SAVREMENI RAZVOJ KONSTRUKCIJE I …mf.unze.ba/wp-content/uploads/2016/04/Masinstvo-num2-1999.pdfeach rotor lobe segment. ... of screw compressor design and development prac-tice

Ma{instvo 2(3), 63 - 78, (1999) N.Sto{i},..: SAVREMENI RAZVOJ KONSTRUKCIJE...

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Vij~ani kompresori su rotacione volumetrijske ma{inejednostavne konstrukcije koje mogu raditi na vrlovisokim brojevima obrtaja u {irokom dijapazonu radnihpritisaka i protoka ostvaruju}i visok stepen iskori{tenja.Oni su kompaktni i pouzdani tako da su danas natrzi{tu zastupljeni u vi{e od 80% slu~ajeva dok se upogonu ve} nalazi oko 50% vij~anih kompresora uodnosu na ukupan broj industrijskih kompresora.Osnovni razlog za ovako zna~ajan uspjeh vij~anihkompresora na trì{tu valja traìti u savremenom razvo-ju proizvodne tehnike koja je omogu}ila da se line-arne tolerancije pri proizvodnji rotora preciznim profil-nim glodanjem ili bru{enjem svedu na vrijednost niù

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Prof. dr Nikola Sto{i} i mr Ahmed Kova~evi}, Centre for Positive DisplacementCompressor Technology, City University, London EC1V OHB, U.K.

REZIME

Vij~ani kompresori dominiraju u oblasti kompresije zraka, procesnih plinova i u rashladnoj tehnici.Razvoj matematskih modela i unapre|enja u oblasti ra~unarske simulacije kombinovani sa rezulatimaeksperimentalnih istraìvanja ~ine snaàn sistem za analizu procesa i optimizaciju konstrukcije vij~anogkompresora. Kao rezultat, u nekoliko zadnjih godina profil zuba rotora vij~anog kompresora zna~ajnoje evoluirao i na taj na~in su pobolj{ane performanse ma{ine. Iako efikasnost rada vij~anog kom-presora najvi{e zavisi od profila zuba rotora kao i distribucije zazora izme|u rotora i izme|u rotora iku}i{ta kompresora, ostale komponente, kao {to su otvori na ku}i{tu, leàjevi, zaptivke i sistem zapodmazivanje, moraju biti tako projektovani da se u potpunosti iskoristi potencijal ostvaren razvojemprofila rotora.

Klju~ne rije~i: vij~ani kompresori, konstrukcija, proizvodnja

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Nikola Sto{i}, Ph.D. and Ahmed Kova~evi}, Ms.C., Centre for PositiveDisplacement Compressor Technology, City University, London EC1V OHB, U.K.

SUMMARY

Screw compressor dominate today compression of air, process gas and refrigerants. The recentadvances in mathematical modelling and computer simulation combined with experimental test dataform a powerful tool for process analysis and design optimisation. As a result, the screw rotors lobeprofiles have evolved over the past few years enhancing machine performance. Although an efficientoperation of screw compressors is mainly dependent on a rotor profile and clearance distribution,other components, like housing, ports, bearings, seals and lubrication system sholud be designed totake advantage of their potential if the full performance gains are to be achieved.

Key words: screw compressors, construction, manufacturing

1 INTRODUCTION

Screw compressors are rotary positive displace-ment machines of simple design with the movingparts comprising only two rotors rotating in fourto six bearings. They are capable of efficientoperation at high speeds over a wide range ofoperating pressures and flow rates. They aretherefore both reliable and compact and conse-quently they comprise 80% of all positive dis-placement compressors now sold and 50% ofthose currently in operation. Their remarkable suc-cess is mainly due to improvements in high accu-racy profile milling and grinding which now makeit possible to reduce linear tolerances to below

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od 10 µm. Na taj na~in se ostvaruje ekonomi~naproizvodnja rotora sa me|usobnim zazorima u grani-cama od 35-50 µm. Unutra{nje curenje se time svodina mali dio vrijednosti ostvarenih u prija{njim kon-strukcijama vij~anih kompresora. Kao rezultat se dobi-va manji vij~ani kompresor sa ve}im stepenom isko-ri{tenja u pore|enju sa ostalim tipovima kompresora.

Vij~ane ma{ine se danas upotrebljavaju kao kompre-sori ili kao ekspanderi i imaju najraznovrsnije namjene.Oni rade sa razli~itim vrstama radnih fluida koji mogubiti gasovi, pare ili vi{efazne mje{avine sa promjenomfaze unutar ma{ine. Mogu raditi bez unutra{njeg pod-mazivanja, ili kao uljno podmazivani, ili sa drugim flu-idom koji se ubrizgava u radni prostor za vrijemeprocesa kompresije ili ekspanzije ili prije ili poslije njih.Da bi se postigle optimalne karakteristike kompresora,razli~ite aplikacije vij~anog kompresora zahtijevajurazli~itu konstrukciju i druk~iji na~in rada. Zbog toganije mogu}e upotrebljavati univerzalne rotore ili izabratiuniverzalne radne parametre koji }e dati optimalnuefikasnost ~ak unutar vrlo uskog dijapazona radama{ine. Detaljna termodinamska analiza i poznavanjeuticaja razli~itih konstruktivnih parametara na karakte-ristike vij~ane ma{ine su, zbog raznolikosti primjene igeometrijske kompleksnosti ma{ine, sigurno mnogozna~ajniji i sloèniji nego u slu~aju drugih sli~nihma{ina. Odavde slijedi da je za optimalne performansema{ine za odre|enu primjenu neophodno dobropostaviti optimizacione kriterije. Ovakav pristup je, istotako, od velikog zna~aja za eventualna unapre|enjapostoje}ih konstrukcija vij~anih ma{ina i za pro{irenjedomena njihove primjene.

Industrijski kompresori komprimiraju zrak, rashladnefluide ili procesne plinove. Za svaku od ovih na-mjena konstrukcija ma{ine se mora razlikovati kakobi se postigli o~ekivani rezultati. U rashladnimma{inama i kod kompresije procesnih plinova, gdjeje vrijeme rada kompresora zna~ajno duè od vre-mena stajanja, obi~no se kao osnovni preduslovpostavlja visok stepen iskori{tenja kompresora. Zazra~ne kompresore, posebno u mobilnim agregatima,efikasnost moè biti nià i obi~no je manje znaàjnaod veli~ine kompresora i njegove cijene.Oblast kompresije zraka je, kako u sluàju suhoradnihtako i u slu~aju uljno podmazivanih kompresora, goto-vo isklju~ivo pokrivena vij~anim kompresorima. Situacijaje vrlo sli~na i u procesnoj industriji, dok se u ras-hladnoj tehnici klipni i lamelni kompresori sve vi{ezamjenjuju vij~anim kompresorima, tako da se u nare-dnim godinama moè o~ekivati dramati~no pove}anjezahtjeva za vij~anim rashladnim kompresorima.Veli~ina vij~anih kompresora koji se danas koriste ukomercijalne svrhe je izmedju 75 i 620 mm u

Ma{instvo 2(3), 63 - 78, (1999) N.Sto{i},...: SAVREMENI RAZVOJ KONSTRUKCIJE...

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10 µm. This permits rotors to be manufacturedwith interlobe clearances of 30-50 µm at an eco-nomic cost. Internal leakages are thus far lessthan in earlier machines of this type and as aresult, twin screw compressors are more efficientthan other types.

Screw machines are used today for different appli-cations both as compressors and expanders. Theyoperate on a variety of working fluids which maybe gases, dry vapours or multi-phase mixtureswith phase changes taking place within themachine. They may operate with oil flooding, withother fluids injected during the compression orexpansion process, or without any form of inter-nal lubrication. Their geometry may vary depend-ing on the number of lobes in each rotor, thebasic rotor profile and the relative proportions ofeach rotor lobe segment. It follows that there isno universal configuration which would be thebest for all applications. Hence, detailed ther-modynamic analysis of the compression processand evaluation of the influence of the variousdesign parameters on performance is more impor-tant to obtain the best results from thesemachines than from other types which could beused for the same application. It follows that aset of well defined criteria governed by an opti-misation procedure is a prerequisite for achievingthe best design for each application. Such guide-lines are also essential for the further improve-ment of existing screw machine designs andbroadening their range of uses.

Typically, refrigeration and process gas compres-sors, which operate for long periods, must bedesigned to have a high efficiency. In the case ofair compressors, especially for mobile applications,efficiency may be less important than size andcost.

For both dry and oil free air compression, screwcompressors are used almost exclusively. This isalso gradually becoming the case for process gascompression. In the field of refrigeration, the useof reciprocating and vane compressors isdecreasing and a dramatic increase in favour ofscrew machines is expected in the next fewyears.

Screw compressors in normal commercial usagetoday have main rotors whose outer diameters varybetween 75 mm and 620 mm. These deliverbetween 0.6 m3/min and 600 m3/min of compressedgas. The normal pressure ratios attained in a single

stage are 3.5:1 for dry compressors and up to 15:1for oil flooded machines. Normal stage pressuredifferences are up to 15 bars, but maximum valuessometimes exceed 40 bars. Typically, for oil flood-ed air compression applications, the volumetric effi-ciency of these machines now exceeds 90 % whilespecific power inputs, which are both size and per-formance dependent, have been reduced to valueswhich were regarded as unattainable only a fewyears ago.

2 SCREW COMPRESSOR PRACTICE

Svenska Rotor Maskiner (SRM), a Swedish compa-ny, was the pioneer and are still leaders in the fieldof screw compressor design and development prac-tice. Other companies, such as Compair in the U.K,Atlas-Copco in Belgium, Ingersoll-Rand and DenverGardner in the USA and GHH in Germany are themain air compressor manufacturers. York, Trane andCarrier in the USA lead in refrigeration and air con-ditioning applications. Japanese screw compressormanufacturers, such as Hitachi, Mycom and Kobe-Steel are also well known. In recent years therehave been a number of mergers and buy outs ofsmaller companies by these larger ones. New mar-kets in China, India and other developing countriesin the Middle and Far East have led to new screwcompressor companies being founded there as wellas factories being built there by the major manu-facturers. Although they do not manufacture com-pressors, Holroyd, a British company is the world'slargest screw rotor manufacturer. They are alsoworld leaders in tool design and machine tool pro-duction for the manufacture of screw compressorrotors.

Despite the rapid growth in screw compressorusage, public knowledge of the scientific basis oftheir design is still limited. Three classical screwcompressor textbooks were published in Russia inthe early nineteen sixties. [40] 1960 gives a fullanalysis on how to generate circular, elliptic andcycloidal rotor profiles as well as a russian asym-metric profile later named SKBK. The method of pro-file generation in this book was based on an enve-lope approach. [2], 1961 demonstrates this theoryand, in addition, makes a contribution to the fieldof rotor tool profile generation. [15], 1964, is a moregeneral textbook but its section on screw compres-sors is very interesting and informative. A Russianhandbook, [1], published in 1977, gives a repro-ducible presentation of how to generate the SRM

pre~niku vode}eg rotora. Dobava tih kompresora jeizmedju 0,6 i 600 m3/min gasa na uslovima usisa.Odnos pritisaka je oko 3.5 za suhoradne kompre-sore dok se za uljnopodmazivane kre}e do 15.Uobi~ajena razlika pritisaka je do 15 bara ali se unekim slu~ajevima de{ava da ona prelazi 40 bara.Volumetrijsko iskori{tenje uljno podmazivanih vij~anihkompresora obi~no je preko 90%, tako da je danasspecifi~na snaga vij~anih kompresora svedena navrijednosti koje su se prije samo nekoliko godinasmatrale nemogu}ima.

2 SKRIVENI DETALJI

[vedska kompanija SRM je pionir u razvoju i pri-mjeni vij~anih kompresora. I drugi proizvo|a}i, kao{to su Compair u Velikoj Britaniji, Atlas-Copco uBelgiji, Ingersol-Rand i Denver Gardner u Americi,GHH u Njema~koj, nalaze se neposredno do njih.York, Trane, Carrier i Bitzer su vode}e kompanijekoje vij~ane kompresore koriste u rashladnoj tehni-ci i klimatizaciji. Japanski proizvo|a}i vij~anih kom-presora, kao {to su Hitachi, Mycom i Kobe-Steel sutako|er vrlo dobro poznati. U zadnje vrijeme se naSrednjem i Dalekom Istoku pojavljuje veliki broj kom-panija koje se se bave vij~anim kompresorima.Otvaranjem novih trì{ta, u Kini i Indiji, a i u drugimzemljama u razvoju dolazi do otvaranja fabrikavij~anih kompresora. Iako se ne bavi proizvodnjomvij~anih kompresora, Britanska kompanija Holroyd jenajve}i proizvo|a} rotora za vij~ane kompresore ivode}i konstruktor i proizvo|a} alata i ma{ina zaproizvodnju rotora vij~anih kompresora.

Iako popularnost vij~anog kompresora raste iz danau dan, otvorena literatura je u toj oblasti jo{ uvijekograni~ena. Tri klasi~ne knjige o vij~anim kompre-sorima su publikovane na ruskom jeziku u ranim{ezdesetim godinama. [40] 1960, daje potpuni pre-gled na~ina generisanja kru`nog, elipti~nog i cik-loidnog profila i u detalje izvodi ruski asimetri~niprofil kasnije nazvan SKBK. Na~in generisanja profi-la opisan u toj knjizi bazira se na takozvanom meto-du obvojnice. [2] 1961. ponavlja teoriju generacijeprofila time daju}i svoj doprinos oblasti profilisanjaalata za proizvodnju rotora. [15] je knjiga sa gene-ralnom kompresorskom tematikom, ali je dio ovij~anim kompresorima vrlo interesantan i informati-van. Priru~nik [1] na ruskom jeziku iz 1977 godinedaje potpuno reproducibilan prikaz asimetri~nogSRM profila 5 godina nakon {to je ovaj patentiranskupa sa Lysholmovim profilom. Dvije knjige su pub-likovane na njema~kom jeziku [35] 1979, prezentirametod generacije profila baziran na teoriji zup~anika


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kako bi rekonstruisao SRM asimetri~ni profil 7 go-dina nakon {to je patentiran, a [23] 1988, publikujeneke inènjerske aspekte vij~anih kompresora.Mali je broj knjiga koje se bave vij~anim kompre-sorima objavljen na engleskom jeziku: [32] 1993, oindustrijskim kompresorima i [3] 1994 o rotacionimkompresorima sa dva vratila. Me|utim, sve one susuvi{e generalne da bi bile razmatrane kao refer-entna literatura o vij~anim kompresorima. Nekoliko priru~nika o vij~anim kompresorima suobjavili proizvo|a}i vij~anih kompresora, isto kao iodre|eni broj bro{ura koje daju korisne informacije,ali su one ili povjerljive ili su nedostupne i dalekood javnosti. Neke od njih, kao {to je, na primjer,SRM Data Book, ina~e dobro ~uvane i dostupnesamo licensorima, ~esto su citirane kao literatura izoblasti vij~anih kompresora.

Me|utim, broj patenata koji su se pojavili u zadnjihtrideset godina je neproporcionalno velik, moè sere~i da je patenata objavljeno na hiljade. Samo jeSRM objavio 750 patenata. Svi se patenti baverazli~itim aspektima vij~anih kompresora a njihovnajve}i broj profilima rotora. SRM je objavio patente[33] 1946 simetri~nog, [41] 1973 za asimetri~ni i [4]1982 za "D" profil. Oni su klasi~na referentna liter-atura koja prikazuje vje{tinu profilisanja rotoravij~anog kompresora. Jo{ neki patenti mogu sespomenuti kao primjer uspje{nog na~ina generacijeprofila: Atlas-Copco, Compair [19], Denver Gardner[9], Hitachi [20], Ingersol-Rand. U posljednjih jenekoliko godina jedan broj relativno malih kompani-ja objavio vi{e izuzetno uspje{nih patenata, kao {tosu, na primjer, [24] i [8]. Potpuno novi pristup gen-eraciji profila po kojem se polazne krive zadaju nazup~astom stapu objavljen je u [37] i u [50].

Svi patentirani profili su generisani na osnovu nekevaljane metode, ali su korisne informacije okori{tenim metodama pa`ljivo uklonjene iz patenta iliiz prate}ih publikovanih radova. Informacije u paten-tima su ili sakrivene ili je iz njih gotovo nemogu}edirektno dobiti profil. Ova se ~injenica moè ilus-trovati kroz tri primjera. U radu [29] 1978 objavljujese izvodjenje simetri~nog kru`nog profila koji jepatentiran 32 godine prije toga. U [35] se koristiklasi~nim uslovima sprezanja konjugovanih zup~anikada bi reprodukovao asimetri~ni SRM profil 9 godinanakon {to se patent pojavio. Kao kuriozitet moè sepomenuti da je jedan SRM-ov licencor, nakon 13godina proizvodnje kompresora, iskoristio savakademski potencijal kako bi analiti~ki reprodukovaoSRM "D" profil.


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asymmetric profile only 5 years after it was patent-ed as well as the classical Lysholm profile. Thereare two German textbooks. [35], 1979, used a pro-file generation method based on gear theory toreconstruct the SRM asymmetric profile 7 years afterit was patented. [23], 1988, published some engi-neering aspects of screw compressors.

Only recently have any textbooks on screw com-pressors been published in English. [32], 1993, wason industrial compressors and [3], 1994, was onrotary twin shaft compressors. However, these aretoo general to be useful as detailed reference liter-ature.

A few compressor manufacturers' handbooks onscrew compressors and a number of brochures giveuseful information, but they are either classified orof very limited accessibility. Some, like the SRMData Book, although cited in screw compressor lit-erature, are available only to SRM licencees.

Literally thousands of patents have been awardedon screw compressors in the past thirty years andSRM alone has 750. They cover various aspects ofscrew compressor design but are mainly for rotorprofiles. SRM patents [33], 1946, for symmetric,[41], 1973, for asymmetric and [4], 1982, for the"D" profiles are classical examples of state of theart screw compressor profile generation. Othersuccesful profiling patents are those of Atlas-Copco,Compair [19], Denver Gardner [9], Hitachi [20] andIngersoll-Rand [6]. In recent years, several highlysuccessful patents such as [24] and [8] have beengranted to relatively small companies. A freshapproach to profile generation based on the use ofa rack for the primary curves was published in [37]and [50].

Although all patented profiles were generated bywell defined procedures, so little of the methods onwhich they were based was published that it wasvery difficult to reproduce them. Thus details of howto derive the circular symmetric profile, [29], werenot published until 1978, 32 years after it waspatented. Similarly, a derivation of the SRM asym-metric profile based on classical gear conjugacy cri-teria, [35], was not published until 9 years after thepatent appeared. It is even more interesting to notethat one SRM licencee funded a university researchprogramme to obtain an analytical derivation of theSRM "D" profile in 1995, after 13 years of manu-facturing it.

Me|u patentima iz podru~ja vij~anih kompresora moguse na}i i oni koji se bave drugim aspektima oveoblasti. Uglavnom su patentirane sve dobro poznatekarakteristike vij~anih kompresora, kao {to je ubrizga-vanje ulja, usisni i tla~ni otvori koji prate helikoidurotora, kompenzacija aksijalnih sila, rastere~enje kom-presora, usisni klip, ekonomajzerski otvor, uglavnom odstrane SRM-a, ali i neke druge kompanije tako|er vrlorevnosno objavljuju patente. Izgleda da patentnistru~njaci za vij~ane kompresore imaju isti ili sli~anzna~aj kao i inènjeri koji se bave njihovim razvojem.

Iako su ~lanci o vij~anim kompresorima rijetkost u~asopisima, oni su izuzetno korisna literatura o kom-presorima mada ne odaju mogo detalja o profilisanjuvij~anih kompresora. Tako Lysholmovi klasi~ni ~lanci[26] iz 1942 i [27] iz 1966 ne spomenju ni jedan detaljo profilisanju koje je autor koristio u svojoj uspje{nojpraksi da bi pobolj{ao zaptivenost kompresora. ^lanci[45] i [46] se mogu vi{e smatrati izuzetkom nego prak-som. U posljednje vrijeme je objavljivano ne{to vi{ematerijala o vij~anim komopresorima u ~asopisima, {toje podstaknuto od strane nekoliko institucija, kao {tosu International Institution of Refrigeration [15] i [48],IMechEng [44], [12], [13], [55] i [57] i ASME [16] i [51].Ovakvom aktivno{}u je u nekoliko zadnjih godina u~asopisima distribuirano vi{e informacija o vij~animkompresorima nego {to je objavljeno tokom svihprethodnih godina zajedno. [52] je primjer ~lanka kojije objavljen u skladu sa najmodernijim trendovima vre-menski dobro izabranog trenutka za publikovanje.

Tri kompresorske konferencije su u potpunosti ili djelo-mi~no orjentisane na vij~ane kompresore: PurdueCompressor Technology Conference u Lafayette, SAD,IMechEng konferencija o industrijskim kompresorima uLondonu, Engleska i "VDI SchraubenkompressorenTagung" u Dortmundu, Njema~ka. Usprkos obilju~lanaka o vij~anim kompresorima, samo mali broj~lanaka sa konferencija daje korisne informacije o pro-filisanju rotora vij~anog kompresora i o konstrukcijamakompresora. Svi ~lanci sa konferencija daju valjanprikaz obavljenih istraìvanja ali skoro ni jedan od njihne daje reproducibilne informacije koje se odnose nakori{tene metode profilisanja. ^lanci kakakteristi~ni zaPurdue konferenciju su oni koji se vrlo ~esto citiraju,ali iz kojih ~italac moè saznati vrlo malo o generacijiprofila, kao {to su: [11], [47] i [49], a tako|er i [42],[43], [53] i [56]. ^lanci [34], [58], [59] i [60] ukazuju na toda je teorija obvojnice naj~e{}e kori{tena metoda zaizra~unavanje geometrijskih karakteristika rotora. Uzbornik radova sa Dortmundske konferencije nalazi seodre|eni broj vrlo interesantnih ~lanaka o vij~animkompresorima. [36] iz 1984 prezentira na~in gene-risanja profila na bazi zup~astog {tapa pri ~emu dajepotpuno reproducibilan patent [37] baziran na klasi~noj


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Most of the well known characteristics of screwcompressors, such as oil flooding, making the suc-tion and discharge ports follow the rotor tip helices,axial force compensation, unloading, the slide valveand the economizer port, were also patented, main-ly by SRM. However other companies were equal-ly keen to file patents. It appears that, in the fieldof screw compressors, patent experts are as impor-tant as engineers.

There are surprisingly few journal publications onscrew compressors in the technical literature.Notable exceptions are Lysholm's [26-27] classicalpapers of 1942 and 1966. However neither ofthese described any of the profiling details whichhe developed successfully in order to reduce theblow-hole area. Other exceptions are [45] and[46]. In recent years, journal publication of screwcompressor material has been encouraged by theInternational Institution of Refrigeration [15] and[48], the IMechE [44], [12], [13], [55] and [57] andASME [16] and [51]. This led to more informa-tion on screw compressors in journals duringrecent years than in all previous years together.[52] is an example of the modern practice of moretimely publishing.

There are three compressor conferences which dealexclusively or partly with screw compressors. Theseare: the Purdue University compressor technologyconferences in the U.S.A, the ImechE conferenceson industrial compressors in England and the "VDISchraubenkompressoren Tagung" in Germany.Despite the wealth of screw compressor paperswhich these contain, very few give useful informa-tion on rotor profiling procedures and compressordesign.

Typical Purdue papers, frequently cited, from whicha reader will gain a little on profile generation are:[11], [47] and [49] , also [42], [43], [53], [56]. Refs[34], [58], [59], and [60] indicate that envelope theo-ry was used to calculate some geometric featuresof their rotors.

The "VDI Schraubenkompressoren Tagung" pro-ceedings contain some interesting screw com-pressor papers. [36] 1984 presents a rack methodof rotor profile generation, based on classicalgearing theory, which is fully reproducible.Unfortunately, although soundly conceived, profilesproduced by this method were not commerciallysuccessfull because of their poor tightness. [16]and [18] give some more details on profiling andmanufacturing control. [21], [22] and [54] are typi-

cal examples of successful university researchapplied to solve real engineering problems. [38]and [39] may be regarded as examples of fineengineering work.

Although relatively infrequent, the London compres-sor conferences included some interesting papers,such as [10].

Many reference textbooks on gears give a usefulbackground to screw rotor profiling. However all ofthem are limited to the classical gear conjugateaction condition. One example of this is [7]. [25] isan exception to this practice which contains geartheory directly applicable to screw compressor pro-filing.

3 RECENT DEVELOPMENTS

The efficient operation of screw compressors ismainly dependent on proper rotor design. An addi-tional and important requirement for the successfuldesign of all types of compressor is the ability topredict accurately the effects on performance ofthe change in any design parameter such as clear-ance, rotor profile shape, oil or fluid injection posi-tion and rate, rotor diameter and proportions andspeed.

Now that tight clearances are achievable, internalcompressor leakage rates become small. Hence, fur-ther improvements are only possible by the introduc-tion of more refined design principles. The mainrequirement is to improve the rotor profiles so thatthe internal flow area through the compressor is max-imised while the leakage path is minimised and inter-nal friction due to relative motion between the con-tacting rotor surfaces is made as small as possible.

Although rotor profiling procedures may appear to befully defined, substantial improvements are still pos-sible. The most promising approach for this seemsto be through rack profile generation which givesstronger but lighter rotors with higher throughput andlower contact stress. The latter enables fluids withlower viscosity than oil to be used for lubrication.

Rotor housings with better shaped ports can bedesigned using multivariable optimization techniques.Flow losses may thereby be reduced permittinghigher rotor speeds and hence more effective com-pressors.

teoriji zup~anika. Me|utim, naàlost, na prikazani na~indobiveni profil, iako baziran na odli~nim osnovamanema velik komercijalni zna~aj zbog vrlo slabog za-ptivanja. [16] i [18] daju ne{to vi{e detalja o profilisanjui kontroli proizvodnje. [21], [22] i [54] su tipi~ni primjeriuspje{nog akademskog istraìvanja primjenjenog nastvarno inènjerstvo. [38] i [39] se mogu nazvati pri-mjerom prakti~ne primjene preciznog inènjerskograda. Londonska kompresorska konferencija, iako netako u~estala, dala je nekoliko vrlo interesantnih ~lana-ka kao {to je, na primjer [10].Mnoge referentne knjige o zup~anicima su korisnapolazna osnova za profilisanje rotora vij~anog kom-presora, ali je ve~ina od njih ograni~ena na klasi~euslove sprezanja zup~anika. Kao primjer se moèista}i klasi~na knjiga [7]. Knjiga [25] se moè sma-trati izuzetkom od ovog pravila jer daje teorijusprezanja zup~anika koja se direktno moè primijenitii na profilisanje rotora vij~anog kompresora.

3 SAVREMENI RAZVOJ VIJÂNOGKOMPRESORA

Efikasan rad vij~anog kompresora uglavnom zavisiod pravilne konstrukcije njegovih rotora. Dodatno sekao uslov za uspje{nu konstrukciju razli~itih vrstakompresora postavlja i sposobnost da se radnekarakteristike mogu precizno predvidjeti u slu~aju dase promijeni bilo koji parametar kao {to je na pri-mjer zazor, oblik profila rotora, pozicija i koli~inaubrizganog ulja ili nekog drugog fluida u radni pro-stor, pre~nik i proporcija rotora i brzina obrtanja.

Danas, kad su zazori u kompresoru mali, unutra{njecurenje koje ima veliki uticaj na efikasnost sve vi{ezavisi od duìne linije dodira rotora, tako da kaomogu}nost za pobolj{anje kompresora ostaje jo{samo bolje profilisanje rotora. Tako se posebnapa`nja posve}uje unapredjenju karakteristika rotorada se, {to je god vi{e mogu}e, pove}a unutra{njiprotok kompresora a da se linija dodira izmedjurotora smanji, te da se istovremeno unutra{nje tre-nje usljed relativnog klizanja dodirnih povr{ina roto-ra u~ini {to je mogu}e manjim.Mada na prvi pogled izgleda da je u profilisanju roto-ra dosad u~injeno sve {to je bilo mogu}e, to jedaleko od istine. U stvari, ima jo{ mnogo prostora zazna~ajna pobolj{anja. îni se da na~in profilisanja kojikao polaznu osnovu uzima zup~asti {tap, ima najvi{eizgleda da postigne najbolje rezultate jer se njimemogu dobiti ja~i i lak{i rotori sa ve}om dobavom imanjim kontaktnim naponima. Ovo posljednjeomogu}ava da se u radni prostor kompreora ubriz-gava fluid niè viskoznosti.Kori{tenjem metoda vi{eparametarske optimizacijedobivaju se sve bolje oblikovani otvori na ku~i{tuvij~anog kompresora. Time se smanjuju gubici na


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usisu i na izlazu {to omogu}ava pove}anje brojaobrtaja kompresora, a time se direktno pove~ava injegova efektivnost.Zna~ajni uspjesi su u nekoliko zadnjih godina posti-gnuti i u razvoju leàjeva za kompresore, ~ime je omo-gu}eno podmazivanje kompresora fluidom viskoznostimanje nego kod obi~no kori{tenih ulja. Zaptiva~i su,takodjer, mnogo efikasniji nego ranije. Sve ovo je dalodobru osnovu za efikasniji rad kompresora.

3.1 Profili rotora

Naj~e{}e kori{ten metod generacije profila rotoravij~anog kompresora je da se defini{e primarni pro-fil na jednom od rotora a da se nakon toga traèodgovaraju}e krive na drugom rotoru primjenomrazli~itih uslova sprezanja. Na osnovnom rotoru jemogu}e definisati bilo koju krivu liniju ali je tradi-cionalno naj~e{}e kori{tena kriva upravo kru`nica.Bilo koja kru`nica sa centrom na podionom krugugenerisa}e sli~nu kru`nicu na drugom rotoru. Istasituacija se dobije ako je centar kru`nice u osi roto-ra. Kru`nice sa centrom van podionog kruga na istina~in kao i ostale krive: elipsa, parabola ili hiperbo-la proizve{}e na drugom rotoru neku generisanukrivu, koja se naziva trohoida. Sli~no tome, ta~kakoja je fiksirana na jednom rotoru generisa}e epi- ilihipocikloidu na drugom rotoru. Sva vje{tina profi-lisanja rotora se decenijama svodila na pravilan izborprimarnih krivih na jednom rotoru koje }e omogu}itiizvo|enje odgovaraju}eg profila na drugom rotoru.

Kru`ni simetri~ni profil se sastoji samo od kru`nica,dok se Lysholmov profil, osim od kru`nica posta-vljenih u centar podionog kruga, sastoji od sistemacikloida na strani visokog pritiska ~ime je dobivenprvi asimetri~ni profil rotora vij~anog kompresora. Zaasimetri~ni SRM profil je prvi put iskori{tena eks-centri~na kru`nica na strani niskog pritiska navo|enom rotoru dok je na SKBK profilu isto ura|enona vode}em rotoru. U oba slu~aja su izvedene kriveanaliti~ki definisane kao epi- ili hipocikloide. SRM"D" profil se sastoji samo od kru`nica od kojih suneke sasvim male, ali su sve ekscentri~no postavl-jene na vode}em ili vo|enom rotoru. Svi patenti kojislijede nakon toga baziraju se na definisanju jednogod rotora i izvo|enju drugog, i svi su, vjerovatno,bazirani na klasi~nom sprezanju zup~anika ili nanekim sli~nim uslovima. Tek u posljednje vrijemekru`nice su postepeno zamjenjuju nekim drugimkrivuljama kao {to su: elipsa kod FuSheng profila[24], parabola na Compair [19] i Hitachi profilima ihiperbola na "hyper" profilu [8]. îni se da je hiper-bola na posljednjem profilu odgovaraju}a zamjena zaostale krive, jer daje najbolji odnos dobave rotora iduìne linije zaptivanja.


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3.1 Rotor Profiles

The normal procedure used to generate rotor pro-files is to create primary profile curves on one rotorand, by use of an appropriate conjugate criterion,a corresponding secondary profile curve on theother. Any curve can be used as the primary one,but traditionally a circle is the most comon. All cir-cles with their centres on the pitch circle generatea similar circle on the other rotor. This is also trueif the circle centres are at the rotor axes. Circleswith centres not on the pitch circle and othercurves, like ellipses, parabolae and hyperbolaerequire more elaborate curves to be generated, onthe other rotor which are described as trochoids.Similarly, points located on one rotor will cut epi-or hypocycloids on the other rotor. For decades,the skill required to produce rotors was limited tothe ability to choose a primary arc which wouldpermit the derivation of an appropriate secondaryprofile.

The symmetric circular profile consist of circles only.Apart from the use of pitch circle centred circles,Lysholm introduced a set of cycloids on the highpressure side to form the first asymmetric screwrotor profile. Later the SKBK profile used the samecurves. The SRM asymmetric profile employs aneccentric circle on the low pressure side of thegate rotor. In all these cases the curves evolvedanalytically from them were epi- or hypocycloids.The SRM "D" profile consists exclusively of circles,almost all of them eccentrically positioned on themain or gate rotor. All patents which followed, spec-ify primary curves on one rotor and secondary gen-erated curves on the other rotor. All are probablyderived from classical gear contact theory or a sim-ilar alternative criterion. More recently, circles havegradually been replaced by other curves such asellipsae in the FuSheng profiles [24], parabolae inthe Compair [19] and Hitachi [20] profiles and hyper-bolae in the 'Hyper' [8] profile. Replacing the circleby a hyperbola in the latest profile, seems to givethe best ratio of rotor displacement to sealing linelength.

Another method of rotor profile generation is toconsider imaginary, or 'nonphysical' rotors. Sinceall gearing equations are independent of the coor-dinate system in which they are expressed, it ispossible to define primary arcs as given curvesusing a coordinate system which is independent ofboth rotors. By this means, in many cases thedefining equations may be simplified. Also, the

Drugi na~in na koji je mogu}e definisati profil roto-ra je da se osnovne krive izaberu na nekomzami{ljenom, "nefizikalnom" rotoru. Po{to su svejedna~ine zup~anika neovisne od koordinatnog siste-ma u kojem su izraène, primarni luk je mogu}edefinisati i u nekom koordinatnom sistemu koji je neovisi ni o jednom rotoru. U ve~ini slu~ajeva se nataj na~in jedna~ine mogu pojednostaviti. Upotrebajednog koordinatnog sistema za definisanje svih kri-vih na rotoru tako|er moè pojednostaviti procesprofilisanja. Tako se polazni profil u cijelosti moèdefinisati u koordinatnom sistemu koji ne zavisi odrotora, {to vrijedi i za rotor sa beskona~nimpre~nikom koji se naziva zup~asti {tap. Prvi ikadapublikovani patent koji prikazuje ovakvu generacijiprofila rotora [30] objavljen 1977, iako nije prakti~noprimjenljiv, vje{to koristi pomenutu teoriju. [37] i kas-nije [50] prvi daju dobru osnovu za generaciju pro-fila vij~anog kompresora.

Efikasan vij~ani kompresor mora imati rotore ~iji pro-fil osigurava veliki proto~ni presjek, kratku liniju zap-tivanja i mali nezaptiveni prostor na vrhu rotora. Tozna~i, da je za ve}i proto~ni presjek i broj obrtajakompresora, i dobava kompresora ve}a. Kra}e linijedodira i manji nezaptiveni prostor smanji}e unutra{njecurenje. Ve}a dobava i manje curenje }e pove}ativolumetrijski stepen iskori{tenja kompresora, koji jedefini{an kao dobava podijeljena zbirom ukupnogprotoka i curenja. Time se dalje pove}ava adijabat-ski stepen iskori{tenja, jer se za kompresiju gasa kojirecirkuli{e unutar kompresora tro{i manje snage.

Izbor odnosa veli~ine nezaptivenog prostora i brojaradnih zapremina zavisi}e od namjene kompresora.Kako je za manje razlike pritisaka curenje propor-cionalno manje, dobici postignuti velikim proto~nimpresjekom mogu poni{titi ili smanjiti gubitke nastaleusljed velikog nezaptivenog prostora. Na sli~an na~inse moè dobiti optimalni broj zuba vij~anog kom-presora, po{to manji broj zuba daje ve}i proto~nipresjek ali i rezultira u ve}oj razlici pritiska izme|uradnih prostora.

Sa smanjenjem zazora izmedju rotora, bez obzira napodmazivanje kompresora uljem, vjerovatno}a dire-ktnog dodira me|u rotorima sa pove}ava. Dodirme|u rotorima dovodi do pove}anja kontaktnih sila ioptere}enja rotora {to dalje uzrokuje deformacijuvo|enog rotora. Zbog toga, njegov profil mora bitikonstruisan tako da se rizik od pucanja ili plasti~nedeformacije rotora smanji na najmanju mogu}u mjeru.

Brzi razvoj metoda matematskog modeliranja ira~unarske simulacije je, u posljednje vrijeme, pod-stakao i olak{ao istraìvanje novih profila rotora.


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use of one coordinate system to define all thecurves, simplifies the design process. Typically, thetemplate is specified in a rotor independent coor-dinate system. This is valid for a rotor of infiniteradius, which is a rack. From this, a secondary arcon some of the rotors is obtained by a procedure,which is called 'rack generation'. The first patenton rack generation published, [30], is based onthis theory but lacks practicality. [37] and, morerecently, [50] give a good basis for rotor profilegeneration.

For a screw compressor to be efficient, the rotorprofile must form a large flow cross section area, ashort sealing line and a small blow-hole area. Thelarger the cross section area, the higher the flowrate for the same rotor sizes and speeds. Shortersealing lines and a smaller blow-hole reduce leak-ages. Higher flow and smaller leakage rates bothincrease the compressor volumetric efficiency, whichis the rate of flow delivered as a fraction of thesum of the flow plus leakages. This in turn increas-es the adiabatic efficiency because less power iswasted in the compression of gas which is recir-culated internally.

The optimum choice between blow hole and flowareas depends on the compressor duty since, forlow pressure differences, the leakage rate will berelatively small and hence the gains achieved bya large cross section area may outweigh the loss-es associated with a larger blow-hole. Similar con-siderations determine the best choice for the num-ber of lobes since fewer lobes imply greater flowarea but increased pressure difference betweenthem.

As precise manufacture permits rotor clearances tobe reduced, despite oil flooding, the likeliehood ofdirect rotor contact is increased. Hard rotor contactleads to deformation of the gate rotor, increasedcontact forces and ultimately rotor seizure. Hencethe profile should be designed so that the risk ofseizure is minimised.

The search for new profiles has been both stimu-lated and facilitated by recent advances in mathe-matical modelling and computer simulation. Theseanalytical methods may be combined to form apowerful tool for process analysis and optimisationand thereby eliminate the earlier approach of intu-itive changes, verified by tedious trial and error test-ing. As a result, this approach to the optimumdesign of screw rotor lobe profiles has substantial-

Analiti~ke metode je mogu}e kombinovati na tajna~in da se dobije mo}no sredstvo za analizu i opti-mizaciju procesa vij~anog kompresora, ~ime se upotpunosti moè zaobi}i ranije kori{tena metoda intu-itivne konstrukcije zasnovana na mukotrpnom metodupoku{aja i pogre{ke. Kao rezultat, ovaj pristup opti-malnom konstruisanju rotora vij~anog kompresorazna~ajno je evoluirao u nekoliko zadnjih godina savelikim {ansama da se u narednim godinamapostignu dalja pobolj{anja karakteristika ma{ine.Me|utim, i geometrija rotora, isto kao i radni procesu vij~anom kompresoru su toliko kompleksni da jepotrebno uvesti niz aproksimacija kako bi modeliran-je bilo ostvarivo. Kao posljedica, u otvorenoj litera-turi se mogu na}i matematski modeli i numeri~kikodovi sa vrlo {arolikim pristupom problemu i sarazli~itim matematskim nivoima modeliranja fenomenau vij~anom kompresoru. Nedostatak uporediviheksperimentalnih rezultata jo{ uvijek onemogu}avaverifikaciju i svestranu ocjenu razli~itih koncepcijamodeliranja. Uprkos tome, matematsko modeliranje isimulacija ra~unarom sve vi{e dobivaju na popu-larnosti i sve se vi{e koriste za unapre|enje kon-struktivnih karakteristika vij~anog kompresora.

Na slici 1. prikazan je niz rotora vij~anog kompre-sora tako da se oni mogu me|usobno usporediti.Profili su ozna~eni brojevima u zagradama, koji upopisu literature ukazuju na patente za te rotore.

U prvu prikazanu grupu spadaju rotori sa 4 zuba navode}em i 6 zubi na vo|enom rotoru. Ovakva kon-figuracija rotora je kori{tena skoro za svaku aplikaci-ju. Asimetri~ni SRM profil [41], koji se moè sma-trati do sada najuspje{nijim profilom rotora vij~anogkompresora, nalazi se na po~etku. Slijede}i je SRM"D" profil [4]. Na kraju je prikazan profil generisanna osnovu zup~astog {tapa - rack generisan profil[50]. Izbor i raspored osnovnih krivih na zup~astom{tapu pomo}u kojih su generisani ovi rotori dajeve}i popre~ni presjek me|uzublja i ja~i zub vo|enogrotora u odnosu bilo koji drugi poznati profil rotoravij~anog kompresora ove konfiguracije.

Konfiguracija vij~anog kompresora sa 5 zubi vode}egi 6 zubi vo|enog rotora postaje sve popularnija, jerse njome postize kompromis izmedju velike dobave ivelikog tla~nog otvora sa skoro nenadma{nim struj-nim karakteristikama za manji pre~nik rotora.Kompresori sa ovakvom konfiguracijom rotora su jed-nako pogodni za kompresiju zraka kao i za rashla-dnu tehniku ili za klimatizaciju. U nastavku je, radiupore|enja, data ve}a skupina ovih rotora kojapo~inje sa SRM "D" profilom [4], nakon toga slijede"Sigma" profil [5], FuSheng [24] i "Hyper" profil [8].Svi ovi profili su 'rotor generisani' profili a osnovna


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ly evolved over the past few years and is likely tolead to further improvements in machine perfor-mance in the near future.

A comparison of several pairs of screw compressorrotors is shown in Fig. 1. Each pair is labeled bya number in brackets which denotes its patent.

The first group gives rotors with 4 lobes on themain and 6 lobes on the gate rotor. This rotor con-figuration is the most universally accepted for almostany application. The SRM asymmetric profile [41],which historically was the most successful, is on thetop. The next one is the SRM "D" profile [4]. TheIngersol-Rand profile, [6], shows how attempts weremade to produce more displacement from the samecompresor size. Finally, rack generated rotors [50]are presented.

The second group shown are 4/5 rotors which isbecoming a very popular combination for oil-flood-ed air compressors. The first pair, SRM "D" [4]rotors are applied in "Tamrotor" compressors whichare regarded as best compressors in their class.They are followed by "Cyclon" [19] rotors. The lastin this group are 'rack-generated' rotors [50]. Theselection and distribution of primary curves on therack which was used to create these rotors, givesa larger cross section area with stronger gate rotorlobes than any other known screw compressorrotor pair.

The largest group of rotors presented has a 5/6configuration. This is becoming the most popularrotor combination because it permits a good com-promise between large displacement and large dis-charge ports with favourable load characteristics insmall rotor sizes. These rotors are equally success-ful for air compression and refrigeration and air-con-ditioning applications. The group starts with the SRM"D" profile, [4], followed by the "Sigma", [5],FuSheng, [24] and "Hyper" [8] profiles. All are 'rotor-generated' profiles and the main diference betweenthem is in the leading lobe which is mainly aneccentric circle followed by a line, ellipse andhyperbola respectively. The hyperbola appeared tobe the best possible geometrical solution for thatpurpose. However at the end of the group are tworack-generated profiles, [37] and [50]. The last ofthese shows the best delivery for its size. it alsohas two additional features. Firstly, the rotors retaina seal over the entire contact length while main-taining a small blow-hole, which was not the casein [37]. Secondly, two contact bands in the prox-


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Slika 1. Upore|enje nekih rotora vij~anih kompresoraFigure 1. A comparison of several pairs of screw compresor rotors

razlika izme|u njih se uo~ava na vode}em rotoru kojipo~inje sa ekscentri~nom kru`nicom a nastavlja selinijom, elipsom ili hiperbolom respektivno. Pokazujese da je hiperbola najbolje mogu}e primjenjivogeometrijsko rje{enje. Na kraju grupe se nalaze dva'rack generisana' profila [37] i [50]. Moè se vidjeti daposljednji profil ima najve}u dobavu. Tako|er, moguse uo~iti jo{ dvije osobine koje karakteri{u te rotorei favorizuju ih u odnosu na ostale. Postignuto je zap-tivanje du` cijele linije dodira i time manji nezaptiveniprostor, {to nije slu~aj kod profila [37]. Dodatno, kon-taktne povr{ine sa jedne i druge strane profila u blizi-ni podionog kruga su ravne linije na zup~astom {taputako da formiraju evolventu na rotorima. Zbog toga{to je relativno kretanje jednog rotora u odnosu nadrugi gotovo ~isto kotrljanje, to je najbolji dodir {toga je mogu}e posti}i izme|u rotora. Rack generisanirotori konfiguracije 5/6 su prikazani na slici 2.

Posljednja grupa rotora sa 4 i 5 rotora u vode}emi vo|enom vijku respektivno, postaje sve vi{e pop-ularna za uljnopodmazivane zra~ne kompresore. Prvipar rotora su "Cyclon" rotori [19]. Iza njih su SRM"D" rotori [4] i na kraju grupe rotori generisanipomo}u zup~astog {tapa [50].

3.2 Konstrukcija kompresora

Iako je moderan profil rotora neophodan uslov dabi vij~ani kompresor bio efikasan, sve ostale kom-ponente tako|er moraju biti konstruisane tako da sena najbolji na~in iskoristi potencijal rotora i ostvarenajbolje mogu}e performanse kompresora. Zbogtoga je vrlo va`no pravilno odabrati zazor izme|uku}i{ta i rotora, posebno na strani visokog pritiska.To, povratno, zahtijeva ili skuplje leàjeve sa manjimzazorima ili jeftinije leàjeve kod kojih su pred-naprezanjem zazori svedeni na prihvatljivu veli~inu. Vij~ani kompresor je op}enito, a slu~aju uljnopod-mazivanog kompresora, kada radi sa velikom ra-zlikom pritisaka, posebno optere}en aksijalnim i radi-jalnim silama koje se na ku}i{te prenose prekoleàjeva. Za vij~ane kompresore malog i srednjegkapaciteta obi~no se koriste kotrljaju}i leàjevi, kojiu tom slu~aju moraju biti tako dobro odabrani dazadovolje sve zadane uslove rada. Obi~no se koristedva leàja na tla~noj strani vratila rotora kako bi seaksijalne i radijalne sile na ku}i{te prenijele odvo-jeno. Tako|er je bitno je da je me|uosno rastojan-je djelimi~no odre|eno i veli~inom leàjeva i nji-hovim unutra{njim zazorima.

Kontaktne sile, koje su definisane obrtnim momentomkoji se prenosi izme|u rotora, igraju klju~nu ulogukod kompresora sa direktnim dodirom rotora. Ove susile relativno male u slu~aju pogona preko vode}eg


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imity of the pitch circles are straight lines on therack which form involutes on the rotors. Hence therelative motion between the rotors is close to purerolling which is the best possible.

3.2 Compressor Design

Screw compressor design has gradually evolved andthe trend is to get as small as possible a machineto meet the required performance. This means thatrotor tip speeds are as high as possible within thelimits imposed by efficiency requirements. Normalpractice is to use rolling element bearings wherev-er possible because these permit smaller clearancesthan journal bearings. Similarly, the ports are madeas large as possible to minimize suction and dis-charge gas speeds. These features lead to greatsimilarity in all designs for any specified application.

Although advanced rotor profiles are a necessarycondition for a screw compressor to be efficient, allother components must be designed to minimiselosses if maximum improvements are to beachieved. Thus the rotor to housing clearances mustbe properly selected, especially at the high pres-sure end. This in turn requires either expensivebearings with small clearances or cheaper bearingswith their clearances reduced to an acceptablevalue by preloading.

A screw compressor, especially of the oil floodedtype, operates with high pressure differences.These create large axial and radial bearing forces.Rolling element bearings are normally chosen forsmall and medium screw compressors and thesemust be carefully selected to obtain a satisfactorydesign since, inter alia, the distance between therotor centre lines is in part determined by them. Itmust be added that recent advances in the devel-opment of advanced low friction rolling elementbearings greatly contributes to this choice [31].Usually two bearings are fitted at the high pressureend of the rotor shafts in order to absorb the radi-al and axial loads separately.

The contact force between the rotors is determinedby the torque transferred between them and is verysignificant when they make direct contact. It is rel-atively small when the compressor drive is throughthe main rotor. However, when the drive is throughthe gate rotor, the contact force is substantially larg-er and, as far as possible, this arrangement shouldbe avoided.

rotora. Pogon preko vo|enog rotora uzrokujezna~ajno pove}anje kontaktnih sila tako da se ovajslu~aj mora isklju~iti iz bilo kakvog ozbiljnijeg raz-matranja.Ulje koje se u vij~anom kompresoru ubrizgava izme|urotora za podmazivanje, hladjenje i zaptivanje, koristise i za podmazivanje leàjeva. Pri tom je vrlo va`nouspostaviti odvojen sistem snabdijevanja leàjevauljem i sistem za evakuaciju ulja iz leàjeva da bi segubici usljed trenja smanjili. Ulje se u radni prostorkompresora ubrizgava na onom mjestu na kojem se,prema termodinamskim prora~unima, temperatureradnog fluida i ulja podudaraju. Poloàj otvora zaubrizgavanje ulja je definisan uglom na helikoidi roto-ra ali se obi~no postavlja tako da ulje tangencijalnoulazi u radni prostor kako bi se iskoristilo {to je godmogu}e vi{e njegove kineti~ke energije.Kompresor moderne konstrukcije treba imati malegubitke na usisu i potisu. Zato se usisni otvor unutarku}i{ta kompresora postavlja tako da usisani gas nasvom putu {to manje mijenja smijer kretanja te dabi imao malu brzinu strujanja. To se postièpove}anjem zapremine usisnog otvora. Veli~ina ioblik tla~nog otvora definisani su ugra|enim odno-som pritiska koji }e dati optimalne termodinamskeperformanse kompresora. Nakon toga se popre~nipresjek izlaznog toka dodatno pove}ava da bi sesmanjila brzina toka na izlazu i time postigla mini-mizacija gubitaka u unutra{njem i izlaznom toku.

Ku}i{te treba da bude pa`ljivo dimenzionisano kakobi se smanjila teìna kompresora a jedan od na~inada se to postigne je ugradnja pre~ke u usisnomotvoru u cilju pove}anja ~vrsto}a kompresora navi{im pritiscima.Vij~ani kompresor je vrlo jednostavna toplotna ma{ina


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The oil which is injected into the compressor forflooding is also used for bearing lubrication but, tominimise friction losses, the bearing feed and returnsystem is separate. The position in the compres-sor chamber where the oil is injected is set at thepoint where thermodynamic calculations show thegas and oil inlet temperatures to coincide. It isdefined on the rotor helix with the injection holelocated so that the oil enters tangentially in line withthe gate rotor tip in order to recover as much aspossible of the oil kinetic energy.

To minimise flow losses in the suction and dis-charge ports, the following features must be includ-ed. The suction port should be positioned in thehousing to let the gas enter with the fewest possi-ble bends and the gas approach velocity kept lowby making the flow area as large as possible. Thedischarge port size is first determined by estimatingthe built-in-volume ratio required for optimum ther-modynamic performance. It is then increased inorder to reduce the exit gas velocity and henceobtain the minimum combination of internal and dis-charge flow losses.

The casing should be carefully dimensioned to min-imize its weight and contain reinforcing bars acrossthe suction port to improve its rigidity at higherpressures.

Slika 2. Rack generisani rotori vij~anog kompresora konfiguracije 5/6Figure 2. A pair of 5/6 rack generated screw compressor rotors

sa samo nekoliko pokretnih dijelova: dva rotora iobi~no ~etiri ili {est leàjeva. Tokom njegovog razvo-ja do{lo se do vrlo tipi~nog oblika po ~emu posta-je vrlo prepoznatljiv. Tendencija je da se dobije {toje god mogu}e manja ma{ina koja }e jo{ uvijek datizadovoljavaju}e performanse. To zna~i da se brzinavrha zuba mora {to je mogu}e vi{e pove}ati, ali jetreba jo{ uvijek dràti u granicama koje daju pri-hvatljive mehani~ke gubitke. Upotreba kotrljaju~ihumjesto kliznih leàjeva skoro da se moè postavitikao pravilo koje treba uvijek po{tovati, jer su zazorina kotrljaju~im leàjevima, a i gubici zna~ajno manji.Otvori za komunikaciju radnog fluida moraju biti {toje god mogu}e otvoreniji da bi se smanjile brzinegasa na usisu i izlazu. Sve ovo dovodi do vrlo sli~nihkonstrukcija kompresora tako da su izuzetci vrlo rije-tki i skoro zanemarivi. Primjer savremene konstrukci-je uljnopodmazivanog vij~anog kompresora sa reduk-torom dat je na slici 3.

Valja tako|er napomenuti da je u zadnje vrijemedosta uradjeno na razvoju kotrljaju~ih leàjeva savrlo niskim trenjem [31], {to }e zna~ajno doprinijetipobolj{anju performansi kompresora.Na slici 4. prikazuju se svi vitalni dijelovi modernoguljnopodmazivanog vij~anog kompresora.

4 ZAKLJUÂK

Vij~ani kompresor je proizvod koji je dorastaotrenutku smjene vijekova. Pa`ljivo usmjereni naporivelikog broja kompanija dirigovani zahtjevima trì{tarezultirali su kompaktnom i efikasnom vij~anomma{inom. U razvoju vij~anih kompresora do{lo se ufazu kad se unapre|enja razmatraju do najsitnijihdetalja. Male razlike dovode do malih ali zna~ajnihpomaka koji ~ine individualne prednosti svakog odkompresora.Iako se ~ini da se samo kontinualnim razvojemvij~ani kompresori mogu promijeniti na bolje, jo{ uvi-jek ima dosta mjesta za primjenu manje ili vi{e rev-olucionarnih metoda ili procedura koje }e rezultiratiboljim proizvodom. îni se da je najperspektivnijimetod generacije profila pomo}u zup~astog {tapakoji daje ja~e, ali i lak{e rotore sa ve}om dobavomi manjim kontaktnim naponima me|u rotorima.


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4. CONCLUSIONS

At the onset of the millenium, the twin screw com-pressor has become a mature product. As a resultof orchestrated efforts by a large number of com-panies, driven by market forces, it has become acompact, efficient and reliable machine. Every detailcounts today. Even small advances in any featurewill give distinctive improvements which may beused to gain commercial advantage. Hence,despite its now established role in industry, effortscontinue to make advances in every aspect of itsdesign, manufacture and mode of operation.

Although improvements so gained are most likely tobe evolutionary, there is still scope for revolutionarymethods or procedures to achieve a better product.The most promising development appears to berack profile generation to produce stronger butlighter rotors with higher displacementand lower contact stress.

LITERATURA - REFERENCES

[1] Amosov P.E et al, 1977: Vintovie kompresorniemashinii - Spravochnik (Screw CompressionMachines - Handbook), Mashinstroienie, Leningrad

[2] Andreev P.A, 1961: Vintovie kompressorniemashinii (Screw Compression Machines), SUDPROMLeninngrad

[3] Arbon I.M, 1994: The Design and Application ofRotary Twin-shaft Compressors in the Oil and GasProcess Industry, MEP London


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[4] Astberg A, 1982: Patent GB 2092676B

[5] Bammert K, 1979: Patent Application FRG2911415

[6] Bowman J.L, 1983: US Patent 4,412,796

[7] Buckingham E, 1963: Analytical Mechanics ofGears, Dover Publ, N.York

[8] Chia-Hsing C, 1995: US Patent 5,454,701

Slika 3. Konstrukcija vij~anog kompresora sa reduktoromFigure 3. A screw compressor with a gearbox design

Slika 4. Sastavni dijelovi modernog uljnopodmazivanog vij~anog kompresoraFigure 4. A modern oil floded screw compressor parts

[9] Edstrom S.E, 1974: US Patent 3,787,154

[10] Edstrom S.E, 1989: Quality Classes for screwCompressor Rotors, Proc IMechE ConferenceDevelopment in Industrial Compressors, 83

[11] Edstrom S.E, 1992: A Modern Way to GoodScrew Compressors, International CompressorEngineering Conference At Purdue, 18

[12] Fleming J.S, Tang Y, 1994: The Analysis ofLeakage in a Twin Screw Compressor and itsApplication to Performance Improvement, ProcIMechE, Journal of Process Mechanical Engineering,Vol 209, 125

[13] Fleming J.S, Tang Y, Cook G, 1998: The TwinHelical Screw Compressor, Part 1: Development,Applications and Competetive Position, P. 2:AMathematical Model of the Working process, ProcIMechE, Journal of Mechanical Engineering Science,Vol 212, p369

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[15] Golovintsov A. G et al, 1964: Rotatsionii kom-presorii (Rotary Compressors), Mashinostroenie,Moscow

[16] Hanjali} K, Sto{i} N, 1994: Application of math-ematical modeling of screw engines to the opti-mization of lobe profiles, Proc. VDI Tagung"Schraubenmaschinen 94" Dortmund VDI Berichte1135

[17] Hanjali} K, Sto{i} N, 1997: Development andOptimization of Screw Machines with a SimulationModel, Part II: Thermodynamic PerformanceSimulation and Design, ASME Transactions, Journalof Fluids Engineering, Vol 119, p 664

[18] Holmes C.S, 1994: Towards a Core program forthe Measurement of Screw Rotor Bodies by Co-ordi-nate Measuring Machine, Proc. VDI Tagung"Schraubenmaschinen 94", Dortmund VDI Berichte1135

[19] Hough D, Morris S.J, 1984: Patent ApplicationGB 8413619

[20] Kasuya K. et al, 1983: US Patent 4,406,602

[21] Kauder K, Harling H.B, 1994: Visualisierung derOlverteilung in Schraubenkompressoren (Visualisation


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of Oil Effects in Screw Compressors), Proc. VDITagung "Schraubenmaschinen 94", Dortmund VDIBerichte 1135

[22] Kauder K, Helpertz M, 1998: Einlauf- undHybridschichten für Schraubenkompressoren (Run-inand Hybrid Coatings for Twin-Screw Compressors),Proc. VDI Tagung "Schraubenmaschinen 98",Dortmund VDI Berichte 1391

[23] Konka K-H, 1988: Schraubenkompressoren(Screw Compressors) VDI-Verlag, Duesseldorf

[24] Lee H-T, 1988: US Patent 4,890,992

[25] Litvin F.L, 1956: Teoria zubchatiih zaceplenii(Theory of Gearing), Nauka Moscow, second edition1968, also Gear Geometry and Applied TheoryPrentice-Hill, Englewood Cliffs, NJ 1994

[26] Lysholm A, 1942: A New Rotary Compressor,Proc. I.Mech.E. 150,11

[27] Lysholm A, 1966: The Fundamentals of a NewScrew Engine, ASME Paper No 66-GT-86

[28] Lysholm A, 1967: US Patent 3,314,598

[29] Margolis D.L, 1978: Analytical Modelling ofHelical Screw Turbines for Performance Prediction,J.Engr.for Power 100(3)482

[30] Menssen E, 1977: US Patent 4,028,026

[31] Meyers K, 1997: Creating the Right Environmentfor Compressor Bearings, Evolution, SKF Ind.Journal,Vol 4, 21

[32] O'Neill P.A, 1993: Industrial Compressors,Theory and Equipment, Butterworth-Heinemann,Oxford

[33] Nilson, 1952: US Patent 2,622,787

[34]Peng N, Xing Z, 1990: New Rotor Profile and itsPerformance Prediction of Screw Compressor,International Compressor Engineering Conference AtPurdue, 18

[35] Rinder L, 1979: Schraubenverdichter (ScrewCompressors), Springer Verlag, New York

[36] Rinder L, 1984: Schraubenverdichterl?ufer mitEvolventenflanken (Screw Compressor Rotor withInvolute Lobes), Proc. VDI Tagung"Schraubenmaschinen 84" VDI Berichte Nr. 521

[37] Rinder L, 1987: US Patent 4,643,654

[38] Sauls J, 1994: The Influence of Leakage on thePerformance of Refrigerant Screw Compressors,Proc. VDI Tagung "Schraubenmaschinen 94",Dortmund VDI Berichte 1135

[39] Sauls J, 1998: An Analytical Study of the Effectsof Manufacturing on Screw Rotor Profiles and RotorPair Clearances, Proc. VDI Tagung"Schraubenmaschinen 98", Dortmund VDI Berichte1391

[40] Sakun I.A, 1960: Vintovie kompresorii (ScrewCompressors), Mashinostroenie Leningrad

[41] Shibbie, 1979: US Patent 4,140,445

[42] Singh P.J, Onuschak A.D, 1984: AComprehensive Computerized Method For TwinScrew Rotor Profile Generation and Analysis, PurdueCompressor Technology Conference 544

[43] Singh P.J, Schwartz J.R, 1990: Exact AnalyticalRepresentation of Screw Compressor RotorGeometry, International Compressor EngineeringConference At Purdue, 925

[44] Smith I. K, Sto{i} N, Aldis C. A, 1996:Development of the trilateral flash cycle system, Part3: The design of high efficiency two-phase screwexpanders, Proc IMechE, Journal of Power andEnergy, Vol 210, p 75

[45] Sto{i} N, Hanjali} K, 1977: Contribution towardsModelling of Two-Stage Reciprocating Compressors,Int.J.Mech.Sci. 19, 439

[46] Sto{i} N, Hanjali} K, Koprivica J, Lovren N,Ivanovi} M, 1986: CAD of Screw CompressorElements, Strojarstvo Journal Zagreb 28, 181

[47] Sto{i} N, Kova~evi} A, Hanjali} K, Milutinovi}Lj, 1988: Mathematical Modelling of the OilInfluence upon the Working Cycle of ScrewCompressors, International Compressor EngineeringConference at Purdue, 355

[48] Sto{i} N, Milutinovi} Lj., Hanjali} K, Kova~evi}A, 1992: Investigation of the Influence of OilInjection upon the Screw Compressor WorkingProcess, Int.J.Refrig. 15,4,206

[49] Sto{i} N, Hanjali} K, 1994: Development andoptimization of screw engine rotor pairs on the basisof computer modeling, Proc. XVII Conference onCompressor Engineering at Purdue, 55

[50] Sto{i} N, 1996: Patent Application GB9610289.2

[51] Sto{i} N, Hanjali} K, 1997: Development andOptimization of Screw Machines with a SimulationModel, Part I: Profile Generation, ASME Transactions,Journal of Fluids Engineering, Vol 119, p 659

[52] Sto{i} N, Smith I K, Kova~evi} A, Aldis C A,1997: The Design of a Twin-screw CompressorBased on a New Profile, Journal of EngineeringDesign, Vol 8, 389

[53] Sto{i} N, Kova~evi} A. and Smith I.K, 1998:Modelling of Screw Compressor Capacity Control,Proc. XIV Conference on Compressor Engineering atPurdue, 607

[54] Sto{i} N, Smith I.K, Brasz J.J, Sishtla V, 1998:The Performance of a Screw Compressor withInvolute Contact Rotors in a Low Viscosity Gas-Liquid Mixture Environment, Proc. VDI Tagung"Schraubenmaschinen 98", Dortmund VDI Berichte1391

[55] Sto{i} N, 1998: On Gearing of Helical ScrewCompressor Rotors, Proc IMechE, Journal ofMechanical Engineering Science, Vol 212, 587

[56] Tang Y, Fleming J.S, 1992: Obtaining theOptimum Geometrical Parameters of a RefrigerationHelical Screw Compressor, International CompressorEngineering Conference at Purdue 213

[57] Tang Y, Fleming J.S, 1994: Clearances betweenthe Rotors of Helical Screw Compressors: Theirdetermination, Optimization and ThermodynamicConsequences, Proc IMechE, J. of ProcessMechanical Engineering, Vol 208, 155

[58] Xion Z. Dagang X, 1986: Study on Actual ProfileSurface and Engaging Clearance of ScrewCompressor Rotors, Purdue Compressor TechnologyConference 239

[59] Zenan X, 1984: The Dynamic Measurement andMating Design of a Screw Compressor Rotor Pair,Purdue Compressor Technology Conference 314

[60] Zhang L, Hamilton J.F, 1992: Main GeometricCharacteristics of the Twin Screw Compressor,International Compressor Engineering Conference atPurdue 2136


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Ma{instvo 2(3), 79 – 92, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE...

KOMPJUTERSKO UPRAVLJANJE TOLERANCIJAMA U KONSTRUIRANJU TRODIMENZIONALNOG SKLOPA

E. Chirone; S. Tornincasa, Dipartimento di Ingegneria Meccanica, Università di Brescia, Italy, [email protected]; ++39030-3715423;fax 3702448

REZIME

Izbor tolerancija igra klju~nu ulogu u kona~noj cijeni promoè smanjiti tro{kove proizvodnje, pove}ati kvalitet i obeinènjeringa. Iz tog razloga, na Politehnici u Torinu je razvtolerancija sklopova. Tipi~an CAD sistem kreira solid mkoja je idealizacija proizvoda. Da bi se dio predstavio samodel sklopa, koji je zatim integrisan putem odgovarajinterfejs izme|u parametarskog CAD sistema i funkcionalda se izvr{i izbor kota, baziran na funkciji dijela i Predloèni metod je implementiran u okruènju SolidWorkinterfejsa, a pogodan je za integraciju sa drugim komercij

Klju~ne rije~i: tolerancije, kompjutersko upravljanje

COMPUTER AIDED TO3-D DESIGN FOR

E. Chirone; S. Tornincasa, Dipartimento di IngBrescia, Italy, [email protected]; ++39030-371

SUMMARY

The effect of the tolerance design is actually a main product. Such engineering function can indeed reduceprovide a key factor in Concurrent Engineering practice. Fassembly tolerance modeling and analysis has been devesystem creates a solid model, representing the nominmanufactured piece. In order to represent a part with toassembly is developed, and integrated with an approprbetween a parametric CAD system and the functional dorder to create datum selection, based on the functionanalysis and allocation. The proposed method is implemedefined application programming interface (API)) and is sCAD systems.

Key words: tolerance, computer aided,

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PRETHODNO SAOP[TENJE

izvoda. Ovakva inènjerska funkcija zapravo zbijediti klju~ni faktor u praksi Konkurentnog ijen sistem za modeliranje i analizu sloènih odel, koji predstavlja nominalnu geometriju, tolerisanim povr{inama, razvijen je relacijski u}e sheme tolerancija. Razvijen je direktni nog okruènja za dimenzionisanje s ciljem automatskoj analizi i raspodjeli tolerancija. s uz kori{tenje definiranog API programskog alnim CAD sistemima.

LERANCE IN ASSEMBLY

egneria Meccanica, Università di 542

point maor thlopedal geleraniate imen of nted uitabl

3;fax 3702448

PRELIMINARY NOTES

on the final cost of a manufactured nufacturing cost, improve quality and is reason, a comprehensive system for at Politecnico of Turin. A typical CAD ometry, that is an idealization of the ced surfaces, a relational model of an tolerance scheme . A direct interface sioning environment was developed in the part and an automatic tolerances in the SolidWorks environment using a e for integration with other commercial


1. UVOD U ma{inskoj industriji, ~esto su se koristili samo tehni~ki crteì da bi se odredilo kako }e se dio proizvesti i smjestiti u sklop. Dio se proizvodio prema crteìma, a zatim pregledao, i ako se komponente ne bi pravilno uklapale, crteì su se vra}ali konstruktorima da se ponovo prora~unaju dimenzione ili geometrijske varijacije koje bi omogu}ile odgovaraju}e uklapanje [1]. Danas, visoko konkurentna priroda sjetskog trì{ta proizvoda zahtijeva ~este promjene konstrukcije proizvoda i strategija proizvodnje. Da bi se skratilo vrijeme potrebno za razvoj proizvoda, poèljno je da se funkcionalnost dijelova provjeri jo{ na 3D CAD modelu u fazi konstruiranja, kad su tolerancije dijelova sastavni dio geometrijskih modela elemenata i sklopova. Va`na funkcija u konstruiranju proizvoda je raspodjela tolerancija na pojedina~ne komponente sklopa, tako da konstruktor moè provjeriti da kombinovano dejstvo akumulacije svih tih tolerancija (sloèna tolerancja) ne dovede do zaribavanja sklopa, da se proizvod moè ekonomi~no proizvesti i da ispravno funkcioni{e.

Konstruktor moè izabrati relativno uske tolerancije za svaki dio da bi obezbijedio o~ekivanu konsruktivnu funkciju, ali to naravno zahtijeva ve}e proizvodne tro{kove. Smanjenje tolerancija svakog dijela, s druge strane, smanjuje tro{kove, ali moè dovesti do neprihvatljivog smanjenja kvaliteta i lo{im performansama, {to kupca ~ini nezadovoljnim. Ovi suprotni ciljevi izme|u konstruiranja i proizvodnje (slika 1) imaju ogroman uticaj na kona~nu cijenu prozvoda. zato su razvijeni novi alati za analizu tolerancija, koji konstruktoru omogu}uju da osigura naj{ire mogu}e tolerancije, a da dio zadrì svoju funkcionalnost [2]. Pravi na~in mora biti taj da se pove}aju specifikacije tolerancija zadràvanjem ispravne funkcije, {to bi zna~ilo u~initi konstrukciju robusnom prema devijacijama lanaca procesa. Ve}ina dana{njih CAD sistema podràvaju korisnika u propisivanju tolerancija, ali ne prikazuju mogu}e varijacije oblika i dimenzija; prikaz tolerancija je najzna~ajniji u analizi i sintezi tolerancija. Na osnovu ovih zahtjeva, implementiran je direktni interfejs izme|u parametarskog CAD sistema i funkcionalnog dimenzionalnog okruènja. Mogu}nost da se CAD program prilagodi korisniku pomo}u programskog jezika kao {to je Visual Basic koristi jedan vaàn dio objektne tehnologije koji se naziva OLE (Object Linking and Embedding) automatizacija.

1. INTRODUCTION In mechanical industry, blueprints were often the only means to determine how a part would be manufactured and placed into an assembly. Interpreting the blueprint, the part was produced and inspected, and when the components did not fit together properly, the blueprints went back to the engineering design in order to recalculate the dimensional or geometrical variations that allowed the suitable fit [1]. Today, the highly competitive nature of the global market of manufactured products requires frequent changes of the product design and manufacturing strategies; in order to shorten the time required for the development of the product, it is desirable for the functionality of parts to be verified by the 3D CAD model during the design stage, when the tolerances on the parts are stored together with their geometric models and their assembled state. An important function in product design is the assignment of tolerances to individual component of an assembly so the designer can check that the combined effect of accumulation of all these tolerances (tolerances stackup) does not cause a malfunctioning assembly and the product can be produced economically and function properly.

The designer may assign relatively tight tolerances to each part to ensure the expected design function, but this normally requires higher manufacturing cost. Reducing tolerances on each component, on the other hand, reduces costs, but can result an unacceptable loss of quality and poor performance, leading to customer dissatisfaction. These conflicting goals between design and manufacturing (fig. 1) have an enormous influence on the final cost of a manufactured product. Therefore new tolerance analysis tools are being developed allowing a designer to assure the widest possible tolerance maintaining part functionality [2]. The right way must be to increase tolerance specifications by keeping the correct function, which would mean making the Most of the currently CAD system are supporting the user in the prescription of tolerances, but do not represent the possible shape or dimensional variation; the representation of tolerances is essential for the tolerance synthesis and analysis. Based on these requirements, a direct interface between a parametric CAD system and the functional dimensioning environment was implemented. The capability to customize CAD program using a programming language as Visual Basic uses an important part of the object technology called OLE (Object Linking and Embedding) Automation.

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Slika 1. Specifikacije tolerancija postaju kriti~na veza izme|u inènjeringa (uske tolerancije koje osiguravaju

funkcionalnost) i proizvodnje ({iroke tolerancije, koje su jeftinije sa stanovi{ta proizvodnje). Figure 1. Tolerance specifications become a critical link between engineering (tight tolerances to assure

appropriate functionality) and manufacturing (loose tolerances, less expensive to produce). Prikazan je metod za prikazivanje modela sklopa sa stanovi{ta njegove geometrije i me|uzavisnosti dijelova. Model je prikladan za analizu i sintezu tolerancija, i u potpunosti je integriran u parametarski, feature-based CAD software. Ovaj metod omogu}uje skra}enje analize konstrukcije i pove}anje kvaliteta u odnosu na tradicionalnu analizu. Kori{tenjem interfejsa za automatizaciju, razvili smo Microsoft Visual Basic programe koji su potpuno integrirani u okruènje SolidWorks; ovaj alat se tako|e koristi i u po~etnom te~aju inènjerskog crtanja. Student moè vidjeti i manipulirati solid modelima jednostavnih objekata i ma{inskih elemenata, rotirati i osmatrati ih sa razli~itih mjesta, {to olak{ava razumijevanje veza izme|u 3D realisti~ne slike i njenog prevo|enja u 2D ravan. Na vi{em nivou mogu}e je razviti uzajamnu vezu izme|u dijelova i funkcionalnih zahtjeva; sa automatskom provjerom sloènih tolerancija i alokacijom komponentnih tolerancija.

2. GEOMETRIJSKE TOLERANCIJE U MODELU SKLOPA

2.1. Relacijski model Kod konvencionalnog CAD modela mogu}e je provjeriti masene osobine ili preklapanje dijelova; ali to nije pogodno za prikaz geometrisjkih tolerancija ili za analizu tolerancija

A method for representing the assembly model in terms of its geometry and mating relationships is presented. The model is suitable for tolerance analysis and synthesis, and is completely integrated with a parametric, feature-based CAD software. This method allows to reduce the time for design analysis and to improve quality with respect to the traditional analysis. Using the automation interfaces, we have developed a Microsoft Visual Basic programs fully integrated in SolidWorks environment; this tools is also used in a basic course in engineering drawing. The student can view and manipulate solid models of simple objects and mechanical parts, rotate and observe them from different point of view and this makes easier understanding the links between the 3D realistic image and its translation on a 2D plane. At higher level it is possible evaluate the mutual relationship between the parts and the functional requirements; with automatic checks of the tolerance stack and the allocation of tolerance components.

2. GEOMETRIC TOLERANCES IN THE ASSEMBLY MODEL

2.1. The relational model With a conventional CAD model it is possible to check the mass properties or the interference between parts; but it is inadequate for the representation of geometric tolerances or for the tolerance analysis;

Functional Functional requirements requirements

sasafety fety Performance Reliability Reliability

Product Life Maintenance Maintenance

Performance

Product Life

Engineering

design Production Cost

Machine and process Operator skills Operator skills

Production Cost Machine and process

Asse Assembly mbly Inspection Inspection

Manufacturing

design design

Tight Loose

Engineering Manufacturing

design

Tolerance

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Zbog toga, implementiran je relacijski model da bi se opisale eksplicitno razli~ite logi~ke i fizi~ke veze me|u komponentama sklopa [4,5]. Relacijski model sklopa se sastoji od: 1) matemati~kog opisa dijelova; 2) definicije redoslijeda komponenti sklopa i

dimenzija parova; 3) tolerancija komponenti. Model sklopa sa n zavisnih komponenti je prikazan skupom objekata:

C= {c1,c2,….cn} Gdje je c1:

ci = <Xi, LFi, Pi>, i ∈ [1,….,n]

♦ Xi sadrì niz od 13 elemenata koji definira transformaciju i predstavlja prostornu relaciju izme|u zavisnih komponenti i po~etne komponente u sklopu. Prvih devet su elementi matrice 3x3 koja defini{e rotaciju, sljede}a tri defini{u translaciju, a sljede}a je faktor pove}anja.

♦ LFi=< Ai, Bi> redom pokaziva~ na komponentu i na tijelo objekta i-tog dijela.

♦ Pi =<Fi,Ekh,Zkh> gdje je Fi = {F1,F2,……,Fk} lista objekata k-te povr{ine dijela, Ekh lista h-tih ivica povr{ine k, Zkh atribut ivice h.

Atribut je informacija (hrapavost, tolerancija) koja se moè pridruìti Povr{ini, Ivici, Ta~ki ili Elementu. Mogu}e je prenijeti atribut-objekat i promijeniti njegove parametarske vrijednosti. Naprimjer, atribut koji sadrì informacije za NC obradu rezanjem moè se pridruìti Povr{ini. Relacijski model sklopa se dobije kombiniranjem parova sa informacijama o sklopu, i deini{e se skupom:

<C, M>

♦ M = {M1, M2,…..Mj} omogu}uje pristup parovima objekata i definiciji parova sklopa; j je broj relacije izme|u komponenti u sklopu, jmax=n(n-1). Mi, i ∈ [1,…,j] se opisuje preko seta od tri objekta:

Mi= <ca, cb, Sab>

♦ Gdje ca,cb ∈ C i Sab iznose NULL ako nema relacije izme|u komponenti ca, cb, u suprotnom je:

Sab = {R1, R2,…..Rm}

♦ R opisuje listu m relacija izme|u komponenti ca i cb:

Ri = <Dp,Dq,Wpq,Ppq>, i ∈ [1,…,m]

For this reason, a relational model has been implemented to describe explicitly various logical and physical relationships among the component of the assembly [4,5]. A relational model of an assembly contains: 1) the mathematical descriptions of the parts; 2) a definition of assembly sequence and mating

relationships dimensions; 3) the component tolerances. An assembly model of n children components is represented by an object collection:

C= {c1,c2,….cn} Where c1 is:

ci = <Xi, LFi, Pi>, i ∈ [1,….,n]

♦ Xi contains a 13 element array defining the transform and representing the spatial relationship between children component and root component in the assembly. The first nine are elements of 3x3 matrix defining the rotation, the next three define translation and the next one is scaling.

♦ LFi=< Ai, Bi> respectively a pointer to the component and to body object of the i part.

♦ Pi =<Fi,Ekh,Zkh> where Fi = {F1,F2,……,Fk} is the list of k face object of the part, Ekh the list of the h edges of face k, Zkh the attribute of edge h.

An attribute is a piece of information (roughness, tolerances) that can be stored on a Face, Edge, Vertex, or Feature object. It is possible to grab the attribute object and query or change its parameter values. For example, an attribute containing NC machining information could be placed on a Face. The relational model of the assembly is obtained by combining mate traversal with assembly traversal information, and it is defined by collection

<C, M>

♦ M = {M1, M2,…..Mj} allows access to mated objects and the assembly mate definition; j is the relation number between components in the assembly, jmax=n(n-1). Mi, i ∈ [1,…,j] is described by a set of three object:

Mi= <ca, cb, Sab>

♦ Where ca,cb ∈ C and Sab is NULL if no relations exist between component ca, cb, otherwise is:

Sab = {R1, R2,…..Rm}

♦ R describes a list of the m mating relations between components ca and cb:

Ri = <Dp,Dq,Wpq,Ppq>, i ∈ [1,…,m]

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♦ Dp,Dq daje dva vezana entiteta (povr{ine, ivica, osa), a Wpq daje vrstu veze (podudaranje, koncentri~nost, okomitost, paralelnost, tangentnost, udaljenost, ugao). Ppq daje listu parametara ove veze i predstavlja X,Y,Z lokaciju te veze u modelskom prostoru sklopa.

♦ Dp,Dq returns two mate entities (faces, edge, axis), and Wpq returns the type of mate (coincident, concentric, perpendicular, parallel, tangent, distance, angle). Ppq list the parameters of this particular mate entity and represents the X,Y,Z location of this mate entity in the assembly model space.

Slika 3. SolidWorks API objekat Figure 3. SolidWorks API Object

2.2. Primjer relacije sklopa Slika 4 prikazuje sklop zateza~a remena sastavljen od n = 7 dijelova: postolje, u{ka [2], osovina, podlo{ka [2] i to~ak. Polazna komponenta je nosa~. Maksimalni broj relacije jmax je: jmax = n(n-1) = 7(7-1) = 42; j = 12 (vidi tabelu I) Uzmimo u obzir relaciju veze sa slike 5 izme|u osnove (1) i u{ke (2). Broj od m = 3 relacije veze izme|u komponenti je: ca = osnova, cb = u{ka, m=3, Sab = {F1,F2,F3}

♦ F1 = <A1,A2,podudarnost,P12>, F2 = <B1,B2,podudarnost,P12>, F3 = <C1,C2,podudarnost,P12>

Par entiteta su dvije povr{ine na svakoj komponenti (A1,A2) (B1,B2) i jedna osa C1,C2 (tab. II).

2.2. Example of an assembly relation The figure 4 shows a belt tensioner assembly composed by n = 7 parts: base, bracket [2], shaft, bushing [2] and a pulley. The root component is the base . The max relation number jmax is: jmax = n(n-1) = 7(7-1) = 42; j = 12 (see table I) Let’s consider the mating relation of figure 5 between the base (1) and the bracket (2). The m =3 mating relations between components is: ca = base, cb = bracket, m=3, Sab = {F1,F2,F3}

♦ F1 = <A1,A2,coincident,P12>, F2 = <B1,B2,coincident,P12>, F3 = <C1,C2,coincident,P12>

The mate entity are two faces on each component (A1,A2) (B1,B2) and one axis C1,C2 (tab. II).

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Relations

Base

Bracket1

Bracket2

Pulley

Bushing1

Bushing2

Shaft

2 Base 1 1 0 0 0 02 Bracket1 1 0 0 0 1 02 Bracket2 1 0 0 1 0 01 Pulley 0 0 0 0 0 11 Bushing1 0 0 1 0 0 11 Bushing2 0 1 0 0 0 13 Shaft 0 0 0 1 1 112 2 2 2 1 1 1 3

Tabela I: Tablica relacija za sklop zateza~a remena

Table I: The assembly relation table of the belt tensioner

Slika 4: Sklop zateza~a remena Figure 4: The belt tensioner assembly

Face Axisbase A1,B1 C1bracket A2,B2 C2

Tabela II. Broj od m =3 relacija veze izme|u osnove i u{ke Table II. The m =3 mating relations between base and bracket

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Relacije veze izme|u u{ke (2) i podlo{ke (5) su: ca = u{ka, cb =podlo{ka, m=2, Sab = {F1,F2}

♦ F1 = <E2,E3,podudarnost,P23>, F2 = <D2,D3,podudarnost,P23>

Par entiteta su jedna povr{ina na svakoj komponenti D2, D3 i jedna osa E2,E3 (tab. III)

The mating relations between bracket (2) and bushing (5) are: ca = bracket, cb =bushing, m=2, Sab = {F1,F2}

♦ F1 = <E2,E3,coincident,P23>, F2 = <D2,D3,coincident,P23>

The mate entity are one face on each component D2, D3 and one axis E2,E3 (tab. III)

Face AxisBushing D3 E3bracket D2 E2

Tabela III. Broj od m =2 relacija veze izme|u u{ke i podlo{ke Table III. The m =2 mating relations between bracket and bushing

Slika 5. Relacija veze izme|u osnove, u{ke i podlo{ke

Figure 5. Mating relation between base, bracket and bushing

3. IZBOR KOTA Relacije sklopa se koriste za provo|enje analize kota, tako da inènjering, proizvodnja i inspekcija mogu izvesti okvir referentnih kota (DRF). Izbor kota bi se trebao zasnivati na funkciji dijela (kako se uparuje, kako se uklapa u sklop i kako se instalira). Izbor kota zasnovan na funkcionalnim zahtjevima obezbje|uje konstruktoru organiziran, metodi~ki, relaisti~an metod za prora~un tolerancija.

DATUM SELECTION The assembly relations are used to perform datum analysis, so that engineering, manufacturing and inspection can derive the datum reference frame (DRF). The selection of datums should be based on the function of the part (how it mates, how it assembles and how it is installed). The datum selection based on functional requirements supplies the designer with an organized, methodical, realistic method to calculate tolerance.

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Ovo }e zauzvrat obezbijediti maksimalne proizvodne tolerancije zasnovane na funkciji, kao {to su autori ilustrovali u drugom radu [5].

This, in turn, will provide maximum-manufacturing tolerances based on function, as the authors illustrate in other paper [5].

Slika 6. Automatski izbor kota: ravan kotiranja A osa kotiranja B

Figure 6. Automatic datum selection: datum plane A and datum axis B

3.1. Utvr|ivanje kota Na slici 6 je dat ekranski prikaz kote osnove sklopa. Na osnovi uzajamne relacije veze izme|u komponenti, upotrijebljeni sistem prototipa implicira izbor kota (ravan i osu), zasnovan na funkciji dijela.

3.1. Establishing datums Figure 6 shows a screen representation of the datum of a base in the assembly. On the basis of the mating relationship between components, the prototype system currently implemented suggests a datum selection (a plane and an axis), based on the function of the part.

Slika 7. Samo dvije kote su kori{tene u okviru kontrole elemenata, po{to rotacija niza otvora oko ose kote nema uticaja na funkciju dijela.

Figure 7. Only two datum features are referenced in the feature control frame, as the rotation of pattern of holes about the datum axis has no effect on the function of the part.

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Software predlaè primarnu kotu A; kako je sekundarna kota B cilindri~na, povezana je sa dvije teoretske ravnine. Kota cilindri~ne povr{ine je osa prave geometrijske kopije kote. Ta osa je presjek druge i tre}e ravnine kote (slika 7).

The software suggests the primary datum A; since secondary datum feature B is cylindrical, it is associated with two theoretical planes. The datum of a cylindrical surface is the axis of the true geometric countepart of the datum feature. This axis is the intersection of the second and third datum planes (fig. 7).

Slika 8. Crte` sa tolerancijom poloàja Figure 8. The drawing with the positional tolerance

Na slici 8 je prikazan crte` sa tolerancijom poloàja; niz otvora je smje{ten u odnosu na kotu povr{ine A i kotu ose B. Da bi se pove}ale zone tolerancija, mora se koristiti princip maksimuma materijala.

3.1.1. Sekundarne i tercijalne kote Na slici 9 je va`na ugaona orijentacija dijela, tako da se tercijalna kota odnosi na kontrolni okvir elementa. Na osnovu relacija veze, software predlaè tri kote: kota ravnine A (prava geometrijska kopija kote A), kota ose B (princip maksimuma materijala okomito na kotu ravnine A) i centralna ravnina, poravnata sa kotom ose B i okomita na kotu ravnine A (slika 10).

The figure 8 shows the drawing with the positional tolerance; the pattern of the holes are located in relation of the surface datum A and the axis datum B. To enlarge tolerance zones, the Maximum-Material-Condition should be used.

3.1.1. Secondary and tertiary datum features In the figure 9 the angular orientation of the part is important, therefore a tertiary datum feature is referenced in the feature control frame. On the basis of the mating relations, the software suggests three datum: the datum plane A (true geometric countepart of datum feature A), the datum axis B (maximum material condition perpendicular to datum plane A) and center plane C, aligned with datum axis B and perpendicular to datum plane A (fig. 10).

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Slika 9. Dio u kojem je va`na ugaona orijentacija Figure 9. Part where angular orientation is important

Slika 10. Razvoj okvira referentnih kota za dio sa slike 9.

Figure 10. Development of a datum reference frame for part in figure 9. Na slici 11 je prikazan crte` sa tolerancijom poloàja; niz otvora je smje{ten u odnosu na kotu povr{ine A, kotu ose B i centralnu ravninu utora C.

4. RASPODJELA TOLERANCIJA U SolidWorks okruènju software moè automatski proizvesti geometriju za ortogonalni i dodatne poglede; crtanje se moè pobolj{ati dodatnom skiciranom geometrijom, dimenzijama, napomenama; sklopovi, dijelovi i crteì se mogu prikazati istovremeno, a usljed asocijativnosti izme|u ovih datoteka, promjene na jednom se reflektuju na datoteku koja je na nju vezana.

The figure 11 shows the drawing with the positional tolerance; the pattern of the holes are located in relation of the surface datum A, the axis datum B and the center plane of the slot C.

4. TOLERANCE ASSIGNMENT In the SolidWorks environment the software can automatically produce geometry for orthographic and auxiliary views; drafting can be enhanced with additional sketch geometry, dimensions, notes; assemblies, parts and drawings may be displayed simultaneously, and by reason of the associativity between these files, changes to one file will be reflected in the associated file.

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Slika 11. Crte` sa tolerancijom poloàja; da bi se uspostavila orijentacija rotacije dvije ravnine oko ose kote,

automatski se uzima u obzir tercijalna kota (centralna ravnina C utora) Figure 11. The drawing with the positional tolerance ; to establish rotational orientation of two planes about

a datum axis, a tertiary datum feature is automatically referenced (the center plane C of the slot)

Slika 12. Raspodjela tolerancija u modulu za crtanje paketa SolidWorks. Grafi~ka forma prikazuje zonu

tolerancija, i ISO simbole; automatski su na crte` dodate granice dimenzija. Figure 12. Tolerance assignment in the drawing module of the SolidWorks. A graphic form shows the

tolerance zone, and the ISO symbols; the dimension limits are automatically added to drawing.

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Uspostavljen je direktni interfejs izme|u parametarskog CAD sistema i funkcionalnog dimenzionalnog okruènja. Mogu}nost da se CAD program prilagodi korisniku pomo}u programskog jezika kao {to je Visual Basic koristi jedan vaàn dio objektne tehnologije koji se naziva OLE (Object Linking and Embedding) automatizacija. Application Programming Interface (API) je OLE programski interfejs za SolidWorks. API sadrì stotine funkcija koje se mogu pozivati iz Visual Basic-a, VBA (Excel, Access, itd.), C, C++, ili SolidWorks macro datoteka. Te funkcije omogu}uju programeru da direkno pristupa funkcionalnosti SolidWorks-a, kao {to su kreiranje linije, izlva~enje ~vora ili provjera parametara povr{ine. Bilo je te{ko primijeniti tolerancije u CAD zato {to u CAD modelu nije mogu}e prikazati mogu}e varijacije dimenzija. U software-u koji je upotrijebljen, konstruktor izabere ivicu na modelu dijela i dodijeli joj toleranciju dimenzije; ta informacija se ~uva u Zkh prethodno opisanog relacijskog modela sklopa. [tavi{e, korisnik moè provjeriti tolerancije preko prikaza najve}e i najmanje devijacije dijela. Koriste}i formu Visual Basic-a (slika 12), korisnik moè dodijeliti tolerancije dimenzija i u modulu za crtanje; mogu}e je izabrati ISO simbole za predstavljanje metri~kih preklapanja i za provjeravanje zazora, prelaznih polja ili preklopa. Osim toga, grafi~ka forma prikazuje tolerancijsko polje, a grani~ne dimenzije se automatski unose na crte`.

5. ANALIZA TOLERANCIJA U MODELU SKLOPA Ovim projektom se upravlja iz Excel tabele (slika 13) i raspodjeljuju tolerancije metodom najgoreg slu~aja, tako da su svi proizvedeni dijelovi me|usobno zamjenjivi jer se koriste maksimalne vrijednosti. [tavi{e, predloèni metod omogu}uje da se izra~unaju komponentne tolerancije i da se tolerancija sklopa automatski raspodijeli po komponentama. U stvari, dok analiza tolerancija odre|je zazor sklopa uz poznate tolerancije komponenti, kod sinteze tolerancija (distribucija tolerancija, alokacija tolerancija) zazor sklopa je zadat a treba odrediti tolerancije komponenti. Najva`nija informacija za alokaciju tolerancija se izvodi iz varijable atributa Zkh. Koraci u kreiranju sinteze tolerancija su: 1) odre|ivanje komponenti koje odre|uju zazor

sklopa; 2) izvo|enje dimenzija kriti~nih komponenti; 3) vektorska petlja koja predstavlja sloènu

toleranciju; 4) alokacija komponenti tolerancije.

A direct interface between a parametric CAD system and the functional dimensioning environment was implemented. The capability to customize CAD program using a programming language as Visual Basic applies an important part of the object technology called OLE (Object Linking and Embedding) Automation. The Application Programming Interface (API) is an OLE programming interface to SolidWorks. The API contains hundreds of functions that can be called from Visual Basic, VBA (Excel, Access, etc.), C, C++, or SolidWorks macro files. These functions provide the programmer with direct access to SolidWorks functionality such as creating a line, extruding a boss, or verifying the parameters of a surface. Tolerances have been difficult to apply in a CAD because in the CAD model it is not possible to represent the possible variations in dimension. In the software implemented, the designer picks a edge on the part model and assigns a dimensional tolerance; this information is stored in the Zkh of the relational assembly model previous described. Moreover the user can check the tolerances by displaying the maximum and minimum deviations of parts. By using a Visual Basic form (fig. 12), the user can assign dimensional tolerances also in the drawing module; it is possible to choose the ISO symbols to represent metric fits and to check clearance, transition and interference fits. In addition, a graphic form shows the tolerance zone, and the dimensional limits are automatically added to drawing.

5. TOLERANCES ANALYSIS IN ASSEMBLY MODEL This project is driven from an Excel spreadsheet (fig. 13) and allocates the tolerances with the worst case method, so that all manufactured parts are interchangeable since the maximum values are used. Moreover the proposed method enables to calculate the component tolerances and to distribute automatically the assembly tolerance among the components. In fact, while tolerance analysis determines the assembly clearance and the component tolerances are known, in tolerance synthesis (also called tolerance distribution or allocation) the assembly clearance is specified and the component tolerance are to be determined. The essential information for tolerance allocation is restored from attribute variable Zkh. The steps in creating a tolerance synthesis are: 1) determination of the components which

determine the assembly clearance; 2) derivation of critical component dimensions; 3) vector loop representation of the tolerance

stack; 4) allocation of tolerance components.

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Ulaz ~ine zazori i ukupne dimenzije sklopa, koje su kriti~ne za rad i funkcionalnost. Korisnik interaktivno bira kriti~ne komponente sklopa i smjer 2D vektorske petlje. Relacijski model sklopa uspostavlja veze izme|u parova komponenti tako da se izvedu nazivne dimenzije svakog kriti~nog elementa koji odre|uje varijacije zazora. Nakon {to su definisane tolerancije na modelu, one se mogu koristiti u skladu sa ograni~enjima sklopa, tako da je mogu}e uspostaviti vektorske petlje unutar sklopa za analizu i sintezu toleancija. Ovaj projekat koristi Excel tabelu za unos i kontrolu dimenzija komponenti direktno iz realcijskog modela. Prikazani su dodijeljeni atributi tolerancija i izvode se rezultiraju}e varijacije dimenzija kriti~nih komponenti da bi se vidjelo da li }e se prekora~iti konstruktivna ograni~enja. Dodaju se faktori zna~aja svakoj dimenziji u lancu; na taj na~in ve}e tolerancije se dodjeljuju komponentama koje su skuplje ili se teè proizvode.

The input is the clearances and overall dimensions of an assembly, which are critical to performance and functionality. The user interactively selects the assembly critical components and the direction of 2D-vector loop. The relational model of the assembly establish the connectivities between the pairs of components so that to derive the nominal dimensions of each critical feature which determines the clearance variation. Once tolerances on a model have been defined, they can be used in conjunction with assembly constraints, such as it is possible to establish vector loops within the assembly for tolerance analysis and synthesis. This project provides an Excel spreadsheet to input and control the dimensions of the components directly from relational model. Assigned tolerance attributes are introduced and the resulting variation of critical component dimensions is evaluated to see if design limits will be exceeded. Weight factors are added to each dimensions of the chain; in this way larger tolerances are assigned to components more costly or difficult to produce.

Slika 13. Alokacijom tolerancija se upravlja iz Excel tabele Figure 13. The tolerance allocation is driven from an Excel spreadsheet

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6. ZAKLJUÂK Prikazan je metod za predstavljanje modela sklopa u smislu njegove geometrije i uzajamnih relacija, dodatno unaprije|en u odnosu na prethodni prijedlog. Model je primjenjiv za analizu i sintezu tolerancija, i potpuno je integriran u parametarski, feature-based CAD software. Kako je SolidWorks 3D feature-based CAD paket, ali sa vrlo ograni~enim mogu}nostima analize tolerancija, razvijen je direktni interfejs s ciljem da se kreira izbor kota zasnovan na funkciji dijela i automatska analiza i alokacija tolerancija. Da bi se obezbijedili pouzdaniji rezultati u optimalnom konstruiranju tolerancija, razvoj ovog rada koristi punu integraciju sa statisti~kim tehnikama za izbor tolerancija i izvo|enje vektorskog modela sklopa direktno i automatski iz relacijskog modela sklopa.

6. CONCLUSION A further improved method for representing the assembly model in terms of its geometry and mating relationships has been presented, increasing former proposal. The model is suitable for tolerance analysis and synthesis, and is completely integrated with a parametric, feature-based CAD software. As SolidWorks is a 3D feature-based CAD package, but it provides very limited tolerance analysis capability, a direct interface between a parametric CAD system and the functional dimensioning environment was developed in order to create datum selection, based on the function of the part and an automatic tolerances analysis and allocation. In order to provide more reliable results in optimal tolerance design, developments of this work take up full integration with statistical tolerancing techniques and extraction of the vector assembly model directly and automatically from the assembly relational model.

7. LITERATURA - REFERENCE [1] Gehrke, T. , Blueprint never lie?, Machine Design, 12, 1992, 83-86 [2] Chirone, E., Tornincasa S., Some applications of

Geometric Dimensioning and Tolerancing in the industrial practice, Proc.3rd Int. Congress of Project Engineering, Barcelona, 1996, vol. 2, pp. 702-709

[3] Chase, K.W., Gao, J., Generalized 2-D Tolerance

Analysis of mechanical assemblies with small kinematic adjustments, Journal of Design and Manufacturing, 1995, pp. 263-274.

[4] Chirone, E., Tornincasa S., Disegno Tecnico

Industriale, vol I, II, ed. Il Capitello, Torino, 1997.

[5] Chirone, E., Tornincasa S., Functional

dimensioning and tolerancing analysis in the parametric/relational assembly modeling, Int. Design Conference “Design 98”, Dubrovnik, 1998.

[6] Weber C., Thome O., Britten W., Improving

Computer Aided Tolerancing by using Feature Technology, Proc. Int. Design Conference “Design ‘98”, pp. 117-122, Dubrovnik, 1998

[7] Chirone E., Tornincasa S., Più produttività e

intercambiabilità con le tolleranze geometriche, Il Progettista Industriale, 3, 1998, p. 96-102

[8] Park S., Lee K., Verification of assemblability

between toleranced parts, Computer-Aided Design, 30,2, 1998, 95-104

[9] Kenneth W., Spencer P., A comprehensive

System for Computer-Aided Tolerance Analysis of 2-D and 3-D Mechanical Assemblies, Proc. Of 5th Int. Seminar on Computer Aided Tolerancing, Toronto, 1997

[10] Concheri G., Computer Aided Tolerance

Analysis of mechanical parts based on variational geometry techniques, Proc. 10th ADM Conference “Design Tools and Methods”, pp. 549-558, Florence, 1997

[11] Chirone E:, Tornincasa S., “ A Tolerance

Stacks Analysis In The Design for Assembly”, IV International Congress of project Engineering, Cordoba, 0ttobre 1998

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Ma{instvo 2(3), 93 – 104, (1999) E.Ekinovi},...: MATEMATI^KO MODELIRANJE...

MATEMATI^KO MODELIRANJE FENOMENA TEORIJSKE MEHANIKE

Ekinovi} dr. Sabahudin, docent, Ma{inski fakultet u Zenici, Fakultetska 1., Zenica, Hadìkaduni} Fuad, dipl.in`., asistent, Ma{inski fakultet u Zenici, Vukojevi} Nedeljko, dipl.in`.,ŽBH Steel Co. "Zenica"

D REZIME

U ovom radu je prikazan postupak matemati~kog mokori{tenjem dvofaktornog eksperimentalnog plana (prvog i eksperimenta nim ta~kama. Disperzionom i regresionom anaopisuju navedene fenomene (centralni udar i kosi uda pokazala je zna~ajnije odstupanje teorijskih od eksperimentaln

lr)

ft

Klju~ne rije~i: planiranje eksperimenta, teorijska mehanika.

MATHEMATICAL MODELLING MECHANICS PHEN

Ekinovi} Sabahudin, PhD., Assistant Professor, Fa

in Zenica, Fakultetska 1., ZHadìkaduni} Fuad, B.Sc., Assistant, Faculty of MVukojevi} Nedeljko, B.Sc., Iron and Steel Works "Z

SUMMARY

A method of mathematical modelling o theoretical mexperimental plan (first and second order) with replica ion inthis paper. According to dispersion and regression analysiadequate described above-mentioned phenomena (central conditions. The analysis of results was showed significexperimental results in case of oblique collision.

Key words: experimental design, theoretical mechanic.

1. UVOD Fenomeni teorijske mehanike koji se susre}u u svakodnevnoj inènjerskoj praksi se rje{avaju kori{tenjem obrazaca koji tu pojavu (fenomen) tretiraju sa unaprijed utvr|enim uslovima. Naime, radi lak{eg rje{avanja postavljenog problema koriste se odre|ena pojednostavljenja i aproksimacije kako bi se {to brè i jednostavnije do{lo do rje{enja. Ta pojednostavljenja i aproksimacije u principu udaljavaju od ta~nog rje{enja s jedne strane, a s druge strane, olak{avaju rje{enje datog problema.

1. INT Phenomepresenteforms, wconditioninduced,approximapproximthe one problems

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IZVORNI NAU^NI RA

deliranja fenomena teo ijske mehanike drugog reda) sa ponavljanjem u svim lizom dobiveni su izrazi koji adekvatno u realnim uslovima. Analiza podataka ih rezultata za slu~aj kosog udara.

r

OF THEORETICAL OMENA

culty of Mechanical Engineering enica, echanical Engineering in Zenica, enica".
ORIGINAL SCIENTIFIC PAPER
rechanics phenomena using two-facto all experimental points is presented in s the regression models obtained here and oblique collision) under the real ant deviation between theoretical and

RODUCTION

na of theoretical mechanics, which are d in engineer practice, are solved by using hich these phenomena treat with prejudiced s. For easier solution of problems that are the definite simplifications and ations were used. These simplifications and ations remove from correctly solutions on hand, but make easier solving of induced on the other hand.


Kolika su ta odstupanja i da li se mogu prihvatiti prikazuje ovaj rad u kojem se analizira jedan od fenomena teorijske mehanike – udar ili sudar, i to: vertikalni udar tijela o nepokretnu podlogu i kosi udar tijela o nepokretnu podlogu. Pojava pri kojoj u beskona~no malom intervalu vremena, uslijed trenutnog dejstva sila, brzine ta~aka tijela dobivaju kona~ne promjene, naziva se udar, odnosno sudar, ako su u pitanju dva materijalna tijela. Udar je vrlo sloèna pojava i nemogu}e ga je definisati u potpunosti bez uvo|enja odre|enih hipoteza o strukturi tijela. Trenutne sile koje dejstvuju u toku udara, djeluju u vrlo kratkim vremenskim intervalima i dostiù vrlo velike vrijednosti. Ove sile se nazivaju udarnim ili trenutnim silama. U samom procesu udara, udarna sila raste od nule do neke maksimalne vrijednosti, a zatim opada i postaje jednaka nuli u trenutku prestanka kontakta. Zato je pojava udara neposredno vezana sa deformacijama tijela u okolini ta~ke dodira, tako da se ovdje moraju uvaìti i elasti~na svojstva tijela, {to odudara od osnovne postavke da su tijela koja se posmatraju kruta.

The magnitude of this digression and its acceptance are presented in this work, in which one of the theoretical mechanics phenomenon – blow or collision is analyzed (central and oblique collision of the bead to fixed basis). The phenomenon because of immediately strength activity, in infinitely small interval of time, velocities of two material bodies get definite changes is called collision. The collision is very composed phenomenon and it is impossible to complete define without using hypothesis of body structure. The immediately forces which work upon throughout the collision in small interval of time have very large values. These forces are called strike or immediate forces. In strike process, strike forces grows from zero to some maximal value, and at the moment when the contact is finished decreases to zero. The collision phenomenon is connected to body deformation in the area of contact point, so the elasticity properties of the body has to be taken into consideration. It means that bodies are not rigid.

2. VERTIKALNI CENTRALNI UDAR DVA TIJELA 2.1. Opis problema Problem koji se èli ovdje prezentirati sastoji se u tome, da je potrebno izmjeriti odskok koji kuglica odgovaraju~eg promjera, pu{tena slobodnim padom sa odgovaraju}e visine, postiè na odgovaraju}em materijalu. Ovdje se radi o tzv. centralnom (upravnom) udaru, s obzirom da se teì{ta tijela nalaze na vertikalnoj osi, a tako|er ulazna brzina i brzina nakon udara su kolinearne, ali ne i jednake. Upravo odnos intenziteta brzine tijela na kraju udara i intenziteta njegove brzine neposredno prije udara, pri pravom udaru o nepomi~nu podlogu naziva se koeficijentom restitucije pri udaru, a koji se moè predstaviti obrascem:

vvk′

= .... (1)

Na osnovu zakona o promjeni kineti~ke energije moè se na}i brzina kojom kuglica udari o podlogu, kao i brzina kuglice nakon udara:

1gh2v = , 2gh2v =′ , ... (2)

gdje je: v - brzina kuglice pri udaru o podlogu v′ - brzina kuglice poslije udara o podlogu

2. VERTICAL (CENTRAL) COLLISION OF TWO BODIES 2.1 Problem description In the problem that is presented, it is essential to measure the bounce of the bead with corresponding diameter, after free fail from corresponding height, to corresponding material. The position of gravity center of bodies is on the vertical axis, input and output velocities are collinear but not equal. This phenomenon is called central (vertical) collision. The ratio of velocity intensities before and after the vertical collision of bodies to the fixed basis is called the collision restitution coefficient, and it would be denoted as:

vvk′

= ...(1)

The velocities of bead, before and after collision, are deduced from the act of kinetic energy variation:

1gh2v = . 2gh2v =′ ...(2)

Where are: v – velocity of bead during collision to basis v′ - velocity of bead after collision to basis

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g – ubrzanje zemljine teè h1 – visina sa koje se pu{ta kuglica h2 – visina odskoka kuglice Dakle, odnos ovih brzina predstavlja koeficijent restitucije:

1

2

hh

vvk =′

= . ... (3)

Vrijednost koeficijenta restitucije kre}e se izme|u 0 i 1 koji zapravo predstavljaju grani~ne situacije potpuno plasti~nog udara (k=0) i potpuno elasti~nog udara (k=1). Upravo ovaj koeficijent restitucije, koji je poznat za odnos materijala koji se koristi u ovom eksperimentu, olak{ava uspostavljanje odnosa izme|u ulaznih i izlaznih veli~ina ovog eksperimenta. Taj odnos moè se definisati kako slijedi:

.... (4) 12

2 hkh ⋅= Problem se dakle sastoji u definisanju matemati~kog modela (jedna~ine) kojim }e se adekvatno opisati uticaj visine sa koje pada kuglica i promjera kuglice (kao izabranih ulaznih veli~ina), na visinu odskoka kuglice nakon udara o podlogu (izlazna veli~ina).

g – gravity acceleration h1 – releasing height of bead h2 – rebounce height of bead So, the ratio of these velocities is coefficient of restitution:

1

2

hh

vvk =′

=

...(3)

The magnitude of coefficient of restitution is between 0 and 1 which are extreme situations of total elastic collision (k=0) and plastic collision (k=1). Exactly this coefficient of restitution, which is known for used materials ratio in this experiment, relieves establishing of relation between input and output values of this experiment. This ratio is defined as follows:

h ...(4) 12

2 hk ⋅= The problem consists of adequate mathematical model definition (equation) as adequate description of influence releasing height of bead and bead diameter (as chosen input values) relation to rebound height of bead after blow to basis (output value).

2.2. Planiranje eksperimenta Korak koji analogijom prethodi procesu izvo|enja eksperimenta jeste izbor eksperimentalnog modela po kojem }e se eksperiment izvesti i rezultati matematski obraditi. Eksperimentom se variraju dva faktora: h1 – visina sa koje se pu{ta kuglica i d – promjer kuglice. Ostali uticajni parametri kao {to su npr. materijali kuglica i podloge drè se na konstantnom nivou. U definisanju funkcije oblika h2 = f(d,h1) polazi se od dvofaktornog potpunog ortogonalnog plana prvog reda tipa N = 2k sa ponavljanjem eksperimenta u svakoj ta~ki modela. U tabeli 1 prikazane su odabrane prirodne i korespondentne kodirane vrijednosti faktora.

2.2 Experimental design Analogous step before the experiment performs process is choosing of experimental model for experiment performing and mathematical treating. Two factors are varied in this experiment:: h1 – releasing height of bead, and d – bead diameter. Other influence parameters as materials of beads and basis are constants. Two-factor complete orthogonal first order plan N=2k with replication in all experimental points is used for function form h2=f(d,h1) defining. The natural and corespondent coded values of factors are shown in Table 1.

Tabela 1. Nivoi faktora modela Table 1. Level of the factors

FAKTOR FACTOR

Donji nivo Low level

Gornji nivo High level

Interval varijacije Interval of variation

d, mm 6 16 Promjer kuglice Bead diameter x1 -1 +1

5

h1 , mm 300 900 Visina slobodnog pada Fall height x2 -1 +1

300

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2.3. Izvo|enje eksperimenta Na slici 1 prikazan je {ematski postupak izvo|enja eksperimenta sa karakteristi~nim veli~inama.

2.3 Experimental work The schematic method of experiment perform with characteristic values is shown at Figure 1.

d(x)

900

vo = 0 800

700

600

h1(x2) 500

400

h2(y) 300

V' 200

V Slika 1. Vertikalni udar tijela o nepokretnu podlogu Figure 1. Vertical collision of the body to fixed basis Materijal svih kuglica je ~elik, a raspoloìvi pre~nici kuglica su ∅ 6 i ∅ 16. Materijal podloge je tako|er ~elik. Prema plan-matrici eksperimenta, odabere se kuglica odgovaraju}eg pre~nika i pusti da slobodno padne sa njoj pripadaju}e visine na ~eli~nu podlogu. Kuglica nakon udara o podlogu odsko~i na odgovaraju}u visinu, a vrijednosti dobivene nakon dva ponovljena eksperimenta u svakoj ta~ki plana predstavljaju rezultate mjerenja. Za slu~aj dvofaktornog eksperimenta sa dva ponavljanja u svakoj ta~ki eksperimenta polazni regresioni model je:

, ... (5) 22110 xbxbby ++= pri ~emu su jedna~ine transformacije:

i

i0ii w

XXx

−= , ... (6)

gdje je: xi – kodirana vrijednost faktora, Xi – prirodna vrijednost faktora, Xoi – osnovni nivo i wi – interval varijacije.

U tabeli 2 prikazana je plan-matrica eksperimenta kao i rezultati mjerenja.

Materials of beads are steel material, and available bead diameters are ∅ 6 and ∅ 16. The basis material is steel too. According to the plan-matrix, chosen bead with adequate diameter relieves from adequate height to steel basis. The bead rebounds to the appropriate height from basis, and after two replications of an experiment in all experimental plan-matrix points obtained as experimental values. For the case of two-factor experiment with two replications in all experiment points the initial regression model is:

, ...(5) 22110 xbxbby ++= where the transformation equation is:

i

i0ii w

XXx

−= , ...(6)

where are: xi – coded value of factor, Xi – natural value of factor, Xoi – fundamental level, and

wi – interval of variation. The plan matrix of an experiment and measuremet results are shown in Table 2.

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Tabela 2. Plan matrica eksperimenta i rezultati mjerenja Table 2. Plan-matrix and results of investigation

Plan-matrica Plan-matrix

Rezultati mjerenja Experimental results

Modelska vrijednost Model’s value Redni broj

No. exp. x0 x1 x2 y1 y2 y y

1 1 -1 -1 95 100 97,5 95 2 1 +1 -1 90 95 92,5 95 3 1 -1 +1 275 280 277,5 275 4 1 +1 +1 270 275 272,5 275

2.4. Analiza rezultata Ve} je re~eno da je teoretska postavka problema iskazana jedna~inom (4) iz koje se vidi linearna veza izme|u vrijednosti odskoka h2 i po~etne visine pada h1. Zna~i, na veli~inu odskoka kuglice uti~u po~etna visina pada kuglice, koeficijent restitucije k (koji je za ~elik po ~eliku k=5/9), odnosno materijal kuglice i podloge, dok veli~ina tijela nema uticaja. To je upravo i razlog {to je za izvo|enje eksperimenta upotrijebljen regresioni model prvog reda. Analiza signifikantnosti parametara modela (5) je pokazala gore navedenu tvrdnju, tj. veli~ina, odnosno masa kuglice, bar u odabranom intervalu variranja, ne uti~e zna~ajno na veli~inu odskoka kuglice, tako da se dobije regresioni model:

, .... (7) 1x90185y ⋅+= odnosno prelaskom na prirodne koordinate:

, .... (8) 12 h3,05h ⋅+= Analiza adekvatnosti modela (7) je pokazala da je isti adekvatan, tj. da se modelom (7) odnosno (8) moè adekvatno opisati zavisnost veli~ine odskoka kuglice od vrijednosti po~etne visine pada kuglice. Osim toga, dobivena je vrlo velika vrijednost koeficijenta korelacije R=0,99, a isto tako i vrlo mala vrijednost standardne gre{ke procjene za

veli~inu odskoka kuglice =3,5 mm. Uporedba

teoretskih vrijednosti i modelskih rezultata za tri vrijednosti po~etne visine h

2hs

1=300, 600 i 900 mm, prikazana je u tabeli 3.

2.4. Analysis of the results As it is mentioned the theoretical assumption is declared by equation (4) which shows linear relation between rebound value h2 and release height h1. It means to the bead rebound magnitude release height, coefficient of restitution k (which is for steel/steel k=5/9) influence, respectively the material of bead and basis, since the magnitude of the body has no influence. It is the reason of first order regression model using for experiment performing. Significance analysis of model (5) parameters confirms aforesaid contention, it means the bead mass, at chosen interval of variation, has no significance influence on bead rebound magnitude, so the regression model is:

, ...(7) 1x90185y ⋅+= respectively teasing to the natural co-ordinates:

, ...(8) 12 h3,05h ⋅+= Model adequacy analysis (7) showed that the model is adequate, it means the relationship between the magnitude of bead rebound and this model can adequately illustrate release height of the bead. Furthermore, the great value of correlation coefficient (R=0,99), so as very small value standard error for the bead rebound estimate

( =3,5 mm) are obtained. Comparison of

theoretical values and model results for three values of release height h

2hs

1=300, 600 and 900 mm, are shown in Table 3.

Tabela 3. Uporedba teoretskih vrijednosti i modelskih rezultata Table 3. Comparison of theoretical and experimental results

Odskok, Rebound, h2, mm Po~etna visina pada, Release height,

h1, mm

Teorijska vrijednost, Theoretical value,

Izraz, Expression (4)

Modelska vrijednost, Model’s value,

Izraz, Expression (8)

Odstupanje, Deviation,

%

300 92,59 95 2,54 600 185,185 185 0,1 900 277,778 275 1,0

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3. KOSI UDAR DVA TIJELA

3.1. Opis problema Potrebno je ispitati domet ~eli~ne kuglice koja vr{i kosi udar o ~eli~nu podlogu i odska~e na duìnu D, slika 2. Matemati~ki zakon kretanja kuglice je poznat, teoretski izvedena to je funkcija drugog reda - parabola. Ovaj zakon kretanja odre|uje glavne faktore (nezavisno promjenljive): po~etna brzina v0 i ugao odskoka γ. Matemati~ki zakon kretanja kuglice nakon odskoka u pravcu horizontalne ose glasi:

g2sinv

D20 γ⋅

= , .... (9)

Po~etna brzina vo je brzina kuglice poslije udara o nepokretnu podlogu, pod uglom β u odnosu na normalu. Ova brzina odre|uje se pomo}u brzine v1 koja predstavlja brzinu kojom kuglica udara o podlogu pod uglom α u odnosu na normalu. Odnos tangensa navedenih uglova predstavlja koeficijent udara, k=tgα.

Brzina nakon udara vo po intenzitetu iznosi:

αα 22210 cosksinvv ⋅+⋅= .... (10)

Brzina v1 kojom kuglica udara o podlogu odre|uje se iz sljede}e jedna~ine:

... (11) RFIcosGNymFsinGxm

trc

tr

⋅=⋅−=⋅

−=⋅

ϕα

α

&&

&&

&&

gdje je : m - masa kuglice,

yx &&&& , - ubrzanje u pravcu x i y ose,

ϕ&& - ugaono ubrzanje,

Ftr - sila trenja klizanja, G – teìna kuglice, g - ubrzanje zemljine teè, N - normalna sila,

R – pre~nik kuglice i

IC = 2

52 Rm ⋅ - moment inercije za kuglicu

Za pretpostavku da se kuglica kotrlja bez klizanja je:

, ... (12) ϕ

ϕ&&&&

&&&

⋅=⋅==

RxRxv

c

c1

3. TWO BODIES OBLIQUE COLLISION

3.1. Problem description It is necessary to ascertain carry of steel bead professing the oblique collision over steel basis and rebounding to the length D, Figure 2. The mathematical law of bead motion is known, it is theoreticaly the second order function – parable. This law of this motion defines main factors (independent factors): the elementary velocity v0 and the rebound angle γ. The mathematical act of bead movement after its rebounding in horizontal axis direct is:

g2sinv

D20 γ⋅

= , ...(9)

The initial velocity vo is the velocity after impact to fixed basis, with angle β in relation to normal axis. This velocity is defined with velocity v1, which is impact velocity of bead with angle α in relation to normal axis. The ratio of tangent values of these angles is called coefficient of restitution, k = tg α. The velocity after the impact vo as values is:

αα 22210 cosksinv ⋅+⋅=v ...(10)

The velocity v1 of the bead before its impact to fixed basis is:

...(11)

RFIcosGNymFsinGxm

trc

tr

⋅=⋅−=⋅

−=⋅

ϕα

α

&&

&&

&&

where are: m – bead mass - the velocity in direction of x i y yx &&&& , axis

ϕ&& - angle acceleration

Ftr – friction slide force G – bead weight g - gravity acceleration N – normal force

R – bead diameter

IC = 2

52 Rm ⋅ - moment of inertia

For the assumption of bead bowling without sliding:

, ...(12) ϕ

ϕ&&&&

&&&

⋅=⋅==

RxRxv

c

c1

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Iz jedna~ina (11) i (12) i uvr{tavajući vrijednost za Ic slijedi:

ctr xm52F &&⋅= , .... (13)

Uvr{tavaju}i prvu jedna~inu iz jedna~ina (11) slijede jedna~ine za ubrzanje, brzinu i putanju kuglice u pravcu xc ose:

2c

c

c

tsing145x

tsing75x

sing75x

⋅⋅=

⋅⋅=

⋅=

α

α

α

&

&&

... (14)

uz uslove za t =0 slijedi da je =0 , i xcx& c = 0.

Poznavaju}i duìnu trase xc = 0,3 m i za uglove α=15° do 60° iz jedna~ina (14) odre|uje se vrijeme t i brzina kojom kuglica udara o podlogu

= vcx& 1. Na osnovu gore navedenih jedna~ina i iz

njih dobijenih podataka slijede ra~unske vrijednosti doskoka kuglice za razli~ite uglove nagiba strme ravni ϕ, koje su prikazane u tabeli 4.

From equations (11) and (12) and the equation for Ic follows:

ctr xm52F &&⋅= , ...(13)

After the first equation of (11) follows equations for acceleration, velocity and the bead path in direction of xc axis:

2c

c

c

tsing145x

tsing75x

sing75x

⋅⋅=

⋅⋅=

⋅=

α

α

α

&

&&

...(14)

with conditions for t =0 follows =0 , and xcx& c =

0. For the length of the path xc = 0,3 m and for angels α = 15° to 60° from equations (14), the time t and the impact velocity = vcx& 1 are known.

After precedent equations and its data, different values of carries for different values of precipitate flat angels ϕ, are shown in Table 4.

Tabela 4. Vrijednosti doskoka D u zavisnosti od ugla nagiba strme ravni ϕ Table 4. Values of carries D subordinates of precipitate flat angles ϕ

ϕ, ° α, ° β, ° γ, ° v1, m/s v0, m/s D, mm 30 60 72,21 17,78 1,44 1,31 103 45 45 60,94 29,05 1,72 1,39 168 52,5 37,5 54,09 39,9 1,82 1,37 188 60 30 46,1 43,89 1,9 1,32 178 75 15 25,75 64,25 2,01 1,19 114

Teorijski matemati~ki model vaì u odgovaraju}im idealiziranim uslovima na primjer za kosi djelimi~no elasti~ni udar tijela (0<k<1) o nepomi~nu podlogu, povr{ina tijela i podloge se smatraju apsolutno glatkim i sl. Takvu idealizaciju je nemogu}e posti}i u realnim uslovima kao i izbje}i pojavu trenja izme|u kuglice i kose ravni po kojoj se kuglica spu{ta. Prema tome, eksperimentalnim putem dobiven model koji opisuje domet ~eli~ne kuglice nakon kosog udara o ~eli~nu podlogu vrijedio bi za realne uslove.

The theoretical mathematics model applies in corresponding optimum conditions as slope partial elastic impact of the body (0<k<1 ) to fixed basis, the surface of the body and the basis are absolutely smooth, etc. It is impossible to get this ideal situation in real conditions, as avoiding friction between the bead and the precipitate flat. Accordingly the model, which is got by experimental way, describing the steel bead carry after oblique collision to steel basis appropriates to real conditions.

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3.2. Planiranje eksperimenta Polazi se od modela drugog reda:

,... (15) 2iiijiijii0 xbxxbxbby ΣΣΣ +++=

pri ~emu su kao faktori modela uzeti promjer kuglice d i ugao nagiba strme ravni ϕ. Odabran je centralni kompozicioni ortogonalni plan, a nivoi faktora u prirodnim i kodiranim vrijednostima prikazani su u tabeli 5.

3.2. Experimental design

Preliminary model is second order model:

...(15) 2iiijiijii0 xbxxbxbby ΣΣΣ +++=

There are as factors modeled the diameter of bead d and angle of precipitate flat ϕ. Chosen central composition orthogonal plan, and levels of factors in natural and coded values are reported in Table 5.

Tabela 5. Nivoi faktora modela Table 5. Level of the factors

FAKTOR FACTOR

Donji nivo Low level

Osnovni nivo Basic level

Gornji nivo High level

Interval varijacije Interval of variation

d, mm 6 11 16 Promjer kuglice Bead diameter x1 -1 0 +1

5

ϕ, ° 30 52,5 75 Ugao nagiba strme ravni Precitipate flat angle x2 -1 0 +1

22,5

Ostali uticajni faktori se drè na istom nivou na primjer, duìna strme ravni, povr{ina po kojoj se kotrlja kuglica i sl. Prema tome, uslovi u kojima je izveden eksperiment odredjuju granice validnosti eksperimentalnih rezultata, tj. rezultati vrijede samo za odre|enu duìnu strme ravni, odre|enu hrapavost povr{ine, osobine podloge o koju kuglica udara.

The other instance factors are held on the same level for example: length of the precipitate flat, bowling surface etc. Accordingly, conditions in which the experiment is performed designate limits of significance of experimental results; it is valid only for definite length of precipitate flat and definite roughness and properties of impact basis.

3.3. Izvo|enje eksperimenta Kako je ve} navedeno, za eksperiment je potrebna strma ravan kojoj se mijenja ugao nagiba ϕ pri ~emu duìna trase po kojoj se kuglica kotrlja ostaje ista, slika 2. Uvode se pretpostavke: kuglice se smatraju homogenim sferama, u po~etnom trenutku kuglice miruju, kuglice se kotrljaju bez klizanja, a otpor kotrljanja se zanemaruje. Eksperiment se izvodi tako {to se kuglice razli~itog promjera pu{taju niz strmu ravan pri ~emu se ugao nagiba strme ravni tako|er mijenja prema planu eksperimenta prikazanog u tabeli 6. Kuglica udara o podlogu i odska~e, te na odre|enoj udaljenosti D ponovo udara o podlogu. Da bi se mogao mjeriti domet kuglice na podlogu je postavljen indigo-papir koji ostavlja trag na podlozi nakon udara kuglice. S ciljem prora~una gre{ke eksperimenta vr{ena su ponovljena mjerenja u svakoj ta~ki eksperimentalnog plana. Broj eksperimentalnih ta~aka je N=2k+2k+n0 = 22+2⋅2+1=9.

3.3. Experimental work As was already quoted for experiment is necessaries the precipitate flat with changeable incline angle ϕ where the length of bowling path remains unchangeable. The suppositions are introduced; beads are homogeneous spheres, in starting moment the beads conciliate, then bowls without sliding, and bowling resistance is ignored. The experiment is performed so that the different diameter of beads are set free downhill and the incline angle is changed according to experimental plan which is shown in Table 6. The bead blow to the basis and bounds then on the definite distance D blows to the basis again. The range of the bead on the basis is measured using the indigo-paper that makes the trail on the basis after the collision. The measurements were performed with several replications in every point of experimental plan with intention to estimate experimental errors. The number of experimental points is: N=2K+2K+n0 = 22+2⋅2+1=9.

x

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Slika 2. Kosi udar dva tijela Figure 2. Two bodies oblique collision

Tabela 6. Plan matrica eksperimenta i rezultati mjerenja Table 6. Plan-matrix and results of investigation

Plan matrica, Plan-matrix

Eksperimantalni rezultati Experimantal results

Modelski rezultati, Model’s results

Red. broj, No. exp

x0 x1 x2 x12 x22 x1x2 x′1 x′2 y1 y2 y y 1 +1 +1 +1 +1 +1 +1 1/3 1/3 168 172 170 173,7 2 +1 -1 +1 +1 +1 -1 1/3 1/3 117 127 122 127,2 3 +1 +1 -1 +1 +1 -1 1/3 1/3 106 114 110 106,88 4 +1 -1 -1 +1 +1 +1 1/3 1/3 90 102 96 94,38 5 +1 +1 0 +1 0 0 1/3 -2/3 188 200 194 194,5 6 +1 -1 0 +1 0 0 1/3 -2/3 165 170 167,5 146,04 7 +1 0 +1 0 +1 0 -2/3 1/3 160 164 162 153,2 8 +1 0 -1 0 +1 0 -2/3 1/3 102 95 98,5 103,38 9 +1 0 0 0 0 0 -2/3 -2/3 170 185 177,5 181,5

3.4. Analiza rezultata

Regresionom obradom podataka dobijen je model drugog reda:

3.4. Analysis results The second order model is obtained by regression analysis:

2122

2121 XX075,0X105,0X11,0X32,11X403,1682,168y +−−++−= , ...(16)

gdje su X1 i X2 prirodne vrijednosti faktora modela. Analiza signifikantnosti je pokazala da su oba faktora signifikantna, tj da zna~ajno uti~u na veli~inu doskoka. Tako|er i analiza adekvatnosti je pokazala da model (16) adekvatno opisuje ispitivani proces, a koeficijent korelacije ima vrlo visoku vrijednost R=0,99.

where are: X1 and X2 natural values of model factors, the bead diameter and the incline angle. Significance analysis was shown that booths factors are significant, significaty instance to greatness of range. Also and adequacy analysis was showen that model (16) corectly describe researced process, and coefficient of correlation (multiple regression) has a very high value R=0,99.

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S druge strane, vrijednost standardne gre{ke procjene za doskok kuglice je vrlo mala sD=7,8 mm. U tabeli 7 prikazani su rezultati dobijeni ra~unskim putem prema teorijskim izrazima (9) do (14) i oni dobijeni iz regresionog modela (16) za razli~ite promjere kuglice i uglove nagiba strme ravni. Iz odnosa se vidi da vrijednosti dobivene

preko regresionog modela i vrijednosti dobijene ra~unskim putem odstupaju u granicama od oko ±10%. Ova odstupanja se mogu objasniti gre{kom eksperimenta s jedne strane i uticaja drugih, eksperimentom neobuhva}enih faktora (trenje i sl.), s druge strane. Tako|er se s razlogom moè posumnjati na veliki broj pojednostavljenja i idealizacija koje su uzete pri teoretskim postavkama u izrazima (9) do (14), {to moè rezultirati navedenom razlikom rezultata.

Dy /ˆ

On the oder hand, the value of standard error is very small sD = 7,8 mm. Estimated results according to theoretical forms (9) to (14) and results got from regression model (16) for different beads and different angles are shown in Table 7.

Relation demonstrates that values from

regression model and estimate values has deviations at limits ±10%. These deviations have been able to explain through the experimental errors on the one hand and by other not included factors on the second hand. Also one of reasons can be great numbers of approximation and idealization took in theoretical forms (9) to (14), that can generate named deviations of results.

Dy /ˆ

Tabela 7. Uporedba teoretskih vrijednosti i modelskih rezultata Table 7. Comparison of theoretical and experimental values

Promjer, Diameter, d, mm

ϕ, ° y , mm y , mm D, mm Dy /ˆ

75 122 127,2 114 1,115 52,5 167,5 164,046 188 0,87 ∅ 6

30 96 84,38 103 0,91 75 162 153,21 114 1,34 52,5 177,5 181,5 188 0,965 ∅ 11

30 98,5 103,38 103 1,003 75 170 173,7 114 1,52 52,5 194 193,54 188 1,029 ∅ 16

30 110 106,88 103 1,037

U tabeli 7 se tako|er uo~avaju dvije vrijednosti koje ekstremno odstupaju odnosom i to za

kuglice ∅ 11 i ∅ 16 a za ugao ϕ=75°. Ovo odstupanje se moè objasniti time {to se u teorijskoj mehanici pretpostavlja kotrljanje bez klizanja. Ako se pretpostavi da kuglica kliè niz strmu ravan slijedi:

Dy /ˆ

m ... (17) µα FsinGxc −⋅=⋅ && αµµ cosGF ⋅⋅= ... (18)

Uz µ = 0,15 za ~elik/~elik dobije se:

... (19)

( )( )( ) 2/tcossingx

tcossingxcossingx

2c

c

c

⋅⋅−=

⋅⋅−=⋅−=

αµα

αµααµα

&

&&

uz uslove t=0, , x0=cx& c=0.

Two values deviates with extremely ratio

(beads ∅ 11 and ∅ 16 for the angle ϕ=75°) are shown in table 7. These deviations can be explained with supposition that bead rolls without sliding. If the assumption is that the bead slides downhill, results are:

Dy /ˆ

...(17) µα FsinGxm c −⋅=⋅ && ...(18) αµµ cosGF ⋅⋅= For µ=0,15 and steel/steel:

...(19)

( )( )( ) 2/tcossingx

tcossingxcossingx

2c

c

c

⋅⋅−=

⋅⋅−=⋅−=

αµα

αµααµα

&

&&

and conditions t=0, , x0=cx& c=0 and 1vxc =&

- 102 -


Iz jedna~ine (19) slijede vrijednosti za t, xc=v1, pa vrijednost izra~unatog doskoka iznosi D=153 mm, tj. za ϕ=75° i ∅ 11 =153,21 , D=153 i

=1,001 a za ϕ=75° i ∅ 16 =173,7 ,

D=153 i =1,13.

yDy /ˆ y

Dy /ˆZna~i sada se dobije zadovoljavaju}i odnos ,

te se moè re}i da se za uglove ve}e od 60°, za slu~aj kotrljanja ~elik/~elik, ta~niji rezultati dobiju ako se uzme da kuglica kliè po podlozi, a za uglove ispod 60° slu~aj kotrljanja bez klizanja.

Dy /ˆ

Values for t follows from form (19), xc=v1, so calculated value for range is D=153 mm, it means for ϕ=75° and ∅ 11, =153,21, D=153, and

=1,001. Also, for ϕ=75°, and ∅ 16,

=173,7, D=153 and =1,13.

y

D/Dy /ˆ

y yThe ratio is satisfactory. It means for angles

over 60° (rolling steel/steel) the bead slides along the slope plan and the result is correctly. In case of angles under 60° the bead rolls without sliding.

Dy /ˆ

4. ZAKLJU^NA RAZMATRANJA Na osnovu provedenih eksperimentalnih ispitivanja, te na osnovu analize rezultata mogu se donijeti sljede}i osnovni zaklju~ci:

• Primjenom planiranog eksperimenta se mogu

adekvatno opisati i fenomeni teorijske mehanike. U ovom slu~aju to su fenomeni vertikalnog i kosog udara tijela o nepokretnu podlogu,

• U slu~aju vertikalnog udara vrijednosti odskoka dobivene na osnovu eksperimentalnog modela: h2 = 5+0,3h1 se vrlo malo razlikuju od teoretskih. Grafi~ka interpretacija ovih rezultata prikazana je na slici 3.

4. CONCLUSIONS Based on presented experimental research and results ana ysis, following can be concluded: l • Theoretical mechanics phenomena can be

adequately presented by application of experiment design.

• In the case of vertical blow the difference between theoretical and experimental values is very small. The experimental model is presented with the form as follows: h2=5+0,3h1. The graphic interpretation is presented in Figure 3.

80

100

120

140

160

180

200

220

240

260

280

250 350 450 550 650 750 850 950h1, m m

h 2, m

m

Teorijskavrijednost,h2,mm

Modelskavrijednost,h2,mm

Slika 3. Uporedba teoretskih i eksperimentalnih rezultata za vertkalni odskok Figure 3. Comparison of theoretical and experimental results for vertical collision

• U slu~aju kosog udara vrijednosti odskoka dobivene

na osnovu eksperimentalnog modela: D = -168,682 + 1,403 d + 11,32⋅ϕ – 0,11 d2 – 0,105 ϕ2 + 0,075 d⋅ϕ se zna~ajnije razlikuju od teoretskih. To se moè objasniti gre{kom eksperimenta ali i evidentnim aproksimacijama kod teoretskih izraza, kojima se ne uzimaju u obzir razli~iti otpori, zatim u~e{}e trenja klizanja i kotrljanja itd.

• In the case of oblique collision the difference between theoretical and experimental values is significantly. The experimental model is presented through the form: D=-168,682+ 1,403X1+11,32X2–0,11X12–0,105X22+0,075X1X2. That can be explained with experimental errors and approximations by theoretical forms.

- 103 -


100

110

120

130

140

150

160

170

180

190

200

30 40 50 60 70 80ϕ ,o

D, m

m

Teorijskavrijednost,D,mm

Modelskavrijednost,D,mm

Slika 4. Uporedba teoretskih i eksperimentalnih rezultata za kosi doskok Figure 4. Comparison of theoretical and eksperimantal results for oblique collision

Ovo je naro~ito izraèno pri uglovima nagiba strme ravni ϕ>60°, gdje o~igledno postoji trenje klizanja, a ne trenje kotrljanja. Na slici 4 prikazana je uporedba teoretskih i modelskih vrijednosti doskoka u zavisnosti od ugla nagiba strme ravni, a za tri razli~ita promjera kuglica.

• Navedeno ispitivanje pokazuje da je za

konkretne tehni~ke probleme koji se modeliraju problemima teorijske mehanike potrebno izvr{iti i adekvatno eksperimentalno ispitivanje u koju svrhu moè efikasno posluìti metodologija planiranog eksperimenta.

Different resistance and frictions (sliding and rolling) are nit included in theoretical forms. This is the special expressive by incline angles over 60° where, obviously, exists sliding friction. The comparison of theoretical and model values depends of incline angle of slope plane for three different bead diameters. Comparison of theoretical and experimental results is showed in Figure 4. • Aforesaid experimental research showed that for

concrete technical problems, which are modeled by theoretical mechanics phenomena, are necessary to realize adequacy experimental research. Methods of an experimental design can be used for effective experimental research.

5. LITERATURA – REFERENCES [1] J. Stani}: Metod inènjerskih mjerenja, Ma{inski fakultet u Beogradu, Beograd, 1990. [2] M.I. Batj, G.J. D@andzelize, A.S. Kelzon: Re{eni zadaci iz Teorijske mehanike sa izvodima iz teorije – Dinamika II, Ma{inski fakultet u Beogradu, Beograd, 1990.

[3] D. Vukojevi}: Dinamika, Ma{inski fakultet u Zenici, Zenica, 1990. [4] S. Ekinovi}: Metode statisti~ke analize u MICROSOFT-EXCELU, Ma{inski fakultet u Zenici, Zenica,1997. [5] M.R. Spiegel: Theory and Problems of Theoretical Mechanics, McGraw-Hill Book Co., New York, 1967.

- 104 -

Ma{instvo 2(3), 105 - 111, (1999) S.Klari}: POTREBA ZA UNAPRE\ENJEM...

1. UVOD

Dana{nje vrijeme, bez sumnje karakteri{e kvalitet. Onje postao klju~ni dio poslovne politike i pokreta~kasnaga razvoja privrede u visoko razvijenim zemljama.Sve vi{e sazrijeva spoznaja da je kvalitet proizvodai usluga najva`niji faktor konkurentnosti i poslovneuspje{nosti. Na opstanak, jo{ manje na pove}anjeobima plasmana na{ih proizvoda na vanjskimtrì{tima nije mogu}e ra~unati, ako nismo spremnida se neprestano prilago|avamo zahtjevima kupcaodnosno tih trì{ta po pitanju kvaliteta.

Globalizacija svjetskih kretanja i uslovi me|unarodnerazmjene dobara zahtijevali su izradu i objavljivanjestandarda za globalno trì{te. Svjetska trgovinskaorganizacija WTO-World Trade Organization poziva sena odre|ene standarde koji defini{u uslove kojetreba prethodno da ispune zemlje koje èle dapostanu njeni ~lanovi. Pripremu i objavljivanje tih standarda vr{i Me|unaro-

PPOOTTRREEBBAA ZZAA UUNNAAPPRREE\\EENNJJEEMM KKVVAALLIITTEETTAAUU BBOOSSNNII II HHEERRCCEEGGOOVVIINNII

Mr. Smail Klari}, Univerzitet "Dèmal Bijedi}", Ma{inski fakultet - Mostar

REZIME

U radu se analizira stanje kvaliteta u Bosni i Hercegovini i potreba za njegovim unapre|enjem krozsistem kvaliteta. Navedeni su razlozi zbog kojih Bosna i Hercegovina, u ovoj oblasti, treba da uradizna~ajan napor da bi se pribliìla Evropi i svijetu i nazna~en pravac za akciju. Krajnji rezultat bi tre-bao da bude Dràvni program kvaliteta Bosne i Hercegovine.

Klju~ne rije~i: kvalitet, sistem kvaliteta, standard, organizacija

TTHHEE NNEEEEDD FFOORR IIMMPPRROOVVIINNGG OOFF QQUUAALLIITTYYIINN BBOOSSNNIIAA AANNDD HHEERRCCEEGGOOVVIINNAA

MSc Smail Klari}, University "Dèmal Bijedi}", Faculty of Mechanical Engineering,Mostar

SUMMARY

In the papers the state of the quality in Bosnia and Herzegovina is analyzed and the need for itsapproval trought the system of quality. The reasons for change in the field in Bosnia and Herzegovinahave been listed because it is necessary to do a great effort in the field to come closer to Europeand world. The way to start with it has been defined, too. The result of it should be the StateProgram of Quality in Bosnia and Herzegovina.

Key words: quality, quality system, standard, organization

1. INTRODUCTION

Current time is undoubtedly characterised by the qual-ity. It became key part of business politics and start-ing force of the development of economy in highlydeveloped countries. More and more comprehensionmatures that the product and service quality is themost important factor of competitiveness and businesssuccess. We can not count on survival or on increasein pierce of our products to foreign markets, if weare not ready to constantly adjust to requests of cus-tomers or these markets in the matter of quality.

Globalisation of world changes and conditions ofinternational goods exchange required creation andpublication of standards for global market. WTO-World Trade Organisation relies on certain standards,which define conditions to be fulfilled by countriesthat wish to become members of it. Preparation andpublication of these standards is performed byInternational Organisation for Standardisation, which

SSTTRRUU^NNII RRAADD

PPRROOFFEESSSSIIOONNAALL PPAAPPEERR

dna organizacija za standardizaciju ISO-InternationalOrganization for Standardization, koja danas brojipreko 120 zemalja ~lanica, ~ijih vi{e od 30000eksperata u~estvuje u pripremi standarda. Me|u,preko 11000 objavljenih standarda, nalaze se dobropoznati standardi serija ISO 9000, ISO 14000 i ISO10000. Ovi standardi opisuju sistem upravljanja kvalite-tom i sistem upravljanja okolinom. Bosna iHercegovina je ~lan ili eli da postane ~lan odre|enihme|unarodnih organizacija, ali za prijem u ~lanstvotreba da ispuni uslove koji su definisani standardima.

2. OP[TE O KVALITETU I SISTEMUKVALITETA

Kvalitet je uvijek bio vaàn faktor pri ugovaranju inaru~ivanju proizvoda i usluga, pri razvoju i pripre-mi proizvodnje, nabavi i proizvodnji, te isporuci ikori{tenju proizvoda. U svijetu se pristup premakvalitetu stalno mijenja, odnosno dopunjava sadodatnim zahtjevima koje kupac postavlja premaisporu~iocima / proizvo|a~ima. Danas smo suo~enisa novim uslovima u kojima su kupci i proizvo|a~izapleteni u potpuno nove probleme me|u kojimasu:

* Neefikasnost organizacija da na|u pravovremeneodgovore na vrlo brze poraste proizvodnih tro{kovazbog visokih cijena ulaznih elemenata i stalnogtehnolo{kog napretka koji se ne moè realizovati bezzna~ajnih investicionih ulaganja. Zbog toga cijeneproizvoda i usluga koje se formiraju nisukonkurentne na trì{tu, a niè cijene proizvoda iusluga ne podmiruju tro{kove poslovanja i dovodeorganizacije u gubitak.* Savremeni kupac zahtijeva vi{i kvalitet proizvoda iusluga, niè cijene i kra}i rok isporuke. Kupac zahti-jeva povjerenje u sposobnost isporu~ioca, da }estalno isporu~ivati proizvode i usluge ugovorenogkvaliteta. Postalo je uobi~ajeno da ovu sposobnostisporu~ilac dokazuje certifikatom sistema kvaliteta, ada se postupak dokazivanja obavlja kod ovla{teneme|unarodne institucije. Proizvo|a~ koji ne udovoljièljama i zahtjevima kupca gubi kupca i trì{te, atime ugroàva i svoj opstanak. * Ekonomsko zao{travanje i politi~ka nestabilnost uodre|enim podru~jima, sa kojima smo suo~eni,naro~ito uslo`njavaju navedene probleme i ra|ajunove koji su te{ko otklonjivi.

Iskustva razli~itih organizacija u svijetu, a i kod nas,pokazuju da je primjena savremenih i efikasnih pro-grama kvaliteta najbolja investicija koju zemlje i orga-nizacije mogu provoditi u sada{njim uslovima.


has over 120 member countries, from which morethan 30.000 experts take part in preparation of stan-dards. Between over 11.000 published standardsthere are well known standards of series ISO 9000,ISO 14000 and ISO 10000. These standardsdescribe system of quality management and systemof environment management. Bosnia andHerzegovina is member or wants to become mem-ber of certain international organisations, but tobecome member it has to fulfil conditions definedby these standards.

2. ABOUT THE QUALITY AND THE SYSTEM OF QUALITY IN GENERAL

Quality was always important factor in agreementsand orders of products and services, in develop-ment and preparation of the production, supply andproduction, and deliverance and use of products.Worldwide, the approach to the quality is constant-ly being changed and complemented with extrarequirements that customer sets to deliverers andproducers. Today we are faced to new conditionswhere customers and producers are involved intocompletely new problems, such as:

* Inefficiency of organisations to find right-timeanswers to very rapid increase of production costsbecause of high prices of input elements and con-stant technological progress that can not be realisedwithout significant investments. Because of that theprices of products and services being formed arenot competitive on the market, and lower prices ofproducts and services can not cover costs of busi-ness and they lead organisations to a loss.* Modern customer requires higher quality of products andservices, lower prices and shorter delivery time. The cus-tomer requires confidence to deliverer capability that hewill constantly deliver products and services that haveagreed quality. It became common that such capability isproved by certificate of the quality system, and that pro-cedure of proving capability is performed at authorisedinternational institution. Producer who does not fulfil wish-es and requests of the customer loses customer and themarket, and such endangers its survival.* Economic sharpening and political instability incertain areas, that we are faced, especially compli-cates these problems and they create new ones thatare hardly removable.

Experiences of different organisations in the world,as well as in our country, show that application ofmodern and efficient quality programs is the bestinvestment that countries and organisations can per-

form in present conditions. Present conditions ofeconomy lead to new impacts and influence of qual-ity to business and development of every organisa-tion and wider community. Orientation to new mar-kets, involving in co-operation in the world market,especially with European Community, together withuse of al natural and human resources are reasonsfor significant change of attitudes toward quality.Quality programs ensure placement of products andservices to world market, increase in productivity anddecrease in costs for such increased profit.Organisations, which realised significant increase inbusiness, state that they had embossed action in thearea of quality management. The key of their strengthis in that they are based on efficient and economi-cal system of quality management that ensures busi-ness and technological basis for complete transfor-mation of the organisation towards quality manage-ment, i.e. realisation of complete customer satisfac-tion in the matter of quality, time limits and the price.

Modern quality programs are widely used in leadingorganisations in USA, Europe, Japan and the rest ofthe world, and also new programs are being devel-oped. They widely affect development of new com-petitive quality standards. In the last decade, a lotof things changed worldwide. Today, "quality system"is being observed as a quality of organisation as awhole, that is business system that accepts marketand competitors as only criteria of success.Therefore, definition of the term "product" is alsochanged from material to nonmaterial human sphere- services.

3. BOSNIA AND HERZEGOVINA ANDTHE QUALITY

Consequences of the past war in the area of Bosniaand Herzegovina are catastrophic for its economy.Most of production capacities are destroyed. Largenumber of experts left the country. Besides such sit-uation some production capacities are being restart-ed. In the period of renewal of the economy, andlater on, the quality of products and services shouldhave the key role.Bosnia and Herzegovina in its exchange of goods andservices, like in the period before the war, will bemostly connected to Europe and processes that occurin Europe. That requires compatibility of our technicalregulations with regulations of European Union andinternational organisations for standardisation, metrolo-gy and protection of industrial property, and fulfillingthese regulations by our industrial and non-industrialorganisations. We should expect large changes.

Sada{nji uslovi privre|ivanja dovode do novih pod-sticaja i uticaja kvaliteta na poslovanje i razvoj svakeorganizacije i {ire zajednice. Orjentacija na novatrì{ta, uklju~ivanje u saradnju na svjetskom trì{tu,pogotovo sa Evropskom unijom, uz istovremenokori{tenje svih prirodnih i ljudskih resursa razlozi suza bitnu promjenu odnosa prema kvalitetu. Programikvaliteta obezbje|uju plasman proizvoda i usluga nasvjetskom trì{tu, porast produktivnosti i smanjenjetro{kova te pove}anje dobiti. Organizacije koje suostvarile zna~ajan porast poslovanja isti~u da suimale nagla{eno djelovanje u oblasti upravljanjakvalitetom. Klju~ njihove snage leì u tome {to subazirani na efikasnom i ekonomi~nom sistemuupravljanja kvalitetom, koji obezbje|uje poslovnu itehnolo{ku osnovu za prelazak organizacije na pot-punu aktivnost u cilju upravljanja kvalitetom, tj. ostva-rivanja potpunog zadovoljenja kupaca u pogledukvaliteta, roka i cijene.

Savremeni programi kvaliteta su ve} u punomzamahu u vode}im organizacijama SAD, Evrope,Japana i ostalog svijeta, a radi se i na razvijanjunovih programa. Oni u velikoj mjeri uti~u i na razvojnovih konkurentskih standarda kvaliteta. U svijetu se,u tom pogledu, zadnjih desetak godina, dosta togapromijenilo. Danas se pod pojmom "sistem kvaliteta"podrazumijeva kvalitet organizacije kao cjeline,odnosno sistem poslovanja koji prihvata trì{te ikonkurenciju kao jedine kriterije uspje{nosti. Pritome, promijenila se i definicija pojma "proizvod" izmaterijalne i u nematerijalnu sferu ljudske djelatno-sti-usluga.

3. BOSNA I HERCEGOVINA IKVALITET

Posljedice proteklog rata na prostoru Bosne iHercegovine su katastrofalne za njenu privredu.Najve}i broj proizvodnih kapaciteta je uni{ten. Velikbroj stru~nih kadrova je napustio zemlju. I poredtakve situacije po~elo je pokretanje odre|enihproizvodnih kapaciteta. U periodu obnavljanjaprivrede, a i kasnije, kvalitet proizvoda i usluga trebada ima presudnu ulogu.Bosna i Hercegovina u svojoj robnoj i nerobnojrazmjeni, kao i u periodu prije rata, bi}e najvi{evezana za Evropu i procese koji se u Evropi odvi-jaju. To zahtijeva usagla{enost na{e tehni~ke regu-lative sa regulativom Evropske unije i me|unarodnihorganizacija za standardizaciju, mjeriteljstvo i za{tituindustrijske svojine, a i po{tivanje te regulative odstrane na{ih privrednih i neprivrednih organizacija.O~ekuju nas velike promjene.


Bitka za promjenama postala je klju~na preokupaci-ja svakog pojedinca, organizacije (preduze}a, insti-tucije) i dru{tva u cjelini. Su{tina toga je kako seza{tititi od neprestanih promjena u okruènju.Odgovor je veoma jednostavan: po{to su promjeneprirodan proces koji se de{ava svakodnevno, od njihse ne treba braniti, ve} naprotiv-treba im i}i u sus-ret. Rje{enje treba traìti u stvaranju dru{tvenogambijenta za promjene. Pod tim se, u prvom redu,podrazumijeva stvaranje dru{tvene svijesti oneophodnosti promjena i pripremi ljudi za njihovoizvo|enje.

Iako ne postoje recepti za rje{enje svih na{ih pro-blema, sigurno je da rje{enja moraju biti zasnovanana savremenim saznanjima i na prou~avanju rele-vantnih faktora koji mogu biti od uticaja u konkre-tnim uslovima. Pri tome se ne smije zaboraviti dasu promjene proces, a ne doga|aj. Su{tina rje{enjaje u osmi{ljavanju procesa stvaranja ambijenta zapromjene. To nije nimalo jednostavan proces za bilokoju sredinu, jer se pojavljuju specifi~ni problemikoji predstavljaju, na neki na~in, "kulturne faktore" tesredine. Ovi faktori su izuzetno zna~ajni jer nedjeluju izolovano, te{ko se mijenjaju i te{ko ihmogu razumjeti ljudi sa strane. Po~etni korak pred-stavlja mjerenje i odre|ivanje vlastitog poloàja uodnosu na razvijeni svijet, a zatim razmatranjemogu}nosti nadokna|ivanja tog zaostajanja. Bezrealnog sagledavanja postoje}eg stanja, male su{anse da se postave realni ciljevi, a nikakve da seti ciljevi ostvare.Slijede}i korak bio bi stvaranje kriti~ne mase potreb-ne za po~etak akcije, odnosno stvaranje timova odljudi koji se ne}e upla{iti kada krenu u proces pro-mjena. Samo postavljanje zadatka i njegovo razma-tranje od strane tima izuzetno uti~e na stvaranje po-zitivne klime, dok postignuti rezultati povratno uti~una {ire okruènje. Posebnu pa`nju treba posvetitiprimjenjenoj nauci, jer je time prostor za djelovanjeveoma {irok.

Unapre|enje kvaliteta kroz uvo|enje savremenih sis-tema kvaliteta, odnosno sistema za kvalitetan rad usvim oblastima ljudskog djelovanja, predstavlja kom-pleksan i ambiciozan projekat. Da bi se takav pro-jekat uspje{no realizovao potrebno je znanje koje semora neprestano inovirati. Su{tina problema se svodina pronalaènje efikasnog oru`ja za savladavanje"organizacionog haosa", a su{tina rje{enja jeste ukori{tenju tog oru`ja u svakodnevnim bitkama i nasvim nivoima. Na osnovu naprijed re~enog, kod unapre|enjakvaliteta u Bosni i Hercegovini, treba imati u viduslijede}e:


The battle for changes became key preoccupationof every person, organisation (company, institution)and the whole society. The essence of that is howto protect oneself from constant changes in theenvironment. The answer is very simple: since thechanges are natural processes that occur every day,we should not protect ourselves from them but togo to meet them. The solution should be looked forin creation of social ambient for changes. Thatmeans, in first hand, creation of social sense aboutnecessity of changes and preparation of people toperform them.

Although there are no recipes for solution of all ourproblems, it is sure that solutions have to be basedon modern knowledge and on researching of rele-vant factors, which can occur in concrete circum-stances. But we must not forget that changes areprocess and not an event. The essence of the solu-tion is in process of ambient preparation forchanges. It is not simple process for any environ-ment, because there are specific problems that rep-resent, in a way, "cultural factors" of that environ-ment. These factors are extremely important becausethey do not act independently, they change hardlyand they are hardly understandable by foreign peo-ple. First step is measurement and estimation ofones position relative to the developed world, andthen observing possibility to compensate that rem-nant. Without real observation of current state, thereare small chances to estimate real goals, and nochances to realise them.Next step is creation of critical mass needed forstart of action, that is creation of teams of peoplewho will not be scared when the process ofchanges begins. The estimation of tasks itself andtheir observation by the team extremely affects cre-ation of positive climate, while achieved resultsaffect back to wider environment. Special careshould be taken to applied science, because thatwidens the area of activity.

Improving quality through introduction of modernquality systems, that are systems for quality work inall areas of human activities, represent complex andambitious project. To successfully realise such pro-ject the knowledge that should be constantly inno-vated is necessary. The essence of the problem isin finding efficient weapon to defeat "organisationalchaos", and the essence of solution is in use ofthat weapon in everyday battles and in all levels.According to what is said before, in improvement ofquality in Bosnia and Herzegovina we should havein mind following:

* Kvalitet se moè unaprijediti samo uspostavljanjemsistema kvaliteta. Standardi ISO 9000 predstavljajuminimalne zahtjeve koji se moraju ispuniti da bi seobezbijedila komunikacija sa okruènjem.Istovremeno, oni su neophodan preduslov za daljunadogradnju sistema poslovanja svake organizacijena putu prema potpunom upravljanju kvalitetom(Total Quality Management-TQM).* Primjena standarda ISO 9000 je prakti~noneograni~ena i oni vaè za sve oblasti ljudskogdjelovanja - od privrednih preduze}a i institucija doorgana uprave i dràve.* Treba raditi na stvaranju kriti~ne mase znanja izoblasti sistema kvaliteta i na stvaranju vlastitih insti-tucija koje }e biti u stanju da ispune me|unarodnezahtjeve za akreditaciju i integraciju u evropske isvjetske procese.* Naprijed re~eno najbolje se moè realizovati krozizradu i implementaciju Dràvnog programa kvalitetaBosne i Hercegovine, pri ~emu treba koristiti tu|aiskustva, ne polaze}i od problema sa kojima se BiHsusre}e, ve} od prednosti kojih BiH ima dosta(sklonost ka timskom radu, internacionalno iskustvo,poznavanje vlastite situacije itd.).

4. DR@AVNI PROGRAM KVALITETA

Sve ovo ukazuje da se problemu upravljanja kvalite-tom treba pristupiti smi{ljeno i organizovano. Zaprivredu malog obima i visoke zavisnosti odspoljnotrgovinske razmjene, kakva je bosanskoherce-gova~ka, kvalitet proizvoda i usluga predstavlja pri-oritet od prvorazrednog zna~aja. Ali, kvalitet se nemoè nametnuti. On mora biti potreba. Mora bitiodraz mentalnog sklopa dru{tva, u kojem nastaje.Zato kvalitet ima multidisciplinarnost koja name}esistemski pristup. To, zapravo zna~i, proètost cijel-og dru{tvenog djelovanja, uzimaju}i u obzirprivredne, organizacijske, pravne, zdravstvene,ekolo{ke, socijalne, eti~ke i druge elemente kvalite-ta, koji u harmoni~nim odnosima treba da doprine-su pobolj{anom kvalitetu ìvljenja u BiH.

Da bi se to postiglo treba u~initi napor nadràvnom nivou u uspostavi jedinstvenog i trans-parentnog sistema kvaliteta, a to se moè ostvaritikonsenzusom svih segmenata oko dràvne strategi-je kvaliteta. Samo takav pristup }e dati BiH sis-temska i cjelovita rje{enja koja su transparentna uevropskom i svjetskom okruènju. Uspje{na strate-gija pripreme na{e dràve za neprekidnoprilago|avanje i u~e{}e u promjenama koje sede{avaju na me|unarodnom trì{tu se mora oslan-jati na nauku, znanje i na{e prirodne prednosti.


* Quality can be improved only through establish-ment of the quality system. ISO 9000 standards. ISO9000 standards represent minimum requirements thatshould be fulfilled to provide communication withenvironment. At the same time, they are necessaryprecondition for further upgrade of business systemon its way to the Total Quality Management (TQM).* Application of ISO 9000 standards system is prac-tically unlimited and they are valid for all areas ofhuman activities - from industrial companies to gov-ernmental organisations.* The one should work on creation of critical massof knowledge in the area of quality systems andcreation of own institutions that will be capable tofulfil international prerequisites for accreditation andintegration into European and world processes. * What is said before, an be realised best throughcreation and implementation of State program ofquality of Bosnia and Herzegovina, while weshould use foreign experiences, not starting fromproblems that BiH has, but from advantages thatBiH has a lot (capability for team work, interna-tional experience, the knowledge about own situ-ation etc.).

4. STATE PROGRAM OF QUALITY

All this shows that approach to the problem ofquality management should be organised and pre-pared. For the small economy with high depen-dence on foreign trade exchange, such asBosnian, the quality of products and services rep-resents first-level priority. But the quality can notbe imposed. It has to be a need. It has to bereflection of mental assembly of society withinwhich it originates from. Because of that quality ismultidisciplinary that requires systematic approach.That means that complete society should beinvolved, including industrial, organisational, legal,health, ecological, social, ethic and other elementsof quality, that in harmonic relations should help toimprove quality of life in BiH.

To achieve that, the whole state should do somethingon creation of unique and transparent system of qual-ity, and that can be realised through consensus ofall segments about state strategy of quality. Only suchapproach will give to BiH systematic and completesolutions that are transparent in European and worldenvironment. Successful strategy of preparation of ourcountry for constant adjusting and taking part inchanges that occur in international market should relyon science, knowledge and our natural advantages.Actual processes in the domain of technological

development in the world show that development ofnew technologies, materials and products are lessand less credit of genial individuals, but more andmore credit of well organised and properly lead mul-tidisciplinary teams of experts, who are able to realiserapid development of economy through their commonactivities. Without successful economic development(of industry and services) it is not possible to devel-op society, to increase population, their employment,to increase quality of life, which are basic strategicgoals of every well-organised society. It seems to benecessary that remnants in this area can easiest andbest be overcome through creation of State programof quality of Bosnia and Herzegovina. This project hasall conditions to be the most significant Bosnian pro-ject oriented to essential renewal of the economy andthe whole society. It is necessary at least becauseof following reasons:

1. Bosnia and Herzegovina have interest and needto join European Union.2. Bosnia and Herzegovina should become fullmember of World Trade Organisation - WTO.3. Bosnia and Herzegovina have interest and needto take part of international work exchange, andbefore that it should accept European and worldstandards.4. It is necessary to make Bosnian companies com-petitive and profitable and in that sense to givethem systematic support in introduction of systemsdefined in international standards ISO 9000 and ISO14000 and European standards EN 45000.5. Protection of Bosnian citizen from inferior domes-tic and imported products and services is neces-sary.6. It is necessary to be involved into increase ofefficiency of ministries, governmental agencies andpublic companies, encouraging them through appro-priate help, to introduce quality systems in accor-dance with standards ISO 9000.7. Equalisation of criteria from this area in wholeBosnia and Herzegovina.

5. CONCLUSION

Complexity of situation of Bosnia and Herzegovina,imposes rapid work on adjusting to changes, inwhich Bosnia and Herzegovina was late even beforethe war. That delay increased in the meantime.Bosnia and Herzegovina is a small country and itshould look for its chance in selling its productsand services on markets of rich neighbours (devel-oped European countries). To achieve that, it shouldadjust to conditions set by these neighbours, thus

Aktuelni procesi u domenu tehnolo{kog razvoja usvijetu pokazuju da je razvoj novih tehnologija,materijala i proizvoda sve manje zasluga genijalnihpojedinaca, a sve vi{e dobro organizovanih iuspje{no vo|enih multidisciplinarnih timova ekspe-rata, koji zajedni~kim djelovanjem mogu ostvariti brzirazvoj privrede. Bez uspje{nog privrednog razvoja(industrija i usluga) nije mogu} razvoj dru{tva,pove}anje broja stanovnika, njihovo zapo{ljavanje,pove}anje kvaliteta ìvljenja, {to su osnovni strate{kiciljevi svakog organizaovanog dru{tva. îni senu`nim da se zaostaci u ovoj oblasti najlak{e inajbolje mogu prevazi}i izradom Dràvnog programakvaliteta Bosne i Hercegovine. Ovaj projekat imasve uslove da bude najzna~ajniji bosanskohercego-va~ki projekat orjentisan na su{tinski preporodprivrede i dru{tva u cjelini. On je neophodan iz naj-manje slijede}ih razloga:

1. Bosna i Hercegovina ima interes i potrebu da sepriklju~i Evropskoj uniji.2. Bosna i Hercegovina treba da postane punopra-van ~lan Svjetske trgovinske organizacije-WTO.3. Bosna i Hercegovina ima interes i potrebu da seuklju~i u me|unarodnu podjelu rada, a prije togamora da prihvati evropske i me|unarodne stan-darde.4. Potrebno je bosanskohercegova~ke firme u~initikonkurentnim i profitabilnim i u tom smislu pruìti imsistematsku pomo} pri uvo|enju sistema definisanihu me|unarodnim standardima serija ISO 9000 i ISO14000 i evropskom serijom standarda EN 45000. 5. Neophodna je za{tita bosanskohercegova~koggra|anina od nekvalitetnih doma}ih i uvoznihproizvoda i usluga.6. Potrebno je uticati na pove}anje efikasnosti radaministarstava, vladinih agencija i javnih preduze}apoticaju}i ih, uz pruànje odgovaraju}e pomo}i, nauvo|enje sistema kvaliteta u skladu sa standardimaserije ISO 9000.7. Ujedna~enje kriterija iz ove oblasti na prostorima~itave Bosne i Hercegovine.

5. ZAKLJUÂK

Kompleksnost situacije, u kojoj se nalazi Bosna iHercegovina, nalaè brz rad na prilago|avanju pro-mjenama u ~emu je BiH i prije rata kasnila. Toka{njenje se u me|uvremenu pove}alo. Bosna iHercegovina je mala zemlja koja svoju {ansu trebada traì u prodaji proizvoda i usluga na trì{timabogatih susjeda (razvijene Evropske zemlje). Da bito postigla, treba da se prilagodi uslovima koje suti susjedi postavili i time stvorili barijere za bh


proizvode i usluge.

Bosna i Hercegovina treba da za{titi svoje gra|aneod nekvalitetnih stranih i doma}ih proizvoda. Tomoè da postigne ako razvije standardizaciju,mjeriteljstvo, akreditaciju i certifikaciju koji treba dabudu kompatibilni sa sistemima me|unarodnih orga-nizacija. Te sisteme su prihvatile i primjenile razvi-jene zemlje.

Da bi sve ovo postigla, Bosna i Hercegovina trebada angaùje sve raspoloìve resurse dràvne uprave,institucija i pojedinaca na izradi i implementacijitakvog dràvnog programa kvaliteta koji }e nasnajbrè uklju~iti u evropske i svjetske tokove.

6. LITERATURA

[1] I. Bakija, "Osiguranje kvaliteta po ISO 9000", NIPPrivredni Vijesnik, Zagreb, 1991.

[2] M. Omanovi}, " Uvod u Total QualityManagement", EQNET, Zenica, 1996.

[3] "..", "The New Approach of Goods in Europe",CEN/CENELEC, Brussels, 1997.


creating barriers for Bosnian products and services.

Bosnia and Herzegovina should protect its citizensfrom inferior foreign and domestic products. Thatcan be achieved through development of standard-isation, metrology, accreditation, and certification,which should be compatible with systems of inter-national organisations. These systems are acceptedand used by developed countries.

To achieve all that, Bosnia and Herzegovina shouldengage all available resources of government, insti-tution and individuals to create and implement suchstate program of quality that will include us intoEuropean and world flows the most rapidly.

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