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

Transcription

1 Ma{instvo (3), 63-78, (1999) N.Sto{i},..: SAVREMENI RAZVOJ KONSTRUKCIJE... SAVREMENI RAZVOJ KONSTRUKCIJE I PROIZVODNJE VIJ^ANIH KOMPRESORA Prof. dr Nikola Sto{i} i mr Ahmed Kova~evi}, Centre for Positive Displacement Compressor Technology, City University, London EC1V OHB, U.K. REZIME PREGLEDNI RAD 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 rezulatima eksperimentalnih istra`ivanja ~ine sna`an sistem za analizu procesa i optimizaciju konstrukcije vij~anog kompresora. Kao rezultat, u nekoliko zadnjih godina profil zuba rotora vij~anog kompresora zna~ajno je evoluirao i na taj na~in su pobolj{ane performanse ma{ine. Iako efikasnost rada vij~anog kompresora najvi{e zavisi od profila zuba rotora kao i distribucije zazora izme u rotora i izme u rotora i ku}i{ta kompresora, ostale komponente, kao {to su otvori na ku}i{tu, le`ajevi, zaptivke i sistem za podmazivanje, moraju biti tako projektovani da se u potpunosti iskoristi potencijal ostvaren razvojem profila rotora. Klju~ne rije~i: vij~ani kompresori, konstrukcija, proizvodnja RECENT DEVELOPMENTS IN SCREW COMPRESSORS Nikola Sto{i}, Ph.D. and Ahmed Kova~evi}, Ms.C., Centre for Positive Displacement Compressor Technology, City University, London EC1V OHB, U.K. SUMMARY SUBJECT REVIEW Screw compressor dominate today compression of air, process gas and refrigerants. The recent advances in mathematical modelling and computer simulation combined with experimental test data form a powerful tool for process analysis and design optimisation. As a result, the screw rotors lobe profiles have evolved over the past few years enhancing machine performance. Although an efficient operation 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 to take advantage of their potential if the full performance gains are to be achieved. Key words: screw compressors, construction, manufacturing 1 UVOD Vij~ani kompresori su rotacione volumetrijske ma{ine jednostavne konstrukcije koje mogu raditi na vrlo visokim brojevima obrtaja u {irokom dijapazonu radnih pritisaka i protoka ostvaruju}i visok stepen iskori{tenja. Oni su kompaktni i pouzdani tako da su danas na trzi{tu zastupljeni u vi{e od 80% slu~ajeva dok se u pogonu ve} nalazi oko 50% vij~anih kompresora u odnosu na ukupan broj industrijskih kompresora. Osnovni razlog za ovako zna~ajan uspjeh vij~anih kompresora na tr`i{tu valja tra`iti u savremenom razvoju proizvodne tehnike koja je omogu}ila da se linearne tolerancije pri proizvodnji rotora preciznim profilnim glodanjem ili bru{enjem svedu na vrijednost ni`u 1 INTRODUCTION Screw compressors are rotary positive displacement machines of simple design with the moving parts comprising only two rotors rotating in four to six bearings. They are capable of efficient operation at high speeds over a wide range of operating pressures and flow rates. They are therefore both reliable and compact and consequently they comprise 80% of all positive displacement compressors now sold and 50% of those currently in operation. Their remarkable success is mainly due to improvements in high accuracy profile milling and grinding which now make it possible to reduce linear tolerances to below

2 Ma{instvo (3), 63-78, (1999) N.Sto{i},...: SAVREMENI RAZVOJ KONSTRUKCIJE... od 10 µm. Na taj na~in se ostvaruje ekonomi~na proizvodnja rotora sa me usobnim zazorima u granicama od µm. Unutra{nje curenje se time svodi na mali dio vrijednosti ostvarenih u prija{njim konstrukcijama vij~anih kompresora. Kao rezultat se dobiva manji vij~ani kompresor sa ve}im stepenom iskori{tenja u pore enju sa ostalim tipovima kompresora. Vij~ane ma{ine se danas upotrebljavaju kao kompresori ili kao ekspanderi i imaju najraznovrsnije namjene. Oni rade sa razli~itim vrstama radnih fluida koji mogu biti gasovi, pare ili vi{efazne mje{avine sa promjenom faze unutar ma{ine. Mogu raditi bez unutra{njeg podmazivanja, ili kao uljno podmazivani, ili sa drugim fluidom koji se ubrizgava u radni prostor za vrijeme procesa kompresije ili ekspanzije ili prije ili poslije njih. Da bi se postigle optimalne karakteristike kompresora, razli~ite aplikacije vij~anog kompresora zahtijevaju razli~itu konstrukciju i druk~iji na~in rada. Zbog toga nije mogu}e upotrebljavati univerzalne rotore ili izabrati univerzalne radne parametre koji }e dati optimalnu efikasnost ~ak unutar vrlo uskog dijapazona rada ma{ine. Detaljna termodinamska analiza i poznavanje uticaja razli~itih konstruktivnih parametara na karakteristike vij~ane ma{ine su, zbog raznolikosti primjene i geometrijske kompleksnosti ma{ine, sigurno mnogo zna~ajniji i slo`eniji nego u slu~aju drugih sli~nih ma{ina. Odavde slijedi da je za optimalne performanse ma{ine za odre enu primjenu neophodno dobro postaviti optimizacione kriterije. Ovakav pristup je, isto tako, od velikog zna~aja za eventualna unapre enja postoje}ih konstrukcija vij~anih ma{ina i za pro{irenje domena njihove primjene. 10 µm. This permits rotors to be manufactured with interlobe clearances of µm at an economic cost. Internal leakages are thus far less than in earlier machines of this type and as a result, twin screw compressors are more efficient than other types. Screw machines are used today for different applications both as compressors and expanders. They operate on a variety of working fluids which may be gases, dry vapours or multi-phase mixtures with phase changes taking place within the machine. They may operate with oil flooding, with other fluids injected during the compression or expansion process, or without any form of internal lubrication. Their geometry may vary depending on the number of lobes in each rotor, the basic rotor profile and the relative proportions of each rotor lobe segment. It follows that there is no universal configuration which would be the best for all applications. Hence, detailed thermodynamic analysis of the compression process and evaluation of the influence of the various design parameters on performance is more important to obtain the best results from these machines than from other types which could be used for the same application. It follows that a set of well defined criteria governed by an optimisation procedure is a prerequisite for achieving the best design for each application. Such guidelines are also essential for the further improvement of existing screw machine designs and broadening their range of uses. Industrijski kompresori komprimiraju zrak, rashladne fluide ili procesne plinove. Za svaku od ovih namjena konstrukcija ma{ine se mora razlikovati kako bi se postigli o~ekivani rezultati. U rashladnim ma{inama i kod kompresije procesnih plinova, gdje je vrijeme rada kompresora zna~ajno du`e od vremena stajanja, obi~no se kao osnovni preduslov postavlja visok stepen iskori{tenja kompresora. Za zra~ne kompresore, posebno u mobilnim agregatima, efikasnost mo`e biti ni`a i obi~no je manje zna`ajna od veli~ine kompresora i njegove cijene. Oblast kompresije zraka je, kako u slu`aju suhoradnih tako i u slu~aju uljno podmazivanih kompresora, gotovo isklju~ivo pokrivena vij~anim kompresorima. Situacija je vrlo sli~na i u procesnoj industriji, dok se u rashladnoj tehnici klipni i lamelni kompresori sve vi{e zamjenjuju vij~anim kompresorima, tako da se u narednim godinama mo`e o~ekivati dramati~no pove}anje zahtjeva za vij~anim rashladnim kompresorima. Veli~ina vij~anih kompresora koji se danas koriste u komercijalne svrhe je izmedju 75 i 60 mm u Typically, refrigeration and process gas compressors, which operate for long periods, must be designed to have a high efficiency. In the case of air compressors, especially for mobile applications, efficiency may be less important than size and cost. For both dry and oil free air compression, screw compressors are used almost exclusively. This is also gradually becoming the case for process gas compression. In the field of refrigeration, the use of reciprocating and vane compressors is decreasing and a dramatic increase in favour of screw machines is expected in the next few years. Screw compressors in normal commercial usage today have main rotors whose outer diameters vary between 75 mm and 60 mm. These deliver between 0.6 m3/min and 600 m 3 /min of compressed gas. The normal pressure ratios attained in a single

3 Ma{instvo (3), 63-78, (1999) N.Sto{i},..: SAVREMENI RAZVOJ KONSTRUKCIJE... pre~niku vode}eg rotora. Dobava tih kompresora je izmedju 0,6 i 600 m 3 /min gasa na uslovima usisa. Odnos pritisaka je oko 3.5 za suhoradne kompresore dok se za uljnopodmazivane kre}e do 15. Uobi~ajena razlika pritisaka je do 15 bara ali se u nekim slu~ajevima de{ava da ona prelazi 40 bara. Volumetrijsko iskori{tenje uljno podmazivanih vij~anih kompresora obi~no je preko 90%, tako da je danas specifi~na snaga vij~anih kompresora svedena na vrijednosti koje su se prije samo nekoliko godina smatrale nemogu}ima. stage are 3.5:1 for dry compressors and up to 15:1 for oil flooded machines. Normal stage pressure differences are up to 15 bars, but maximum values sometimes exceed 40 bars. Typically, for oil flooded air compression applications, the volumetric efficiency of these machines now exceeds 90 % while specific power inputs, which are both size and performance dependent, have been reduced to values which were regarded as unattainable only a few years ago. SKRIVENI DETALJI SCREW COMPRESSOR PRACTICE [vedska kompanija SRM je pionir u razvoju i primjeni vij~anih kompresora. I drugi proizvo a}i, kao {to su Compair u Velikoj Britaniji, Atlas-Copco u Belgiji, Ingersol-Rand i Denver Gardner u Americi, GHH u Njema~koj, nalaze se neposredno do njih. York, Trane, Carrier i Bitzer su vode}e kompanije koje vij~ane kompresore koriste u rashladnoj tehnici i klimatizaciji. Japanski proizvo a}i vij~anih kompresora, kao {to su Hitachi, Mycom i Kobe-Steel su tako er vrlo dobro poznati. U zadnje vrijeme se na Srednjem i Dalekom Istoku pojavljuje veliki broj kompanija koje se se bave vij~anim kompresorima. Otvaranjem novih tr`i{ta, u Kini i Indiji, a i u drugim zemljama u razvoju dolazi do otvaranja fabrika vij~anih kompresora. Iako se ne bavi proizvodnjom vij~anih kompresora, Britanska kompanija Holroyd je najve}i proizvo a} rotora za vij~ane kompresore i vode}i konstruktor i proizvo a} alata i ma{ina za proizvodnju rotora vij~anih kompresora. Iako popularnost vij~anog kompresora raste iz dana u dan, otvorena literatura je u toj oblasti jo{ uvijek ograni~ena. Tri klasi~ne knjige o vij~anim kompresorima su publikovane na ruskom jeziku u ranim {ezdesetim godinama. [40] 1960, daje potpuni pregled na~ina generisanja kru`nog, elipti~nog i cikloidnog profila i u detalje izvodi ruski asimetri~ni profil kasnije nazvan SKBK. Na~in generisanja profila opisan u toj knjizi bazira se na takozvanom metodu obvojnice. [] ponavlja teoriju generacije profila time daju}i svoj doprinos oblasti profilisanja alata za proizvodnju rotora. [15] je knjiga sa generalnom kompresorskom tematikom, ali je dio o vij~anim kompresorima vrlo interesantan i informativan. Priru~nik [1] na ruskom jeziku iz 1977 godine daje potpuno reproducibilan prikaz asimetri~nog SRM profila 5 godina nakon {to je ovaj patentiran skupa sa Lysholmovim profilom. Dvije knjige su publikovane na njema~kom jeziku [35] 1979, prezentira metod generacije profila baziran na teoriji zup~anika Svenska Rotor Maskiner (SRM), a Swedish company, was the pioneer and are still leaders in the field of screw compressor design and development practice. Other companies, such as Compair in the U.K, Atlas-Copco in Belgium, Ingersoll-Rand and Denver Gardner in the USA and GHH in Germany are the main air compressor manufacturers. York, Trane and Carrier in the USA lead in refrigeration and air conditioning applications. Japanese screw compressor manufacturers, such as Hitachi, Mycom and Kobe- Steel are also well known. In recent years there have been a number of mergers and buy outs of smaller companies by these larger ones. New markets in China, India and other developing countries in the Middle and Far East have led to new screw compressor companies being founded there as well as factories being built there by the major manufacturers. Although they do not manufacture compressors, Holroyd, a British company is the world's largest screw rotor manufacturer. They are also world leaders in tool design and machine tool production for the manufacture of screw compressor rotors. Despite the rapid growth in screw compressor usage, public knowledge of the scientific basis of their design is still limited. Three classical screw compressor textbooks were published in Russia in the early nineteen sixties. [40] 1960 gives a full analysis on how to generate circular, elliptic and cycloidal rotor profiles as well as a russian asymmetric profile later named SKBK. The method of profile generation in this book was based on an envelope approach. [], 1961 demonstrates this theory and, in addition, makes a contribution to the field of rotor tool profile generation. [15], 1964, is a more general textbook but its section on screw compressors is very interesting and informative. A Russian handbook, [1], published in 1977, gives a reproducible presentation of how to generate the SRM

4 Ma{instvo (3), 63-78, (1999) N.Sto{i},...: SAVREMENI RAZVOJ KONSTRUKCIJE... kako bi rekonstruisao SRM asimetri~ni profil 7 godina nakon {to je patentiran, a [3] 1988, publikuje neke in`enjerske aspekte vij~anih kompresora. Mali je broj knjiga koje se bave vij~anim kompresorima objavljen na engleskom jeziku: [3] 1993, o industrijskim kompresorima i [3] 1994 o rotacionim kompresorima sa dva vratila. Me utim, sve one su suvi{e generalne da bi bile razmatrane kao referentna literatura o vij~anim kompresorima. Nekoliko priru~nika o vij~anim kompresorima su objavili proizvo a}i vij~anih kompresora, isto kao i odre eni broj bro{ura koje daju korisne informacije, ali su one ili povjerljive ili su nedostupne i daleko od javnosti. Neke od njih, kao {to je, na primjer, SRM Data Book, ina~e dobro ~uvane i dostupne samo licensorima, ~esto su citirane kao literatura iz oblasti vij~anih kompresora. Me utim, broj patenata koji su se pojavili u zadnjih trideset godina je neproporcionalno velik, mo`e se re~i da je patenata objavljeno na hiljade. Samo je SRM objavio 750 patenata. Svi se patenti bave razli~itim aspektima vij~anih kompresora a njihov najve}i broj profilima rotora. SRM je objavio patente [33] 1946 simetri~nog, [41] 1973 za asimetri~ni i [4] 198 za "D" profil. Oni su klasi~na referentna literatura koja prikazuje vje{tinu profilisanja rotora vij~anog kompresora. Jo{ neki patenti mogu se spomenuti kao primjer uspje{nog na~ina generacije profila: Atlas-Copco, Compair [19], Denver Gardner [9], Hitachi [0], Ingersol-Rand. U posljednjih je nekoliko godina jedan broj relativno malih kompanija objavio vi{e izuzetno uspje{nih patenata, kao {to su, na primjer, [4] i [8]. Potpuno novi pristup generaciji profila po kojem se polazne krive zadaju na zup~astom stapu objavljen je u [37] i u [50]. Svi patentirani profili su generisani na osnovu neke valjane metode, ali su korisne informacije o kori{tenim metodama pa`ljivo uklonjene iz patenta ili iz prate}ih publikovanih radova. Informacije u patentima su ili sakrivene ili je iz njih gotovo nemogu}e direktno dobiti profil. Ova se ~injenica mo`e ilustrovati kroz tri primjera. U radu [9] 1978 objavljuje se izvodjenje simetri~nog kru`nog profila koji je patentiran 3 godine prije toga. U [35] se koristi klasi~nim uslovima sprezanja konjugovanih zup~anika da bi reprodukovao asimetri~ni SRM profil 9 godina nakon {to se patent pojavio. Kao kuriozitet mo`e se pomenuti da je jedan SRM-ov licencor, nakon 13 godina proizvodnje kompresora, iskoristio sav akademski potencijal kako bi analiti~ki reprodukovao SRM "D" profil. asymmetric profile only 5 years after it was patented as well as the classical Lysholm profile. There are two German textbooks. [35], 1979, used a profile generation method based on gear theory to reconstruct the SRM asymmetric profile 7 years after it was patented. [3], 1988, published some engineering aspects of screw compressors. Only recently have any textbooks on screw compressors been published in English. [3], 1993, was on industrial compressors and [3], 1994, was on rotary twin shaft compressors. However, these are too general to be useful as detailed reference literature. A few compressor manufacturers' handbooks on screw compressors and a number of brochures give useful information, but they are either classified or of very limited accessibility. Some, like the SRM Data Book, although cited in screw compressor literature, are available only to SRM licencees. Literally thousands of patents have been awarded on screw compressors in the past thirty years and SRM alone has 750. They cover various aspects of screw compressor design but are mainly for rotor profiles. SRM patents [33], 1946, for symmetric, [41], 1973, for asymmetric and [4], 198, for the "D" profiles are classical examples of state of the art screw compressor profile generation. Other succesful profiling patents are those of Atlas-Copco, Compair [19], Denver Gardner [9], Hitachi [0] and Ingersoll-Rand [6]. In recent years, several highly successful patents such as [4] and [8] have been granted to relatively small companies. A fresh approach to profile generation based on the use of a rack for the primary curves was published in [37] and [50]. Although all patented profiles were generated by well defined procedures, so little of the methods on which they were based was published that it was very difficult to reproduce them. Thus details of how to derive the circular symmetric profile, [9], were not published until 1978, 3 years after it was patented. Similarly, a derivation of the SRM asymmetric profile based on classical gear conjugacy criteria, [35], was not published until 9 years after the patent appeared. It is even more interesting to note that one SRM licencee funded a university research programme to obtain an analytical derivation of the SRM "D" profile in 1995, after 13 years of manufacturing it

5 Ma{instvo (3), 63-78, (1999) N.Sto{i},..: SAVREMENI RAZVOJ KONSTRUKCIJE... Me u patentima iz podru~ja vij~anih kompresora mogu se na}i i oni koji se bave drugim aspektima ove oblasti. Uglavnom su patentirane sve dobro poznate karakteristike vij~anih kompresora, kao {to je ubrizgavanje ulja, usisni i tla~ni otvori koji prate helikoidu rotora, kompenzacija aksijalnih sila, rastere~enje kompresora, usisni klip, ekonomajzerski otvor, uglavnom od strane SRM-a, ali i neke druge kompanije tako er vrlo revnosno objavljuju patente. Izgleda da patentni stru~njaci za vij~ane kompresore imaju isti ili sli~an zna~aj kao i in`enjeri koji se bave njihovim razvojem. Iako su ~lanci o vij~anim kompresorima rijetkost u ~asopisima, oni su izuzetno korisna literatura o kompresorima mada ne odaju mogo detalja o profilisanju vij~anih kompresora. Tako Lysholmovi klasi~ni ~lanci [6] iz 194 i [7] iz 1966 ne spomenju ni jedan detalj o profilisanju koje je autor koristio u svojoj uspje{noj praksi da bi pobolj{ao zaptivenost kompresora. ^lanci [45] i [46] se mogu vi{e smatrati izuzetkom nego praksom. U posljednje vrijeme je objavljivano ne{to vi{e materijala o vij~anim komopresorima u ~asopisima, {to je podstaknuto od strane nekoliko institucija, kao {to su International Institution of Refrigeration [15] i [48], IMechEng [44], [1], [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~anim kompresorima nego {to je objavljeno tokom svih prethodnih godina zajedno. [5] je primjer ~lanka koji je objavljen u skladu sa najmodernijim trendovima vremenski dobro izabranog trenutka za publikovanje. Tri kompresorske konferencije su u potpunosti ili djelomi~no orjentisane na vij~ane kompresore: Purdue Compressor Technology Conference u Lafayette, SAD, IMechEng konferencija o industrijskim kompresorima u Londonu, Engleska i "VDI Schraubenkompressoren Tagung" u Dortmundu, Njema~ka. Usprkos obilju ~lanaka o vij~anim kompresorima, samo mali broj ~lanaka sa konferencija daje korisne informacije o profilisanju rotora vij~anog kompresora i o konstrukcijama kompresora. Svi ~lanci sa konferencija daju valjan prikaz obavljenih istra`ivanja ali skoro ni jedan od njih ne daje reproducibilne informacije koje se odnose na kori{tene metode profilisanja. ^lanci kakakteristi~ni za Purdue konferenciju su oni koji se vrlo ~esto citiraju, ali iz kojih ~italac mo`e saznati vrlo malo o generaciji profila, kao {to su: [11], [47] i [49], a tako er i [4], [43], [53] i [56]. ^lanci [34], [58], [59] i [60] ukazuju na to da je teorija obvojnice naj~e{}e kori{tena metoda za izra~unavanje geometrijskih karakteristika rotora. U zbornik radova sa Dortmundske konferencije nalazi se odre eni broj vrlo interesantnih ~lanaka o vij~anim kompresorima. [36] iz 1984 prezentira na~in generisanja profila na bazi zup~astog {tapa pri ~emu daje potpuno reproducibilan patent [37] baziran na klasi~noj Most of the well known characteristics of screw compressors, such as oil flooding, making the suction and discharge ports follow the rotor tip helices, axial force compensation, unloading, the slide valve and the economizer port, were also patented, mainly by SRM. However other companies were equally keen to file patents. It appears that, in the field of screw compressors, patent experts are as important as engineers. There are surprisingly few journal publications on screw compressors in the technical literature. Notable exceptions are Lysholm's [6-7] classical papers of 194 and However neither of these described any of the profiling details which he developed successfully in order to reduce the blow-hole area. Other exceptions are [45] and [46]. In recent years, journal publication of screw compressor material has been encouraged by the International Institution of Refrigeration [15] and [48], the IMechE [44], [1], [13], [55] and [57] and ASME [16] and [51]. This led to more information on screw compressors in journals during recent years than in all previous years together. [5] is an example of the modern practice of more timely publishing. There are three compressor conferences which deal exclusively or partly with screw compressors. These are: the Purdue University compressor technology conferences in the U.S.A, the ImechE conferences on industrial compressors in England and the "VDI Schraubenkompressoren Tagung" in Germany. Despite the wealth of screw compressor papers which these contain, very few give useful information on rotor profiling procedures and compressor design. Typical Purdue papers, frequently cited, from which a reader will gain a little on profile generation are: [11], [47] and [49], also [4], [43], [53], [56]. Refs [34], [58], [59], and [60] indicate that envelope theory was used to calculate some geometric features of their rotors. The "VDI Schraubenkompressoren Tagung" proceedings contain some interesting screw compressor papers. [36] 1984 presents a rack method of rotor profile generation, based on classical gearing theory, which is fully reproducible. Unfortunately, although soundly conceived, profiles produced by this method were not commercially successfull because of their poor tightness. [16] and [18] give some more details on profiling and manufacturing control. [1], [] and [54] are typi

6 Ma{instvo (3), 63-78, (1999) N.Sto{i},...: SAVREMENI RAZVOJ KONSTRUKCIJE... teoriji zup~anika. Me utim, na`alost, na prikazani na~in dobiveni profil, iako baziran na odli~nim osnovama nema velik komercijalni zna~aj zbog vrlo slabog zaptivanja. [16] i [18] daju ne{to vi{e detalja o profilisanju i kontroli proizvodnje. [1], [] i [54] su tipi~ni primjeri uspje{nog akademskog istra`ivanja primjenjenog na stvarno in`enjerstvo. [38] i [39] se mogu nazvati primjerom prakti~ne primjene preciznog in`enjerskog rada. Londonska kompresorska konferencija, iako ne tako u~estala, dala je nekoliko vrlo interesantnih ~lanaka kao {to je, na primjer [10]. Mnoge referentne knjige o zup~anicima su korisna polazna osnova za profilisanje rotora vij~anog kompresora, ali je ve~ina od njih ograni~ena na klasi~e uslove sprezanja zup~anika. Kao primjer se mo`e ista}i klasi~na knjiga [7]. Knjiga [5] se mo`e smatrati izuzetkom od ovog pravila jer daje teoriju sprezanja zup~anika koja se direktno mo`e primijeniti i na profilisanje rotora vij~anog kompresora. 3 SAVREMENI RAZVOJ VIJ^ANOG KOMPRESORA Efikasan rad vij~anog kompresora uglavnom zavisi od pravilne konstrukcije njegovih rotora. Dodatno se kao uslov za uspje{nu konstrukciju razli~itih vrsta kompresora postavlja i sposobnost da se radne karakteristike mogu precizno predvidjeti u slu~aju da se promijeni bilo koji parametar kao {to je na primjer zazor, oblik profila rotora, pozicija i koli~ina ubrizganog ulja ili nekog drugog fluida u radni prostor, pre~nik i proporcija rotora i brzina obrtanja. Danas, kad su zazori u kompresoru mali, unutra{nje curenje koje ima veliki uticaj na efikasnost sve vi{e zavisi od du`ine linije dodira rotora, tako da kao mogu}nost za pobolj{anje kompresora ostaje jo{ samo bolje profilisanje rotora. Tako se posebna pa`nja posve}uje unapredjenju karakteristika rotora da se, {to je god vi{e mogu}e, pove}a unutra{nji protok kompresora a da se linija dodira izmedju rotora smanji, te da se istovremeno unutra{nje trenje usljed relativnog klizanja dodirnih povr{ina rotora u~ini {to je mogu}e manjim. Mada na prvi pogled izgleda da je u profilisanju rotora dosad u~injeno sve {to je bilo mogu}e, to je daleko od istine. U stvari, ima jo{ mnogo prostora za zna~ajna pobolj{anja. ^ini se da na~in profilisanja koji kao polaznu osnovu uzima zup~asti {tap, ima najvi{e izgleda da postigne najbolje rezultate jer se njime mogu dobiti ja~i i lak{i rotori sa ve}om dobavom i manjim kontaktnim naponima. Ovo posljednje omogu}ava da se u radni prostor kompreora ubrizgava fluid ni`e viskoznosti. Kori{tenjem metoda vi{eparametarske optimizacije dobivaju se sve bolje oblikovani otvori na ku~i{tu vij~anog kompresora. Time se smanjuju gubici na cal examples of successful university research applied to solve real engineering problems. [38] and [39] may be regarded as examples of fine engineering work. Although relatively infrequent, the London compressor conferences included some interesting papers, such as [10]. Many reference textbooks on gears give a useful background to screw rotor profiling. However all of them are limited to the classical gear conjugate action condition. One example of this is [7]. [5] is an exception to this practice which contains gear theory directly applicable to screw compressor profiling. 3 RECENT DEVELOPMENTS The efficient operation of screw compressors is mainly dependent on proper rotor design. An additional and important requirement for the successful design of all types of compressor is the ability to predict accurately the effects on performance of the change in any design parameter such as clearance, rotor profile shape, oil or fluid injection position and rate, rotor diameter and proportions and speed. Now that tight clearances are achievable, internal compressor leakage rates become small. Hence, further improvements are only possible by the introduction of more refined design principles. The main requirement is to improve the rotor profiles so that the internal flow area through the compressor is maximised while the leakage path is minimised and internal friction due to relative motion between the contacting rotor surfaces is made as small as possible. Although rotor profiling procedures may appear to be fully defined, substantial improvements are still possible. The most promising approach for this seems to be through rack profile generation which gives stronger but lighter rotors with higher throughput and lower contact stress. The latter enables fluids with lower viscosity than oil to be used for lubrication. Rotor housings with better shaped ports can be designed using multivariable optimization techniques. Flow losses may thereby be reduced permitting higher rotor speeds and hence more effective compressors

7 Ma{instvo (3), 63-78, (1999) N.Sto{i},..: SAVREMENI RAZVOJ KONSTRUKCIJE... usisu i na izlazu {to omogu}ava pove}anje broja obrtaja kompresora, a time se direktno pove~ava i njegova efektivnost. Zna~ajni uspjesi su u nekoliko zadnjih godina postignuti i u razvoju le`ajeva za kompresore, ~ime je omogu}eno podmazivanje kompresora fluidom viskoznosti manje nego kod obi~no kori{tenih ulja. Zaptiva~i su, takodjer, mnogo efikasniji nego ranije. Sve ovo je dalo dobru osnovu za efikasniji rad kompresora. 3.1 Profili rotora Naj~e{}e kori{ten metod generacije profila rotora vij~anog kompresora je da se defini{e primarni profil na jednom od rotora a da se nakon toga tra`e odgovaraju}e krive na drugom rotoru primjenom razli~itih uslova sprezanja. Na osnovnom rotoru je mogu}e definisati bilo koju krivu liniju ali je tradicionalno naj~e{}e kori{tena kriva upravo kru`nica. Bilo koja kru`nica sa centrom na podionom krugu generisa}e sli~nu kru`nicu na drugom rotoru. Ista situacija se dobije ako je centar kru`nice u osi rotora. Kru`nice sa centrom van podionog kruga na isti na~in kao i ostale krive: elipsa, parabola ili hiperbola proizve{}e na drugom rotoru neku generisanu krivu, koja se naziva trohoida. Sli~no tome, ta~ka koja je fiksirana na jednom rotoru generisa}e epi- ili hipocikloidu na drugom rotoru. Sva vje{tina profilisanja rotora se decenijama svodila na pravilan izbor primarnih krivih na jednom rotoru koje }e omogu}iti izvo 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 postavljenih u centar podionog kruga, sastoji od sistema cikloida na strani visokog pritiska ~ime je dobiven prvi asimetri~ni profil rotora vij~anog kompresora. Za asimetri~ni SRM profil je prvi put iskori{tena ekscentri~na kru`nica na strani niskog pritiska na vo enom rotoru dok je na SKBK profilu isto ura eno na vode}em rotoru. U oba slu~aja su izvedene krive analiti~ki definisane kao epi- ili hipocikloide. SRM "D" profil se sastoji samo od kru`nica od kojih su neke sasvim male, ali su sve ekscentri~no postavljene na vode}em ili vo enom rotoru. Svi patenti koji slijede nakon toga baziraju se na definisanju jednog od rotora i izvo enju drugog, i svi su, vjerovatno, bazirani na klasi~nom sprezanju zup~anika ili na nekim sli~nim uslovima. Tek u posljednje vrijeme kru`nice su postepeno zamjenjuju nekim drugim krivuljama kao {to su: elipsa kod FuSheng profila [4], parabola na Compair [19] i Hitachi profilima i hiperbola na "hyper" profilu [8]. ^ini se da je hiperbola na posljednjem profilu odgovaraju}a zamjena za ostale krive, jer daje najbolji odnos dobave rotora i du`ine linije zaptivanja. 3.1 Rotor Profiles The normal procedure used to generate rotor profiles is to create primary profile curves on one rotor and, by use of an appropriate conjugate criterion, a corresponding secondary profile curve on the other. Any curve can be used as the primary one, but traditionally a circle is the most comon. All circles with their centres on the pitch circle generate a similar circle on the other rotor. This is also true if the circle centres are at the rotor axes. Circles with centres not on the pitch circle and other curves, like ellipses, parabolae and hyperbolae require more elaborate curves to be generated, on the other rotor which are described as trochoids. Similarly, points located on one rotor will cut epior hypocycloids on the other rotor. For decades, the skill required to produce rotors was limited to the ability to choose a primary arc which would permit the derivation of an appropriate secondary profile. 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 high pressure side to form the first asymmetric screw rotor profile. Later the SKBK profile used the same curves. The SRM asymmetric profile employs an eccentric circle on the low pressure side of the gate rotor. In all these cases the curves evolved analytically from them were epi- or hypocycloids. The SRM "D" profile consists exclusively of circles, almost all of them eccentrically positioned on the main or gate rotor. All patents which followed, specify primary curves on one rotor and secondary generated curves on the other rotor. All are probably derived from classical gear contact theory or a similar alternative criterion. More recently, circles have gradually been replaced by other curves such as ellipsae in the FuSheng profiles [4], parabolae in the Compair [19] and Hitachi [0] profiles and hyperbolae in the 'Hyper' [8] profile. Replacing the circle by a hyperbola in the latest profile, seems to give the best ratio of rotor displacement to sealing line length. Another method of rotor profile generation is to consider imaginary, or 'nonphysical' rotors. Since all gearing equations are independent of the coordinate system in which they are expressed, it is possible to define primary arcs as given curves using a coordinate system which is independent of both rotors. By this means, in many cases the defining equations may be simplified. Also, the

8 Ma{instvo (3), 63-78, (1999) N.Sto{i},...: SAVREMENI RAZVOJ KONSTRUKCIJE... Drugi na~in na koji je mogu}e definisati profil rotora je da se osnovne krive izaberu na nekom zami{ljenom, "nefizikalnom" rotoru. Po{to su sve jedna~ine zup~anika neovisne od koordinatnog sistema u kojem su izra`ene, primarni luk je mogu}e definisati i u nekom koordinatnom sistemu koji je ne ovisi ni o jednom rotoru. U ve~ini slu~ajeva se na taj na~in jedna~ine mogu pojednostaviti. Upotreba jednog koordinatnog sistema za definisanje svih krivih na rotoru tako er mo`e pojednostaviti proces profilisanja. Tako se polazni profil u cijelosti mo`e definisati u koordinatnom sistemu koji ne zavisi od rotora, {to vrijedi i za rotor sa beskona~nim pre~nikom koji se naziva zup~asti {tap. Prvi ikada publikovani patent koji prikazuje ovakvu generaciji profila rotora [30] objavljen 1977, iako nije prakti~no primjenljiv, vje{to koristi pomenutu teoriju. [37] i kasnije [50] prvi daju dobru osnovu za generaciju profila vij~anog kompresora. Efikasan vij~ani kompresor mora imati rotore ~iji profil osigurava veliki proto~ni presjek, kratku liniju zaptivanja i mali nezaptiveni prostor na vrhu rotora. To zna~i, da je za ve}i proto~ni presjek i broj obrtaja kompresora, i dobava kompresora ve}a. Kra}e linije dodira i manji nezaptiveni prostor smanji}e unutra{nje curenje. Ve}a dobava i manje curenje }e pove}ati volumetrijski stepen iskori{tenja kompresora, koji je defini{an kao dobava podijeljena zbirom ukupnog protoka i curenja. Time se dalje pove}ava adijabatski stepen iskori{tenja, jer se za kompresiju gasa koji recirkuli{e unutar kompresora tro{i manje snage. Izbor odnosa veli~ine nezaptivenog prostora i broja radnih zapremina zavisi}e od namjene kompresora. Kako je za manje razlike pritisaka curenje proporcionalno manje, dobici postignuti velikim proto~nim presjekom mogu poni{titi ili smanjiti gubitke nastale usljed velikog nezaptivenog prostora. Na sli~an na~in se mo`e dobiti optimalni broj zuba vij~anog kompresora, po{to manji broj zuba daje ve}i proto~ni presjek ali i rezultira u ve}oj razlici pritiska izme u radnih prostora. Sa smanjenjem zazora izmedju rotora, bez obzira na podmazivanje kompresora uljem, vjerovatno}a direktnog dodira me u rotorima sa pove}ava. Dodir me u rotorima dovodi do pove}anja kontaktnih sila i optere}enja rotora {to dalje uzrokuje deformaciju vo enog rotora. Zbog toga, njegov profil mora biti konstruisan tako da se rizik od pucanja ili plasti~ne deformacije rotora smanji na najmanju mogu}u mjeru. Brzi razvoj metoda matematskog modeliranja i ra~unarske simulacije je, u posljednje vrijeme, podstakao i olak{ao istra`ivanje novih profila rotora. use of one coordinate system to define all the curves, simplifies the design process. Typically, the template is specified in a rotor independent coordinate system. This is valid for a rotor of infinite radius, which is a rack. From this, a secondary arc on some of the rotors is obtained by a procedure, which is called 'rack generation'. The first patent on rack generation published, [30], is based on this theory but lacks practicality. [37] and, more recently, [50] give a good basis for rotor profile generation. For a screw compressor to be efficient, the rotor profile must form a large flow cross section area, a short sealing line and a small blow-hole area. The larger the cross section area, the higher the flow rate for the same rotor sizes and speeds. Shorter sealing lines and a smaller blow-hole reduce leakages. Higher flow and smaller leakage rates both increase the compressor volumetric efficiency, which is the rate of flow delivered as a fraction of the sum of the flow plus leakages. This in turn increases the adiabatic efficiency because less power is wasted in the compression of gas which is recirculated internally. The optimum choice between blow hole and flow areas depends on the compressor duty since, for low pressure differences, the leakage rate will be relatively small and hence the gains achieved by a large cross section area may outweigh the losses associated with a larger blow-hole. Similar considerations determine the best choice for the number of lobes since fewer lobes imply greater flow area but increased pressure difference between them. As precise manufacture permits rotor clearances to be reduced, despite oil flooding, the likeliehood of direct rotor contact is increased. Hard rotor contact leads to deformation of the gate rotor, increased contact forces and ultimately rotor seizure. Hence the profile should be designed so that the risk of seizure is minimised. The search for new profiles has been both stimulated and facilitated by recent advances in mathematical modelling and computer simulation. These analytical methods may be combined to form a powerful tool for process analysis and optimisation and thereby eliminate the earlier approach of intuitive changes, verified by tedious trial and error testing. As a result, this approach to the optimum design of screw rotor lobe profiles has substantial

9 Ma{instvo (3), 63-78, (1999) N.Sto{i},..: SAVREMENI RAZVOJ KONSTRUKCIJE... Analiti~ke metode je mogu}e kombinovati na taj na~in da se dobije mo}no sredstvo za analizu i optimizaciju procesa vij~anog kompresora, ~ime se u potpunosti mo`e zaobi}i ranije kori{tena metoda intuitivne konstrukcije zasnovana na mukotrpnom metodu poku{aja i pogre{ke. Kao rezultat, ovaj pristup optimalnom konstruisanju rotora vij~anog kompresora zna~ajno je evoluirao u nekoliko zadnjih godina sa velikim {ansama da se u narednim godinama postignu dalja pobolj{anja karakteristika ma{ine. Me utim, i geometrija rotora, isto kao i radni proces u vij~anom kompresoru su toliko kompleksni da je potrebno uvesti niz aproksimacija kako bi modeliranje bilo ostvarivo. Kao posljedica, u otvorenoj literaturi se mogu na}i matematski modeli i numeri~ki kodovi sa vrlo {arolikim pristupom problemu i sa razli~itim matematskim nivoima modeliranja fenomena u vij~anom kompresoru. Nedostatak uporedivih eksperimentalnih rezultata jo{ uvijek onemogu}ava verifikaciju i svestranu ocjenu razli~itih koncepcija modeliranja. Uprkos tome, matematsko modeliranje i simulacija ra~unarom sve vi{e dobivaju na popularnosti i sve se vi{e koriste za unapre enje konstruktivnih karakteristika vij~anog kompresora. Na slici 1. prikazan je niz rotora vij~anog kompresora tako da se oni mogu me usobno usporediti. Profili su ozna~eni brojevima u zagradama, koji u popisu literature ukazuju na patente za te rotore. U prvu prikazanu grupu spadaju rotori sa 4 zuba na vode}em i 6 zubi na vo enom rotoru. Ovakva konfiguracija rotora je kori{tena skoro za svaku aplikaciju. Asimetri~ni SRM profil [41], koji se mo`e smatrati do sada najuspje{nijim profilom rotora vij~anog kompresora, nalazi se na po~etku. Slijede}i je SRM "D" profil [4]. Na kraju je prikazan profil generisan na osnovu zup~astog {tapa - rack generisan profil [50]. Izbor i raspored osnovnih krivih na zup~astom {tapu pomo}u kojih su generisani ovi rotori daje ve}i popre~ni presjek me uzublja i ja~i zub vo enog rotora u odnosu bilo koji drugi poznati profil rotora vij~anog kompresora ove konfiguracije. Konfiguracija vij~anog kompresora sa 5 zubi vode}eg i 6 zubi vo enog rotora postaje sve popularnija, jer se njome postize kompromis izmedju velike dobave i velikog tla~nog otvora sa skoro nenadma{nim strujnim karakteristikama za manji pre~nik rotora. Kompresori sa ovakvom konfiguracijom rotora su jednako pogodni za kompresiju zraka kao i za rashladnu tehniku ili za klimatizaciju. U nastavku je, radi upore enja, data ve}a skupina ovih rotora koja po~inje sa SRM "D" profilom [4], nakon toga slijede "Sigma" profil [5], FuSheng [4] i "Hyper" profil [8]. Svi ovi profili su 'rotor generisani' profili a osnovna ly evolved over the past few years and is likely to lead to further improvements in machine performance in the near future. A comparison of several pairs of screw compressor rotors is shown in Fig. 1. Each pair is labeled by a number in brackets which denotes its patent. The first group gives rotors with 4 lobes on the main and 6 lobes on the gate rotor. This rotor configuration is the most universally accepted for almost any application. The SRM asymmetric profile [41], which historically was the most successful, is on the top. The next one is the SRM "D" profile [4]. The Ingersol-Rand profile, [6], shows how attempts were made to produce more displacement from the same compresor size. Finally, rack generated rotors [50] are presented. The second group shown are 4/5 rotors which is becoming a very popular combination for oil-flooded air compressors. The first pair, SRM "D" [4] rotors are applied in "Tamrotor" compressors which are regarded as best compressors in their class. They are followed by "Cyclon" [19] rotors. The last in this group are 'rack-generated' rotors [50]. The selection and distribution of primary curves on the rack which was used to create these rotors, gives a larger cross section area with stronger gate rotor lobes than any other known screw compressor rotor pair. The largest group of rotors presented has a 5/6 configuration. This is becoming the most popular rotor combination because it permits a good compromise between large displacement and large discharge ports with favourable load characteristics in small rotor sizes. These rotors are equally successful for air compression and refrigeration and air-conditioning applications. The group starts with the SRM "D" profile, [4], followed by the "Sigma", [5], FuSheng, [4] and "Hyper" [8] profiles. All are 'rotorgenerated' profiles and the main diference between them is in the leading lobe which is mainly an eccentric circle followed by a line, ellipse and hyperbola respectively. The hyperbola appeared to be the best possible geometrical solution for that purpose. However at the end of the group are two rack-generated profiles, [37] and [50]. The last of these shows the best delivery for its size. it also has two additional features. Firstly, the rotors retain a seal over the entire contact length while maintaining a small blow-hole, which was not the case in [37]. Secondly, two contact bands in the prox

10 Ma{instvo (3), 63-78, (1999) N.Sto{i},...: SAVREMENI RAZVOJ KONSTRUKCIJE... Slika 1. Upore enje nekih rotora vij~anih kompresora Figure 1. A comparison of several pairs of screw compresor rotors - 7 -

11 Ma{instvo (3), 63-78, (1999) N.Sto{i},..: SAVREMENI RAZVOJ KONSTRUKCIJE... razlika izme u njih se uo~ava na vode}em rotoru koji po~inje sa ekscentri~nom kru`nicom a nastavlja se linijom, elipsom ili hiperbolom respektivno. Pokazuje se da je hiperbola najbolje mogu}e primjenjivo geometrijsko rje{enje. Na kraju grupe se nalaze dva 'rack generisana' profila [37] i [50]. Mo`e se vidjeti da posljednji profil ima najve}u dobavu. Tako er, mogu se uo~iti jo{ dvije osobine koje karakteri{u te rotore i favorizuju ih u odnosu na ostale. Postignuto je zaptivanje du` cijele linije dodira i time manji nezaptiveni prostor, {to nije slu~aj kod profila [37]. Dodatno, kontaktne povr{ine sa jedne i druge strane profila u blizini podionog kruga su ravne linije na zup~astom {tapu tako da formiraju evolventu na rotorima. Zbog toga {to je relativno kretanje jednog rotora u odnosu na drugi gotovo ~isto kotrljanje, to je najbolji dodir {to ga je mogu}e posti}i izme u rotora. Rack generisani rotori konfiguracije 5/6 su prikazani na slici. Posljednja grupa rotora sa 4 i 5 rotora u vode}em i vo enom vijku respektivno, postaje sve vi{e popularna za uljnopodmazivane zra~ne kompresore. Prvi par rotora su "Cyclon" rotori [19]. Iza njih su SRM "D" rotori [4] i na kraju grupe rotori generisani pomo}u zup~astog {tapa [50]. 3. Konstrukcija kompresora Iako je moderan profil rotora neophodan uslov da bi vij~ani kompresor bio efikasan, sve ostale komponente tako er moraju biti konstruisane tako da se na najbolji na~in iskoristi potencijal rotora i ostvare najbolje mogu}e performanse kompresora. Zbog toga je vrlo va`no pravilno odabrati zazor izme u ku}i{ta i rotora, posebno na strani visokog pritiska. To, povratno, zahtijeva ili skuplje le`ajeve sa manjim zazorima ili jeftinije le`ajeve kod kojih su prednaprezanjem zazori svedeni na prihvatljivu veli~inu. Vij~ani kompresor je op}enito, a slu~aju uljnopodmazivanog kompresora, kada radi sa velikom razlikom pritisaka, posebno optere}en aksijalnim i radijalnim silama koje se na ku}i{te prenose preko le`ajeva. Za vij~ane kompresore malog i srednjeg kapaciteta obi~no se koriste kotrljaju}i le`ajevi, koji u tom slu~aju moraju biti tako dobro odabrani da zadovolje sve zadane uslove rada. Obi~no se koriste dva le`aja na tla~noj strani vratila rotora kako bi se aksijalne i radijalne sile na ku}i{te prenijele odvojeno. Tako er je bitno je da je me uosno rastojanje djelimi~no odre eno i veli~inom le`ajeva i njihovim unutra{njim zazorima. Kontaktne sile, koje su definisane obrtnim momentom koji se prenosi izme u rotora, igraju klju~nu ulogu kod kompresora sa direktnim dodirom rotora. Ove su sile relativno male u slu~aju pogona preko vode}eg imity of the pitch circles are straight lines on the rack which form involutes on the rotors. Hence the relative motion between the rotors is close to pure rolling which is the best possible. 3. Compressor Design Screw compressor design has gradually evolved and the trend is to get as small as possible a machine to meet the required performance. This means that rotor tip speeds are as high as possible within the limits imposed by efficiency requirements. Normal practice is to use rolling element bearings wherever possible because these permit smaller clearances than journal bearings. Similarly, the ports are made as large as possible to minimize suction and discharge gas speeds. These features lead to great similarity in all designs for any specified application. Although advanced rotor profiles are a necessary condition for a screw compressor to be efficient, all other components must be designed to minimise losses if maximum improvements are to be achieved. Thus the rotor to housing clearances must be properly selected, especially at the high pressure end. This in turn requires either expensive bearings with small clearances or cheaper bearings with their clearances reduced to an acceptable value by preloading. A screw compressor, especially of the oil flooded type, operates with high pressure differences. These create large axial and radial bearing forces. Rolling element bearings are normally chosen for small and medium screw compressors and these must be carefully selected to obtain a satisfactory design since, inter alia, the distance between the rotor centre lines is in part determined by them. It must be added that recent advances in the development of advanced low friction rolling element bearings greatly contributes to this choice [31]. Usually two bearings are fitted at the high pressure end of the rotor shafts in order to absorb the radial and axial loads separately. The contact force between the rotors is determined by the torque transferred between them and is very significant when they make direct contact. It is relatively small when the compressor drive is through the main rotor. However, when the drive is through the gate rotor, the contact force is substantially larger and, as far as possible, this arrangement should be avoided

12 Ma{instvo (3), 63-78, (1999) N.Sto{i},...: SAVREMENI RAZVOJ KONSTRUKCIJE... Slika. Rack generisani rotori vij~anog kompresora konfiguracije 5/6 Figure. A pair of 5/6 rack generated screw compressor rotors rotora. Pogon preko vo enog rotora uzrokuje zna~ajno pove}anje kontaktnih sila tako da se ovaj slu~aj mora isklju~iti iz bilo kakvog ozbiljnijeg razmatranja. Ulje koje se u vij~anom kompresoru ubrizgava izme u rotora za podmazivanje, hladjenje i zaptivanje, koristi se i za podmazivanje le`ajeva. Pri tom je vrlo va`no uspostaviti odvojen sistem snabdijevanja le`ajeva uljem i sistem za evakuaciju ulja iz le`ajeva da bi se gubici usljed trenja smanjili. Ulje se u radni prostor kompresora ubrizgava na onom mjestu na kojem se, prema termodinamskim prora~unima, temperature radnog fluida i ulja podudaraju. Polo`aj otvora za ubrizgavanje ulja je definisan uglom na helikoidi rotora ali se obi~no postavlja tako da ulje tangencijalno ulazi u radni prostor kako bi se iskoristilo {to je god mogu}e vi{e njegove kineti~ke energije. Kompresor moderne konstrukcije treba imati male gubitke na usisu i potisu. Zato se usisni otvor unutar ku}i{ta kompresora postavlja tako da usisani gas na svom putu {to manje mijenja smijer kretanja te da bi imao malu brzinu strujanja. To se posti`e pove}anjem zapremine usisnog otvora. Veli~ina i oblik tla~nog otvora definisani su ugra enim odnosom pritiska koji }e dati optimalne termodinamske performanse kompresora. Nakon toga se popre~ni presjek izlaznog toka dodatno pove}ava da bi se smanjila brzina toka na izlazu i time postigla minimizacija gubitaka u unutra{njem i izlaznom toku. Ku}i{te treba da bude pa`ljivo dimenzionisano kako bi se smanjila te`ina kompresora a jedan od na~ina da se to postigne je ugradnja pre~ke u usisnom otvoru u cilju pove}anja ~vrsto}a kompresora na vi{im pritiscima. Vij~ani kompresor je vrlo jednostavna toplotna ma{ina The oil which is injected into the compressor for flooding is also used for bearing lubrication but, to minimise friction losses, the bearing feed and return system is separate. The position in the compressor chamber where the oil is injected is set at the point where thermodynamic calculations show the gas and oil inlet temperatures to coincide. It is defined on the rotor helix with the injection hole located so that the oil enters tangentially in line with the gate rotor tip in order to recover as much as possible of the oil kinetic energy. To minimise flow losses in the suction and discharge ports, the following features must be included. The suction port should be positioned in the housing to let the gas enter with the fewest possible bends and the gas approach velocity kept low by making the flow area as large as possible. The discharge port size is first determined by estimating the built-in-volume ratio required for optimum thermodynamic performance. It is then increased in order to reduce the exit gas velocity and hence obtain the minimum combination of internal and discharge flow losses. The casing should be carefully dimensioned to minimize its weight and contain reinforcing bars across the suction port to improve its rigidity at higher pressures

13 Ma{instvo (3), 63-78, (1999) N.Sto{i},..: SAVREMENI RAZVOJ KONSTRUKCIJE... sa samo nekoliko pokretnih dijelova: dva rotora i obi~no ~etiri ili {est le`ajeva. Tokom njegovog razvoja do{lo se do vrlo tipi~nog oblika po ~emu postaje vrlo prepoznatljiv. Tendencija je da se dobije {to je god mogu}e manja ma{ina koja }e jo{ uvijek dati zadovoljavaju}e performanse. To zna~i da se brzina vrha zuba mora {to je mogu}e vi{e pove}ati, ali je treba jo{ uvijek dr`ati u granicama koje daju prihvatljive mehani~ke gubitke. Upotreba kotrljaju~ih umjesto kliznih le`ajeva skoro da se mo`e postaviti kao pravilo koje treba uvijek po{tovati, jer su zazori na kotrljaju~im le`ajevima, a i gubici zna~ajno manji. Otvori za komunikaciju radnog fluida moraju biti {to je god mogu}e otvoreniji da bi se smanjile brzine gasa na usisu i izlazu. Sve ovo dovodi do vrlo sli~nih konstrukcija kompresora tako da su izuzetci vrlo rijetki i skoro zanemarivi. Primjer savremene konstrukcije uljnopodmazivanog vij~anog kompresora sa reduktorom dat je na slici 3. Valja tako er napomenuti da je u zadnje vrijeme dosta uradjeno na razvoju kotrljaju~ih le`ajeva sa vrlo niskim trenjem [31], {to }e zna~ajno doprinijeti pobolj{anju performansi kompresora. Na slici 4. prikazuju se svi vitalni dijelovi modernog uljnopodmazivanog vij~anog kompresora. 4. CONCLUSIONS At the onset of the millenium, the twin screw compressor has become a mature product. As a result of orchestrated efforts by a large number of companies, driven by market forces, it has become a compact, efficient and reliable machine. Every detail counts today. Even small advances in any feature will give distinctive improvements which may be used to gain commercial advantage. Hence, despite its now established role in industry, efforts continue to make advances in every aspect of its design, manufacture and mode of operation. Although improvements so gained are most likely to be evolutionary, there is still scope for revolutionary methods or procedures to achieve a better product. The most promising development appears to be rack profile generation to produce stronger but lighter rotors with higher displacement and lower contact stress. 4 ZAKLJU^AK Vij~ani kompresor je proizvod koji je dorastao trenutku smjene vijekova. Pa`ljivo usmjereni napori velikog broja kompanija dirigovani zahtjevima tr`i{ta rezultirali su kompaktnom i efikasnom vij~anom ma{inom. U razvoju vij~anih kompresora do{lo se u fazu kad se unapre enja razmatraju do najsitnijih detalja. Male razlike dovode do malih ali zna~ajnih pomaka koji ~ine individualne prednosti svakog od kompresora. Iako se ~ini da se samo kontinualnim razvojem vij~ani kompresori mogu promijeniti na bolje, jo{ uvijek ima dosta mjesta za primjenu manje ili vi{e revolucionarnih metoda ili procedura koje }e rezultirati boljim proizvodom. ^ini se da je najperspektivniji metod generacije profila pomo}u zup~astog {tapa koji daje ja~e, ali i lak{e rotore sa ve}om dobavom i manjim kontaktnim naponima me u rotorima

14 Ma{instvo (3), 63-78, (1999) N.Sto{i},...: SAVREMENI RAZVOJ KONSTRUKCIJE... Slika 3. Konstrukcija vij~anog kompresora sa reduktorom Figure 3. A screw compressor with a gearbox design Slika 4. Sastavni dijelovi modernog uljnopodmazivanog vij~anog kompresora Figure 4. A modern oil floded screw compressor parts LITERATURA - REFERENCES [1] Amosov P.E et al, 1977: Vintovie kompresornie mashinii - Spravochnik (Screw Compression Machines - Handbook), Mashinstroienie, Leningrad [] Andreev P.A, 1961: Vintovie kompressornie mashinii (Screw Compression Machines), SUDPROM Leninngrad [3] Arbon I.M, 1994: The Design and Application of Rotary Twin-shaft Compressors in the Oil and Gas Process Industry, MEP London [4] Astberg A, 198: Patent GB 09676B [5] Bammert K, 1979: Patent Application FRG [6] Bowman J.L, 1983: US Patent 4,41,796 [7] Buckingham E, 1963: Analytical Mechanics of Gears, Dover Publ, N.York [8] Chia-Hsing C, 1995: US Patent 5,454,

15 Ma{instvo (3), 63-78, (1999) N.Sto{i},..: SAVREMENI RAZVOJ KONSTRUKCIJE... [9] Edstrom S.E, 1974: US Patent 3,787,154 [10] Edstrom S.E, 1989: Quality Classes for screw Compressor Rotors, Proc IMechE Conference Development in Industrial Compressors, 83 [11] Edstrom S.E, 199: A Modern Way to Good Screw Compressors, International Compressor Engineering Conference At Purdue, 18 [1] Fleming J.S, Tang Y, 1994: The Analysis of Leakage in a Twin Screw Compressor and its Application to Performance Improvement, Proc IMechE, Journal of Process Mechanical Engineering, Vol 09, 15 [13] Fleming J.S, Tang Y, Cook G, 1998: The Twin Helical Screw Compressor, Part 1: Development, Applications and Competetive Position, P. :A Mathematical Model of the Working process, Proc IMechE, Journal of Mechanical Engineering Science, Vol 1, p369 [14] Fujiwara M, Osada Y, 1995: Performance Analysis of Oil Injected Screw Compressors and their Application, Int J Refrig Vol 18, 4 [15] Golovintsov A. G et al, 1964: Rotatsionii kompresorii (Rotary Compressors), Mashinostroenie, Moscow [16] Hanjali} K, Sto{i} N, 1994: Application of mathematical modeling of screw engines to the optimization of lobe profiles, Proc. VDI Tagung "Schraubenmaschinen 94" Dortmund VDI Berichte 1135 [17] Hanjali} K, Sto{i} N, 1997: Development and Optimization of Screw Machines with a Simulation Model, Part II: Thermodynamic Performance Simulation and Design, ASME Transactions, Journal of Fluids Engineering, Vol 119, p 664 [18] Holmes C.S, 1994: Towards a Core program for the Measurement of Screw Rotor Bodies by Co-ordinate Measuring Machine, Proc. VDI Tagung "Schraubenmaschinen 94", Dortmund VDI Berichte 1135 [19] Hough D, Morris S.J, 1984: Patent Application GB [0] Kasuya K. et al, 1983: US Patent 4,406,60 [1] Kauder K, Harling H.B, 1994: Visualisierung der Olverteilung in Schraubenkompressoren (Visualisation of Oil Effects in Screw Compressors), Proc. VDI Tagung "Schraubenmaschinen 94", Dortmund VDI Berichte 1135 [] Kauder K, Helpertz M, 1998: Einlauf- und Hybridschichten für Schraubenkompressoren (Run-in and Hybrid Coatings for Twin-Screw Compressors), Proc. VDI Tagung "Schraubenmaschinen 98", Dortmund VDI Berichte 1391 [3] Konka K-H, 1988: Schraubenkompressoren (Screw Compressors) VDI-Verlag, Duesseldorf [4] Lee H-T, 1988: US Patent 4,890,99 [5] Litvin F.L, 1956: Teoria zubchatiih zaceplenii (Theory of Gearing), Nauka Moscow, second edition 1968, also Gear Geometry and Applied Theory Prentice-Hill, Englewood Cliffs, NJ 1994 [6] Lysholm A, 194: A New Rotary Compressor, Proc. I.Mech.E. 150,11 [7] Lysholm A, 1966: The Fundamentals of a New Screw Engine, ASME Paper No 66-GT-86 [8] Lysholm A, 1967: US Patent 3,314,598 [9] Margolis D.L, 1978: Analytical Modelling of Helical Screw Turbines for Performance Prediction, J.Engr.for Power 100(3)48 [30] Menssen E, 1977: US Patent 4,08,06 [31] Meyers K, 1997: Creating the Right Environment for Compressor Bearings, Evolution, SKF Ind.Journal, Vol 4, 1 [3] O'Neill P.A, 1993: Industrial Compressors, Theory and Equipment, Butterworth-Heinemann, Oxford [33] Nilson, 195: US Patent,6,787 [34]Peng N, Xing Z, 1990: New Rotor Profile and its Performance Prediction of Screw Compressor, International Compressor Engineering Conference At Purdue, 18 [35] Rinder L, 1979: Schraubenverdichter (Screw Compressors), Springer Verlag, New York [36] Rinder L, 1984: Schraubenverdichterl?ufer mit Evolventenflanken (Screw Compressor Rotor with Involute Lobes), Proc. VDI Tagung "Schraubenmaschinen 84" VDI Berichte Nr

16 Ma{instvo (3), 63-78, (1999) N.Sto{i},...: SAVREMENI RAZVOJ KONSTRUKCIJE... [37] Rinder L, 1987: US Patent 4,643,654 [38] Sauls J, 1994: The Influence of Leakage on the Performance of Refrigerant Screw Compressors, Proc. VDI Tagung "Schraubenmaschinen 94", Dortmund VDI Berichte 1135 [39] Sauls J, 1998: An Analytical Study of the Effects of Manufacturing on Screw Rotor Profiles and Rotor Pair Clearances, Proc. VDI Tagung "Schraubenmaschinen 98", Dortmund VDI Berichte 1391 [40] Sakun I.A, 1960: Vintovie kompresorii (Screw Compressors), Mashinostroenie Leningrad [41] Shibbie, 1979: US Patent 4,140,445 [4] Singh P.J, Onuschak A.D, 1984: A Comprehensive Computerized Method For Twin Screw Rotor Profile Generation and Analysis, Purdue Compressor Technology Conference 544 [43] Singh P.J, Schwartz J.R, 1990: Exact Analytical Representation of Screw Compressor Rotor Geometry, International Compressor Engineering Conference At Purdue, 95 [44] Smith I. K, Sto{i} N, Aldis C. A, 1996: Development of the trilateral flash cycle system, Part 3: The design of high efficiency two-phase screw expanders, Proc IMechE, Journal of Power and Energy, Vol 10, p 75 [45] Sto{i} N, Hanjali} K, 1977: Contribution towards Modelling 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 Compressor Elements, Strojarstvo Journal Zagreb 8, 181 [47] Sto{i} N, Kova~evi} A, Hanjali} K, Milutinovi} Lj, 1988: Mathematical Modelling of the Oil Influence upon the Working Cycle of Screw Compressors, International Compressor Engineering Conference at Purdue, 355 [48] Sto{i} N, Milutinovi} Lj., Hanjali} K, Kova~evi} A, 199: Investigation of the Influence of Oil Injection upon the Screw Compressor Working Process, Int.J.Refrig. 15,4,06 [49] Sto{i} N, Hanjali} K, 1994: Development and optimization of screw engine rotor pairs on the basis of computer modeling, Proc. XVII Conference on Compressor Engineering at Purdue, 55 [50] Sto{i} N, 1996: Patent Application GB [51] Sto{i} N, Hanjali} K, 1997: Development and Optimization of Screw Machines with a Simulation Model, Part I: Profile Generation, ASME Transactions, Journal of Fluids Engineering, Vol 119, p 659 [5] Sto{i} N, Smith I K, Kova~evi} A, Aldis C A, 1997: The Design of a Twin-screw Compressor Based on a New Profile, Journal of Engineering Design, 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 at Purdue, 607 [54] Sto{i} N, Smith I.K, Brasz J.J, Sishtla V, 1998: The Performance of a Screw Compressor with Involute Contact Rotors in a Low Viscosity Gas- Liquid Mixture Environment, Proc. VDI Tagung "Schraubenmaschinen 98", Dortmund VDI Berichte 1391 [55] Sto{i} N, 1998: On Gearing of Helical Screw Compressor Rotors, Proc IMechE, Journal of Mechanical Engineering Science, Vol 1, 587 [56] Tang Y, Fleming J.S, 199: Obtaining the Optimum Geometrical Parameters of a Refrigeration Helical Screw Compressor, International Compressor Engineering Conference at Purdue 13 [57] Tang Y, Fleming J.S, 1994: Clearances between the Rotors of Helical Screw Compressors: Their determination, Optimization and Thermodynamic Consequences, Proc IMechE, J. of Process Mechanical Engineering, Vol 08, 155 [58] Xion Z. Dagang X, 1986: Study on Actual Profile Surface and Engaging Clearance of Screw Compressor Rotors, Purdue Compressor Technology Conference 39 [59] Zenan X, 1984: The Dynamic Measurement and Mating Design of a Screw Compressor Rotor Pair, Purdue Compressor Technology Conference 314 [60] Zhang L, Hamilton J.F, 199: Main Geometric Characteristics of the Twin Screw Compressor, International Compressor Engineering Conference at Purdue

17 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... KOMPJUTERSKO UPRAVLJANJE TOLERANCIJAMA U KONSTRUIRANJU TRODIMENZIONALNOG SKLOPA E. Chirone; S. Tornincasa, Dipartimento di Ingegneria Meccanica, Università di Brescia, Italy, chirone@ing.unibs.it; ;fax REZIME PRETHODNO SAOP[TENJE Izbor tolerancija igra klju~nu ulogu u kona~noj cijeni proizvoda. Ovakva in`enjerska funkcija zapravo mo`e smanjiti tro{kove proizvodnje, pove}ati kvalitet i obezbijediti klju~ni faktor u praksi Konkurentnog in`enjeringa. Iz tog razloga, na Politehnici u Torinu je razvijen sistem za modeliranje i analizu slo`enih tolerancija sklopova. Tipi~an CAD sistem kreira solid model, koji predstavlja nominalnu geometriju, koja je idealizacija proizvoda. Da bi se dio predstavio sa tolerisanim povr{inama, razvijen je relacijski model sklopa, koji je zatim integrisan putem odgovaraju}e sheme tolerancija. Razvijen je direktni interfejs izme u parametarskog CAD sistema i funkcionalnog okru`enja za dimenzionisanje s ciljem da se izvr{i izbor kota, baziran na funkciji dijela i automatskoj analizi i raspodjeli tolerancija. Predlo`eni metod je implementiran u okru`enju SolidWorks uz kori{tenje definiranog API programskog interfejsa, a pogodan je za integraciju sa drugim komercijalnim CAD sistemima. Klju~ne rije~i: tolerancije, kompjutersko upravljanje COMPUTER AIDED TOLERANCE IN 3-D DESIGN FOR ASSEMBLY E. Chirone; S. Tornincasa, Dipartimento di Ingegneria Meccanica, Università di Brescia, Italy, chirone@ing.unibs.it; ;fax SUMMARY PRELIMINARY NOTES The effect of the tolerance design is actually a main point on the final cost of a manufactured product. Such engineering function can indeed reduce manufacturing cost, improve quality and provide a key factor in Concurrent Engineering practice. For this reason, a comprehensive system for assembly tolerance modeling and analysis has been developed at Politecnico of Turin. A typical CAD system creates a solid model, representing the nominal geometry, that is an idealization of the manufactured piece. In order to represent a part with toleranced surfaces, a relational model of an assembly is developed, and integrated with an appropriate tolerance scheme. 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. The proposed method is implemented in the SolidWorks environment using a defined application programming interface (API)) and is suitable for integration with other commercial CAD systems. Key words: tolerance, computer aided,

18 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE UVOD U ma{inskoj industriji, ~esto su se koristili samo tehni~ki crte`i da bi se odredilo kako }e se dio proizvesti i smjestiti u sklop. Dio se proizvodio prema crte`ima, a zatim pregledao, i ako se komponente ne bi pravilno uklapale, crte`i 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 tr`i{ta proizvoda zahtijeva ~este promjene konstrukcije proizvoda i strategija proizvodnje. Da bi se skratilo vrijeme potrebno za razvoj proizvoda, po`eljno 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 mo`e provjeriti da kombinovano dejstvo akumulacije svih tih tolerancija (slo`ena tolerancja) ne dovede do zaribavanja sklopa, da se proizvod mo`e ekonomi~no proizvesti i da ispravno funkcioni{e. Konstruktor mo`e 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 mo`e 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 zadr`i svoju funkcionalnost []. Pravi na~in mora biti taj da se pove}aju specifikacije tolerancija zadr`avanjem ispravne funkcije, {to bi zna~ilo u~initi konstrukciju robusnom prema devijacijama lanaca procesa. Ve}ina dana{njih CAD sistema podr`avaju 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 okru`enja. Mogu}nost da se CAD program prilagodi korisniku pomo}u programskog jezika kao {to je Visual Basic koristi jedan va`an 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 []. 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

19 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... Engineering design Functional requirements safety Performance Reliability Product Life Maintenance Manufacturing design Production Cost Machine and process Operator skills Assembly Inspection Tight Tolerance Loose Slika 1. Specifikacije tolerancija postaju kriti~na veza izme u in`enjeringa (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 okru`enje SolidWorks; ovaj alat se tako e koristi i u po~etnom te~aju in`enjerskog crtanja. Student mo`e 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 D ravan. Na vi{em nivou mogu}e je razviti uzajamnu vezu izme u dijelova i funkcionalnih zahtjeva; sa automatskom provjerom slo`enih tolerancija i alokacijom komponentnih 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 D 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.. GEOMETRIJSKE TOLERANCIJE U MODELU SKLOPA.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. GEOMETRIC TOLERANCES IN THE ASSEMBLY MODEL.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;

20 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... 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; ) definicije redoslijeda komponenti sklopa i dimenzija parova; 3) tolerancija komponenti. Model sklopa sa n zavisnih komponenti je prikazan skupom objekata: C= {c 1,c,.c n } Gdje je c 1 : c i = <Xi, LFi, Pi>, i [1,.,n] Xi sadr`i 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. LF i =< A i, B i > redom pokaziva~ na komponentu i na tijelo objekta i-tog dijela. P i =<F i,e kh,z kh > gdje je Fi = {F 1,F,,F k } lista objekata k-te povr{ine dijela, E kh lista h-tih ivica povr{ine k, Z kh atribut ivice h. Atribut je informacija (hrapavost, tolerancija) koja se mo`e pridru`iti Povr{ini, Ivici, Ta~ki ili Elementu. Mogu}e je prenijeti atribut-objekat i promijeniti njegove parametarske vrijednosti. Naprimjer, atribut koji sadr`i informacije za NC obradu rezanjem mo`e se pridru`iti Povr{ini. Relacijski model sklopa se dobije kombiniranjem parova sa informacijama o sklopu, i deini{e se skupom: <C, M> M = {M 1, M,..M j } omogu}uje pristup parovima objekata i definiciji parova sklopa; j je broj relacije izme u komponenti u sklopu, j max =n(n- 1). M i, i [1,,j] se opisuje preko seta od tri objekta: Mi= <c a, c b, S ab > Gdje c a,c b C i S ab iznose NULL ako nema relacije izme u komponenti c a, c b, u suprotnom je: S ab = {R 1, R,..R m } R opisuje listu m relacija izme u komponenti c a i c b : R i = <D p,d q,w pq,p pq >, 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; ) 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= {c 1,c,.c n } Where c 1 is: c i = <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. LF i =< A i, B i > respectively a pointer to the component and to body object of the i part. P i =<F i,e kh,z kh > where Fi = {F 1,F,,F k } is the list of k face object of the part, E kh the list of the h edges of face k, Z kh 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 = {M 1, M,..M j } allows access to mated objects and the assembly mate definition; j is the relation number between components in the assembly, j max =n(n-1). M i, i [1,,j] is described by a set of three object: Mi= <c a, c b, S ab > Where c a,c b C and S ab is NULL if no relations exist between component c a, c b, otherwise is: S ab = {R 1, R,..R m } R describes a list of the m mating relations between components c a and c b : R i = <D p,d q,w pq,p pq >, i [1,,m] - 8 -

21 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... D p,d q daje dva vezana entiteta (povr{ine, ivica, osa), a W pq daje vrstu veze (podudaranje, koncentri~nost, okomitost, paralelnost, tangentnost, udaljenost, ugao). P pq daje listu parametara ove veze i predstavlja X,Y,Z lokaciju te veze u modelskom prostoru sklopa. D p,d q returns two mate entities (faces, edge, axis), and W pq returns the type of mate (coincident, concentric, perpendicular, parallel, tangent, distance, angle). P pq 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.. Primjer relacije sklopa Slika 4 prikazuje sklop zateza~a remena sastavljen od n = 7 dijelova: postolje, u{ka [], osovina, podlo{ka [] i to~ak. Polazna komponenta je nosa~. Maksimalni broj relacije j max je: j max = n(n-1) = 7(7-1) = 4; j = 1 (vidi tabelu I) Uzmimo u obzir relaciju veze sa slike 5 izme u osnove (1) i u{ke (). Broj od m = 3 relacije veze izme u komponenti je: c a = osnova, c b = u{ka, m=3, S ab = {F 1,F,F 3 } F 1 = <A 1,A,podudarnost,P 1 >, F = <B 1,B,podudarnost,P 1 >, F 3 = <C 1,C,podudarnost,P 1 > Par entiteta su dvije povr{ine na svakoj komponenti (A 1,A ) (B 1,B ) i jedna osa C 1,C (tab. II)... Example of an assembly relation The figure 4 shows a belt tensioner assembly composed by n = 7 parts: base, bracket [], shaft, bushing [] and a pulley. The root component is the base. The max relation number j max is: j max = n(n-1) = 7(7-1) = 4; j = 1 (see table I) Let s consider the mating relation of figure 5 between the base (1) and the bracket (). The m =3 mating relations between components is: c a = base, c b = bracket, m=3, S ab = {F 1,F,F 3 } F 1 = <A 1,A,coincident,P 1 >, F = <B 1,B,coincident,P 1 >, F 3 = <C 1,C,coincident,P 1 > The mate entity are two faces on each component (A 1,A ) (B 1,B ) and one axis C 1,C (tab. II)

22 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... Relations Base Bracket1 Bracket Pulley Bushing1 Bushing Shaft Base Bracket Bracket Pulley Bushing Bushing Shaft 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 Axis base A 1,B 1 C 1 bracket A,B C 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

23 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... Relacije veze izme u u{ke () i podlo{ke (5) su: c a = u{ka, c b =podlo{ka, m=, Sab = {F 1,F } F 1 = <E,E 3,podudarnost,P 3 >, F = <D,D 3,podudarnost,P 3 > Par entiteta su jedna povr{ina na svakoj komponenti D, D 3 i jedna osa E,E 3 (tab. III) The mating relations between bracket () and bushing (5) are: c a = bracket, c b =bushing, m=, Sab = {F 1,F } F 1 = <E,E 3,coincident,P 3 >, F = <D,D 3,coincident,P 3 > The mate entity are one face on each component D, D 3 and one axis E,E 3 (tab. III) Face Axis Bushing D 3 E 3 bracket D E Tabela III. Broj od m = relacija veze izme u u{ke i podlo{ke Table III. The m = 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 in`enjering, 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

24 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... 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 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

25 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... Software predla`e 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 polo`aja Figure 8. The drawing with the positional tolerance Na slici 8 je prikazan crte` sa tolerancijom polo`aja; 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 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 predla`e 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 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)

26 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... 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 polo`aja; 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 okru`enju software mo`e automatski proizvesti geometriju za ortogonalni i dodatne poglede; crtanje se mo`e pobolj{ati dodatnom skiciranom geometrijom, dimenzijama, napomenama; sklopovi, dijelovi i crte`i 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

27 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... Slika 11. Crte` sa tolerancijom polo`aja; 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 1. 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 1. 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

28 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... Uspostavljen je direktni interfejs izme u parametarskog CAD sistema i funkcionalnog dimenzionalnog okru`enja. Mogu}nost da se CAD program prilagodi korisniku pomo}u programskog jezika kao {to je Visual Basic koristi jedan va`an dio objektne tehnologije koji se naziva OLE (Object Linking and Embedding) automatizacija. Application Programming Interface (API) je OLE programski interfejs za SolidWorks. API sadr`i 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 Z kh prethodno opisanog relacijskog modela sklopa. [tavi{e, korisnik mo`e provjeriti tolerancije preko prikaza najve}e i najmanje devijacije dijela. Koriste}i formu Visual Basic-a (slika 1), korisnik mo`e 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, predlo`eni 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 Z kh. Koraci u kreiranju sinteze tolerancija su: 1) odre ivanje komponenti koje odre uju zazor sklopa; ) izvo enje dimenzija kriti~nih komponenti; 3) vektorska petlja koja predstavlja slo`enu 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 Z kh 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. 1), 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 Z kh. The steps in creating a tolerance synthesis are: 1) determination of the components which determine the assembly clearance; ) derivation of critical component dimensions; 3) vector loop representation of the tolerance stack; 4) allocation of tolerance components

29 Ma{instvo (3), 79 9, (1999) E.Chirone,...: KOMPJUTERSKO UPRAVLJANJE... Ulaz ~ine zazori i ukupne dimenzije sklopa, koje su kriti~ne za rad i funkcionalnost. Korisnik interaktivno bira kriti~ne komponente sklopa i smjer D 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 te`e 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 D-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