method of vibration diagnostics of aircraft mechanical

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 711-720

© Research India Publications. http://www.ripublication.com

711

Method of Vibration Diagnostics of Aircraft Mechanical Components

in Civil Aviation

A.A. San’ko

Ph.D., Associate Professor, Institution of Education "Minsk State Higher Aviation College",

Republic of Belarus

A.L. Starichenkov

Doctor of Engineering Science, Professor, St. Petersburg State University of Civil Aviation,

38, Pilotov str., St. Petersburg, 196210, Russia.

E.A. Kuklev



Y.V. Vedernikov



S. A. Kabanov



Abstract The article presents the designed system of automated vibration

diagnostics of basic mechanical components of the helicopter.

The system allows for automated diagnosis of technical condition

of main and control rotors, and the main gearbox of the

helicopter, using the vibration control method and neural network.

The authors present the mathematical model of stable low-

frequency vibrations of the helicopter excited by variable forces

and moments acting from the helicopter main rotor taking into

account the influence of the conditions and control regimes.

Keywords: vibration, helicopter, diagnosis, neural network.

INTRODUCTION

The maintenance costs of the helicopter flying hour are several

times greater than those of the aircraft. This is due to the presence

of complex mechanical systems in helicopter design: main and

control rotor, main gearbox and other transmission components.

In most cases, malfunctions of these systems lead to catastrophic

situations.

Unfortunately, the locally-produced helicopters have low

testability level, and the fault and defects detection is performed

mainly using the visually-optical method (75%) or directly by the

helicopter crew by the helicopter vibration sensation. A

significant disadvantage of these methods is their relatively low

resolving ability. The process of faults finding is often intuitive,

and requires a lot of time and material costs [18]. Therefore,

based on the flight safety requirements, the main mechanical

components of a helicopter are operated until they exhaust their

life span, which in the process of long-term operation leads to

unnecessarily high material costs.

It is well known that the condition-based operation in which the

volume and content of the rehabilitation works shall be fixed in

accordance with the actual technical condition (hereinafter –TC)

of the objects is more efficient in economic terms (cost

reduction of up to 30%) [18], and in terms of reliability. But

a prerequisite for its implementation is a high level of the

components controllability, allowing to track their diagnostic

features (hereinafter – DF) while in operation [1].

The problem may be resolved by improving the design of

helicopters, creating airborne and ground-based diagnostic

systems using advanced methods of nondestructive testing

and data analysis.

METHODS The studies have shown that for mechanical components one

of the most promising methods of non-destructive testing is a

vibration one (up to 82% of faults of the machines with

rotating components is determined using the vibration

diagnostics methods [5]). The studies have shown that the

spectral characteristics of the helicopter vibrations also are

complex and reflect the TC of the assemblies and parts of the

main rotor (hereinafter – the MR), control rotor (hereinafter –

CR), power plant, gearboxes and other mechanical

components (Fig. 1).

However, the development of specific methods of

vibration diagnostics of complex mechanical assemblies,

based on traditional methods of statistical data analysis,

causes considerable difficulties. This is due to the need to

take into account a large number of factors, the accumulation

of a considerable volume of statistical data and, as a result,

high material costs. For helicopters, the accumulation of a

considerable volume of statistical data is difficult, due to the

high flight costs and the impossibility of flight with faulty

mechanical components. Therefore, currently the combined

techniques using artificial intelligence technologies (artificial

neural networks, fuzzy logic, expert systems, genetic

algorithms, etc.) [19-20] are becoming more common,



712

improving the accuracy of diagnosis results in uncertainty at

small amounts of experimental data and the heterogeneity of the

initial information.

Figure 1. Vibration spectra of Mi-8 and Mi-24 helicopters in various TC and their

Components

Thus, using modern methods of non-destructive testing and

intelligent components, the system of automated vibration

diagnostics of the Mi-8 helicopter basic components was

developed. No analogues of this system exist in the CIS

countries, or they are under development.

RESULTS AND DISCUSSION

The functional scheme of a developed onboard system of

vibration diagnostics of the helicopter mechanical

components is shown in Fig. 2.

Hz

Hz

defect

defect

defect

b) a)

Vib

rati

on

acc

eler

atio

n,

mm

/s2

Hz

Vib

rati

on

acc

eler

atio

n,

mm

/s2

c)

Vib

rati

on a

ccel

erat

ion,

mm

/s2

d)

Vib

rati

on a

ccel

erat

ion,

mm

/s2

No defect

Mi-8

Mi-24

MR imbalance in

tolerance

Oz axis

Oz axis

Oy axis Oy axis

Mi-8

Mi-24

No defect No defect

Hz

a − CR blade defect; b – MR imbalance without tolerance; c – CR gear shaft defect; d – CR intermediate gear shaft

transmission defect



713

Figure 2. Functional diagram of the on-board system of vibration diagnostics of the helicopter mechanical components

Depending on the values of control conditions (the height and

speed of flight, balance characteristics and weight of the

helicopter, the place of the vibration sensor installation) – CC and

control modes ("Earth", "Air") – CM, there are formed [2,4]:

− vector of signals received from the regular control sensors

(oil temperature in the main and tail gearbox, oil pressure

in the main gearbox and the discrete signal "Chips in the

oil of main gearbox") SY ;

− vector of reference values of diagnostic features

(hereinafter DF) REFY ;

− vector of helicopter vibration signals in the time domain

tY .

The RMS values (hereinafter – RMS) of the amplitudes of the

harmonic components of the helicopter vibration acceleration at

the rotor speeds were used as the informative DF of the

propellers. As the DF, characterizing the TC of the helicopter

main gearbox, the RMS of harmonic vibration acceleration

components, calculated at the tooth rotation speeds of the

transmission of its drives, were used [3, 6].

The helicopter vibration was measured in three mutually

perpendicular axes. Oxyz – the coordinate system is rigidly

"connected" with the helicopter structure. The origin of

coordinates lies in the center of the helicopter masses, the

longitudinal Ox axis is directed along the fuselage

construction axis in the direction of the flight. The Oy axis is

located in the symmetry plane and is directed to the top of the

helicopter. The Oz axis is perpendicular to the plane of

symmetry of the helicopter in the direction of its starboard

side.

When recording the helicopter vibration signal, the speed of

the power plant turbine (hereinafter – PP) cannot be

stationary due to external and internal influences.

As can be seen from Fig.3, in case of the PP turbine speed

unsteadiness, the correct calculation of the DF on the range

of helicopter vibration is practically impossible [7].

Thus, to obtain a definite diagnosis of theTC of the helicopter

mechanical components using its vibration signals, it is

necessary to carry out the vibration signal steady-state

analysis.

Helicopter

vibration measurement

system

Helicopter

main

mechanical

components

Subsystem of analysis

of stationarity

of vibration

signal

Mathematical dependencies of

DF reference values

on the control conditions

and modes

Preprocessing

subsystem

DF calculation

and their scaling

subsystem

Fuzzy

relation

table

Output

mechanism

Neural

network classifier

Initial information processing system

x

tY

SY REFY

REFy

*

YM

*

Ky1y qq

Reco

gn

ition

system

CM

y

tY z

tY

x

tYy

tY z

tY

C CM

z

f

y

f

x

f YYY ,,

CC

User



714

a − the turbine speed falls; b − the turbine speed is constant

Figure 3. The low-frequency spectrum of Mi-8 vibration acceleration

The pretreatment subsystem preprocesses provisional

vibration signals measured in three mutually perpendicular axes

of the helicopter, by performing their spectral transformation [9].

The signals obtained

z

f

y

f

x

f YYY ,, are transferred to

the DF calculation and scaling subsystem. A fragment of

informative frequencies of the vibration spectrum of the Mi-8

helicopter is presented in Table 1.

Table 1. Fragment of informative frequencies of the Mi-8 helicopter vibration spectrum

The power frame, located in the cargo compartment under the

main gear of the helicopter in the area of the helicopter mass

center, was used as the installation location of the piezoelectric

vibration sensor (Fig.4) [8].

Figure 4. Location of installation of the piezoelectric vibration sensor on the Mi-8 helicopter

Transmission

drive to

Tooth

rotation

speed, Hz

Transmission

drive to

Tooth rotation

speed, Hz

Rotor

type

MR and CR rotation

speeds during engine

speed of 95%, Hz

CR 1,339.5 pumps 1,898 MR 3.14

3rd pass of gearing 100 oil pump unit 2,318 CR 18.4

fan 3,350 compressor 3,397

Vibration sensor

Vibration

diagnostics

equipment

Vibration sensor

a

)

Vib

rati

on

acc

eler

atio

n, m

m/s

2

Hz

1st harmonical

components of the

CR rotation speed

b)

Vib

rati

on

acc

eler

atio

n, m

m/s

2

a)

Hz



715

The selection of the vibration sensor installation location was due

to highly informational value of the vibration signal, ease of

mounting and safety of installation, as well as minimizing the

impact of resonance phenomena of the helicopter fuselage

shell (Figure 5) [11].

Figure 5. The low-frequency spectrum of the Mi-8 vibration acceleration during the vibration sensor installation

The main elements of the vector of DF reference values are

calculated using: mathematical models of steady low-frequency

vibrations of the helicopter excited by variable forces and

moments acting from the MR and CR, the results of simulation-

factorial experiment and statistical processing of vibration

measurements of the fleet of helicopters of the same type.

The block diagram of a mathematical model of steady

low-frequency vibrations of the helicopter excited by variable

forces and moments acting from the MR is shown in Fig.6

[10].

a – on the power frame, in the area of the helicopter c.m.; b – on helicopter shell

b)

a)

Ox

Oy

Oz

Vib

rati

on

acc

eler

atio

n, m

m/s

2

Ox Oy

Oz

Vib

rati

on a

ccel

erat

ion, m

m/s

2

Hz

Hz

10 40 80

10 40 80

0

0



716

Figure 6. Block diagram of a mathematical model of steady low-frequency vibrations of the helicopter

In Fig. 6: T ,

S , H – variables from the azimuthal

position of force generated by the MR;

XM ,

ZM – variables

from the azimuthal position longitudinal and transverse moment,

created for MR hubs due to separation of flapping hinges

(hereinafter – FH); xI , zI – the helicopter moments of inertia

on the respective axes; – MR rigging angle; hm – helicopter

flight weight; MR MR MR MR MR, , , , x y z x zV V V linear

and angular vibrations of the helicopter; DY , Тx – vertical and

longitudinal center of gravity position of the helicopter; MD –

the gear ratio between the angle of MR cone axis deviation and

the angle of deviation of the swash plate (hereinafter – SP); , –

balancing angles of SP deviation in the transverse and

longitudinal plane; efy – efficient vertical alignment, taking into

account the effect of separation of the FH; GA helicopter

gliding angle; flapping angle;

)(1 Daa MR attack angle:

helicopter pitch attitude; SP additional balancing

deviation angle in the longitudinal plane from GA ; FHL

stagger of MR FH; MR MR rotational speed; bm

blade weight; 1, , bi k (where 5bk number of

MR blades); K0, (where 20K the number of

estimated azimuths); 1 average part of dimensionless

induced velocity; – blade swirl angle; ck – blade pitch-

flap coupling; V,Н – speed and altitude of helicopter

Calculation of

AI rotor angles

and helicopter

parameters

Calculation of

the blade

cross section

velocity of

streaming

Calculation of

the blade

section angle

Calculation

of forces in

the blade

section

Calculation of

the blade step

in section

Calculation of

the blade

angle of

deviation

relative to VH

Calculation of

the lifting

strength and

the blade drag

force

Calculation of

the lifting

strength and

the blade drag

force

Calculation of

aerodynamic and

inertial moments of

blades relative to

FH

Calculation of

the blade

total forces

and moments

Calculation of the parameters of the

helicopter vibrations from the MR:

⍵𝑿𝑴𝑹 =

𝟏

𝑳𝑿((𝑺ᴪ + 𝑻𝑫M𝜼)𝒚𝒆𝒇 − 𝑴𝑿

ᴪ) ;

⍵𝑿𝑴𝑹 =

𝟏

𝑳𝒁(

𝑴𝒁ᴪ + 𝑻ᴪ𝒄𝒐𝒔𝜺𝒙𝑻 +

+(𝑯ᴪ + 𝑻ᴪ𝑫M𝝌)𝒄𝒐𝒔𝜺𝒚𝒆𝒇

) ;

𝑽𝑿𝑴𝑹 = −

𝟏

𝒎𝒉((𝑯ᴪ + 𝑻ᴪ𝑫M𝝌) 𝐜𝐨𝐬 𝜺)

+ ⍵𝑿MR𝒀𝑫;

𝑽𝒀𝑴𝑹 =

𝟏

𝒎𝒉𝑻ᴪ 𝐜𝐨𝐬 𝜺

𝑽𝑿𝑴𝑹 = −

𝟏

𝒎𝒉

(𝑺ᴪ + 𝑻ᴪ𝑫M𝜼) + ⍵𝑿𝑴𝑹𝒀𝑫;

Calculation of

the MR total

forces and

moments

𝛽𝐺𝐴 𝑉 𝑚ℎ

𝑌CR

𝜀

𝝌 𝜼

𝛼MR

𝐿𝐹𝐻 𝛽𝒊𝝍

𝜈1 𝛽𝒊𝝍

𝑈𝒙𝒓𝒊𝝍

𝜑𝒓𝒊𝝍

𝑈𝒚𝒓𝒊𝝍

𝑈𝒚𝒓𝒊𝝍

𝛽𝒊𝝍

𝑈𝒙𝒓𝒊𝝍

𝛼𝒓𝒊𝝍

𝑇𝑨𝒓𝒊𝝍

𝑄𝑨𝒓𝒊𝝍

𝑇𝑨𝒋𝝍

𝑄𝑨𝒊𝝍

𝑚𝑖

𝑚ℎ

𝐻

V

𝛽𝒊𝝍

𝑚𝑖

𝑘𝑐𝑖

𝛥𝜑 𝛽𝒊𝝍

𝜑𝛰𝑖 ⍵MR 𝐿FH

𝜉𝒊𝝍

⍵MR

𝛽𝒊𝝍

𝛽𝒊𝝍

𝑇𝝍

𝐻𝑱𝒊𝝍

𝑆𝑱𝒊𝝍

𝐻𝑨𝒊𝝍

𝑆𝑨𝒊𝝍

𝛽𝒊𝝍

𝐿𝐹𝐻 𝑇𝑱𝒊𝝍

𝑆𝒊𝝍

𝐻𝒊𝝍

𝑀𝒛𝒊𝝍

𝑀𝒙𝒊𝝍

𝑆𝝍

𝐻𝝍

𝑀𝒛𝝍

𝑀𝒙𝝍

𝑀𝒛𝑱𝒊𝝍

𝑀𝒙𝑱𝒊𝝍

𝑀𝒛𝑨𝒊𝝍

⍵MR



717

flight; 0 MR blade angle of incidence at the butt; ξ angle of

rotation of the blades relative to VH [12,16].

As a result of the calculation the variable linear and angular

accelerations of the helicopter vibrations are determined by

azimuth, and can be represented as a Fourier series with up to

five members (Fig.7). Methods of calculating the total forces

and moments from the MR are presented in papers [13-15].

a field measurement; b mathematical model

Figure 7. The values of the amplitudes of the Mi-8 fuselage vibrations harmonic at frequencies that are multiples of the

MR rotation frequency

The mathematical dependence of DF values of MR

characteristic on the control conditions obtained using

mathematical model (see Fig.6), the results of simulation-factorial

experiment and statistical processing of vibration measurements

of fleet of helicopters of the same type, have the

following form:

− for "Air" regime:

MR

0 1 h 2 3 4 MR 5 h 6 h 7 h MR

8 9 MR 10 MR

y a a m a V a Н a n a m V a m Н a m n

a НV a n V a n Н

(1)

− for "Earth" regime:

0 1 h 2 os 3 MRrefy a a m a a n , (2)

where

MRMR MR

maxy y y – the value of the MR DF

in relative units under given control conditions; MRy ,

MR

maxy –

the MR DF value under given control conditions and its

maximum value.

As a result of calculation of current DF values

and their scaling using the mathematical dependencies,

for example (1-2), the synthesis DF vector is formed at

the subsystem output – refy , which arrives at the input

of a neural network classifier (hereinafter – NNC). NNC

by the formula (3) provides for the detection of a

reference DF vector in a table of fuzzy relationship by

the observed vector elements refy .

n harmonic number

1 2 3 4 5 n

5A

1A the amplitude of the

first harmonic component

of MR vibration

0

0

.

1

5

0

.

4

5

0

.

7

5

1A

5A

a)

mm/s2

Hz

b)

А1

А5

A

A

A



718

Table 2. Fragment of fuzzy relation table

Values of the elements

of the reference DF vector

TC class number

1refy …

refNy 1 2 … K

1 1 … 0 11y 21y … Ky1

… … … … … … … …

q 0 … 0 1qy 2qy … Ky

q

Table 2 shows: Kyq degree of accessory of the

reference DP vector with the q number to the K-th class of TC of

the diagnostic object (possesses the value from 0 to 1,by

processing information obtained from the experts, K,s 1 ,

where K is the number of specified TC classes); N,i 1 ,

where N is the amount of elements in DF vector; q,1 ,

where q is the number of reference DF vectors.

Using the LevenbergMarquard (3) learning algorithm

the NNC training was reduced to minimization of functionality of

type:

add

M

i

eM

e 1

*1 , (3)

where M,i 1 ( M − the total number of TC

component classes in the training set); * − the value of the

number of the DF reference vector in a fuzzy relation table

recognized by the observed signals of the helicopter vibration and

signals from regular control systems; − the number of the

reference vector in a DF fuzzy relations table.

Studies have shown that the effectiveness of the neural

network as a classifier of TC of mechanical units in a helicopter

under the conditions of noise of input information if about 30%

higher compared to "classical" methods of classifying (clustering)

(Fig.8).

Figure 8. The probability of correct classification of TC of

the basic mechanical components of a helicopter using

different methods of additive component of the noise

measurement

Using the NNC output signal:

− the expression (4) is used to calculate the degree

of membership of the observed DF vector to the -th number

of the reference DF vector indicated in the table of fuzzy

relations:

2*

e*;

(4)

− in the output mechanism the information

obtained is defuzzificated using the formula(5):

KyyM qqY ** ,,1max

, (5)

where Kyq is the degree of membership

of the -th of the reference DF vector to the K-th class of TC

of the diagnosable component; YM − information in

numerical form on the TC of the diagnosable component (the

a INC of forward propagation of signal and back

propagation of error; b K-means algorithm; c

discriminant functions

kP



719

maximum value of a set of values of products of arguments). For

example, the drive of the oil pump unit of the gearbox is defective

with probability of0.8.

Conclusion Thus, in the course of the research, there was developed a system

of automated vibration diagnostics of the main helicopter

mechanical components. Software implementation of the

developed system, is embedded in a production equipment used in

the Air Force and air defense establishments in the form of

methodical software that implements a system of vibration

diagnostics of basic mechanical units of the Mi-8 helicopter [17].

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