let. - vol. -45 C1999J št. - no. "7/B STROJNIŠKI VESTNI K V/8 JOURNAL OF MECHANICAL ENGINEERING strani - pages 2B5 - 3CB ISSN-0039-24B0 . Stroj V . STJVAX cena SCO SIT [j modelB procesa in strul^ indukcijsko keljenje The Development of b Model for Process a Con*. System for an Hardeml »aliza dm sistemov s 'rezovolnitTii Analysis of Dynamic Systems wi[ Bond - Graphs upa pralnih strojev. irabo dusilnih materialov The Reduction of W& ig Machl, Noise by the Use of Muffling Materials pametri opt je varjenia za \.p atrženako žico tipa RD 971 Optimisation of Welding Parami for the New Tubular Cored Electrod Type RD 971 ^^ © Strojni{ki vestnik 45(1999)7/8,265 Mese~nik ISSN 0039-2480 © Journal of Mechanical Engineering 45(1999)7/8,265 Published monthly ISSN 0039-2480 Vsebina Contents Strojni{ki vestnik - Journal of Mechanical Engineering letnik - volume 45, (1999), {tevilka - number 7/8 Uvodnik Editorial P. Novak: Kako v prihodnje? 266 P. Novak: Where do We Go from Here? Razprave Papers Cajner, F., Grilec, J., Landek, D.: Razvoj modela Cajner, F., Grilec, J., Landek, D.: The Development procesa in strukture krmilnega sistema delovne of a Model for the Process and Structure of a enote za indukcijsko kaljenje 267 Controll System for an Induction Hardening Cell Hussu, A.: Analiza dinamičnih sistemov s Hussu, A.: Analysis of Dynamic Systems with povezovalnimi grafi 278 Bond-Graphs Holeček, N.: Zmanjšanje hrupa pralnih strojev z Holeček, N.: The Reduction of Washing Machine uporabo dušilnih materialov 287 Noise by the Use of Muffling Materials Meško, J., Leždik, V., Mičian, M.: Parametri optimizacije varjenja za novo stržensko žico tipa of Welding Parameters for the New Tubular RD 971 294 Cored Electrode Type RD 971 Strokovna literatura 301 Professional Literature Osebne vesti 303 Personal Events Navodila avtorjem 305 Instructions for Authors I gfin=i(purMini5nLn 99 stran 265 I^HsSTTlMlDC © Strojni{ki vestnik 45(1999)7/8,266 ISSN 0039-2480 Uvodnik © Journal of Mechanical Engineering 45(1999)7/8,266 ISSN 0039-2480 Editorial Uvodnik Editorial Kako v prihodnje? Where do We Go from Here? Počitniški čas se bliža koncu. Pred nami so vpisi na univerzi. Tehniške fakultete so že vrsto let soočene z zmanjšanim vpisom. Slovenska strojna industrija se bori za preživetje. Vlaganja MŠŠ v pedagoške laboratorije na tehniki so bila v zadnjem desetletju minimalna. Ali bomo lahko zdržali tekmo s tujino? Pedagoško osebje se počasi pomlajuje, vendar smo priča le skromnemu povečanjuštevila pedagoškega osebja. Ali bo novi minister prof.dr. Pavle Zgaga dojel usodnost zaostajanja vlaganj v pedagoške laboratorije na tehniških fakultetah za ekonomski razvoj slovenske družbe. Ni moderne industrije, niti izvoza znanja, brez dobro izobraženih inženirjev. Živimo v stoletju tehnike in desetletju informatike, zato je pomembno, kako bomo izobraževali vodilno osebje za proizvodnjo in intelektualne storitve. Novo vrednost v Sloveniji, razen majhnega deleža kmetijstva, ustvarjaše vedno industrija. Zaradi napačnih predpostavk o družbenem razvoju se vsi hvalijo z visokim BDP. Malokdo pa ve, da se je ob manjši proizvodnji v Sloveniji, kakor je bila leta 1985 (ko je bil BDP okoli 4000 USD), zvečal v letu 1998 na 11500 USD po zaslugi trgovine. Medtem ko smo imeli leta 1990 le 1,5 milijarde USD zunanjega dolga ali 750 USD/preb., smo ga v letu 1999 (junij) pridelali že 5,4 milijarde USD ali 2700 USD/preb. Ker je izvozni delež kmetijstva, turizma in znanja relativno majhen (skupaj manj ko 30 %), bo morala za vračanje dolga poskrbeti industrija z ustvarjanjem nove vrednosti. Vstop v EU nam bo sicer povečal možnosti za bolj enakopravno prodajo, toda ob tem bomo morali poskrbeti za tehnološko, oblikovno in cenovno konkurenčnost naših izdelkov. Zato je nujno treba omogočiti, ne samo fakultetam za strojništvo, ampak celotni “tehniki” modernizacijo pouka. To še posebej velja za visoke strokovne šole, ki v Nemčiji pomenijo glavno oporo pri tehnološkem napredku v proizvodnji. Na univerzitetnem študiju, kjer se oblikujejo ustvarjalci novih tehnologij, izdelkov in znanja, pa moramo študentom omogočiti dostop do sodobnih orodij ter obnoviti celotno informacijsko infrastrukturo. Zakaj to poudarjamo. Zato, ker vemo, da je sredstev malo. Zato jih moramo vlagati tja, kjer je doba njihovega vračanja najkrajša. Da je to primer pri izobraževanju inženirjev, menda ni treba dopovedovati nikomur. Upam, da bo te vrstice bral tudi kdo od odgovornih in ustrezno ukrepal. Seveda bi pa morale tehniške fakultete obeh univerz sestaviti svoj program razvoja in vlaganja ter ga prek univerz posredovati v državni zbor. MŠŠ ima preveč obveznosti in premalo moči, da bi negativni tok vlaganj obrnilo navzgor. Prof. dr. Peter Novak This year’s holidays are coming to a close. We are coming up to enrolment time at the universities. The engineering faculties have seen reductions in the number of new students for several years now. The Slovenian engineering industry is fighting for survival. The Ministry of Education and Sport investment into pedagogical laboratories in the engineering field have been minimal over the past decade. Will we be able to keep pace with competitors abroad? Our pedagogical personnel are slowly being renewed but the increase in their numbers has been extremely modest. Will the new Minister, Prof. Dr. Pavle Zgaga, see the fatal effects of lagging behind in investment into pedagogic laboratories at engineering faculties for the economic development of Slovenian society as a whole? No modern industry or export of knowledge can exist without well-educated engineers. We are living in a century of technology and a decade of Informatics, so it is important how we educate our leading personnel in production companies and intellectual services. New wealth in Slovenia (apart from a small share of agriculture) is still created by industry. Due to incorrect assumptions regarding social development, everyone boasts of a high GNP, but few know that in 1998, with lower production in Slovenia than that of 1985 (when GNP was about 4000 USD), GNP increased to 11500 USD thanks to trade. While in 1990 Slovenia had only 1.5 billion USD of foreign debt or 750 USD per capita, it increased to 5.4 billion USD or 2700 USD per capita by June 1999. Since the export share of Slovenian agriculture, tourism and knowledge is relatively low (together less than 30%), industry will need to ensure the repayment of the debt by creating new wealth. Accession to the EU will increase Slovenia’s opportunities for more equal sales, but we will have to ensure the competitiveness of our products in terms of technology, design and price. It is therefore essential that we enable not only mechanical engineering faculties but also the entire engineering field to modernise education. This applies especially to higher professional education which, for example, is the main pillar of technological advances in the field of production in Germany. University study, which educates the creators of new technologies, products and knowledge, should enable students access to modern tools and renew the entire information infrastructure. Why am I emphasising this point? Because it is well known that funds are scarce. And so they need to be invested in places where the return period is the shortest. I’m sure that nobody needs to be told that this is the case in the education of engineers. I hope people in responsible positions will read these points and act accordingly. Naturally, engineering faculties from both universities should prepare their own programs for development and investment and pass it to the National Assembly via the universities. Ministry of Education and Sport has too many obligations and too little power to turn round the negative flow of investments. Prof. Dr. Peter Novak 8 SšnnstsfcflM]! mn stran 266 © Strojni{ki vestnik 45(1999)7/8,267-277 © Journal of Mechanical Engineering 45(1999)7/8,267-277 ISSN 0039-2480 ISSN 0039-2480 UDK 621.785.6:681.51 UDC 621.785.6:681.51 Predhodna objava (1.03) Preliminary paper (1.03) Razvoj modela procesa in strukture krmilnega sistema delovne enote za indukcijsko kaljenje The Development of a Model for the Process and Structure of a Control System for an Induction Hardening Cell Franjo Cajner - Josip Grilec - Darko Landek Da bi dosegli kakovostnejše in bolj prilagodljivo izvajanje postopka indukcijskega kaljenja, je potrebna računalniško podprta priprava in krmiljenje procesa. Prispevek opisuje in določi model procesa indukcijskega kaljenja, s katerim, ob zahtevanih parametrih postopka, dosežemo predpisano kakovost zakaljenega sloja. Nadalje obravnava vplivne dejavnike, ki opredelijo in uvajajo krmilni sistem, s katerim vodimo proces indukcijskega kaljenja v prilagodljivi delovni enoti. © 1999 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: kaljenje induktivno, modeliranje procesov, sistemi krmilni, celice fleksibilne) In order to achieve higher quality and a more flexible execution of the induction hardening process, a computer assisted program for undertaking and controlling of this process is needed. This paper proposes and describes a model for the induction hardening process, the application of which achieves a specified quality of the hardened layer, within all the parameters of the process. All the influencing factors, which define and implement the control environment used in the application of the process within the flexible working cell, are systematically analyzed. © 1999 Journal of Mechanical Engineering. All rights reserved. (Keywords: induction hardening, process modelling, control systems, flexible cell) 0 UVOD Indukcijsko kaljenje je postopek površinske toplotne obdelave, med katerim se, zaradi elektromagnetne indukcije, tanek površinski sloj na določenih površinah jeklenega obdelovanca hitro segreva do temperature avstenitizacije, nato pa se z gašenjem dosežeta želeni martenzitna mikrostruktura in trdota. S tem se zagotovi obrabna odpornost torno obremenjenih površin obdelovanca brez strukturnih sprememb v jedru obdelovanca ([1] do [3]). Da bi dosegli želene lastnosti, mora biti površinski sloj predpisane oblike, predpisana pa sta tudi globina kaljenja in površinska trdota. Pri tem ne sme priti do sprememb izmer in oblike obdelovanca. Za dosego teh zahtev je treba razviti [4]: - matematični model za optimizacijo oblike induktorjev in simuliranje procesa, - ustrezno bazo podatkov za spremljanje lastnosti materiala in delovnih karakteristik opreme, - krmilne algoritme procesa za določen material, geometrijsko obliko obdelovanca in enofrekvenčno (ali dvofrekvenčno) obdelavo, ki omogoča želeno kakovost zakaljenega sloja. 0 INTRODUCTION Induction hardening is a process by which thin surface layers, at specified areas of the steel workpiece, are heated rapidly to an austenitization temperature by electromagnetic induction, and the desired hardness and the martensitic structure is achieved by quenching. Thus, at the workpiece’s contact surfaces the wear resistance is achieved while allowing the rest of the material to be unaffected by the process ([1] to [3]). To achieve these properties the hardened surface layer has to be of a predefined shape, predefined depth of quench hardening and predefined surface hardness. To meet these requirements and produce quality results, it is necessary to develop [4]: - computational models for the optimal shape of inductors and for the simulation of the process, - appropriate database systems for observing the properties of the material and the working characteristics of the machinery, - control algorithms for the application of the process to a given material, to the geometric shape of the workpiece and to the monofrequency ( respectively dualfrequency ) treatment, which will result in the desired quality of the hardened layer. | gfin=i(purMini5nLn 99 stran 267 I^HsSTTlMlDC F. Cajner - J. Grilec - D. Landek V članku so prikazana načela in osnutek bodoče programske podpore projektiranju tehnologije indukcijskega kaljenja, posebej za obdelovance zahtevnejših oblik. Podan je prikaz nadzornega in diagnostičnega algoritma, ki omogoča povezavo z generatorjem, obdelovalnim sistemom, sistemom za gašenje in krmilnim sistemom za prilagodljivo delovno enoto. 1 OSNUTEK RAZVOJA PROGRAMA ZA SIMULIRANJE IN OPTIMIZACIJO INDUKCIJSKEGA KALJENJA Podatke o materialu in izmerah obdelovanca ter podatke o induktivni delovni enoti je najbolje organizirati v modularno povezane operativne in povezovalne baze podatkov. Računalniški programi, ki se uporabljajo za obdelavo tovrstnih podatkov, že obstajajo in so lahko dostopni. Za uporabo simulirnega programa indukcijskega kaljenja in programa za optimizacijo oblike induktorja so potrebne tri operativne baze podatkov: 1. baza podatkov o tehničnih značilnostih in vzdrževanju indukcijske delovne enote; 2. baza podatkov o lastnostih materiala; 3. izhodiščna tehnološka baza, tj. uspešno izvedenih in preverjenih optimizacij za posamezne materiale in obdelovance. Izvedensko znanje o procesu indukcijskega kaljenja in rešenih tehnoloških primerih je shranjeno v izhodiščni tehnološki bazi. V njo se po uspešni optimizaciji induktorja ter simuliranja indukcijskega kaljenja shranijo podatki o obliki in izmerah induktorja, parametrih segrevanja in ohlajanja ter rezultati metalografske analize preskušanca. S tem se ob vsakem reševanju problemov pri indukcijskem kaljenju razširi in poglobi znanje, kar vpliva na proces učenja in pridobivanje izkušenj. Algoritem za numerično simuliranje indukcijskega kaljenja in optimizacijo induktorja (sl. 1), je definiran na podlagi vpogleda v poročila in rezultate uporabe posameznih komercialnih in raziskovalnih simuliranj programa ([3] do [5]). Kakovost indukcijsko zakaljenega sloja -zaradi katere se izvaja simuliranje procesa in optimizacija induktorja - je definirana z obliko zakaljene cone, globino kaljenja in s površinsko trdoto. Vhodne veličine simulirnega programa morajo zbirati najpomembnejše vplive, ki odločajo o kakovosti zakaljenega sloja. Popis vplivov in njihov učinek na posamezne lastnosti sloja je prikazan v preglednici 1. Optimizacijski algoritmi, ki naj bi bili vgrajeni v omenjeni program, bodo upoštevali vplivnost navedenih dejavnikov in opozarjali uporabnika na njihovo ustrezno uporabo. 8 ^nn3@mMlŽKD | ^BSfirTMlliC | stran 268 This paper describes the principles and the concept for a future system support program for the design of induction quench hardening technology. It focuses in particular on the hardening of complex shapes. Furthermore, it illustrates the control and the diagnostic algorithm that enables linking of the power supply, the workhandling system, the quenching system and the process control and monitoring system in the flexible work cell. 1 THE CONCEPT OF PROGRAM DEVELOPMENT FOR THE SIMULATION AND OPTIMIZATION OF INDUCTION HARDENING It is important to organize all the data relating to the material, about the dimensions of the workpiece to be treated and the induction work cell, into a modular and operationally related database. Readily available computer programs already exist for the design of such data. To use the induction hardening simulation program as well as the inductor shape optimizing program, three operational databases are necessary. 1. A database relating to the technical characteristics and maintenance of the induction work cell. 2. A database of material properties. 3. A technological initialization base, i.e. of successfully carried out and verified optimization for single materials and workpieces. Expert knowledge about the induction hardening process and case by case technical solutions are stored in the technological initialization base. After successfully completing the optimizing of the inductors, and the simulation of induction hardening, the following data are then fed in to the technological base: details about the shape and the dimensions of the inductor, the heating and cooling parameters, and the results of the metallographic analysis of the experimental sample. Thus, with each solution to problems that relate to the induction hardening, the knowledge system grows and improves and acquires more elements of technical expertise. The algorithm for a numerical simulation of the induction hardening and the optimization of the inductor is defined on the basis of information received from individual research and commercial simulation programs ([3] to [5]) (Fig. 1). The quality of the induction hardened layer -the assurance of which is the reason for undertaking the simulation of the process and the optimization of the inductor- is defined by the shape, the depth and the surface hardness of the quench hardened zone. The initial scope of the simulation program must include the factors which most influence the quality of the quench-hardened layer. These factors and their significance with respect to individual cases are listed in Table 1. During the development, optimizing algorithms will be included into the above mentioned program and will take into consideration the influence of the specified factors, so the user will be well informed about their adequate use. Razvoj modela krmilnega sistema - The Development of a Control System Ob začetku izvajanja simuliranja je treba določiti porazdelitev vira toplote (spremenljivo v času in prostoru) z reševanjem elektrodinamičnih enačb magnetnega polja pri podanih robnih pogojih. Postavljeni model obsega obdelovanec, induktor in zračno režo med njima. Začetna porazdelitev polja toplotnega vira pomeni vhodno spremenljivko za izračun neustaljenega temperaturnega polja in z njim povezanih faznih premen v času pregrevanja. Spremenljive fizikalne lastnosti materiala, ki so odvisne od temperature, so v modelu popisane z ustreznimi interpolacijskimi temperaturno odvisnimi zlepki, ki izhajajo iz rezultatov prejšnjih preskusov ali iz literature. Omenjena odvisnost lastnosti od temperature vnaša nelinearnost v magnetno-termodinamičen proces, kar terja iterativno izračunavanje razvite moči z uporabo numeričnih metod (npr. metodo končnih elementov, metodo robnih elementov) ([3] do [7]). At the start of the simulation procedure the heat source distribution (variable according to time and place) should be determined by solving the electro-dynamic magnetic field equations for the established boundary conditions. The corresponding model includes the workpiece, the coil and the air gap. The initial distribution of heat sources represents the input variable for the computation of the nonstationary temperature field and the interacting phase transformation during heating. The changeable physical properties of the material which depend on temperature are included in the model via corresponding spline temperature dependent functions, derived from experiments or literature sources. The dependence of properties on temperature produces nonlinear data in the magneto-thermal procedure, thus necessitating iterative calculations of the dissipated power using numerical methods (i.e. Finite Element method, Boundary Element Method etc.) ([3] to [7]). Preglednica 1. Veličine, ki vplivajo na obliko zakaljenega sloja, globino kaljenja in potek trdot po zakaljenem sloju in jih popisujejo vhodni parametri simulacijsko optimizacijskega modela Table 1. Influencing factors on the appearance of the quench-hardened area, the depth and hardness of the hardened area included in the initial scope of the simulation optimizing model VPLIVNE VELIČINE kot VHODNI PARAMETRI MODELA INFLUENCING FACTORS as THE INITIAL SCOPE OF THE MODEL PARAMETRI, KI OPREDELJUJEJO KAKOVOST ZAKALJENEGA SLOJA CHECK MARKS OF THE QUENCH-HARDENED ZONE Oblika zakaljenega sloja Shape of the zone Oblika in izmere obdelovanca The shape and dimensions of the workpiece Kemijska sestava materiala Chemical composition of the material Toplotne lastnosti materiala obdelovanca Thermal properties of the workpiece material Električne in magnetne lastnosti materiala Electrical and magnetic properties of the material Temperatura avstenitizacije pri hitrem segrevanju Austenitizing temperature due to rapid heating Zgornja kritična hitrost gašenja Upper critical quenching speed X XX XX Poprejšnja toplotna obdelava in izhodiščna mikrostruktura Previous heat treatment and initial microstructure Postopek indukcijskega kaljenja Method of induction hardening Lega induktorja glede na obdelovanec Workpiece to induction coil location Izhodna oblika, izmere in material induktorja The initial shape, dimensions and material of the inductor Delovna frekvenca Working frequency Moč, napetost in tok induktorske tuljave Power, voltage or current of the induction coil Čas segrevanja ali premik obdelovanca Heating time or the scan speed of the workpiece Podatki o gašenju (sredstvo, temperatura, čistost in koncentracija) Quench data (media, temperature, purity, concentration) Pretok ali tlak sredstva za gašenje Flow or pressure of the quench media Koeficient toplotne prestopnosti Heat transfer coefficient____________ X Globina kaljenja Depth of hardness Trdota površine Surface hardness XX XX XX XX XX XX XX XX XX | gfin=i(purMini5nLn 99 stran 269 I^HsSTTlMlDC F. Cajner - J. Grilec - D. Landek Vnos (ali sklic na bazo podatkov) vhodnih parametrov: - geometrijski model z izmerami in pozicioniranjem obdelovanca v induktor, - robni pogoji, - fizikalne in metalurške lastnosti materiala, - parametri segrevanja in gašenja. Enter (or import from database) the initial scope: - the geometrical model with dimensions and positioning of workpiece and the inductor, - the boundary conditions, - the material physical and metallurgical properties, - the parameters of heating and quenching. INICIALIZACIJA: - izračunavanje elektromagnetnega polja, - izračunavanje toplotnih virov, - postavitev začetnega prostorskega in časovnega koraka. INITIALIZATION: - computation of the electromagnetic field, - computation of the heat sources, - initial spatial and time increments. BAZA PODATKOV o: 1. INDUKCIJSKI DELOVNI ENOTI 2. OBDELOVANCIH in MATERIALIH 3. TEHNOLOŠKIH PODATKIH DATABASE about: 1. The INDUCTION WORK CELL 2 The WORKPIECES and MATERIALS 3. TECHNICAL RECORDS MAGNETNOTERMODINAMIČNA ANALIZA (nelinearni problem) MAGNETO-THERMODYNAMIC ANALYSIS (nonlinear problem) TERMOMIKROSTRUKTURNA ANALIZA faznih premen med SEGREVANJEM THERMO-METALLURGICAL ANALYSIS of phase transformation during HEATING NE NO Ali sta globina in oblika avstenitnega sloja sprejemljivi? Acceptable depth and shape of austenised zone? DA YES Prikaz: porazdelitve magnetnega polja in notranjih toplotnih izvorov, temperaturno polje obdelovanca, porazdelitev mikrostrukturnih faz v segretem sloju. Displays of: distribution of magnetic field and the internal sources, workpiece temperature field, heated zone phase distribution. OBRNJENO MODELIRANJE: izračunavanje koeficienta prenosa toplote iz merilnih rezultatov INVERSE MODELLING: calculation of heat transfer coefficient from measured values TERMOMIKROSTRUKTURNA ANALIZA faznih premen med GAŠENJEM na podlagi faznih diagramov čas-temperatura-transformacija THERMO-METALLURGICAL ANALYSIS of phase transformations during QUENCHING based on time-temperature-transformation diagrams NE NO Shranjevanje Store x Ali je dosežena površinska trdota brez odstopanj? Satisfying surface hardness without flaws? DA YES________________ KONEC END Prikaz: potek trdot v zakaljenem sloju, porazdelitev faz v zakaljenem sloju. Displays of: hardness profile of the hardened zone, phase distribution into hardened zone. Sl.1. Algoritem simuliranja indukcijskega kaljenja Fig. 1. Induction hardening simulation algorithm 8 SšnnsOJiM]! ma stran 270 Razvoj modela krmilnega sistema - The Development of a Control System Da bi določili doseženo globino avstenitizacije, izračunamo temperaturno polje z upoštevanjem faznih premen pri hitrem segrevanju v časovno-temperaturnem diagramu avstenitizacije (TTS) pri podanem izhodiščnem mikrostrukturnem stanju. Če je dosežena globina pregretja neustrezna, se znotraj določenih meja najprej spremenijo parametri segrevanja (delovna moč induktorja, trajanje, pomik), šele nato spremenimo velikost in obliko induktorja. Z upoštevanjem temperaturne porazdelitve po procesu segrevanja, se izvedeta simuliranje in optimizacija gašenja. Za natančnejše določanje hitrosti ohlajanja je treba poprej razrešiti inverzni termodinamični problem [6] in izračunati spremembo koeficienta prestopa toplote a (W/m2K) v odvisnosti od temperature. Z uporabo faznih diagramov TTT in enačb fazne kinetike se izračunajo krivulje ohlajanja in po njih nastala mikrostruktura in njena trdota. Ta postopek je uporaben v primeru enojnega indukcijskega kaljenja. Za simuliranje je treba hkrati analizirati indukcijsko kaljenje, segrevanje in hlajenje. Zaradi napak v izračunavanju lastnosti materiala in nenatančnosti matematičnega modela procesa, je potrebna eksperimentalna potrditev modela. Izvedemo jo s snemanjem časovnega spreminjanja temperatur med procesom in z merjenjem dosežene mikrostrukture in trdot po kaljenju. Pred podrobno raziskavo in optimizacijo postopka za novo obliko obdelovanca in induktorja je priporočljivo potrditi model [7]. Overitev ni potrebna, če uporabimo podoben induktor ali obdelovanec. Modeliranje in simuliranje je priporočljivo izvajati s posebnim programom, ki ga lahko razširimo z lastnimi moduli. Za vsakdanjo tehnično uporabo in preliminarne raziskave zadostujejo enodimenzionalni računalniški programi (samo za reševanje elektromagnetnih in termodinamičnih problemov). Drugi korak simuliranja se izvaja z dvodimenzionalnimi in tridimenzionalnimi programi, ki so natančnejši pri načrtovanju in simuliranju [7]. Uporaba računalniških programov ne izključuje sodelovanja s tehnologom za indukcijsko kaljenje, ki mora uporabljati lastne izkušnje in intuicijo med izvajanjem kritičnih progamskih korakov (posamezni izbor po ustrezni analizi). Na ta način dosežemo optimalno temperaturno in mikrostrukturno porazdelitev v najkrajšem času in z najmanjšo potrebno močjo. Po določitvi geometrijske oblike induktorja, vrste sredstva za gašenje in intenzitete gašenja, se parametri indukcijskega kaljenja shranijo v bazo podatkov za krmiljenje procesa in izhodiščno tehnološko bazo. Izstopne veličine simulacijsko-optimi-zacijskega programa, ki se hkrati postavljajo kot referenčne veličine krmiljenja, so prikazane v preglednici 2. In order to determine the achieved depth of austenitization, the temperature field must be calculated. All the phase transformations, according to the Time-Temperature-Austenitizing diagrams, for a given initial microstructure must also be taken into account. Should an unsatisfactory depth of austenitisation be reached, initially the parameters which relate to heating (the power, voltage or current of the induction coil, the heating time, or scan speed) would be modified, within their boundaries. Should these modifications prove inadequate, the size and the shape of the inductor must be altered. Starting from the temperature distribution after heating, the quenching phase is simulated and optimized. In order to exactly establish the rate of cooling, after solving the inverse thermodynamic problem first, the alteration of the heat transfer coefficient a (W/m2 K) which depends on the temperature has to be calculated [6]. The cooling curves are calculated using the phase transformation and the phase kinetics Time-Temperature-Transformation diagrams. This procedure is suitable in the case of single-shot induction hardening. For simulation the scanning induction hardening, heating and cooling must be analyzed simultaneously. Because of errors in the calculation of the properties of the material and a faulty mathematical model of the process, an experimental confirmation of the model, by recording the time-sequence temperatures during the process as well as the obtained micro-structure and hardness after treatment, becomes necessary. It is advisable to verify the model before any detailed research and optimization of the procedure for a new shape of workpiece or inductor is undertaken [7]. This is not necessary for a similar inductor or workpiece. To execute a new model or simulation it is advisable to use a special software program which is expanded with self-development modules. For everyday technical use and preliminary research 1-D computer programs are adequate (for solving only electromagnetic-thermodynamic problems). The next simulation step is done via 2-D and 3D programs for better predictability and a more accurate simulation. The use of computer programs does not, however, exclude the induction hardening technician, who must rely on his experience and intuition (making choices after adequate analysis), in the critical programming steps, to achieve the optimal temperature field and microstructure distribution at the surface layer, in the shortest time with the minimum consumption of power. After the inductor geometry has been determined, the parameters of the induction quench hardening are stored into the process control database and the technological initialization base data. The application range of the simulation-optimization program, which is also used as the reference range for the controller, is illustrated in Table 2. | gfin=i(gurMini5nLn 99/8 stran 271 I^BSSIfTMlGC F. Cajner - J. Grilec - D. Landek Preglednica 2. Izstopni parametri optimizacijsko simulacijskega programa, ki so hkrati krmiljene veličine med izvajanjem procesa indukcijskega kaljenja in mesta merjenja teh parametrov Table 2. Application range of the simulation-optimization program also used as the range of control in the induction hardening process and their measuring points IZSTOPNE KRMILJENE VELIČINE APPLICATION CONTROL SCOPE Generator in induktorska tuljava Power supply and inductor coil Vpenjalni in pomični sistem Workhandling system Sistem za gašenje Quenching system Obdelovanec Workpiece Lega obdelovanca v induktorski tuljavi Position of workpiece within the induction coil X Vhodna moč induktorske tuljave Induction coil input power X Tok in napetost induktorske tuljave Coil current or voltage X Čas segrevanja Heating time X Hitrost pomika obdelovanca Workpiece scanning speed X Koncentracija in čistost sredstva za gašenje Concentration and purity of the quench media X Tlak in pretok sredstva za gašenje Quench media flow and pressure X Temperatura sredstva za gašenje Quench media temperature X Površinska temperatura obdelovanca po postopku gretja Workpiece surface temperature after heating process X Globina zakaljenega sloja, ki jo izmerimo z vrtinčnimi tokovi Depth of workpiece surface hardening verified by eddy current testing X 2 KRMILNI SISTEM DELOVNE ENOTE ZA INDUKCIJSKO KALJENJE Računalniško podprt krmilni sistem je zasnovan na merjenju krmiljenih parametrov procesa in primerjavi z referenčnimi parametri. To je osnutek krmiljenja procesa s t.im. “zapisom procesnih parametrov” (procesni diagrami) optimalno izvedenega procesa. Če kateri od opazovanih parametrov izstopi iz tolerančnega polja, krmilnik signalizira stanje procesa in zahteva njegovo prilagoditev referenčnemu procesu. Znotraj tolerančnega polja krmilnik sam usklajuje potrebne parametre procesa [8]. Pri indukcijskem kaljenju se dandanes, tako kakor pri drugih običajnih postopkih kaljenja, za krmiljenje moči induktorja, premik obdelovanca (ali induktorja) in parametre gašenja, uporabljajo programljivi logični krmilniki (PLK). Običajno se opremi za indukcijsko kaljenje doda večji mikroprocesor. Referenčni (krmilni) parametri in preostali podatki, potrebni za delovanje enote za 2 THE OPERATING SYSTEM OF THE INDUCTION HARDENING CELL The computer driven control system is based on the comparison between the range of tolerances of the process and the size of the frame of references. This is the process conducting concept according to the so called “recorded process range” (process diagrams) of the optimally conducted procedure. As soon as one of the elements of the observed range steps out of the field of tolerances, a controller signals the status of the procedure and instructs its adaptation to the process frame of references [8]. The execution of induction as well as conventional hardening processes use programmable logical controls (PLC) for the operation of the power of inductor, the mobility of the workpiece and the parameters of quenching. It is customary to add to the induction hardening equipment a host-microprocessor. The operating range and other information for the functioning of the system are programmed into the operation database. They are programmed 99-7/8 grin^(afcflM]SCLD I ^BSfiTTMlllC | stran 272 Razvoj modela krmilnega sistema - The Development of a Control System indukcijsko kaljenje, so shranjeni v operacijski bazi podatkov, iz katere jih v realnem času in po potrebah nadziranja procesa razbira enota PLK. Zaradi obdelave signala na digitalnem računalniku morajo biti analogni parametri poprej spremenjeni v digitalne z uporabo A/D pretvornikov na kartici PLK. 2.1 Diagnostika procesa Pred začetkom delovnega kroga je treba overiti stanje in delovne parametre vseh podsestavov delovne enote. V primeru manjših in starejših delovnih enot diagnostiko procesa izvaja operater enote. Ob izvajanju poprej računalniško simuliranega indukcijskega kaljenja je nujno potrebno avtomatsko krmiljenje delovnega kroga ob spremljanju minimalnega števila delovnih parametrov na zaslonu (video display terminal - VDT). Primer tipičnega avtomatskega diagnostičnega algoritma delovne enote za indukcijsko kaljenje za delo v avtomatski proizvodni liniji prikazuje (slika 2) ([8] in [9]). into the PLC according to the real time needed for the execution of the procedure. Because of the computation of the signal on a digital computer (measurable information in the feedback), analog signals have to be first converted into digital via an analog/digital converter-card on a PLC. 2.1 Process diagnostic Before the start of the work cycle, it is necessary to verify the condition and the functionality of all the supporting parts of the work cell. In the case of smaller and older work cells the diagnostic work is performed by the operator of the cell. To first conduct a computer simulation of the induction hardening process, an automated work cycle has to be initiated observing the minimal number of operating functions on a VDT (video display terminal). A typical diagnostic algorithm for an induction hardening work cell, designed for an automated production line, is shown in Fig. 2 ([8] and [9]). Ali so vse okvare in pomanjkljivosti odpravljene? \ ZAČETEK delovnega kroga Have all failures and \ START work cycle shortcomings been eliminated? KRMILNI SISTEM: - določitev parametrov moči induktorja med delovnim ciklusom, - določitev hitrosti pomika, - določitev pretoka, tlaka in temperature izbranega sredstva za gašenje, - določitev dovoljenega odstopanja površinske temperature obdelovanca med segrevanjem. CONTROL SYSTEM: - establishing induction coil power, - establishing scan speed cycle parameters, - establishing quench flow, pressure and temperature of the chosen media - establishing the workpiece surface temperature tolerances during heating. Napačno Faulty Pravilno: začeti proces ali nadaljevati delo Correct: start process or continue work PREVERJANJE STANJA: - nastavitev premika, - nastavitev hitrosti vrtenja obdelovanca, - pregled delovanja črpalk, - pregled mazalnega sistema, - temperatura sredstva za gašenje, - izbira želenega indukcijskega gretja, - prepustnost vhodnega in izhodnega tekočega traku, - druge delovne karakteristike. STATUS CHECKING: - setting the scanner limit switches, - setting the rotation speed of workpiece, - the proper functioning of pumps, - the proper functioning of lubrication, - the quench media temperature, - choosing desired induction cycle, - congestion at the entrance and exit of the conveyor belt, - other work characteristics. Sl. 2. Diagnostični algoritem za indukcijsko delovno enoto Fig. 2. Representation of the diagnostic algorithm for the induction work cell stran 273 BCšD9 nnME€ F. Cajner - J. Grilec - D. Landek Pred začetkom delovnega kroga diagnostični sistem preveri stanje delovne enote in izvede primerjavo znanih parametrov z vnesenimi. Primerjava se izvaja tudi med procesom kaljenja. Če odstopanja parametrov presežejo vnaprej določene meje, sistem obvesti operaterja in zahteva njegovo posredovanje pri reševanju nastalega problema. 2.2 Krmilni algoritem V večini delovnih enot za indukcijsko kaljenje nadzorujemo dva parametra: relativni premik med induktorjem in obdelovancem ter moč indukcijskega generatorja. Drugi parametri enote ostanejo nespremenjeni oziroma jih skušamo ohranjati nespremenjene. Krmiljenje lahko izvajamo ročno (z nastavljanjem ustreznih potenciometrov) ali avtomatsko (spreminjanje krmilne napetosti, dovedene z računalnika prek D/A pretvornika na kartici PLK). Krmilne napetosti, podane z računalnikom, običajno pripravljamo s prosto izbiro krmilnih operacij ali pa jih pripravljamo kot vhodne podatke, pridobljene iz datotek simulirnih programov po določenem operacijskem zaporedju. Pri enostavni krmilni zanki se razbiranje vhodnih podatkov iz A/D pretvornika izvaja diskretno. Po izvedbi krmilnega algoritma se na D/A pretvorniku pojavijo novi podatki. V ozadju teh dejavnosti lahko računalnik izvaja druge opravke, npr. prenos in obdelavo podatkov. Diskretizacija omogoča ustavitev glavnega uporabniškega programa s skokom na postopek za ustavitev krmilnega algoritma. Princip dela za ustavitev je shematsko podan na sliki 3. Before the start of the work cycle, the diagnostic system verifies the status of the work cell, and compares the existing parameters with the new ones. In the where case the new parameters exceed the defined parameters, the operator is called and asked to solve the problem. 2.2. Control algorithm In most conventional work cells for induction hardening the operation is based on two variables: the scan speed of the intake mechanism and the power of the induction generators. Other aspects of the work cell are made unalterable or are maintained as such. The operation can be manual (an adjustment of corresponding potentiometers) or automatic (altering the control voltage via computer through the D/A converter on the PLC card). Controlled voltages fed by the computer are usually program generated with a free choice in a controlled operation, or generated through the input of data obtained from databases of simulation programs in sequential operation. In a basic control loop the input of data from the A/D channel is performed during selectivity, and after the execution of the control algorithm new information is fed into the A/D channels. In the background during these operations, the computer can perform other tasks such as the transfer and organization of data. Selectivity enables the interruption of the main running program in order to leap to the routine executing of the control algorithm. The principle of performing the routine interruption is illustrated in Fig. 3. ZAČETEK START Uporabniški program Communication program / Inicializacija \ aparaturne opreme Hardvare initiation Digitalni vhod/izhod , Digital input/output , Komunikacijski program za povezavo računalnika z okoljem Interface of computer with environment Sl. 3. Diagram poteka programa z uporabo prekinjevalnega postopka Fig. 3. Program flowchart with interruption routine 8 &nnBjfokJ][p)l]Olf|i[gO | | ^SsfirWEIK | stran 274 Razvoj modela krmilnega sistema - The Development of a Control System Med programiranjem krmilnih aplikacij je treba posebno pozornost posvetiti vodenju sistema v realnem času, zbiranju podatkov z vhodov A/D pretvornika, njihovi obdelavi in na podlagi tega krmiljenja krmilnih parametrov prek izhodnih kanalov D/A pretvornika. Krmilne aplikacije je priporočljivo izdelati v programskem jeziku, ki je soroden zbirnemu jeziku (assembler) in ki hkrati vsebuje tudi lastnosti višjih programskih jezikov (programski jezik C in njegove nadgradnje). Takšni programi so prenosljivi, njihove izvirne kode pa se brez sprememb lahko izvajajo na različnih računalnikih in z različnimi operacijskimi sistemi. Reševanje problemov pri krmiljenju se izvaja z uporabo podprogramov, ki jih lahko logično poenotimo pri gradnji krmilnih programov. Poenostavljena shema digitalnega krmiljenja procesa (izhodna moč indukcijskega generatorja in premik obdelovanca) je prikazana na sliki 4. Premik obdelovanca Workpiece scan speed Moč induktorske tuljave Power of the induction coil During the programming of control applications special attention should be paid to the control of running the system in real time, to gathering information from the A/D input, its treatment and on the basis of this perform the control scope through the output D/A channels. It is recommended that the control applications should be performed using a program language which is close to that of the assembler which has the ability of many languages, similar to human languages (e.g. program language C, or C++). Such programs have a very high degree of transferability and the resultant codes can be used with various computers under different operational systems. The control program is produced by the use of subprograms and their logical unification. For the simplification of the digital process control (e.g. the outgoing induction generator power and the workpiece scanning speed) see Fig. 4. Površinska temperatura obdelovanca Surface temperature of workpiece D/A pretvornik D/A converter Ura za realni čas Real time clock Sl. 4. Poenostavljena shema digitalnega krmiljenja procesa Fig. 4. The simplification of the digital process control diagram 2.3 Problemi uvajanja digitalnega krmilnega 2.3. Problems in the implementation of the digital sistema control system Digitalni krmilni sistemi so diskretni sistemi v pogledu amplitude in časa. Vhodno izhodni parametri digitalnega krmilnega sistema lahko zajemajo le določene celoštevilčne vrednosti, katerih razpon je določen z A/D in D/A pretvorniki. Te pretvornike je treba izbrati tako, da njihove karakteristike (hitrost, ločljivost) omogočajo krmiljenje procesa v realnem času. Z namenom, da bi omogočili krmiljenje z uporabo računalnika je eden od prednostnih problemov povezava računalnika z realnim indukcijskim procesom. Ker računalnik deluje pod nizkim energetskim nivojem (istosmerna napetost do 12 V), ga moramo z izoliranimi ojačevalniki galvansko ločiti od indukcijskega procesa (napetosti anode visokofrekvenčnega generatorja znašajo tudi do 12 kV). Digital control systems are discrete in terms of time and amplitude. The input/output power of a digitally controlled system can accept only integers whose support is defined by the A/D and D/A converters. The converters should be chosen based on their ability to perform the control process (speed, resolution) in real time. In order to make the computer control possible, the problem of the link-up between the computer and the real induction hardening process becomes a priority. Since the computer functions only at low energy levels (direct current of up to 12V) it has to be completely insulated and well separated from the induction process (the power of a HF generator anode can reach levels of 12 kV). gfin^OtJJlMISCSD 99-7/8 stran 275 |^BSSIrTMlGC F. Cajner - J. Grilec - D. Landek Pri diskretizaciji signalov moramo veliko pozornosti posvetiti hitrosti vzorčenja merjenih parametrov z namenom, da bi diskretizirani signal ustrezno ponazoril stalni signal. Pogosto je treba prilagoditi krmilni signal (z ojačitvijo na potreben energijski nivo), da bi lahko vplivali na objekt krmiljenja v skladu z algoritmom krmiljenja in vektorjem referenčnih parametrov. 3 SKLEP Za kvalitetno indukcijsko kaljenje je treba analizirati procese segrevanja in ohladitve z računalniškim simuliranjem in zagotoviti avtomatsko krmiljenje celotnega procesa. Zaradi pospešitve tehnološke priprave pri oblikovanju induktorja zadošča simuliranje segrevanja obdelovanca z eno od uporabnih numeričnih metod s komercialno razvitimi enodimenzionalnimi računalniškimi programi. Za napovedovanje površinske trdote in porazdelitve zaostalih napetosti po kaljenju je treba simulirati nastale fazne premene in mehanske napetosti pri gašenju, kar pomeni zapleteno nalogo in terja veliko računalniškega časa ter uporabo dvo- in tridimenzionalnih programov. Simulirni programi se izkažejo za koristne pri uporabi oblikovno podobnih ali enakih obdelovancev, za katere je potrebno popolno razumevanje fizikalnih pojavov v procesu in pravilno izvedbo simuliranja. Pomemben prvi pogoj za natančnost simuliranja je tudi pravilna izbira robnih pogojev in dobro poznavanje lastnosti materialov obdelovancev. Za simulirne programe je treba organizirati operativne podatkovne baze, ki se uporabljajo med izvajanjem programov in za shranjevanje rezultatov izračunov. Dobro organizirane podatkovne baze rabijo kot vir znanja in pridobljenih izkušenj pri vsakem novem reševanju problemov indukcijskega kaljenja. Z uporabo računalniških simuliranj je čas projektiranja postopka indukcijskega kaljenja znatno krajši. Induktor, oblikovan za določen obdelovanec, ima lahko, poleg specifične oblike indukcijske zanke, tudi koncentrirana mesta magnetnega pretoka, kar zahteva razvoj posebnih diagramov sprememb procesnih parametrov in ustrezni krmilni algoritem delovne enote. Izhodni parametri simulirnega programa, ki definirajo procesne diagrame (npr. spremembe delovne moči generatorja in spremembe premikov obdelovanca med delovnim krogom) zahtevajo avtomatsko krmiljenje z uporabo PLK. Za diagnostiko delovanja indukcijske enote in za spremljanje parametrov procesa je koristno krmilne parametre prikazati na zaslonu. 8 ^nn3@mMlŽKD | ^BSfirTMlliC | stran 276 When selecting of the signal, special attention has to be paid to the speed induced pattern of the measured volume so that the selected signal matches closely the continuous signal. It is often necessary to approximate the controlling signals (amplifying them to reach the required energy level) in order to affect the controlled system so that it conforms with the algorithm of control and the vector of the reference parameters. 3 CONCLUSION For quality quench hardening induction, it is necessary to analyze the heating and quenching operations by means of a computer and insure the automatic control of the entire process. To speed up technical preparations for the shaping of the inductor, it is sufficient to simulate the heating of the sample workpiece with one of the available numerical methods and with the help of some commercially developed 1-D computer programs. To predict the surface hardness and the profile of residual stresses after hardening, a simulation of the resulting phase transformations and mechanical stresses at the quenching stage become necessary. This is a complex task requiring considerable computer time and 2-D and 3-D programs. Simulation programs are usually well suited for a selected group of similar or identical tasks. It is, however, necessary to completely understand the physical outcomes of the process in order to design and conduct a successful operation. The important preconditions for an accurate simulation are the setting up of an adequate framework and knowledge of the material properties of the sample. For simulation programs, the operative database must be organized for the servicing of the program and storing of the results of the calculations. By organizing a database it is possible to classify a system of knowledge with each solution to an induction hardening problem, that provides the simulation program with elements of learning. Using computer simulation, the time for the design of the induction hardening operation can be significantly shortened. The inductor, formed for a concrete task other than the specific induction angle shape, could have concentrators and magnetic flow screens that demand specifically developed diagrams, changed processing parameters and a compatible work cell control algorithm. The application scope of simulation programs that define process diagrams (e.g. the change in the working power of the generators and the changes in the mobility of the sample during the work cycle) require an automatic control and a PLC driven process. For the diagnosis of the work of the induction cell, as well as for the observation of the process parameters, it is useful to show the control parameters and the metering scope with a VDT diagram. Razvoj modela krmilnega sistema - The Development of a Control System Krmiljenje znanih indukcijskih sistemov starejše izvedbe z ročnim in polavtomatskim krmiljem je mogoče posodobiti z uporabo ustreznih krmilnih algoritmov. Pri novih in sodobnih indukcijskih sistemih se bodo simulirni programi uporabljali predvsem za hitro dimenzioniranje induktorjev in za definiranje optimalnih procesnih parametrov indukcijskega segrevanja oz. kaljenja. The existing induction hardening equipment of an older generation with manual or semi-automatic controls could be made more reliable by adapting applicable control parameters and by designing an adequate control algorithm. When purchasing new and contemporary induction equipment, future state of the art programs could be built-in for a successful and quick sizing of the inductors and for defining the optimal processing parameters for high frequency hardening. 4 LITERATURA 4 REFERENCES [1] Hassell, PA., N. V. Ross (1994) Induction heat treating of steel. ASM Handbook Part 4. 9th edition, Metals Park, Ohio, USA, 164-202. [2] Liščič, B., Stupnišek, M., Cajner, F., T Filetin (1992) Toplinska obradba - praktikum. FSB Sveučilišta u Zagrebu. [3] Rudnev, V.I. et. al. (1997) Induction heat treatment. Steel heat treatment handbook, ed. by G. E. Totten, M. A. H. Howes, M. Dekker Inc. USA, 765-871. [4] Kelly J.B. (1995) Intelligent induction hardening. Advanced Materials & Process, 12/95, 36Q-36R. [5] Schopfel, A., K. Strorzel (1997) Optimization of process parameters for induction heat treating by means of numerical simulation. Proceedings of the 17th Heat Treating Society Conference and Expositions, and 1st International Induction Heat Treating Symposium, 15.-18. September, Indianapolis, Indiana, USA, 595-600. [6] Liščič, B., Tensy, H., W. Luty (1995) Theory and technology of quenching. Springer-Verlag. [7] Nemkov, V.S. et. al. (1997) Computer simulation on effective creative tools for development of induction heat treating processes. Proceedings of the 17th Heat Treating Society Conference and Expositions, and 1st International Induction Heat Treating Symposium, 15.-18. September, Indianapolis, Indiana, USA, 786- 792. [8] Baines, A.P (1988) Induction heating quality assurance monitoring systems. Report 10th ASM Heat Treating Conference & Expositions in Heat Treatment of Metals 1988.1, 9-10. [9] Myers, R. (1992) Diagnostic - a powerful tool for induction heating. Advanced Materials & Processes, 7/ 92, 41-43. Naslov avtorjev: profdr. Franjo Cajner mag. Josip Grilec Darko Landek Fakultet strojarstva i brodogradnje Sveučilišta u Zagrebu Ivana Lučiča 5 10000 Zagreb, Hrvaška Prejeto: 17.11.1998 Received: Authors’ Address: Prof.Dr. Franjo Cajner Mag. Josip Grilec Darko Landek Faculty of Mechanical Engineering and Naval Architecture University of Zagreb Ivana Lučiča 5 10000 Zagreb, Croatia Sprejeto: 15.9.1999 Accepted: stran 277 BCšD9 nnME€ © Strojni{ki vestnik 45(1999)7/8,278-286 © Journal of Mechanical Engineering 45(1999)7/8,278-286 ISSN 0039-2480 ISSN 0039-2480 UDK 519.87:629.3.015 UDC 519.87:629.3.015 Strokovni ~lanek (1.04) Speciality paper (1.04) Analiza dinami~nih sistemov s povezovalnimi grafi Analysis of Dynamic Systems by Bond-Graphs Alojz Hussu Modeliranje in simuliranje sistemov so vse pogosteje uporabljani postopki, ponujajo cenejše, hitrejše in za okolje manj obremenjujoče poti do analize in načrtovanja sistemov. Z razvojem računalništva so se razvile tudi nekatere nove metode. Mednje sodi tudi modeliranje sistemov s povezovalnimi grafi. V prispevku je predstavljen paket BONK, ki skupaj z grafičnim vmesnikom omogoča hitro in raznovrstno analizo dinamičnih sistemov. © 1999 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: sistemi dinamični, modeliranje sistemov, grafi povezovalni, paketi programski) The modelling and simulation of systems is receiving increasing attention as it offers a cheaper, faster, and environmentally freendly method for the analysis and design of systems. In parallel with the development of computers some new methods of modelling and simulation, such as bond-graphs, have also been developed. In this paper we present the program BONK, which together with a graphical interface offers a quick and manifold analysis of dynamic systems. © 1999 Journal of Mechanical Engineering. All rights reserved. (Keywords: dynamic systems, systems modelling, bond graphs, software packages) 0 UVOD Trenutne razmere v poslovnem svetu terjajo hitro ukrepanje, hitro izrabo novih možnosti in hiter razvoj. Tako je npr. tudi pri proizvodnji avtomobilov. Končni proizvajalci iščejo najugodnejše, najcenejše in najhitrejše izdelovalce podsklopov. Po oceni avtomobilske industrije skrajšanje roka postavitve novega modela avtomobila na trg za en dan prihrani dva milijona ameriških dolarjev [1]. Zaradi takih razmišljanj nastajajo avtomatizirane proizvodne linije in se gradijo informacijski sistemi, ki naj po eni strani povežejo vse faze izdelave avtomobila, od zamisli, načrtovanja podsklopov, preskusov, načrtovanja izdelovalnih postopkov in podobno, po drugi strani pa dajejo ustrezno logistično podporo soizdelovalcem in nazadnje sestavo po želji kupcev in samo prodajo. Avtomatizacija je vedno bolj opazna tudi pri načrtovanju, ne samo na proizvodnih linijah. Uporabljajo razne programske pakete, ki naj pospešijo in pocenijo izračune in preverjanja s simuliranjem. Eno od področij pri načrtovanju avtomobilov je analiza dinamičnih lastnosti. V tem 0 INTRODUCTION The present day demands of manufacturing industry require swift reaction, the ability to take advantage of new opportunities and rapid development. This is particularly true of the car manufacturing sector. End producers are seeking the best, the quickest, the cheapest producers of subassemblies. The car industry estimates that reducing the lead-time to market of a new car model by one day saves 2 million US dollars. This kind of thinking results in the introduction of automated production lines and the construction of information systems connecting all phases of car production. Systems play a vital role in linking initial ideas with development, testing, production planning and production and to the logistics, connecting producers of subassemblies with the final producers of the cars according to the demands of buyers and sales departments. Automation receives more attention not only on the production lines but also in the development and design stages. Different program packages are used to speed up and reduce costs of calculations and testing through simulation. Designing a new car requires analysis of its dynamic properties, of 99-7/8 grin^(afcflM]SCLD I ^BSfiTTMlliC | stran 278 Analiza dinami~nih sistemov - Analysis of Dynamic Systems okviru so zanimivi pospeški in pojemki, na udobnost in varnost vožnje pa zelo vpliva vzmetenje avtomobila. Lahko se posvetimo tudi pogonskim podsklopom avtomobila, npr. motorju. V zadnjem času pospešeno rešujejo, z razvojem ustreznih elektronskih krmilnikov, problem najprimernejšega vžiga goriva v valjih, da bi zmanjšali vibracije motorja. Z izbiro trenutka vžiga in/ali z oblikovanjem najprimernejših sesalnih in izpušnih cevi skušajo vplivati na porabo goriva za dano moč motorja. Ali s porazdelitvijo navora motorja in zavor na posamična kolesa vplivati na varnost in udobnost vožnje, tu velja omeniti domač prispevek na tem področju [2]. V nadaljevanju bomo najprej kratko orisali program BONK, ki omogoča preprosto analizo dinamičnih sistemov, modeliranih oziroma opisanih z povezovalnimi grafi. Sledi opis grafičnega vmesnika, ki še dodatno poenostavi uporabo programa oz. pripravo podatkov. Uporabo programa ponazorimo z analizo dinamičnih lastnosti preprostega modela vzmetenja avtomobila. Sledita povzetek in literatura. 1 PROGRAM BONK Dinamične sisteme matematično opisujemo z linearnimi ali nelinearnimi navadnimi diferencialnimi enačbami ali parcialnimi diferencialnimi enačbami. Če želimo analizirati obnašanje takih sistemov, je na voljo več poti. Ena od njih je izvedba ustreznih preskusov na stvarnih sistemih. Preskusi na stvarnem sistemu so včasih dragi, včasih jih je nemogoče izvesti, včasih pa sistem sploh še ni zgrajen in šele iščemo najprimernejšo izvedbo, ki naj bi jo s poprejšnjo analizo obnašanja sistema določili. V primerih, ko se moramo odreči preskušanju stvarnega sistema, skušamo določiti obnašanje sistema z uporabo opisov sistema, ki so na voljo. Če je to matematični model sistema (opis z diferencialno enačbo ali s sistemom diferencialnih enačb prvega reda), skušamo poiskati rešitev te oziroma teh diferencialnih enačb pri pogojih, pri katerih lahko v zadovoljivi meri sklepamo o obnašanju dejanskega sistema v stvarnih razmerah. Reševanje diferencialnih enačb je rutinsko samo v preprostih primerih. Pogosto moramo posegati po numeričnih postopkih. Pri linearnih diferencialnih enačbah včasih uporabljamo različne transformacijske postopke, npr. iz časovnega prostora se z Laplaceovo transformacijo prestavimo v prostor kompleksne spremenljivke s oziroma v frekvenčni postor. Če želimo reševati diferencialne enačbe, jih moramo najprej zapisati, kar tudi ni vedno preprosto in hitro. Tako kakor pri numeričnem reševanju diferencialnih enačb uporabljamo orodja, računalnike, lahko tudi za sam zapis diferencialnih enačb uporabljamo orodja, tudi računalnike, z particular interest are acceleration and deceleration; comfort and safety depend very much on the suspension. However, power-train subsystems are also of interest, the engine for example. Electronic controllers for the optimum timing of fuel ignition in the cylinders are studied to reduce the motor vibrations and, in connection with the most appropriate intake and exhaust manifolds, to reduce the fuel consumption for a given engine power. The torque distribution of the engine and the wheel braking system are studied, in order to improve comfort and promote safe driving conditions. Here, a Slovenian contribution should be mentioned [2]. In the next section the BONK program is described. The program attempts to simplify the analysis of dynamic systems, described or modelled by bond graphs. There follows a description of a graphical interface, which simplifies additional data preparation and the use of the program, which is illustrated by the analysis of a car suspension model. Conclusion and references end the article. 1 PROGRAM BONK Dynamic systems are mathematically described by differential equations, linear or nonlinear, ordinary or partial. There are several ways to analyze the dynamic properties of such systems. Making appropriate tests on real systems is one method, however making tests on a real system can be expensive and in some situations, impossible. In other cases the real system does not yet exist and we just require a thorough preliminary analysis in order to determine the most appropriate realization. In situations when testing of real systems is not possible, we try to draw conclusions from the descriptions available. If it happens that a mathematical model of the system (first order differential equation or system of equations) is available, we try solving it under conditions that allow a reliable guess as to what can happen to the system in the real world. Solving differential equations is a routine procedure only in simple cases. Usually numerical procedures may be used. When we have linear differential equations, transformation procedures like Laplace transforms are sometimes used, switching from the time (or some other variable) domain to the space of a complex variable s or to the frequency space respectively. If a solution to the differential equations is required, we first have to write them down, which is not always a simple and quick process. In the same way as various tools, like computers, are used to obtain numerical solutions to differential equations, computers with suitable programs can also be used to obtain differential equations. However, for the | gfin=i(gurMini5nLn 99/8 stran 279 I^BSSIfTMlGC A. Hussu ustreznimi programi. Vendar moramo sistem, ki mu želimo določiti matematični model, opis z diferencialnimi enačbami, poznati oziroma ga tako opisati, da je iz opisa mogoče izluščiti diferencialne enačbe z uporabo računalniškega programa. To početje je primerno tedaj, če lahko preprosteje in/ali hitreje določimo opis sistema, iz katerega določimo diferencialne enačbe, kakor pa sam opis z diferencialnimi enačbami. Tak opis sistemov so npr. povezovalni grafi ([3], [4], [9] in [10]). Omogočajo opis strukture sistemov. Sisteme opišemo kot skupek povezanih preprostih elementov, za vsak element sta značilni napetostna in pretočna spremenljivka. Povezave med elementi ponazarjajo pretakanja moči med elementi. Povezovalni grafi so zlasti primerni za področje strojništva, ker lahko na enovit način prikažemo oziroma opišemo sisteme, ki združujejo različne podsisteme, npr. mehanske, hidravlične, električne itn. Osnovni pojmi o povezovalnih grafih in obširni seznam dodatne literature so bili podani v [3]. Tam sta tudi dva zgleda določevanja diferencialnih enačb iz povezovalnega grafa. Za določevanje in kasneje reševanje diferencialnih enačb je avtor sestavil program BONK. Poglejmo, kako pripravimo podatke, kako ga uporabljamo in kaj omogoča. Uporaba programa BONK je doslej zahtevala pripravo podatkov v besedni datoteki, ki jo zapišemo na podlagi narisanega povezovalnega grafa ([4] in [5]). Datoteka ima več blokov: - komentar, ki besedno opiše obravnavani primer, - seznam elementov povezovalnega grafa, kolikšne so vrednosti posameznih elementov in preko katere (če je samo ena) oz. katerih povezav je povezan z drugimi elementi povezovalnega grafa (opis strukture), - seznam aktivnih povezav, - seznam povezav, ki imajo vnaprej predpisano smer pretoka moči, - seznam povezav, ki imajo vnaprej predpisano vzročnost, - seznam izhodov, - dolžino koraka neodvisne spremenljivke (najpogosteje časa), če želimo npr. določiti časovne odzive oziroma diskretne modele, - opis funkcij, ali vhodnih ali nelinearnosti ali obojih. Vsi bloki niso potrebni, nujno potreben je blok z elementi in povezavami, drugi so odvisni od posebnosti problema, ki ga obravnavamo in vrste analize, ki jo želimo izvesti. BONK omogoča določiti: - zvezni in diskretni matematični model sistema (sistem linearnih diferencialnih oz. diferenčnih enačb prvega reda), - prenosne funkcije (zvezne in diskretne), - ničle in pole prenosnih funkcij, - Nyquistov in Bodejev diagram prenosnih funkcij, 8 ^nn3@mMlŽKD | ^BSfirTMlliC | stran 280 system we are studying we have to have an appropriate description, from which we can obtain the differential equations with the aid of computers. All this makes sense only in the case when it is easier and/or quicker to get a description from which differential equations are obtained, rather than to get differential equations directly. Bond-graphs ([3], [4], [9] and [10]) are such a description of systems, which enable to describe the structure of the systems. The structure is described as an assembly of connected simple elements with each element having a characteristic effort and flow variable. Bonds between the elements represent the flow of the power between elements. Bond-graphs are a particularly suitable modelling tool in mechanical engineering, where all the subsystems (for example mechanical, hydraulic or electrical) incorporated in the systems, are modelled in some uniform way. The basic ideas relating to bond-graphs and an extensive list of references are given in [3]. There are also two examples showing how differential equations are obtained from the bond-graphs. To obtain differential equations from bond-graphs and then to solve them the author has written the program BONK. We will look at how data for it is prepared, how it is used and what it offers. Until now it was necessary for the program BONK to prepare data in a text file, based on the drawn bond-graph ([4] and [5]). The file has several blocks: - comment, describing the problem we have to deal with, - list of elements of the bond-graph, their values and their bonds to the other elements (description of the structure), - list of active bonds, - list of bonds with an in advance ascribed direction of power flow, - list of bonds with an in advance ascribed causality, - list of outputs, - length of the step of the independent variable (mostly time), if time responses or discrete models are desired, for example, - description of either input functions or nonlinearities or both. All of these blocks are not necessary, what is required is the block with elements and bonds, others are included depending on the problem and the kind(s) of analysis we want to do. With BONK we can determine: - the continuous or discrete mathematical model of the system (system of differential or difference equations of the first order), - transfer functions (continuous and discrete), - zeros and poles of transfer functions, - Nyquist and Bode plots of transfer functions, Analiza dinami~nih sistemov - Analysis of Dynamic Systems - odzive na izbrane vstopne funkcije, - korenske krivulje in - občutjivost sistema na vrednosti parametrov. Če imamo opraviti z nelinearnimi sistemi, za katere ne moremo določiti primernih linearnih modelov, ostane samo določitev in analiza odzivov [5]. Uporaba programa BONK zahteva, da za sistem, ki ga želimo analizirati, narišemo povezovalni graf. V grafu oštevilčimo elemente in povezave in podatke iz grafa zapišemo v datoteko kot blok elementov in povezav. Dodati moramo vrednosti posameznih elementov. Določimo izhode (napetostne in/ali tokovne spremenljivke na izbranih elementih). Vhodi so že vnaprej podani z napetostnimi in/ali tokovnimi viri, ki so upoštevani v modelu. Določitev smeri pretoka moči in vzročnosti na posameznih povezavah lahko določimo sami in opišemo v posebnem bloku datoteke, lahko pa prepustimo programu BONK, da jih določi namesto nas. Včasih, v izjemnih primerih, je potreben popravek določitve. Na podlagi pripravljenih podatkov BONK določi matematični model sistema, ki je osnova za nadaljnje izbrane vrste analize. Analizo pogosto uporabljamo kot sestavni del načrtovanja sistemov, ki običajno poteka iterativno. Najprej si zamislimo sistem, analiziramo delovanje, po rezultatih analize spremenimo oziroma izboljšamo sistem, ponovno analiziramo, izboljšamo itn., dokler ne najdemo ustrezne rešitve, ali pa za nadaljevanje zmanjka denarja, časa ali česa drugega. Lahko da iskane oziroma želene rešitve sploh ni. Program BONK zahteva opis sistema v datoteki, ki jo dobimo iz povezovalnega grafa sistema. Imamo dva opisa sistema, narisan povezovalni graf sistema in datoteko na podlagi povezovalnega grafa. Če spreminjamo sistem, moramo spremeniti povezovalni graf in preglednico. Spremembe moramo spremljati in dokumentirati v vseh opisih sistema, da ni neskladnosti med opisi. Za lažjo uporabo programa BONK je bil zamišljen grafični vmesnik ([6] in [7]) za neposredni, grafični vnos podatkov. Na njegovi podlagi je bil napisan vmesniški program, ki omogoča preprostejše in hitrejše delo pri analizi sistemov in preprostejšo in bolj usklajeno dokumentacijo. Usklajevanje podatkov pri spreminjanju strukture ali vrednosti parametrov ni več potrebno. 2 GRAFIČNI VMESNIK PROGRAMA BONK Grafični vmesnik omogoča preprostejšo in preglednejšo pripravo podatkov. Povezovalni graf sistema, brez vmesnih datotek, zadošča kot ustrezen opis sistema, iz katerega BONK določi diferencialne enačbe sistema in jih kasneje obdela. Ker je BONK dokaj zapleten in bi posegi vanj terjali preveč časa, - responses to selected input functions - root-locus plots - sensitivity of the system to the parameter values. If we have a nonlinear system and we are not able to get a suitable linear model for it, then studying the response of the system is the only possible analysis [5]. Before analyzing a system with BONK, we have to draw the bond-graph of the system. Elements and bonds have to be uniquely numbered. The data with the values for the elements are then written to the file. Outputs (effort and/or flow variables on selected bonds) are added. Inputs are given in advance as effort and/or flow sources in the model. Direction of power flow and causality on bonds can be given in advance or determined by BONK. Sometimes, in exceptional cases, corrections have to be made. Based on the data supplied, BONK determines the mathematical model of the system that is later on used as the basis for the selected analysis of the system. The analysis is often used as part of the system design, which is mostly done in an iterative way. An initial concept of the system is first made, it is analyzed, based on the results of the analysis an improvement is made, the system is analyzed again, improved upon, analyzed, improved upon and so on, until we find a good solution, or we exhaust available resources. It can happen that the desired solution does not exist or that there is no solution. BONK uses data written in a file. Data for the file are taken from the bond-graph. So we have at least two descriptions of the system. If changes are made to the system, everything has to be updated otherwise inconsistencies between descriptions are possible. To ease the use of the program BONK a graphical interface was conceived ([6] and [7]), for direct graphical input of the data. On this basis a program was written for simpler and quicker analysis and easier and consistent documentation. There is no need to update different sorts of documentation when the structure or values of the parameters are changed. 2 GRAPHICAL INTERFACE TO THE PROGRAM BONK Graphical interface offers an easier and more transparent preparation of data. The bond-graph, without any intermediate files, represents the input data, from which differential equations are determined by BONK and later worked on. As BONK is a complicated program, changing its | gfin=i(gurMini5nLn 99/8 stran 281 I^BSSIfTMlGC A. Hussu od grafičnega vmesnika zahtevamo: - da omogoča risanje povezovalnih grafov, določitev vrednosti elementov, funkcij, označitev, aktiviranja in vsega drugega, kar je potrebno pri opisu sistemov s povezovalnimi grafi in avtomatizira nekatere postopke, - da po končanem risanju pripravi ustrezno datoteko za uporabo programa BONK. Popoln opis nekega sistema s povezovalnim grafom zahteva označitev smeri pretoka moči, vzročnosti in morebitnih aktiviranj povezav. Te opise želimo imeti v povezovalnem grafu, določajo jih pa postopki znotraj programa BONK. Da odpravimo nujno potrebno povratno zvezo med grafičnim vmesnikom in programom BONK, so postopki za določevanje smeri pretokov moči in vzročnosti dodani tudi v sam grafični vmesnik. Aktivne povezave moramo vedno sami označiti. Oba programa, BONK in grafični vmesnik sta povezana v celoto prek datoteke s podatki, ki za uporabnika programa ni nujno potrebna. Je pa ohranjena kot različica besednega opisa problema oziroma povezovalnega grafa. Za ponazoritev uporabe grafičnega vmesnika je na sliki 1 prikazano okno, ki je na voljo uporabniku za risanje povezovalnega grafa. Narisani povezovalni graf je opis problema, ki ga obravnavamo v naslednji točki. Orodjarna obsega tri skupine gumbov, z leve strani so najprej gumbi za delo z datotekami, za shranjevanje slik, izpis, brisanje, sledijo elementi povezovalnih grafov, od napetostnega vira do povezave, zadnja skupina so gumbi za urejanje (spreminjanje) opisov elementov, premike in brisanje posameznih elementov. Običajna uporaba je taka, da nazadnje workings was deemed not appropriate. So for the graphical interface we have the following requirements: - to enable drawing of bond-graphs, inserting values, functions, assignments, activations and everything else which is necessary to describe a system with a bond-graph and to automate certain procedures, - when the bond-graph is completed to write the file with data for the program BONK. For a full description of a system with a bond-graph, power directions and causality on bonds have to be specified. These are determined by procedures inside BONK. But we want them also in bond-graphs. To make the feedback from BONK to the graphical interface unnecessary, routines for power directions and causality are also included in the graphical interface. Activation of bonds we always do ourselves. Both programs, BONK and the graphical interface, are connected through the data file, which for the user is not essential, however it is kept available as a textual version of the bond-graph. To illustrate the use of the graphical interface, Figure 1 represents the window a user has at his disposal for drawing bond-graphs. The drawn bond-graph is connected with the problem we will look into in the next section. The toolbar has three sets of buttons, the first set on the left is for working with files, storing and recalling them, storing bond-graphs as pictures, printing them, erasing them. Next follows the elements of bond-graphs, from sources to the bonds. The last set is for editing, moving, deleting and help. When drawing, bonds are drawn between Sl. 1. Okno z orodjarno za risanje povezovalnih grafov in povezovalni graf četrtinskega modela avtomobila za analizo vzmetenja Fig. 1. Window with toolbar for drawing bond graphs with a bond graph of a quarter car model for analysis of car s suspension 99-7/8 grin^sfcflMiscsD | ^BSfiTTMlliC | stran 282 Analiza dinami~nih sistemov - Analysis of Dynamic Systems vstavljamo povezave med že nameščene druge elemente povezovalnega grafa. Če neki element zbrišemo, hkrati zbrišemo tudi njegove povezave. 3 ANALIZA VZMETENJA AVTOMOBILA Vzmetenje je poleg vrste sistemov eden od pomembnejših dinamičnih sistemov v avtomobilu. Mora biti dovolj mehko, da je vožnja udobna in hkrati dovolj trdo, da ne pride do nihanj vozila in morebitnih udarcev vozila ob vozno površino, ali da bi kolesa izgubila stik z njo. Zahteve si pogosto nasprotujejo, iskanje najprimernejše rešitve je težavno. Izbiro si olajšamo z uporabo orodij, npr. programov za simuliranje vzmetenja. Program BONK je že takšno orodje. Problem vzmetenja ni preprost. Vozna površina običajno ni idealna ravnina, zato moramo upoštevati gibanje avtomobila v treh koordinatnih smereh in še vrtenje okoli treh osi. Da so problemi obvladljivi, jih poenostavljajo. Pri avtomobilu je tak preprost model četrtinski model avtomobila: - obravnavamo samo eno kolo in četrtino mase avtomobila, - dovoljeno gibanje je samo v navpični smeri, - obravnavano kolo je povezano s četrtinko avtomobila z vzmetjo in dušilnim elementom, - pnevmatiko ponazorimo z vzmetjo (boljši modeli dodajo še dušilni element). Na sliki 2 je skica obravnavanega sistema vzmetenja z označbami elementov. Vrednosti elementov smo povzeli po literaturi [8] in so: M = 267 kg m = 36,6 kg K = 18700 N/m k = 184000 N/m B = 1398 Ns/m already placed elements. If an element is deleted, bonds that are connected to the deleted element are also deleted. 3 ANALYSIS OF A CAR SUSPENSION Suspension is one of the most important dynamic systems on a car. It has to be soft enough so that the driving is comfortable, but it has to be stiff enough to prevent oscillations and contact with the driving surface or tires loosing contact with the driving surface. These requirements are often in contradiction, searching for a good solution is not easy. Progress is easier, if tools such as the program BONK are used. As has already been stated, dealing with suspension is not an easy problem. The driving surface is not ideal, so moving of a vehicle in 3D space and rotation around three axes must be taken into account. To make problems manageable, they are simplified. A simple model of a car’s suspension is a so-called quarter car model: - only one wheel is considered and 1/4 of the car’s mass, movements only in the vertical direction are allowed, the wheel is connected with 1/4 of the car through a spring and a damper, the tire is approximated with a spring (better models add a damper). A schematic model of the simple suspension is shown in Figure 2. The values of elements taken from [8] are: M = 267kg m = 36.6 kg K = 18700 N/m k = 184000 N/m B = 1398 Ns/m v2(t) K (vzmet, spring) B (dušilnik, damper) m: masa kolesa m: mass of the wheel v1(t) (pnevmatika tire) v0(t) Sl. 2. Četrtinski model vzmetenja avtomobila Fig. 2. Quarter car model of car s suspension stran 283 BCšD9 nrM]G€ k A. Hussu Po skici sistema in po postopkih, obravnavanih v [3], [4], [9] in [10], lahko narišemo povezovalni graf sistema vzmetenja. Vidimo ga na sliki 1. Označene so tudi smeri toka moči in vzročnosti. Izbran je en sam izhod (y1 na povezavi 4). Iz lege označbe izhoda glede na označbo povezave lahko sklepamo, ali nas zanima napetostna spremenljivka ali tokovna (ali obe). Napetostni izhodi so nad označbo povezav, tokovni pod. Kot izhod nas torej zanima pretočna spremenljivka na povezavi 4, to je hitrost mase M (=I1), v2(t). Kje so vhodi? V grafu niso posebej označeni, so pa vidni. To so viri. V našem primeru imamo en sam vir, tokovni, hitrost spreminjanja višine vozne površine, v0(t). Vsak element ima lahko označbo, kaj pomeni, ime, različni elementi istega tipa se razlikujejo v indeksih, ki jih lahko poljubno definiramo (v okviru tromestnih števil), pod označbo tipa in indeksa je vrednost elementa ali pa ime funkcije, če je element nelinearen. Funkcije so definirane v posebnem oknu. Ko je povezovalni graf narisan in opremljen s potrebnimi podatki (smer toka moči in vzročnost na povezavah ni treba označiti, to stori program, vendar nariše v graf, da lahko preverimo pravilnost označitve in spremenimo, če je potrebno), lahko aktiviramo program BONK da izdela matematični model, nakar lahko izberemo eno ali več vrst analize. Kaj bi lahko bilo zanimivo? Če je sistem linearen, naš poenostavljeni model je, nas najpogosteje zanimajo prenosne funkcije. Za ponazoritev uporabe programa si oglejmo frekvenčni potek oziroma Bodejev diagram prenosne funkcije: With the described mechanical model and by following the procedures in [3], [4], [9] and [10], a bond-graph of the suspension system is drawn, see Figure 1. Power directions and causality are given as well. Only one output is selected (y1 on bond 4). The position of the output symbol relative to the bond index tells whether the effort or flow variable is of interest (or both). The effort output variables are above the labels, the flow output variables below. So we are interested in the flow variable on bond 4, which is the velocity v2(t) of the mass M (=I1). Where are the inputs? They are not explicitly given but still visible. They are sources and in our case there is only one source, the source of flow, the velocity v0(t) of the driving surface in the vertical direction. Each element can be assigned a label, a name, elements of the same type differ in indices limited to numbers with at most three places. Under the type symbol is either the value of the element or the function name, if the element is nonlinear. Functions are defined in a separate window. With the bond-graph drawn, power directions and causality assigned (either by the user or preferably by the program, changes, if necessary, are possible), BONK can be activated. After the mathematical model is computed, desired analysis, either one or more is selected. What can be of interest? If the system is linear and this is the case with our simplified model, transfer functions are most often of interest. In order to illustrate we can have a look at the frequency response or Bode chart of the transfer function: G(s) V2(s) V0(s) G(s) = V2(s) V0(s) 10 dB ojačenje 0 dB OdB -20 dB OdB ¦40 dB OdB ¦60 dB ¦70 dB OdB \ v ^\ \ \ \ o fazni kot stopinie -30 phase angle degrees 100.00 CQ s-1 \ 1000.00 Sl. 3. Amplitudni in fazni potek prenosne funkcije G(s) Fig. 3. Amplitude and phase diagrams of the transfer function G(s) 99-7/8 grin^(afcflM]SCLD | ^BSfiTTMlliC | stran 284 Analiza dinami~nih sistemov - Analysis of Dynamic Systems na sliki 3, korene imenovalca prenosne funkcije v s ravnini na sliki 4 in na sliki 5 časovni odziv na koračno spremembo v0(t). Iz frekvenčnega diagrama ali iz lege korenov ali iz odziva lahko ugotovimo, da sistem nima dobrih lastnosti, da je premalo dušen. Potrebna bi bila poprava sistema, izbrati bi morali druge, primernejše vrednosti elementov, da bi dobili zadovoljive razmere. To bi lahko naredili, orodje je na voljo. Omejili smo se na eno samo prenosno funkcijo. Za podrobnejšo analizo bi morali upoštevati še druge, npr. stik pnevmatike s cestiščem, s kakšno silo pritiska kolo na cestišče. Koračna funkcija kot vhod je za določitev prehodnih pojavov zelo koristna, za boljšo oceno delovanja v stvarnih razmerah pa bi morali imeti tudi bolj stvarne vhodne funkcije. V [8], [9] in [11] do [14] lahko najdemo dodatne zglede za uporabo povezovalnih grafov na področju vozil in motorjev. in Figure 3, or at the poles of the transfer function in the s-plane in Figure 4 and the time response to a step change in v0(t) in Figure 5. Either from the frequency diagram or plot of the roots or from the time response a conclusion can be drawn that there is not enough damping in the system. A correction of the system is necessary with a more suitable set of parameters for the suspension system to show a better response. This correction can be achieved since the tool is available, however it will not be described here. In this example we have chosen only one transfer function, it is much better to take into account others as well, for example the contact of the tire with the driving surface. The step function is a very useful testing function, but for a good assesement of the car in real conditions, more real input functions are needed. In [8], [9] and [11] to [14] there are more examples of bond-graph usage in connection with vehicles and engines. Sl. 4 Fig. 4. Po . Poli pren les of the osne funkc ransfer fu ije G(s) in nction G(s) njihova le and their ga v s-rav location in nini s-plane v2(t) m/s nn 3.0 / S Sl. 5. Časovni odziv prenosne funkcije G(s) na koračno spremembo 1m/s ob času t = 0 s hitrosti v0(t) Fig. 5. Time response of the transfer function G(s) to the step change of 1m/s at t = 0 s of the velocity v0(t) ^vmskmsmm 99-7/8 stran 285 |^BSSITIMIGC A. Hussu 4 SKLEP Predstavljen je program BONK, ki z grafičnim vmesnikom za neposredni vnos povezovalnih grafov omogoča preprosto in hitro modeliranje in simuliranje linearnih in nelinearnih sistemov. Kot zgled in prikaz nekaterih zmogljivosti programa je bil obdelan preprost četrtinski model vzmetenja avtomobila. Delo na programskem paketu nadaljujemo, povečati želimo izbiro novih elementov v povezovalnih grafih in olajšati primerjave analiz. 4 CONCLUSION The program BONK and its graphical interface for entering bond-graphs directly as input data was presented. Through it, quick and simple modelling and simulation of linear and nonlinear systems is possible. As an example and to show some of the program’s capabilities a simple quarter car model of the car’s suspension was described. Work on the program is continuing, it is planned to include greater selection of bond-graph elements and easier comparison of analysis results. 5. LITERATURA 5. REFERENCES [I] Doherty C.,Uslander T, Plug-and-play software hones car and plane manufacture, IEEE Spectrum, Vol.35,No.10,Oct 1998,39-42 [2] Jurejevčič T,Fajdiga M., Applicability of Bond graph method to dynamic analysis of vehicle power transmissions, Ninth World Congress on the Theory of machines and Mechanisms, IFToMM’95, Proc.Vol.4, Trends in machines and mechanisms design, pp.1471-1474, Edizioni Unicopli, Milano, 29.8-1.9.1995 [3] Hussu A., Modeliranje sistemov in povezovalni grafi, Strojniški vestnik, 32,1-3,Mar 1986, 1-8 [4] Hussu A, Modeliranje s povezovalnimi grafi, Zbornik prve A, 28-30 sep.1992, Portorož, Slovenija Uredila B.Zajc, F.Solina Ljubljana, Slov.sekcija IEEE,1992, 173-176 [5] Hussu A., Povezovalni grafi in nelinearnosti, Zbornik tretje elektrotehniške in računalniške konference ERK’94, Zvezek A, 26-28 sep.1994, Portorož, Slovenija. Uredila B.Zajc, FSolina. Ljubljana, Slov.sekcija IEEE,1994, 233-236 [6] Hussu A., Grafični vmesnik za modeliranje s povezovalnimi grafi, Zbornik pete elektrotehniške in računalniške konference ERK’96, Zvezek B, 19-21 sep.1996, Portorož, Slovenija. Uredila B.Zajc, FSolina. Ljubljana, Slov.sekcija IEEE,1996, 99-102 [7] Hussu A., Entering Bond-graphs as graphs, Proc.EUROSIM’98, (Ed.KJuslin) Federation of European Simulation Societies,14-15.apr.1998, Helsinki, str. 277-279 [8] Redfield R.C.,Karnopp D.C., Performance sensitivity of an actively damped vehicle suspension to feedback variation, J.of Dynamic Sys.Mea.and Control, Vol.111,No1,mar.1989,51-60 [9] Karnopp,D.C.,Margolis,DL.,Rosenberg,R.C, System dynamics: A unified approach, Wiley, 1990 [10] Thoma,JU.,Simulation by Bondgraphs, Springer-Verlag,1990 [II] Cho D.,Hedrick J.K., Automotive powertrain modeling for control, J.of Dynamic Sys. Meas.and Control, Vol.111, No.4,Dec.1989, 586-576 [12] Karmel A.M., Design and analysis of a trasmission hydraulic system for an engine-flywheell hybrid-vehicle, J.of Dynamic Sys. Meas.and Control, Vol.112,No.2,Jun.1990,253-260 [13] Yang W.C.,Glidewell J.M.,Tobler W.E.,Chui G.K., Dynamic modelling and analysis of automotive multi-port electronic fuel delivery system, J.of Dynamic Sys. Meas.and Control, Vol.113,Mar.1991,143-151 [14] Rault A., Mechatronics and Bond graphs, 101-110 Karnopp D., A simple bond graph vehicle handling model including roll effects, 89-100 Bond Graphs for Engineers, (Breeedveld PC, Dauphin-Tanguy G, ed), North-Holland, Amsterdam, 1992 Avtorjev naslov: profdr. Alojz Hussu Fakulteta za strojništvo Univerze v Ljubljani Aškerčeva 6 1000 Ljubljana Author’s Adress: Prof.dr. Alojz Hussu Faculty of Mechanical Engineering University of Ljubljana Aškerčeva 6 1000 Ljubljana, Slovenia Prejeto: Received: 11.11.1998 Sprejeto: Accepted: 15.9.1999 8 SšnnstsfcflM]! ma stran 286 © Strojni{ki vestnik 45(1999)7/8,287-293 © Journal of Mechanical Engineering 45(1999)7/8,287-293 ISSN 0039-2480 ISSN 0039-2480 UDK 648.23:534.83 UDC 648.23:534.83 Strokovni ~lanek (1.04) Speciality paper (1.04) Zmanj{anje hrupa pralnih strojev z uporabo du{ilnih materialov The Reduction of Washing Machine Noise by the Use of Muffling Materials Nikola Hole~ek V članku je najprej prikazan pregled modeliranja vibracij pralnikov Gorenje. Sledi prikaz eksperimentalne metode določanja zvočne moči in potek zniževanja hrupa pralnika z uporabo dusilnih materialov. © 1999 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: stroji pralni, modeliranje vibracij, hrupnost strojev, materiali dušilni) This paper begins with an overview of the modelling of the dynamical behaviour of Gorenje washing machines. Subsequently there is a presentation of the experimental method of defining sound intensity and the procedure for the reduction of washing machine noise by the use of muffling materials. © 1999 Journal of Mechanical Engineering. All rights reserved. (Keywords: washing machine, vibration modells, machine noise, muffling materials) 0 UVOD Razvoj velikih gospodinjskih aparatov se v zadnjih letih vedno bolj usmerja k zmanjševanju hrupnosti strojev. Od leta 1996 je v veljavi priporočilo evropskega združenja 92/ 75/EWG, ki predpisuje razglasitev emisijske ravni hrupa pralnih strojev in informiranje porabnikov z ustrezno nalepko, ki vsebuje podatek o ravni zvočne moči pri pranju in ožemanju. Svetovni trg terja mirnejše, tišje in varčnejše pralne stroje z večjo vrtilno frekvenco bobna pri ožemanju. Dinamične obremenitve se večajo s kvadratom vrtilne frekvence, kar se kaže v manjši mirnosti teka pralnika in v višji ravni hrupnosti. Sedanja priporočila za raven zvočne moči predpisujejo celotno raven manjšo od 65 dB pri ožemanju, ne glede na vrtilno frekvenco ožemanja. Metode za merjenje zvočne moči so standardizirane (ISO 3745), prav tako je predpisan način delovanja naprave, ki jo merimo (IEC 704-2-4 za pralne stroje). Poudariti je treba, da se mencanje in centrifuga glede problematike zmanjšanja hrupnosti povsem izključujeta. Medtem ko na 0 INTRODUCTION In recent years one of the trends in the development of large household appliances is the reduction of noise. In 1996 the Directive of European Community 92/75/EWG came into force, according to which the noise levels of individual washing machines have to be declared, and customers have to be informed by means of an appropriate label containing information about the level of sound power during washing as well as during spinning. The world market demands quieter and more economical washing machines with higher rotation speed of the drum during spinning. Dynamic loading is increased by the square of the rotation speed which can cause vibration of the washing machine and higher noise levels. The present recommendations for the level of sound power define the total level to be lower than 65 dB during spinning, regardless of the rotation speed of the machine. The methods for measuring the sound power are standardised (ISO 3745), as well as the way in which the appliance is operated, which for washing machines is IEC 704-2-4. It should be pointed out that tumbling and spinning are, as far as the problem of noise reduction is concerned, mutually exclusive. While the gfin^OtJJIMISCSD 99-7/8 stran 287 |^BSSITIMIGC N. Hole~ek hrupnost pri mencanju vpliva predvsem elektromotor, vpliva pri centrifugi, zaradi problemov z neuravnoteženostjo perila, na hrupnost konstrukcija pralnega stroja in elastični deli, ki blažijo vibracije in udarce. V prispevku je v nadaljevanju najprej na kratko prikazan potek modeliranja vibracij pralne skupine v domačem strokovnem okolju. 1 PREGLED MODELIRANJA VIBRACIJ Modeliranje dinamičnega obnašanja pralnika ter predvsem njegove pralne skupine se je odvijalo v okviru Laboratorija za dinamiko strojev in konstrukcij Fakultete za strojništvo v Ljubljani. Na začetku je bil postavljen osnovni ravninski model pralne skupine s tremi prostostnimi stopnjami. Pri preučevanju zagona smo uporabljali izmerjeni časovni potek vrtilne frekvence bobna pri ožemanju. V nadaljevanju smo preučevali ujetje sistema v resonančnem področju ter vpliv sile teže rotorja na dinamično obnašanje pralnika. Sledila je razširitev modela z vključitvijo gibanja okrova pralnika, kar je pomenilo upoštevanje sedem prostostnih stopenj. Izkazalo se je, da so prednosti tako razširjenega modela premajhne glede na obsežnost dela. Nato je sledila poglobitev teoretičnega postopka modeliranja z uporabo modernih metod iz teorije nelinearnih dinamskih sistemov. Obravnavo dinamičnega obnašanja pralne skupine smo razširili na fazni prostor, tako na pravi fazni prostor na podlagi integracije gibalnih diferencialnih enačb kakor tudi na rekonstruirani na podlagi meritve ene same spremenljivke. Dobili smo dobro ujemanje pri oceni korelacijske dimenzije med modelom in preskusom. y electromotor influences the noise during tumbling, the design of the washing machine and the elastic parts, which reduce vibrations and strokes, due to problems with unbalanced laundry, influence the noise level during spinning. In this paper, first of all, a short overview describing the modelling of the dynamical behaviour of the washing machine in Slovenian institutions is given. 1 AN OVERVIEW OF MODELLING VIBRATIONS The modelling of the vibrational behaviour of the washing machine was conducted in the Laboratory for Dynamics of Machines and Structures, Faculty of Mechanical Engineering in Ljubljana. Initially, the basic planar model that consisted of three degrees of freedom was set up. Startup behaviour was studied by employing the measured drum angular velocity. The next step introduced the study of spin-up through resonance including the influence of the drum weight. The basic planar model was also extended into a system of two planar rigid bodies with seven degrees of freedom. However, the benefit from such an extension was not sufficient when compared to the increased level of complexity. The next important step in theoretical modelling was orientated towards modern methods from the theory of non-linear dynamical systems. The description of the dynamical behaviour of the washing complex was expanded into the phase space of the system. The real phase space was based on the integration of the governing differential equations of motion while the reconstructed one was based on a single measured time history, employing the embedding theorem. In the estimation of the correlation dimension, good agreement between the model and the experiment was found. Sl. 1. Model pralne skupine Fig. 1. Model of washing group 99-7/8 grin^(afcflM]SCLD I ^BSfiTTMlliC | stran 288 Zmanj{anje hrupa pralnih strojev - The Reduction of Washing Machine Noise V zadnjem času je bila izvedena tudi bispektralna analiza dinamičnih odzivov pralne skupine pri ožemanju. Vrednosti kvadratične bikoherence so dokazale kvadratično sklapljanje faz med posameznimi frekvenčnimi komponentami dinamike pralne skupine ter s tem povezano nelinearnostjo sistema. Glavnina povzetega dela pri modeliranju dinamike pralnika je opisana v [1] do [3], sam model pa je prikazan na sliki 1. Ne glede na obseg modeliranja vibracij ter na njihov nadzor pri realnem pralniku se vibracijam ne da izogniti. Zato pri praktičnem zmanjševanju hrupnosti pralnika uporabimo tudi dušenje strukturnega hrupa z dodajanjem izolacijskih materialov. 2 AKUSTIČNE MERITVE Pri meritvah smo uporabljali metodo merjenja zvočne moči. Zvočna moč da informacijo o zvoku tako po smeri kakor po vrednosti: Just recently, the bispectral analysis of the vibrational responses of the washing complex at spinning was performed. The values of bicoherence squared showed some quadratic phase coupling between spectral components and thus confirmed the non-linearity of the system. The major part of the described theoretical modelling is shown in [1] to [3]. The model itself is shown in Fig. 1. Irrespective of the extent of vibrational modelling as well as their control on a real washing machine, the vibrations cannot be avoided. Consequently, the noise as a result of the remaining vibrations must be tackled also in a passive way. In the following, the use of insulating materials in order to reduce structure-born noise is described. 2 ACOUSTIC MEASUREMENTS The method of measuring sound intensity was used. Sound intensity provides information about the sound direction as well as its value: I WF A A v = p- v (1). V nasprotju z meritvami zvočnega tlaka (merimo ga neposredno z mikrofoni), zvočno moč določamo v dejanskem času z merjenjem zvočnega tlaka in hitrosti delcev. Odjemnik, ki hkrati meri zvočni tlak in hitrost delcev, je sonda za jakost. Sonda ima dva nasprotno si ležeča mikrofona za zvočni tlak. Mikrofona sta na razdalji Dr (sl. 2) [4]. Unlike noise pressure measurements (it is measured directly by microphones), noise intensity is determined in real time by measuring the sound pressure and the speed of the particles. The receiver, which simultaneously measures sound pressure and the speed of the particles, is the probe for intensity. The probe has two microphones for sound pressure which are placed opposite each other. The distance between the microphones is Dr (Fig.2) [4]. Ar PlTt) Sl. 2. Sonda za merjenje zvočne jakosti Fig. 2. Probe for measuring sound intensity 2.1 Merjenje hitrosti delcev na podlagi razlike 2.1 Measuring the speed of particles on the basis tlakov of pressure difference Ce je povprečni zvočni tlak p = vzdolž merilne sonde [5] do [7]: je jakost p1+p2 2 , In=p-vn = p1 + p2 If the average sound pressure is p = p1+p2 , the intensity along the measuring probe is [5] to [7]: p1+p2 1 p1 -p2 Dr 2pDr 2r0 \(p1-p2)dt dt (2). stran 289 | \^B©TTIMD[rS N. Hole~ek 2.2 Sonda za merjenje zvočne jakosti Sonda ima dva nasprotno si ležeča mikrofona, ki sta fazno prilagojena. Med mikrofonoma je vgrajen ustrezen vmesnik, glede na frekvenčno območje, ki ga merimo. Za področje 50 Hz do 6300 Hz se uporablja 0,5 palčni mikrofon, za višje frekvence so bolj primerni 0,25 palčni mikrofoni. Iz merilne sonde vodimo signal na analizator zvočne jakosti. Pomembno vlogo za natančnost meritev ima fazna prilagojenost mikrofonov in ustrezni vmesnik [6]. 2.2 Probe for measuring sound intensity The probe has two microphones placed opposite each other and phase adjusted. There is an appropriate interface built between the microphones, according to the frequency range which is being measured. For the range from 50 Hz to 6300 Hz a 0.5 inch microphone is used, whereas 0.25 inch microphones are more suitable for higher frequencies. The signal is fed from the measuring probe into the sound intensity analyser. Phase adjustment of the microphones and an appropriate interface play an important role in precise measurements [6]. tlak jakost t & ADP ADC 1/3-octave digital filters Ar *t> 1/3-oktavni digitalni filter I ADP ADC 1/3-octave digital filters eksponentno ali linearno povprečenje exponential or linear averaging Sl. 3. Shema izračuna zvočne jakosti Fig. 3. Scheme of calculation of sound intensity 3 ZMANJŠANJE HRUPA Hrupnost pralnega stroja je odvisna od: konstrukcije, elektromotorja, gumijastih delov, ki blažijo vibracije, ter od zvočne izolacije. Vsak od navedenih delov ima svoje lastnosti, ki prispevajo k zmanjšanju ali povečanju hrupnosti. Čeprav je zmanjševanje hrupa na poti njegovega širjenja tehnično najbolj učinkovito (uporaba dušilnih materialov ali materialov, ki dušijo prenašanje vibracij - kompozitna pločevina), smo svoja prizadevanja usmerjali tudi na zmanj sevanje hrupa na izvoru, ker je to z energetskega in ekološkega vidika najbolj upravičeno. Po deležu seveda k zmanjšanju hrupnosti največ prispeva izolacija. Zato smo ji tudi posvetili največraziskav. Ker smo si zadali tudi cenovno omejitev, je bilo potrebno s čim manj izolacije in s čim cenejšo izolacijo doseči našo ciljno vrednost. Opravljena je bila množica meritev v polgluhi komori laboratorija za akustiko in vibracije. Z merjenjem zvočne moči po vseh petih sevalnih površinah smo določili mesta največjih sevanj in se je temu primerno oblikovala tudi izolacija. Kot izolacijske materiale smo preskušali: - kompozitno pločevino, - poliuretansko peno (gladko in piramidno), - cefrana odpadna tekstilna vlakna bombaža, - težke mase. 3 NOISE REDUCTION The noise of a washing machine depends on: the design of the washing machine, the electromotor, rubber parts for absorbing vibrations, and sound insulation of the washing machine itself. Each of the mentioned parts has its own characteristics which contribute to the increase or reduction in noise. Although noise reduction during its transfer is technically the most effective (use of muffling materials or materials which muffle transfer of vibrations -composite sheet metal), our efforts have been directed also to the reduction of noise at its origin, which is the most justified from the energy and ecology point of view. Insulation is certainly the most important method for noise reduction and this is why most research has been dedicated to it. As we also took into account cost limitations it was necessary to reach our target value with the cheapest insulation possible. Numerous measurements were done in the half deaf chamber of the laboratory for acoustics and vibrations. By measuring sound intensity along all five radiation surfaces the places of the highest radiation were localised and insulation was created according to this. We have tested the following as potential insulation materials: - composite sheet metal, - polyurethane foam (smooth and pyramid), - frayed waste textile cotton fibres, - heavy masses. 8 Lšfrrr°yowj[ftj]pjI|s[]^[] | |^[MlfirTMlGC | stran 290 Zmanj{anje hrupa pralnih strojev - The Reduction of Washing Machine Noise magnituda jakosti v dB intensity mag. in dB frekv./freq. 100-10.0kHz nad/above 64 63-64 62 -63 6] -62 60-61 zgoraj/up ? u r 59 - 60 58-59 57 - 5S 56-57 55-56 54-55 53-54 52 - S3 51-52 50-51 levo/left spredaj/front pod/below 50 Sl. 4. Ozemanje - delno izoliran stroj - zorni kot spredaj-levo Fig. 4. Spinning - partly insulated machine - angle of sight front-left zgoraj/up magnituda jakosti v dB .. • L. jj^ ~f *-..... intensity mag. in dB •-¦....;¦¦ frekv./freq. 100-10.0kHz J < ^^ i-V^S^C "";::¦- ¦ nad/above 64 ^^ ¦ «3-64 caI | 62-63 .tin' r&J j 61-62 ^----' T5 5 59-60 levo/left 1'"'' (P ^_-- 1 ?8 - 59 ] 57-58 -*fr r^ ,^-- | 56-57 ^^_ 1 55 - 56 ^^_ | 54 - 55 -dB | 53 - 54 ifir^" j 52 - 53 u- "T | 51-52 " :;^^ 1^^^ ¦ j 50-51 C? ¦ pod/below 50 spredaj/front Sl. 5. Ozemanje - v celoti izoliran stroj - zorni kot spredaj-levo Fig. 5. Spinning - totally insulated machine - angle of sight front-left Primerjava med meritvijo delno in v celoti izoliranega stroja tako pri mencanju kakor ožemanju kaže, da nam je z izolacijo uspelo znižati hrup na vseh kritičnih mestih. Dodatna izolacija BORGERS (cefrana odpadna tekstilna vlakna bombaža) ima veliko večji učinek na zmanjšanje zvočne moči stroja pri mencanju - za 7,7 dB - kakor pri ožemanju - za 2,5 dB. Pri ožemanju je bistveni element dobro izolirana prednja stena. Posebno pozornost velja posvetiti tudi robovom na dnu stroja. Vse stranice na stroju so lahko znaten vir hrupa, zato je pomembno, da je izolirana celotna naprava. To velja tudi za zadnjo steno, katera sicer ni izpostavljena velikim vibracijam kakor sprednja ali bočne stene, vendar lahko kljub temu oddaja veliko zvočno moč. Pri meritvi zvočne moči delno izoliranega stroja je bila zadnja stena najmanj izolirana od vseh (samo spodnji rob ob pokrovu). Primerjava po zvočni moči med stranicami je pri ožemanju pokazala, da je zadnja stena najglasnejša. The comparison between measurements of the partly and totally insulated machine in tumbling as well as during spinning show that we have succeeded in reducing the noise at all critical places. Additional insulation BORGERS has a much larger effect on the reduction of sound power of the appliance during tumbling - by 7.7 dB - than during spinning - by 2.5 dB. It seems that an essential element during spinning is a good insulation of the front wall. Special attention should be paid to the edges at the bottom of the appliance. All the sides of the appliance may be significant in terms of the origin of noise, so it is important that the whole appliance is insulated. This is true also for the back wall, which is not subject to such large vibrations as the front and side walls, but it can emit a high sound power. During measurements of the sound intensity of a partly insulated appliance the least insulated was the back wall (only the bottom edge near the cover). Comparison of the sound power from the sides during spinning has shown that the back wall is the loudest. stran 291 BCšD9 nnME€ N. Hole~ek A-vrednoteno/A-weighted frekv./freq.: 100-10,0k Hz zadaj/back spredaj/front desno/right levo/left zgoraj/up z 63,3 dB+ 60,3 dB+ 59.2 dB+ 58,9 dB+ 55.3 dB+ zadaj/back spredaj/front desno/right levo/left zgoraj/up D 59,2 dB+ 58.7 dB+ 56,2 dB+ 55,9 dB+ 51.8 dB+ Sl. 6. Ožemanje - delno izoliran stroj: zvočna moč po posameznih stranicah Fig. 6. Spinning - partly insulated appliance: sound power by individual sides Sl. 7. Ožemanje - v celoti izoliran stroj: zvočna moč po posameznih stranicah Fig. 7. Spinning -totally insulated appliance: sound power by individual sides Razpredelnica 1. Zvočna moč naprave po posameznih spremembah Table 1. Sound power of the appliance by individual changes izolacija insulation zvočna moč pri mencanju v dB(A) sound power in tumbling in dB(A) zvočna moč pri ožemanju v dB(A) sound power in spinning in dB(A) BORGERS debeline 15mm: delovna plošča in dno BORGES 15 mm thick: working panel and bottom 57,3 70,3 dodatno: izolacija na levi in desni stranici povišana do 600mm additional: insulation on the left and the right side raised to 600 mm 52,6 69,9 dodatno: leva in desna stran izolirana v celoti na dnu dodatno izolirani robovi additional: left and right side insulated in total and at the bottom additionally insulated edges 49,6 67,8 4 SKLEP Hrupnosti pralnikov se samo z nadzorom vibracij ne da znižati do meje, ki jo dandanes terjajo zahtevni svetovni trgi. V članku smo najprej na kratko podali pregled teoretičnega modeliranja vibracij. Pri praktičnem zmanjševanju hrupnosti smo pred spremembo in po njej naredili podrobnejšo akustično analizo pralnika. To omogoča metoda meritve zvočne moči. Zvočna moč (aktivna komponenta gostote energijskega toka zvočnega valovanja) je vektor in z njim lahko dobimo informacijo o velikosti in smeri širjenja zvočne energije [7]. V nadaljevanju smo z izolacijo zniževali hrup na kritičnih mestih in smo se priporočenim vrednostim povsem približali. Tako se lahko pohvalimo, da so naši pralni stroji SUPER SILENT med najtišjimi na tržišču. 4 CONCLUSION Vibration control alone is not sufficient to reduce the noise of washing machines to the level that is required by the demanding world markets of today. In this paper first a short overview of the theoretical vibrational modelling was given. During practical noise reduction a detailed acoustic analysis of the washing machine was conducted before and after the change, which is enabled by the method of measuring sound intensity. Sound intensity (active component of the density of the energy flow of the sound wave) is a vector delivering information about the value and direction of sound energy spreading [7]. Subsequently noise at critical points was being reduced by insulation and we reached the recommended values. Today we are proud to claim that our SUPER SILENT washing machines are among the quietest on the market. 8 &nnBjfokJ][p)l]Olf|i[gO | | ^SSfiFlMlGC | stran 292 Zmanj{anje hrupa pralnih strojev - The Reduction of Washing Machine Noise 5 SEZNAM SPREMENLJIVK 5 NOMENCLATURE zvočni tlak zvočna moč moč sila gostota hitrost p I W F Pa, dB W/m2, dB W, d B N kg/m3 m/s Zahvala sound pressure sound intensity power force density velocity Acknowledgement Avtor se zahvaljuje doc. dr. Mihu Boltežarju iz Laboratorija za dinamiko strojev in konstrukcij Fakultete za strojništvo Univerze v Ljubljani za pomoč pri pisanju članka. Thanks are due to Doc.Dr. Miha Boltežar from Laboratory for Dynamics of Machines and Structures, Faculty of Mechanical Engineering, University of Ljubljana for the help in writing this paper. 6 LITERATURA 6 REFERENCE [1] Boltežar M., N. Jakšič, A. Kuhelj (1998) Quantitative phase space analysis of the nonlinear planar oscillatory system. Zeitschrift fur Angewandte Mathematik und Mechanik, 78(S1), 287-288. [2] Jakšič N, Boltežar, M., Simonovski, I., A. Kuhelj (1999) Dynamical behaviour of the planar non-linear mechanical system - Part I: Theoretical Modelling. Journal of Sound and Vibration. (sprejeto v objavo/ accepted for publication). [3] Boltežar, M., Jakšič, N, Simonovski, I., A. Kuhelj (1999) Dynamical behaviour of the planar non-linear mechanical system - Part II: Experiment. Journal of Sound and Vibration. (sprejeto v objavo/accepted for publication). [4] Fahy, Frank J. (1989) Sound Intensity, Elsevier Science Publisher Ltd., London. [5] Beranek, L. (1988) Noise and Vibration Control, Institute of noise control engineering, Washington. [6] Sound Power measurements (1992) Application Note 1230 Hewlett Packard. [7] Holeček, N. (1992) Identifikacija virov hrupa in določanje zvočne moči, seminar podiplomskega študija, Fakulteta za strojništvo, Ljubljana. Naslov avtorja: Nikola Holeček Gorenje d.d. Laboratorij za akustiko 3503 Velenje Author’s Address: Nikola Holeček Gorenje Ltd. Laboratory for Acoustics 3503 Velenje, Slovenia Prejeto: Received: 11.1.1999 Sprejeto: Accepted: 15.9.1999 stran 293 BCšD9 nnME€ r v © Strojni{ki vestnik 45(1999)7/8,294-300 © Journal of Mechanical Engineering 45(1999)7/8,294-300 ISSN 0039-2480 ISSN 0039-2480 UDK 621.791:621.791.04 UDC 621.791:621.791.04 Strokovni ~lanek (1.04) Speciality paper (1.04) Parametri optimizacije varjenja za novo str`ensko `ico tipa RD 971 Optimisation of Welding Parameters for the New Tubular Cored Electrode Type RD 971 Jozef Me{ko - Viliam Le`dík - Milo{ Mi~ian Namen članka je pokazati možnosti optimiranja varilnih parametrov za novo stržensko žico tipa RD 971, ki je izvedena z matematično - statističnim vrednotenjem varilnega toka in napetosti. Vsi preskusi so bili narejeni z novim dodajnim materialom - s stržensko žico tipa RD 971, ki je bila razvita na Tehnološki fakulteti, Univerze v Žilni, v sodelovanju z Institutom za varjenje v Bratislavi © 1999 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: žice strženske, optimiranje varjenja, stabilnost procesov, kriteriji stabilnosti) The aim of this paper is to show how the parameters can be optimised using a mathematical - statistical evaluation of the time dependence of the electric current and voltage with the new tubular cored wire type RD 971. This contribution demonstrates the abilities of the new filler material - tubular cored wire type RD 971, that was developed at the Department of Technological Engineering, University ofŽilina in co-operation with VUZ - Bratislava. © 1999 Journal of Mechanical Engineering. All rights reserved. (Keywords: cored wire electrodes, optimum welding conditions, stability of process, stability criterion) 0 UVOD Podobno kakor pri drugih postopkih obločnega varjenja, se, zaradi brizganja, pojavljajo velike izgube dodajnega materiala tudi pri varjenju v zaščitnih atmosferah. Ta način varjenja je zahtevnejši glede vzdrževanja procesa v okviru pogojev optimalne stabilnosti. Vrednotenje stabilnosti varilnega obloka je zasnovano na optimizaciji delovnih področij. Optimalna delovna področja je mogoče ugotoviti pri različnih načinih prehajanja dodajnega materiala. Za optimalna delovna področja je značilno, da ni brizganja in da je zvarni spoj kakovosten. Delovna področja optimalnih varilnih parametrov so vezana na določen vir varilnega toka, določen dodajni material in zaščitni plin ([1] in [7]). 1 ANALIZA KRATKOSTIČNEGA PREHAJANJA MATERIALA Za stabilnost varilnih procesov velja običajno pravilo, da mora biti hitrost odtaljevanja enaka hitrosti dovajanja dodajnega materiala. Če je hitrost dovajanja dodajnega materiala večja od hitrosti odtaljevanja, potem se kapljice potapljajo v zvarno kopel. Ob pojavu kratkega stika med elektrodo in talino se začne zmanjševati hitrost odtaljevanja in pride do znižanja varilne napetosti [4]. 0 INTRODUCTION The arc welding method with shielding gas has large losses due to splashing, similar to other arc welding methods. The arc welding with shielding gas is more appropriate to keep the weld process in the optimum area of stability. The evaluation of stability arcing is based on optimum working areas. We can find optimum working areas in different weld metal transmittal modes. The welding areas chosen from the working process are characterised by minimum splashing and weld joint quality. The optimum parameters are determined from working areas, more specifically the welding source of current, filler metal and shielding gas ([1] and [7]). 1 THE SHORT CIRCUIT PROCESS ANALYSIS It is a common rule that for a stable welding processes, the wire melting speed must be balanced with the speed of the feed in the base material direction. If the electrode feed speed is higher than the melting speed, then the melt metal drop at the end of electrode is in the welding bath during the short circuit. After the short circuit process starts (the short circuit process is realized in large-scale welding parameter areas), lower melting speeds or lowering of the values of the voltage occur [4]. 99-7/8 grin^(afcflM]SCLD I ^BSfiTTMlliC | stran 294 Parametri optimizacije varjenja - Optimisation of Welding Parameters Proces kratkostičnega prehajanja se lahko razdeli v kratkostično fazo x in fazo gorenja obloka x (ki včasih izostane - faza izostajanja x). Za interval kratkega stika je značilno znižanje varilne napetosti na vsega nekaj voltov. Čas znižane varilne napetosti je sorazmerno odvisen od velikosti nastale kapljice. V času trajanja kratkega stika z uporovnim segrevanjem prostega konca elektrode se napetost postopno zvišuje. Tok ne more slediti spremembi napetosti kratkega stika, ker je odvisen od časovne konstante vira in od induktivnosti varilnega tokokroga. Ob pojavu kratkega stika se prične tok eksponentno zvečevati in doseže največjo vrednost na koncu tega obdobja. Pojav največje jakosti kratkostičnega toka povzroči, da pride ob ponovni vzpostavitvi obloka do brizganja taline. Ob vžigu obloka dosežena jakost kratkostičnega toka ni odvisna samo od njegovega zvečevanja, pomembno je odvisna tudi od dinamičnih lastnosti vira toka in obenem od največje vrednosti varilnega toka. Po prekinitvi kratkega stika se jakost toka zmanjša na srednjo vrednost varilnega toka. Ob prekinitvi kratkega stika se pojavi tudi kratkotrajno povišanje varilne napetosti ([5] in [6]). Potek kratkostičnega obdobja s fazami prehajanja materiala prikazuje slika 1. The short circuit process can by divided into the short circuit phase xs , and the arcing phase xo (sometimes the phase absence xa). The short circuit section is defined as the decrease of the voltage to a value of a few volts. The time of the voltage decrease during the short circuit is proportional to the size of the drop causing the short circuit. During the short circuit the voltage slowly rises up to a value equal to the heating-up resistance . The current can not follow the course of voltage because it is influenced by the time welding constant of the source and the circuit. As the short circuit begins, the current starts to rise exponentially and at the end of the short circuit it reaches its maximum intensity. These phenomena cause splashing of the metal during the short circuit phase, where not only the ratio of current increase is of importance (it is a function of the welding source dynamic properties), but also the maximum value of the welding current. At the end of the short circuit process the welding current decreases to the average value. The phenomenon causes the short-time rising of the voltage after the finish of the short circuit process ([5] and [6]). The short circuit phase of metal transfer is demonstrated in Fig. 1. 1. 2. 3. 4. 5. 6. I, A področje zvečevanja kratkostičnega toka current increase section področje zmanjševanja jakosti toka current ' sectkase n ; področje varilnega toka current constant section U, V čas trajanja kratkega stika short circut phase ^ čas gorenja obloka arcing phase t, s Sl. 1. Shematski prikaz varilnega kroga s potekom jakosti toka in napetosti ter fazami prehajanja materiala med kratkim stikom in gorenjem obloka Fig. 1. A schematic diagram showing the cycle of current and voltage continuance with metal transfer at the short circuit phase and arcing phase stran 295 I^HsSTTlMlDC J. Me{ko - V. Le`dík - M. Mi~ian 1.1 Kriteriji stabilnosti pri kratkostičnem 1.1 The stability criterion for the short circuit varilnem procesu welding process Pogosto se presoja stabilnost varilnega procesa samo na temelju vidnih in zvočnih pojavov v obloku in v skladu z obliko zvara. Za to metodo ocenjevanja optimalnih nastavitev so potrebne bogate praktične izkušnje in strokovna kritičnost ocenjevalca. Zato je bilo razvitih več načinov statističnega vrednotenja varilnih parametrov, ki se spreminjajo okoli srednje vrednosti, npr.: varilne napetosti ali varilnega toka [1]. Podrobno matematično-statistično vrednotenje toka in napetosti omogoča, da za različne varilne razmere te vrednosti ponazorimo s histogrami. Ti histogrami ponazarjajo relativno pojavljanje v času, ko se vrednosti toka in napetosti pojavljajo na različnih ravneh ([1] in [2]). Za vrednotenje stabilnosti varilnega procesa se lahko uporabijo različne metode in kriteriji. Pogosto se izkaže, da izbor kriterija izhaja iz relativne širine histograma. Eden od kriterijev stabilnosti je ocenjen s sekundarnimi parametri; zlasti s časom gorenja obloka x in časom kratkega stika x. Kriteriji pomenijo za te parametre izačunana odstopanja S. Varilni proces z majhno vrednostjo S je stabilen. Kratkostični proces se kaže kot niz povezanih pojavov kratkih stikov obloka in pekinitev obloka. Kriterij stabilnosti kratkostičnega varilnega procesa je mogoče definirati z indeksom stabilnosti W, ki je sestavljen iz vrste časovnih variacijskih koeficientov posameznih faz procesa: The stability of the welding process can often be judged only with the help of visual and acoustic demonstration of the arc and according to the form of the weld. The present method of evaluation of the optimum settings requires plenty of practical experience. As a result several workers have used statistical evaluation of the values of welding parameter decomposition around their average values, for example voltage or current [1]. A detailed mathematical - statistical evaluation of the variation of current and voltage allows the creation of histograms of decomposition of these quantities under different welding conditions. These histograms demonstrate the percentile distribution of now, these quantities are affected with time ([1] and [2]). Different methods and criteria can be used to asses the stability of the welding process. The choice of criterion often comes from investigating the relative width of the histogram. One important assessment of stability requires is evaluation of the secondary parameters. In particular the parameter types: time arcing x0 and time short circuit xs. The criterion is position at the calculations decisive aberration S these parameters. The process with a low value of S is shown as stable. The short circuit process is shown as a series of casual actions, short circuits of arcing and absences. The stability criteria short circuit welding process can be defined by the index of stability W, which are constituted from the summary time variations coefficient of individual phases: s s Vi - koeficient variiranja, izračunan iz časa trajanja posamezne faze, o - faza gorenja obloka, s - faza kratkega stika, a - faza prekinitve, ti- relativni delež posamezne faze v varilnem procesu: W = ts Vs + toVo + taVa % aa (1), Vi - is the variation coefficient for the times of existence for individual phases, o - phase of arc, s - phase of short circuit, a - phase of interruption, ti- phase relative share in the welding process: ti = tc (2), kjer je: YjXi - vsota dejansko končanih faz [s], tc - celotni čas opazovanja varilnega procesa [s]. Variacijski koeficient je določen z izrazom: Vi = kjer sta: di - standardna deviacija parametrov, xi - povprečna vrednost veličine. when: EX- the summary of existent phase elapsed [s], tc - the global read cycle time of existing quantity [s]. The variation coefficient is determined from the formula: •100 % (3), when: di- standard deviation of parameters, x - average parameters of quantity. 8 SšnnstsfcflM]! ma stran 296 Parametri optimizacije varjenja - Optimisation of Welding Parameters Če upoštevamo definicijo kriterija stabilnosti, je razumljivo, da se z nizanjem vrednosti varilnih parametrov začne večati delež ustavitev v skupnem času varjenja. Težave z vžiganjem obloka ob kratkem stiku se izražajo z nepravilnostmi pri nastajanju zvara. Varilni proces je časovno stabilen ob pravilnem prehajanju dodajnega materiala v talino zvara, ko ima kriterij stabilnosti W najmanjšo vrednost. 2 EKSPERIMENTALNI DEL Za statistično obdelavo izmerjenih vrednosti varilne napetosti v področju kratkostičnega prehajanja materiala je bil uporabljen indeks stabilnosti W. Merilni sistem je prikazan na sliki 2. If the stability criterion for the welding process is taken into consideration, it becomes clear that with lower values of the welding parameters the absence portion of the summary welding time begins to grow. There are problems with the ignition of the arc after a phase of short circuit the consequence of wich is the observed anomaly in the formation of the welding bead. The welding process is time stable and requires regular transition filler metal in the welding bath if the stability criterion W takes its minimum values [2]. 2 EXPERIMENTAL PART The index stability W was applied to show how the criterion for an area short circuit transfer metal could be stated from the voltage measurement course using statistical interpretation. The appertaining schema is showed in Fig.2. I osciloskop oscilloscope V/I enota I/O unit mikroprocesor microprocessor bralni pomnilnik ROM bralno pisalni pomnilnik RAM V/I enota 1 I/O unit 1 V/I enota 2 I/O unit 2 a branje podatkov data reader proces varjenja welding process Sl. 2. Shema merilne naprave za odbiranje varilne napetosti in toka Fig. 2. A schematic of the measuring equipment for reading of voltage and current in the welding process Preskusni varjenci dimenzij 60 x 15 x 160 mm iz jeklene perlitne litine so bili predgrevani na temperaturo T = 650°C. Preskusi so bili narejeni s tremi vrednostmi jakosti varilnih tokov: Iz = 210, 250 in 280 A. Varilna napetost se je spreminjala v področju Uz=18 do 30 V, tako da je potekal varilni proces v področju kratkostičnega prehajanja materiala. Naslednji varilni parametri so bili konstantni: - dolžina prostega konca žice: l = 25 mm, premer: f 2 mm - v = 50 mm/s - induktivnost varilnega tokokroga: L = 4,25 mH, - pretok zaščitnega plina: Q = 15 l/min, Argon 4,6 (99,996% Ar), For the experimental test we used casting slabs of size 60 x 15 x 160 mm produced from fer-rite-pearlite ductile iron and preheated to the temperature T = 650 0C. Three levels of welding current were used p / = 210, 250 and 280 A. The voltage ranged from Uz=18 to 30 V when the welding process ran in the short circuit area transfer. The following welding parameters were constant: - the push outing of electrode: l= 25 mm, rightward welding technique, electrode diameter: f 2 mm - the welding rate: v = 50 mm/s, - the induction of welding circuit: L = 4,25 mH, - the shielding gas - Argon 4,6 (99,996% Ar), quantity gas: Q = 15 l/min, | gfin=i(purMini5nLn 99 stran 297 I^HsSTrlMlGC J. Me{ko - V. Le`dík - M. Mi~ian Kot delovno področje je bil uporabljen proces, pri katerem je bila frekvenca kratkih stikov višja od 10 s-1.. Ta omejitev je bila v skladu z disertacijo [5]. Indeks stabilnosti W je odvisen od varilne napetosti [5]. Ta funkcija ima svoj minimum v področju največje stabilnosti. Za vse nastavitve varilnih parametrov je bil odbran potek varilne napetosti in analiziran čas gorenja obloka in čas kratkega stika (faza ustavitve - odsotnosti procesa je bila zelo neizrazita, zato ni bila upoštevana). Te vrednosti so v skladu z ravnijo varilne napetosti, ki je najpogosteje uporabljana za izdelavo histograma. Histogram relativne pogostosti pojavljanja različnih ravni napetosti in toka za prikazana časovna poteka obeh parametrov, za stržensko elektrodo tipa RD 971, prikazuje slika 3. I, A 400 350 300 250 200 150 100 50 In the working area a process was maintained with short circuit frequency attaining values as high as 10 s-1. This boundary was specified according to the thesis [5]. The index stability W is dependent on the welding voltage, according to [5]. The function has a minimum which determines the area with the highest stability. For all setting values the welding voltage course displaying the arcing time xo and the short circuit time xs was recorded (the absence phase had been few expressive, therefore it was not included). These values corresponded to the level of voltage which has been mostly used for drawing a histogram. The histogram depending on the distribution time P for different levels of current and voltage for the tubular cored electrode RD 971 is showed in Fig. 3. / «rVM V*V H/ ^ P, % 0 0,975 0,985 0,995 1,005 1,015 1,025 t, s U, V 40 35 30 25 20 15 10 5 0 vvww \w*ff / >Aa / P, % 0,975 0,985 0,995 1,005 1,015 1,025 t s Sl. 3. Potek napetosti, toka in histograma relativne pogostosti P za različne ravni toka in napetosti za stržensko elektrodo tipa RD 971, varjene z U = 27V in I = 210 A Fig. 3. The continuance of voltage, current and histograms - percentage distribution time P with different levels of current and voltage for tubular cored electrode type RD 971, U=27 V and I=210 A Na sliki 3 prikazan potek varilne napetosti je bil posnet v optimalnih varilnih razmerah, ker je bila tedaj vrednost indeksa stabilnosti minimalna. Takrat je dejansko varilni proces časovno stabilen in je prehajanje materiala v talino zvara normalno. The welding voltage in Fig.3 is optimised for the existing welding conditions, because processes at these voltages have minimum value index stability W. It was proved, that the welding process is time stable and the transition of the filler metal into the welding bath is normal. 99-7/8 grin^(afcflM]SCLD I ^BSfiTTMlliC | stran 298 Parametri optimizacije varjenja - Optimisation of Welding Parameters Na sliki 4 je prikazana krivulja indeksa sabilnosti W za različne vrednosti napetosti U, pri varilnem toku Iz = 250 A. Dodajni material je bil strženska elektroda tipa RD 971. Krivulja indeksa stabilnosti W je bila določena z regresijsko analizo drugega reda. Uporabljena je bila varilna napetost, ki je ustrezala ekstremnemu indeksu stabilnosti, to je pri njegovi najmanjši vrednosti. % W In Fig. 4 values for the index of stability W for different welding voltage Uz and welding current Iz = 250 A are shown. The filler metal was tubular cored electrode type RD 971. The 2nd order method regression analysis was used. The welding voltage used corresponded to the extreme value of the stability index which was a minimum. 20 21 22 23 24 25 26 27 28 29 Uz V Sl. 4. Indeks stabilnosti v odvisnosti od varilne napetosti U pri varjenju s stržensko elektrodo tipa RD 971 s tokom I = 250 A Fig. 4. The index stability W dependence at welding voltage U for tubular cored electrode type RD 971 and current I = 250 A V preglednici 1 so prikazani optimalni varilni parametri in vrednosti brizganja