, GRW and GRZ can be described by a quotient of power spectral density of output and input signals. [2, 4, 5, 7]

yu OW uu

S

Y

G

U

S



(10) ( ) ( )( ) u w y RW w y w y S U G W Y S       (11) ( ) ( )( ) y z u OZ z u z u S Y G Z U S       (12) uy RZ yy S U G Y S   (13)

Thus transfer functions HW, HZ and HWZ based on formulas (5), (6) and (7) takes the form: ( ) ( )( ) ( ) ( ) ₍ ₎₍ ₎ ₍ ₎ ( )( )

1

yu u w y uu w y w y yu u w y W yu u w y _uu _{w y w y} _yu _{u w y} uu w y w y

S

S S

H

S

_{S S}

S

     _ _ _  





(14) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( )( )

1

y z u z u z u yy y z u Z y z u uy yy z u z u uy y z u z u z u yy

S

S S

H

S

_{S S}

S

     _ _ _  





(15) ( ) yu u w y WZ S S H   ( )( ) ( )( ) ( ) ( ) w y w y uu w y w y yu u w y u w y S S S S S S         ( )( ) ( )( ) ( ) yu w y w y uu w y w y yu u w y S S S S S S        (16)

There is no similarity between the HW (5) and HZ (6). However, such similarity exists between the transfer functions HW and HWZ and further between HWZ and HZ. So by setting the HWZ it is possible to determine HZ.

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When assumed that step response „y” from „z” is searched based on the response from „w” then receive:

(1 ) (1 )(1 ) (1 ) yy y u Z yy u u uy y u S S H S S S S       (17) (1 )(1 ) (1 )(1 ) (1 ) yu y y WZ uu y y yu u y S S H S S S S        (18)

When assumed that impulse response „y” from „z” is searched based on the response from „w” then receive:

( ) ( )( ) ( ) yy y u Z yy u u uy y u S S H S S S S       (19) ( )( ) ( )( ) ( ) yu y y WZ uu y y yu u y S S H S S S S        (20) Where: S₍__u₎₍__u₎S_uu ( y)( y) yy S_ _ S Then: ( ) ( ) yy y u Z yy uu uy y u S S H S S S S     (21) ( )( ) ( )( ) ( ) yu y y WZ uu y y yu u y S S H S S S S        (22)

Next assumed that: S_u₍__y₎S₍__{y u}₎ Next, following formulas are received:

( ) ( ) yy y u Z yy uu uy u y S S H S S S S     (23) ( ) yu yy WZ uu yy uy u y S S H S S S S    (24)

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This means that transfer function HWZ will be equivalent with HZ when Syu (24) will be replace by Sy-u (23) ("u" recorded during ground tests must be enter with sign "-". So, there is a strict relationship between transfer functions HWZ and HZ.

Can be written: ( ) ( ) ( ) ( ) yy y u yy uu uy u y y u Z yu yy WZ yu yy uu uy u y S S S S S S S H S S H S S S S S         (25) ( ) y u Z WZ yu S H H S   (26)

and finally substituting the (24) to (26):

yu Z S H  ( ) ( ) yy _y _u uu yy uy u y yu S _S S S S S S     (27)

Thus, based on the transfer function HWZ the transfer function HZ can be determined. The transfer function HZ is the qualitative and quantitative relationship between the signals “y” and “z”, (which is its significant attribute) determined as a transfer function HWZ based on signals “y” and “u”. Transfer function HZ allows to determine the characteristics from “z” (ground and flight) based on signals recorded during ground tests. )[4, 5].

4. Conclusion

Using the results obtained during the standard test conducted on ground from set value "w" it is possible to infer the state of a turbine jet engine regulation from noise signal "z". This problem is very important because such an control state improvement from the signal "w" gives the deterioration of the control state of "z" which is especially important during the flight of an airplane. The ability to predict engine response to specific accidents occurring during the flight (such as air blast, firing rockets) allows for such adjustments to minimize its sensitivity to occurring environment variables (eg, to prevent engine stalling).

"The publication is co-financed by the European Union from the European Social Fund under the" Scholarships for PhD students as a key of developing region. Podlasie " (Project No. WND-POKL.08.02.01-20-070/11)

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5. References

[1] W. Balicki, S. Szczeciński: „Diagnozowanie lotniczych silników turbinowych. Zastosowanie symulacyjnych modeli silników do wyboru i optymalizacji zbioru parametrów diagnostycznych”, Biblioteka Naukowa Instytutu Lotnictwa, Warszawa 2001.

[2] Bendat J. S., Piersol A. G., Engineering Applications of Correlation and Spectral Analysis, John Willey & Sons, Inc, New York 1980.

[3] Bodner W. A., Automatyka silników lotniczych, Wydawnictwo Ministerstwa Obrony Narodowej, Warszawa 1958.

[4] Golak K.: Method of regulation condition assessment of turbine jet engine in flight basing on signals recorded during ground tests, Journal of KONES, Vol.19, nr 3 (2012).

[5] Golak K.: Validity Check of the Assessment of a Jet Turbine Engine Regulation in Flight Using a Computer Simulation, Solid State Phenomena, Durnten-Zurich 2013.

[6] Lindstedt P., Praktyczna regulacja maszyn i jej teoretyczne podstawy, Wydawnictwo Instytutu Technicznego Wojsk Lotniczych, Warszawa 2010. [7] Osiowski J., Zarys rachunku operatorowego, teoria i zastosowanie w

elektrotechnice, Wydawnictwo Naukowo-Techniczne, Warszawa 1981. [8] Szczeciński S.: „Napęd samolotu I-22 IRYDA” WPTiL nr 3/1995, Warszawa

1995.

[9] Staniszewski R., Sterowanie zespołów napędowych, WKŁ, Warsaw 1980. [10] Szevjakow A. A., Awtomatika awiacionnych i rakietnych siłowych

ustanowok, Maszinostrojenije, Moscow 1970.

Prof. Paweł Lindstedt, DSc., Eng. professor of the Technical

University in Białystok, associate professor of Air Force Institute of Technology. Research subjects: Design and application of machinery, applied automatics, diagnostics and reliability of equipment. His works concern diagnostics of aircraft engines, hydraulic and bearing systems with application of functional, vibro-acoustic and wear methods

M.Sc., Eng Karol Golak, PhD student of the Department of

Mechanical Engineering at the Bialystok Technical University. Research subject: technical diagnostics of turbojet engine, reliability and control of mechanical objects.