© Strojni{ki vestnik 50(2004)2,80-93 ISSN 0039-2480 UDK 658.512.2:519.61/.64 Izvirni znanstveni ~lanek (1.01) © Journal of Mechanical Engineering 50(2004)2,80-93 ISSN 0039-2480 UDC 658.512.2:519.61/.64 Original scientific paper (1.01) Vklju~itev numeri~nih analiz v zgodnjih fazah konstrukcijskega postopka Introducing Numerical Analyses in the Early Phases of the Design Process Toma` Bu~ar - Miha Jane`i~ - Primo` Panger{i~ - Matija Fajdiga Odločitve, sprejete v razvojnem postopku izdelka, bistveno vplivajo na končno ceno, zmogljivost, zanesljivost, varnost in vpliv izdelka na okolico. Ker je poznavanje konstrukcijskih zahtev in omejitev v zgodnjih fazah proizvodnega postopka izdelka pogosto omejeno, je sprejemanje vsakršnih odločitev za konstrukterja zelo zahtevno. Soočeni s tako zapletenostjo so se posamezni konstrukterji omejili na ozke in dobro opredeljene podnaloge, kar ima za posledico neenotnost napredka na tem področju. V mnogih primerih je bil razvojni postopek izboljšan z računalniško podprtim konstruiranjem (RPK) in tehnikami numeričnih vrednotenj, kakor je metoda končnih elementov (MKE). Združitev obeh postopkov omogoča izračun napetostno-deformacijskih stanj izdelka in njegovo obnašanje pri različnih oblikovnih variantah. Podatke o napetostno-deformacijskih stanjih lahko pridobimo tudi z eksperimentalno analizo fizičnih preizkusancev, toda prednost postopka RPK-MKE je možnost spreminjanja oblikovnih in materialnih parametrov izdelka ter takojšnja numerična vrednotenja pred izdelavo fizičnih prototipov. Ker so računalniški modeli zgrajeni na podlagi mnogih predpostavk in omejitev, tudi rezultati analiz z metodo končnih elementov brez ustrezne razlage nimajo prave vrednosti. V prispevku je zato predlagana metoda za pridobitev referenčne baze podatkov, na podlagi katere poteka vrednotenje rezultatov numeričnih izračunov. Postopek gradnje baze podatkov je prikazan na konkretnem primeru ročne zavore in zavornega pedala osebnega vozila. © 2004 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: procesi konstruiranja, CAD, metode končnih elementov, načrtovanje preskusov) Decisions made during the product development process have a significant influence on factors such as costs, performance, reliability, safety and the environmental impact of a product. However, since the knowledge of all the design requirements and constraints during this early phase of a product’s life cycle is usually imprecise, approximate or unknown, the designer s decision-making is a very demanding task. Faced with such complexity, individual designers have restricted themselves to narrow, well-defined sub-tasks and, as a result, progress in this area has been patchy and spasmodic. In many cases, product design has been improved by the help of computer-aided design (CAD) and structural analyses based on the finite-element method (FEM). These two methods, coupled together, allow the calculation of mechanical quantities (such as stresses, deformations and contact pressures) and the investigation of the different behaviour of products with various designs. Such quantities can also be measured by means of in-vitro tests, but the advantage of CAD-FEM is the possibility of changing the geometrical and material properties of the product and evaluating its different behaviour before manufacturing prototypes. However, because the numerical models are based on many suppositions and restrictions, without proper interpretation the finite-element analysis (FEA) results are also of almost no use. Thus, in this article a method of acquiring a reference database, which serves for FEA results validation, is suggested. The procedure of building a suitable reference database is demonstrated by means of two examples, a car’s handbrake and brake pedal. © 2004 Journal of Mechanical Engineering. All rights reserved. (Keywords: product design, CAD, finite element methods, experiment planning) 0 UVOD Konstruiranje je zahteven postopek, s katerim se zamisel o zadostitvi nove funkcije v naravi smiselno opredeli do najmanjše podrobnosti in predstavi v nematerialni obliki kot izdelek. Postopek 0 INTRODUCTION Product design is a complex, iterative, deci-sion-making engineering process, the result of which is transforming an abstract principle into a concrete technical solution. It usually starts with the identifi- grin^SfcflMISDSD VH^tTPsDDIK stran 80 Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses konstruiranja se običajno prične z razpoznavanjem in analizo naloge, ki jima sledi zaporedje dejavnosti, s katerimi iščemo optimalno rešitev problema, in konča s podrobnim opisom izdelka. Posamezne faze konstrukcijskega postopka so pri različnih avtorjih modelov opredeljene različno. Pregled najbolj znanih metod je podan v [1]. V splošnem je konstrukcijski postopek razdeljen na štiri glavne faze [2]. Prva faza je specifikacija naloge, pri kateri se natančno zberejo in določijo informacije o izdelku. Zasnova je druga faza konstrukcijskega postopka, katerega osnovni namen je iskanje idejnih rešitev, ki izpolnijo dano nalogo. Fazi zasnove sledi faza snovanja. V tej fazi se izdela natančen osnutek z določenimi osnovnimi merami in končno obliko. Zadnja faza je dodelava, ki vključuje optimiranje podrobnosti in izdelavo vse potrebne dokumentacije za izdelavo prototipov. S to fazo se konča konstrukcijski postopek v ožjem pomenu, kateremu sledijo še izdelava in preizkusi prototipov. Vse omenjene faze konstruiranja so prikazane na sliki 1. Računalniško podprta orodja so uveljavljena predvsem v končnih fazah konstruiranja, ki obsega določanje oblike in izmer. Razširitev računalniške podpore na zgodnje faze konstruiranja je v zadnjih letih glavni cilj raziskav na tem področju. Nekateri rezultati tovrstnih raziskav so podani v [3] do [5]. Običajno je končna oblika izdelka potrjena šele po intenzivnih in uspešnih eksperimentalnih vrednotenjih dragih fizičnih prototipov. Če testiranja niso uspešna, je treba izdelek na podlagi povratnih informacij večkrat popravljati, kar pomeni dodatne razvojne stroške in je lahko časovno precej zamudno. Da se izognemo nepotrebnemu izdelovanju dragih fizičnih prototipov, se razvoj računalniške podpore konstruiranju vedno bolj usmerja tudi na uporabo numeričnih vrednotenj in računalniških prototipov. Uporaba tehnik numeričnih analiz omogoča sprotno in učinkovito vrednotenje izdelkov brez izdelave fizičnih prototipov. Namen tega prispevka je prikazati trdnostno analizo z metodo končnih elementov kot eno od tehnik numeričnih vrednotenj, ki bo uporabna v zgodnjih fazah konstrukcijskega postopka (sl. 1). Ker tovrstne numerične analize temeljijo na poenostavljenih matematičnih modelih, je treba imeti za vrednotenje rezultatov na voljo primerjalno bazo podatkov. Glavni cilj raziskovalnega dela je zato razviti ustrezno metodo, ki bo ob najmanjšem dodatnem delu in stroških omogočala gradnjo kakovostne baze primerjalnih podatkov. Z uporabo kombinacije numeričnih vrednotenj in tehnik postopka RMS (FMEA, FTA) [6] lahko pridemo v zgodnjih fazah razvoja izdelka bistveno hitreje in z manj porabljenimi sredstvi do kakovostnih rešitev. V nadaljevanju prispevka je najprej opisana predlagana metoda za gradnjo omenjene primerjalne baze podatkov. Uporaba metode je nato prikazana na dveh dejanskih primerih. Na koncu so podane še nekatere ugotovitve in sklepi. cation of a need, proceeds through a sequence of ac-tivities to seek an optimal solution to the problem, and ends with a detailed description of the product. Re-searchers define individual phases of the design proc-ess in various ways. An overview of the most-known methods can be found in [1]. Generally, a design proc-ess consists of four phases [2]. The first phase is prod-uct design specification, where information about the product is collected and defined in precise yet neutral terms. Conceptual design represents the second phase of the design process, whose primary concern is the generation of physical solutions to meet the design specification. The conceptual design phase is followed by the embodiment design phase. In this phase, the precise layout and the form of the final product are developed. The final phase is the detailed design, where final decisions on dimensions, arrangement and shapes of individual components and materials are made and production documentation for manufacturing proto-types is completed. With this phase the product design, in a narrow sense, is concluded and followed by prototype manufacturing and testing. Figure 1 summa-rizes all the mentioned phases of the design process. Computer-aided tools are well established in the later phases of the design process, namely detailing and embodiment with modelling. Extending computer support to the early phases of the design process has been the main research aim in this area in the past few years. Some findings acquired in such researches can be found in [3] to [5]. Usually, the final product form is confirmed after intensive and successful experimental analyses of expensive physical prototypes. Unless experimental test-ing is successful, the product needs to be redesigned according to feedback information, which leads to further costs and time consumption. In order to avoid ex-pensive and unnecessary prototype manufacturing, computer support for design is aimed at numerical vali-dation and computer prototypes. The use of numerical analysis methods allows a consistent and efficient prod-uct evaluation without the need for expensive physical prototypes. The aim of this paper is to demonstrate the structural analysis based on FEM as a numerical analy-sis method applicable in the early phases of the design process (see Fig. 1). Since such numerical analyses are founded on simplified numerical models, a reliable reference database is required for the validation of FEA re-sults. The main objective of such an approach, and therefore the focus of this paper, is to develop a suitable method that enables us to build a reference database of high quality with minimal additional efforts and costs. Using a combination of numerical analyses and RMS methods (FMEA, FTA) [6] in the early phases of the product design, we can solve the problem in a signifi-cantly faster and cheaper fashion. In the next sections the method for acquir-ing the reference database is proposed and the procedure is then demonstrated in practice. To end with, some conclusions are given. | lgfinHi(s)bJ][M]lfi[j;?n 04-2_____ stran 81 I^BSSIfTMlGC Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses Določitev naloge Zamisel Snovanje Izdelava tehnične dokumentacije 'Mehanske analizel z MKE J" L fMehanske analize7 T> z MKE Sl. 1. Faze konstrukcijskega postopka 1 GRADNJA PRIMERJALNE BAZE PODATKOV V fazi razvoja izdelka se za numerične analize z metodo končnih elementov uporabljajo bolj ali manj zahtevni matematični modeli, ki temeljijo na različnih omejitvah in predpostavkah. Tako ustvarjeni matematični modeli so nenatančni in dejanski izdelek opišejo le približno. Ker so zaradi tega približni tudi rezultati numeričnih analiz, morajo za njihovo vrednotenje obstajati primerne primerjalne vrednosti. Primerjavo za vrednotenje rezultatov pomeni primerjalna baza podatkov, ki jo pridobimo s predhodnimi numeričnimi izračuni in preizkusi. Predlagana metoda gradnje baze primerjalnih podatkov je prikazana na sliki 2. Predstavljeni postopek se opravi le enkrat, bodisi na že znanem izdelku ali na izdelku v razvoju. Izdelano primerjalno bazo podatkov je mogoče uporabiti tudi pri razvoju sorodnih izdelkov. Konstrukcijski postopek izdelkov se tako pospeši, saj ovrednoteni rezultati numeričnih analiz v veliki meri nadomestijo izdelavo in eksperimentalno analizo dejanskih prototipov. Uvajanje sprotnega in učinkovitega vrednotenja ter preizkušanja izdelkov na tako imenovanih računalniških prototipih je torej naš glavni namen. Kakor smo že omenili, je na sliki 2 prikazan postopek za gradnjo kakovostne baze podatkov, na podlagi katere se v zgodnjih fazah razvoja izdelka vrednotijo rezultati numeričnih izračunov. V pretočnem diagramu je nazorno prikazano zaporedje posameznih grin^SfcflMISDSD Task clarification Conceptual design Embodiment design I Detail design <|- ^fStructural analyses! *1 based on FEM J" ^Structural analysesl »[ based on FEM J" Prototype manufacturing Prototype testing Fig. 1. The phases of product design 1 REFERENCE DATABASE ACQUISITION During product design, various numerical models based on many suppositions and restrictions are used for finite-element analyses. Thus, such models are inaccurate and describe the physical product only approximately. Consequently, FEA results are also approximate, which is why comparative exam-ples are required for their validation. These compara-tive examples are a reliable reference database that is acquired through preceding numerical calculations and experimental analyses. The suggested method for building a reference database is shown in Figure 2. The shown procedure is performed only once on the existing product or on the product in the development process. The elaborated reference database can also be used in the development of similar products. This way the product development process is accelerated, for the evaluated FEA results largely sub-stitute for expensive prototype manufacturing and experimental analyses. The introduction of a con-sistent and efficient product evaluation using so-called computer prototypes is therefore our main purpose. As mentioned, Figure 2 presents the procedure for reference database elaboration on which the evaluation of numerical calculations in the early phases of product design are based. The block diagram shows the sequence of tasks clearly. It is worth VBgfFMK stran 82 Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses 3D računalniški model 3D CAD model ^ Izbira obremenitvenih primerov •Preliminarna analiza z MKE • Analiza rezultatov začetnega MKE izračuna: > določitev merjenih veličin in merilnih območij > izbira merilnih mest > izračun dejanskih obremenitev (glede na nosilnost materiala izdelka) • Določitev natančnosti meritve glede na podane zahteve I T •Selection of load cases • Preliminary FEA I • Analysis of the preliminary FEA results: > determine measured variables and their limits > select measurement locations > calculate real loads (according to the strength of product material) • Defining measurement accuracy according to given requirement •Načrtovanje merilne verige (uporaba metod grobega načrtovanja): > izbira merilne opreme > izračun merilne negotovosti Ne Dosežena^ zahtevana natančnost ? Da • Izdelava računalniške podpore za potek meritve in zajem ter obdelavo podatkov • Izdelava komponent za krmiljenje poteka meritve • Izdelava vpenjalnih pripomočkov za vpetje preizkušanca in vnos sile I •Planning measurement system (using robust deign methods): > select measuring equipement > calculate measurement uncertainty No -Is required accuracy ^achieved? rYes •Making computer aid for experimental process and data aquisition • Making additional components for experimental process control • Making appliances for fastening tested product and load application •Izvedba eksperimenta •Analiza rezultatov I • Performing experimental analyses • Analysing experimental results •Ponovitev MKE analize z uporabljenimi izsledki iz meritev I I • Repeating FEA using discoveries of the experiments____________ •Primerjava rezultatov MKE analize in eksperimenta • Zbiranje ugotovitev in graditev primerjalne baze podatkov T I •Comparing FEA results with experimental results • Collecting findings and acquire reference database____________ Primerjalna baza podatkov I Reliable reference database Sl. 2. Metoda za gradnjo primerjalne baze podatkov opravil, podrobnejša razlaga pa sledi na stvarnih primerih. Omeniti je treba le to, da je eksperimentalno preverjanje numeričnih rezultatov mogoče le z zelo kakovostnimi in premišljeno načrtovanimi preizkusi ([7] in [8]). Ker ima pri tem primeren in pravilno zasnovan merilni sistem pomembno vlogo, si pri izdelavi zamisli meritve pomagamo tudi z metodami grobega načrtovanja ([9] in [10]). Glavno načelo omenjene metode je izboljšanje kakovosti eksperimentalne analize z zmanjšanjem občutljivosti Fig. 2. The method for reference database acquisi-tion mentioning that experimental verification of the FEA results is only possible by means of perfected and well-planned tests ([7] and [8]). Since a suitable and properly conceptualised measurement system plays an important role here, the method of robust design ([9] and [10]) can be of great help when preparing the experiment concept. The key principle of this method is to improve the quality of the experimental analysis through reducing the measurement sys-tem’s sensitivity to disturbing factors. Our task is Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses merilnega sistema na motilne dejavnike. Naša naloga je torej, da izberemo komponente merilnega sistema tako, da bo na izhodu iz sistema vpliv motilnih signalov na želenega čim manjši. Postopek izgradnje primerjalne baze podatkov bo v nadaljevanju prikazan na dveh realnih primerih. to select the components of the measurement system in such a way that the influence of the disturb-ing signals on the chosen one is minimised. In the rest of the paper the procedure of reference database acquisition is demonstrated by means of two practical examples. 2 ZGLEDI 2 EXAMPLES 2.1 Ročna zavora 2.1 Handbrake V tem poglavju je predstavljen sistem eksperimentalnega preverjanja numerične analize ([12] in [13]), s kakršnim na izdelkih določenega tipa gradimo bazo znanja. S tako pridobljeno bazo podatkov si v konstrukcijskem postopku podobnih izdelkov pomagamo pri gradnji modelov končnih elementov in pri vrednotenju rezultatov. Da bi pred meritvami bolje spoznali napetostno in deformacijsko stanje pri izbranih obremenitvah, je bila izdelana začetna analiza z metodo končnih elementov. Z začetno analizo napetostnega stanja smo določili najprimernejša mesta na konstrukciji za merjenje napetosti. Ker smo za merjenje mehanskih napetosti izbrali merilne lističe, morajo imeti merilna mesta pri vseh obremenitvenih primerih razmeroma veliko napetost, njen gradient po površini pa naj bi bil čim manjši. Merilno mesto mora biti tudi geometrijsko primerno za namestitev merilnega lističa. Na podlagi rezultatov začetne analize sta se za najugodnejši mesti za merjenje napetosti izkazali mesti SG1 in SG2 (sl. 3). Na teh mestih se pojavijo razmeroma velike napetosti pri vseh obremenitvenih primerih. Izbrani mesti sta geometrijsko ustrezni za namestitev merilnih lističev in sta eno na ročici drugo pa na nosilu ročne zavore. Merilno mesto za merjenje sile v pletenicah. LAV Measurement location for measuring forces in wires. In this section we present a system for the experimental validation of numerical analysis ([12] and [13]) with which we can build a reference database that would help us when designing and validating similar structures. Such a database can, in the design processes of similar structures, help us to build finite-ele-ment models and validate numerical simulation results. A preliminary analysis using the finite-element method was made in order to get to know better the stress and strain states in the chosen load cases. This preliminary stress-state analysis helped us define the most suitable locations to measure the stresses on the structure. Since we chose strain gauges to measure the mechanical stresses, all the measurement locations need to have a relatively high stress in all load cases, and the stress gradient on the surface needs to be as low as possible. Measurement locations also have to be geometrically suitable for placing strain gauges. On the basis of a preliminary analysis we found that the best locations for stress measurement were locations SG1 and SG2 (see Fig. 3). On these locations stresses are relatively high in all the load cases. They are also geometrically suitable for placing strain gauges: one is on the handbrake handle and the other on its holder. Merilno mesto za merjenje napetosti v ročici SG1 Measurement location for measuring stresses in hand brake handle Merilno mesto za merjenje napetosti v nosilu SG2 Measurement location for measuring stresses in hand brake handler Sl. 3. Merilna mesta Fig. 3. Measurement locations grin^rskJirMigcc] VH^tTPsDDIK stran 84 Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses T ESTNI O BJEKT MERILNA VERIGA 2 ZAVORNO POSTROJENJE BREAK ASSEMBLY F*i k vpetišča Wire fastening displacement g point t Sl. 4. Sistemska slika preizkuševališča Fig. 4. Experimental system scheme Celotno merilno verigo, uporabljeno pri eksperimentalnem delu, prikazuje slika 4. Poleg mehanskih napetosti so bile merjene tudi naslednje veličine: sila obremenjevanja ročne zavore, pomik točke vnosa obremenitev, sila v pletenicah in pomik vpetišča pletenic. Napetosti na predhodno izbranih mestih so bile določene na podlagi deformacij, ki so bile merjene z merilnimi lističi s tremi mrežami HBM-RY91. Enako načelo je bilo uporabljeno tudi za merjenje sile v pletenicah, le da so bili pri tem uporabljeni merilni lističi z dvema mrežama HBM-XY11. Za merjenje sile obremenjevanja ročne zavore je bila uporabljena tlačno/natezna sonda proizvajalca HBM z znanimi karakteristikami. Merjenje pomika točke vnosa sile je bilo izvedeno z vrtljivo merilno letvijo (PMS-RML), ki deluje na načelu prirastkovnega dajalnika sunkov. Pomik vpetišča pletenic je bil merjen z linearnim variabilnim diferencialnim transformatorjem (LVDT). Karakteristike obeh zaznaval za merjenje pomikov so bile podane od izdelovalca. Za celoten merilni sistem je bila izdelana tudi analiza merilne negotovosti [11]. Obremenitveni primeri so bili prilagojeni za preračun z metodo končnih elementov. Za osnovo je rabil prevod tehničnih določil naročnika. V tem dokumentu bo obravnavan le najznačilnejši obremenitveni primer, tj. obremenitev ročice navzgor (sl. 5). Poleg tega sta bila obravnavana še obremenitvena primera z bočno obremenitvijo, in sicer prvi v sproščenem in drugi v napetem stanju. Slika 6 prikazuje z metodo končnih elementov dobljeno porazdelitev napetosti na mestih, kjer sta pri meritvi nameščena merilna lističa, pri obremenitvi 248 N. Na podlagi takšnih slik pri različnih obremenitvah dobimo sliko spreminjanja povprečne napetosti na merilnem mestu v odvisnosti od obremenitve. Primerjavo tako dobljenih rezultatov analize z MKE in The complete measurement chain in the experiment is shown in Figure 4. Besides mechanical stresses the following quantities were also measured: handbrake loading force, displacement of the load-applying point, force in the wire and displacement of the wire-fastening point. Stresses on the preliminarily chosen loca-tions were defined on the basis of deformations that were measured by 3-grid strain gauges HBM-RY91. The same method was used for measuring the force in the wire, but 2-grid strain gauges HBM-XY11 were applied. To measure the handbrake loading force we used an HBM load cell RSCA 1t with known charac-teristics. The displacement of the load-applying point was measured by means of a linear incremental encoder (PMS-RML), which functions on the incremen-tal rotary encoder principle, and the displacement of the wire-fastening point was measured by means of a linear variable differential transformer (LVDT). The characteristics of both sensors used were defined by the producers. For the entire measurement system an analysis of the measurement uncertainty was also performed [11]. All load cases were adapted for the finite-element method calculation, and based on the cus-tomer’s technical specifications. This paper deals only with the most typical load case, that is, when the handle is loaded upwards (see Fig. 5). In addition to this, however, we also studied two load cases with the load directed sideways, one with the handbrake in loose state and the other in pretense state. Figure 6 describes the stress distribution on the strain-gauge locations at maximum load 248 N as obtained with the finite-element analysis. On the basis of such figures at different loads, we can get a chart representing the dependence of the average stresses at measuring locations on the applied load. Figure 7 shows the comparison of the results obtained with the finite-element analysis with the results obtained from meas- isfFIsJBJbJJIMlSlCšD I stran 85 glTMDDC Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses F Sl. 5. Vnos obremenitve Fig. 5. Load application eksperimentalne analize prikazuje slika 7. Na ta način pridemo do spoznanja o velikosti odstopanja rezultatov simulacij od rezultatov meritev. Ker se rezultati simulacij nikdar ne ujemajo popolnoma z rezultati meritev, takšne primerjave ponovimo večkrat na podobnih konstrukcijah. Ob večkratnem ponavljanju meritev na podobnih konstrukcijah najdemo povezavo med rezultati simulacij in rezultati meritev. Takšni izsledki so že pomemben del baze znanja, ki bo pri prihodnjih konstrukcijah namenjena za to, da bomo lahko s simulacijo kar se da natančno ugotovili napetostno deformacijsko stanje ročne zavore. Krivulji na sliki 8 prikazujeta drugo vrsto rezultatov, ki prav tako sodijo v bazo znanja. Omenjeni potek predstavlja odvisnost sile v vpetišču pletenic od pomika le-tega, torej predstavlja togost celotnega zavornega sistema. V obravnavanem primeru se je izkazalo, da je izmerjena karakteristika bilinearna. To je sicer bolj ali manj splošno znano dejstvo, pa vendar značilen primer ugotovitve meritev, ki skupaj z numeričnima vrednostma obeh togosti sodi v bazo znanja. Značilna ugotovitev, ki sledi iz takšnega spoznanja je, da za natančno analizo podobnih konstrukcij z MKE uporaba linearnih reševanj zaradi nelinearnosti robnih pogojev ni zadostna. Za nadaljnje numerične simulacije podobnih konstrukcij je torej pomembno, da poprej pridobimo ali izmerimo podatek o togosti zavornega sistema ter nato izdelamo nelinearno analizo z MKE. Vsa zgoraj našteta spoznanja pa nenazadnje pripomorejo k znatnemu skrajšanju časa, potrebnega za izvedbo podobnih simulacij ob hkratnem izboljšanju zanesljivosti rezultatov. Matematični model ročne zavore je bil v konkretnem primeru zgrajen z uporabo končnih elementov, izračunane vrednosti so nato primerjane z izmerjenimi vrednostmi. Po pričakovanju se je izkazalo, da se med dobljenimi rezultati pojavi določeno razhajanje, kar je v veliki meri posledica poenostavitev in predpostavk, uporabljenih pri analizi z MKE, ki dejanski model idealizirajo, npr. zveza med napetostjo in deformacijo je v celotnem območju obremenjevanja linearna (Hookeov zakon), vrednost elastičnega modula E je stalna, material je izotropen, debelina pločevine je po končnem elementu nespremenljiva. urements. From this we can find the difference between the simulation results and the measurement results. Since the simulation results always vary from the measure-ment results, the comparison between the simulation and the measurement should be repeated and statisti-cally treated on similar structures. With this method, the general rules of dependency between the measured and the simulated results that apply well to other similar structures can be acquired. Such general rules are an important part of a reference database, which would help us with an accurate stress-state estimation with simulations on similar structures in the future. The diagram in Figure 8 shows other kinds of results, which can also play a significant role in building a quality reference database. This diagram represents the measured results of the dependency of the force in the wire on the displacement of the wire-fastening point, which represents the stiffness of the whole breaking system. In the discussed case, we can see that the stiffness has a bilinear characteristic. Although this is more or less a com-monly known fact, it is still a characteristic example of a measurement result, which, together with both values of stiffness, belongs to a reference database. A characteristic finding, which follows from such a result, is that because of the nonlinearities (bilinear) included in restraints of this and similar structures, a simple, linear finite-element analy-sis for estimating stress states of this type of structure cannot be used. For further finite-elements analyses it is very important to measure or somehow provide a breaking system’s stiffness characteristics and to use appropriate non-linear finite-element solvers. Finally, all the findings mentioned above contribute to a considerable shortening of the time needed for a realization of a finite-element analy-sis of similar structures and a simultaneous improvement of the results’ reliability. The mathematical handbrake model in this case was constructed with the help of finite elements. The calculated values are compared to the measured values. As we anticipated, it turned out that there was a consid-erable difference between the results obtained with each method, particularly with respect to the stresses. The finite-element analysis is based on a set of simplifications and suppositions that idealize the real model, e.g., the relationship between stress and strain is linear every-where (Hooke’s law), the value of Young’s modulus (E) is constant, the material is isotropic, the thickness of the sheet is constant according to the finite element, etc. grin^SfcflMISDSD VBgfFMK stran 86 Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses a) Ročicao*25MPa b) Nosilec a*75MPa a) Handle o*25MPa b) Holder a*75MPa Sl. 6. Napetosti, dobljene z MKE na mestih merilnih lističev pri največji obremenitvi Fig. 6. Stress distribution at strain-gauge locations during maximum load, obtained by FEA 160 140 120 100 80 60 40 20 Napetost v ročici - meritev Stress in handle - experiment Napetost v nosilcu - meritev Stress in holder - experiment — Napetost v ročici - MKE Stress in handle - FEA — Napetost v nosilcu - MKE Stress in holder FEA 100 150 200 250 300 Obremenitev [N] Load [N] Sl. 7. Napetosti kot funkcije obremenitve Fig. 7. Stresses in the handbrake 1600 1400 1200 1000 800 600 400 200 0,5 1 1,5 2 2,5 3 3,5 Pomik vpetišča pletenic [mm] Deformation of wire fixture [mm] Sl. 8. Togost zavornega sistema Fig. 8. Stiffness of the whole braking system 4,5 Sin^ObJJPsflDslJSD I stran 87 glTMDDC 0 0 0 4 Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses Pri izdelavi matematičnega modela se pojavlja tudi vprašanje modeliranja zračnosti in naleganja posameznih sestavnih delov. V primeru, da je naleganje dveh elementov v matematičnem modelu napačno, dobimo močno spremenjen fizikalni sistem, ki obravnavani dejanski sistem opiše napačno. Za izboljšanje zanesljivosti rezultatov simulacij in nenazadnje tudi baze znanja, bi bilo treba natančno raziskati tudi vpliv zgoraj navedenih parametrov na rezultate numeričnih simulacij in predvsem na njihovo odstopanje od rezultatov meritev. 2.2 Zavorna stopalka Drugi zgled ustvarjanja baze podatkov in izpopolnjevanja postopka konstruiranja je predstavljen na primeru zavorne stopalke [14]. Na sedanji konstrukciji je bilo treba odpraviti problem prevelike bočne deformacije, ki se je pojavila v primeru testiranja ene od konstrukcijskih zahtev. Problem se je pokazal v primeru simulacije izstopanja voznika iz vozila, pri čemer si pomaga z odrivanjem desne noge od stopalke zavore. Za izboljšanje togosti konstrukcije je bilo treba to spremeniti, vendar s poudarkom na najmanjših stroških, ki bi spremljali to spremembo. Poglavitni namen je bil poiskati najšibkejši del konstrukcije in ga ustrezno izboljšati, tako da bi konstrukcija ustrezala predpisani zahtevi, tj. dovoljena bočna deformacija sredine stopalke zavore, kar je prikazano na sliki 9. Za sedanjo konstrukcijo je bila najprej izdelana linearna napetostno-deformacijska analiza z MKE. Dobljeni rezultati vedno pomenijo določeno odstopanje od dejanskega stanja, zato je nujno potrebno določiti velikostni razred odstopanja. Tega določimo z ustrezno izvedenim preizkusom oziroma meritvijo, ustreznost rezultatov meritev pa je mogoča le z natančno izdelanim merilnim sistemom. Do razlik pride zaradi poenostavitev pri analitičnem delu in merilne negotovosti pri eksperimentalnem delu. Ob poznavanju obeh pa lahko določimo usmeritev oz. neko bazo znanja, ki omogoči cenejše in hitrejše When making the mathematical model, we face two problems: how to model looseness and how to model contacts between component parts. If the con-tact between two elements in the mathematical model is not correct, we get a totally different physical system, which describes the discussed real model incorrectly. To improve the reliability of the simulation results and the reliability of the reference database, we should make an exact investigation of the influence of the mentioned parameters on the results of the numerical simulations and on their deviation from the measurement results. 2.2 Brake Pedal The second example of database acquisi-tion and the imperfection of the design procedure is shown for the case of a pedal assembly [14]. The existing design needed to be improved because its lateral deformation, when testing one of the struc-tural demands, was too large. This boundary condi-tion simulates a driver leaving the vehicle, while us-ing the brake pedal as a support for his/her right leg. The design had to be modified to improve the stiff-ness, but with minimum costs. The weakest part of the structure was identified and improved so that the new structure will fulfil all the structural demands, in particular the allowed size of the lateral deformation (the centre of stepping area of a brake pedal - point P), shown in Fig.9. A linear stress-strain analysis was made for the existing structure with a finite-element method (FEM). The results always deviate from reality, so the magnitude of the deviation had to be established. This was done with an appropriately performed experiment together with an exact measurement system. The dif-ferences are a result of simplifications in the analytical work and the measurement uncertainty of the experiment. When both of them are known, a database can be created, and this can be helpful when cheaper and faster modifications to similar structures have to be produced. The results of the strength analysis can be Bočni pomik (Side deformation) Sl. 9. Predmet testiranja Fig. 9. Testing object grvT^dfcfflMleKn VBgrTOEBS stran 88 Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses spreminjanje sorodnih konstrukcij s podobnimi very helpful when planning the measurement system poenostavitvami. Pri načrtovanju merilnega sistema because it is easier to define a measurement range and torej bistveno pomagajo rezultati analitičnega dela, choose the appropriate equipment. tj. trdnostnih analiz, s katerimi določimo npr. velikost The strength analysis was made in two merilnih območij in ustrezno izberemo merilno opremo. steps. First, the whole structure was analyzed. The Trdnostna analiza je potekala v dveh delih. results showed that the most deformable part of the Prvi del analize je potekal na celotnem sestavu zavore structure is the brake pedal and not the support. The in rezultat je pokazal, da se večinoma deformira areas with stresses higher than the yield stress are stopalko zavore, nosilo pa precej manj. Posebej veliko on the top of the brake pedal and around the joint of področje velike napetosti v materialu naj bi bilo na the pedal and the steel tube (= revolution point). The zgornjem delu stopalke zavore in okoli spoja med joint on the existing structure was made with a stopalko in jekleno cevjo (=vrtišče). Omenjeni spoj compressive forming technology, and because the na sedanji konstrukciji je bil izveden kot krčni nased results of the stress analysis imply that this joint in rezultat prvega dela trdnostne analize je nakazoval, could have a large influence on the magnitude of da ta spoj lahko bistveno prispeva k velikosti bočne lateral deformations and its modifications could re- deformacije. S preoblikovanjem tega spoja bi torej sult in resolving the problem. The second step of the lahko zmanjšali nastali problem. Drugi del trdnostne strength analysis was done on a more exact model of analize je bil narejen na bolj natančnem modelu the brake pedal, where the plastic sliding elements in stopalke zavore, s tem, da so bile upoštevane tudi the revolution joint were also considered. Because plastične puše, ki so montirane v vrtišču stopalke. the stress-strain state in the compression joint can- Ker stanja v krčnem nasedu med stopalko in cevjo ne not be modelled satisfactorily, a compromise between moremo zadovoljivo modelirati, je bila uporabljena the compression-forged joint and welded joint of the srednja možnost med krčnim nasedom in varjenjem pedal and tube was used. Basically, the idea of how pedala in cevi. Torej smo že uporabili zamisel, kako bi to modify the existing brake pedal had been already preoblikovali sedanjo stopalko zavore. Tudi used. The results of the second step of the strength natančnejša analiza je potrdila velike napetosti v analysis confirmed that areas of high stress appear okolici spoja cevi in stopalke (sl. 10). around the joint of the pedal and tube (see Fig.10). Glede na dobljene rezultate drugega dela According to the results of the second part of trdnostne analize smo povzeli, da ta del konstrukcije the strength analysis we concluded that this structural bistveno prispeva k velikosti bočnih deformacij, part contributes significantly to the size of the lateral predvsem zaostalih bočnih deformacij v primeru deformations, mostly to the residual deformations in preobremenitev. To predpostavko je bilo treba the case of overloading. This assumption should be potrditi ali ovreči z izvedbo meritve na stopalki confirmed or refuted with an experiment. The results of zavore. Dobljeni rezultati so pomagali pri nadaljnji the strength analysis were helpful when we planned the izbiri merilne opreme in načrtovanju merilnega mesta. measurement system and choose equipment for it. Be- Zaradi prej omenjenega dogovora pri modeliranju cause the model used for the FEA was a compromise stopalke zavore smo načrtovali izvajanje meritev na between a compressed and a welded joint, measure- sedanji in spremenjeni izvedbi stopalke zavore. Pri ments were planned for both the existing and the modi- varjeni izvedbi smo pričakovali boljše ujemanje fied brake pedal. The results for the welded brake pedal rezultatov. were expected to be closer to the results of the FEA. Sl. 10. Rezultati napetostno deformacijske analize – primerjalna napetost Fig. 10. Results of stress-strain analysis – comparative stress | lgfinHi(s)bJ][M]lfi[j;?n 04-2_____ stran 89 I^BSSIfTMlGC Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses Predpisani pogoji preizkušanja zahtevajo, da je merilni sistem sestavljen tako, da je mogoče nadzorovati dejanske vhodne signale glede na zahtevane vhodne signale (dejanska sila FD proti zahtevani obremenitvi F R). Med testiranjem je treba zbirati podatke v točki P (pomik). Na izbiro elementov merilnega sistema so bistveno vplivali rezultati trdnostne analize, saj smo tako lahko določili zahtevano merilno območje opreme in zaznaval ter preverili merilno negotovost obeh merilnih verig, ki naj bi bila nižja od 0,5%. Negotovost je bila določena za vsako merilno verigo posebej, in sicer z metodo najmanjših kvadratov. Zaradi statične obremenitve konstrukcije so bile za nas pomembne statične karakteristike merilne opreme. Na slikah 12 in 13 je v shemah prikazana izbira merilne opreme. Meritve bočnih deformacij smo izvedli na treh nakrčenih stopalkah in treh varjenih stopalkah. Dobljeni rezultati meritev so potrdili naše domneve, ki so izhajale iz rezultatov trdnostnih analiz z MKE. S slike 14 je razvidno, da so razlike med analitičnimi in eksperimentalnimi rezultati, pri obremenitvi 1000 N, manjše kakor pri obremenitvi 1500 N, kar je posledica omejitev linearne trdnostne analize, saj ta ne upošteva plastifikacije materiala. Dobljeni rezultati potrjujejo domneve, da so rezultati pri varjeni izvedbi bližje rezultatom analize z MKE. Ugotovimo lahko, da nakrčena izvedba stopalke zavore omogoča večje bočne pomike pri preobremenitvi s silo 1500 N kakor varjena izvedba. Prav tako pa se pojavijo večje trajne deformacije The prescribed testing conditions state that the measurement system should be able to control the true input signal given by the reference input signal (FD vs. FR). During the testing procedure a data acquisition of the displacements of the point P should be performed automatically. The selection of the elements for the measure-ment system (the measurement range of the sensors and other equipment) was influenced by the results of the strength analysis. The measurement uncertainty for both measurement systems was checked. It needed to be lower than 0.5%. The measurement uncertainty was calculated with a mean-square method. The implied load was static, and that is the reason why we were only interested in the static characteristics of the measure-ment equipment. Figures 12 and 13 show the equipment that was chosen for both measurement systems. A measurement of the deformation was car-ried out on three brake pedals with a compression-formed joint and on three pedals with a welded joint. The re-sults of the experiment confirmed our assumptions based on the FEA results. Figure 14 shows that the differences between the analytical and the experimental results at the lower load (1000N) are smaller than at the higher load (1500N). The reason for this is that the linear strength analysis does not consider different material properties after the yield-stress limit is reached. The results of the experiment for the welded pedal also con-firmed our assumption that the FEA results should be closer to the experimental results. We concluded that the compressed joint allows a larger lateral deformation when an overload of 1500N is applied. After the load is Referenčna sila Reference force = 1500 N Krmilje Controls Linearni izvršilnik Linear actuator True Force Dejanska sila Objekt TESTIRANJA J Stopalni sklop Pedal assembly Deformation Deformacija Merilna veriga I. Measurement system I Merilna veriga Kontrola INPUT-a Measurement system INPUT control Analiza REZULTATOV Pomik točke P Displacement of P Merjena vstopna veličina F0 Measured INPUT = Rezultati testiranj Test Results Sl. 11. Shema merilnega sistema Fig. 11. The measurement system scheme U=220 V- Dejanska sila Napajanje Charging U=220 V -U=220 V Merilna doza Tensile load cell [mV] Ojaevalnik U [V] A/D Dig. P C T=Napajanje- Display Sl. 12. Merilna shema - merilna veriga nadzora vstopnega signala Fig. 12. Measurement scheme - measurement system: control of input grüT^SkfflMlöKn VBgfFMK stran 90 - U Testing Object * Result Analysis Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses -U=5 V- Napajanje Charging U=220 V deformacijsk pomikr i Vrtilna merilna letev Rotation ladder vrtenje Vrtilno prirastkovno Rotationa znava remental -«c Paramatri števca Counter — parameters Datoteka "File Dig. signal -Y- Zaslon (Display) Krmilni signal Lastnosti števca „ Counter characteristics Nastavitev tevca Paramatri Parameters Sl. 13. Merilna shema - veriga I Fig. 13. Measurement scheme - system I po razbremenitvi stopalke. To je potrdilo rezultate trdnostne analize, da je pedal eden kritičnih delov, ki jih moramo spremeniti, da bi izpolnili zahtevane pogoje. Stopalka zavore prispeva precejšen delež k velikosti zaostalih deformacij tudi takrat, ko je montiran v sestavu stopalke. Nakrčen spoj očitno omogoča lokalne deformacije oziroma popustitev pri preobremenitvi. Varjena izvedba se zato izkaže za ugodno spremembo pri postopku izdelave, kljub temu, da to prispeva nekaj dodatnih stroškov. Ta izvedba pomeni zmanjšanje elastične in trajne bočne deformacije pedala. Slednja se zmanjša za približno 1 mm. Izkazalo se je, da je način s katerim smo se lotili reševanja problema pravilen in da se s tem precej skrajša celoten postopek popravljanja sedanje konstrukcije. Z izdelavo analize sedanje konstrukcije smo dovolj dobro ocenili kritična mesta in sestavne dele, ki pojasnujejo problem, tj. prevelika trajna bočna deformacija sredine stopalke zavore. Na vsak način je treba poznati omejitve programa, s katerim je bilo opravljeno analitično delo, in seveda vse poenostavitve, ki smo jih privzeli pri izdelavi modela, ki naj bi pomenili približek k dejanskemu stanju. Rezultate trdnostnih analiz smo uporabili le kot smernice k načrtovanju merilnega mesta za testiranje, saj zaradi poenostavitev modela ne morejo biti izraz dejanskega stanja. Dejansko stanje smo določili z eksperimentalnim delom. Dobljene smernice so pomenile predvsem določitev kritičnega elementa konstrukcije (stopalka zavore) in pričakovano merilno območje (0 do 20 mm), ki ga bodo morala pokrivati zaznavala. Po teh podatkih je potekalo načrtovanje merilnega mesta in določitev merilne negotovosti za posamezno merilno verigo. Pokazala se je pomembnost te faze načrtovanja merilnega mesta, saj se je izkazalo, da izbrana oprema omogoČa zahtevano natančnost meritev (0,5%). Rezultati testiranj so potrdili kritičnost sestavnega dela, ki smo ga določili s trdnostno analizo. Ker so razlike med analitičnimi in eksperimentalnimi rezultati razmeroma velike, se je z opisanim postopkom ustvarila pomembna primerjalna baza podatkov za vrednotenje rezultatov podobnih analiz z MKE. removed, the remaining permanent deformation is also bigger. That is why we are convinced that the pedal is one of critical parts in the structure that had to be changed to satisfy structural demands. The brake pedal contributes a significant share to the total deformation of a structure when it is mounted. A compression-formed joint obviously al-lows local deformations to appear when an overload is applied. We saw that this joint suddenly relaxes. Although the welded joint is more expensive it does have benefits. This modification results in a reduc-tion of the elastic and residual plastic deformation of the brake pedal by approximately 1mm. We showed that the method used for re-solving the problem was correct. The process of design modification was shortened. Based on the results of the FEA we are able to correctly define the weakest part of a structure, which is the rea-son for the inadequate stiffness of the overall structure. However, we have to keep in mind the limitations of the FEA software and all the simplifications used to create the finite-element model. The results of the FEA were only used as guideline for system measurement planning and they are not a true representation of reality. The real stress-strain state of the structure was de-fined by the experiment. Guidelines were used to define the weakest part of structure (the brake pedal) and to define the measurement range (0-20mm) of the sensors. Based on those data we planned the measurement systems and later de-fined the measurement uncertainty. Our work showed the importance of this phase, because it proved that the measurements were accurate (0.5% deviation). The test results proved that using FEA the defined critical part is the actual one. Because the differences between the ana-lytical and the experimental results were still rela-tively large, the described method helped us to supplement the comparative database for similar structures and similar analyses. Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses 0,90 0,35 0 2000 0 ^^^15, 60 ^H*0"^^^ ^ 13,40 ^^ -8,90 - pomik P (F n EA) —t omik P (1000 N) pomik P (1500 N) ^^^f 17,10 ^X***^ j^^ ^ 13,40 ^^ -8,90 ------pomik P (FEA)-----pomik P (1000 N) pomik P (1500 N) translation translation translation 15,20 ^-^ 13,40 8,90 -pomik P (FEA) -pomik P (1000 N) pomik P (1500 N) t ranslati on 1000 Load / Obremenitev [N] 1000 Load / Obremenitev [N] nakrčen spoj compressed joint varjen spoj welded joint Sl. 14. Primerjava rezultatov meritev in trdnostne analize nakrčene in varjene izvedbe spoja na stopalki zavore Fig. 14. Comparisons of the experimental results and the results of the FEA on compressed and welded joints 3 SKLEP Glavni cilj raziskave je vpeljava trdnostnih analiz z metodo končnih elementov v zgodnje faze konstrukcijskega postopka. Rezultati tovrstnih analiz brez ustrezne razlage žal nimajo prave vrednosti. V prispevku je zato predlagana in na stvarnih primerih prikazana metoda za pridobitev primerjalne baze podatkov, na podlagi katere poteka vrednotenje rezultatov numeričnih izračunov. Glavna značilnost omenjene metode je ugotoviti ujemanje rezultatov preračuna z metodo končnih elementov in rezultatov eksperimentalne analize, s čimer se dokaže pravilnost v numeričnem modelu narejenih predpostavk in poenostavitev. Prednost numeričnih analiz, kakor je npr. analiza z metodo končnih elementov je velika stopnja prilagodljivosti, saj tovrstne analize omogočajo izračun napetostno-deformacijskih in drugih stanj izdelka pri različnih vrednostih konstrukcijskih parametrov brez izdelave fizičnih prototipov, če so na voljo le ustrezni trirazsežni računalniŠki modeli. 3 CONCLUSION The objective of the study was to introduce structural analyses based on the finite-element method in the early phases of the design process. Unfortunately, the results of such analyses without a proper interpretation are of almost no use. There-fore, in this article we suggest a method for acquiring the reference database, which serves for the valida-tion of the FEA results. The main characteristic of this method is to find out the consistency of the results computed on the basis of the FEM model with the experimental analyses, which proves the correctness of the assumptions concerning the static scheme of the mechanical structure. The advantages of the FEM lie in its great flexibility, which means that many design parameters can be changed to predict how they can influence the mechanical behaviour of the product without prototyping new models, once the 3D CAD files are available. grin^SfcflMISDSD VBgfFMK stran 92 20 20 15 15 10 10 500 1000 Load / Obremenitev [N] 1500 500 1000 Load / Obremenitev [N] 1500 2000 20 20 15 15 10 10 1,12 500 1000 Load / Obremenitev [N] 1500 2000 500 1000 Load / Obremenitev [N] 1500 2000 20 20 15 15 10 10 0,94 0,37 500 1500 2000 500 1500 2000 Bu~ar T. et al.: Vklju~itev numeri~nih analiz - Introducing Numerical Analyses Če povzamemo, numerične in eksperimentalne analize imajo pomembno vlogo pri konstruiranju zanesljivih izdelkov. Prve so uporabne za vrednotenje rešitev v zgodnjih fazah konstrukcijskega postopka, ko se ukvarjamo z izbiro materialnih lastnosti, izmer posameznih komponent, strukturo, obliko dotikalnih površin itn. Eksperimentalne analize se v tem primeru uporabljajo le za potrditev ustreznosti končnega fizičnega prototipa, pri katerem se izvaja testiranje oblike, materiala in tehnološkega postopka. In conclusion, both computational and ex-perimental methods play an important role in design-ing reliable products. The former is useful in the evaluation of the initial designing phase, where some parameters dealing with material properties, dimensions of components, structures and the shapes of con-tacting surfaces have to be chosen. The latter finds its proper application in the validation phase where a final prototype, which includes shape, material and technological process, has to be tested. 4 LITERATURA 4 REFERENCES [I] Duhovnik, J., J. Tavčar (2000) Elektronsko poslovanje in tehnični informacijski sistemi: PDMS-product data and management systems. Fakulteta za strojništvo, Ljubljana. [2] Pahl, G., W. Beitz (1993) Konstruktionslehre. Springer Verlag, Heidelberg, New York. [3] Golob B., A. Jezernik (2003) Predlog funkcijskih značilnosti faze zasnove v konstrukcijskem postopku. Strojniški vestnik, 49(2003)5, 275-286. [4] Hsu, W., I.M.Y. Won (1998) Current research in the conceptual design of mechanical products. Computer- Aided Design, Vol. 30, No. 5, 377-389. [5] Brunetti, G., B. Golob (2000) A feature-based approach towards an integrated product model including conceptual design information, Computer-Aided Design, 32, 877-887. [6] SAE (1995) RMS - Reliability, maintainability and supportability guidebook, 3rd edition. Society of Automotive Engineers. [7] Holman, J.P (1984) Experimental methods for engineers, 4th edition. McGraw-Hill international, Singapore. [8] Pallas-Areny, R., J.G. Webster (2001) Sensors and signal conditioning. John Wiley & Sons, NewYork. [9] Peace, G.S. (1993) Taguchi methods: a hands-on approach. Addison-Wesley. [10] Phadke, M.S. (1989) Quality engineering using robust design. Prentice-Hall international, London. [II] Janežič, M., T. Bučar (2003) Seminarska naloga pri predmetu Eksperimentalne metode v raziskovalnem delu. Fakulteta za strojništvo, Ljubljana. [12] Bučar, T, M. Janežič, M. Fajdiga (2003) Eksperimentalna analiza napetostno deformacijskega stanja ročne zavore. 6th Conference and Exhibition Innovative Automotive Technology IAT03, Portorož. [13] Janežič, M., T. Bučar, M. Fajdiga (2003) Primerjava numerične in eksperimentalne analize napetostno deformacijskega stanja ročne zavore. 6th Conference and Exhibition Innovative Automotive Technology IAT’03, Portorož. [14] Pangeršič, P, M. Fajdiga (2003) Eksperimentalno preverjanje numeričnih analiz mehanskih sklopov. 6th Conference and Exhibition Innovative Automotive Technology IAT’03, Portorož. Naslov avtorjev: Tomaž Bučar Authors’ Address: Tomaž Bučar Miha Janežič Miha Janežič Primož Pangeršič Primož Pangeršič prof.dr. Matija Fajdiga Prof.Dr. Matija Fajdiga Univerza v Ljubljani University of Ljubljana Fakulteta za strojništvo Faculty of Mechanical Eng. Aškerčeva 6 Aškerčeva 6 1000 Ljubljana SI-1000, Ljubljana, Slovenia tomaz.bucar@fs.uni-lj.si tomaz.bucar@fs.uni-lj.si miha.janezic@fs.uni-lj.si miha.janezic@fs.uni-lj.si primoz.pangersic@fs.uni-lj.si primoz.pangersic@fs.uni-lj.si matija.fajdiga@fs.uni-lj.si matija.fajdiga@fs.uni-lj.si Prejeto: Sprejeto: Odprto za diskusijo: 1 leto 11.11.2003 Received: Accepted: 8.4.2004 Open for discussion: 1 year