Diagnostics of working machine hydraulic systems

TOMASZ KAŁACZYēSKI UTP WIM POiG Bydgoszcz PWSZ Piła

Summary

In the study there were introduced elements of methodology for working ma-chine system diagnosing, containing selected and preferred methods for determina-tion of hydraulic system state set and diagnostic parameters, defining of observadetermina-tion matrix and determination of the diagnostic test for state control and defect localiza-tion. Diagnostic examinations using it, in order to get reliable diagnostic informa-tion should be based on fulfilling unequivocally determined condiinforma-tions referring to personnel realizing the research, its range, equipment and research station.

The methodology proposed here can contribute in searching new forms and methods for machine hydraulic system diagnosing as well as diagnosing system de-velopment.

Keywords: Diagnosing of hydraulic systems, status features and diagnostic parameters, diagnostic test

1. Introduction

Diagnosing working machine hydraulic systems covers their construction, manufacturing, quality and exploitation. This activity should be performed according to procedures contained in diagnostic methodology. Taking into account theoretical foundations of technical diagnostics and exploitation pragmatics, it can be assumed that diagnosis methodology of hydraulic systems should take into account the definition of system state set and diagnosis parameters, as well as parameter dependence on a state, and setting a diagnostic test for state control and defect localiza-tion.

2. Definition of system state set

Assuming that an object technical state depends on the state of its elements, the definition of its technical state is possible when functions performed by these elements and relations between them are known. Then, a working machine hydraulic system structure can be presented as a graph:

>

=<

X

W

P

G

,

,

₍₁₎

where: X – set of functional elements of a system,

W – set of structural and functional relations between system elements, P – predicate expressing interactions between the elements.

The analysis of hydraulic system state problems resulting from the analysis of bibliography, as well as from own research results concerning reasons for defectiveness and system diagnostic susceptibility, indicates that among known methods for state set definition such as: system work

safety associated with machine exploitation lifetime, weak link and element defect probability, it is rational to assume the safety method.

The machine work safety method consists in using machine element wear course character in different exploitation periods, in which different wearing processes take place. The course of wearing of sets during exploitation depends on which of the wearing processes is dominant. Thus, for all the sets of working machine hydraulic system where sliding friction exists there are usually three periods of wearing (introductory ageing, normal wearing period, accelerated wearing period) affecting machine work safety.

The work safety method associated with machine exploitation phases consists in using ma-chine work safety criterion setting apart mama-chine defects which cause a change of work parameters e.g. lifting capacity, work movement acceleration, work movement delay, influencing machine work safety. Such differentiated states cover defects which do not allow to use the working ma-chine hydraulic system according to its designation; they are danger to work safety for people and environment and should be a basis for sending the system to repair. If a working machine system set state W(tn) at a time moment tn can be characterized with a diagnostics parameter value set {yj(t); j=1,2,...,m}, then the hydraulic system at time tn is in an ability state W 0, when the follow-ing condition is fulfilled:

W(tn ) = W 0⇔ ∀ (j=1,..., m) [{yj,d} ≤ {yj (tn)} ≤ {yj,g}] (2)

where: {yj,d}, {yj,g} – sets of lower and upper limit values for diagnostic parameters.

Referring the above expression to machine lifetime curve (Fig. 1), you can formulate a dependence linking a machine lifetime tn with its:

ƒ ability state W0_,

ƒ inability state without a threat to machine work safety operation W1_,

ƒ inability state with a threat to machine work safety operation W11.

Fig. 1. Characteristics of set wear in a working machine hydraulic system EXPLOITATION PERIOD Ability state Exploitation time Inability state t1 t2 t3 Zgr tgr Wear of element t/

Then respectively: For time t1:

W(t1 ) = W 0⇔ ∀ (j=1,..., m) [{yj,d} ≤ {yj (t1)} ≤ {yj,g}] (3)

For time t2:

W(t2 ) = W 1⇔ ∀ (j=1,..., m) [{yj,d} ≤ {yj (t2)} ≤ {yj,g}] (4.15) (4)

In case of a hydraulic system, for time t2 it is possible to set aside example states W1, which

do not present a threat to machine exploitation safety. They are, for example, insignificant exploi-tation wear of hydraulic pressing pumps, oil container deformations, insignificant exploiexploi-tation wear of a metal surface of hydraulic separators.

In case of time t3:

W(t3 ) = W 11⇔ ∀ (j=1,..., m) [{yj,d} ≥ {yj (t3)} ≥ {yj,g}] (5) where set W11 _{can, for example, contain such states as a defect of hydraulic pressing pumps}

(excessive wear of working area sealing), pressure regulator defect (e.g. spring break, defect of valve faying faces, defect of regulating screws), defects of piston rods (significant scratches of outer piston rod surface, shape change i.e. bucklings).

3. Definition of a system diagnostic parameter set

Machine structure parameters

W

are variable values changing in time

W

= W

( )

Θ

and in exploitation period they depend on the processes forcing the machine ageing. The technical state of a hydraulic system depends on the values of structure parameters and it is determined by them.

Basing on analyses found in literature and on own research, it was established that diagnostic parameters reflecting a machine technical state depend on the change of structure parameters and exploitation time of a working machine hydraulic system.

Y

= W

f

(

(

Θ

))

(6)

Y

= g

(

Θ

)

(7) Assuming additionally a stationary character of diagnostic parameter values, we can, basing on the observation of machine parameter diagnostic values in time

ϑ

_i

∈

ϑ

, conclude about parameter values in the whole time range.

A set of diagnostic parameters Y differentiates from output parameter set YWY, which

de-scribes the course of output processes (work and associated processes), depending on the technical state of a hydraulic system. Mutual relation of structure parameters W and output parameters allows (while fulfilling below given conditions) to treat output parameters

y

_wyj

∈

Y

_WY provision-ally as diagnostic parameters and define measurement points in a working machine hydraulic system. These conditions are as follow:

1. Unequivocality condition – each value of structure parameter value

w

_i

∈

W

corresponds to only one determined value of output parameter

_y

_wyj

_∈

_Y

_WY.

2. Field width change condition – the biggest relative change of an output parameter

WY

wyj

Y

y

∈

for an assumed structure parameter value

w

_i

∈

W

.

3. Output parameter measurement availability condition – is characterized by measurement cost indicator cj or measurement time tj, and these indicators have to be minimized.

Fulfilling the above-introduced conditions

1

∧

2

∧

3

lets us introductorily discriminate a set

Y

from set

Y

_WY. More precise discrimination of a set

Y

⊂

Y

_WY is possible using many methods: minimum diagnosis error, information capacity, correlation with the technical condition and a preferred method: diagnostic parameter value similarity method.

Diagnostic parameter value similarity method consists in checking the diagnostic parame-ter assignment correctness to particular classes of hydraulic system states [49]. It uses a relationship saying that a matrix of a total sum of observation deviation squares from observation weight centre

T

is a total sum of deviation squares

W

from inter-class averages and a total sum of inter-class deviation from global average

B

. A classification algorithm for diagnostic parame-ter value observation was presented in Fig. 2.

In this method, general or total variance function decreasing velocity is examined, calculated on the basis of

W

. The end of the classification process, i.e. assignment of particular observations to classes, follows reaching the minimum value for the global criterion. As a result of this method implementation, we obtain respectively diagnostic parameter sets for state control test

D

_KS or for defect localization test DLU.

Calculation of global criterion value Kglob.:

¦ ¦

= ∈ = K i x C ji glob i j

d

K 1 2 .

End of the classification process when a global criterion value reaches the minimum. Definition of a class number and calculation of matrices W and B:

T j i K j x C j i x x x x W i i ¸ ¹ · ¨ © § − ¸ ¹ · ¨ © § − =

¦ ¦

= ∈ _ 1 _ T j j K j j x x x x n B ¸ ¹ · ¨ © § − ¸ ¹ · ¨ © § − =

¦

= _ _ 1

where nj is a number of observations in class j designated as Cj.

Introductory assignment of observations to K number of classes.

Definition of a distance measurement method (Euclidean distance method).

Calculation of class characteristics: • Average vector xi _; • Co-variance matrix Si

Calculation of modified reversed matrix to covariance matrix:

¦

− − = 1 1 ) det( i

S

i m Si

Modification was introduced to avoid one-point classes.

Calculation of a square of observation distance

from an average vector in each class basing on the calculated characteristics

n j dla x x x x _i j i T i j ji

d

2 _ 1 _¸ ₌1,2...,3 ¹ · ¨ © § − ¸ ¹ · ¨ © § − =

¦

−

Assignment of observation xj to a different from previous class Ci while satisfying the condition:

d

d

ji jl 2

min

2 =

4. Definition of a relation in diagnostics

Relations between diagnostic parameters and state features are, as a rule, stochastic relations. These relations in machine diagnostic practice can be defined by Boolean observation matrix and preferred observation matrix according to relation: diagnostic parameter – working machine exploitation time.

Observation method for the relation: parameter – exploitation time consists in defining observation matrix for different values of time tn at which defects of the hydraulic system occur

(referring to selected levels of system decomposition), changing diagnostic parameter values which affect machine work safety. So defined observation matrix can be a base to designate a test of state control and defect localization, definition of hydraulic system defect intensity and designa-tion of time for machine exploitadesigna-tion deadline. Limiting values of diagnostic parameters are established to fulfil producer’s demands, and they have their relation to the time of machine fitness for use. N j 2 1, y , , y, , y y 11 3 1 2 1 1 2 0 1  







»

»

»

»

»

»

»

»

»

¼

º

«

«

«

«

«

«

«

«

«

¬

ª

→

→

→

→

=

s

t

s

t

s

t

s

t

M

d _i b (8)

Such a shape of observation matrix seems to be especially useful in the research of a relation state – diagnostic parameter in case of a passive experiment event, which often takes place in case of working machines.

5. Diagnostic tests for state control and defect localization

Basing on the analyses of research possibility for diagnostic parameter relation to hydraulic system state, it is believed that for designation methods the most interesting are methods of desig-nation of state control tests and for defect localization which use Boolean observation matrix and parameter – working machine exploitation time observation matrix. One of them is a method of state classification.

Hydraulic system state classification method consists in a principle that as a result of de-termination of diagnostic parameter set with diagnostic parameter – exploitation time relation observation method, we obtain relation pairs: diagnostic parameter set {

y

_j}– suitability set S0_,

diagnostic parameter set {

y

_j}– inability states Si,

j

=

1

,

m

,

i

=

1

,

k

, which let us use the

diagnostic parameter set {yj} (in a special event it is a single element set) for the designation of test KS

D

:

D

_KS

=

{ }

y

_j (9)

D

KS

=

{ }

d

j (10) where: dj – checking of yj parameter value.

In case of determining the elements of tests

D

_LU , as a result of state classification method re-alization (state pair subsets Sl, Si;

l

=

1

,

k

;

i

=

1,

k

;i≠l), we obtain a diagnostic parameter set {yj}

for the determination of test

D

_LU . Then, test

D

_LUtakes the following shape:

D

LU

=

{ }

y

j (11)

D

LU

=

{ }

d

j (12) An alternative to these procedures for determining state control and defect location test is us-ing a check vector, defined on the basis of Boolean matrix

Y

=

{

y

_n

};

n

=

1

,

N

. Then, e.g. test DLU takes shape:

DLU = < y1, …, yn > = < 1, …, 0 > – state Si – defect of set i of this working machine

hydraulic system set

Recapitulating the presented considerations referring to the methods of determining diagnostic tests, there is a need to say that on account of preference of the similarity method in diagnostic method choice and the way of examination of the diagnostic parameter – state relation, the state classification method is optimal.

6. Conclusion

The study introduced elements of methodology for working machine system diagnosing, con-taining selected and preferred methods of determination of hydraulic system state set and diagnos-tic parameters defining an observation matrix and determination of a diagnosdiagnos-tic test for state control and defect localization. Diagnostic examinations, in order to get reliable diagnostic infor-mation, should be based on fulfilling unequivocally determined conditions referring to the person-nel conducting the research, its range, equipment and research station. The methodology proposed here can contribute to searching new forms and methods for machine hydraulic system diagnosis, as well as diagnosing system development.

Bibliography

1. NiziĔski S., Michalski R.: Diagnostyka obiektów technicznych.(The Diagnostics of Techni-cal Objects). Wydawnictwo i Zakład Poligrafii Instytutu Technologii Eksploatacji, Radom 2002

2. Surówka L.: Identyfikacja modelu diagnostycznego układów hydraulicznych.(The Identifi-cation of Hydraulic System Diagnostic Model). Mechanika, Wydawnictwo ATR, Bydgoszcz 2001

3. Surówka L.: Badanie stanu technicznego układu hydraulicznego maszyny roboczej. (The Examination of Hydraulic System Technical State of Working Machine). Ph.D Thesis, Akademia Techniczno – Rolnicza, Bydgoszcz 2005.

4. Tylicki H.: Optymalizacja procesu prognozowania stanu technicznego pojazdów mecha-nicznych.(The Optimization of Prognosis Process for Technical State of Mechanic Vehic-les) Wydawnictwa Uczelniane ATR w Bydgoszczy, Bydgoszcz.1998

5. ĩółtowski B.: Podstawy diagnostyki maszyn.(The Foundations of Machine Diagnostics). Wydawnictwo ATR w Bydgoszczy, Bydgoszcz 1996.

DIAGNOZOWANIE UKŁADÓW HYDRAULICZNYCH MASZYN ROBOCZYCH Streszczenie

Diagnozowanie układów hydraulicznych maszyn roboczych powinno byü reali-zowane według procedur w zawartych w metodyce diagnozowania. UwzglĊdniając podstawy teoretyczne diagnostyki technicznej oraz pragmatykĊ eksploatacyjną w tym wzglĊdzie, w artykule opisano wybrane metody okreĞlania zbiorów stanów układów hydraulicznych oraz metody okreĞlania parametrów diagnostycznych. Opisano rów-nieĪ wybrane metody okreĞlenia relacji: parametr diagnostyczny – stan techniczny oraz wyznaczenia testu diagnostycznego kontroli stanu i lokalizacji uszkodzeĔ układu hydraulicznego.

Słowa kluczowe: diagnozowanie, stany i parametry diagnostyczne układów hydraulicznych oraz ich relacje, testy diagnostyczne

*This paper is a part of WND-POIG.01.03.01-00-212/09 project.

Leszek Surówka Tomasz KałaczyĔski UTP WIM POiG Bydgoszcz PWSZ Piła