let. - vol. A~7 C2Q01D st. - no. 1 D STROJNIŠKI VESTNI K 10 JOURNAL OF MECHANICAL ENGINEERII strani - pages 531 - 6-40 STJVAX 5. konferenca IAT'01 Razstava Inovativna avtomobilska tehnologija 5. - 6. april 2001 Ljubljana, Slovenija Modeliranje padavinskih matrik z mešanico Gaussovih funkcij The Modelling of Rainflow Matrices with a Mixture of Gaussian Functions Uporaba numeničnih simuliranj pni razvoju orodij za izdelavo pločevinastih sestavnih delov avtomobilov The Use of Numerical Simulations in the Development of Tools for the Sheet-Metal Parts of Cans Analiza sistemov za neposredno vbrizgavanje goriva v sodobne hitnotekoče dizelske motorje An Analysis of Fuel-Injection Systems for Advanced High-Speed Diesel Engines Obravnavanje curka plinskega olja Diesel-Spray Analysis 5. Conference IAT'01 Exhibition Innovative Automotive Technology April 5th - 6th 2001 Ljubljana, Slovenia :M © Strojni{ki vestnik 47(2001)10,591 Mese~nik ISSN 0039-2480 © Journal of Mechanical Engineering 47(2001)10,591 Published monthly ISSN 0039-2480 Vsebina Contents Strojni{ki vestnik - Journal of Mechanical Engineering letnik - volume 47, (2001), {tevilka - number 10 Uvodnik Editorial Uvodne besede ob objavi izbranih prispevkov s Introduction to the Selected Papers from the IAT’01 konference IAT’01 592 Conference Razprave Papers Klemenc, J., Fajdiga, M.: Modeliranje padavinskih Klemenc, J., Fajdiga, M.: The Modelling of Rainflow matrik z mešanico Gaussovih funkcij 593 Matrices with a Mixture of Gaussian Functions Gantar, G, Ljevar, M., Kuzman, K: Uporaba numeričnih Gantar, G., Ljevar, M., Kuzman, K.: The Use of Nu- simuliranj pri razvoju orodij za izdelavo merical Simulations in the Development of 605 Tools for the Sheet-Metal Parts of Cars Dolenc, A., Trenc, F.: Analiza sistemov za Dolenc, A., Trenc, F.: An Analysis of Fuel-Injec- neposredno vbrizgavanje goriva v sodobne tion Systems for Advanced High-Speed Die- hitrotekoče dizelske motorje 615 sel Engines Volmajer, M., Kegl, B.: Obravnavanje curka Volmajer, M., Kegl, B.: Diesel-Spray Analysis plinskega olja 627 Strokovna literatura 637 Professional Literature Osebne vesti 638 Personal Events Navodila avtorjem 639 Instructions for Authors | |5fin=i(purMini5nLn 01 stran 591 I^HsSTTlMlDC © Strojni{ki vestnik 47(2001)10,592 © Journal of Mechanical Engineering 47(2001)10,592 ISSN 0039-2480 ISSN 0039-2480 Uvodnik Editorial Uvodnik Editorial Uvodne besede ob objavi izbranih prispevkov s konference IAT’01 Introduction to the Selected Papers from the IAT’01 Conference Zveza inženirjev in tehnikov Slovenije -Skupina za vozila in motorje je skupaj s Fakulteto za strojništvo Univerze v Ljubljani že leta 1993 organizirala konferenco “Inovativna avtomobilska tehnologija - IAT’01”, ki je skupaj z razstavo prvič v samostojni Sloveniji združila strokovnjake za področje avtomobilizma in spremljevalnih dejavnosti iz Slovenije in tujine. V okviru programa že pete zaporedne konference, ki je med tem časom postala periodična, dvoletna, mednarodna in znanstvena konferenca pod okriljem svetovnega združenja FISITA (Federation Internationale des Societes d’ Ingenieurs des Techniques de l’Automobile) in evropskega združenja EAEC (European Automotive Engineers Cooperation), je bilo predstavljenih 45 prispevkov avtorjev iz domovine in tujine. S predstavljenimi deli so želeli organizatorji IAT’01 prikazati stanje vključevanja in povezanosti znanstvenega in strokovnega kadra s sodobno tehnologijo predvsem v slovenski družbi. Osnovni poudarek, ki je bil začrtan že pred leti, je še naprej namenjen problematiki sodelovanja med finalisti in dobavitelji, saj takšne uspešne povezave v avtomobilski in spremljajoči industriji omogočajo uspešno vključevanje tudi v ustrezne mednarodne tokove. Organizatorji konference opažajo v zadnjem času povečanje zanimanja za področje avtomobilske tehnologije, iz vsebine predstavljenih člankov pa je viden tudi napredek v kakovosti objavljenih del. Napredek je opazen tudi v smeri povezovanja razvojnoraziskovalnih kadrov visokošolskih organizacij in razvojnih oddelkov organizacij, ki se ukvarjajo z avtomobilsko stroko. Kakovostni izdelki naše skupne konference IAT’01 bodo tako tudi v prihodnje vir novih informacij in predmet povezovanja vseh, ki kakorkoli sodelujejo pri razvojno-raziskovalnem delu v avtomobilski tehnologiji. Kakor je že v navadi, je organizator po konferenci ustanovil posebno strokovno komisijo, ki je ponovno ocenila vsa predstavljena dela in najuspešnejša predlagala za objavo tudi v Strojniškem vestniku. Izbrana dela bodo objavljena v treh zaporednih številkah Strojniškega vestnika. Organizacijski in Programski odbor konference IAT ‘01 The Association of Mechanical Engineers and Technicians of Slovenia - Group for Vehicles and Engines, has, together with the Faculty of Mechanical Engineering, University of Ljubljana, organised the “Innovative Automotive Technology - IAT’01” conference since 1993. These conferences, which are held in Slovenia every two years, bring together experts from the automotive and related fields from Slovenia and abroad. The IAT’01 conference, which was the fifth in the series and organised under the auspices of the FISITA (Federation Internationale des Societes d’ Ingenieurs des Techniques de l’Automobile) and the EAEC (European Automotive Engineers Cooperation), involved the presentation of 45 papers by authors from home and abroad. With the presented papers the organisers of IAT’01 wanted to show the links and collaborations between scientists and engineers working in modern technologies, especially within Slovenian society. The main aim, which was determined some years ago, is to promote cooperation between suppliers and the manufacturers of finished products. Such a successful collaboration in the automotive and associated industries enables their effective inclusion into the appropriate international markets. The conference organisers have become aware of a recent increase of interest in the field of automotive technology. From the contents of the advanced proceedings it is clear that there has also been qualitative progress in the contributed papers. Progress is also evident in the area of research-and-development staff at the various faculties and the project organisations dealing with automotive technologies. The published papers from the IAT’01 conference will be a source of new information in the future and will help all specialists working in research and development in the automotive technology. It is common practice that after the conference the organisers appoint a special commission to re-evaluate all the presented papers and select the best for publication in the Journal of Mechanical Engineering. These selected papers will appear in the next three issues. Organising and Programme Committee of the IAT’01 Conference 0 &nnBjfokJ][p)l]Olf|i[gO | | ^SSfiflMlGC | stran 592 © Strojni{ki vestnik 47(2001)10,593-604 © Journal of Mechanical Engineering 47(2001)10,593-604 ISSN 0039-2480 ISSN 0039-2480 UDK 620.178.3:004.94 UDC 620.178.3:004.94 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Modeliranje padavinskih* matrik z me{anico Gaussovih funkcij The Modelling of Rainflow Matrices with a Mixture of Gaussian Functions Jernej Klemenc - Matija Fajdiga Za vrednotenje dinamično obremenjenih konstrukcij z vidika utrujanja, je treba poznati dinamične obremenitve konstrukcije, ki jih dobimo z meritvami ali simuliranji. Tako dobljene časovne poteke obremenitev nato spremenimo v obliko, ki je primerna za napoved utrujenostne poškodbe. Ker je utrujenostna poškodba odvisna od obremenitvenih ponovitev, ki so vsebovani v časovnem poteku obremenitev, iz časovnega poteka obremenitev najprej izločimo obremenitvene ponovitve z uporabo števnih metod. V ta namen se v avtomobilski industriji pogosto uporablja padavinska števna metoda, katere rezultat je matrika relativnih frekvenc obremenitvenih ponovitev. Z aproksimacijo padavinske matrike z ustrezno zvezno funkcijo gostote porazdelitve verjetnosti izločimo naključne fluktuacije relatiw frekvenc v matriki in omogočimo ekstrapolacijo verjetnosti v področje obremenitvenih ponovitev, ki se niso pojavili v izmerjeni ali simuliranem časovnem poteku obremenitev. V prispevku je prikazana metoda modeliranja padavinskih matrik z mešanico Gaussovih funkcij. Ocena neznanih parametrov mešanice Gaussovih funkcij je izvedena z metodo največje verjetnosti. Uspešnost te metode je ocenjena na primerih realnih časovnih potekov obremenitev. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: funkcije Gauss, gostota porazdelitve verjetnosti, metode maksimalne verjetnosti, algoritem EM) To evaluate the fatigue damage of a dynamically loaded structure, a time history of the structure load should be acquired first. This can be done by means of experiments or simulations. When the time history of the loads is known, it should be transformed into a form that is suitable for the prediction of the fatigue damage. This fatigue damage of the structure depends heavily on the load cycles that are included in the load time history. Load cycles are extracted from the load time history with different counting methods. A rainflow counting method is widely used in the automotive industry. The rainflow counting method results in a matrix of the relative frequencies of the load cycles, which are included in the load time history. With an approximation of the rainflow matrix by a continuous probability density function, random fluctuations of the relative frequencies are reduced and an extrapolation of the probability of the load cycles that were not actually recorded is made possible. In our paper a method of modelling the rainflow matrices by means of a mixture of Gaussian functions will be presented. Unknown parameters of the normal mixture will be estimated with a maximum-likelihood method. The effectiveness of this method will be presented and discussed with an example of the load time histories of a real structure. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: Gaussian functions, probability density, maximum likelihood methods, EM algorithm) 0 UVOD Doba obstojnosti konstrukcij je odvisna od obremenitvenih stanj konstrukcij in zdržljivosti materiala Splošen postopek napovedi dobe trajanja dinamično obremenjenih konstrukcij je tak da v razvojnem postopku skušamo oceniti povezavo med zdržljivostjo materiala in dobo trajanja konstrukcije [8]. Zdržljivost materiala je navadno podana v obliki krivulj zdržljivosti za primer dinamičnega obremenjevanja z nespremenljivo amplitudo * v angleščini: rainflow 0 INTRODUCTION The fatigue life of structures depends on load states and material endurance. A general approach to the fatigue-life prediction of random loaded structures is that a correlation between the fatigue life, the random load states and the endurance of the material is determined [8]. The endurance of materials is generally known and is usually given in the form of S-N (stress-number of rever- J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices obremenitvenih ponovitev in je v splošnem poznana. Obremenitvena stanja konstrukcij v splošnem predstavljajo neznanko, zato jih je treba ovrednotiti, bodisi s preskusi, bodisi s simuliranji. Napoved dobe trajanja dinamično obremenjenih konstrukcij nato poteka tako, da najprej izločimo obremenitvene ponovitve iz časovnega poteka obremenitev naše konstrukcije, nakar z ustrezno hipotezo o akumulaciji poškodb in podatkov o zdržljivosti materiala ocenimo poškodbo, ki jo povzročijo posamezne obremenitvene ponovitve. Celotna poškodba je enaka vsoti poškodb, ki jo povzročijo posamezne obremenitvene ponovitve Za napoved poškodb dinamično obremenjenih konstrukcij pogosto uporabljamo Palmgren-Minerjevo hipotezo o akumulaciji poškodb. Čeprav je Palmgren-Minerjeva hipoteza ena izmed najbolj uporabljanih metod za napoved poškodbe dinamično obremenjenih konstrukcij, je natančnost te metode sorazmerno majhna. Zato jo uporabljamo predvsem v zgodnejših fazah razvojnega postopka. Natančnejšo oceno dobe trajanja izvajamo v kasnejših fazah razvojnega postopka z dinamičnimi preskusi konstrukcij. Če za napoved poškodbe uporabljamo Palmgren-Minerjevo hipotezo, ponavadi izločimo obremenitvene ponovitve iz časovnih potekov obremenitev z padavinsko števno metodo, ker tako izločene obremenitvene ponovitve ustrezajo sklenjenim histereznim zankam v diagramu ct-e [6]. V praksi uporabljamo več različic Palmgren-Minerjeve hipoteze o akumulaciji poškodb. Najpreprostejši način ocene dobe tajanja je, da poškodbo izračunamo na podlagi amplitude obremenitvenih ponovitev S . Tak način ocene dobe tajanjaje primeren, če lahko vpliv srednjih vrednosti obremenitvenih ponovitev zanemarimo. V primeru, ko se poškodba pojavi zaradi velikega števila obremenitvenih ponovitev z majhnimi amplitudami in različnimi srednjimi vrednostmi, vpliva srednjih vrednosti ne smemo zanemariti [7]. Tedaj je treba izločiti obremenitvene ponovitve iz časovnega poteka obremenitev z dvoparametrično padavinsko števno metodo. V tem primeru je obremenitvena ponovitev predstavljena z vektorsko spremenljivko S=(S ,S ), ki ima dve komponenti: amplitudo obremenitvene ponovitve S in srednjo vrednost obremenitvene ponovitve S . Rezultat štetja z dvoparametrično padavinsko metodo je tako matrika relativnih frekvenc obremenitvenih ponovitev. Poškodba ki jo povzroči ena obremenitvena ponovitev je odvisna od amplitude S in srednje vrednosti S obremenitvene ponovitve. " V primeru naključnih obremenitvenih stanj, ki so opisana z razmeroma kratkimi časovnimi poteki obremenitev, je treba za bolj zanesljivo napoved dobe trajanja izvesti ekstrapolacijo v področje obremenitvenih ponovitev z majhno verjetnostjo realizacije. Tega ni mogoče storiti s sedanjo padavinsko matriko. Zato smo se odločili, da porazdelitev obremenitvenih ponovitev v padavinski domeni opišemo z zvezno gostoto porazdelitve verjetnosti (GPV) (S) obremenitvenih ponovitev S. Velikost poškodbe D, ki jo povzroči N obremenitvenih 0 srinataleflMllflilrSO | ^BSfirTMlliC | stran 594 sals) curves for constant-amplitude loading. The load states of structures are generally unknown and need to be evaluated by means of experiments or simulations. In the process of fatigue-life prediction, load cycles are first extracted from time-dependent load histories. Next, a proper damage rule is chosen and the damage caused by individual load cycles is calculated. The total damage equals the sum the of damages resulting from individual load cycles. One of the most widely used damage rules is the Palmgren-Miners linear damage rule. However, though this method is one of the most widely used, its accuracy can be quite poor. That is why it tends to be used in earlier phases of the R&D process. A more accurate fatigue-life prediction is achieved in the final phases of the R&D process by testing the structures dynamically. When the Palmgren-Miners damage rule is used for the fatigue damage estimation, a rainflow counting method is generally used for extracting the load cycles from the load histories, because the load cycles extracted in this manner correspond to closed hysteresis loops in the s-e diagram [6]. In practice many different forms of the Palmgren-Miners damage rule are used. In its most simple variation the fatigue damage is estimated only on the basis of load-cycle amplitudes Sa. Such an approach is appropriate when the influence of the load cycle means that Sm can be neglected. However, if the fracture occurs due to a large number of load cycles with small amplitudes and very different means, the influence of load-cycle means should not be underestimated [7]. When load-cycle means also need to be considered in the estimation of the fatigue damage, the extraction of the load cycles from the load histories is performed with a two-parametric rainflow method. A load cycle is then represented as a vector S=(Sa,Sm) with two components: a load-cycle amplitude Sa and a load-cycle mean Sm. Cycle counting with the two-parametric rainflow method results in a matrix of load-cycle relative frequencies. The damage caused by individual load-cycles then depends on a load cycle amplitude and a load-cycle mean. In the case of random load states that are composed of relatively short random load histories, it is necessary to extrapolate the distribution of load cycles to the region where there are no measured data for a more reliable assessment of the fatigue life. This cannot be done with the rainflow matrix that relates to the extracted load cycles. So a decision was made to model the distribution of the load cycles in a rainflow domain with a continuous multivariate probability density function (PDF) f(S) of load cycles S. The total damage caused by Ntot load cycles with J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices ponovitev z zvezno gostoto porazdelitve f(S) lahko v the probability density function f(S) can be calcu- splošnem izračunamo z integralom po območju možnih lated by integrating over the domain of possible realizacij obremenitvenih ponovitev ([4] in [7]): realisations of the load cycles ([4] and [7]): D jJNtot-f(S)/Nf(S)dSadSm (1). Zdržljivost materiala Nf(S) je poznana, treba pa je oceniti zvezno večdimenzionalno GPV obremenitvenih ponovitev f(S) obremenitvenih ponovitev, ki so bile izločene iz časovnih potekov obremenitev s padavinsko števno metodo. Večdimenzionalna GPV f(S) mora ustrezati porazdelitvi izločenih obremenitvenih ponovitev in omogočati ekstrapolacijo v področje obremenitvenih ponovitev z majhno verjetnostjo realizacije. 1 NASTAVEK ZA REŠITEV PROBLEMA Namen raziskave je določitev takšne zvezne večvariantne GPV obremenitvenih ponovitev f(S), da bo le-ta izpolnila zahtevi, podani v uvodu. Zato smo se odločili, da bomo zvezno GPV obremenitvenih ponovitev f(S) modelirali z mešanico dvodimenzionalnih Gaussovih funkcij [1]: f (S)= f (Sa,Sm) The endurance of material Nf(S) is generally known. What is needed is an estimation of the continuous multivariate PDF f(S) of the load cycles. The estimation of the function f(S) should be based on the distribution of the load cycles S=(Sa,Sm), extracted from the load histories by the two-parametric rainflow method. The multivariate PDF f(S) must adequately represent the probability distribution of the load cycles and must allow extrapolation to the region where there are no measured data. 1 THE BASIS FOR THE SOLUTION OF THE PROBLEM The goal of the research was to define a functional structure of the multivariate PDF of the load cycles f(S) that will fulfil both requirements that were introduced at the end of section 0. That is why a decision was made to model the continuous multi-variate PDF of the load cycles f(S) with a mixture of two-dimensional Gaussian functions [1]: K ^Uk-N(fik,i:k N ((i,2:) = (2-p )-d/2->/det(2:-1)-exp 1 ( S-ii)-E-^S-ii) (2), (3). Pri tem pomenijo: Uk - utež, jl - vektor srednjih vrednosti, * - kovariančno matriko, d = dvodimenzijske k-te večdimenzionalne Gaussove funkcije v mešanici. S je naključna spremenljivka, ki pomeni obremenitvene ponovitve. Ko smo izbrali funkcionalno obliko zvezne GPV obremenitvenih ponovitev f(S), moramo oceniti njene neznane parametre. Oceno neznanih parametrov funkcije f(S) izvedemo z metodo največje verjetnosti, ki jo dopolnimo z algoritmom matematičnega pričakovanja (EM). Z izbrano metodo je mogoče neznane parametre funkcije f(S) oceniti bodisi na podlagi izločenih obremenitvenih ponovitev, bodisi na podlagi matrike relativnih frekvenc obremenitvenih ponovitev. V prispevku bosta prikazana oba postopka ocene neznanih parametrov. Kriterij za ovrednotenje uspešnosti ocene neznanih parametrov funkcije f(S) je ujemanje izmerjenih in modeliranih obrobnih GPV in ustreznih obrobnih obremenitvenih kolektivov (OK) amplitud in srednjih vrednosti obremenitvenih ponovitev. 2 PRIPRAVA PODATKOV ZA MODELIRANJE ZVEZNE FUNKCIJE GPV OBREMENITVENIH PONOVITEV Za prikaz uspešnosti ocene neznanih parametrov mešanice Gaussovih funkcij z metodo Where Uk is a weight factor of the k-th mul-tivariate Gaussian function; mk and Sk are its mean vector and covariance matrix, respectively. S is a random variable that represents load cycles. After the functional structure of the multivari-ate PDF of the load cycles f(S) has been determined, its unknown parameters must be estimated. This is done by means of the maximum-likelihood method, supplemented with an Expectiation Maximization (EM) algorithm. With this method it is possible to estimate unknown parameters of the normal mixture f(S) on the basis of the extracted load cycles or their corresponding rainflow matrix. Both variants of the estimation of the normal mixture parameters will be presented in this paper. The criterion for the assessment of the efficiency of the unknown parameter estimation is the agreement of marginal probability density functions and the loading spectra (LS) that belong to numerically modelled and experimentally obtained multivari-ate PDFs, respectively. 2 PREPARATION OF THE DATA FOR MODELLING THE CONTINUOUS PDF OF THE LOAD CYCLES Both variants of the maximum-likelihood method, used for the estimation of the unknown pa- J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices največje verjetnosti je bilo izbrano realno obremenitveno stanje viličarja z nosilnostjo 2500 kg. Izbrano obremenitveno stanje je predstavljeno z naborom šestih časovnih potekov obremenitev sile v nagibnem hidravličnem valju F . Vseh šest časovnih potekov obremenitev je bilo vh izmerjenih pri stalnih obratovalnih razmerah: vožnja naprej z največjo hitrostjo, masa bremena je enaka polovični nosilnosti viličarja. Dolžine posameznih časovnih potekov obremenitev so enake 10 s [9]. Obremenitvenih ponovitev z amplitudo, manjšo od ene dvaintridesetine amplitude največje obremenitvene ponovitve, nismo upoštevali. Porazdelitev obremenitvenih ponovitev, izločenih iz vseh šestih časovnih potekov obremenitev, in pripadajoča matrika relativnih frekvenc (RF), sta prikazani na sliki 1. rameters of the normal mixture, will be applied to the example of a real load state: a forklift truck with a load capacity of 2500 kg. The load state of the forklift truck is composed of a group of six real load histories of a normal force Fvnh in a hydraulic cylinder, which is used for the adjustment of the inclination of a lifting mechanism. The load histories under consideration were measured during the operation of the forklift under constant operating conditions: straight forward drive with a maximum speed and a load of one half of the maximum load capacity. The duration of each load history in a group is 10 s [9]. Load cycles with an amplitude lower than 1/32 of the maximum measured amplitude were filtered out. The distribution of load cycles, extracted from six filtered load histories, and the corresponding matrix of relative frequencies (RF), are presented in Fig. 1. Porazdelitev obr. ponovitev / Distribution of load cycles 1.2 1.0 0.8 0.6 0.4 0.2 0.0 ¦ ¦ ¦ ¦ ¦ • ¦ ¦ ¦ ¦ * ¦ ¦ ¦ ¦ 0.0 0.2 0.4 0.6 Amplituda / Amplitude [V] Padavinska matrika / Rainflow matrix 0. 035 0.030 0.025 0.020 0. 015 0.010 0.005 0.000 0.8 1.0 0.03 0. 26 Amplituda / Amplitude [V] 0.030-0.035 0.025-0.030 0.020-0.025 0.015-0.020 0.010-0.015 0.005-0.010 0.000-0.005 0.39 0.09 1.00 0.70 Sred. vred. / Mean [V] Sl. 1. Padavinsek obremenitvene ponovitve in pripadajoča matrika relativnih frekvenc za silo v nagibnem hidravličnem valju F h ; kaliber 1 V = 26.5 kN Fig. 1. Distribution of rainflow load cycles and the corresponding rainflow matrix of the normal force F ; calibre: 1 V = 26.5 kN 0 BnnBjfokJ][p)l]Olf|i[gO | | ^SsFvWEIK | stran 596 J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices 3 MODELIRANJE ZVEZNE FUNKCIJE GPV OBREMENITVENIH PONOVITEV 3.1 Ocena parametrov mešanice Gaussovih funkcij z metodo največje verjetnosti na podlagi izločenih obremenitvenih ponovitev Naj {S1,...,SN} pomeni množico iVobreme-nitvenih ponovitev S =(S i,S ), izločenih iz časovnih potekov obremenitev, ki m, sestavljajo naključno obremenitveno stanje. Če metodo največje verjetnosti za oceno neznanih parametrov gostote porazdelitve verjetnosti dopolnimo z EM postopkom, tedaj neznane parametre mešanice Gaussovih funkcij Uk, mk in Sk ocenimo na podlagi množice obremenitvenih ponovitev {S1,..., SN} z naslednjim sistemom iteracijskih enačb ([1] do [5]): 1 3 MODELLING OF THE CONTINUOUS PDF OF THE LOAD CYCLES 3.1 Estimation of Parameters of the Normal Mixture with the Maximum-Likelihood method on the Basis of the Extracted Load Cycles Let {S1,..., SN} represent a set of N load cycles Si=(S i,S ), extracted from the load histories that make up the i load state under consideration. If the maximum-likelihood method, supplemented with the EM algorithm, is applied for the estimation of the unknown parameters of the normal mixture and the set of load cycles {S1,..., SN} is used as the basis for this estimation, then parameters Uk, mk and Sk can be estimated with the following system of iterative equations ([1] to [5]): N 2>(Si,nl(t ),El(t ),Ul(t))Si fl(t+1) N>(Si,nl(t ),El(t ),Ul(t))Si N zl(t+1) X/( Si, fl (t ),zl(t ),Ul(t )) ISi-*l(t+1)il N>(Si,nl(t ),zl (t ),Ul(t )) (4), (5), (6). Pri tem velja: Here: U />(S,(l ,El,Ul) Wdet(El1)' exp .( S-^T.^-( S-nl ) XUk-Jdet^- )-exp -^ ( S-nk ).E-1^S-nk ) Si=(Sa,i ,Sm,) (7), (8), t je indeks iteracije. Število Gaussovih funkcij v mešanici K je treba izbrati vnaprej pred začetkom iteracijskega postopka. Z večanjem števila Gaussovih funkcij v mešanici v splošnem izboljšujemo ujemanje izmerjene in modelirane GPV. Nasprotno pa z zmanjševanjem števila Gaussovih funkcij v mešanici izboljšujemo ekstrapolacijske zmožnosti modelirane GPV. Zato je treba pri izbiri števila Gaussovih funkcij v mešanici narediti kompromis med dobrim ujemanjem izmerjene in modelirane GPV in dobrimi ekstrapolacijskimi zmožnostmi modelirane GPV. Začetne pogoje za iteracijo lahko izberemo poljubno ali tako, da že upoštevamo nekatere značilnosti porazdelitve obremenitvenih ponovitev. Mešanica treh Gaussovih funkcij, ki ustreza porazdelitvi obremenitvenih ponovitev na sliki 1, je prikazana na sliki 2. Primerjava ustreznih obrobnih izmerjenih in modeliranih porazdelitev verjetnosti je prikazana na sliki 3. Mešanica petih Gaussovih funkcij, ki ustreza isti porazdelitvi obremenitvenih ponovitev, je prikazana na sliki 4. where t is the index of an iteration. The number K of the Gaussian functions in the normal mixture must be chosen before the start of the iterative process. Good adaptation is generally achieved by increasing the number of Gaussian functions in the normal mixture. In contrast, a good extrapolation ability is usually achieved by decreasing the number of Gaussian functions in the normal mixture. So when choosing the number of Gaussian functions in the normal mixture, a compromise between good adaptation of the normal mixture to the distribution of load cycles and a good extrapolation ability of the normal mixture must be made. Initial conditions for the iterative process can be chosen randomly or systematically, based on some preliminary knowledge about the distribution of load cycles. A normal mixture with three Gaussian functions, which correspond to the distribution of load cycles presented in Fig. 1, is presented in Fig. 2. A comparison of its marginal probability distributions and measured marginal probability distributions is presented in Fig. 3. A normal mixture with five Gaussian functions that correspond to the same distri- griTMBlJJIMISCSD 01-10 stran 597 |^BSSIrTMlGC J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices Primerjava ustreznih modeliranih in izmerjenih obrobnih porazdelitev verjetnosti je prikazana na sliki 5. V obeh primerih so bili neznani parametri mešanice Gaussovih funkcij ocenjeni na podlagi množice N=579 obremenitvenih ponovitev. Začetni pogoji za iteracijski postopek so bili v obeh primerih izbrani tako, da smo začetne vektorje srednjih vrednosti Gaussovih funkcij postavili v območje večje gostote obremenitvenih ponovitev. bution of load cycles is presented in Fig. 4. A comparison of its marginal probability distributions and measured marginal probability distributions is presented in Fig. 5. The unknown parameters of the normal mixtures were, in both cases, estimated on the basis of N=579 extracted load cycles. Initial conditions for the iterative process were, in both cases, determined systematically by setting up initial mean vectors of Gaussian functions in regions of higher densities of load cycles. GPV obermenitvenih ponovitev / PDF of load cycles 40.00 35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 -0.13 -0.11 Amplituda / Amplitude [V] 0.50 0.82 0.30 Sred. vred. / Mean [V] 35.00-40.00 30.00-35.00 25.00-30.00 20.00-25.00 15.00-20.00 10.00-15.00 5.00-10.00 0.00-5.00 Sl. 2. Mešanica treh večdimenzionalnih Gaussovih funkcij; parametri mešanice, ocenjeni na podlagi izločenih obremenitvenih ponovitev; kaliber: 1 V = 26,5 kN Fig. 2. A normal mixture with three Gaussian functions; unknown parameters of the normal mixture are estimated on the basis of extracted load cycles; calibre: 1 V = 26.5 kN GPV amplitud / PDF of amplitudes Obremenitveni kolektiv (OK) amplitud / Loading spectrum (LS) of amplitudes 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 1 1 1 N___________ r h IX— 0.0 0.2 0.4 0.6 0.8 1.0 Amplituda / Amplitude [V] Modelirana GPV / Modelled PDF Izmerjena GPV / Measured PDF GPV srednjih vrednosti / PDF of means 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.5 0.0 0.5 1.0 Srednja vrednost / Mean [V] 1.5 ^—----^ 1 10 100 10 Število obremenitvenih ponovitev / Number of load cycles [-] 00 Modeliran OK / Modelled LS Izmerjen OK / Measured LS OK srednjih vrednosti / LS of means -^3=^ 1 10 100 10 Število obremenitvenih ponovitev / Number of load cycles [-] 00 Modeliran OK / Modelled LS Izmerjen OK / Measured LS -----Modelirana GPV / Modelled PDF— Izmerjena GPV / Measured PDF Sl. 3. Primerjava obrobnih porazdelitev verjetnosti za mešanico treh Gaussovih funkcij; parametri mešanice, ocenjeni na podlagi izločenih obremenitvenih ponovitev; kaliber: 1 V = 26,5 kN Fig. 3. Comparison of marginal probability distributions for the mixture of three Gaussian functions; unknown parameters of the normal mixture are estimated on the basis of extracted load cycles; calibre: 1 V = 265 kN 0 BnnBjfokJ][p)l]Olf|i[gO | | ^SifirlMlGC | stran 598 J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices GPV obremenitvenih ponovitev / PDF of load cycles 40.00 35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 -0.13 Amplituda / Amplitude [V] -0.11 0.50 0.82 0.30 Sred. vred. / Mean [V] 35.00-40.00 30.00-35.00 25.00-30.00 20.00-25.00 15.00-20.00 10.00-15.00 5.00-10.00 0.00-5.00 Sl. 4. Mešanica petih večdimenzionalnih Gaussovih funkcij; parametri mešanice, ocenjeni na podlagi izločenih obremenitvenih ponovitev; kaliber: 1 V = 26,5 kN Fig. 4. A normal mixture with five Gaussian functions; unknown parameters of the normal mixture are estimated on the basis of extracted load cycles; calibre: 1 V = 26.5 kN 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 GPV amplitud / PDF of amplitudes OK amplitud / LS of amplitudes 0.8 0.7 0.6 0.5 0.4 0.3- 0.2 0.1 " 0 - 1 \ ¦¦¦~«^___ 1 ' 11 w— 0.0 0.2 0.4 0.6 0.8 1.0 Amplituda / Amplitude [V] Modelirana GPV / Modelled PDF Izmerjena GPV / Measured PDF GP V srednjih vrednosti / PDF of means 6.0 5.0 4.0 3.0 2.0 1.0 0.0 J) I J \ F V ^d ^SsAm^ 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1 10 100 1000 Število obremenitvenih ponovitev / Number of load cycles [-] -----Modeliran OK / Modelled LS — Izmerjen OK / Measured LS OK srednjih vrednosti / LS of means -0.5 0.0 0.5 1.0 Srednja vrednost / Mean [V] 1.5 1 10 100 1000 Število obremenitvenih ponovitev / Number of load cycles [-] Modelirana GPV / Modelled PDF Izmerjena GPV / Measured PDF Modeliran OK / Modelled LS Izmerjen OK / Measured LS Sl. 5. Primerjava obrobnih porazdelitev verjetnosti za mešanico petih Gaussovih funkcij; parametri mešanice, ocenjeni na podlagi izločenih obremenitvenih ponovitev; kaliber: 1 V = 26,5 kN Fig. 5. Comparison of marginal probability distributions for the mixture of five Gaussian functions; unknown parameters of the normal mixture are estimated on the basis of extracted load cycles; calibre: 1 V = 26.5 kN 3.2 Ocena parametrov mešanice Gaussovih funkcij z metodo največje verjetnosti na podlagi matrike relativnih frekvenc obremenitvenih ponovitev Porazdelitev obremenitvenih ponovitev S=(Sa ,S ), izločenih iz časovnih potekov obremenitev, ki sestavljajo naključno obremenitveno stanje, je sedaj predstavljena z matriko relativnih frekvenc: 3.2 Estimation of the Parameters of the Normal Mixture with the Maximum-Likelihood method on the Basis of the Rainflow Matrix, Corresponding to the Extracted Load Cycles The distribution of rainflow load cycles S=(Sa,Sm), extracted from load histories, is now represented with a matrix of relative frequencies: J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices pij=p(Sa,i,Sm, j) ; i = 1,...,Ma;j = 1,...,Mm S a,i =S a,min +i-DS a S mj =S m,min +j-DS m (9), (10), (11), kjer sta M - število razredov matrike relativnih frekvenc v smeri amplitud S , M - število razredov matrike relativnih frekvenc v smeri srednjih vrednosti S . Sistem iteracijskih enačb za oceno neznanih parametrov mešanice Gaussovih funkcij Uk, mk in Sk dobimo z modifikacijo sistema iteracijskih enačb, ki je bil predstavljen v poglavju 3.1 - (glej tudi [1] do [5]): with M being the number of classes of the rainflow matrix in the direction of load-cycle-amplitudes S, and M being the number of classes of the rainflow matrix in the direction of load-cycle-means S . The system of iterative equations for the estimation of normal mixture parameters Uk, mk and Sk can be obtained with a modification of the system of iterative equations that was presented in section 3.1 - see also [1] to [5]: Ul(t + 1) = MajMmjpij-p(Sij,til (t),T.l(t),Ul(t)) iil(t+1) i=1 j=1 Ll(t + 1) i=1 j=1 i=1 j=1 Pri tem velja: Here: (12), (13), (14). i=1 j=1 U p(S,Hl^Ul) rjdet^-1). exp ¦ ( S-v)-i.-1 ( S-vl ) K Uk-Jdet(^1)-exp -•( S-^ ).E-1 ^S-^ ) (7), (15). Izpeljava sistema iteracijskih enačb (12), (13) in (14) prav tako temelji na metodi največje verjetnosti, ki smo jo dopolnili z EM postopkom. Pri tem pomenita: t - indeks iteracije, K - število Gaussovih funkcij v mešanici. Tudi v tem primeru imamo pri izbiri števila Gaussovih funkcij v mešanici enak problem, kakor v primeru, ko so neznani parametri mešanice ocenjeni na podlagi porazdelitve obremenitvenih ponovitev, ker je število K Gaussovih funkcij v mešanici spet treba izbrati vnaprej. Zato je ponovno treba narediti kompromis med dobrim ujemanjem izmerjene in modelirane GPV in dobrimi ekstrapolacijskimi zmožnostmi modelirane GPV. Začetne pogoje za iteracijo lahko ponovno izberemo poljubno ali tako, da že upoštevamo nekatere značilnosti porazdelitve obremenitvenih ponovitev. Mešanica treh Gaussovih funkcij, ki ustreza porazdelitvi obremenitvenih ponovitev na sliki 1, je prikazana na sliki 6. Primerjava ustreznih obrobnih izmerjenih in modeliranih porazdelitev verjetnosti je prikazana na sliki 7. Mešanica petih Gaussovih funkcij, ki ustreza isti porazdelitvi obremenitvenih ponovitev, je prikazana na sliki 8. Primerjava ustreznih The derivation of the system of iterative equations (12), (13) and (14) is also based on the maximum-likelihood method, supplemented with an EM algorithm. t is an iteration index and K is the number of Gaussian functions in the normal mixture. The problem of choosing a suitable number of Gaussian functions is the same as it was in the case of the estimation of the normal mixture parameters, based on extracted load cycles, because the number K of the Gaussian functions in the normal mixture must again be chosen in advance. So a compromise between good adaptation of the normal mixture to the distribution of load cycles and a good extrapolation ability of the normal mixture must be made again. Initial conditions can be chosen randomly or systematically, based on some preliminary knowledge about the distribution of load cycles. A normal mixture with three Gaussian functions, which correspond to the distribution of load cycles, presented in Fig. 1, is presented in Fig. 6. A comparison of its marginal probability distributions and measured marginal probability distributions is presented in Fig. 7. A normal mixture with five Gaussian functions that correspond to the same distribution of 0 BnnBjfokJ][p)l]Olf|i[gO | | ^SSfinMlGC | stran 600 J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices modeliranih in izmerjenih obrobnih porazdelitev verjetnosti je na sliki 9. V obeh primerih so bili neznani parametri mešanice Gaussovih funkcij ocenjeni na podlagi matrike relativnih frekvenc, ki ima število razredov v smeri amplitud in srednjih vrednosti enako M=M =64 in pripada obremenitvenemu stanju, opisanem v poglavju 2. Začetni pogoji za iteracijski postopek so bili v obeh primerih izbrani tako, da smo začetne vektorje srednjih vrednosti Gaussovih funkcij load cycles is presented in Fig. 8. A comparison of its marginal probability distributions and measured marginal probability distributions is presented in Fig. 9. Unknown parameters of both normal mixtures were estimated on the basis of the rainflow matrix of relative frequencies, with an equal number of classes in the direction of load-cycle amplitudes and load-cycle means: Ma=Mm=64. Initial conditions for the iterative process were again determined systematically by set- GPV obremenitvenih ponovitev / PDF of load cycles 40.00 35.00 30.00 25.00 20.00 15.00 10.00 5.00 0.00 -0.13 -0.11 0.30 35.00-40.00 30.00-35.00 25.00-30.00 20.00-25.00 15.00-20.00 10.00-15.00 5.00-10.00 0.00-5.00 0.51 Sred. vred. / Mean [V] Amplituda / Amplitude [V] 0.83 Sl. 6. Mešanica treh večdimenzionalnih Gaussovih funkcij; parametri mešanice, ocenjeni na podlagi matrike relativnih frekvenc; kaliber: 1 V = 26,5 kN Fig. 6. A normal mixture with three Gaussian functions; unknown parameters of the normal mixture are estimated on the basis of the rainflow matrix; calibre: 1 V = 26.5 kN GPV amplitud / PDF of amplitudes 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 OK amplitud / LS of amplitudes ^—----^ 0.0 0.2 0.8 1.0 0.4 0.6 Amplituda / Amplitude [V] Modelirana GPV / Modelled PDF Izmerjena GPV / Measured PDF GPV srednjih vrednosti / PDF of means 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -0.5 0.0 0.5 1.0 1.5 Srednja vrednost / Mean [V] Modelirana GPV / Modelled PDF Izmerjena GPV / Measured PDF 1 10 100 1000 Število obremenitvenih ponovitev / Number of load cycles [-] I, \ }f i / % y V ^f V^SAm^ 1.2 1.0 0.8 0.6 0.4 0.2 0.0 Modeliran OK / Modelled LS Izmerjen OK / Measured LS OK srednjih vrednosti / LS of means '—^^*r?- 1 10 100 1000 Število obremenitvenih ponovitev / Number of load cycles [-] -----Modeliran OK / Modelled LS — Izmerjen OK / Measured LS Sl. 7. Primerjava obrobnih porazdelitev verjetnosti za mešanico treh Gaussovih funkcij; parametri mešanice, ocenjeni na matrike relativnih frekvenc; kaliber: 1 V = 26,5 kN Fig. 7. Comparison of marginal probability distributions for the mixture of three Gaussian functions; unknown parameters of the normal mixture are estimated on the basis of the rainflow matrix; calibre: 1 V = 26.5 kN J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices GPV obremenitvenih ponovitev / PDF of load cycles 24.00 21.00 18.00 15.00 12.00 9.00 6.00 3.00 0.00 -0.13 -0.11 0.30 21.00-24.00 18.00-21.00 15.00-18.00 12.00-15.00 9.00-12.00 6.00-9.00 3.00-6.00 0.00-3.00 0.51 Sred. vred. / Mean [V] Amplituda / Amplitude [V] 0 83 Sl. 8. Mešanica petih večdimenzionalnih Gaussovih funkcij; parametri mešanice, ocenjeni na podlagi matrike relativnih frekvenc; kaliber: 1 V = 26,5 kN Fig. 8. A normal mixture with five Gaussian functions; unknown parameters of the normal mixture are estimated on the basis of the rainflow matrix; calibre: 1 V = 26.5 kN GPV amplitud / PDF of amplitudes 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 OK amplitud / LS of amplitudes ~~~—«-^-«-, 0.0 0.2 0.4 0.6 0.8 1.0 Amplituda / Amplitude [V] Modelirana GPV / Modelled PDF Izmerjena GPV / Measured PDF GPV srednjih vrednosti / PDF of means 0.0 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1 10 100 1000 Število obremenitvenih ponovitev / Number of load cycles [-] -----Modeliran OK / Modelled LS — Izmerjen OK / Measured LS OK srednjih vrednosti / LS of means -0.5 0.0 0.5 1.0 Srednja vrednost / Mean [V] 1.5 1 10 100 1000 Število obremenitvenih ponovitev / Number of load cycles [-] Modelirana GPV / Modelled PDF Izmerjena GPV / Measured PDF Modeliran OK / Modelled LS Izmerjen OK / Measured LS Sl. 9. Primerjava obrobnih porazdelitev verjetnosti za mešanico petih Gaussovih funkcij; parametri mešanice, ocenjeni na matrike relativnih frekvenc; kaliber: 1 V = 26,5 kN Fig. 9. Comparison of marginal probability distributions for the mixture of five Gaussian functions; unknown parameters of the normal mixture are estimated on the basis of the rainflow matrix; calibre: 1 V = 26.5 kN postavili v območje večje gostote obremenitvenih ponovitev. Njihove komponente so enake kakor v primeru ocene neznanih parametrov na temelju izločenih obremenitvenih ponovitev. 4 SKLEP ting up initial mean vectors of Gaussian functions in regions of higher densities of load cycles and are the same as in the case of the estimation of the normal mixture parameters on the basis of extracted load cycles. 4 CONCLUSION Če primerjamo ujemanje izmerjenih in It can be seen from the comparison of the modeliranih GPV, vidimo, da je ujemanje bistveno measured and the modelled marginal probability 0 BnnBjfokJ][p)l]Olf|i[gO | | ^SSfiflMlGC | stran 602 J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices boljše, če je GPV modelirana s petimi namesto s tremi Gaussovimi funkcijami. Ta sklep velja tako za primer ocene neznanih parametrov mešanice Gaussovih funkcij na podlagi porazdelitve obremenitvenih ponovitev kakor tudi za primer ocene neznanih parametrov mešanice Gaussovih funkcij na temelju matrike relativnih frekvenc obremenitvenih ponovitev. Tak rezultat je logičen, saj je mešanica Gaussovih funkcij, ki vsebuje več Gaussovih funkcij, bolj prilagodljiva, če so izmerjene porazdelitve obremenitvenih ponovitev močno razgibane. Izkazalo se je tudi, da ekstrapolacijske zmožnosti mešanice petih Gaussovih funkcij ne zaostajajo bistveno za ekstrapolacijskimi zmožnostmi treh Gaussovih funkcij. Zatorej lahko sklepamo, da je izbira mešanice petih Gaussovih funkcij v tem primeru bolj upravičena. Iz rezultatov je tudi razvidno, da praktično ni razlike, če neznane parametre GPV ocenimo na podlagi izločenih obremenitvenih ponovitev ali na podlagi matrike relativnih frekvenc obremenitvenih ponovitev. To pomeni, da se je rešitev pri obeh postopkih približala k istemu lokalnemu vrhu funkcije verjetnosti, kar je tudi posledica enakih začetnih pogojev pri obeh postopkih. Kljub temu, da smo dobili enake rezultate, pa hitrost konvergence pri posameznih postopkih ni enaka. Hitrost konvergence pri izbranem številu Gaussovih funkcij v mešanici je odvisna od števila izločenih obremenitvenih ponovitev, če neznane parametre GPV ocenjujemo na temelju izločenih obremenitvenih ponovitev, oziroma od števila od nič različnih elementov v matriki relativnih frekvenc, če neznane parametre GPV ocenjujemo na podlagi matrike relativnih frekvenc. Z večanjem števila izločenih obremenitvenih ponovitev ali števila od nič različnih elementov padavinske matrike se hitrost iteracijskega postopka zmanjšuje. Nasvet za izbiro ustreznega postopka bi bil takšen: če je red velikosti števila izločenih obremenitvenih ponovitev enak redu velikosti števila od nič različnih elementov v matriki relativnih frekvenc, tedaj neznane parametre GPV ocenimo na temelju izločenih obremenitvenih ponovitev, sicer pa neznane parametre GPV ocenimo na temelju matrike relativnih frekvenc. Ujemanje izmerjenih in modeliranih GPV je zadovoljivo v vseh štirih prikazanih primerih, iz česar je mogoče sklepati, da je metoda največje verjetnosti, dopolnjena z EM algoritmom, primerna metoda za modeliranje zvezne GPV obremenitvenih ponovitev. Morebitna pomanjkljivost te metode je, da so rezultati iteracijskega postopka včasih odvisni od začetnih vrednosti parametrov GPV. Vendar lahko to pomanjkljivost odpravimo, če začetnih vrednosti za iteracijski postopek ne izbiramo na slepo, ampak upoštevamo nekatere značilnosti porazdelitve naključne spremenljivke. densities that better agreement between the measured and the modelled PDFs can obtained if the PDF of the load cycles is modelled with the normal mixture consisting of five instead of three Gaussian functions. This is true for the estimation of normal mixture parameters based on extracted load cycles as well as for the estimation of normal mixture parameters based on the rainflow matrix. Such a result is logical, because of the better adaptation ability of the normal mixture with five Gaussian functions when compared to the normal mixture with three Gaussian functions. At the same time it turned out that the extrapolation abilities of normal mixtures with five and three Gaussian functions are almost the same for our example of load state. So it can be concluded that the normal mixture with five Gaussian functions is a better choice in this case. The results appertaining to normal mixtures consisting of the same number of Gaussian functions are similar, if the estimation of the normal mixture parameters was made on the basis of the extracted load cycles or on the basis of the rainflow matrix. This is a consequence of the fact that solutions of the system of the iterative equation have converged to the same local maximum of the likelihood function, regardless of the variant of the estimation of the normal mixture parameters. The reason for this can be found in the same initial conditions for the iterative process in both variants of the estimation of the normal mixture parameters. However, the speed of convergence for different variants of the estimation was not the same. If the number of Gaussian functions in the normal mixture is fixed to some specified value, then the speed of convergence depends only on the number of load cycles, when the estimation is done on the basis of extracted load cycles, or on the number of nonzero elements of the rainflow matrix when the estimation is done on the basis of the rainflow matrix. The greater the number of extracted load cycles or the number of nonzero elements of the rainflow matrix, the lower the speed of the iterative process. So when the number of extracted load cycles is of the same order of magnitude as the number of non-zero elements of the rainflow matrix, the estimation of the normal mixture parameters should be made on the basis of the extracted load cycles, otherwise it should be made on the basis of the rainflow matrix. Nevertheless, good agreement between the measured and the modelled probability distribution can be seen in all the presented results. This means that the maximum-likelihood method, supplemented with the EM algorithm, is a good method for modelling the PDF of the load cycles. In spite of all that, one drawback of this method should be mentioned at the end. Namely, the result of the iterative process for the parameter estimation sometimes depends on the initial conditions of the iterative process. But this can be overcome if the initial conditions are chosen systematically, based on some preliminary knowledge of the distribution of the load cycles. | lgfinHi(š)bJ][M]lfi[j;?n 0110 stran 603 I^BSSIfTMlGC J. Klemenc - M. Fajdiga: Modeliranje matrik - The Modelling of Matrices 5 LITERATURA 5 REFERENCES [1] Kokol, M., I. Grabec (1994) Training of elliptical basis function NN, World Congress on Neural Networks, San Diego, California, Vol. II, editor: Erlbaum L., INNS Press, New Jersey, 379-384. [2] Duda, R. O., P.E. Hart (1973) Pattern classification and scene analysis, John Willey and Sons, New York. [3] Bishop, C. M. (1996) Neural networks for pattern recognition, Clarendon Press, Oxford. [4] Klemenc, J.(2000) Description of statistical dependencies of parameters of random load state (Dependency of random load parameters), International Journal of Fatigue, Vol. 22, No. 5, Elsevier Science Ltd, Oxford 357-367. [5] Klemenc, J. (1999) Popis zveze med parametri naključnih obremenitvenih stanj konstrukcij, Magistrsko delo, Fakulteta za strojništvo, Ljubljana. [6] Amzallag, C, J.P Gerey, J.L. Robert., J. Bauhaud (1994) Standardization of the rainflow counting method for fatigue analysis, Fatigue, Vol. 16, No. 6, Butterworth-Heinemann Ltd, 287-293. [7] Billy, M. (1989) Dependability of mechanical systems, Elsevier, New York, Amsterdam. [8] Fajdiga, M., T Jurejevčič, J. Kernc (1996) Reliability prediction in early phases of product design, Journal of Engineering Design, Vol. 7, No. 2, 107-128. [9] Fajdiga, M., M. Nagode (1997) Analiza obremenitvenega stanja viličarja INDOS nosilnosti 2500 kg, Poročilo, Fakulteta za strojnisvo, Ljubljana. Naslov avtorjev: mag. Jernej Klemenc profdr. Matija Fajdiga Fakulteta za strojništvo Univerza v Ljubljani Aškerčeva 6 1000 Ljubljana Authors’ Address: Mag. Jernej Klemenc Prof. Dr. Matija Fajdiga University of Ljubljana Faculty of Mechanical Eng. Aškerčeva 6 SI-1000 Ljubljana, Slovenia Prejeto: Received: 12.7.2001 Sprejeto: Accepted: 7.12.2001 0 SšnrKitafcflM]! ma stran 604 © Strojni{ki vestnik 47(2001)10,605-614 © Journal of Mechanical Engineering 47(2001)10,605-614 ISSN 0039-2480 ISSN 0039-2480 UDK 004.94:621.753.5:621.7 UDC 004.94:621.753.5:621.7 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Uporaba numeri~nih simuliranj pri razvoju orodij za izdelavo plo~evinastih sestavnih delov avtomobilov The Use of Numerical Simulations in the Development of Tools for the Sheet-Metal Parts of Cars Ga{per Gantar - Marko Ljevar - Karl Kuzman V Sloveniji obstaja veliko orodjarn, ki izdelujejo orodja za izdelavo avtomobilskih pločevinastih sestavnih delov. Z namenom, da bi skrajšali razvojne čase in zmanjšali število napak na orodjih, se v zadnjem času intenzivno uporabljajo numerična simuliranja na podlagi metode končnih elementov (MKE). Izdelovalne tehnologije so v ti navideznem okolju preverjene še pred izdelavo orodij. Napake so odkrite v zgodnji fazi razvojnega kroga, zato je njihovo odpravljanje cenejše. V prispevku je prikazan postopek vključevanja numeričnih simuliranj v krog razvoja orodja za izdelavo novega izdelka. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: preoblikovanje pločevine, simuliranje numerično, razvoj izdelkov, optimiranje) Many tool-manufacturing companies in Slovenia are producing the tools required for the sheet-metal parts of cars. Numerical simulations based on the finite-element method (FEM) have recently become widely used in order to reduce the development times and the number of mistakes associated with the manufacture of these tools. Production technologies are tested in the so-called virtual environment before the tools are produced. Mistakes are detected at an early phase of the development cycle, and as a result, their removal is cost effective. In this paper we present the implementation of numerical simulations in the development cycle of a tool for a new product. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: sheet metal forming, numerical simulations, product development, optimization) 0 UVOD Potek postopkov preoblikovanja pločevine je odvisen od številnih parametrov, ki jih je težko nadzorovati. Za določitev optimalne kombinacije teh parametrov so potrebni testi, za katere je treba izdelati testna orodja, zato so ti testi dragi in dolgotrajni. Kadar testi niso uspešni, je treba testna orodja predelati ali izdelati nova in teste ponoviti, kar še podaljša čas do zagona redne proizvodnje. Preoblikovalne postopke je zato smiselno preveriti z uporabo numeričnih simuliranj v t.i. “navideznem okolju” še preden so narejena orodja. 1 UPORABA NUMERIČNIH SIMULIRANJ V KROGU RAZVOJA NOVEGA IZDELKA Postopek uvedbe novega izdelka je predstavljen na sliki 1. Numerična simuliranja je primerno uporabljati v različnih fazah. Uporaba mora biti čimbolj organizirana. Na začetku je za grobo oceno velikega števila konstrukcijskih rešitev smiselno uporabljati hitrejše toda manj zanesljive tehnike, 0 INTRODUCTION Stamping processes depend on numerous parameters that are hard to control, and so tests are needed to determine the best combination of these parameters. As prototype tools have to be produced, such tests are costly and time consuming. If the tests are not successful the tools need to be remade or new prototype tools need to be manufactured, and as a result the start of production is delayed. It is reasonable, therefore, to test the forming processes by means of numerical simulations in the virtual environment before the forming tools are produced. 1 THE USE OF NUMERICAL SIMULATIONS IN THE PRODUCT DEVELOPMENT CYCLE The product development cycle is presented in Figure 1. It makes sense to perform the numerical simulations at different stages and it is important that the procedure is as organised as possible. At the beginning a lot of design solutions should be roughly evaluated by quick but less reliable gfin^OtJJIMISCSD 01-10 stran 605 |^BSSITIMIGC G. Gantar - M. Ljevar - K. Kuzman: Uporaba numeri~nih simuliranj - The Use of Numerical Simulations kasneje pa je treba uporabiti bolj zanesljive a tudi časovno potratne tehnike za končno optimizacijo izbrane rešitve, kakor je prikazano na sliki 1. V prispevku je prikazan primer, pri katerem so bila numerična simuliranja uporabljena šele v orodjarni, ki je izdelala proizvajalna orodja, zato je bil uporabljen programski paket, ki omogoča izvedbo natančnih koračnih numeričnih simuliranj. techniques, only later should more reliable but also more time-consuming techniques be used for the final optimisation of the selected solution, as presented in Figure 1. In this paper we present an example where numerical simulations were used in a tool-manufacturing company producing forming tools, therefore, software that performs a reliable incremental numerical simulation was used. CAS TIME STROŠKI COSTS KAKOVOST QUALITY Lokalne analize Local analysis Analize z grobo mrežo Coarse mesh analysis Inverzne analize Inverse analysis X V ENEM KORAKU ONE STEP Koračne simulacije Incremental simulations ODDELKI i DEPARTMENTS TRŽENJE MARKETING CAE IZDELAVA ORODIJ TOOL MANUFACTURING HITRA IZDELAVA PROTOTIPOV RAPID PROTOTYPING OBLIKOVANJE DESIGN RAZVOJ DEVELOPMENT NUMERIČNE SIMULACIJE NUMERICAL SIMULATIONS 1. 2. 3. * I__________f Cas Time .OD IDEJE DO MASOVNE PROIZVODNJE, Čas FROM IDEA TO THE MASS PRODUCTION? Time Sl. 1. Postopek uvedbe novega izdelka [1] Fig. 1. The product development cycle [1] Numerična simuliranja predstavljajo zanesljivo orodje za napovedovanje poteka preoblikovalnih postopkov in omogočajo napovedovanje: trganja, gubanja, končne debeline pločevine, zaostalih napetosti, površinskih napak in elastičnega izravnavanja obdelovanca, optimalno začetno geometrijsko obliko platine ter sil in pritiskov na aktivne površine orodja [1]. V tujini z uporabo numeričnih simuliranj preverijo izdelovalne tehnologije za več ko 30% glavnih pločevinskih sestavnih delov. Na ta način vnaprej napovejo in preprečijo več ko 50% napak [2]. Numerična simuliranja predstavljajo tudi eno od orodij za uvajanje in izvajanje sočasnega inženirstva, saj omogočajo vnaprejšnje Numerical simulations represent a reliable tool for the prediction of forming processes and enable the prediction of the following: tearing, wrinkling, final sheet thickness, residual stresses, surface defects, springback, optimum initial blank shape, forces and pressures on the active surfaces of the tool [1]. The forming technologies for more than 30% of major sheet-metal parts in other countries are tested by means of numerical simulations. In this way more than 50% of errors are predicted and prevented [2]. Numerical simulations also represent one of the fundamental tools for establishing and performing concurrent engineering, as they enable early predictions and simplify the exchange of information between the 0 BnnBjfokJ][p)l]Olf|i[gO | | ^SSfiFlMlGC | stran 606 G. Gantar - M. Ljevar - K. Kuzman: Uporaba numeri~nih simuliranj - The Use of Numerical Simulations napovedovanje in poenostavijo dialog med člani razvojne skupine. Konstrukter izdelka, tehnolog in izvajalec numeričnih simuliranj vzpostavijo boljši dialog pri sočasnem razvoju izdelka. 2 ANALIZA POKROVNEGA DELA PREČNEGA NOSILCA Orodja za izdelavo dveh pločevinskih sestavnih delov za podvozje nove VW limuzine, ki sta predstavljena na sliki 2, so bila naročena v slovenski orodjarni. Ker sta dela simetrična, so v orodjarni, predlagali, da bi izdelalovali oba hkrati v enem preoblikovalnem orodju in ju v zadnji operaciji prerezali na dva dela. Predlagana rešitev je omogočila zmanjšanje stroškov za izdelavo orodja in povečanje produktivnosti v proizvodnji (s vsakim gibom pehala bi bila izdelana dva izdelka). Oblika, sestavljena iz obeh delov, ki jo je treba izdelati v prvi operaciji globokega vleka, je zelo zapletena, zato so bila za testiranje in optimizacijo proizvodne tehnologije uporabljena numerična simuliranja. members of the development team. The product designer, the production-process designer and the numerical-simulation expert can establish a much better dialog during the concurrent development of the product. 2 ANALYSIS OF THE COVER OF THE TRANSVERSAL RAIL The tools for the production of two sheet-metal chassis parts for a new VW limousine, presented in Figure 2, have been ordered from a Slovenian tool-manufacturing company. Since the parts are symmetrical the tool-manufacturing company had the idea to produce both of them in the same tool-set and cut them into two during the final forming operation. The idea promised a large reduction in tool-manufacturing costs and an increased productivity (two parts are produced by each punch stroke). The geometry combined from both parts, which has to be produced by deep drawing in the first forming stage was very complex. Numerical simulations were used to test and optimise the production technology. Sl. 2. Pločevinasta sestavna dela Fig. 2. Sheet-metal chassis parts Predstavljeno numerično simuliranje je bilo izvedeno s programskim paketom PAM-STAMP MKE model za prvo operacijo globokega vleka je predstavljen na sliki 3. Ker je izdelek simetričen, je bil uporabljen polovični model. Preostale preoblikovalne operacije: rezanje, luknjanje in upogibanje niso bile vprašljive in niso bile preučevane. Površine delov orodja so bile diskretizirane s trikotnimi in štirikotnimi elementi kot popolnoma toge, platina je bila diskretizirana s štirikotnimi elementi z elasto-plastičnim reološkim modelom. Za popis utrjevanja je bil uporabljen Krupkowskijev zakon. Celoten model je sestavljen iz 22400 elementov. Trenje med platino in deli orodja je bilo upoštevano s Coulombovim zakonom trenja. V nadaljevnaju so predstavljeni samo tisti rezultati numeričnih simuliranj, ki so bili pomembni za odločanje. The numerical simulation was performed using PAM-STAMP software. The FEM model for the first deep-drawing operation is presented in Figure 3. Since the product is symmetrical, a half-model was used. Other forming stages: cutting, piercing and bending were not critical and were excluded from the study. The surfaces of the tool parts were discretized with triangular and quadrangular surface elements, which were assumed to be perfectly rigid. The blank sheet was discretized with quadrangular elements, representing the material with an elasto-plastic constitutive law. For the material-hardening determination, the Krupkowski law was used. The model consisted of 22400 elements. The friction between the blank and the tool parts was modelled using Coulomb’s law. Only the results of the numerical simulations that were important for the decision-making process are presented. gfin^OtJJlMISCSD 01-10 stran 607 |^BSSITIMIGC G. Gantar - M. Ljevar - K. Kuzman: Uporaba numeri~nih simuliranj - The Use of Numerical Simulations MATERIAL: VW11-ZSt E220 Zakon utrjevanja af = 547 • q,0,24 (1) Napetost tečenja R = 240 MPa Koef. anizotropije r0 = 1,72 r = 1,72 r = 1,72 Debelina pločevine s = 1,5 mm Koeficienti trenja : = 0,12 (pestič) / 0,08 (držalo, matrica) Dolžina delovnega giba = 256 mm PESHČ/PUNCH ZAVORNA LETEV DRAWBEAD PLOČEVINSKO DRŽALO BLANKHOLDER PLATINA /BLANK MATRICA/DIE ( 8 fy+ •5 3,5 MATERIAL: VW11-ZSt E220 Hardening law af = 547 • q,0,24 (1) Yield stress Rp = 240 MPa Coef. of anisotropy r0 = r = r = 1,72 Sheet thickness s = 1,5 mm Coefficients of friction : H = 0,12 (punch) / 0,08 (die, blankholder) Punch stroke = 256 mm Sl. 3. Model MKE Fig. 3. FEM model 2.1 Rezultati prvega numeričnega simuliranja Ker platina na koncu obdelovalnega postopka na nekaterih mestih ni v stiku z držalom pločevine, je bilo pričakovano gubanje in zato je bilo prvo numerično simuliranje izvedeno z zavornimi letvami dolžine 790 mm. Zavorne letve, katerih geometrijska oblika je predstavljena na sliki 3, zavirajo tok materiala v srednjem delu orodja in s tem zmanjšujejo nevarnost gubanja. Pred simuliranjem je bila izvedena kalibracija zavorne letve, ki je pokazala, da zavorna letev zavira tok pločevine s silo Fd=330N/mm in poskuša razpreti matrico in držalo s silo F=800N/mm. Glede na izkušnje zaposlenih v orodjarni, je bila izbrana platina velikosti AxB=1000x750mm. Z uporabo Sieblove enačbe smo izračunali primerno silo držala Fdr .= 1000 kN [4]. Rezultati numeričnega simuliranja so napovedali porušitev obdelovanca na več mestih že precej pred koncem obdelovalne operacije (preglednica 1). Trganje je bilo napovedovano s primerjavo deformacijskih stanj v elementih modela s krivuljo mejne deformljivosti (KMD), ki je bila izračunana teoretično [5]. Deformacijska stanja, ki ležijo nad zgornjo krivuljo, napovedujejo porušitev. Gubanje pločevine ni bilo napovedano. 2.2 Rezultati drugega numeričnega simuliranja Numerično simuliranje je bilo izvedeno še enkrat brez zavornih letev in z manjšo silo držala 2.1 Results of the first numerical simulation Since the blank is not in contact with the blankholder in some places at the end of the forming process we expected wrinkling, therefore, the first numerical simulation was performed with drawbeads of length 790 mm. Drawbeads, the geometry of which is presented in Figure 3, constrain the material flow in the central part of the tool and reduce the danger of wrinkling. Drawbead calibration, performed before the numerical simulation, showed that the drawbead brakes the sheet metal with the force Fd=330N/mm and lifts the blankholder with the uplift force F =800N/ mm. The initial blank dimensions AxB=1000x570mm were determined, based on the previous experience of the process designers in the tool-manufacturing company. The appropriate blankholder force Fd. = 1000kN was calculated with the Siebel equation [4] . The results of the numerical simulations predicted the fracture of the work-piece at several places, long before the end of the forming operation (see Table 1). The fracture prediction was made by comparing the strain states in the elements of the model to the forming limit curve (FLC) of the given material, which was calculated theoretically [5]. The strain states above the upper curve predict fracture. No wrinkling was predicted in the first numerical simulation. 2.2 Results of the second numerical simulation The numerical simulation was repeated without the drawbeads and with a lower blankholder 0 SšnrKitafcflM]! ma stran 608 G. Gantar - M. Ljevar - K. Kuzman: Uporaba numeri~nih simuliranj - The Use of Numerical Simulations Preglednica 1. Rezultati prvega numeričnega simuliranja Table 1. Results of the first numerical simulation 1. NUMERIČNO SIMULIRANJE (ustavljena 72 mm pred koncem delovnega giba) Fdr=1000kN , zavorne letve=DA, velikost platine AxB=1000x750 mm 1st NUMERICAL SIMULATION: (stopped 72 mm before the end of the tool stroke) Fm = 1000kN , Drawbeads = YES , blank dimensions AxB = 1000 x 750 mm Diagram mejne preoblikovalnosti Forming limit diagram 3,0 2,4 1,8 1,2 0,6 -0,6 -0,4 -0,2 0 0,2 Druga glavna deformacija (1) Minor strain 0,4 Mesta, kjer je napovedano trganje Places of predicted fracture x Preglednica 2. Rezultati drugega numeričnega simuliranja Table 2. Results of the second numerical simulation 2. NUMERIČNO SIMULIRANJE F^=540kN , zavorne letve=NE, velikost platine AxB=1000x750 mm 2nd NUMERICAL SIMULATION Fdr = 540 kN , Drawbeads = NO , blank dimensions AxB = 1000 x 750 mm Diagram mejne preoblikovalnosti Forming limit diagram 2,5 2,0 1,5 1,0 0,5 0 -0,6 -0,4 -0,2 0 Druga glavna deformacija Minor strain 0,2 0,4 (1) Oblika obdelovanca Shape of the work-piece 114 Mesta, kjer je napovedano trganje Places of predicted fracture | IgfinHŽšlbJlIMlIgiCšD I stran 609 SUMEČ G. Gantar - M. Ljevar - K. Kuzman: Uporaba numeri~nih simuliranj - The Use of Numerical Simulations Fdr =540kN z namenom, da se izboljša tok materiala v orodje in na ta način bistveno zmanjša nevarnost trganja. Nevarnost gubanja je večja, toda ker preučevana izdelka nista na vidnem mestu, so manjše gube sprejemljive. Numerično simuliranje je tudi tokrat napovedalo trganje pločevine, a samo na enem kritičnem mestu obdelovanca. 2.3 Rezultati tretjega numeričnega simuliranja Če primerjamo obliko obdelovanca po izvedbi operacije globokega vleka in končnih sestavnih delov (preglednica 2), ugotovimo, da na kritičnem mestu obdelovanca ostane po operaciji globokega vleka precej odvečnega materiala. Sile držala ni bilo več mogoče zmanjšati, zato je bila edina možnost za izdelavo sestavnega dela z eno operacijo globokega vleka nadaljnje zmanjšanje začetne velikosti platine. Tretje numerično simuliranje je bilo izvedeno z manjšo platino. Stik med platino in držalom je bil bistveno zmanjšan in pričakovano je bilo gubanje platine. Kako bi potekal globki vlek manjše platine, smo poskušali napovedati s tretjim numeričnim simuliranjem. Preglednica 3. Rezultati tretjega numeričnega simuliranja Table 3. Results of the third numerical simulation force F =540kN in order to improve the flow of the material into the die and therefore to considerably reduce the danger of fracture. The danger of wrinkling is increased but since the studied parts are not visible the minor wrinkles are acceptable. The numerical simulation once again predicted the fracture but this time only in one critical area of the work-piece. 2.3 Results of the third numerical simulation If we compare the shape of the work-piece after the first deep-drawing operation and the shape of the final product (Table 2) we can see that there is a lot of residual material around the critical area of the work-piece. The blankholder force could not be reduced any more, therefore, the only way to produce the part in a single deep-drawing operation was to further reduce the initial blank size. The third numerical simulation was performed with a smaller blank. The contact between the blank and the blankholder was reduced considerably and therefore wrinkling was expected. The deep-drawing process with the smaller initial blank size was predicted with the third numerical simulation. 3. SIMULIRANJE (gubanje 14 mm pred koncem delovnega giba) Fdrž=540kN , zavorne letve=NE, velikost platine AxB=890x750 mm 3rd NUMERICAL SIMULATION (wrinkling 14mm before the end of the tool stroke) Fm = 540 kN , Drawbeads = NO , blank dimensions AxB = 890 x 750 mm Diagram mejne preoblikovalnosti Forming limit diagram 1,2 0,9 0,6 0,3 0 -0,6 -0,4 -0,2 0 Druga glavna deformacija Minor strain 0,2 (1) 0,4 Mesta, kjer je napovedano gubanje Prediction of predicted wrinkling Napoved gubanja Prediction of wrinkling Rezultati numeričnega simuliranja so napovedali, da je operacija globokega vleka izvedljiva brez porušitve (deformacijska stanja v vseh elementih ležijo pod KMD). Napovedano je bilo intenzivno gubanje. Gube se ob koncu preoblikovalnega giba v orodju izravnajo. Na obdelovancu se kjub temu še vedno poznajo odtiski in manjše gube. Ker predstavljeni izdelki niso na vidnem mestu, so bile manjše gube in odtiski za kupca sprejemljivi. Orodje je bilo izdelano in preskušeno. The results of the numerical simulation predicted that the deep-drawing operation was feasible without the danger of fracture (strain states in all elements are below the FLC), however, heavy wrinkling was predicted. At the end of the punch stroke the wrinkles were ironed in the die, but some minor wrinkles and marks on the product surface still remained. Since the parts are not visible, minor wrinkles and marks on the surface were acceptable for the customer. The tool was produced and tested. 0 BnnBjfokJ][p)l]Olf|i[gO | | ^SSfiFlMlGC | stran 610 G. Gantar - M. Ljevar - K. Kuzman: Uporaba numeri~nih simuliranj - The Use of Numerical Simulations 3 PRIMERJAVA REZULTATOV TRETJEGA NUMERIČNEGA SIMULIRANJA IN REZULTATOV PRESKUSOV Na podlagi rezultatov numeriČnih simuliranj je bilo izdelano in preskušeno preoblikovalno orodje. Na sliki 5 desno je prikazan preskušanec, pri katerem je bil gib pestiča ustavljen 14 mm pred koncem preoblikovalne operacije z namenom, da laže opazujemo gubanje. 3 COMPARISON OF THE RESULTS OF THE THIRD NUMERICAL SIMULATION AND THE RESULTS OF TESTING Based on the results of the numerical simulations the forming tool was produced and tested. In Figure 5 the test-piece is presented, with the punch stroke stopped 14 mm before the end of the forming operation in order to see the wrinkles clearly. Intenzivno gubanje Heavy wrinkling Sl. 5. Testiranje orodja in testni izdelek Fig. 5. Testing of the tool and test-piece Ugotovimo lahko, da je obdelovanec res brez razpok in naguban na napovedanih mestih. Na sliki 6 je prikazano še celotno transferno orodje za izdelavo pokrovnih delov prečnih nosilcev. It can be concluded that no fracture occurred on the test-piece and the wrinkles are visible at the predicted places. In Figure 6 the whole transfer tool for the production of the covers of the transversal rails is presented. Sl. 6. Končno transferno orodje Fig. 6. Final transfer tool stran 611 G. Gantar - M. Ljevar - K. Kuzman: Uporaba numeri~nih simuliranj - The Use of Numerical Simulations 4 ZANESLJIVOST REZULTATOV, STROŠKI, PREDNOSTI IN ČASI, POTREBNI ZA IZVEDBO NUMERIČNIH SIMULIRANJ Na podlagi izkušenj, predstavljenih v prispevku in pridobljenih na drugih industrijskih primerih, pri katerih smo primerjali rezultate numeričnih simuliranj z rezultati preskusov, je bila narejena naslednja preglednica, ki opisuje zanesljivost numeričnih simuliranj. Zavedati pa se moramo, da je za doseganje velike zanesljivosti rezultatov treba poprej kalibrirati uporabljani programski paket ter vanj vnesti pravilne in natančne materialne podatke, ki jih je moč dobiti z enoosnim nateznih preskusom. V nasprotnem primeru so lahko rezultati numeričnih simuliranj zavajajoči. 4 RELIABILITY OF THE RESULTS, COSTS, BENEFITS AND TIMES REQUIRED FOR PERFORMING THE NUMERICAL SIMULATIONS Based on the experience presented in this paper and gained from other industrial examples where numerical simulation results were compared to the results of the testing, the following table presenting the reliability of numerical simulations has been made. Previous calibration of the software is required in order to achieve high reliability of the results. Exact material data, which can be obtained by a uni-axial tensile test, must be inserted into the software or the results of the numerical simulation can be misleading. Preglednica 4. Zanesljivost numeričnih simuliranj ([6] do [9]) Table 4. Reliability of the results of numerical simulations ([6] to [9]) Namen Aim Zanesljivot Reliability določitev optimalne začetne oblike platine determination of optimum initial blank geometry ZZ napoved trganja prediction of tearing ZZ napoved končne debeline pločevine prediction of final sheet thickness ZZ napoved gubanja prediction of wrinkling Z napoved elastičnega izravnavanja prediction of springback DZ ocena sil in pritiskov na orodje evaluation of forces and pressures acting on the tool ZZ napoved površinskih poškodb prediction of surface defects NZ ZZ = zelo zanesljivo , Z = zanesljivo , DZ = delno zanesljivo , NZ = nezanesljivo ZZ = very reliable , Z = reliable , DZ = partly reliable , NZ = unreliable Napoved elastičnega izravnavanja in površinskih poškodb še ni na zadovoljivi ravni. Drugi avtorji, ki se ukvarjajo z numeričnimi simuliranji, poročajo o istih težavah, ne glede na to, kateri programski paket uporabljajo ([6] in [7]). Čas za izračun predstavljenega primera je znašal 70 ur na delovni postaji Silicon Graphics Indigo2. Če upoštevamo še čas, potreben za pripravo modela in analizo rezultatov, lahko želene napovedi dobimo v nekaj dneh. Kljub dejstvu, da so numerična simuliranja draga in rezultati niso povsem zanesljivi, je uporaba numeričnih simuliranj smiselna. Večino težav je mogoče vnaprej napovedati. Konstrukcijo orodja je v zgodnji fazi razvoja treba preprosto spremeniti z minimalnimi stroški. Minimizirane so tudi zamude pri dobavi. 5 SKLEP Podjetja, ki delujejo kot poddobavitelji avtomobilskih proizvajalcev, se soočajo z izrednimi zahtevami za zvečanje kakovosti proizvodov ob The prediction of springback and surface defects is still not at a satisfactory level. Other authors dealing with numerical simulations report the same problems, regardless of the software used ([6] and [7]). The calculation time of the presented examples was 70 hours on a Silicon Graphics Indigo2 machine. When taking into account the time required for the preparation of the model and the analysis of the results, the necessary prediction can be obtained within a few days. The use of numerical simulations is reasonable, despite the fact that the use of a numerical simulation is expensive and the results are not completely reliable. The majority of the problems can be predicted in advance. Tool design is easily changed at an early design stage with minimum costs. Delivery delays are also minimised. 5 CONCLUSION Suppliers to the automotive industry are facing extraordinary demands for increasing the quality of products, while at the same time lowering 0 BnnBjfokJ][p)l]Olf|i[gO | | ^SsFvWEIK | stran 612 G. Gantar - M. Ljevar - K. Kuzman: Uporaba numeri~nih simuliranj - The Use of Numerical Simulations hkratnem zmanjševanju razvojnih časov in proizvajalnih stroškov. Kljub temu, da so sestavni deli avtomobilov čedalje bolj zapleteni in so zaradi tega bolj zapletena tudi orodja za njihovo izdelavo, so zamude in dodatni stroški zaradi dodatnih popravil orodij za kupce nesprejemljivi. Osnovni razvoj numeričnih simuliranj, ki temeljijo na metodi MKE, se je začel pred desetletji. Danes so paketi za izvedbo simuliranj in računalniki razviti do take stopnje, da pomenijo zanesljivo in tudi dovolj hitro orodje za industrijsko uporabo. Na industrijskem primeru je prikazano, kako je mogoče z uporabo numeričnih simuliranj vnaprej napovedati napake pri konstrukciji orodja in načrtovanju tehnološkega procesa. Optimirano orodje je delovalo pravilno in ga po izdelavi ni bilo treba popravljati. V primerih, ko orodjarna uporablja numerična simuliranja, lahko vzpostavi boljši dialog z naročnikom orodja. Laže se je dogovoriti za spremembe na izdelku, ki ne spremenijo njegove uporabnosti, a izboljšajo njegovo preoblikovalnost. Naročniki orodij se zavedajo prednosti, ki jih prinaša uporaba numeričnih simuliranj, zato raje sodelujejo z orodjarnami, ki so numerična simuliranja že uvedle v svoje razvojne cikle. Zahvala Programski paket PAM-STAMP in računalniška oprema, ki je bila uporabljena za izvedbo numeričnih simuliranj, predstavljenih v pričujočem prispevku, je last TECOSa - razvojnega centa orodjarstva Slovenije. TECOSu se zahvaljujemo za uporabo opreme. development times and costs. The delays and additional costs for repairs to the tools are unacceptable for customers, even though the complexity of the car components and the tools for their production is increasing constantly. Fundamental research and development of numerical simulations based on a FEM approach began several decades ago. Nowadays, the software for performing numerical simulations and hardware are developed to the level where they represent a reliable and fast tool for industrial use. We have shown, using an industrial example, that numerical simulations can predict mistakes in tool design and production-process planning in advance. The optimised tool was working properly and no repairs were necessary after the production of the tool. When numerical simulations are used by a tool-manufacturing company a much better dialog can be established with the customer. It is easier to discuss changes to the design of the product that do not change its functionality but achieve better formability. The customers are aware of the benefits of the use of numerical simulations, therefore, they prefer the tool-manufacturing companies that have already implemented numerical simulations into their development cycles. Acknowledgement The PAM-STAMP program package and the hardware used for performing the numerical simulation were provided by TECOS - the Slovenian Tool and Die Development Centre. We would like to thank TECOS for the use of the equipment. meja tečenja napetost tečenja koeficinet anizotropije koeficient trenja zaviralna sila zavorne letve razpiralna sila zavorne letve velikost platine sila držala debelina pločevine R r p H Fd F Ab 6 SIMBOLI 6 SYMBOLS MPa MPa - - N/mm N/mm mm N mm flow stress yield stress coefficient of anisotropy coefficient of friction constraining force of the drawbead uplifting force of the drawbead blank dimensions blankholder force sheet thickness 7 LITERATURA 7 REFERENCE [1] Pepelnjak, T, G. Gantar, K. Kuzman (1999) Optimisation of the forming process by numerical simulations. International Sheet Metal Review, vol. 1, No. 4, 44-48. [2] Kampuš, Z. (1999) Analysis of factors influencing accuracy in the drawing of round rods. J. Mater. Process. Technol., vol. 87, No. 1/3, 90-96. [3] Gantar, G., T. Pepelnjak, K. Kuzman (1999) Use of numerical simulations in product and production process gfin^OtJJlMISCSD 01-10 stran 613 |^BSSITIMIGC G. Gantar - M. Ljevar - K. Kuzman: Uporaba numeri~nih simuliranj - The Use of Numerical Simulations optimisation. Proceedings of the4th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes NUMISHEET’99, vol. 1, 323-328. [4] Kuzman, K., J. Pipan, Z. Kampuš (1995) Priporočila za načrtovanje tehnologij. Univerza v Ljubljani, Fakulteta za strojništvo. [5] Gantar, G. (1998) Metode za načrtovanje procesov preoblikovanja pločevine. Univerza v Ljubljani, Fakulteta za strojništvo, magistrsko delo. [6] Makinouchi, A., C. Teodosiu, T. Nakagawa (1998) Advance in FEM simulation and its related technologies in sheet metal forming. CIRP Annals - Manufacturing Technology, Vol. 47/2/1998, 641-646. [7] Schmidt, H., T.C. Vu, L. Recke (1996) Sheet forming simulation - The breakthrough of a new technology. Proceedings of the 3rd Int. Conference NUMISHEET96. [8] Pepelnjak, T., Z. Kampuš (2001) Analize kakovosti pridrževanja pločevine pri globokem vleku. Strojniški vestnik, 2(2001), Vol. 47, str. 94-105, [9] Pepelnjak, T., G. Gantar, K. Kuzman (2001) Numerical simulations in optimisation of product and forming process. Journal of Materials Processing Technology, Vol. 115, No. 1, 122-126. Naslova avtorjev: mag Gašper Gantar prof.dr. Karl Kuzman Fakulteta za strojništvo Univerza v Ljubljani Aškerčeva 6 1000 Ljubljana mag. Marko Ljevar M.P.P. tehnološka oprema d.o.o. Ptujska c. 184 2000 Maribor Authors’ Addresses: Mag. Gašper Gantar ProfDr. Karl Kuzman Faculty of Mechanical Eng. University of Ljubljana Aškerčeva 6 1000 Ljubljana, Slovenia Mag. Marko Ljevar M.PP Technol. Equip. Ltd. Ptujska c. 184 2000 Maribor, Slovenia Prejeto: Received: 20.8.2001 Sprejeto: Accepted: 7.12.2001 0 SšnrKitafcflM]! ma stran 614 © Strojni{ki vestnik 47(2001)10,615-626 © Journal of Mechanical Engineering 47(2001)10,615-626 ISSN 0039-2480 ISSN 0039-2480 UDK 621.436:621.43.038 UDC 621.436:621.43.038 Pregledni znanstveni ~lanek (1.02) Review scientific paper (1.02) Analiza sistemov za neposredno vbrizgavanje goriva v sodobne hitroteko~e dizelske motorje An Analysis of Fuel-Injection Systems for Advanced High-Speed Diesel Engines Anton Dolenc - Ferdinand Trenc Razvoj hitrotekočih dizelskih motorjev se je začel v Evropi pred 22 leti. Največje težave pri razvoju so bile povezane z opremo za visokotlačno vbrizgavanje goriva. Doseči je treba visoke tlake vbrizgavanja, pravilen potek tlaka vbrizgavanja, možnost znižanja hrupa zgorevanja in seveda tudi zmanjšanja količine škodljivih snovi v izpušnih plinih. Značilnosti, primerjave tehničnih karakteristik ter predvidevanja za razvoj vbrizgalnih sistemov v prihodnosti so prikazane v tem prispevku. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: motorji dizelski, motorji hitrohodni, vbrizgavanje goriva, vbrizgavanje direktno) The development of the high-speed Diesel engines began in Europe 22 years ago. Since this time major technical problems have been encountered with the fuel system and its components. Different technical requirements have been met simultaneously: very high injection pressures, suitable pressure-to-time distribution, sophisticated injection timing control, reduced combustion noise and very stringent exhaust emission standards. General features, a comparison between some of the most advanced fuel-injection systems, and guidelines for the future are presented in the paper. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: Diesel engines, high speed engines, fuel injection, direct injection) 0 UVOD Že v začetku 20. stoletja smo bili tehnično zmožni izdelati počasne dizelske motorje z neposrednim vbrizgavanjem goriva. Dizelski motorji z neposrednim vbrizgavanjem dosežejo v primerjavi z vsemi drugimi motorji z notranjim zgorevanjem največji izkoristek. Razvoj sistemov za vbrizgavanje je v začetku tridesetih let omogočil doseganje tlakov vbrizgavanj goriva okoli 700 bar. S tako visokim tlakom vbrizgavanja goriva smo bili v stanju izdelati dizelske motorje, ki so se vrteli z 2000 do 2500 vrtljaji v minuti. Začela se je izdelava 4-taktnih dizelskih motorjev z neposrednim vbrizgavanjem, in sicer za pogon tovornih vozil in za nevozne potrebe. Motorji so se izkazali kot zelo zanesljivi, tako da so bila v naslednjih 20 letih praktično vsa tovorna vozila v zahodni Evropi opremljena s takšnimi motorji. Omejeno število vrtljajev in potrebni presežek zraka sta omejevala specifično moč motorja. Z dvotaktnimi in s štiri-taktnimi tlačno polnjenimi motorji je bilo tehnično mogoče povečati specifično moč motorjev. Pri dvotaktnih motorjih je bilo potrebno nadaljnje povečanje tlaka za 0 INTRODUCTION At the beginning of the 20th century engineers were capable of making low-speed Diesel engines with direct fuel injection. It is well known that this type of the internal combustion engine has the highest thermal efficiency. Fuel-injection systems of the 30s were capable of working at pressures of about 700 bar. As a result, faster – 2000 to 2500 rpm — four-stroke Diesel engines with direct fuel injection were produced for stationary applications as well as for driving commercial vehicles. The engines were quite reliable and replaced most of the power units in Western Europe over the next 20 years. A relatively low engine speed and large amounts of air needed for combustion, however, prevented any increase in the specific power of Diesel engines. Advanced two-stroke and four-stroke supercharged engines brought the advantage of a higher specific output power for the engine. Fuel-injection systems with higher operating pressures were developed for up- to-date two-stroke engines gfin^OtJJlMISCSD 01-10 stran 615 |^BSSITIMIGC A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems vbrizgavanje, kar so v Ameriki dosegli z vbrizgovalnim sistemom “Unit-Injector” (sistem združene tlačilke in šobe za vbrizgavanje goriva). Za velike nevozne motorje smo imeli na voljo zanesljiva turbopuhala že v začetku štiridesetih let, za manjše motorje za pogon tovornih vozil pa so se učinkovita in zanesljiva turbopuhala pojavila šele ob koncu šestdesetih let. Za pogon osebnih avtomobilov in lahkih tovornjakov uporabljamo lahke, hitrotekoče motorje z večjim številom vrtljajev. Konec štiridesetih let so bili razviti prvi hitrotekoči dizelski motorji s predkomoro. Temu ustrezne zahteve za sistem vbrizgavanja niso bile velike, toda specifična moč motorjev je bila s takim sistemom zelo omejena. Tudi uporaba turbopuhala na takšnih motorjih je bila zaradi velike toplotne obremenitve bata omejena na srednje vrednosti specifične moči. Poraba goriva je bila majhna pri nizkih obremenitvah, z uvedbo tlačne polnitve pa je bila poraba goriva dizelskega motorja s predkomoro samo še neznatno manjša od sodobnega bencinskega motorja ([1] do [3]). 1 LASTNOSTI, KI JIH ZAHTEVAMO OD SODOBNIH VBRIZGALNIH SISTEMOV Da bi hitrotekoči dizelski motor mogel tekmovati s sodobnim bencinskim motorjem, mora imeti naslednje lastnosti: - enako moč kakor bencinski motor; - nizko raven hrupa, ki je primerljiva tisti pri bencinskem motorju; - lahek in takojšnji zagon motorja pri temperaturah okolice do -40°C; - dolgo življenjsko doba trajanja motorja v primerjavi z bencinskim motorjem pri enaki obremenitvi; - doseganje največje moči motorja vsaj pri 4000 min1; - največje število vrtljajev vsaj 5200 min1; - nizko raven vibracij; - majhne stroške izdelave - največ 10% nad ceno bencinskega motorja s primerljivo močjo in ob približno enakem številu izdelanih enot; - preprosto zanesljivost in vzdrževanje; - nizko raven vseh škodljivih in zakonsko preverjenih sestavin v izpušnih plinih. Da bi lahko vsem opisanim zahtevam ugodili, postavljamo zelo velike zahteve za sistem vbrizgavanja goriva. Predvsem je treba vbrizgati velike količine goriva v zelo kratkem času (velika moč motorja in veliko število vrtljajev). To gorivo je treba vbrizgati skozi zelo majhne luknjice v šobi, da se doseže izrazita razpršitev vbrizganega goriva. Zato potrebujemo visoke tlake vbrizgavanja. Najvišji tlaki vbrizgavanja vse do 2500 bar imajo prednost. Prednost tlakov vbrizgavanja, ki presegajo 2000 bar ni več zelo velika. Toda samo zagotavljanje visokih tlakov vbrizgavanja še ne zadošča. Zahteve, ki jih mora izpolniti celotni sistem vbrizgavanja so: 0 srinataleflMllflilrSO | ^BSfirTMlliC | stran 616 and unit injectors were developed in the USA for this reason. Large stationary engines were equipped with relatively modern turbochargers in the 40s, whereas small and reliable turbochargers for high-speed engines were not available until the end of the 60s. Passenger cars and light trucks need light, high-speed engines. The first high-speed pre-cham-ber diesel engines were available at the end of the 40s. There was no special technical demand for adequate fuel-injection systems, but the engine’s specific rated output was limited. The thermal load of the engine piston was also a limiting factor that prevented the use of the turbochargers and the development of a higher specific engine power. Specific fuel consumption was relatively low at low engine loads, however, at higher engine loads and with a turbocharged prechamber Diesel engine almost the same fuel consumption as by a modern petrol engine was achieved ([1] to [3]). 1 REQUIREMENTS FOR A MODERN FUEL-INJECTION SYSTEM A modern, high-speed Diesel engine can compete with a modern petrol engine if it fulfils the following requirements: - it must develop the same power output; - the noise level must not exceed the level of a comparable petrol engine; - reliable start-up must be ensured at very low ambient temperatures of about -40 oC; - the longevity of the engine must be higher than a petrol engine under the same operating conditions; - the rated engine speed must exceed 4000 rpm; - the maximum engine speed must be at least 5200 rpm. - the level of the engine’s mechanical vibrations must be kept low; - production costs of a Diesel engine must be low; they can only exceed the cost of a comparable petrol engine for the same production volume by a maximum of 10%; - the engine must be reliable and the maintenance must be simple; - the exhaust gases must be clean; all regulated polutants must be within the prescribed limits. Very high standards are required of a fuel-injection system (FIS) in order to fulfil all the above-mentioned requirements. Large quantities of fuel need to be injected in a relatively short time to ensure a high engine output at higher engine speeds. Fuel must be injected through tiny nozzle holes to obtain intensive atomization; very high pressures are required and pressures of up to 2500 bar can be achieved in modern fuel systems. The advantage of the extremely high injection pressure deminishes when 2000 bar is exceeded. Some extra conditions concerning optimum injection must therefore be fulfiled. The following requirements must be taken into account with a new injection system: A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems - visok povprečni tlak vbrizgavanja; - visoki tlaki ob koncu postopka vbrizgavanja; - zelo visoki gradient znižanja tlaka ob koncu vbrizgavanja; - krmiljenje tlakov vbrizgavanja v skladu s potrebami motorja; - časovni potek tlaka vbrizgavanja, ki se zvišuje proti koncu vbrizgavanja; - vžig dela goriva preden so večje količine goriva vbrizgane v zgorevalni prostor motorja (predvbrizg goriva); - krmiljenje začetka vbrizgavanja, ki je odvisno od temperature motorja, srednjega efektivnega tlaka (obremenitve motorja), števila vrtljajev motorja in certifikacijskim (emisijskim) zahtevam vozila; - enakomerna porazdelitev goriva po vseh valjih; - spremenljiv prerez luknjic vbrizgovalne šobe brez dušenja curka (za zdaj še ni doseženo z nobenim sistemom). Večkratno delno vbrizgavanje goriva z dobro razporeditvijo goriva po prostoru bi imelo podoben učinek; - celotno trajanje vbrizga pri polni obremenitvi motorja naj ne bi preseglo 25° zasuka ročične gredi; - dosegljivost emisijskih predpisov “Euro 4”; - majhen mehanično-hidravlični hrup sistema za vbrizgavanje; - zelo majhne kavitacijske poškodbe v sistemu; - velika mehanična zanesljivost sistema; - preproste zahteve po opremljenosti servisnih postaj; - dimenzije vbrizgalne šobe, ki omogočajo gradnjo v valjevo glavo s po štirimi ventili; - majhni stroški izdelave in vgradnje; - majhni stroški vzdrževanja (servisa); - možnost prilagodljive konstrukcije motorja; - mogoča velika specifična moč motorja. Pri tem so pomembne tudi mehanske zahteve, ki jih mora izpolnjevati šoba za vbrizgavanje goriva: - konstrukcija šobe mora omogočati in trajno zdržati tlake vbrizgavanja nad 2200 bar; - pri majhnih zračnostih (natančno prileganje) med iglo in vrtino šobe ne sme priti pri vgradnji do škodljivih deformacij, ki bi lahko preprečile prosto gibanje igle v šobi; - vrtina - vodilo igle šobe mora biti čim daljša, obenem pa ne sme segati v področje šobe s previsoko temperaturo; - razdalja med vrtino za dovod goriva pod tlakom v spodnji del šobe in vodilno vrtino igle šobe mora biti čim večja, da se izognemo prevelikim mehanskim napetostim in deformacijam v okrovu šobe; - vrtina za dovod goriva v spodnji del šobe in vodilna vrtina igle šobe ne smejo biti vzporedne; - very high mean injection pressure; - very high injection pressure decrease in the final sequence of the fuel delivery; - very high gradients of presure decrease at the end of the fuel-injection process; - suitable control of the injection pressure history according to the requirements of the engine; - adequate pressure-time pattern that must increase throughout most of the injection process; - ignition of a small portion of the injected fuel prior to the injection of the major part of the fuel into the engine combustion chamber (pre-injection); - control of the start of fuel injection depending on the engine temperature, speed, load and the exhaust emission requirements of the vehicle; - uniform fuel distribution in all engine cylinders; - adjustable area of the fuel-nozzle holes without excessive choking effects — this has not yet been developed. Multiple sequential fuel injection during the same engine working cycle with optimum fuel spray distribution within the combustion chamber might have a similar effect; - duration of the fuel injection at the engine’s rated operating conditions should not exceed a 25 0 crank angle; - implementation of the “Euro 4” exhaust emission standards; - low mechanically and hydraulically born noise generated by the FIS; - negligible damage to the FIS due to cavitation; - high mechanical reliability of the FIS; - relatively low requirements for special equipment in service stations; - restricted dimensions of the FIS can lead to easy installation even in multi-valve cylinder head; - low production and installation costs; - low maintenance (service) costs; - flexible engine design; - high specific engine power. In addition to the very high mechanical and strength standards that need to be taken into account when advanced FISs are considered. The following requirements are also crucial: - the fuel-injection nozzle must operate continuously and reliably at 2200 bar; - the extremely small clearance between the injector needle and its leading surface (bore) must, under no circumstances, be affected by the mechanical deformations caused during the installation of the injector holder; - the supporting-leading surface of the needle must be as long as possible and must be removed from the bottom – the thermally highly loaded area; - the high-pressure fuel-inlet borehole in the injector body (holder) must be moved away from the needle leading bore to prevent excess mechanical deformations; - both high-pressure channels mentioned in the point above must not run parallel; | lgfinHi(š)bJ][M]lfi[j;?n 0110 stran 617 I^BSSIfTMlGC A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems - tesnilka vbrizgalne šobe ne sme povzročiti dodatnih sil in napetosti, ki bi povzročile deformacijo vrtine šobe pri vgradnji; - sila udarca pri nasedu igle šobe na sedež mora biti omejena; - zaobliti je treba notranje robove luknjic na vrtinah šobe. Že iz samih zahtev vidimo, da vsega, kar bi radi dosegli z novimi konstrukcijam ni mogoče doseči brez kompromisov. Visoki tlaki vbrizganja omogočajo skrajšani čas vbrizgavanja pri isti izmeri luknjic šobe. Na tak način je mogoče vbrizgati gorivo kasneje in obenem lahko znižamo emisijo dušikovih oksidov (NOx) motorja. S kasnejšim vbrizgom so tudi tlaki zgorevanja nižji, kar dopušča uporabo višjega kompresijskega razmerja in s tem tudi boljše pogoje za delovanje motorja pri nizkih temperaturah okolice. Vsi novi sistemi so zgrajeni z upoštevanjem kompromisnih rešitev, ki so bolj ali manj uspešne. Pri tem uporabljamo dandanes sisteme s prostorninskim krmiljenjem količine vbrizganega goriva (najbolj enakomerna porazdelitev goriva po vseh valjih) in časovnim krmiljenjem količine vbrizganega goriva. Z zaokroženimi vtočnimi vrtinami luknjic z notranje strani šobe, ki ustrezajo kalibriranemu (primerjalnemu) uporu pretoka goriva je mogoče doseči izboljšano enakomernost razporeditve goriva med valji tudi pri sistemih s časovnim krmiljenjem količine goriva. 2 PREDSTAVITEV SODOBNIH SISTEMOV ZA VBRIZGAVANJE GORIVA V novih, sodobnih hitrotekočih dizelskih motorjih imamo dandanes vgrajene naslednje vbrizgalne sisteme: Visokotlačna porazdelilna (distribucijska) tlačilka Visokotlačna distribucijska tlačilka za gorivo, kombinirana z dvostopenjskim odpiranjem šobe, je prikazana na sliki 1a in b. Ta sistem je uporabljen pri sodobnih vozilih znamk VW, Seat, Audi, Škoda, DB, Rover in Renault. Z novimi izboljšanimi konstrukcijskimi rešitvami je bilo mogoče doseči tlake (izmerjeni pri tlačilki) 1300 bar in z dinamičnim procesom nihanj v visokotlačni cevi za gorivo med tlačilko inšobo tudi tlake do 1600 bar. Časovni potek tlaka vbrizgavanja pri tem sistemu ni posebej ugoden Prostorninsko krmiljenje količine goriva omogoča enakomerno porazdelitev vbrizganega goriva po vseh valjih. Ta sistem ima prednosti pri predelavi starejšega motorja z deljenim zgorevalnim prostorom. Stroški opisanega sistema so večinoma majhni. Z dvostopenjsko vbrizgalno šobo je mogoče doseči nizko raven hrupa zgorevanja. Zaradi dolgih cevi med tlačilko in šobo morajo biti tlaki za odpiranje v šobi sorazmerno nizki (pri prvi stopnji ~ 200, pri drugi pa ~350 bar). Tlak vbrizgavanja ni optimalen za vse pogoje delovanja motorja (po celotni 0 srinataleflMllflilrSO | ^BSfirTMlliC | stran 618 - the sealing (element) under the injector body must not provoke additional deformations during the assembly procedure; - the impact force at the injector needle closure must be limited; - the intake edges of the injector spray holes must be carefully rounded. It can be concluded from the above-mentioned requirements that compromises are necessary in the design of new FISs. A high injection pressure means a shorter duration of the fuel injection if the geometry of the nozzle holes remains unchanged. It is therefore possible to delay the injection sequence and simultanously reduce the NOx content in the exhaust gasses. In addition, lower peak combustion pressures are obtained and higher engine compression ratios -for more economic engine operation at lower ambient temperatures - can be used. All newly developed FISs involve compromises. Today, two types of FIS are in use to control the injected fuel per cycle: volumetic control of the injected fuel, which ensures uniform fuel distribution in all engine cylinders, and time-controlled fuel distribution. The intake radius at the fuel-injector holes can be adjusted and used for the mass-calibration of the particular fuel injectors to obtain a more uniform distribution of the fuel in particular engine cylinders even if a FIS with time control of the injected fuel is applied. 2 DESCRIPTION OF SOME ADVANCED FISs The following FISs can be found in new high-speed Diesel engines: High-pressure fuel distributor pump A high-pressure distributor pump combined with a two-stage fuel injector is schematically presented in Fig. 1a and b and is used by several car manufacturers: VW, Seat, Audi, Škoda, DB, Rover, and Renault. New design solutions in the above-mentioned FIS have led to maximum operating pressures of about 1300 bar (measured at the fuel pump outlet) and maximum dynamic pressures up to 1600 bar. The shape of the pressure-time history of the fuel injection is not ideal. Volumetric control of the injected fuel means a very uniform distribution of the fuel in the engine cylinders. This FIS can also be easily adapted to a traditionally designed indirect injection pre-chamber engine. The costs for the above-mentioned FIS are low. A two-stage injection greatly reduces the combustion noise. Relatively long fuel lines between the high-pressure pump and the injectors require a relatively low opening pressure of the needle: 200 bar for the first stage A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems delovni karakteristiki motorja). Vrtilni moment je zaradi tega pri nizkih vrtljajih motorja nižji v primerjavi z vrednostmi, ki jih dosegamo s sodobnimi sistemi vbrizgavanja. Z omenjenim sistemom lahko dosežemo specifično (litrsko) moč motorja 45 kW/dm3 delovne prostornine valja. Doseganje te vrednosti je seveda odvisno tudi od mehanične vzdržljivosti motorja za določen namen uporabe. Sistem tlačilke s sobo a) Z mehaničnim pogonom Obstajata izvedbi bodisi s kombiniranim dvostopenjskim odpiranjem igle v šobi (Steyr [3] in Lucas [4]), (sl. 2, 3), ali pa izvedba, ki je kombinirana z dinamično pripravo za predvbrizg goriva (Bosch, sl. 4). Steyerjev Unit-Injector je opremljen s prostorninskim krmiljenjem vbrizgane količine goriva, ki uravnava začetek vbrizgavanja samo v odvisnosti od obremenitve motorja. Za popolno krmiljenje začetka vbrizga je potrebna dodatna naprava, ki obrača os nihajnega vzvoda in zato poveča stroške sistema na raven sistema s solenoidnim (elektromagnetni krmilni ventil) krmiljenjem. Steyrjev sistem omogoča doseganje tlakov do 2000 bar z ugodnim časovnim potekom tlaka vbrizgavanja. S stalnim merjenjem lege bata tlačilke obstaja razmeroma zanesljiva povratna informacija -podatek za računalnik o prostornini vbrizganega goriva. Konstrukcija je zelo prilagojena zmanjšanju deformacije pri vgradnji in omogoča zelo veliko zanesljivost delovanja tudi pri zelo visokih obremenitvah motorja. Časovni gradient znižanja tlaka na koncu vbrizgavanja je razmeroma ugoden in znaša 50 . 106 bar/s, diagram 1. Še bolj strmo znižanje tlaka bi bilo dobrodošlo, toda pojavila bi se nevarnost poškodb sistema zaradi kavitacije. Tlak vbrizgavanja določajo: oblika odmikalne krivulje, elastičnost mehaničnega pogona in količina goriva med tlačilko in vbrizgalno šobo sistema. Rezultat je sicer dober, toda povečani tlak goriva v področju vrtljajev motorja med 800 in 1500 min 1 bi tam še dodatno zvečal vrtilni moment. Z opisanim sistemom se dandanes lahko doseže specifična moč motorja 62 kW/dm3 delovne prostornine motorja. Pri tem moramo seveda upoštevati mehanično vzdržljivost motorja za določen način uporabe. Predpisi o emisiji izpušnih plinov - stopnja “Euro 3” so dosegljivi. Za doseganje stopnje “Euro 4 “ je potrebna oprema skupaj s sodobnim samočistilnim filtrom za delce v izpušnih plinih, ki pa za zdaj še ni razvita. Tlačilke s šobo Bosch in Lucas vodi elektronsko krmiljeni ventil: uravnava trenutek začetka vbrizgovanja in časovno prirejeno količino vbrizganega goriva. Bat tlačilke ima veliko tesnilno površino, kar omogoča doseganje višjih tlakov and approximately 350 bar for the second stage. Pressure distribution is not adjusted for all engine running conditions: peak engine torque is relatively small at lower engine speeds when compared to the engines with other advanced FISs. A specific engine output of 45 kW/dm3 of the engine working displacement can be achieved, as a general consequence of the engine design. Unit-Injector a) Mechanically driven unit-injector Two general systems can be found today: one with the combined two-stage needle lift (two-stage injection – Steyr [3] and Lucas [4]), Fig.2 and 3, and a unit-injector with a mechanically actuated two-stage pre-in-jection – Bosch, Fig.4. Steyr’s unit-injector applies volumetric control of the injected fuel and controls the start of the injection sequence as function of the engine load only. A separate suplementary unit should be introduced to enable perfect control of the fuel-injection process. Production costs would be substantially increased and would be comparable to the costs of the electronically controlled unit-injector with a solenoid valve. With the Steyr unit-injector operational pressures of up to 2000 bar can be obtained and the time-pressure history is appropriate as well. Continuous inspection of the plunger position gives reliable feedback information on the quantity of the injected fuel. The design of the FIS is reliable, eliminates most of the possible deformations provoked by the installation and ensures safe and continuous engine operation, even at very high engine loads. The gradient of the pressure release (GPR) at the end of the fuel-injection event is suitable when us. ing the above FIS and amounts to 50 106 bar/s, diagram 1. A still steeper GPR would be an advantage, but it could probably introduce certain problems and damage the FIS. The pressure history is determined by the shape of the cam of the mechanically driven unit-injector and the quantity of pressurized fuel between the fuel pump and the injector nozzle. The injection characteristic is generally appropriate, but still higher injection pressures in the lower engine-speed range between 800 and 1500 rpm would increase the engine torque. Today, a specific power of 62 kW/dm3 engine displacement can be achieved with the presented FIS. High mechanical stresses and its achievable reliability must be taken into account when such an extreme engine output is considered. The “Euro 3” exhaust emission standards can also be achieved with this FIS. The introduction of an extra self-cleaning exhaust particulate trap, which has not been developed yet, is required to fulfil the forthcoming “Euro 4” Diesel exhaust emission standards. Bosch and Lucas unit-injectors are equipped with an electronic solenoid control: the start of the injection as well as the time-dependent quantity of the injected fuel are controlled. The pumping element (plunger) has a relatively large sealing surface: | lgfinHi(š)bJ][M]lfi[j;?n 0110 stran 619 I^BSSIfTMlGC A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems Intenziteta vbrizganega goriva Intensity of injected fuel Idealni potek intenzitete vbrizgavanja z dvostopenjsko šobo Ideal characteristic of the injected fuel intensity - two stage injection S Steyr tlačilko s šobo dosežena intenzivnost vbrizgavanja Intensity of injected fuel with Steyr Unit Injector J n čas time Diagram 1. Primerjava idealnega poteka intenzitete vbrizgavanja goriva in poteka s Steyr-jevo tlačilko s šobo pri polni obremenitvi motorja. Ostale različice omogočajo podobno karakteristiko vbrizgovanja Diagram 1. Comparison between the ideal intensity of the fuel distribution and the time-dependant fuel distribution of the Steyr Unit-Injector Similar characteristic can be obtained by the application of other Unit-Injectors vbrizga - približno 2.200 bar. Mehanični deli solenoidnega krmilnega ventila in velike tesnilne površine bata obenem povečujejo občutljivost sistema na premalo očiščeno gorivo. Poleg tega je potrebna zelo selektivna vgradnja, da bi dosegli enakomerno porazdelitev goriva po valjih. Z opisanim sistemom se lahko doseže specifična moč motorja 60 kW/dm3 delovne prostornine valja, pri tem pa moramo upoštevati mehansko vzdržljivost in namembnost motorja. Predpisi o emisijah stopnje “Euro 3” so dosegljivi. Za stopnjo “Euro 4” je potrebna oprema skupaj s sodobnim samočistilnim filtrom za delce v izpušnih plinih, ki pa še ni na voljo izdelovalcem motorjev: Ta sistem je uporabljen za hitrotekoče motorje pri vozilih znamke VW, Seat, Audi, Škoda in Rover. Opisani sistem za vbrizgavanje ni veliko dražji od sistema z običajno porazdelilno tlačilko za gorivo, ki je kombiniran z dvostopenjskim odpiranjem igle v šobi. Sistem ima velike prednosti pred porazdelilno tlačilko, toda potrebna je prilagojena konstrukcija motorja, ki zahteva povečane stroške razvoja. Tudi višina motorja se s tlačilko s šobo nekoliko poveča. Razen tega do sedaj znane izvedbe tlačilk s šobo s svojimi izmerami ne dopuščajo vgraditve tlačilke s šobo v motorje s štirimi ventili v glavi vsakega valja. b) Sistem združene tlačilke in sobe s hidravličnim pogonom Tlačilka s šobo s hidravličnim pogonom in z dodatnim hidravličnim ojačevalnikom je prikazan na sliki 5. To je najmlajši - najnovejši koncept za vbrizgavanje goriva v dizelske motorje. Razvoj tega very high injection pressures of approximately 2200 bar can therefore be achieved. However, excessive high-pressure surfaces and the mechanical parts are sensitive to unsatisfactorily cleaned fuel. In addtion, a very high degree of selection of the described FIS elements is required to ensure uniform fuel distribution for all engine cylinders. A specific engine power up to 60 kW/ dm3 engine displacement can be obtained, however, the application of the appropriate engine should certainly be taken into the consideration. The “Euro 3” exhaust emission standards can be met with the described FIS, however “Euro 4” can only be achieved by the application of a modern - so far not yet developed - self-cleaning exhaust particulate trap. The “Bosch” unit-injector is applied by the engine manufacturers: VW, Seat, Audi, Škoda and Rover. It is not much more expensive than a conventional FIS with a distribution pump combined with a two-stage needle lift. There are many advantages of the presented high-pressure unit-injectior FIS, however, a substantial redesign of an already existing engine is required to replace a conventional FIS, and as a consequence the development costs are increased. The overall engine height is also increased by the FIS. Available up-to-date unit-injector FIS designs with their overall dimensions are not compatible with multi-valve cylinder-head technology. b) Hydraulically operated Unit-injector (HOUI) A HOUI with a supplementary hydraulically operated intensifier is the newest and the most advanced concept of fuel injection for modern Diesel engines. The system was invented by John Beck from 0 BnnBjfokJ][p)l]Olf|i[gO | | ^SSffJlMlGC | stran 620 A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems sistema je pričel Američan John Beck iz Kalifornije. Sistem sedaj izdelujejo v podjetjih Caterpillar [8] in Siemens-USA. Uporablja se predvsem za motorje, ki se vrtijo do 3500 min1. S tem sistemom še ni bil rešen problem hrupa zgorevanja. Specifična moč motorjev je omejena na približno 30 kW/dm3 delovne prostornine motorja. Vgrajen je predvsem v ameriške motorje za lahka tovorna vozila. Za hidravlični pogon tlačilke se uporablja srednji tlak iz skupne napajalne cevi. To je pravzaprav obenem tudi vrsta sistema za vbrizgavanje s skupnim visokotlačnim vodom in skupno visokotlačno tlačilko goriva, ki je kombinirana s tlačilko s šobo: gorivni sistem vbrizgavanja s skupnim zbiralnikom - vodom, iz katerega se napajajo posamezne enote. Omenjeni sistem ne omogoča izrazitega predvbrizga. Zvišanje tlaka, ki ga dosežemo s sedanjimi konstrukcijskimi izvedbami je premajhno za doseganje visokih tlakov vbrizgavanja in ne omogoča doseganja večjih specifičnih moči motorja. Potek tlaka vbrizgavanja ne ustreza zahtevam zakonov zgorevanja. Za pogon osebnih vozil je težko doseči emisijsko stopnjo “Euro 2” celo z majhnimi specifičnimi močmi motorja. Pri vgradnji v vozila s skupno maso nad 3500 kg lahko zadostimo zahtevam ustreznih emisijskih predpisov. V nasprotju s sistemom s skupnim vodom so tlaki goriva v skupnem zbiralniku nizki, zato je potrebna le nizkotlačna tlačilka za gorivo. Igla šobe je, podobno kakor pri tlačilki sšobo, izpostavljena visokim tlakom samo v času vbrizgavanja. Sistem je preprost in ne zahteva izjemno zahtevne tehnološke opreme. Vzdrževanje je preprosto. Navkljub sedaj pretežno negativnim rezultatom menimo, da temu načinu vbrizgavanja pripada prihodnost. Tudi Cummins v ZDA dela v razvoju na modificirani konstrukciji, ki deluje po opisanem načelu. Ta sistem lahko tudi opišemo z besedami: “Ameriška pot v tehniki”. Sistem za vbrizgavanje s skupnim visokotlačnim vodom in skupno visokotlačno tlačilko goriva (SViT - Common-Rail) ([6] in [7]) Po tem načelu je začel delati prof. Eichelberg na ETH v Zurichu v začetku tridesetih let, raziskovalno delo pa so nadaljevale kar štiri generacije strokovnjakov na omenjeni ustanovi. Z razvojem moderne elektronike, z moderno tehnologijo obdelave in z ustreznimi merilnimi instrumenti je postal razvoj omenjene opreme za vbrizgavanje tudi industrijsko pomemben. Bosch je pripeljal ta sistem do industrijske uporabe in izdelave. Sistem uporablja osrednjo tlačilko, ki pošilja gorivo v skupni zbiralnik za vse valje motorja (sl. 6). S konstrukcijo je možno doseči tlake vbrizgavanja do 1400 bar, toda z izjemno visokim časovnim gradientom znižanja tlaka ob koncu vbrizgavanja. Tlaki vbrizganja niso tako visoki kakor pri tlačilki s šobo, toda izredno California and is manufacturated by Caterpillar [8] and Siemens in the USA. It is generally applied for the engines running up to 3500 rpm and not exceeding 30 kW/dm3 cylinder displacement. Combustion-born noise has not been eliminated by this FIS yet. It has been applied for light commercial vehicles in the US. Fuel with moderate pressure from a common-rail is applied for hydraulic operation of the high-pressure system. It is in fact a type of Common-Rail system combined with a unity-injector: the Common-Rail, as the first stage, feeds particular uniti-injectors of particular engine cylinders. Intensive pre-injection of the fuel cannot be achieved with this system. The pressure gradient of the existing design solutions is too moderate and does not lead to very high injection pressures and consequently to a high engine-specific power. The pressure-time injection characteristic does not fit the requirements for optimum combustion. The “Euro 2” emission standards can hardly be met with the above-mentioned FIS despite the relatively low specific power of the engine. If the engine is used to drive a vehicle weighing over 3500 kg, appropriate emission standards can be met. Pressure in the feeding common-rail is relatively low; an ordinary pressure pump is therefore required to operate the first phase of the described system. The injector needle is exposed to very high pressures, however, as with the other unit-injector FISs this is only during the fuel-injection period. The described FIS is simple and does not require extremely demanding technology. Maintenance of the FIS is also simple. The author of the system considers this system to be the prevailing FIS for the future, although the existing results are not very promising. Cummins, of the USA, makes efforts to develop a new design of the modified hydraulically operated FIS. This system was marketed with the slogan “The American Way of Engineering”. Common–Rail FIS ([6] and [7]) This FIS was first examined by Prof. Eichelberg from ETH Zuerich at the beginning of the 30; four generations of experts continued his work at the same institution over the next decades. The common-rail system became suitable for industrial applications with the development of modern technology, electronics and advanced measurement techniques. Bosch was the first to introduce the Common-Rail (CR) system into mass production. A central high-pressure pump feeds the fuel into a common-rail for all engine cylinders, Fig.6. Injection pressures up to 1400 bar can be achieved today with a modern CR FIS; an extremely steep gradient of GPR can be obtained at the end of the injection period. Peak pressures are far below the pres- | lgfinHi(š)bJ][M]lfi[j;?n 0110 stran 621 I^BSSIfTMlGC A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems Intenziteta vbrizganega goriva Intensity of injected fuel Idealni potek intenzitete vbrizgavanja z dvostopenjsko šobo Ideal characteristic of fuel the injection intensity Možnosti SViT-a Capability of the Common Rail FI čas time Diagram 2. Primerjava idealnega časovnega poteka intenzitete vbrizgavanja z ustrezno karakteristiko SViT sistema pri polni obremenitvi motorja Diagram 2. Comparison between the ideal time-dependant distribution of the fuel and the appropriate characteristic obtained with the Common-Rail at the engine full load visok gradient znižanja tlaka ob koncu vbrizga delno nadomesti to pomanjkljivost. Za uspešno delovanje sistema so potrebne štiri zelo kakovostne in skrbno prilagojene komponente s selektivno vgradnjo. Pri teh delih prihaja v primerjavi z drugimi sistemi do večje nenadzorovane izgube goriva zaradi iztekanja skozi špranje. Elektronski krmilni sistem nima nobenega podatka, ki bi predstavljal (meril) dejanski tok goriva skozi šobo. Ta pomanjkljivost dodatno otežuje enakomerno porazdelitev goriva po vseh valjih motorja in dodatno podraži sistem zaradi potrebnega selektivnega sestavljanje komponent za doseganje enakomernejše porazdelitve goriva po vsakem valju. Visoki tlak ki vlada v skupnem zbiralniku, stalno deluje na sedež igle v vbrizgalnišobi. S tem faktorjem je povezano tudi tveganje, da bi gorivo pri poškodovanem sedežu igle skozi špranjo lahko nenadzorovano iztekalo v valj in v najkrajšem času uničilo motor. Vbrizgalni sistem SViT potrebuje visokotlačno tlačilko, zelo zahtevni zbiralnik ter zelo zahtevno elektronsko krmiljenje šob za vbrizgovanje. Stroški izdelave so večji kakor pri drugih sistemih. Rezultati zgorevanja in dosegljiva največja specifična moč motorja so zelo podobni vrednostim, ki jih dosežemo s tlačilko s šobo. Ob vseh zgoraj navedenih pomanjkljivostih pa ima sistem SViT štiri velike prednosti: - Vbrizgalnašoba ima pri SViT-u razmeroma majhen premer in jo lahko vgradimo v motor s po štirimi ventili na valjevo glavo. - Sistem SViT je lahko integrirati v obstoječe konstrukcije motorjev brez velikih sprememb. - Proces optimiranja opisanega vbrizgovalnega sistema za neki motor je razmeroma kratek, ker lahko pomembne parametre vbrizgavanja zelo hitro sures obtained with the UIs, but a very high gradient (GPR) at the closure of the injector needle almost compensates for this disadvantage. Successful operation of the CR FIS requires four perfectly mutually tuned and selected components and a very careful installation. Uncontrolled leakage is typical for a CR in comparison with other modern FISs. There are no suitable input data available for the electronic control system that could measure the injected quantity of the fuel. This disadvantage affects uniform delivery of the fuel for all engine cylinders and increases the costs of the described components due to higher selection of the required components. High pressure in the CR acts continuously on the injection needle; there is a risk of uncontrolled fuel leakage through the needle seat and, in the worst case, complete failure of the engine. A CR requires a high-pressure fuel pump, a relatively complicated common container – rail, and highly demanding electronic control for the particular engine injectors. Total manufacturing costs are higher in comparison with the other FISs. The quality of the combustion and the highest developed engine-specific output is in the range of the other advanced UI FISs. In spite of the above- mentioned disadvantages, the CR system offers four big advantages: - The fuel injector is small enough to be easily built in a multi-valve cylinder head. - No special redesign of an old engine is required to introduce a CR system. - The optimisation process of a new engine with the CR is relatively simple and short; injection parameters, especially the optimum injection 0 BnnBjfokJ][p)l]Olf|i[gO | | ^SSffJlMlGC | stran 622 A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems spremenimo. Predvsem lahko hitro prilagodimo optimalni tlak vbrizgavanja zahtevam motorja. SViT ponuja teoretično možnost večkratnega vbrizgavanja goriva v istem delovnem ciklu motorja. Z uspešnim načinom večkratnega vbrizgavanja z zelo pozno zadnjo fazo vbrizga, ki jo kombiniramo s filtrom za delce v izpušnih plinih, obstaja možnost uporabe samočistilnega filtra za delce. Na tak način je bilo že mogoče znižati raven vseh škodljivih in zakonsko predpisanih komponent v izpušnih plinih na raven predpisa “Euro 4”. Z zelo poznim dodatnim vbrizganjem se lahko poveča temperatura izpušnih plinov, ne da bi vplivali na zahtevano moč motorja. Z uporabo sistema SViT so dokazali, da je to dejansko mogoče doseči. Pri sistemu vbrizgavanja s SViT ne moremo spremeniti tlaka vbrizgavanja v posameznih fazah deljenega vbrizga in v istem delovnem krogu motorja. Zaradi enakega -visokega tlaka vbrizgavanja, ki se nadaljuje po glavnem vbrizgavanju tudi v zadnjo fazo dodatnega vbrizga goriva ter zaradi bistveno manjše gostote ostankov zgorevanja v valju (globoko v fazi ekspanzije), pride zaradi pressure, can be altered and adjusted very quickly according to the demands of the engine. CR provides the advantage of multiple fuel injection during the same engine working process. Interaction of the very late (last) phase of the multiple fuel injection together with the exhaust particulate trap leads to a practical solution for a self-cleaning particu-late trap. This was proved (in research) to be a realistic possibility to ful fill the requirements of the “Euro 4” exhaust emission standards. Very late fuel injection increases the exhaust temperature without influencing the output power of the engine. However it has not yet been possible to alternate the injection pressure of particular phases of a single multiple fuel-injection process. As the result of the very high injection pressures in the late phase expansion and therefore a substantially higher penetration of the fuel through the lower density cylinder content there is always the possibility of a direct wetting of the cylin- Preglednica 1. Primerjava sedanjih sistemov za neposredno vbrizgavanje v hitrotekoče dizelske motorje. Vrednotenje je opravljeno na temelju informacij, dostopnih avtorju. Z nadaljnjim razvojem lahko pričakujemo spremembe. Najboljše vrednosti so tiskane poudarjeno. Table 1. Comparison of diverese advanced FIS for high-speed DI Diesel engines. Evaluation is based on the available informations and data. With the future development change of data is to be expected. The best results and values are marked bold. ZAHTEVE ZA SISTEM VBRIZGAVANJA GORIVA REQUIREMENTS FOR ADVANCED FIS Nepristranska ocena stopnje popolnosti posameznih tehničnih karakteristik sistemov za vbrizgavanje goriva Impartial evaluation of completion of particular FIS characteristic 1 Visok srednji tlak vbrizgavanja 1 Very high mean injection pressure Visok tlak na koncu vbrizgalnega procesa 2 High pressure at the end of injection period Zelo visok tlak na koncu vbrizgavanja 3 Very high injection pressure gradient at the end of injection Krmiljenje tlaka vbrizgavanja po potrebi motorja 4 Control of the injection pressure according to the engine requirements Kakovost poteka tlaka vbrizgavanja, ki narašča proti koncu vbrizgavanja 5 Quality of the progressive injection - pressure characteristic towards the end of injection______________________________________________________ Predvbrizg goriva 6 Multi - stage fuel injection 7 Krmiljenje začetka vbrizgavanja Control of the begin of fuel injection Visokotlačna distribucijska tlačilka Steyr-jeva enotna goriva tlačilka sšobo High pressure Steyr Unit Injector distributor fuel pump_______________ 65% 95% 100% 70% 75% 40% 95% 100% 50% 65% 30% 50% 40% 70% 60% 90% Dvostopenjski two - stage Dvostopenjski two - stage 100% 50% -100% Enotna tlačilka sšobo -Unit Injector s solenoidno regulacijo Lucas - Bosch UI with the solenoid control 45% 65% Dvostopenjski-Pilot vbrizg two - stage - Pilot Unit Injector s hidravličnim pogonom Hydraulically operated UI Tlačilka s skupnim vodom Common Rail 30% 100% 100% 100% Pilot vbrizg Pilot injection 8 Enakomerna porazdelitev goriva po vseh valjih motorja ___Uniform fuel distribution for all cylinders__________________________ 9 Spremenljiv presek luknjic šobe brez dušenja curka ___Variable injection nozzle flow area without excessive pressure losses 95% 95% 90% 0 0 0 85% 90% 0 0 Kratko skupno trajanje vbrizga 10 Short duration of the complete fuel injectio 65% 90% 100% 70% 80% Dosegljivost emisijskuih standardov "Euro 4" danes 1 Actual implementation of the exhaust emission standards "Euro 4" today ni možno not possible ni možno not possible ni možno not possible ni možno not possible možno? possible? 12 Hrup sistema za vbrizgavanje goriva Noise of the FIS 40% 60% 60% 30% 50% Nevarnost kavitacijske poškodbe sistema ___Danger of the cavitation damages on the FIS 30% 10% 14 Mehanična zanesljivost sistema ___Mechanical reliability of the FIS 50% 90% 70% 90% 30% Višina zahtev na opremo za servis 15 Requirements for maintenance of the FIS 80% 20% 6 Možnost vgraditve v glave s po 4-mi ventili n Possibility for installation of the FIS into a m a valj lti - valve cylinder možno possible ni možno not possible ni možno not possible ni možno not possible možno possible 17 I Stroški izdelave in montaže Production and instalation costs Stroški servisa 100% 80%-100% 100% 30% 110% 75% 180% Konstrukcijske zahteve motorja 9 Special design requirements for the FIS (engine) Dosegljiva specifična moč motorja v KW/l 20 Maximum achievable specific engine power (in kW/dm3 engine swept volume) manjše lower velike large večje larger manjše minor manjše minor 45 62 - - 0 A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems prodornosti curka goriva do neposrednega brizganja goriva na steno valja. To seveda zelo hitro pokvari mazanje valja do te mere, da lahko pride celo do težjih poškodb motorja. Pot za veliko zmanjšanje emisije delcev in s tem posredno tudi NOX je z zgornjim opisom sistemov za vbrizgavanje dokazana Potrebno je še dosti razvojnega dela, ki nas bo pripeljalo do uspešnega trženja omenjenega izdelka. Tudi z drugimi prej opisanimi sodobnimi sistemi obstajajo teoretične možnosti za uporabo samočistilnega filtra, toda samo z uporabo SViT-a je dosedaj uspelo doseči emisijske zahteve, ki jih podajajo bodoči predpisi stopnje “Euro 4” . 3 SKLEP Kakor je razvidno iz preglednice 1 so opisani vbrizgalni sistemi prve generacije za vbrizgavanje goriva za hitrotekoče dizelske motorje še nepopolni. Toda doseženi rezultati omogočajo izdelavo homologiranih visokokakovostnih dizelskih motorjev S sodobnimi dizelskimi motorji dandanes dosežemo v primerjavi z bencinskim motorji še nekoliko manjše specifične moči motorjev. Največji za 50% večji moment teh motorjev dosežemo že pri 1600 do 3000 min1. Motor je zato prožen in z njim se vozne sposobnosti na vozilu z enako skupno maso izboljšajo. Upajmo da bo naslednja generacija vbrizgalnih sistemov, na katerih poteka pospešen razvoj, dajala še boljše rezultate. Sl. 1a. Visokotlačna razdelilna tlačilka za gorivo Fig. 1a. High pressure fuel distribution pump 0 srinataleflMllflilrSO | ^BSfiTTMlliC | stran 624 der wall. Lubrication quality is affected and serious engine damage can occur. Nevertheless, this is the way to achieve very low emissions of particulates and NOX. A lot of research and development work needs to be done so that a commercially successful product will be available. There are also some theoretical solutions available for the efficient operation of a self-cleaning particulate filter with the other advanced, high-pressure FISs. But CR has so far been, the only one to overcome the very stringent “Euro 4” exhaust emission standards. 3 CONCLUSION There are some blank spaces in Table 1, where a comparison of different features for the first generation of different advanced FISs is made. However, modern and environmentally suitable engines can be produced today with such a FIS. The rated power of modern Diesel engines is still slightly less than the power of a comparable modern petrol engine. The maximum (50% higher) engine torque can be obtained in the engine speed range from 1600 to 3000 rpm. A very elastic engine torque characteristic can therefore positively affect the driving attributes of a vehicle. We hope to obtain still better results with the next generation of the advanced FISs. Sl. 1b. Sistem za dvostopenjsko odpiranje sobe pri združeni tlačilki s šobo Steyr in Lucas Fig. 1b. Two-stage fuel injection by Steyr and Lucas Unit Injectors A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems Sl. 2. Steyr-jeva naprava za vbrizgavanje goriva z združeno tlačilko s sobo Fig. 2. Steyr’s Unit Injector [1] [2] [3] [4] [5] [6] Sl. 3. Lucas-ov sistem združene tlačilke s sobo s časovnim krmiljenjem količine in dvostopenjskim vbrizgavanjem goriva Fig. 3. Unit Injector Lucas with the time control of the injected fuel and with the two-stage injection zaznavalo za tlak v skupnem vodu pressure sensor in common rail krmilni prelivni ventil control release valve visokotlačna tlačilka high pressure pump vrtljaji motorja položaj stopalka tlak engine speed position za plin polnitve gas pedal boost temp. temp. zraka hlad. vode air–tem- cooling water pressure perature temperature Sl. 4. Shematični prikaz naprave za visokotlačno vbrizgovanje goriva s skupnim vodom Fig. 4. Schematic outline of the Common rail fuel injection system 4 LITERATURA 4 REFERENCES Shahed, S.M. (1998) Turbo 2000 - Turbocharging solutions for the next century, Engine Technology Int., May, 1998. Ashley, S. (1998) Diesel cars come clean, Mechanical Engineering, Vol.119, No.8, 1998. Dolenc, A. (1995) Fuel system for the future high speed DI Diesel engines and the suitable electronic control, uvodno vabljeno predavanje, Koferenca IAT’95, Radenci, 1995. Osenga M. (1998) CAT gears up for next generation fuel systems, Diesel Prograss Int.Edition, Volume XVIII, No.9-10, 1998. Glassey, S.F., et al (1993) HUEI - A new direction for Diesel engine fuel systems”, Int. SAE Congress and Exhibition, Detroit, March, 1993, Paper No. 930270, pp. 1 - 11. Osuka I., et al (1994) Benefits of new fuel injection system technology on cold startability of Diesel engines - Improvement of cold startability and white smoke reduction by means of multy injection with common rail fuel system (ECD-U2), Int. SAE Congress And Exhibition, Detroit, 1994, Paper No. 940586, pp. 7-17. A. Dolenc - F. Trenc: Analiza sistemov za vbrizgavanje goriva - An Analysis Fuel-Injection Systems [7] Stumpp, G., et al. (1996) Common rail - An attractive fuel injection system for passenger car DI Diesel engines, Int. SAE Congress and Exhibition, Detroit, February, 1996, Paper No. 960870, pp. 183 - 191. [8] Greeves, G., et al. (1993) Contribution of EUI-200 and quiescent combustion system towards US94 emissions, Int. SAE Congress and Exhibition, Detroit, March, 1993, Paper No. 930274, pp. 69 - 87. Avtorjev naslov: Anton Dolenc predsednik avtomobilske zveze Avstrijska zveza inženirjev in arhitektov Eschenbachgasse 9 A-1010 Vienna, Avstrija prof.dr. Ferdinand Trenc Univerza v Ljubljani Fakulteta za strojništvo Aškerčeva 6 1000 Ljubljana Authors’ Addresses: Anton Dolenc President Automotive Society Austrian Society of Engineers and Architects Eschenbachgasse 9 A-1010 Vienna, Austria Prof.dr. Ferdinand Trenc University of Ljubljana Faculty of Mechanical Eng. Aškerčeva 6 1000 Ljubljana, Slovenia Prejeto: Received: 17.9.2001 Sprejeto: Accepted: 7.12.2001 0 SšnrKitafcflM]! ma stran 626 © Strojni{ki vestnik 47(2001)10,627-636 © Journal of Mechanical Engineering 47(2001)10,627-636 ISSN 0039-2480 ISSN 0039-2480 UDK 621.43.038:004.94 UDC 621.43.038:004.94 Pregledni znanstveni ~lanek (1.02) Review scientific paper (1.02) Obravnavanje curka plinskega olja Diesel-Spray Analysis Martin Volmajer - Breda Kegl V prispevku je obravnavan proces vbrizgavanja goriva in karakteristike curka dizelskega motorja z uporabo programa računske dinamike tekočin FIRE. Natančnost rezultatov, dobljenih s tem programom, je v veliki meri odvisna od pravilno postavljenih začetnih pogojev. Določevanje nekaterih pogojev je precej zahtevno, saj jih lahko določimo le na temelju izkušenj ali zahtevnih meritev v laboratoriju. V tem prispevku so na podlagi številnih zgledov in primerjav z rezultati, dobljenimi z znanimi empiričnimi izrazi za srednji Sauterjev premer kapljic, podane smernice za postavljanje začetnih pogojev. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: motorji dizelski, šobe za vbrizgavanje, karakteristike curka, računska dinamika tekočin) The fuel injection process and the characteristics of the diesel-fuel spray were simulated using a computational fluid dynamics program FIRE. Initial conditions greatly influenced the accuracy of the results and these conditions can generally only be determined by complicated laboratory measurements. Guidelines to determine more realistic initial conditions based on comparisons of different practical results and empirical expressions for Sauters mean diameter of a droplet are given in the paper. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: diesel engine, fuel injection nozzles, spray characteristics, computational fluid dynamics) 0 UVOD Sodoben dizelski motor mora ustrezati ekološkim in ekonomskim zahtevam. V prvi vrsti mora zagotoviti visoko razmerje med zmogljivostmi in porabo goriva, poceni vzdrževanje ter nenazadnje obratovanje v skladu z vedno strožjimi zakonskimi omejitvami glede največjih dovoljenih emisij produktov zgorevanja. Glede na to, da sta proces zgorevanja in tvorba nezaželenih sestavin ostankov zgorevanja v glavnem vodena s procesom vbrizgavanja in tvorbo curka razpršenega goriva, se veliko vlaga v razvoj novih oziroma izboljšavo sedanjih vbrizgalnih sistemov in analizo curka razpršenega goriva. V zadnjih letih pridobivajo pomen analize z uporabo programov računske dinamike tekočin (RDT -CFD), saj predstavljajo razmeroma preprost način analiziranja procesov vbrizgavanja pri novih, pa tudi spremenjenih sedanjih vbrizgalnih sistemih. Z uporabo paketov RDT lahko prihranimo precej časa namenjenega izdelavi in testiranju vbrizgalnih sistemov. S simuliranjem procesa na računalniku lahko v razmeroma kratkemčasu testiramo veliko število različic ter tako že v začetni fazi izločimo tiste, ki ne prinašajo želenih rezultatov. 0 INTRODUCTION A modern compression-ignition engine should meet ecological and economic requirements. First of all it should have a high ratio of performance to fuel consumption, low maintenance costs and it should be able to operate within prescribed emission regulations. As the process of combustion and the resulting emission of pollutants and noise is mainly affected by the process of fuel injection, a lot of effort is put into developing new or improving existing fuel-injection systems as well as into the analysis of the fuel spray. In recent years, analysis using computational fluid dynamics (CFD) programs became important since this is a relatively easy way to analyse fuel-injection processes in new or re-designed fuel-injection systems. Using CFD programs, a lot of the manufacturing and experimental work is unecessary, since there is no need to produce every design variant. Many variants can be tested using a simulation on the computer. Those variants that show no significant improvement can be eliminated at an early stage. gfin^OtJJIMISCSD 01-10 stran 627 |^BSSITIMIGC M. Volmajer - B. Kegl: Obravnavanje curka plinskega olja - Diesel-Spray Analysis V avtomobilski industriji se uporablja več The automotive industry uses many differ- računalniških paketov računske dinamike tekočin. ent CFD packages. FIRE, which was produced by Eden izmed teh je program FIRE izdelovalca AVL. FIRE AVL Graz, uses the finite-volume method for the uporablja metodo končnih prostornin za analiziranje analysis of the fluid flow characteristics. As it is toka tekočine. Glede na to, da je v prvi vrsti namenjen mainly used by the automotive industry internal com- avtomobilski industriji oziroma uporabi na motorjih z bustion engines, it also includes the spray (two-phase notranjim zgorevanjem, vključuje tudi modula za flow) and combustion modules [1]. simuliranje curka razpršene tekočine in procesov To use the spray module we must begin zgorevanja [1]. with appropriate initial conditions and have an un- Uporaba tega modula in s tem določitev derstanding of fuel-spray formation. Nozzle dimen- začetnih pogojev zahteva dobro poznavanje in sions and the initial conditions are defined prior to razumevanje procesov tvorbe curka goriva. Izmere šobe the investigation in the so-called Spray file. Besides in začetni pogoji se pred začetkom analize definirajo v setting the measured or otherwise known values t.im. “spray” datoteki. Zraven določitve preprosto such as nozzle geometry (number of nozzle holes, merljivih oz. znanih vrednosti, kakor so: geometrijska nozzle hole angles, etc.), injection characteristics oblikašobe (številošob in odprtinšobe, koti porazdelitve and quantity of the injected fluid, other parameters odprtin itn.), karakteristika vbrizgavanja ter količina that depend on estimations or experiences must also vbrizganega goriva, je treba definirati tudi parametre, ki be set. These parameters are the initial droplet di- jih lahko v veliki večini določimo le na temelju ocen mensions, the initial droplet probability distribution oziroma izkušenj. To so: velikost kapljic in verjetnostna defining the probability of certain droplet dimen- porazdelitev kapljic, ki določa verjetnost, da se kapljica sion appearing, and the radial velocity of the fuel z določenim premerom pojavi v zgorevalni komori, ter outflow from the nozzle hole, by which the spray kot pri vrhu stožca in radialna komponenta hitrosti cone angle is defined. iztekanja goriva iz šobe, ki določata obliko stožca. To exactly define the above-mentioned ini- Natančna določitev omenjenih začetnih tial conditions requires expensive experimental equip- pogojev zahteva drago eksperimentalno opremo. Za ment, often these values can be known only by un- razmeroma natančno določitev pa pogosto zadostuje derstanding the full background of the fuel-injection že dobro poznavanje procesa vbrizgavanja in tvorbe and spray-atomisation processes. The purpose of curka. V ta namen smo se odločili, da z analiziranjem this study was to establish how the initial conditions različnih primerov vbrizgavanja ugotovimo, kako affect the mean value of the calculated droplet diam- omenjeni začetni pogoji vplivajo na izračunano eter in the chamber. The values calculated using the velikost kapljic v komori. Hkrati smo izračunane CFD package were subsequently compared with the vrednosti primerjali z rezultati, dobljenimi na podlagi results from the empirical equations for the calcula- znanih empiričnih izrazov za izračun d32. tion of d32. 1 KARAKTERISTIKE CURKA GORIVA 1 FUEL-SPRAY CHARACTERISTICS Pri procesu zgorevanja v dizelskem motorju The fuel is introduced into the combustion dovajamo gorivo v zgorevalni prostor v obliki curka chamber of a Diesel engine through one or more skozi šobo z eno ali več odprtin. Strnjeni valjasti curek, nozzles or orifices. The liquid column leaving the ki z veliko tlačno razliko izstopa iz odprtine v valj v neki nozzle hole under high pressure, disintegrates within končni dolžini-dolžini trganja, razpade na kapljice the cylinder over a finite length called the break-up različnih velikosti. V trenutku, ko tekočina zapusti length. As the liquid moves away from the nozzle the odprtino, se poveča količina zraka v curku, curek se mass of air within the spray increases, the spray then cepi in širi, hitrost gibanja iztekajoče se tekočine pa se diverges, its width increases, and its velocity de- s tem zmanjšuje. Največjo dolžino, ki jo prepotujejo creases. The maximum length the droplets travel is kapljice, imenujemo domet curka. Curek vbrizganega called the spray-tip penetration. Diesel-fuel spray goriva v dizelskem motorju ima običajno stožčasto usually has a conical shape with an angle 0 This obliko s kotom 0 pri vrhu stožca. Takšen način razpada type of disintegration is called atomisation [2]. curka imenujemo atomizacija [2]. The quantities presented above are the mac- Navedene veličine pomenijo makroskopske roscopic parameters of the spray, representing the veličine curka, ki predstavljajo porazdelitev goriva fuel distribution in the combustion chamber. At the po celotnem zgorevalnem prostoru, medtem ko other side the droplet size, i.e. quality of the velikost kapljic oziroma kakovost razpršitve curka atomisation, represents the microscopic parameters. pomeni mikroskopsko veličino. Običajno so mikro These microscopic parameters are usually defined karakteristike curka podane s porazdelitvenimi with probability functions, defining the probability funkcijami, te pomenijo verjetnost pojavljanja kapljice of the appearance of a droplet with a certain diameter. z določenim premerom. V praktičnih primerih se It is usual to use droplet mean diameters rather than 0 srinataleflMllflilrSO | ^BSfiTTMlliC | stran 628 i M. Volmajer - B. Kegl: Obravnavanje curka plinskega olja - Diesel-Spray Analysis namesto porazdelitvenih funkcij uporabljajo srednji premeri kapljic [2]: probability functions. The droplet mean diameter is defined as [2]: 1 j-k (1), kjer sta N - število kapljic, d - premer kapljice. where N is the number of droplets and d is the drop- Najpogosteje se pri procesih vbrizgavanja uporablja let diameter. For fuel-injection processes we usually Sauterjev srednji premer: choose the Sauter mean diameter: d=i d 2 (2), ki pomeni razmerje med celotno prostornino in i which is defined as the ratio of the sum of the drop- površino kapljic. Za izračun d 2 obstajajo številni lets’ volumes to the sum of the droplets’ surfaces. empirični izrazi, med katerimi so najpogosteje For the calculation of d32 several empirical equations uporabljeni empirični izrazi naslednjih avtorjev: [3] were presented by different authors. Some commonly en. (3), [4] en. (4), [5] en. (5), [6] en.(6), [7] en. (7) in used examples are: [3] eq. (3), [4] eq (4), [5] eq (5), [6] (8): eq. (6), [7] eq (7) and (8): d32(m) 2,39•10-3.Dp-0,135./T1.qc0i,k3e1l d32 (mm) d32 (mm) =124,77 585000 0 s 0 K Pa \PfJ 0,25 1+ 3, 31mf d32(m) = 3-105Dp-0,458G0f ,209v0f ,216 ysfPfdh 0,916 A V d,ef J d32(um) = 324,6 Pau02d sf J d32(\m) 6156n 0,385s 0,737 0,737 0,06 rfdhsf m2f r 0f ,737 ra0,06Dp- (3) (4) (5) (6) (7) (8) kjer so: Dp - tlačni padec, qikel - količina vbrizganega goriva na cikel, Gf - pretok goriva, u0 - hitrost na izstopu iz šobe, u - hitrost gibanja zraka, pf - gostota goriva, pa - gostota zraka, sf - površinska" napetost goriva, /u - dinamična viskoznost goriva, v -kinematična viskoznost goriva, dh - premer odprtine šobe, Ad - prerez odprtine šobe in Ad f - efektivni prerez odprtine šobe. Vse vrednosti se vstavljajo v enotah SI, razen v en. (5) dh v mm, en.(6) Gh v kg/h in v en.(8) Dp v bar. 2 ŠTEVILČNI PRIMERI Analiza curka je narejena z uporabo programa FIRE v62b na delovni postaji Hawlett Packard. Proces vbrizgavanja oz. curek je obravnavan na tridimenzionalnem modelu v obliki valja (pregl. 1), ki predstavlja zgorevalno/vbrizgalno komoro. Šoba je postavljena v središče zgornje ploskve valja. Analiza je izvedena na šobah s štirimi odprtinami (4 x 0,35 mm, 4 x 0,25 mm in 4 x 0,40 mm). Lega šobe in izmere so predstavljeni na sliki 1 in v preglednici 2. where: Dp is the pressure difference, qcikel is the quantity of fuel injected per cycle, Gf is the fuel flow, u0 is the velocity at the nozzle outflow, ua is the air velocity, pf is the fuel density,Ais the air density, sf is the surface tension of the fuel, ju is the dynamic viscosity of the fuel, v is the cinematic viscosity of the fuel, d is the nozzle hole diameter, Ad is the nozzle hole cross-sectional area and Ad,f is the effective nozzle hole cross-sectional area All values are in the SI system, except in eq (5), where