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Maritime University of Szczecin

Akademia Morska w Szczecinie

2012, 32(104) z. 1 pp. 81–90 2012, 32(104) z. 1 s. 81–90

The concept of on-board diagnostic system of working

machine hydraulic system

Leszek Surówka

Stanisław Staszic State School of Higher Vocational Education in Piła, Politechnic Institute 64-920 Piła, ul. Podchorążych 10, e-mail: Leszeksurowka@interia.pl

Key words: machine hydraulic systems and their diagnosing, concept of on-board diagnostic system

of working machine hydraulic system

Abstract

In the study a characteristic of working machine hydraulic systems, selected issues of basic methodology of their diagnosing and a concept of an on-board diagnostic system for their condition evaluation were introduced.

Introduction

Diagnosing of working machine hydraulic sys-tems covers their construction, manufacturing qual-ity and exploitation. This activqual-ity should be realized according to procedures contained in diagnostic methodology. Taking into account theoretical foun-dations of technical diagnostics and exploitation pragmatics it can be assumed that diagnosis meth-odology of hydraulic systems should take into ac-count definition of system states set and diagnosis parameters, as well as parameters dependence on a state, and setting a diagnostic test for state control and defect localization.

Characteristics of working machine hydraulic system

Assuming some simplifications it can define designation of working machines hydraulic systems as:

– driving of parts of working units and subunits; – controlling and control supporting of machine

units and subunits;

– greasing of machine cooperating parts; – cooling of machine parts;

– cleaning of machine parts from products of ma-chine aging;

– limiting of degrading atmosphere influence (for example oxidation) on machine elements.

In working machine hydraulic systems it can distinguish the following functional subsystem: – supply;

– control; – realizing;

– diagnostic equipment.

Considering the above the general schedule of hydraulic system in construction and task concept is shown in figure 1.

Functioning of working machine hydraulic sys-tems consists in cooperation of their blocks, which results in continuous transformation of consumed energy (with disturbances) to assumed effects and associating residual processes. The final effect is movement of machine executive element. The residual processed constitute a set of products gen-erated during exploitation of hydraulic system which are not the goal of their action. The physical and chemical processes happening in hydraulic systems during their exploitation are associated with machine functioning and aging processes of their parts, as well as working liquid.

During many analyses results it can distinguish phenomena being sources of emission of many diagnostic signals. Example diagnostic parameters in hydraulic systems assigned to physical and chemical phenomena are shown in table 1.

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Definition of system states set

Assuming that an object technical state depends on its elements state, definition of its technical state is possible when functions realized by these ele-ments 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 system functional elements;

W – set of structural and functional relations between system elements;

P – predicate expressing interactions between the elements.

The analysis of hydraulic system state choice problem, resulting from analysis of bibliography, as well as from own research results concerning reasons for defectiveness and system diagnostic susceptibility indicates, that among the 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 of machine element wear course character in different exploitation periods in which different wearing processes take place. The course of wear-ing of sets durwear-ing exploitation depends on which of the wearing processes is dominant. Thus, for all 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) affect-ing machine work safety.

The work safety method associated with ma-chine exploitation phases consists in using mama-chine

Diagnostic equipment H Y D R A U L I C S Y S T E M Supply Block • oil containers, • filters, • pumps, • hydraulic accumulators, • regulators of pressure and flow, • heaters and coolers,

• safety valves, • intensifiers,

• cables and connectors.

Control Block

• levers, pull rods etc. (mechanic link units); • hydraulic separator; • valves;

• switches, controllers and electric installation;

• micro-processing control compo-nents;

• cables and connectors (hydraulic, electric, pneumatic)

Executive Block

• servo-motors; • amplifiers; • motors;

• cables and connectors.

Driving support system and suspension Engine Mechanical system of driving transfer Executive system Control system Diagnostic Equipment WORKING MACHINE

Fig. 1. Schematic structure of working machine hydraulic system Table 1. Phenomena and signals in hydraulic systems

Item Phenomenon Example diagnostic parameters 1 Part movement Velocity, acceleration, time, range (distance, angle). 2 Working part labour Amount of energy consumed at time, lifting force, deformation

parameters of elements.

3 Vibrations of parts Amplitude, frequency, time, (param-eters of vibrating and acoustic effects).

4 Friction Temperature, surface wear parame-ters, movement parameters. 5 Working fluid flow

Pressure, flow intensity, tempera-ture, working elements movement parameters.

6 Electric current flow Voltage, intensity, resistance. 7 Working fluid properties change Viscosity, water content, kind and amount of fixed pollution.

8 Environment influence

Measurements od corrosive wear (for example depth of corrosion penetration, surface), depth and surface of breaks in rubber parts.

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work safety criterion setting apart these machine defects which cause change in work parameters, e.g. lifting capacity, work movement acceleration, work movement delay, influencing machine work safety. Such differentiated states cover defects which do not let use the working machine hydraulic system according to designation, they are danger to work safety for people and environments and should be 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

hy-draulic system at time tn is in ability state W 0, when

the following condition is fulfilled:

 

 

 

  

jd j n jg

n y t y y m j W t W , , 0 1, ,        (2)

where: {yj,d}, {yj,g} – sets of lower and upper limit

values for diagnostic parameters.

Referring the above expression to machine life-time curve (Fig. 2) it can formulate a dependence linking a machine lifetime tn with its:

– ability state W0;

– inability state without threat to machine work safety operation W 1;

– inability state with threat to machine work safety operation W 11. Then respectively: For time t1:

 

 

 

  

yjd yj t yjg

m j W t W , 1 , 0 1 1, ,        (3) For time t2:

 

 

 

  

yjd yj t yjg

m j W t W , 2 , 1 2 1, ,        (4)

In case of a hydraulic system for time t2, it is

possible to set aside example states W 1, which do

not present threat to machine exploitation safety. They are for example insignificant exploitation wears of hydraulic pressing pumps, oil container deformations, insignificant exploitation wears of a metal surface of hydraulic separators.

In case of time t3:

 

 

 

  

yjd yj t yjg

m j W t W , 3 , 11 3 1, ,        (5)

where set W 11 can for example contain such states

as defect of hydraulic pressing pumps (excessive wear of working area sealing), pressure regulator defect (e.g. spring breaks, defect of valve faying faces, defect of regulating screws), defects of piston rods (significant scratches of outer piston rod sur-face, shape change, i.e. bucklings).

Definition of system diagnostic parameters set

Machine structure parameters W are variable values changing in time W = W() and in exploita-tion period they depend on processes forcing the machine ageing. The technical state of a hydraulic system depends on values of structure parameters and its determined by them.

Basing on analyses found in literature and on own research, it was established that diagnostic

Fig. 2. Characteristics of a set wear in a working machine hydraulic system

EXPLOITATION PERIOD III II I Exploitation time t1 t2 t3 Zgr tgr Wear of element

Ability state Inability state

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parameters reflecting a machine technical state, depend on change of structure parameters and exploitation time of working machine hydraulic system. )) ( (   Wf Y (6) ) (  g Y (7)

Assuming additionally a stationary character of diagnostic parameter values it can, basing on observation of machine parameter diagnostic values in time i  , conclude about parameter values in

the whole time range.

The set of diagnostic parameters Y differentiates from output parameter set YWY, which describes the

course of output processes (work and associated processes), depending on technical state of the hy-draulic system. Mutual relation of structure parame-ters W and output parameparame-ters lets (while fulfilling below given conditions) treat output parameters ywyj  YWY provisionally as diagnostic parameters

and define measurement points in working machine hydraulic system. These conditions are as follow:

Unequivocality condition – each value of struc-ture parameter value wi  W corresponds to only

one determined value of output parameter ywyj  YWY.

Field width change condition – the biggest relative change of output parameter ywyj  YWY

for assumed structure parameter value wi  W.

Output parameter measurement availability condition – is characterized by measurement cost indicator cj or measurement time tj, and these

indi-cators have to be minimized.

Fulfilling the above introduced conditions 1  2  3 lets us introductory discriminate a set Y from set YWY. More precise discrimination of a set

Y  YWY is possible using many methods: minimum

diagnosis error, information capacity, correlation with technical condition and preferred method: diagnostic parameter value similarity method.

The diagnostic parameter value similarity me-thod consists in checking of diagnostic parameter assignment correctness to particular classes of hydraulic system states [1, 2]. It uses a relation saying that a matrix of total sum of observation deviation squares from observation weight center T, is a total sum of deviation squares W from inter-class averages and total sum of inter-inter-class deviation from global average B. The classification algorithm for diagnostic parameter value observation was presented in figure 3.

In this method general or total variance function decrease velocity is examined, calculated basing on

W. The end of classification process, i.e. assign-ment of particular observations to classes follows reaching the minimum vale for the global criterion. As a result of method realization we obtain respec-tively diagnostic parameter sets for state control test DKS or for defect localization test DLU.

Calculation of global criterion value Kglob.:

 

   K i x C ji i j d K 1 2 glob.

End of classification process when global criterion value has reached the minimum.

STOP

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 



T j j K j j x x x x n B

  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 Si m Si

Modification was introduced to avoid one-point classes. Calculation of square of observation distance from aver-age vector in each class basing on calculated characteristics

x x

x x

j n d i j i T i j ji for 1,2...,3 1 2

Assignment of observation xjto a different from previous class Ci while satisfying a condition:

2 2 min jl ji d d  START

Fig. 3. Algorithm for diagnostic parameter value similarity method

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Definition of relation: diagnostics parameter – system technical state

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

Observation method for relation: parameter – exploitation time consists in defining of

observa-tion matrix for different values of time tn at which

defects of hydraulic system occur (referring to se-lected levels of system decomposition) changing diagnostic parameter values which affect machine work safety. Such defined observation matrix can be a base to designate a test of state control and defect localization, definition of hydraulic system defect intensity and designation of time for machine exploitation deadline. Limiting values of diagnostic parameters are established for machine state ful-filling producer’s demands and they have their rela-tion 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                                 s t s t s t s t Md i b (8)

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

Designation of diagnostic test for state control and system defect localization

Basing on 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 designation of state control tests and for defect localization which use Boolean observation matrix and parameter – work-ing machine exploitation time observation matrix. One of them is a method of state classification.

Hydraulic system state classification method consists in principle that as a result of determina-tion of diagnostic parameter set with diagnostic parameter – exploitation time relation observation

method we obtain relation pairs: diagnostic parame-ter set {yi} – suitability set S0, diagnostic parameter

set {yj} – inability states Si, j1,m, i1,k, which

let us use the diagnostic parameter set {yj} (in

spe-cial event it is single element set) for designation of test DKS:

 

yj

DKS (9)

 

dj

D KS (10)

where: dj – checking of parameter yj value.

In case of determining of tests DLU elements as

a result of state classification method realization (state pair subsets Sl, Si; l1,k;i1,k; i  l)

we obtain a diagnostic parameter set {yj} for

deter-mination of test DLU. Then test DLU takes the

following shape:

 

yj

DLU (11)

 

dj

DLU  (12)

The alternative to these procedures for determin-ing of state control and defect location test is usdetermin-ing a check vector, defined from Boolean matrix

N n y

Y{ n}; 1, . Then, e.g. test DLU, will take

shape:

DLU = y1,…,yn = 1,…,0 – state Si – defect of set

i of this working machine hydraulic system set Recapitulating the presented considerations re-ferring to methods of determining diagnostic tests there is need to say that on account on preference in diagnostic method choice of similarity method and the way of examination for diagnostic parameter – state relation, the state classification method is optimal.

The concept of on-board diagnostic system

The researches of working machine hydraulic system state performed by the author using the above described research methodology showed, that it is possible to use the worked out diagnose procedures in the on-board diagnostic system of working machine system. The analysis showed that in the concept of on-board diagnostic system it must be taken in consideration a system description of hardware and software and showing possibility to use the concept in design, production and exploi-tation of working machine hydraulic system.

Resulting from performed work it was assumed that the concept of on-board hydraulics diagnosing system should cover issues from areas of design,

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production and exploitation of hydraulic systems of working machines. They are for example: function-al and construction features of machine hydraulic system, exploitation and service conditions, service back-up potential, economic calculation.

Concerning the results of tests performed it was stated that:

– construction of on-board working machine hydraulic system should use the analysis of pressure change of working liquid in the area of defined working movements;

– a complement of this should be parameters con-cerning: working liquid amount, working liquid temperature, pollution of working liquid filters, rotational speed of pump system driving shaft, moment of tilt of excavator chassis, tilt angle of the body.

It was assumed, that the on-board diagnostic system of working machine hydraulic system should ensure the control of condition and localisa-tion of its defects.

The idea of work of diagnostic system consists in inference about the status a hydraulic system basing on relations between measured values of pressure and reference values of logical structure (set of 0 and 1) of hydraulic system diagnostic ma-trix. For execution of basic functions of the system procedures of object programming are used.

The basic module of on-board diagnostic system is a knowledge base:

OBJECT, ATTRIBUTE (state feature) – VALUE The on-board diagnostic system of a working machine hydraulic system should include the fol-lowing variants of its work:

• usable – refers supervision of hydraulic system during its use;

• diagnostic and maintenance – covers diagnosing of hydraulic system blocks and realizing of its service according to designated service lives and system state;

• informative – refers creation of data base for exploitation history of hydraulic system ensur-ing:

– defining the defect types related to exploita-tion time (performed work – defined for ex-ample by amount of energy consumed by supply unit);

– setting exploitation alert times referred to ex-ploitation safety (first of all people and envi-ronment);

– informing the exploiter about reaching alert time of exploitation by hydraulic system (and state of direct threat for people and environ-ment safety);

– setting dates for next maintenance.

As a result of the above the on-board diagnostic system of a hydraulic system in particular variants of work should provide:

• continuous control of designated diagnostic parameters of hydraulic system blocks;

USE R S U BS YST E M S tart an d se lf -c on tr ol sy ste m Us er co ntro l s yste m

SUBSYSTEM OF DATA INPUT TO KNOWLEDGE BASE Limit parameter values Measurement system Inference rules Visualization system

Work safety supervision system

Machine control systems KNOWLEDGE BASE

Limit parameter

values Measured parameter values Inference

rules

Subsystem conclusions

Fig. 4. Diagram of configuration and operation of on-board diagnostic system of working machine hydraulic system CONCLUSION SYSTEM

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• processing and showing of effects of processed parameters on control panel of working machine (monitor, acoustic signal);

• detailed picturing of incidents when permissible values of parameters were exceeded;

• setting ways of proceeding for operator in certain exploitation situations (maintenance, operation stop, system work stop etc.);

• cooperation with other external diagnostic equipment.

Taking above into account and basing on analy-sis it was assumed that the on-board diagnostic system of working machine hydraulic system should fulfil the following functions:

• informative – refers information including elements of on-board diagnostic system and working machine on following aspects:

– usage; – maintenance;

– technical and exploitation parameters (ad-justment data);

– and also (depending on needs) storing of selected measurement results, referring espe-cially exceeded alert and limit values of diagnostic parameters and related messages generated by subsystem of diagnostic visual-isation (including technical maintenance of hydraulic system);

• diagnostic – refers examining and evaluation of hydraulic system condition, and also self-diag-nostic function of the on-board system;

• control – refers choosing optimal work condi-tions and way of usage of hydraulic system basing on the knowledge base containing basic regulation parameters of particular units and subunits of the hydraulic system: blocks of sup-ply, control and executive ( pressure regulators, amount and temperature of working liquid in the system, cleanness of working liquid filters, rota-tional speed of driving shaft of pump system, speed of work movements, tilt moment and tilt of machine body etc);

• efficiency evaluation of hydraulic system work – refers for example: fuel consumption per time unit by combustion engine driving the pump unit of supply block during work of machine in par-ticular working conditions (parameter defined by machine producer), amount and quality of work done by the machine in particular condi-tions (parameter defined by machine producer); • working safety – refers supervision of proper

function of units and subunits of hydraulic sys-tems, in particular quality of work of devices protecting from:

– overload;

– deflection of working tools outside the area defined by the operator (suitability of work-ing tool brakes);

– machine operation (hydraulic system) in time when the system has not reached required parameters for example: amount and temper-ature of working liquid, pressure of working liquid in supply block – indirectly it refers to parameters of work of the engine driving pump unit (temperature of cooling liquid, oil pressure, exploitation rotations of engine crank shaft).

Considering the above remarks and settlements it is believed that the concept of architecture of on-board diagnostic system of working machine should ensure:

• supervising the work of hydraulic system units during machine use;

• setting dates for technical maintenance accord-ing to programmed time of use and amount of work done;

• generating information for new designed expert systems including use and operation of the sys-tem;

• during each start of the working machine, realiz-ing the self-control function of diagnostic sys-tem covering:

– power supply of diagnostic system; – signal converters;

– condition of the central unit of a diagnostic system;

• current pre-definition of designated diagnostic parameter values (only for certain personnel of system operation);

• in certain range be compatible with other diag-nostic equipment, for example E-OBD mode; • visual and acoustic signalling of exceeding

ac-cessible values of measured diagnostic parame-ters (including alert values);

• generating the procedures of behaviour for an operator in dangerous situations (for example working tool halt, engine stop, fire-protection system alarm).

From analysis of action requirements, configura-tion aspect and needs generated for the concept of on-board diagnostic system result that the architec-ture of the system should ensure:

• system configuration within previously defined requirements, including introduction of amount, limit and alert values including enter of quantity, limit and alert diagnostic values, system work time;

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• measurement and recording of measured diag-nostic signals according to designated condition (measurement start and stop, which values and when recorded);

• diagnostic inference basing on analysis of rela-tions between measured values and observation matrix values;

• visualisation of machine hydraulic condition, including generation of exploitation decisions (suitable or unsuitable, fault localisation, others).

Application of the above concept of the on- -board diagnostic system for hydraulics (Fig. 5) will provide execution of the following tasks: • continuous supervision of diagnostic parameters

representative for certain blocks of hydraulic system;

• recording and storing of diagnostic parameters; • processing of collected data into decisions

ensuring effective functioning of a hydraulic system, for example date of change of working liquid;

• actual information about technical condition (and action processes) of a hydraulic system and alarms for fault states concerning for example: stop of excavator spoon in case of excess tilt of the excavator;

• supporting of decision making process in exploi-tation decisions, concerning for example chang-ing of workchang-ing liquid filters, workchang-ing liquid, cleaning of magnetic filters of working liquid etc.

Conferring rules were developed basing on diagnostic matrix analysis and procedures of KS and LU test determination with a checking vector. For particular blocks of hydraulic system of work-ing machine they are as follows:

1. For supply block:

DLU = y1, y2, y3, y4 = 1 0 0 0 – state S112 –

defective connector of a pressure regulator of a servo-motor supply block.

2. For control block:

DLU = y1, y2, y3, y4 = 0 1 0 1 – state S623

defective hydraulic separator. 3. For execution block

DLU = y1, y2, y3, y4 = 0 0 1 0 – state S232 –

wear of outer layer of elastic cables for servo-motor supply of cylinder channel.

Interpretation of conferring rules in this concept is as follows:

a) If a logical value of checking vector of a diag-nostic parameter assumes value “1” – parameter value is outside the limit value;

b) If a logical value of checking vector of a diag-nostic parameter assumes value “0” – parameter value is within the acceptable value range. Transfer of the generated diagnostic information through the on-board diagnostic system to the oper-ator should be executed on two levels:

• for working machine operator, • for technical service personnel.

y1, y2, ... yn

SOFTWARE NOISE

yp1, yp2, ....ypn

PROCESSING BLOCK OF SIGNALS FROM CDU

MEASUREMENT RESULT ANALYSIS BLOK (PC + SOFTWARE +

EXPERT PANEL)

VISUALISATION

 Monitor (control lamps)  Acoustic signal  Printer (port) yw1, yw2 ... ywn ADAPTATION SYSTEMS CENTRAL DIAGNOSTIC UNIT

BLOCK OF SIGNAL SENSORS (supply, control and executive)

C1 C2 C3 C4 C5 C6 C7 Cn

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It was accepted that monitor and audio infor-mation to operator about condition of machine hydraulic system should have character shown in figure 6, keeping strict rules while additional text in a particular field can inform about a defective state.

Conclusions

Solution of problems of supporting exploitation processes of working machine with tools which optimize their use according to their assigned usage features while ensure required safety conditions for people and environment is still an important matter. One of these problems is evaluation of technical condition of hydraulic systems. Actually, and prob-ably in the distant future, the problem of hydraulic system diagnosing will constitute a very important issue in the aspect of decision making about essen-tial exploitation tasks. It results from improper technical state of most parts of exploited working machines, and also their hydraulic systems. This situation can be avoided by application of the above shown methodology of diagnosing of hydraulic systems and the concept of their application in form of principles for acquisition of diagnostic parame-ters and their conferring rules. Because of different needs in this respect it is advisable, that possibilities of proposed on-board diagnostic system should be based on its modular construction. This will ensure possibility for system configuration responding to buyer (or may be already an owner of a working

machine) needs and possibilities. A solution for such a system will be creation of service units providing:

• specialist consulting in the range of require-ments covering application on-board diagnosis systems for particular systems;

• configuration according to above set PSD ele-ments from produced PSD modular sets;

• assembling of chosen and configured PSD in a particular hydraulic system with its software; • service of PSD installed as above.

The solution introduced here creates possibility of its application in a hydraulic system of a working machine at each stage of its life. The best solution would be implementation of the presented PSD already at design, construction and production stag-es of a working machine.

Additionally, taking into account possibility of application of the concept of on-board diagnostic system for working machine hydraulic system in its exploitation, it must be kept in mind that it refers to needs of working machine users.

References

1. SURÓWKA L.: Identyfikacja modelu diagnostycznego

uk-ładów hydraulicznych (Identification of Diagnostic Model of Hydraulic Systems). Mechanika, Wydawnictwo ATR, Bydgoszcz 2001.

2. ŻÓŁTOWSKI B.: Podstawy diagnostyki maszyn (The

Foun-dations of Machine Diagnostics). Wydawnictwo ATR w Bydgoszczy, Bydgoszcz 1996.

Fig. 6. General view of diagnostic information panel of on-board diagnostic system for working machine hydraulic system Supply Block Control Block Execution Block STTE OF DANGER STATE OF EMERGENCY STATE OF SUITABILITY

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Others

3. NIZIŃSKI S., MICHALSKI R.: Diagnostyka obiektów

tech-nicznych (The Diagnostics of Technical Objects). Wydawnictwo i Zakład Poligrafii Instytutu Technologii Eksploatacji, Radom 2002.

4. SITEK K.: Diagnostyka samochodowa (Car Diagnostics).

Wydawnictwo Auto, Warszawa 1999.

5. STRYCZEK S.: Napęd hydrostatyczny (Hydrostatic Drive).

Wydawnictwo Naukowo-Techniczne, Warszawa 1997. 6. SURÓWKA L.: Badanie stanu technicznego układu

hydrau-licznego maszyny roboczej (The Examination of a Hydrau-lic System Technical State of a Working Machine).

Docto-ral Thesis, Akademia Techniczno-Rolnicza, Bydgoszcz 2005.

7. SZENAJCH W.: Napęd i sterowanie pneumatyczne (Pneuma-tic Drive and Control). Wydawnictwo Naukowo-Techniczne, Warszawa 1997.

8. SZYDELSKI Z.: Napęd i sterowanie hydrauliczne (Hydraulic

Drive and Control). Wydawnictwa Komunikacji i Łączno-ści, Warszawa 1999.

9. TYLICKI H.: Optymalizacja procesu prognozowania stanu

technicznego pojazdów mechanicznych (The Optimization of Prognosis Process for Technical State of Mechanic Ve-hicles). Wydawnictwa Uczelniane ATR w Bydgoszczy, Bydgoszcz 1998.

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