analiza mogu]nosti pove]anja nosivosti...

Ma{instvo 2(7), 105 – 116, (2003) M.Dàferovi}, ...: ANALIZA MOGU]NOSTI POVE]ANJA....

ANALIZA MOGU]NOSTI POVE]ANJA NOSIVOSTI REDUKTORA PRIMJENOM OPTIMALNOG IZBORA

OP]IH PARAMETARA

Mr. Mirsad Dàferovi}1), Prof. dr. Du{an Vukojevi}2), Mr. Nedeljko Vukojevi}2), 1)Op}ina Zavidovi}i, 2) Ma{inski fakultet u Zenici, Fakultetska br. 1, 72 000 Zenica

REZIME:

U cilju iznalaènja i izbora optimalnih parova zup~anika potrebno je provjeriti uticaj svih faktora koji odre|uju nosivost jednog zup~astog para. Za postupak optimalnog izbora osnovnih parametara zup~astog para va`ni su samo osnovni parametri i faktori zubaca koji su u funkciji istih, a da se optere}enje, {irina zup~anika, faktori optere}enja i materijala mogu u postupku optimiranja izostaviti jer su isti. Postupkom optimiranja rezultata izbora osnovnih parametara metodom selekcije prema utvr|enom cilju, mogu}e je dobiti par zup~anika sa osnovnim parametrima koji }e imati i najpovoljnija naponska stanja ili neka druga unaprijed definisana stanja. Provjera navedenih ~injenica provodi se prora~unom nosivosti zup~astih parova postoje}eg reduktora i zup~astog para reduktora definisanog metodom optimiranja osnovnih parametara pomo}u adekvatnih ra~unarskih programa.

Klju~ne rije~i: reduktori, optimizacija, nosivost

ANALYSIS OF THE POTENTIALS FOR INCREASE OF THE REDUCTION GEAR BEARING CAPACITY BY USE OF OPTIMAL SELECTION OF GENERAL PARAMETARS

Mirsad Dàferovi}1), MSc. Mech.Eng.; Du{an Vukojevi}2), PhD professor; Nedeljko Vukojevi}2), MSc. Mech. Eng, Senior asisstant 1)Municipality of Zavidovi}i, 2)Faculty of Mechanical Engineering in Zenica, Fakultetska br. 1. 72000 Zenica, B&H SUMMARY:

In order to find optimal pairs of gears it is necessary to check the impact of all the factors which determine bearing capacity of a pair of gears. Basic parameters and factors of dentils are important for procedure of optimal selection of basic parameters of pair of gears, while load, width of gear, load and material factors can be avoided in the process of optimisation because they have identical values. P ocess of optimisation of choice of basic parameter results by method of selection according to the objective set, it is possible to get a pair of gears with basic parameters which will also have optimal stress notation of other pre-determined states. The above facts can be tested by computing bearing capacity of gear pairs of the existing reduction gears and reduction gear dentated pair defined by method of optimisation of basic parameters, using suitable software.

r

Key words: reduction gears, optimization, bearing capacity

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1. UVOD U smislu pojeftinjenja i podizanja kvaliteta proizvoda nametnula se ideja standardizacije i unifikacije i grupne tehnologije. U sve o{trijoj konkurenciji eminentnih svjetskih proizvo|a~a opreme, a ovdje je konkretno rije~ o ma{inskoj opremi, jedan od bitnih faktora je svakako ujedna~avanje kvaliteta na gotovim proizvodima, koji imaju karakter standarda.

1. INTRODUCTION In order to achieve lower price and better quality of products, the idea of standardisation and unification, as well as group technology has been imposed. Competition is becoming a more and more serious issue for producers worldwide, and here it is about machine equipment, where one of the main factors is unification of quality of final products as well as standardisation.

Upravo na ovoj ideji je, kroz jedan kriti~ki osvrt i analizu postoje}eg reduktora "Krivaja", razvijen je novi kompatibilni mati~ni model u zadatim granicama, primjenom odgovaraju}e ra~unarske podr{ke.

This very idea, through critical view and analysis of the existing “Krivaja” reduction gears, was a starting point for development of a new compatible basic model with determined limits, using suitable software support.

2. KRITI^KA ANALIZA POSTOJE]E KONSTRUKCIJE REDUKTORA

Reduktor »Krivaja« konstrukcijski predstavlja jednu od mogu}ih konstrukcija motor-reduktora op{te industrijske namjene (slika 1). Sva potrebna istra`ivanja, analize, kriti~ke ocjene i zaklju~ke potrebne za utvr|ivanje polaznih osnova za projekat nove familije reduktora se zasnivaju i polaze od postoje}e konstrukcije MRZ-250 iz familije reduktora "Krivaja" koju ~ine reduktori trostepene konstrukcije, istih osnih razmaka za sva tri para zup~anika sa rasponom osnih razmaka od amin=81 do amax=184,6 mm, slika1. Prenosni odnosi familije reduktora "Krivaja" su u rasponu od imin=8,0 do imax=63.

2. CRITICAL ANALYSIS OF THE EXISTING REDUCTION GEARS CONSTRUCTION

“Krivaja” reduction gear, in terms of construction, represent one of the possible solutions for engine-reduction gears for general industrial use (Figure 1). All the research, analyses, critics and conclusions necessary for determination of starting points for design of a new family of reduction gears are based on the existing construction MRZ-250, from the “Krivaja” reduction gear family consisting of three-level construction reduction gears, the same axial distance for all three pairs of gears with axial distance from amin = 81 to amax = 184.6 mm, Figure 1. Transmission ration for the “Krivaja” family reduction gears are in the range from imin = 8.0 to imax = 63.

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Slika 1. Vanjski izgled motor-reduktora "Krivaja"

Figure 1. External view o the “Krivaja” engine-reduction gea f r

a a


Ne analiziraju}i detaljno samo konstrukcijsko rje{enje postoje}eg reduktora mogu se na bazi ozubljenja zup~astih parova, kao osnovnih elemenata sklopa, izvesti sljede}i zaklju~ci: - rje{enje sa istim osnim razmakom »a« i istim parametrima ozubljenja mn i β ima sa stanovi{ta izrade, glodala i kontrole nesumnjive prednosti, - veliki broj parova zup~anika za ostvarivanje razli~itih prenosnih odnosa je neracionalan i nepotreban, jer zahtjeva veliki broj pojedina~nih elemenata reduktora, - nije mogu}e primjeniti princip ugradnje istih dijelova (zup~astih parova) u vi{e razli~itih veli~ina familije reduktora, jer svaka veli~ina reduktora ima razli~it osni razmak, - ve}i utro{ak materijala (s obzirom da te`ina raste sa kvadratom porasta pre~nika) jer su ve}i pre~nici zup~anika prvog i drugog para, - sa uglom nagiba zuba β=8° nisu iskori{tene prednosti kosog ozubljenja (β=10÷20°), - zubi nisu korigovani, te nisu iskori{tene prednosti korigovanih profila zuba u vezi sa pove}anjem nosivosti korijena zuba, izjedna~avanja klizanja bokova zuba u zahvatu itd., - osni razmaci i prenosni odnosi nisu birani iz reda standardnih brojeva pa je isklju~ena mogu}nost standardizacije i tipizacije veli~ina. Po{to su navedene karakteristike za ostale iste uslove: optere}enje, materijal i kvalitet ozubljenja, u direktnoj funkciji od op{tih parametara ozubljenja (mn, β, z1, z2, x1, x2) pretpostavlja se da nije ostvarena maksimalna mogu}a nosivost s obzirom na : - osnovne parametre, - stepen prekrivanja, - klizanje bokova zuba i - raspored parcijalnih prenosnih odnosa po parovima. Navedene pretpostavke treba istra`iti kroz prora~un i uporednu analizu tipskih trostepenih reduktora, stare i nove izvedbe, primjenom metode optimalnog izbora op{tih parametara (programskih paketa) pod istim uslovima.

Without analysing the construction solution of the existing reduction gear, but based on denticulation of pairs of gears, being the basic elements of assembly, the following can be concluded: - the solution which includes the same axial distance «a» and the same denticulation parametars mn i β has indisputable advantages from the point of view of production, lathe and control; - having numerous pairs of gears for realising various transmission ration is not economic and necessary because it requires a great number of reduction gears individual elements - it is not possible to realise the principle of assembly of identical parts (dentated pairs) in several different size families of reduction gears because each size has different axial distance - bigger consumption of materials (taking into account that weight grows with square of diameter growth) because diameters of the first and second pair are bigger - the dentil angle of inclination β = 8° does not exploit the advantages of angled denticulation (β=10-20°) - dentils are not corrected, so the advantages of corrected dentil sections are not exploited in terms of bearing capacity increase of dentil root, equalisation of dentil sides in rotation etc. - axial distances and transmission ratios have not been chosen from standard numbers, the possibility of standardisation and unification of sizes is, therefore, excluded

Since the listed characteristics for the rest of conditions: load, material and quality of denticulation, in direct connection of the general parameters of denticulation (mn, β, z1, z2, x1, x2), it is supposed that the maximum possible load capacity has not been achieved, with regard to:

- basic parameters - degree of covering - slide of dentil backs - arrangement of partial transmission ratios

by pairs The above characteristics should be analysed through computation and parallel analysis of typical three-level reduction gears of old and new production, applying the method of optimal selection of general parameters (softwers) under the same conditions.

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3. OSNOVNI PODACI I POSTAVKE ZA NOVU IZVEDBU REDUKTORA

Da bi se pristupilo projektovanju nove familije reduktora pove}ane nosivosti potrebno je postaviti osnove projekta nove familije reduktora i to: - okvirne veli~ine familije, osni razmaci parova zup~anika i prenosni odnosi - koncepcija konstrukcije reduktora, - prora~un i konstrukcija mati~nog projekta, - standardni brojevi i - zakon modela. Na slici 2 prikazan je trostepeni reduktor koji predstavlja usvojenu novu koncepciju reduktora, osnih razmaka a1, a2, a3 koji zatvaraju trougao. Ulazna osa motora i izlaznog vratila reduktora su u istoj ravnini (ose se poklapaju).

3. GENERAL DATA AND POSTULATES FOR NEW CONSTRUCTION OF REDUCTION GEARS

In order to start designing a new family of reduction gears of increased bearing capacity, it is necessary to determine the design basics, such as: • nominal sizes of the family, axial distance of

gear pairs and transmission rations, • the concept of reduction gear construction, • computation and construction of the basic design, • standard numbers • model rule.

Slika 2. Osni razmaci parova zup~anika Figure 2. Gear pairs axial distances

Ovakva konstrukcija omogu}ava bolje iskori{tenje prostora, tipizaciju dijelova, princip grupne tehnologije i ugradnju istih dijelova u vi{e razli~itih reduktora. Vrijednosti osnih razmaka parova zup~anika i prenosnih odnosa reduktora nove izvedbe se biraju iz reda standardnih brojeva R10 za sljede}e zadate grani~ne veli~ine, koje pokrivaju pro{ireni raspon postoje}eg proizvodnog programa: - osni razmaci parova zup~anika: amin=80 mm i amax=250 mm, - prenosni odnosi reduktora: inmin=8 i inmax=63 i - faktor porasta standardnih brojeva za R10: ϕ=1,25.

A construction like this one enables better use of space, unification of parts, principle of group technology and assembly of identical parts in different reduction gears. The values of gear pairs axial distances and transmission ratios for reduction gears of new construction shall be selected from standard numbers R10 for the following determined limit values, which cover extended range of the existing production program capacity: - axial distances of gear pairs. amin = 80 mm

and amax = 250 mm, - transmission rations of reduction gears: imin =

8 and imax = 63 and factor of standard numbers growth R10; ϕ=1.25

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Nazivne veli~ine reduktora nove izvedbe su odre|ene veli~inom osnog razmaka «a3», posljednjeg spregnutog para, ~ije veli~ine tako|e odgovaraju grani~nim veli~inama osnih razmaka parova zup~anika: a3min=80 mm i a3max=250 mm. Primjenom faktora porasta: ϕ=1,25 iz reda standardnih brojeva R10 dobiju se karakteristi~ne veli~ine prikazane u tabelama 1, 2 i 3.

Nominal values of the new construction reduction gears are determined by the size of axial distance «a3», last composed pair, whose values also comply with the limit values of gear pairs axial distances: a3min = 80 mm and a3max = 250 mm. Using the growth factor: ϕ = 1.25, selected from the standard numbers R10, the characteristic values will be given, as shown in the tables 1, 2 and 3.

Tabela 1 Nazivne veli~ine reduktora ..Table 1 Nominal values of reduction gears

Osni razmaci a3 (mm) Axial distance a3 (mm)

80 100 125 160 200 250

Tabela 2. Parcijalni osni razmaci Table 2. Partial axial distances

Nazivna vel.reduktora Nominal value of reduction gear

80 100 125 160 200 250

a1 (mm) 80 80 80 100 125 160 a2 (mm) 80 80 100 125 160 200 a3 (mm) 80 100 125 160 200 250

Tabela 3. Nazivni prenosni odnosi reduktora » in « Table 3 Nominal transmission ratios for reduction gears «i. n»

Prenosni odnosi* Transmision ratio*

8 10 16 20 25 31,5 40 50 63

*Prenosni odnosi pojedinih parova zup~anika za nazivne prenosne odnose reduktora su odre|eni analizom izbalansirane nosivosti 6 .

*Some gear pair transmission ratios for the reduction gears nominal transmission ratios have been determined by analysing the balanced load capacity [6]. [ ]

4. ANALIZA UTICAJNIH FAKTORA NA NOSIVOST PAROVA ZUPÂNIKA U cilju iznalaènja i izbora optimalnih parova zup~anika za novi model reduktora , potrebno je prethodno provjeriti analizu svih faktora koji odre|uju nosivost jednog zup~astog para. Globalno posmatrano svaki par zup~anika je geometrijski odre|en njegovim osnim razmakom »a« i prenosnim odnosom »i«. Kod projektovanja familije zup~astih parova ili reduktora radi se sa nazivnim prenosnim odnosom » in « koji se moè razlikovati od stvarnog » i « za veli~inu odstupanja » ∆i « koja ne treba biti ve}a od dozvoljenih grani~nih odstupanja ∆imax i ∆imin. Ta~ne dimenzije zup~anika u paru su odre|ene izborom njihovih osnovnih parametara.

4. ANALYSIS OF THE FACTORS INFLUENCING THE GEAR PAIRS LOAD CAPACITY In order to determine and select the optimal gear pairs for the new model of reduction gears, it is necessary to check first the analysis of all the factors which determine a dentated pair bearing capacity. Generally speaking, each pair of gears is geometrically determined by its axial distance «a» and transmission ratio «i». When designing a dentated pairs family or reduction gears, it is important to differentiate between the nominal transmission ration « in », which can differ from the actual « i «, for the deviation value «∆i», which should not be bigger than the allowed limit deviation ∆imax, ∆imin. The precise dimensions of gears in a pair have been determined by selection of their basic parameters.

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Odstupanje stvarnog od nazivnog prenosnog odnosa:

[ ]%1001 ⋅−=∆iii n ......................(1)

Osni razmak:

( ) ([ ]2121 cos2cos2

xxzzma n +++= ββ

) .....(2)

Slijedi zaklju~ak da se zup~asti par definisan osnim razmakom »a« i prenosnim odnosom

»in« kinematski mo`e ostvariti sa razli~itim

osnovnim parametrima (mn, β, z1, z2, x1, x2) u okviru prethodno zadatih grani~nih veli~ina modula mn, odstupanja prenosnog odnosa ∆imax i ∆imin, ugla nagiba bo~ne linije zuba βmax i βmin te faktora pomjeranja profila xmax i xmin, a koje moraju biti u korelacijskoj ovisnosti. Promjenom jedne ili vi{e od ovih osnovnih veli~ina moraju se skladno mijenjati i ostale. Tabela 4 daje primjer jednog para zup~anika osnog razmaka a=140 i in=1,25 sa dozvoljenim odstupanjem ∆i=3%.

Deviation of the accurate from nominal transmission ratio:

[ ]%1001 ⋅−=∆iii n ......................(1)

Axial distance:

( ) ([ ]2121 cos2cos2

xxzzma n +++= ββ

)

r

r r

.....(2)

It can be concluded that the dentated pair defined by axial distance «a» and transmission ration «in» kinetically can be realised with different basic parameters (mn, β, z1, z2, x1, x2), within the predetermined limit values of module mn, transmission ratio, deviations ∆imax and ∆imin, angle of dentil side line inclination βmax and βmin, as well as factors of section translation xmax and xmin, which must be in correlation. Changing one or more of these basic parameters, others must be changed accordingly. Table 4 gives an example of one gear pair, with axial distance of a = 140 and in = 1.25, with allowed deviation ∆i = 3%.

Tabela 4. Mogu}e g upe osnovnih parametara za jedan par zup~anika i za osni razmak a=140 mm i prenosni odnos iu=1,25 Table 4. Possible g oups of basic parameters for one gear pai , for the axial distance a=140 mm and transmission ration iu = 1.25

BROJ ZUBA No of Dentils

mn x1 β P Rb. No.

Z1 Z2 [mm] [-] [o] [kW]

1 30 38 4 0,06 13 133 2 30 38 4 0,09 13 132 3 30 37 4 0,33 13 128 4 30 38 4 0,09 13 132 5 31 38 4 0,14 13 122 6 35 43 3,5 0,07 12 110 7 35 43 3,5 0,10 12 109 8 40 49 3 0,53 13 75 9 40 50 3 0,27 13 78 10 40 51 3 0,03 13 83

Ovako definisani zup~asti parovi imaju, zbog uticaja svakog od osnovnih parametara direktno svojom veli~inom ili faktorima koji su u funkciji tih parametara, razli~ite izra~unate snage, te da je postupak pravilnog izbora osnovnih parametara veoma bitan za njihovu nosivost.

The dentated pairs defined in such a manner, due to the influence of each basic parameter (directly by its value or by factors which are in function of those parameters) have different computed power. The process of correct selection of basic parameters is also very important for their bearing capacity.

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Selekcijom dobivenih rezultata od vi{e mogu}ih osnovnih parametara zup~astog para mogu}e je za pretpostavljeni »CILJ« dobiti najpogodniji »REZULTAT«. Za najve}i broj projektovanih zup~astih parova industrijske namjene kao prioritetan »CILJ« se postavlja njihova sigurnost na nosivost korijena i boka zuba uz zadovoljenje i ostalih karakteristi~nih veli~ina.

Selecting the results from several different basic parameters of dentated pair, it is possible, for a set «OBJECTIVE», to get the most suitable «RESULT». For the majority of designed dentated pairs for industrial use, the priority «OBJECTIVE» is safety in relation to the dentil base and side bearing capacity as well as fulfilling other characteristic values.

4.1. Postupak optimalnog izbora osnovnih parametara

Za postupak optimalnog izbora osnovnih parametara para zup~anika uzima se za pretpostavljeni »CILJ« nosivost korjena i boka zupca para zup~anika odre|enog osnim razmakom »a« i nazivnim prenosnim odnosom »in« za jednako optere}enje, uslove rada, materijal i kvalitet ozubljenja koje je gotovo isklju~ivo u funkciji op{tih parametara (mn, β, z1, z2, x1, x2), {to se zasniva na izrazima za napone [2]: • radni napon korjena zupca

4.1. Procedure of optimal selection of basic parametars

For the purposes of optimal selection of basic parameters, the «OBJECTIVE» set is the bearing capacity of dentil base and the dentated pair side, determined by axial distance «a» and nominal transmission ration «in» for equal load, working conditions, material and quality of dentation that is almost completely in the function of general parameters (mn, β, z1, z2, x1, x2). It is based on the following stress expressions [2]: - Dentil base working stress:

FPSaFaFFVAn

tF YYYYKKKK

mbF

σσ εββα ≤⋅⋅⋅⋅⋅⋅⋅⋅⋅

= ................................(3)

• dozvoljeni napon korjena zupca, •

minlim / FNxRFFP SYYY ⋅⋅⋅= σσ ...........(4)

- Dentil base allowed stess: -

minlim / FNxRFFP SYYY ⋅⋅⋅= σσ ……………………(4)

• radni napon na boku zupca, - Working stress on dentil side:

HPHHVAt

HEH KKKKii

dbF

ZZZZ σσ βαεβ ≤⋅⋅⋅⋅+

⋅⋅

⋅⋅⋅⋅=1

1

.........................(5)

• dozvoljeni napon na boku zupca. - Allowed stress on dentil side:

minlim / HNXWVRLHHP SZZZZZZ ⋅⋅⋅⋅⋅⋅= σσ ..............................(6)

Iz navedenog slijedi zaklju~ak da su za postupak optimalnog izbora osnovnih parametara zup~astog para va`ni samo osnovni geometrijski parametri i faktori zubaca: YFa, YSa, Yβ, Yε, ZH, Zβ, Zε koji su u funkciji istih, a da se optere}enje Ft, {irina zup~anika b, faktori optere}enja i uslova rada (KA, KV, KFα, KFβ, KHα, KHβ) te materijala i kvaliteta ozubljenja (YR, YX, YN, ZL, ZR, ZV, ZW, ZX, ZN, ZE) mogu u postupku optimiranja izostaviti jer su isti. Izostavljanjem ovih veli~ina u izrazima za odre|ivanje napona korijena i boka zuba dobijamo vrijednosti koje mo`emo ozna~iti kao karakteristike tih napona:

dentil factors: YFa, YSa, Yβ, Yε, ZH, Zβ, Zε are important for the procedure of optimal selection of basic parameters of dentated pair, and they are in function of the above. The load Ft, width of dentil b, factors of load and working conditions (KA, KV, KFα, KFβ, KHα, KHβ), as well as material and dentation quality (YR, YX, YN, ZL, ZR, ZV, ZW, ZX, ZN, Z) can be avoided in the process of optimisation, because they have the same values. Omitting these parameters in the expressions for computing dentil base and side stress, we get values which can be referred to as characteristics of those stresses:

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• za korjen zuba: •

nSaFaF m

YYYYk 1⋅⋅⋅⋅= εβσ ...........(7)

• za bok zuba: •

2

1

1

2 1zz

zzZZZk HH ⋅

+⋅⋅⋅= εβσ .............(8)

- for dentil base: -

nSaFaF m

YYYYk 1⋅⋅⋅⋅= εβσ ……………(7)

- for dentil side: -

2

1

1

2 1zz

zzZZZk HH ⋅

+⋅⋅⋅= εβσ …………….…(8)

Ovako dobijene veli~ine se uzimaju za dalji postupak optimiranja izbora osnovnih parametara, a na bazi pore|enja odnosno selekcije dobijenih rezultata karakteristike napona za sve kinematski ostvarljive zup~aste parove osnog razmaka »a« i prenosnog odnosa »in« definisane osnovnim parametrima (mn, β, z1, z2, x1, x2), za prethodno zadate grani~ne veli~ine:

The computed values shall be used in further procedure of optimisation selection of basic parameters, based on comparison i.e. selection of the computed results of the stress characteristics for all the kinetically possible dentil pairs with axial distance «a» and transmission ration «in» defined by basic parameters (mn, β, z1, z2, x1, x2), for predetermined limit values:

Max. odstupanje zadatog prenosnog odnosa ∆imax (%) Maximum deviation of determined transmission ratio Min. odstupanje zadatog prenosnog odnosa ∆imin (%) Minimum deviation of determined transmission ratio Max. ugao nagiba bo~ne linije βmax (°) Maximum angle of side line inclination Min. ugao nagiba bo~ne linije βmin (°) Minimum angle of side line inclination Faktor {irine zuba b/a -- Dentil width factor Max .faktor modula (b/mn)max -- Maximum modul factor Min. faktor modula (b/mn)min -- Minimum modul factor Min. broj zuba zup~anika zmin -- Minimum number of gear dentils Stepen prekrivanja bo~ne linije εβ -- Rate of covering side line Stepen prekrivanja profila εα -- Rate of section covering Specifi~no klizanje bokova zuba ξmax -- Specific slide of dentil sides Max.faktor pomaka profila xmax -- Maximum factor of section translation Min.faktor pomaka profila xmin -- Minimum factor of section translation Selekcija rezultata se vr{i prema vrijednostima karakteristike napona kσF i kσH (zavisno od zadatog prioriteta) pri ~emu moraju biti zadovoljene i prethodno zadate grani~ne veli~ine. Najmanja dobivena vrijednost karakteristike napona odre|uje «IZBOR» osnovnih parametara.

The results are selected according to the values of stress characteristics kσF and kσH (depending of the determined priority), provided that the limit values have been predetermined and fulfilled. The lowest value of the stress characteristics determines the «SELECTION» of the basic parameters.

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Prora~un se izvodi pomo}u programa «ZAROP» [7] koji daje optimalan odnos osnovnih parametara zup~anika za unaprijed odabranu funkciju bilo da se radi o nosivosti, stepenu prekrivanja, klizanju bokova zuba ili ta~nosti zadatog prenosnog odnosa i funkcioni{e na bazi prethodno une{enih, zadatih grani~nih veli~ina (min., max.) navedenih u pregledu ulaznih podataka programa "ZAROP".

Computation is done by software «ZAROP» (7) which gives optimal relation among basic dentil parameters for the predetermined chosen function, whether it is about bearing capacity, rate of covering, slide of dentil sides or accuracy of the determined transmission ratio and it functions based on previous input of the determined limit values (min., max.) listed in the software «ZAROP» review of input.

4.2 Osnovni parametri i nosivost parova zup~anika

Provjera navedenih zaklju~aka se provodi prora~unom nosivosti zup~astih parova za:

a) Zup~aste parove postoje}eg reduktora "Krivaja", tip MRZ-250. Pregled osnovnih parametara prema tehni~koj dokumentaciji dat je u tabeli 5.

b) Zup~aste parove novog reduktora tip MR-250, definisani metodom optimiranja osnovnih parametara pomo}u programa "ZAROP" [7]. Pregled osnovnih parametara je dat u tabeli 6.

4.2. Basic parametars and bearing capacity of gear pairs The above conclusions can be tested by computation of the gear pairs bearing capacity for the: a) dentated pairs of the existing reduction gear

«Krivaja», type MRZ-250. The review of the basic parameters, according to the technical documentation is given in the Table 5.

b) dentated pairs of the new reduction gear, type MR-250, defined by method of optimisation of basic parameters using software «ZAROP» (7). The review of basic parameters is given in the Table 6.

Tabela 5. Osnovni parametri reduktora tip MRZ-250 Table 5. Basic parameters of the reduction gear, type MRZ-250

Rb.-No in* a b mn Z1 z2 β x x1 u di%

PRVI STEPEN – FIRST RATE

1 do 10 4 184,6 74 4,25 18 68 0 0 0 3,77

DRUGI STEPEN – SECOND RATE

1 1,6 184,6 74 4,25 34 52 0 0 0 1,52 2 1,8 184,6 74 4,25 30 56 0 0 0 1,86 3 2,5 184,6 74 4,25 25 61 0 0 0 2,44 4 3,15 184,6 74 4,25 21 65 0 0 0 3,09 5 3,55 184,6 74 4,25 19 67 0 0 0 3,52 6 do 10 4 184,6 74 4,25 18 68 0 0 0 3,77

TRE]I STEPEN – THIRD RATE

1 do 5 1,4 184,6 74 4,25 36 50 0 0 0 1,38 6 1,8 184,6 74 4,25 31 55 0 0 0 1,77 7 2,0 184,6 74 4,25 27 59 0 0 0 2,18 8 2,8 184,6 74 4,25 23 63 0 0 0 2,73 9 3,55 184,6 74 4,25 19 67 0 0 0 3,52 10 4,0 184,6 74 4,25 17 69 0 0 0 4,05

* Uzeti su samo prenosni odnosi parova reduktora MRZ-250 koji odgovaraju pribli`no v ijednostima iz standardnog reda R10.

r

*The table shows only the transmission rations of the MRZ-250 reduction gear pairs, which approximately correspond to the values from standard order R10.

- 113 -


Optimiranje osnovnih parametara zup~astih parova postoje}eg reduktora tip MRZ-250, se izvodi pomo}u programa "ZAROP" (Zahnradoptimirung) [7].

The basic parameters of dentated pairs of the existing MRZ-250 reduction gear are optimised by software «zarop» (Zahnradoptimirung) (7).

Tabela 6. Osnovni parametri novog reduktora tip MR-250 Table 6. Basic parameters of the new reduction gear, type MR-250

Rb.-No. in a b mn z1 z2 β x x1 u di% PRVI STEPEN – FIRST RATE 1 do 10 4 184,6 74 5 15 56 13 0,51 0,27 3,73

DRUGI STEPEN – SECOND RATE

1 1,6 184,6 74 4,5 32 48 12 0,13 0,09 1,50 2 1,8 184,6 74 5 25 46 13 0,51 0,31 1,84 3 2,5 184,6 74 4,5 23 56 13 0,50 0,29 2,43 4 3,15 184,6 74 4 22 67 13 0,50 0,29 3,04 5 3,55 184,6 74 4 20 69 13 0,50 0,28 3,45 6 do 10 4 184,6 74 5 15 56 13 0,51 0,27 3,73

TRE]I STEPEN – THIRD RATE

1 do 5 1,4 184,6 74 4,5 34 46 12 0,13 0,10 1,38 6 1,8 184,6 74 4,5 29 51 12 0,13 0,08 1,75 7 2,0 184,6 74 4,5 25 54 13 0,50 0,31 2,16 8 2,8 184,6 74 5 19 52 13 0,51 0,29 2,73 9 3,55 184,6 74 4 20 69 13 0,50 0,28 3,45 10 4,0 184,6 74 4 18 72 13 -0,03 0,22 4,00

Analizom tabele 5 i tabele 6, mogu}e je uo~iti da su veli~ine osnovnih parametara mn, z, β i x razli~ite za iste vrijednosti prenosnih odnosa, {to je rezultat analiti~kog postupka programa «ZAROP» odnosno selekcije rezultata. Za prora~un nosivosti zup~astih parova kori{ten je program «GEARPAC CX.3.1» [5]. Prora~un se izvodi paralelno za obje grupe parova zup~anika (tabele 5 i 6) istih karakteristika materijala, kvaliteta, broja obrtaja i ostalim potrebnim ulaznim veli~inama. Dokaz primjenjenog postupka je dat tabelarnim i grafi~kim prikazom dobijenih nosivosti (tabela 7 i slika 3) iz kojih je prednost postupka optimizacije o~ita.

Analysing table 5 and table 6, it is possible to notice that the values of basic parameters mn, z, β and x are different for the same values of transmission ratios, which is the result of analytic procedure of software «ZAROP», i.e. the selection of results. For the bearing capacity of dentated pairs computation, the «GEARPAC CX.3.1» software (5) has been used. Computation is done in parallel for both groups of gear pairs (table 5. and table 6.) with the same characteristics of material, quality, number of rotations and other necessary input values. The table below represents the procedure, as well as the chart of the computed bearing capacity values (table 7. and figure 3), which shows advantages of optimisation procedure.

- 114 -


Tabela 7 .Pregled nosivosti parova zup~anika Table 7. List of the gear pairs bearing capacities

i PK PR

1,38 114 133

1,52 104 127

1,77 96 113

1,86 92 107

2,18 81 93

2,44 75 86

2,73 67 78

3,09 55 57

3,52 42 50

3,77 38 47

4,05 33 40

Uporedni pregled nosivosti parova zupčanikaComaprative review of bearing capacity of gear pairs

20

40

60

80

100

120

140

1 1.5 2 2.5 3 3.5 4 4.5

Prenosni odnos-Transmisio ratio i

Doz

volje

na s

naga

-A

llow

ed p

ower

kW

PK PR

Slika 3. Grafi~ki pregled nosivosti parova zup~anika Figure 3. Gear pairs bearing capacity chart

Legenda: PK- nosivost parova zup~anika postoje}eg reduktora ,tip MRZ-250; PR- nosivost optimiranih parova zup~anika reduktora, tip MR-250; Note: PK – gear pairs bearing capacity for the existing reduction gear, type MRZ-250; PR – optimised gear pairs bearing capacity for the reduction gear, type MR-250;

5. ZAKLJU^AK Na osnovu provedene analize mogu se potvrditi sljede}e ~injenice: - Svaki zup~asti par osnog razmaka »a« i prenosnog odnosa »i« je geometrijski odre|en njegovim osnovnim parametrima: mn, z1, z2, β, x1, x2. - Svaki zup~asti par osnog razmaka »a« i prenosnog odnosa »i« mo`e biti realiziran u okviru zadatih grani~nih odstupanja (amax i aimin), razli~itim vrijednostima osnovnih parametara koji su u odgovaraju}em korelacijskom odnosu, pri ~emu je ispunjen uslov:

( ) ( )[ ]ββ

coscos2 2121 xxzzma n +++

⋅= .

- Nazivna optere}enja korijena zuba σF i boka zuba σH zup~astih parova osnog razmaka »a« i prenosnog odnosa »i« optere}enih istim momentom, istih karakteristika materijala i kvaliteta zup~anika su samo u funkciji osnovnih parametara: σF,σH= f (mn, z1, z2, β, x1, x2 ). - Zup~asti parovi istog osnog razmaka »a« i prenosnog odnosa »i« definisani razli~itim osnovnim parametrima, optere}eni istim momentom, istih karakteristika materijala i kvaliteta zup~anika, imaju razli~ite napone korijena i boka zuba.

5. CONCLUSION The above analysis confirms the following facts:

- Each gear pair with axial distance «a» and transmission ratio «i» is geometrically determined by its basic parameters: mn, z1, z2, β, x1, x2.

- Each gear pair with axial distance «a» and transmission ratio «i» can be realised within the determined limit deviation (amax and amin), by different values of the basic parameters which are in certain correlation, where the following condition has been fulfilled:

( ) ( )[ ]ββ

coscos2 2121 xxzzma n +++

⋅=

- Nominal load of dentil base σF and dentil side σH of dentated pairs with axial distance «a» and transmission ration «i», loaded by the same moment, with the same material characteristics and the same quality fo gears are in the function of only the basic parameters:

σF,σH = f (mn, z1, z2, β, x1, x2). - Gear pairs with same axial distance «a» and

transmission ratio «i» defined by different basic parameters, loaded by the same moment, with the same material quality, as well as quality of gears, have different stress of dentil base and side.

- 115 -


- Za iste karakteristike, osni razmak »a« prenosni odnos »i« {irinu zup~anika »b«, materijal, kvalitet ozubljenja, stepene sigurnosti i broj obrtaja pogonskog zup~anika, zup~asti parovi definisani metodom optimiranja osnovnih parametara imaju dozvoljene snage i do 30% ve}e izuzev u jednom slu~aju gdje se vrijednosti poklapaju (tabela 7 i slika 3).

- For the same characteristics, axial distance «a» and transmission ratio «i», gear width «b», material, quality of dentation, sefety degree and number of rotations of engine gear, dentated pairs defined by optimisation of basic parameters method have the allowed power which is up to 30% higher, except in one specific case when the values overlap (table7. and figure 3.).

6. LITERATURA - REFERENCES

[1] Niemann,G.Winter,H.:"Maschinenelemente Band II", Zweite voellig neubearbeitete Auflage, Springer-Verlag, Berlin, 1985.,

[2] Grupa autora: "Inìnjersko-ma{inski

priru~nik II", Zavod za ud`benike i nastavna sredstva, Beograd, 1992.,

[3] Ober{mit,E.:"Ozubljenja i zup~anici",

Liber, Zagreb, 1982.,

[4] Kopri}, S., Tati}. Z.: "Optimizacija cilindri~nih zup~astih parova", Me|unarodni nau~no srtu~ni skup "Tendencije u razvoju ma{inskih konstrukcija i tehnologija-TMT '95", str.240., Zenica, 1995.,

[5] Grupa autora: "Uputstvo za upotrebu

programa GEARPAC CX. 3.1 –prora~un cilindri~nih evolventnih zup~anika", Tehni~ki fakultet Rijeka, Zavod za osnove konstruisanja , Rijeka, 1989.,

[6] Dàferovi},M:"Istraìvanje mogu}nosti

primjene mehanike sli~nosti pri projektovanju reduktora", Magistarski rad, Ma{inski fakultet u Zenici, 2000.,

[7] Kopri},[. i dr.:"Program za optimizaciju

geometrije zup~anika – ZAROP", TTU-Tuzla, 1999.god.

- 116 -

Ma{instvo 3(7), 131 – 142, (2003) A.Werner,....: PRORAÛN TRODIMENZIONALNOG...

PRORAÛN TRODIMENZIONALNOG STACIONARNOG STRUJANJA SA SLOBODNOM POVR[INOM

Andreja Werner, Nastia Degiuli, Zdravko Doliner, Sveu~ili{te u Zagrebu, Fakultet strojarstva i brogogradnje, Ivana Lu~i}a 5 ,10000 Zagreb, Hrvatska

REZIME: P ikazana je numeri~ka panelna metoda za rje{avanje stacionarnog trodimenzionalnog potencijalnog strujanja oko tijela u blizini, ina~e mirne slobodne povr{ine teku}ine. U metodi se koristi razdioba izvora po tijelu i slobodnoj povr{ini. Povr{ina tijela i dio slobodne povr{ine prikazuje se geometrijski pomo}u ~etverokutnih panela na kojima su smje{teni izvori, ~ija se jakost odre|uje iz rubnih uvjeta. Na panelima tijela zadovoljen je egzaktni rubni uvjet. Kinemati~ko-dinami~ki uvjet na slobodnoj povr{ini je lineariziran. Razvijen je ra~unalni program prema izloènoj metodi. Otpor valova uronjenog elipsoida i rotacionog tijela ~ija forma se moè izraziti jednostavnim matemati~kim izrazima je uspore|en sa rezultatima eksperimenta. Dobivene vrijednosti pokazuju dobra slaganja

r

r

r

r r

Klju~ne rije~i: Potecijalno strujanje, Slobodna povr{ina, Rankinovi izvor, Panelna metda, Otpor valova

THREE-DIMENSIONAL STEADY STATE FREE SURFACE FLOW COMPUTATION

Andreja Werner, Nastia Degiuli, Zdravko Doliner, University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Ivana Lu~i}a 5 ,10000 Zagreb, Croatia

SUMMARY: A nume ical panel method for computing the three-dimensional, steady state potential flow around body submerged beneath an otherwise calm free surface is described. The method uses a sources distribution over body wetted surface and on the free surface. The body surface and a part of free surface are geometrically represented by the quadrilateral panels and the source density is determined in such a manner that the boundary conditions are satisfied. On the body panels the exact boundary condition is satisfied. The kinematic-dynamic boundary condition on the free surface is linearized. The compute program has been developed using this method. The wave resistance of submerged spheroid and body of revolution whose form can be expressed by means of simple mathematical relation is compa ed with experiment obtained. Values a e found to be in good agreement.

Keywords: Potential flow, Free surface flow, Rankine source, Panel method, Wave resistance

1. UVOD Ra~unalna dinamika fluida (CFD) korisni je alat u ranoj fazi projektiranja. Primjenom CFD metoda na strujanje oko tijela mogu}e je uo~iti neèljeno strujanje i shodno tome modificirati oblik tijela sa svrhom pobolj{anja performansi. Takva optimalizacija, bazirana na rezultatima CFD, moè biti lak{a od tradicionalnih mjerenja, jer je mogu}e dobiti vi{e informacija o strujanju.

1. INTRODUCTION Computational fluid dynamics (CFD) has recently acquired recognition as a useful tool at early design stages. By applying CFD methods to the flow around the body, undesirable flow features may be recognized and consequently the hull shape modified to improve performance. Such optimization, based on CFD results may be easier than using traditional testing, since much more information on the flow is normally obtained from the numerical solution.

- 131 -


Naravno da je, zbog ograni~ene to~nosti numeri~kih rje{enja, potrebno vr{iti mjerenja, kao nadomjestak za neprihva}ene elemente u numeri~kom modelu i kao kompletna provjera numeri~kih o~ekivanja. Metode potencijalnog strujanja su najpopularniji CFD alat. Razmatra se numeri~ka Rankinova metoda izvora za prora~un stacionarnog potencijalnog strujanja oko tijela uronjenog u blizini slobodne povr{ine. Ova metoda je dio CFD-a temeljena na metodi rubnih elemenata.

Of course, because of limited exactness of the numerical solutions, it is necessary to use testing as a substitute for unacceptable elements in numerical models and as competent check for numerical expectations. Potential flow methods are the most popular CFD tools. A numerical Rankine source method for computing the three-dimensional, steady potential flow around body submerged beneath free surface is considered. This method is a part of CFD based on boundary element method.

2. DEFINICIJA PROBLEMA Rankinova metoda izvora koristi raspodjelu izvora po povr{ini tijela i slobodnoj povr{ini. Ovaj izvor ima jednostavnu funkciju potencijala, ali automatski ne zadovoljava grani~ne uvjete na slobodnoj povr{ini.. Rankinova metoda izvora potje~e od dobro poznate metode Hess and Smith [1] za trodimenzionalno potencijalno strujanje bez slobodne povr{ine. Gadd [2] i Dawson [3] su predlo`ili dva razli~ita na~ina za uzimanje u obzir slobodne povr{ine. Sve do danas Dawsonov pristup je najpopularniji. U ovom radu je predstavljena metoda temeljena na Dawsonovom pristupu. Pretpostavljaju}i stacionarno bezvrtlo`no strujanje neviskoznog i nestla~ivog fluida problem se svodi na problem zadovoljavanja Laplaceove jednad`be za potencijal brzine u domeni fluida s grani~nim uvjetima na tijelu i kinemati~kom i dinamati~kom grani~nom uvjetu na nepoznatoj slobodnoj povr{ini. Na tijelo smje{teno u blizini slobodne povr{ine

nailazi jednoliko strujanje brzinom iUvrr

∞∞ −= ,

gdje je ir jedini~ni vektor u smjeru osi x .

Koordinatni sustav je prikazan na slici 1.

2. DEFINITION OF PROBLEM Rankine source method uses a source distribution over body surface and a free surface. This source has a very simple potential function, but it does not automatically satisfy the free surface boundary conditions. Rankine source method originates from the very well known Hess and Smith method [1] for three-dimensional potential flows without a free surface. Gadd [2] and Dawson [3] proposed two different ways of incorporating the free surface. Up till now the Dawson approach has been the most popular. In this work a method based on Dawson’s approach will be presented. Assuming steady, irrotational flow of an inviscid and incompressible fluid, the problem is reduced to that of satisfying Laplace’s equation for the velocity potential in the fluid domain subject to the boundary condition on the body and kinematic and dynamic boundary condition on the unknown free surface. A body floating beneath the free surface in a

uniform stream iUvrr

∞∞ −= , where iris a unite

vector in the x direction. The coordinate system is shown in Figure 1.

z

x

y

0

Slika 1. Koordinatni sistem Fig. 1 System of coordinates

- 132 -


Os x -je usmjerena prema naprijed suprotno od smjera paralelnog strujanja, -os na lijevo, a os

-prema gore. Uzdu`ni poloàj ishodi{ta je smje{ten na glavnom rebru tijela na neporeme}enoj slobodnoj povr{ini. Povr{ina tijela moè se opisati jednad`bom oblika

yz

0),,( =zyxF (1)

Slobodna povr{ina je dana s

),( yxz ς= (2)

Pretpostavlja se da su neophodni uvjeti ispunjeni tako da se potencijal brzine ),,( zyxϕ moè

implicitno definirati kao

ϕϕ ∇== gradvr (3)

Tada se problem rubnih vrijednosti sastoji od slijede}ih uvjeta:

02 =++=∆=∇ zzyyxx ϕϕϕϕϕ , u fluidu

(4)

0),cos(),cos(),cos( =∂∂

+∂∂

+∂∂

= znz

yny

xnxn

ϕϕϕϕ

, na tijelu (5) Kinemati~ki uvjet na slobodnoj povr{ini ima slijede}i oblik

0=−−= yyxxzn ςϕςϕϕϕ (6)

Dinami~ki uvjet se svodi na jednad`bu 0=p na

slobodnoj povr{ini, gdje je p pretlak. Koriste}i

Bernoullijevu jednad`bu ovaj se uvjet moè izraziti kao

( ) 021 2222 =−+++ ∞Ug zyx ϕϕϕς (7)

U beskona~nosti brzina je neporeme}ena r

iUr

⋅=∇ ∞∞→

ϕlim (8)

Kona~no uvjet radijacije mora biti zadovoljen

∞→>

+−= ∞ r

xr

oxU 1,0,1ϕ (9)

gdje je ς visina vala, g ubrzanje sile teè

. Indeks ozna~ava derivaciju u

odgovaraju}em smjeru.

2222 zxr += y+

The x -axis points forward, opposite to the direction of the uniform flow, the -axis to the

port side, and -axis upwards. The longitudinal position of the origin is located at the middle section of body, on the undisturbed free surface. The surface of the hull can be described by an equation of the form

yz

0),,( =zyxF (1)

The free surface is given by

),( yxz ς= (2)

It is assumed that the necessary conditions exist so that a velocity potential ),,( zyxϕ may be

defined implicitly as

ϕϕ ∇== gradvr (3)

Then the boundary value problem consists of the following conditions:

02 =++=∆=∇ zzyyxx ϕϕϕϕϕ , in the fluid

(4)

0),cos(),cos(),cos( =∂∂

+∂∂

+∂∂

= znz

yny

xnxn

ϕϕϕϕ

, on the body (5) On the free surface the kinematic condition has the following form

0=−−= yyxxzn ςϕςϕϕϕ (6)

The dynamic condition degenerates to the equation

0=p on the free surface, where p is the excess

pressure above atmospheric. Using Bernoulli’s equation this condition may be expressed as

( ) 021 2222 =−+++ ∞Ug zyx ϕϕϕς (7)

At infinity the velocity is undisturbed r

iUr

⋅=∇ ∞∞→

ϕlim (8)

Finally, the radiation condition must be satisfied

∞→>

+−= ∞ r

xr

oxU 1,0,1ϕ (9)

where ς is wave height, g the acceleration of gravity and . The index denotes

differentiation in the corresponding direction.

2z222 yxr ++=

- 133 -


Pretpostavljaju}i da se potencijal brzine i visina vala mogu prikazani kao suma osnovnog (pribli`nog) rje{enja φϕ = i

( )( 220 2

1 φςς ∇−==∞

Ug

), i poreme}ajnih

vrijednosti δϕ i δς , slijedi da

*ϕϕδϕφϕ +=+= ∞ (10)

δςςς += 0 (11)

gdje je ∞ϕ potencijal brzine jednolikog strujanja i

valni poreme}ajni potencijal. *ϕ

Ako se problem linearizira, kinemati~ko-dinami~ki rubni uvjet (6) i (7), nakon jednostavnih matemati~kih operacija mogu biti prikazani u obliku

Assuming that the velocity potential and the wave height may be represented as the sum of the basic (approximate) solution φϕ = and

( )( )220 2

1 φςς ∇−==∞

Ug

, and disturbance

values δϕ and δς , it follows that

*ϕϕδϕφϕ +=+= ∞ (10)

δςςς += 0 (11)

where ∞ϕ is the velocity potential of uniform

stream and the wave disturbance potential. *ϕ

If the problem is linearised, the kinematic-dynamic boundary condition (6) and (7), after simple mathematical operation, may be presented in the form

( )[ ] ( )[ ] ( ) ( )( )( ) ( ) ( )( )yxxyxyyxxyyyyxxxxxx

zyxxyyx

yyyxxxyxxyxyyyyyyxxyxxxx

UU

g

φφφφφφφφφφφφ

ϕϕϕφφ

φϕφϕφφφφφϕφφφφφϕ

++++++=

=+++

++++++++

∞∞ 222

22***

2*2***

(12)

Za poznato osnovno rje{enje ),( 0ςφ , prema [2] i

[3] predloèna je takozvana metoda slika Pretpostavljaju}i da je slobodna povr{ina kruta stijenka, strujanje se prora~unava promatraju}i tijelo i njegovu zrcalnu sliku iznad neporeme}ene slobodne povr{ine. Ovaj problem se moè rije{iti koriste}i originalnu metodu Hessa i Smitha [1]. Uvjet radijacije dovoljno daleko ispred tijela }e biti zadovoljen numeri~ki.

Op}i izraz za potencijal brzine moè biti

napisan u obliku

*ϕ

∫= S dSPPPGP )'()',()(* σϕ (13)

gdje je ),,( zyxP -to~ka polja,

'' ''( , , )P P PP x y z -to~ka na povr{ini,

2'

2'

2' )()()()',( PPP zzyyxxPPr −+−+−=

-udaljenost izme|u P i 'P , )',( PPG -Greenova funkcija,

)'(Pσ -gusto}a izvora.

Rje{enje gore spomenutog problema se temelji na raspodjeli Greenovih funkcija po grani~noj povr{ini,

. Indeks FSB SSS += B ozna~ava tijelo a

slobodnu povr{inu. Najjednostavniji oblik Greenove funkcije je funkcija

FS

,)',(

1)',(PPr

PPG −= (14)

For the known base flow ),( 0ςφ , according to

[2] and [3], a so-called double body solution was suggested. Assuming the free surface to be rigid lid, the flow is computed by considering the body and its mirror image in the undisturbed free surface. This problem may be solved using original Hess and Smith [1] method. The radiation condition starting from the case that the fluid is not disturbed far upstream will be satisfied numerically. The general expression for the velocity potential

my be written in the form *ϕ

∫= S dSPPPGP )'()',()(* σϕ (13)

where ),,( zyxP -field point,

'' ''( , , )P P PP x y z -surface point,

2'

2'

2' )()()()',( PPP zzyyxxPPr −+−+−=

-distance between P and 'P , )',( PPG -Green function,

)'(Pσ -source density.

The solution of the above problem is based on distribution of Green’s functions over boundary surface,

FSB SSS += . The index B stands for body and

free surface. The simplest form of Green function is the function

FS

,)',(

1)',(PPr

PPG −= (14)

- 134 -


Ova funkcija se naziva potencijal Rankinovih izvora [4]. Iz (13) i (14) slijedi

dSPPrPP

FSSBS∫∫−= + )',()'()(* σϕ .

Ja~ina izvora odre|uje se iz rubnog uvjeta na tijelu i slobodnoj povr{ini.

This function is called Rankine source potential [4]. From (13) and (14) follows that

dSPPrPP

FSSBS∫∫−= + )',()'()(* σϕ .

The strength of sources has to be determined from the boundary condition on the body hull and on the free surface.

3. NUMERI^KO RJE[ENJE SA SLOBODNOM POVR[INOM

Tijelo i dio slobodne povr{ine aproksimiraju se kvadrilateralnim elementima, panelima. Kori{tena je metoda prvog reda sa ravnim elementima i konstantnom ja~inom izvora. Takovom diskretizacijom integralne jednad`be se transformiraju u sustav linearnih algebarskih jednad`bi. Pretpostavlja se da su rubni uvjeti na svakom panelu zadovoljeni u jednoj to~ki , obi~no u sredi{tu panela ili kolokacijskoj to~ki. Sumiranjem doprinosa svih panela a slobodne struje, jednad`ba (5) moè se napisati za panele na trupu

01

=⋅+∑ ∞=

vnA iij

N

jj

rrσ , (15) BNi ,1=

gdje je

inr - jedini~ni vektor vanjske normale na i -tom panelu,

jσ -nepoznata ja~ina izvora na j -tom panelu,

dSr

An

jSij

ij ∫∫

=

1, (16)

ijr -udaljenosti izme|u i -te i j -te kolokacijske to~ke,

ijA -utjecajni koeficijent koji je ~isto

geometrijska veli~ina Rubni uvjet na slobodnoj povr{ini je mnogo sloèniji. Potrebno je izra~unati derivacije potencija i valne elevacije u x i smjeru. Derivacije se

izra~unavaju numeri~ki Dawsonovom metodom kona~nih razlika u ~etiri kolokacijske to~ke prema natrag u uzdu`nom i popre~nom smjeru.

y

Dawsonova ideja za izra~unavanje derivacija numeri~ki ima pozitivni utjecaj na uvjet radijacije [5], [6] ako mreà nije pregusta. Me|utim, ako je mreà gusta i brzina velika ( ) vidljive su zna~ajne oscilacije brzina na panelima ispred tijela. To zna~i da je radijacijski uvjet naru{en i da se pojavljuju valovi ispred tijela. Prema [5] primijenjen je mali pomak, suprotno od smjera strujanja, kolokacijskih to~aka u svrhu zadovoljavanja radijacijskog uvjeta.

5.0≥Fn

Brzine u x , i dobivaju se sumiranjem

doprinosa svih panela i paralelnog strujanja

y z

3. NUMERICAL SOLUTION WITH FREE SURFACE

The body and the part of the free surface are approximated by the quadrilateral elements, panels. The first order method with plane elements and constant source strength is used. With such discretization the integral equations are transformed into a set of linear algebraic equations. On each panel the boundary conditions are assumed to hold at one point, normally the panel centroid or collocation point. By summing the contribution from all panels and the free stream, the equation (5) may be written for panels on the body hull

01

=⋅+∑ ∞=

vnA iij

N

jj

rrσ , (15) BNi ,1=

where

inr - the unit outward normal vector on panel , i

jσ -unknown source density on panel j ,

dSr

An

jSij

ij ∫∫

=

1, (16)

ijr -distance between i th and j th collocation point,

ijA -influence coefficient which is purely

geometrical quantity. The boundary condition on the free surface is more complex. Derivatives of the potential, as well as the wave elevation are required both in x and

direction. The derivatives are numerically evaluated by four-point finite backward difference operator applied to the longitudinal and transverse direction.

y

Dawson’s idea to compute the derivatives numerically has a positive effect on the radiation condition [5], [6] if the mesh is not too fine. However, if the mesh is fine and the speed is great ( ) markedly oscillation of the velocity is visible on the panels in front of the body. This means that radiation condition is violated and upstream wave is present. According to [5] a small upstream shift of the collocation points is introduced to enforce the radiation condition.

5.0≥Fn

Velocities in the x , and direction may be

obtained by summing the contribution from all panels and the free stream

y z

- 135 -


ij

FSNBN

jjxi XUv ∑+=

+

=∞

1σ

ij

FSNBN

jjyi Yv ∑=

+

=1σ

jij

FSNBN

jjzi Zv πσσ 2

1−=∑=

+

= (17)

gdje su , ,ij ij ijX Y Z utjecajni koeficijenti

dSr

Xx

jSij

ij ∫

=

1

dSr

Yy

jSij

ij ∫

=

1

dSr

Zz

jSij

ij ∫

=

1 (18)

Ubacivanjem ovih izraza u kinemati~ko-dinami~ki rubni uvjet (14), dobiva se sustav linearnih linearnih jednad`bi za slobodnu povr{inu. Kombinacijom ovih jednad`bi sa jednad`bama trupa (15), sustav je zatvoren. Rje{enje ovih jednad`bi definira jakost izvora. S poznatom ja~inom izvora, iz utjecajnih koeficijenata (18) prora~unavaju se brzine.

Bezdimenzijski koeficijent tlaka prora~unava se

iz Bernoullijeve jednad`be

pC

2

1

∇−=

∞UCp

ϕ (19)

Visina vala moè se dobiti iz dinami~kog rubnog uvjeta (7)

( )( 22

21),( ϕς ∇−= ∞Ug

yx ). (20)

Sa poznatim C koeficijent otpora valova postaje p

jxj

BN

jpj

BB

ww SnC

SSUR

C ∑===∞ 1

2

25.0 ρ

, (21)

gdje je oplakana povr{ina tijela

∑==

BN

jjB SS

1

Kao alternativa integraciji tlaka sluì Lagallyev teorem [7] koji specificira sile kojima singulariteti u potencijalnom strujanju djeluju jedan na drugoga Prema Lagallyevom teoremu, koeficijent otpora valova moè se prikazati u slijede}em obliku

ij

FSNBN

jjxi XUv ∑+=

+

=∞

1σ

ij

FSNBN

jjyi Yv ∑=

+

=1σ

jij

FSNBN

jjzi Zv πσσ 2

1−=∑=

+

= (17)

where influence coefficients , ,ij ij ijX Y Z are

dSr

Xx

jSij

ij ∫

=

1

dSr

Yy

jSij

ij ∫

=

1

dSr

Zz

jSij

ij ∫

=

1 (18)

Inserting these expressions into kinematic-dynamic boundary condition (14), a system of linear equation for the free surface is obtained. Combining these equations with the hull equation (15), the system is closed. The solution of these equations defines the source strength. With known source strength the velocities may be computed from the influence

coefficients (18). The non-dimensional pressure C

may be computed from the Bernoulli equation

p

2

1

∇−=

∞UCp

ϕ (19)

The wave height may be obtained from the dynamic boundary condition (7)

( )( )22

21),( ϕς ∇−= ∞Ug

yx . (20)

With known the wave resistance coefficient

becomes

pC

jxj

BN

jpj

BB

ww SnC

SSUR

C ∑===∞ 1

2

25.0 ρ

, (21)

where body wetted surface is

∑==

BN

jjB SS

1

An alternative to the integration of the pressure is offered by the Lagally’s theorem [7] that specifies the forces that singularities exert upon each other in potential flow. According to the Lagally’s theorem, the wave resistance coefficient may be expressed in the following form

- 136 -


jj

BN

jxSP

BB

ww Sv

SUSUR

C σπρ

∑===∞∞ 1

22

165.0

, (22)

gdje je v xSP x komponenta brzine koju u

kolokacijskoj to~ki na tijelu induciraju svi izvori slobodne povr{ine.

jj

BN

jxSP

BB

ww Sv

SUSUR

C σπρ

∑===∞∞ 1

22

165.0

, (22)

where is the xSPv x component of velocity

induced in the collocation point on the body due to all free surface sources.

4. ANALIZA REZULTA PRORA^UNA Premda je metoda prikladna za uronjena tijela proizvoljnog oblika, u rad je koncentriran na rotacioni elipsoid koji se giba konstantnom brzinom u smjeru svoje horizontalne osi. Prihva}en je rotacioni elipsoid sa omjerom duljine prema promjeru 5:1 . Ovaj slu~aj su ve} ranije analizirali neki autori [8], [9], pa je stoga korisna ishodi{na to~ka za usporedbu rezultata. Fiksiraju}i omjer duljine prema promjeru, problem se mo`e definirati sa tri bezdimenzijske veli~ine: Froudeov broj definiran na temelju ekscentriciteta,

,

LD

( )22 22 )2/(/ DLe +=geUFn ∞=

h

, veli~ina

poreme}aja, kao omjer uronjaja i promjera,

i bezdimenzijski koeficijent otpora valova

definiran prema [9] kao

Dh /

3wRwgUπρ ∞

=C .

Na slici 2 je prikazan otpor valova dobiven eksperimentalno [9] i predstavljenom numeri~kom panelnom metodom, za omjer uronjaja i promjera 0.792. Slika 2 prikazuje da numeri~ka panelna metoda s lineariziranim kinemati~ko-dinami~kim rubnim uvjetom osigurava razumnu aproksimaciju otpora u razmatranom rasponu Froudeova broja. Slika 3 prikazuje vektore brzine u kolokacijskim to~kama na tijelu i na slobodnoj povr{ini. Rezultati se odnose na 4.0=Fn i 26.1/ =hD

5.0

. Bezdimenzijski koeficijent tlaka je prikazan na slici 4. Trodimenzijski prikaz vala generiranog rotacionim elipsoidom u blizini slobodne povr{ine dan je na slici 5. Rezultati se odnose na =Fn

EL

i

. Tako|er su izvr{eni numeri~ki prora~uni za vitko tijelo s o{trim krajevima. Analizirano tijelo se sastoji od prednjeg i stra`njeg

dijela maksimalnog promjera . je duljina

prednjeg tijela, a je ukupna duljina tijela, kao {to je prikazano na slici 6.

26.1/ =hD

DL

4. ANALYSIS OF COMPUTATIONAL RESULTS

Although the method is suitable for arbitrarily shaped submerged bodies, this paper is concentrate on a prolate spheroid moving in the direction of its horizontal axis at steady speed. The spheroid whose length to diameter ratio is 5:1 is considered. This case has been computed previously by several authors [8], [9], and so provides a useful benchmark for comparison of numerical results. Having fixed the length to diameter ratio, the problem can be defined by three non-dimensional quantities: the Froude number based upon eccentricity,

L D

( )22 )2/(2/ DLe += 2,

ge∞UFn =

Dh /

, the

magnitude of disturbance, as the ratio submergence to diameter, and the non-dimensional wave resistance coefficient define,

according to [9], as

h

3wRwgU ∞

C . πρ

=

Figure 2 shows the wave resistance obtained by experiment [9] and by numerical panel method here presented, for submergence to diameter ratio 0.792. The Figure 2 shows that the numerical panel method with linearized kinematic-dynamic boundary condition provides quite a reasonable approximation of the drag over the range of Froude number considered. Figure 3 represents the velocity vectors in collocation points on the body and on the free surface. The results refer to and 4.0=Fn

26.1/ =hD

26.1/

. The non-dimensional pressure coefficient is given in Figure 4. The 3D representations of wave generated by moving the spheroid beneath the free surface are given in Figure 5. The result refers to and 5.0=Fn

=hD

D EL

. The numerical evaluations were carried out for a slender body sharp at both ends too. The analyzed body consists of a fore and an aft part, each having the same maximum diameter

. is the length of the fore body and is

the total length of the body, as shown in Figure 6.

L

- 137 -


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.30 0.35 0.40 0.45 0.50 0.55Fn

103 C

w

exact solution-linear theory , f rom [9] egzaktno rješenje-linearna teorija,prema [9]numerical panel method numerička panelna metodaexperiment, f rom [9] eksperiment, prema [9]

Slika 2. Otpor valova uronjenog elipsoida prema tri razli~ite aproksimacije Fig. 2 Wave resistance of a submerged prolate spheroid according to three different approximations

Slika 3 Vizualizacija strujanja, ellipsoid sa D /h=1.26 pri Fn =0.4

Vektori brzina u kolokacijskim to~kama na tijelu I na slobodnoj povr{ini Fig. 3 Flow visualization, spheroid with D/h=1.26 at Fn =0.4

Velocity vectors in collocation points on the body and on the free surface

Y

X

ZCp0.9920.9090.8250.7420.6580.5750.4910.4080.3250.2410.1580.074

-0.009-0.093-0.176-0.260-0.343-0.426-0.510-0.593

Slika 4. Bezdimenzionalni koeficijent tlaka , ellipsoid sa D/h=1.26 pri Fn =0.4 pC

Fig. 4 Non-dimensional pressure coefficient C , spheroid with D/h=1.26 at Fn =0.4 p

- 138 -


Y

X

Z

Slika 5. Valovi generirani elipsoidom sa D/h=1.26 prit Fn=0.5 Fig. 5 Wave generated by a spheroid with D/h=1.26 at Fn=0.5

D

LE

L

Slika 6 vitko tijelo sa o{trim rubovima “tijelo 34” Fig. 6 Slender body sharp at ends-“body 34”’

Froudeov broj temeljen na je LgLUFn ∞= , i

bezdimenzijski koeficijent otpora valova

SUR

C ww 2

2

∞

=ρ

7.0=L1759.0=S

, gdje je oplakana povr{ina

tijela. Za usporedbu je odabrano tijelo br. 34 s

(m), (m), (m),

(m

S

3.0=EL 12.02 == RD1/2), relativnog uronjaja 0.=Dh ,

[10]. Na slici 7 je dan koeficijent otpora valova izra~unat predlo`enom metodom i dobiven mjerenjima. Predvi|anja su najto~nija pri ni`im brzinama (Fn) dok pri vi{im brzinama precjenjuju otpor. To je nedostatak svih lineariziranih metoda. Pa ipak se smatra da su predvi|anja dovoljno to~na za preliminarne usporedbe. Slika 8 prikazuje izra~unati koeficijent tlaka u kolokacijskim to~kama tijela. Reljef slobodne povr{ine je prikazan na slici 9. Slika 10 prikazuje reljef slobodne povr{ine tijela 34 pri Fn=0.935, sa potpuno nefizikalnom pojavom. Na slici 11 prikazani su rezultati prora~una za blagi uzvodni pomak kolokacijskih to~aka, to jest za 10% duljine panela uz zadovoljenje uvjeta radijacije.

The Froude number is based upon is LgL

UFn ∞= ,

and non-dimensional wave resistance coefficient

SU

RC ww 2

2

∞

=ρ

, where is the wetted surface area of

the body. For purposes of comparison body nr 34 was

chosen, with

S

7.0=L (m), 3.0=EL (m),

12.02 == RD (m), (m1759.0=S0.1

2), with relative

submergence, / =Dh , [10]. The wave resistance coefficient calculated by proposed method and those obtained by measurement is given in Figure 7. The prediction is most accurate at lower speeds (Fn), but overestimates the resistance at the higher speed. This is a shortcoming of all linearized methods. Still the prediction is thought to be accurate enough to be used for comparing variants. Figure 8 shows the calculated pressure coefficient in the collocation points on the body. The wave patterns are included in Figure 9. Figure 10 shows the wave pattern of the body 34 at Fn=0.935, with a totally unphysical appearance. In the calculation represented in the Figure 11 a slight upstream shift of the collocation points, e.g. by 10% of the panel length was imposed, end the radiation condition is satisfied.

- 139 -


0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Fn

103 C

w

numerical panel method numerička panelna metoda

experiment, from [10] eksperiment, prema [10]

Slika 7 Usporedba koeficijenta otpora valova, “tijelo 34”, D/h=1.0

Fig. 7 Wave resistance comparison “body 34”, D/h=1.0

Y

X

Z

0.4400.4030.3660.3280.2910.2540.2170.1790.1420.1050.0680.031

-0.007-0.044-0.081-0.118-0.155-0.193-0.230-0.267

Slika 8. Bezdimenzionalni koeficijent tlaka , “tijelo 34”, Fn =0.476 pCFig. 8 Non-dimensional pressure coefficient , “body 34”, Fn=0.476 pC

Y

X

Z

Slika 9. Valovi generirani gibanjem”‘tijela 34” u blizine slobodne povr{ine , D/h=1.0,Fn=0.476

Fig. 9 Wave generated by a “body 34” moving beneath the free surface , D/h=1.00 at Fn=0.476

- 140 -


YX

Z

Slika 10. Slika valova , “tijelo 34”, Fn=0.935, D/h=1.0, naru{en radijacijski uvjet Fig. 10 Wave pattern of "body 34”, Fn=0.935, D/h=1.0, radiation condition violated

YX

Z

Slika 11. Lokalni pomak (10%) kolokacijskih to~aka uzvodno od ‘pramca’, ‘tijelo 34’, Fn=0.935, D/h=1.0 Fig. 11 Local upstream shift (10%) of collocation points upstream of the ‘bow’, body 34’, Fn=0.935, D/h=1.0,

5. ZAKLJUÂK Ako smo u mogu}nosti izra~unati sile koje djeluju na tijelo tada smo u mogu}nosti modificirati oblik tijela i pobolj{ati efikasnost. Prikazana metoda daje informacije o strujanjima oko proizvoljnih tijela za koja nemamo prikladni analiti~ki alat. Numeri~ka panelna metoda je uspore|ena s eksperimentom. Iako postoji pogre{ka uslijed lineariziranog uvjeta na slobodnoj povr{ini moè se uo~iti da kvaliteta rezultata dobivenih razvijenim ra~unalnim programom zadovoljava. Rad je motiviran èljom da se izra~unaju strujanja oko vi{etrupnih objekata koji plove slobodnom povr{inom. Pokazano je da bi metoda mogla biti prikladna za takove objekte.

5. CONCLUSION If we are able to calculate the forces acting on a body then we are able to modify the body shape and to improve efficiency. The presented method is able to produce some information about flows around arbitrary bodies for which we do not have any appropriate analytic tool. A comparison between numerical panel method and experiments has been made. Although an error exists due to the linearized free surface condition, it can be seen that the quality of results obtained by developed computer program is sufficient. This work was motivated by the desire to compute flows about surface-piercing multi-hull objects. It has been shown that this method could be suitable for surface piercing objects.

6. LITERATURA - REFERENCES [1] Hess, J.L. & Smith, A.M.O. (1962) “Calculation

of non-lifting potential flow about arbitrary three-dimensional bodies”, Douglas Aircraft Company Report, No. ES 40622, Long Beach, Ca.

[2] Gadd, G.E. (1976) “A method of computing

the flow and surface wave pattern around full

forms”, The Royal Institution of Naval Architects, Vol. 118, pp.207-219

[3] Dawson, C.W. (1977) “A practical computer

method for solving ship-wave problems”, Proceedings of the 2nd International Conference on Numerical Ship Hydrodynamics, Berkeley, pp. 30-38

- 141 -


[4] Pinsky, M.A., “Partial Differential Equation and Boundary-Value Problems with Applications”, McGraw Hill Inc., New York, II’nd edition, 1994

[5] Raven, H.C., “Variations on a Theme by Dawson, 17’th Symposium on Naval Hydrodynamics”, pp. 9-28, The Hague, Netherland, August 29.-September 2., 1988

[6] Battistini, A. “A panel method for free surface stationary flows”-Tesi di Dottorato, Dipartimento di Ingegneria Navale, del Mare e per I’Ambiente, Universita degli studi di Trieste, Trieste, Anno accademico 1998/99

[7] Kellog, O.D. “Foundation of Potential Theory”, Dover Publications, New York, reprinted I’st edition, 1995

[8] Bertram, V., Schultz, W.W., Cao, Y. and Beck, R.F., “Nonlinear computations for wave drag, lift and moment of submerged spheroids”, Ship Technology Research 38, 3+5, 1991

[9] Farell, C. and Guven, O., “On the

Experimental Determination of the Resistance Components of a Submerged Spheroid”, Journal of Ship Research, Vol. 17, No.2, June 1973, pp.72-79

[10] Byquist, T. “Wave making resistance of series

of body of revolution”, The Royal Institute of Technology, S-10044 Stockholm 70, Sweden, 1973

7. OZNAKE – NOMENCLATURES a [m] glavna os elipse, 2/La =

main axis of ellipse, 2/La =

pC bezdimenzionalni koeficijent tlaka

non-dimensional pressure coefficient

wC koeficijent otpora valova

221/ ∞= SURw ρCw , ili C

3/ ∞= gURww πρwave resistance coefficient

D [m] promjer diameter (m)

e [m] eksentricitet, ( ) 22 22 )/D(/L +=e

eccentricity

Fn Froudeov broj , gL/∞U , or ge/∞U

Froude number

g [m/s2] ubrzanje sile te`e

acceleration of gravity constant

h [m] uronjaj depth of submergence

L [m] duljina tijela body length

EL [m] ulazna duljina entrance length (m)

inr - jedini~ni vector vanjske normale na panelu i

unit outward normal vector on panel i

BN broj panela na tijelu

number of body panels

FSN broj panela na slobodnoj povr{ini

number of free surface panels

wR [N] sila otpor valova

wave resistance in force unit

S [m2] oplakana povr{ina wetted surface area (m2)

∞Ur

[m/s]- vektor paralelnog strujanja, brzina tijela vector of free stream velocity; velocity of body

zyx ,, - koordinatni system sa ishodi{tem na

neporeme}enoj slobodnoj povr{ini, na sredini tijela coordinate system with the origin on the undisturbed free surface at the center of the body

ijijij ZYX ,, utjecajni koeficijenti

influence coefficients

σ [ m3/s/m2] jakost izvora strength of source

ϕ [m2/s] potencijal brzine

velocity potential

∞ϕ [m2/s] - potencijal brzine paralelnog strujanja velocity potential of uniform stream

*ϕ [m2/s] - potencijal valnog poreme}aja wave disturbance potential (m2/s)

ς [m] - elevacija slobodne povr{ine

free surface elevation

- 142 -

Ma{instvo 3(7), 143 – 150, (2003) V.Alexsa,...: EKSPERIMENTALNA INSTALACIJA U SVRHU...

EKSPERIMENTALNA INSTALACIJA U SVRHU ISTRA@IVANJA PROCESA SIMETRI^NOG I ASIMETRI^NOG PODU@NOG VALJANJA

Lect. Eng. Vasile ALEXA, Dr.Es Sc., Univerzitet „Politehnika” Timi{vara, Ma{inski fakultet Lect. Eng. Imre KISS, Drd.ES Sc., Univerzitet „Politehnika” Timi{vara, Metalur{ki fakultet

SA@ETAK U tehni~koj literaturi se moè na}i mnogo informacija o teorijskim i experimentalnim istraìvanjima simetri~nog procesa valjanja, u kojem se pokre}u oba valjka koji imaju jednake pre~nike i iste brzine. Valjani metal je homogen, kre}e se jednoliko i ima potpuno identi~ne uslove na dodirnoj povr{ini s valjcima. U tom slu~aju, naprezanja i deformacije na valjnoj {ipki su simetri~no raspore|eni u odnosu na valja~ku prugu. Ukoliko valjci imaju razli~ite pre~nike, javljaju se neke osobitosti u distribuciji kontaktnog naprezanja i deformac je po presjeku va jane {ipke, koja, kao rezultat toga, gubi svoju simetri~nost.

i l

rt r

r

Ovaj rad predstavlja jednu novu ideju, sloène instalacije koja se koristi za istraìvanje parametara sile kod simetri~nog i asimetri~nog podu`nog valjanja. Novina kod ove ideje je mogu}nost izvo|enja istraìvanja simetri~nog i asimetri~nog procesa, po{tuju}i uslove tehnolo{ke sli~nosti.

Klju~ne rije~i: simetri~no i asimetri~no podu`no valjanje, parametri sile, sloèna instalacija, dvovaljkasti reverzibilni valja~ki stan, ta~kasti detektor

EXPERIMENTAL INSTALLATION FOR THE RESEARCH ON THE SYMMETRIC AND ASYMMETRIC

LONGITUDINAL ROLLING PROCESS

Lect. Eng. Vasile ALEXA, Dr. Es Sc., University “Politehnica” Timisoara, Faculty of Engineering Hunedoara, Mechanical Department Lect. Eng. Imre KISS, Drd. Es Sc., University “Politehnica” Timisoara, Faculty of Engineering Hunedoara, Metallurgical Department

SUMMARY Technical lite ature contains a large amount of theoretical and experimental research regarding symmetric rolling process when both of the rolls are operated and have equal diame e s and speed rates. The rolled metal is homogenous, moves uniformly and has completely identical conditions on the surface of contact with the rolls. In this case, the stress and the deformations on the rolled bar section are symmetrically distributed in relation to the mill train. If the rolling cylinders have different diameters, there a e particularities in distributing the contact stress and the deformations on the rolled bar section, which, consequently, loses its symmetry. This material introduces an original idea of a complex installation used for research into force parameters of the symmetric and asymmetric longitudinal rolling. The novelty of this idea stands in the possibility of performing the research on the symmetric and asymmetric process, respecting the conditions regarding the technological similarity.

Keywords: symmetric and asymmetric longitudinal rolling, force parameters, complex installation, double reversing mill built, pointlike detectors

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1. UVOD Poznati nedostatak teorije o plasti~noj deformaciji metala i legura je, u ve}ini slu~ajeva, nedostatak procjena u odnosu na prihva}ene abstrakte, te nedostatak pojednostavljenja i hipoteza. Ve}inu navedenog autori ni ne spominju, a kamoli o tome raspravljaju. Stoga se u tehni~koj literaturi proces podu`nog valjanja analizira kao simetri~an u odnosu na srednju horizontalnu ravan metalne {ipke i valjaka. Prakti`no ova hipoteza ne odgovara stvarnim uslovima valjanja, ~ak ni u slu~aju tipi~ne sheme obrade profila koji ima pravougaone presjeke izme|u ravno obra|enih valjaka. Jo{ su ve}a odstupanja u slu~aju kompliciranijih shema, kada se valjanje odvija u kalibrima, kao i kod niza posebnih slu~ajeva, naprimjer: jedan od dva valjaka je pogonski, pre~nici valjaka su razli~iti, valjanje stratificiranih {ipki itd. U tim posebnim slu~ajevima podu`nog valjanja, u kojima postoji zna~ajna namjerna asimetrija, bez poznavanja osobitosti ovih procesa ne moèmo ni razviti njihovu teoriju. Uspje{an razvoj prakse i teorije valjanja iziskuje detaljnu analizu raznih pojava kako bi se mogla de{ifrirati su{tina ovih procesa. I pored mnogih istraìvanja, jo{ uvijek postoji niz nerije{enih problema u vezi s metalnom deformacijom, kinematikom i dinamikom valjanja. Kao rezultat toga, u nekim slu~ajevima, va`nim prakti~nim rje{enjima nedostaje ~vrsta nau~na podloga. Danas, uprkos brojnim istraìva~kim projektima, jo{ uvijek postoji mnogo pitanja na koja treba odgovoriti, posebno onih koja se odnose na osnovne probleme koji imaju prakti~nu vrijednost. [tavi{e, izrada preciznih metoda izra~unavanja mora voditi izradi pojednostavljenih nomograma, koji }e biti korisni u industrijskoj praksi. U tom slu~aju, postoji niz teroijskih hipoteza koje iziskuju eksperimentalnu potvrdu. To u potpunosti vrijedi za simetri~ni proces valjanja, budu}i da je odre|ivanje deformacija i naprezanja koji se javljaju na kontaktnoj povr{ini izme|u valjaka i metala i dalje nejasno. U tehni~koj literaturi se moè na}i mnogo informacija o teorijskim i experimentalnim istraìvanjima simetri~nog procesa valjanja, u kojem su oba valjka pogonska i imaju jednake pre~nike i brzine. Valjani metal je homogen, kre}e se jednoliko i ima potpuno identi~ne uslove na dodirnoj povr{ini s valjcima. U tom slu~aju, naprezanje i deformacije po presjeku {ipke su simetri~no raspore|eni u odnosu na valja~ku prugu. Ukoliko valjci imaju razli~ite pre~nike, javljaju se neke osobitosti u distribuciji kontaktnog naprezanja i deformacija po presjeku valjane {ipke, koji, kao rezultat toga, gube svoju simetri~nost.

1. INTRODUCTION

A well-known disadvantage of the metal and alloy plastic deformation theory is, in most cases, lack of estimations regarding the adopted abstractions, as well as of simplifications and hypotheses. Many of these are not even mentioned by authors, let alone discussed. Thus, in technical literature, longitudinal rolling process is analysed as being symmetric to the median horizontal plane of the metal bar and rolling cylinders. Practically, this hypothesis does not correspond to the real rolling conditions, not even in the case of the typical scheme of machining the profile having rectangular sections between the plane panel rolls. Even more greater are the deviations in the case of more complicated schemes, when the rolling takes place in gauges, as well as in a series of special cases: i.e. one cylinder of the two is operated; the roll diameters are different; when rolling the stratified bars and so on. In those particular cases of longitudinal rolling when there is an intended considerable asymmetry, without knowing the particularities of these processes we cannot develop their theory. A successful development of the rolling practice and theory requires a profound analysis of various phenomena, in order to decipher the essence of this complex process. In spite of the large volume of research, there are still some unsolved problems concerning metal deformation, kinematics and rolling dynamics. As a result, in some cases, important practical solutions lack solid scientific foundations. Nowadays, despite numerous research projects, there are still many answers to be found, answers regarding basic problems that have practical value. Moreover, elaboration of some precise calculus methods must lead to elaboration of some simplified nomograms, useful in the industrial practice. In this case, there is a series of theoretical hypotheses that require experimental confirmation. This is also entirely valid for the asymmetric rolling process because the determination of deformations and stress that appear on the surface of contact between the cylinders and the metal remains unclear. Technical literature contains a large amount of theoretical and experimental research regarding symmetric rolling process when both of the rolls are operated and have equal diameters and speed rates. The rolled metal is homogenous, moves uniformly and has completely identical conditions on the surface of contact with the rolls. In this case, the stress and deformations on the rolled bar section are symmetrically distributed in relation to the mill train. If the rolling cylinders have different diameters, there are particularities in distributing the contact stress and deformations on the rolled bar section, which, consequently, loses its symmetry.

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2. EKSPERIMENTALNA INSTALACIJA U svrhu onog o ~emu je prethodno bilo rije~i, izvedeno je istraìvanje na dvovaljkastom reverzibilnom valja~kom stanu od 170 [mm], instaliranom u laboratoriji za Nekonvencionalne tehnologije za plasti~nu deformaciju pri Ma{inskom fakultetu u Hunedoari. Valjci se pogone istosmjernim motorom snage 33 [kW] sa 1400 [o/min], preko reduktora, prenosnog stana i univerzalnih vretena. Brzina valjanja se kre}e od 0,3 do 0,8 [m/s]. Leàjevi valjaka su kotrljajni sa koni~nim valj~i}ima. U svrhu istraìvanja, i dobivanja {ireg podru~ja obrtanja izme|u odnosa radnih pre~nika, valja~ka pruga je opremljena sa dva posebno izra|ena valjaka od 140 i 170 [mm], leàjevima, ta~kastim detektorima za mjerenje kontaktnog naprazanja, detektorima za mjerenje sile valjanja i bo~nih optere}enja, kao i ure|ajima za pode{avanje potrebne duìne opruge za obezbje|enje kontakta izme|u valjaka i valjanog materijala. Na slikama 1 i 2 su predstavljene ove instalacije smje{tene u laboratoriji Fakulteta. Slika 3 predstavlja jedan op}i pogled instalacije, koju su napravili autori ovog rada i koja, u pore|enju s ostalim valja~kim prugama, omogu}ava istovremeno registriranje parametara procesa simetri~nog i asimetri~nog valjanja:

• sila valjanja (Fd i Fa); • bo~ne sile (Xd i Xa); • pritisak na povr{inu kontakta s gornjim (ps)

i donjim valjkom (pi); • stvarne duìne opruga kontakta s gornjim

(ls) i donjim valjkom (li). Mjerenje glavnih parametara simetri~nog i asimetri~nog podu`nog procesa – odnosno sile valjanja na desnom i lijevom pritisnom vretenu (Fd i Fs). Desne i lijeve bo~ne sile (Xd i Xs) naprezanja na povr{ini kontakta s gornjim i donjim valjakom (ps, odnosno pi) – su izvedeni uz pomo} tenzometrijskih shema bez ikakvog poja~avanja. Impulsi su biljeèni na traci od 120 mm oscilografa N – 700, koji ima 14 kanala, i brzinu trake od 4 [cm/s]. Kao prvi pretvara~i kori{teni su otporni~ki transduceri, koji prevaraju deformaciju u hemijsku modifikaciju otpora. Druga pretvara~ka veza za elektri~ni most. Radni elementi mosta su dva suprotno postavljena zatezna otporni~ka transducera poloèna paralelno sa glavnim pravcem deformacije. Druga dva zatezna otporni~ka transducera predstavljaju kompenzacioni otpornik, postavljeni su odvojeno na jednoj plo~i, zbog ogranI~ene povr{ine na ta~kastim detektorima. Dva valjka (predstavljena na slici 1), pre~nika 140 mm i 170 mm, izra|ena su od kovanog i normaliziranog ~elika OL50 (vrsta ~elika odgovara rumunskom standardu).

2. EXPERIMENTAL INSTALLATION

For the above-mentioned purpose, the research was done on a 170 mm double reversing mill built, installed in the laboratory of Plastic Deformation Unconventional Technologies of the Metallurgical Department at the Faculty of Engineering - Hunedoara. The rolls are operated with a 33 kW continuous current motor (n = 1400 rot/min), using a reducer, pinion stands and universal bars. The rolling speed ranges from 0.3 to 0.8 [m/s]. The roll bearings are conical – roller – angles. For the purpose of the research and obtaining a large turning fork (scope) between the working diameters ratio, the mill was equipped with two special-built rolls of 140 mm and, respectively 170 mm, bearings, pointlike force detectors for the contact stress, rolling force and side effort detectors, as well as with devices for fixing the real length of the springs of contact between the rolls and the metallic material. Figure 1, and figure 2 present this installation, located in the laboratory of the Faculty. Figure 3 shows a general view of the installation, which has been built by the authors of this paper and which, compared to all the other mills, allows simultaneous registering of the symmetric and asymmetric rolling process parameters:

▪ rolling force (Fd and Fa);

▪ side efforts (Xd and Xa);

▪ pressure on the surface of contact with the superior (ps) and the inferior roll (pi);

▪ the real lengths of the springs of contact with the superior (ls) and the inferior roll (li).

The measuring of the main parameters of the symmetric and asymmetric longitudinal process – i.e. the rolling forces for the right and left pressing thumb screws (Fd, respectively, Fs). The right and left side efforts (Xd, respectively, Xs); the stress on the surface of contact with the superior and inferior cylinder (ps, respectively, pi) – was performed using some tensometric schemes with no amplification. The impulses were registered on the 120 mm – wide band of an N – 700 oscillograph having 14 channels and a band moving speed of 4 cm/s. Resistive transducers that turn the deformations into chemical resistance modifications were used as first converters. The second converting link is an electrical bridge. The bridge working elements are two opposed tens resistive transducers, which are stuck parallel to the main direction of deformation. Other two tens resistive transducers represent the compensating resistance, which are placed separately on a plate, because of the limited surface of the pointlike detectors. The two rolls (presented in figure 1), 140 mm and 170 mm in diameters, are made of OL50 – forged and normalised steel (the grade of steel is corresponding to the Romanian standard).

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Oba imaju dva suprotno poloèna podu`na kanala. Da bi se instalirali ta~kasti detektori (specifi~ni pritisak kod valjanja), u centrima kanala i gornjeg i donjeg valjka izbu{en je otvor pre~nika 24 mm. Glave “A” i “B” valjaka imaju poseban diobni sistem koji sluì za utvr|ivanje na oscilogramu, stvarne duìne kontaktnih opruga izme|u materijala i valjaka i poloàja geometrijske ravni izlaza izme|u valjaka. Otvor od 25 mm izbu{en je kroz osu prvog i drugog valjka do sredi{ta plo~e, koji sluì za izlaz kablova ta~kastih detektora koji registruju pritisak kod valjanja. Simetri~ni i asimetri~ni procesi valjanja su dobiveni uvo|enjem segmenata razli~itih polupre~nika u te kanale, {to je omogu}ilo dobivanje sljede}ih odnosa izme|u radnih pre~nika gornjeg (Ds) i donjeg valjka (Di).

200

140;

190

150;

180

160;

170

170

D

D

i

s = [ mm ]

Both of them have two antipodal longitudinal channels. In order to install the pointlike detectors (the specific rolling pressure), a 24 mm – diameter orifice has been drilled in the centres of the channels of both the superior and the inferior cylinder. Heads “A” and “B” of the rolling cylinders have a special dividing system that serves at fixating, on the oscillogram, the real length of the springs of contact between the material and the rolls and the position of the geometrical plane of exiting from between the rolls. We drilled a 25 mm orifice through the first and second roll axis to the centre of the plate, which serves at evacuation of the cables of the pointlike detectors recording the rolling pressure. The symmetric and asymmetric rolling processes were obtained by introducing various radii segments into those particular channels, which allowed us to obtain the following ratios between the working diameters of the superior (Ds) and the inferior roll (Di).

200

140;

190

150;

180

160;

170

170

D

D

i

s = [ mm ]

Slika 1 i slika 2.: Instalacija koja se nalazi u laboratoriji Nekonvencionalnih tehnologija za plasti~nu deformaciju na Odsjeku za metalurgiju, Ma{inski fakultet – Hunedoara (frontalni pogled, odnosno bo~ni pogled)

Figure 1 & Figure 2.: The installation, located in the laboratory of Plastic Deformation Unconventional technologies of the Metallurgical Department at the Faculty of Engineering – Hunedoara

(frontal view, respectively lateral view)

Na~in postavljanja ovih segmenata na valjke da bi se postigle ove kombinacije predstavljen je na slici 4. Valjci moraju nalijegati tako da se mjerenje pritiska valjanja za svaki valjak vr{i u istoj ravni. Segmenti su u~vr{}eni u kanalima valjaka sa ~etiri vijka M8 i dvije konusne ~ivije. U oba segmenta su instalirani ta~kasti detektori za registraciju pritiska na povr{inama kontakta s materijalom za valjanje.

The manner of fitting the segments on the rolls, in order to obtain these combinations, is provided in figure 4. The rolls must be fitted in such a way that the measuring of each cylinder’s rolling pressure is made in the same plane. The segments are fitted into the cylinder channels with four metric 8 screws and two tapered pins. In both of the segments pointlike detectors were installed for recording the pressure on the surfaces of contact with the rolling material.

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Slika 3.: Instalacija u svrhu istraìvanja parametara sile kod procesa simetri~nog i asimetri~nog podu`nog valjanja 1 – 140 [mm] – “A” diobena glava gornjeg valjka; 2 – 170 [mm] – “B” diobena glava donjeg valjka; 3 – R = 70 [mm] – segment za gornji valjak; 4 – R =100 [mm] – segment za donji valjak; 5 –

aparat za registraciju stvarne duìne kontaktnih opruga; 6 – leàj donjeg valjka; 7 – leàj gornjeg valjka; 8 – prijemnik sile valjanja (F); 9 – prijemnik bo~ne sile (X).

Figure 3.: The installation for the research on the force parameters of the symmetric and asymmetric longitudinal rolling process 1 – 140 [mm] – “A” divided head superior roll; 2 – 170 [mm] – “B” divided

head inferior roll; 3 – R = 70 [mm] – segment for the superior roll; 4 – R =100 [mm] – segment for the inferior roll; 5 – device for registering the real length of the contact springs; 6 – inferior roll bearing;

7 – superior roll bearing; 8 – rolling force (F) detector; 9 – side force (X) detector.

Osjetljivi element (Tenzometrijski most)

Sensitiv element (Tensometric bridge)

Aparat za registr.The registering

ice (apparatu

Prvi pretvaračThe first converter

Drugi pretvaračThe second converter

dev s)

Instalacija za napajanje

Feeding installation

Slika 4.:Č Dijagram strukture instalacije za mjerenje parametara

Figure 4.: The structural diagram of the parameter measuring installation Konstrukcijske karakteristike ta~kastih detektora sile za mjerenje pritiska na kontaktu izme|u metala za valjanje i valjaka su sljede}e:

▪ pre~nik osovinica kori{tenih za ove detektore je unaprijed odre|en na 1,13 mm. Zbog toga oscilograf biljeì direktno u kona~nim mjernim jedinicama [N/mm2];

The constructive particularities of the force pointlike detectors for measuring the pressure at the contact between the metal rolling material and the rolls, are related to:

▪ the diameter of the pins used for these detectors is pre-set at 1.13 mm. This determines the oscillograph to perform the recording directly in finite units of measurement [N/mm2];

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▪ izme|u ~eli~ne {ipke osovinice i tijela detektora postoji radijalni zazor od 0,5 mm, {to isklju~uje mogu}nost da se mjerni dio osovinice zaglavi u otvoru segmenta prilikom instaliranja detektora;

▪ tijelo ta~kastog detektora izra|enog od mesinga ima ~etiri podu`na ureza, svaki po 2 mm, kako bi se osigurala potrebna osjetljivost i homogenija distribucija pritiska po presjeku. Pokazalo se da je bilo vrlo jednostavno koristiti ih u eksperimentu, gdje nije bilo potrebno poja~avati impulse. Oni imaju malu ukupnu dimenziju, {to je jako va`no, kao i neophodnu osjetljivost i otpornost na udar itd. Princip njihovog rada se zasniva na izmjeni stvarnog otpora na tenzometri~nom mostu zaljepljenog na zidove ta~kastih detektora, zbog sile koja sabija osovinicu pri ulasku u deformaciono podru~je i {iri zidovime detekrota. Modificiranje otpora odre|uje neravnoteù struje u tenzometri~nom dijagramu, koja je prvobitno bila uravnoteèna. Kriva varijacije struje koju oscilograf biljeì je, u odre|enom omjeru, odraz pritiska koji se razvija na kontaktnoj povr{ini izme|u materijala i valjaka. Spajanje dijagrama se izvodi 10 do 15 minuta prije po~etka oscilografa, radi zagrijavanja. Nakon toga, indikator na galvanometru pokazuje 0 (pozicija 0 na indikatoru se periodi~no biljeì). Koriste}i ove detektore dobivene su krivulje koje prikazuju varijaciju pritiska du` cijele opruge kontakta izme|u metala i valjaka. Na traci oscilografa od 120 mm zabiljeèna je neravnoteà mostova ta~kastog detektora. Osjetljivost detektora i brzina kretanja oscilografske trake su unaprijed odre|eni na taj na~in da skala krivulje na oscilografskoj traci bude dovoljno velika, odnosno, krivulje bi trebalo da budu dovoljno visoke i velike da se mogu lako o~itati. Slika 1 tako|er prikazuje osovinice ta~kastog detektora od 1,13 mm, koje probijaju kroz povr{inu segmenta i dolaze u kontakt s metalnim materijalom. Da bi se postigla krivulja distribucije pritiska koja je {to je mogu}e blià stvarnoj, osovinice moraju imati minimalnu mogu}u dimenziju, kako u pravcu {irine {ipke, tako i u pravcu valjanja. Osovinica detektora sile mora imati istu tvrdo}u kao i segmenti valjaka, a to je oko 70…80 [orovih jedinica. Zbog toga se one prave od iste vrste ~elika i kale se. Glava osovinice je prilago|ena uzimaju}i u obzir povr{inu segmenta, te je pode{ena bru{enjem. Kalibracija ta~kastih detektora je izvedena nakon {to su instalirani u segmente koriste}i specijalni aparat za optere}enje od 0 do 1000 N.

▪ there is a 0.5 mm – radial game between the pin steel bar and the body of the detector. This excludes the possibility of the gauged part of the pin getting stuck in the orifice of the segment when installing the detector;

▪ the body of the pointlike detector, which is made of brass, has four longitudinal cuttings of 2 mm each, in order to insure the necessary sensitivity and a more homogenous pressure distribution per section. Their use in the experiments proved to be easy, without requiring amplification of the impulses. They have little overall dimension–which is extremely important–and the necessary sensitivity and impact resistance etc. Their operating principle is based on changing the true resistance of the tenso-metrical bridge stuck to the walls of the pointlike detectors, because of the force that compresses the pin when it enters the deformation area and expands the detector walls. Modifying the resistance determines an unbalance of the current in the tenso-metrical diagram, which was initially balanced. The current variation curve, recorded by the oscillograph, is, in a certain proportion, the representation of the pressure developing on the surface of contact between the material and the cylinders. The diagram coupling takes place 10 to 15 minutes before the beginning of the oscillograph, in order to pre-heat it. Afterwards, the galvanometer indicator shows 0 (the 0 position of the indicator is periodically verified). Using these detectors, there were obtained curves that show the variation of pressure all along the spring of contact between the metallic material and the rolls. The unbalance of the pointlike detector bridges was recorded on the oscillograph 120 mm – wide band. The detector sensitivity and the oscillograph band moving speed were pre-set in such a way that the curve scale on the oscillograph band are large enough, that is, the curves should be tall and wide enough to be easily read. Figure 1 also shows that the 1.13 mm pointlike detector pins stick through the segment surface and come into contact with the metallic material. In order to obtain the pressure distribution curves as close to the real one as possible, the pin must have a minimum possible dimension both in the direction of the bar width and in the direction of rolling. The force detector pin must have the same hardness as the roll segments that is about 70…80 Shore units. This is the reason why they are made of the same steel type and are subjected to hardening. The pinhead is adjusted by taking into consideration the surface of the segment and is performed after fitting by grinding. The operation of gauging the pointlike detectors was performed after installing them in the segments, by using a special device for loading from 0 to 1000 N.

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Uzimaju}i u obzir vrijednost sile optere}enja i odgovaraju}e amplitude krivulje pritiska na oscilografu napravljen je grafikon kalibracije za detektore u gornjem i donjem valjku, u zavisnosti od promjenjivih:

ps = f (x);

pi = f (x)

x = odstupanje svjetla galvanometra na oscilografu mjereno u [mm]. Instaliranje detektora na radnom postolju s ciljem mjerenja sila valjanja i bo~nih sila predstavljeno je na slici 1. Da bi se mjerile sile valjanja detektori }e biti instalirani ispod pritisnih vretana, a da bi se mjerile bo~ne sile, modificirani su leàjevi donjih valjaka, za instaliranje detektora u njihovo tijelo, okomito na osu leàja. Bo~ne sile koje se javljaju u slu~aju asimetri~nog podu`nog valjanja kad je operativan samo jedan valjak zabiljeène su koriste}i mesingane detektore u tijelu donjeg leì{ta, tako da je njihova podu`na osa okomita na geometrijesku ravan materijala koji se nalazi izme|u valjaka. Izme|u leàjeva valjka i okvira stalka, na stranama detektora, unaprijed je pode{en zazor od 2 mm za bo~ne sile, tako da ih mogu otkriti samo detektori (vidi sliku 1). Kalibriranje detektora za bo~nu silu je izvedeno na istoj mehani~koj presi kao i za sile valjanja sukcesivnim optere}enjima od 0 do 20 [kN]. Nacrtan je kalibracijski dijagram za svaki detektor:

Fd=f(x); Fs=f(x); Xd= f(x); Xs= f(x);

Taking into consideration the loading effort value and the corresponding amplitude of the pressure curve on the oscillograph, there were designed some calibration chart for the detectors in the superior and inferior cylinders, according to the dependencies:

ps = f (x);

pi = f (x)

x=the deviation of the spotlight of the galvanometer of the oscillograph, measured in [mm]. The installation of the detectors on the working stand, in order to measure the rolling forces and the side efforts, is shown in figure 1. Thus, in order to measure the rolling forces, the detectors will be installed under the pressure screws, and, in order to record the side efforts, the inferior rolls bearings were modified, for installing the detectors in their bodies, perpendicularly on the bearing axes. The side efforts that appear in the case of asymmetric longitudinal rolling, or in the case of symmetrical rolling when a single roll is operated, were recorded by using some brass detectors introduced in the body of the inferior bearing, so that their longitudinal axis is perpendicular on the geometric plane of material existing from between the rolls. In between the bearings of the roll and the frame of the stand, on the side of the detectors, for the side efforts there was pre-set a game of 2 mm, so that those efforts can be noticed only by the detectors (see figure 1). Calibrating the detectors for side efforts was performed at the same mechanical press as for the rolling forces, by successive reloading from 0 to 20 [kN]. The calibrating diagrams for each of the detectors were drawn:

Fd=f(x); Fs=f(x); Xd= f(x); Xs= f(x);

3. ZAKLJU^CI

▪ Eksperimantalna instalacija je napravljena kako bi se istovremeno odredili parametri sile kod procesa simetri~nog i asimetri~nog podu`nog valjanja.

▪ Parametri su odre|eni uzimaju}i u obzir pritiske na povr{ini kontakta s valjcima, te sile valjanja i bo~ne sile kod asimetri~nog procesa.

▪ Instalacija i ure|aj }e biti kori{ten u istraìva~ke svrhe, za uspostavljanje odnosa izme|u parametara tehnolo{ke sile procesa valjanja i u prakti~ne svrhe, da bi se odredio stepen naprezanja tehnolo{ke instalacije.

3. CONCLUSIONS

▪ the experimental installation was built in order to determine simultaneously the force parameters in the symmetric and asymmetric longitudinal rolling process.

▪ the determination of the parameters is performed by taking into consideration pressures on the surfaces of contact with the rolls, of rolling forces and the side efforts when the process is asymmetric.

▪ the installation and the device will be used both for research purposes, for establishing some relations between the technological force parameters of the rolling process, and for practical purposes, in order to determine the technological installation degree of stress.

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4. LITERATURA - REFERENCES [1] Constantinescu, I.N.: Masurarea marimilor

mecanice cu ajutorul tensometriei (Tensometrical measurement of the mechanical values), Editura Tehnica Bucureşti, 1989;

[2] Gubkin, S.: Deformarea plastica a metalelor

(Plastic deformation of the metals), Metallurghizdat, Moscova, 1980;

[3] Poluhin, P.L.; Fedosov, N.M.; Koroleov, A.A.;

Matveev, M.: Prokatnae proizvadstvo, Metallurghia, 1982;

[4] White, C.S.; Bronkhorst, C.A.; Anand, I.: Improved isotropic – Kinematic hardening model for moderate deformation metal plasticity, Mechanics of Materials, 1990;

[5] Alexa, V.: Determinarea reducerii liniare la

laminarea longitudinala asimetrica (The linear reduction determination at the asymmetric longitudinal rolling process), Scientific Conference – Hunedoara, 1999

[6] Alexa, V.: Analiza comparativa a unor solutii de

calcul pentru presiune de laminare (Comparative analysis of the rolling pressure determination solutions), Bulletin of University “Politehnica” – Timisoara, 2000

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Ma{instvo 3(7), 151 – 158, (2003) N.Rep~i},...: SIMULACIJA PROCESA OBRADE...

SIMULACIJA PROCESA OBRADE I MODELIRANJE ALATA NA CNC MA[INAMA Win3D-View SOFTVEROM

Prof. dr. Ned`ad Rep~i}, dipl. in`. ma{.; Isad [ari}, dipl. in`. ma{., Univerzitet u Sarajevu, Ma{inski fakultet, Vilsonovo {etali{te 9, Sarajevo

REZIME Te`nja ostvarivanja {to ve}e produktivnosti doma}e proizvodnje, uz {irenje asortimana proizvoda, uslovljava intenzivniju primjenu numeri~ki NC i kompjuterski upravljanih CNC ma{ina i osnovnih sredstava za automatizaciju maloserijske i srednjeserijske proizvodnje kao dominiraju}ih vidova proizvodnje. Zato je razumljiva pa`nja koja se tokom posljednjih godina poklanja uvo|enju sve ve}eg broja CNC ma{ina u proizvodni proces, ~iji je razvoj u tijesnoj vezi sa razvojem elektronike i ra~unarske tehnike. Kompjutersko upravljanje predstavlja osnovu automatizacije obradnog procesa. Sve potrebne informacije za upravljanje i realizaciju obradnog procesa koje se programiraju, sistematizuju se i kodiraju u formi programa, te unose u memoriju upravlja~kog sistema. Pri tome, osnovu pri projektovanju u industrijskoj praksi ~ine grafi~ke simulacije procesa obrade na CNC ma{inama koje se naj~e{}e ostvaruju neovisnim softverom, zavisno od upotrijebljenog tipa kontrole. I neovisni softver Win3D-View, verzija 2.00, ~ije su osnovne karakte istike i mogu}nosti prikazane u radu na primjeru obrade struganjem, razvijen je s tom svrhom. Softver je namijenjen za trodimenzionalnu - 3D grafi~ku simulaciju obrade struganjem i glodanjem na CNC ma{inama, i naj~e{}e je integrisan sa WinNC i WinCTS softverom. Proces obrade koji se grafi~ki simulira na CNC ma{ini prethodno se programira u SINUMERIK 810T kontrolnom formatu (ili se programira jednim od sljede}ih tipova kontrole: SINUMERIK 820T, GE FANUC Series 0-TC, EMCOTRONIC T2). Grafi~ka simulacija, dizajnirana prvenstveno za industrijsku upotrebu, realno prikazuje proces obrade, neobra|eni predmet, alat, stezno sredstvo, i razli~ite poglede i presjeke radnog predmeta koji se obra|uje. P i instalaciji softve a formira se biblioteka sa standardnim alatima iz koje se biraju svi potrebni alati koji }e se koristiti pri obradi radnog predmeta. Tako|er je mogu}e kreirati i vlastite alate za 3D simulaciju, a postupak modeliranja tipi~nog alata za obradu struganjem prikazan je u radu.

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Klju~ne rije~i: NC, CNC, CAD, CAM

SIMULATION OF WORKING PROCESS AND TOOL MODELLING ON CNC MACHINES BY Win3D-View

SOFTWARE

Ned`ad Rep~i}, Ph. D., B. Sc. Mech. Eng.; Isad [ari}, B. Sc. Mech. Eng., University of Sarajevo, Faculty of Mechanical Engineering, Vilsonovo {etali{te 9, Sarajevo

SUMMARY

The urge for achieving highe productivity of domestic production alongside broadening o p oduct assortment conditions more intense application of nume ical NC and compute numerical control CNC machines and of basic devices for automation of small serial and medium serial production as dominating ways of production. It is, there ore easy to unde stand the attention being paid to installing a bigger number of CNC machines in the production process in the last few years, whose development is in close connection to the development of electronics and computing technique. Computer controlling presents the basic automation of a working process. All the pieces of information necessary for controlling and working process realisation that are programmed are systemised and coded in the form of a programme. They are entered in the memory of a controlling system. The basic elements of the design process in industrial practice are graphical simulations of a working process on CNC machines, which are most frequently presented by an independent software, depending on the applied control type. The independent Win3D-View software, version 2.00 with basic characte istics and possibilities presented in the paper on the example of turning has also been developed for that purpose. The software has been created for the purpose of the 3D graphical simulation of turning and milling on CNC machines

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and it is most frequently integrated with WinNC and WinCTS software. The working process that is graphically simulated on the CNC machine is previously programmed in SINUMERIK 810T controlling format (or in one of the following types of control: SINUMERIK 820T, GE FANUC Series 0-TC, EMCOTRONIC T2). The graphical simulation, primarily designed for industrial use, realistically presents the working process, unmachined part, tool, clamp device, and different views and sections of a processing piece. A library with standard tools is formatted during the software installation, from which all the tools necessary for the processing are chosen. It is also possible to create one’s own tools for the 3D simulation. The paper presents a modelling procedure of a typical tool for turning.

Key words: NC, CNC, CAD, CAM

1. UVOD Win3D-View verzija 2.00 je neovisan softver namijenjen za trodimenzionalnu - 3D grafi~ku simulaciju obrade struganjem i glodanjem na CNC ma{inama i naj~e{}e je integrisan sa WinNC i WinCTS softverom. Proces obrade koji se grafi~ki simulira na CNC ma{ini prethodno se programira jednim od sljede}ih tipova kontrole:

• SINUMERIK 810/820T, • GE FANUC Series 0-TC ili • EMCOTRONIC T2.

Pri instalaciji Win3D-View softvera formira se biblioteka sa standardnim alatima iz koje se biraju svi potrebni alati koji }e se koristiti pri obradi radnog predmeta. U radu je na primjeru obrade struganjem odabranog radnog predmeta na CNC strugu PC Turn 55 izvr{eno projektovanje tehnolo{kog procesa, formiran CNC program podràn WinNC kontrolnim softverom [5], prikazana 3D grafi~ka simulacija realnog procesa obrade sa razli~itim pogledima i presjecima radnog predmeta u Win3D-View softveru, te prikazan postupak modeliranja tipi~nog alata za ovaj vid obrade. CNC strug PC Turn 55 moè biti integrisan u fleksibilni proizvodni sistem FMS i/ili CIM sistem kojim se vr{i upravljanje svim aktivnostima u proizvodnom sistemu po~ev od nabavke do marketinga, i kompatibilan je sa CAD/CAM sistemima [7]. Osnovni problemi vezani za izradu radnih predmeta rje{avaju se pri tehnolo{koj pripremi za programiranje [4], dakle znatno prije po~etka obrade, kako bi postupak izrade CNC programa WinNC kontrolnim softverom protekao bez ve}ih te{ko}a.

1. INTRODUCTION

Win3D-View software version 2.00 has been created for the purpose of the 3D graphical simulation of turning and milling on the CNC machines and it is the most frequently integrated with the WinNC and WinCTS software. The working process graphically simulated on the CNC machine is previously programmed in one of the following types of control:

• SINUMERIK 810/820T, • GE FANUC Series 0-TC or • EMCOTRONIC T2.

A library with standard tools is formatted during the software installation, from which all the tools necessary for processing are chosen. The paper presents a design of the technological process on the example of turning of a working object on CNC lathe PC Turn 55, the format of the CNC program supported by WinNC controlling software [5], and a 3D graphical simulation of a realistic process of working with different views and sections of the working example, and finally the modelling procedure of a typical tool for turning during this kind of processing, which has been presented in Win3D-View software. The CNC lathe PC Turn 55 can be integrated into a flexible manufacturing system FMS or/and CIM system, which conducts all activities in manufacturing system starting from the basic activities, such as supplying through to marketing and is compatible with CAD/CAM systems [7]. In order to ease the design procedure of CNC programmes by the controlling software WinNC as much as possible the basic problems related to creation of processing examples are solved long time before the beginning of processing, that is during the technological preparation for programming [4].

2. OSNOVNE KARAKTERISTIKE Win3D-View SOFTVERA

Grafi~ka simulacija, dizajnirana prvenstveno za industrijsku upotrebu, realno prikazuje proces obrade, radno okruènje sa neobra|enim predmetom, alat i stezno sredstvo. Programirano kretanje alata kontrolisano je sistemom koji daje upozorenje u slu~aju pojave kolizije sa steznim sredstvom ili radnim predmetom koji se obra|uje [6]. Osnovne karakteristike Win3D-View softvera su:

2. THE BASIC CHARACTERISTICS OF THE Win3D-View SOFTWARE

The graphical simulation has been designed primarily for industrial purposes and it realistically presents processing, working area with unmachined part, a tool and the clamping device. The programmed tool operating is controlled by the system that gives warnings in case of collision with the clamping device or a work piece [6]. The basic characteristics of the Win3D-View software are:

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• 3D simulacija obrade struganjem i glodanjem, • prikaz radnog okruènja sa neobra|enim

predmetom, alatom i steznim sredstvom, • prikaz punog ili djelimi~nog presjeka radnog

predmeta, • prikaz alata kao solid ili ì~anog modela, • prikaz razli~itih pogleda na radni predmet, • integrisana biblioteka sa standardnim alatima,

kontrola kolizije alata, skaliranje.

• 3D simulation of turning and milling, • representation of the working area with

unmachined part, tool and clamping device, • full or partial sectional representation of a work piece, • tool representation in the form of a solid or

grid model, • representation of view from different angles of

the work piece, • integrated library with standard tools, collision

control of the tool, scaling.

3. PROJEKTOVANJE TEHNOLO[KOG PROCESA, FORMIRANJE CNC PROGRAMA I SIMULACIJA PROCESA OBRADE

3.1 Projektovanje tehnolo{kog procesa Pri razradi tehnolo{kog procesa koristi se crte` radnog predmeta, karta ma{ine, standardi, katalozi specifi~nog i standardnog reznog, mjernog i pomo}nog alata i opreme. Jedan od najsloènijih zadataka koji se rje{avaju pri projektovanju tehnolo{kog procesa je odre|ivanje redoslijeda operacija i izbor reznog alata. Odabrani radni predmet i redoslijed operacija prikazani su na slikama 1. i 2. [3]

3. TECHNOLOGICAL PROCESS PROJECTING, CNC PROGRAMME FORMATTING AND PROCESSING SIMULATION

3.1. Technological process projecting The drawing of work piece is used during the preparation of the technological process, along with maps of the machine, standards, catalogues for specific and standard cutting, measuring and assisting tool and equipment. One of the most complex tasks that is being solved during the projecting of the technological process is the determination of sequence of operations and selection of the cutting device. The selected work piece and sequence of operations are presented in Figures 1. and 2. [3]

1. Gruba obrada - .Roughing 3. Urezivanje žlijeba- Grooving

4) Narezivanje navoja - Threading

2. Fina obrada - Finishing

Slika 1. Radni primjer Slika 2. Redoslijed operacija Figure 1. Work example Figure 2. Sequence of operations

Tabela 1. Izbor reznog alata - Table 1. Choosing tools

Desni alat - Side copy tool right Alat za vanjsko narezivanje navoja

External threading tool Alat za odsijecanje Parting-off tool

T2 T4 T6

Broj korekcije: D2 Offset number: Radijus alata: 0,4 Tool radius: Pozicija alata: 3 Tool position: Brzina: 150/188 m/min Spindle: Posmak: 0,06 mm/o Feed

Broj korekcije: D4 Offset number: Radijus alata:

Broj korekcije: D6 Offset number: Radijus alata:

-

Tool radius: Pozicija alata: 8 Tool position: Brzina: 600 o/min Spindle: Posmak: Feed

Tool radius: Pozicija alata: 8 Tool position: Brzina: 80 m/min Spindle: Posmak: 0,02 mm/o Feed

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3.2. Formiranje CNC programa WinNC kontrolnim softverom

CNC program, podr`an WinNC SINUMERIK 810T kontrolnim softverom [2], za izradu odabranog radnog predmeta od pripremka Ø22x100 mm izgleda ovako:

3.2. CNC programme formatting by WinNC controlling software

This is an example of the CNC program supported by the WinNC SINUMERIK 810T controlling software [2] for manufacturing a chosen raw material work piece Ø22x100 mm:

WinNC, CNC program SINUMERIK 810T %3 N0005 G54 LF N0010 G58 Z100 LF N0015 T2 D2 LF N0020 G96 S150 F0.06 M3 LF N0025 G0 X22 Z1 LF N0030 R20=3 R21=12 R22=0 R24=0.4 R25=0.1 R26=1 R27=42 R29=31 R28=0.06 R30=0.5 L95 P1 LF N0035 G96 S188 F0.04 M3 LF N0040 R20=3 R21=12 R22=0 R24=0 R25=0 R26=1 R27=42 R29=21 R28=0.04 R30=1 L95 P1 LF N0045 G0 X40 LF N0050 T6 D6 LF N0055 G96 S80 F0.02 M3 LF N0060 G0 X23 Z-48.5 LF N0065 G1 X18 G9 LF N0070 G1 X23 LF

N0075 G0 X40 LF N0080 T4 D4 LF N0085 G95 S600 M3 LF N0090 G0 X23 Z-38 LF N0095 R20=1 R21=22 R22=-40 R23=2 R24=-0.61 R25=0.1 R26=2 R27=1 R28=7 R29=30 R31=22 R32=-49 L971 P1 LF N0100 G0 X40 Z5 M5 LF N0105 M30 LF L3 N0005 G1 X16 Z-2 B2 LF N0010 Z-10 LF N0015 X22 Z-20 LF N0020 X16 Z-30 LF N0025 G2 A180 B3 X22 Z-40 LF N0030 M17 LF

3.3. 2D i 3D simulacija procesa obrade Dvodimenzionalnu - 2D grafi~ku simulaciju procesa obrade mogu}e je prikazati WinNC kontrolnim softverom, dok se realni proces obrade mo`e pratiti i trodimenzionalno - 3D grafi~ki simulirati Win3D-View softverom.

3.3. 2D and 3D processing simulation 2D graphical processing simulation can be represented by the WinNC controlling software, whereas the realistic processing can be graphically simulated by the Win3D-View software.

Slika 3. 2D grafi~ka simulacija WinNC kontrolnim softverom i 3D grafi~ka simulacija procesa

obrade Win3D-View softverom Picture 3. 2D graphical simulation by the WinNC controlling software and 3D graphical

processing simulation by the Win3D-View software

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Slika 4. Mogu}nost prikaza razli~itih pogleda i presjeka radnog predmeta Win3D-View softverom

Picture 4. Different possibilities of representation of sections and views from different angles of the work piece by the Win3D-View software

4. MODELIRANJE ALATA Pri 3D simulaciji Win3D-View softverom mogu}e je modelirati alate koji se naj~e{}e koriste za obradu struganjem ili glodanjem radnog predmeta. Modeliranje alata sastoji se iz dva koraka: 1. definisanje parametara alata (duìne, pre~nika,

itd.) u biblioteci alata, 2. definisanje modela alata u fajlu modela alata.

Za kreiranje alata potrebno je formirati dva fajla TOOLxyy.DAT i 3DMODELx.DAT, koji imaju sljede}e zna~enje: TOOLxyy.DAT = biblioteka alata; 3DMODELx.DAT = fajl modela alata; x: metri~ki (M), in~ni (I), yy: Njema~ki (DT), Engleski (EN), Francuski (FR), [panski (SP). Na primjer: TOOLMEN.DAT: biblioteka alata, metri~ki, engleska verzija. Treba napomenuti da se za izmjenu sadràja fajla modela alata koristi Windows ili DOS editor. U radu je prikazan postupak modeliranja tipi~nog desnog alata za obradu struganjem. Prvo su formirani fajlovi TOOLMEN.DAT i 3DMODELM.DAT prethodno obja{njenog zna~enja, a zatim je prikazan sadràj fajla 3DVIEW.INI koji se nalazi u direktoriju podataka ma{ine.

4. TOOL MODELLING

During the 3D simulation by the Win3D-View software it is possible to model tools that are most frequently used for turning and milling process of a work piece. Tool modelling consists of the following two steps: 1. parameter tool defining of (length and

diameter, etc.) in the tool library, 2. defining tool models in the tool model file.

For creation of tools it is necessary to format two files TOOLxyy.DAT and 3DMODELx.DAT with the following meanings: TOOLxyy.DAT = tool library; 3DMODELx.DAT = tool model file; x: metric (M), inch (I), yy: German (DT), English (EN), French (FR), Spanish (SP). For example TOOLMEN.DAT: tool library, metric, English version. It should be pointed out that Windows or DOS editor is used for any changes of content of a tool model file. The paper presents the modelling procedure of a typical side copy tool right for turning. The above-mentioned TOOLMEN.DAT and 3DMODELM.DAT files are formatted first, and then the content of the 3DVIEW.INI file placed in the machine date directory is presented.

File TOOLMEN.DAT [Tool3T] *IndexHolder=0 *ToolAngle=120.500000 *CutAngle=27.500000 *CutRadius=0.400000 *CutLength=7.750000 ToolKind=2 *CutKind=4 *ToolName=Right Copy Tool *Comment= ToolHolderType=VERTICAL ToolModel=RightCopyTool

Napomena: Linije ozna~ene sa * prikazuju se na ekranu u meniju izbora alata Win3D-View softvera.

Note: The lines marked with * will be displayed in the tool selection menu of the Win3D-View software.

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File 3DMODELM.DAT [RightCopyTool] Angle1 = Addition (CutAngle, 90) Angle1 = Subtraction (ToolAngle, Angle1) Angle2 = Addition (ToolAngle, CutAngle) Angle2 = Subtraction (180, Angle2) Sinus1 = Sinus (Angle1) Cosinus1 = Cosinus (Angle1) Sinus2 = Sinus (Angle2) Cosinus2 = Cosinus (Angle2) x1 = Multiplication (CutLength, Sinus1) x1 = Subtraction (0, x1) y1 = Multiplication (CutLength, Cosinus1) x3 = Multiplication (CutLength, Cosinus2) x3 = Subtraction (0, x3) y3 = Multiplication (CutLength, Sinus2) x2 = Addition (x1, x3) y2 = Addition (y1, y3) CutPoints = DefinePoints (0, 0, 0, x1, y1, 0, x2, y2, 0, x3, y3, 0) PntsShaft = DefinePoints (-0.5, 0.5, 0, -16, 12, 0, -16, 60, 0, -5, 60, 0, -5, 14.5, 0, -1, 12, 0) Cutter2D = ConvexPolygon (CutPoints) Shaft2D = SimplePolygon (PntsShaft) CutGraphic = ConvexPolygonGraphic (CutPoints, TURN_2DCUTTERCOLOR, TURN_2DCUTTERCOLOR) ShaftGraphic = SimplePolygonGraphic (PntsShaft, TURN_2DSHAFTCOLOR, TURN_2DSHAFTCOLOR) 2DTool = 2DUnion (ShaftGraphic, CutterGraphic) Cutter3D = ConvexPrism (PointsCutter, 3) Cutter3D = 3DTranslation (Cutter3D, 0, 0, -3) PntsShaft1 = DefinePoints (-0.5, 0.5, 0, -1, 12, 0, -5, 14.5, 0, -16, 12, 0) PntsShaft2 = DefinePoints (-16, 12, 0, -16, 60, 0, -5, 60, 0, -5, 14.5, 0) Shaft3D1 = ConvexPrism (PointsShaft1, 12) Shaft3D2 = ConvexPrism (PointsShaft2, 12) Shaft3D = 3DUnion (Shaft3D1, Shaft3D2) Shaft3D = 3DTranslation (Shaft3D, 0, 0, -12) Cutter3D = 3DRotationX (Cutter3D, 60) Shaft3D = 3DRotation X (Shaft3D, 60) TurnTool(TURN_REMOVECOLOR, Cutter2D, Shaft2D, 2DTool, Cutter3D, TURN_3DCUTTERCOLOR, Shaft3D, TURN_3DSHAFTCOLOR) TOOL_MODEL_END File 3DVIEW.INI [ToolHolders] PCT120/PCT50 T1 = UNIVERSAL/HORIZONTAL T2 = UNIVERSAL/VERTICAL T3 = UNIVERSAL/HORIZONTAL T4 = UNIVERSAL/VERTICAL T5 = UNIVERSAL/HORIZONTAL T6 = UNIVERSAL/VERTRICAL T7 = UNIVERSAL T8 = UNIVERSAL ToolPosition = ABOVE/BELOW [PartingOff] MetricMaxWidth =3 InchMaxWidth = 0.12 [MCodesTailstock] Forward = 20 Back = 21

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[ColorDefinitions] TURN_BACKGROUND = 0.0, 0.0, 0.0, 0 TURN_2DCUTTERCOLOR = 0.875, 0.625, 0.0, 0 TURN_2DTAPCUTTERCOLOR = 1.0, 0.0, 1.0, 0 TURN_2DSHAFTCOLOR = 0.4, 0.4, 0.4, 0 TURN_3DCUTTERCOLOR = 0.375, 0.25, 0.0, 2 TURN_3DTAPCUTTERCOLOR = 1.0, 0.0, 1.0, 2 TURN_3DSHAFTCOLOR = 0.75, 0.75, 0.75, 2 TURN_REMOVECOLOR = 0.5, 0.5, 0.55, 2 TURN_TAPREMOVECOLOR = 1.0, 0.0, 1.0, 2 TURN_CLAMPINGDEVICECOLOR = 0.5, 0.5, 0.5, 2 TURN_TAILSTOCKSECTIONCOLOR = 0.5, 0.5, 0.5, 0 TURN_WORKPIECECOLOR = 0.5, 0.5, 0.55, 2 TURN_SECTIONCOLOR = 0.5, 0.5, 0.55, 2 [MonochromeDefinitions] TURN_BACKGROUND = 0.0, 0.0, 0.0, 0 Pode{avanje boja (RGB model): Boja se defini{e sa ~etiri parametra: Boja = CRVENA ZELENA PLAVA SJENÊNJE Za CRVENU, ZELENU i PLAVU boju unosi se broj izme|u 0 i 1. Unos 0, 0, 0 je crna boja, a unos 1, 1, 1 je bijela boja. Za SJENÊNJE se unosi broj:

Colour setting (RGB model): A colour is defined by four parameters: Colour = RED GREEN BLUE SHADING For RED, GREEN, and BLUE number between 0 and 1 can be entered. The input 0, 0, 0 is black, 1, 1, 1 is white. For SHADING you can enter:

CA .......... Ugao rezanja W1=TA-CA-90° X1=-CL·sin(Ugao 1) Y1=CL·cos(Ugao 1) TA .......... Ugao alata W2=180°-(TA+CA) X3=-CL·cos(Ugao 2) Y3=CL·sin(Ugao 2) CL .......... Dužina rezanja X2=X1+X3 Y2=Y1+Y3 A1 .......... Ugao 1 A2 .......... Ugao 2

Slika 5. Konturne ta~ke strugarskog noà

Figure 5. Contour points of a cutter

Slika 7. Pomjeranje noà alata pri 3D modeliranju Figure 7. Cutter motion during the 3D modelling

CA .......... CutAngle W1=TA-CA-90° X1=-CL·sin(Angle1) Y1=CL·cos(Angle1) TA .......... ToolAngle W2=180°-(TA+CA) X3=-CL·cos(Angle2) Y3=CL·sin(Angle2) CL .......... CutLength X2=X1+X3 Y2=Y1+Y3 A1 .......... Angle1 A2 .......... Angle2

Slika 6. Karakteristi~ne ta~ke poligona nosa~a alata podijeljenog na dva konveksna poligona Figure 6. Characteristic points of a polygon

tool holder separated into two convex polygons

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0 bez sjen~enja, 1 normalno sjen~enje, 2 poja~ano sjen~enje. Napomena: Za izmjenu sadràja fajla 3DVIEW.INI potrebno je iskustvo u radu sa WINDOWS-ima.

0 no shading, 1 normal shading, 2 enhanced shading. Note: For modification of 3DVIEW.INI file content it is necessary to have working experience with Windows.

5. ZAKLJUÂK Osnovna karakteristika savremenog svijeta je ubrzani nau~ni i tehnolo{ki razvoj uz pomo} modernih tehnologija [1]. Na trì{tu se pojavljuje sve ve}i broj upotrebljivih aplikacija, izme|u ostalih i interaktivni Win3D-View softver, sa ciljem ve}e primjene kompjuterskih tehnologija u metaloprera|iva~koj industriji. Upotreba Win3D-View softvera mogu}a je samo u slu~aju ako je aktivan CNC program koji je prethodno pripremljen u SINUMERIK 810T kontrolnom formatu u okruènju WinNC-a, a koji je nastao kao rezultat interaktivnog komuniciranja ~ovjeka i ra~unara. Upotrebom softvera Win3D-View mogu}e je optimizirati reìme obrade i simulirati tehnolo{ki proces na ekranu, te na osnovu toga pove}ati proizvodnju i kvalitet proizvoda, smanjiti tro{kove proizvodnje i pobolj{ati uslove rada. U ovom okruènju mogu}e je i grafi~ki pratiti kretanje alata, ispravljati sadràj datoteke putanje alata, modelirati alate pri obradi struganjem i glodanjem, otkrivati i otklanjati gre{ke u programu, i na taj na~in automatski pode{avati bitne parametre za odràvanje kvaliteta proizvoda. Svrha uvo|enja CAD/CAM i savremenih metoda simulacije je pove}anje kvaliteta proizvoda uz skra}enje radnog vremena i u{tede materijala, te osiguranje visokog tehnolo{kog nivoa i konkurentnosti doma}e proizvodnje. Nove tehnologije, ~iji razvoj zavisi od razvoja informacionih sistema, mogu biti korisne ovoj zemlji da premosti duboki jaz koji je dijeli od razvijenih zemalja svijeta.

5. CONCLUSION The basic characteristic of the modern world is accelerated scientific and technological development assisted by modern technologies [1]. There is an increasing number of useable applications on the market, among which is the interactive Win3D-View software, whose purpose is bigger application of computer technologies in metal industry. The use of the Win3D-View software is possible only if the active CNC programme previously prepared in SINUMERIK 810T controlling format is in the environment WinNC, created as a result of an interactive communication between a man and a computer. The use of the Win3D-View software enables optimisation of the processing regime and simulation of the technological process on the screen. The direct benefit of this will be increase of production and product quality, reduction of production expenses and improvement of working conditions. The options possible in this environment are: graphical track of tool motion, correction of file content of a tool path, tool modelling during turning and milling processes, tracking and neutralizing mistakes in the programme. All these advantages will provide automatic adjusting of essential parameters for maintenance of product quality. The purpose of introduction of CAD/CAM and modern methods of simulation is to increase the product quality, reduce the working time, save the material, and ensure high technological level and competition of domestic production. New technologies, whose development depends on the development of information systems, can help this country bridge the gap dividing it from the developed countries of the world.

6. LITERATURA - REFERENCES [1] R. Cebalo: “Fleksibilni proizvodni sustavi”,

Zagreb, 1995.

[2] “CNC Programme package – SINUMERIK 810/820T”, EMCO MAIER Gesellschaft m.b.H., Hallein, 1999.

[3] E. Finkelstain: “AutoCAD 2002”, Mikroknjiga,

Beograd, 2002. [4] V. Me~anin: “Programiranje obradnih procesa

na CNC ma{inama”, Monografija, Ma{inski fakultet, Kraljevo, 1997.

[5] “Software Description – WinNC SINUMERIK 810/820T”, EMCO MAIER Gesellschaft m.b.H., Hallein, 1996.

[6] “Software Description – Win3D-View Turning”,

EMCO MAIER Gesellschaft m.b.H., Hallein, 1996. [7] “TEACHERS GUIDE for PC Turn 50

SINUMERIK 810/820T”, EMCO MAIER Gesellschaft m.b.H., Hallein, 1995.

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Ma{instvo 3(7), 159 – 164, (2003) T.Hepu,...: POBOLJ[ANJE OBRADE ÊLIKA ZA...

POBOLJ[ANJE OBRADE ÊLIKA ZA METALNE KONSTRUKCIJE – INDUSTRIJSKO ISTRA@IVANJE I

EKSPERIMENTI

Prof. Eng. Teodor Hepuţ, Dr. es Sc., Prof. Eng. Isidor Prejban, Dr. es Sc., Lect. Eng. Imre Kiss, Lect. Eng. Camelia Bretotean-Pinca, Dr. es Sc.,, Universitet “Politehnica” – Timi{vara, Ma{inski fakultet – Hunedoara, Rumunija

SA@ETAK Budu}i da su ovi ~elici namijenjeni za izradu dijelova koji se koriste u uslovima udara, habanja i zamora, name}u se dodatne restrikcije kad su u pitanju na~ini koji }e se koristiti da bi se pobolj{ala lako}a njihove obrade. Dodaci koji su poèljni u slu~aju obrade rezanjem mogu se prihvatiti samo u omjeru u kojem njihova koli~ina, oblik i distribucija nemaju zna~ajnijeg utjecaja na ja~inu na udar, otpornost na zamor, mehani~ke osobine popre~nog presjeka, sposobnost cementiranja, sposobnost otvrdnjavanja itd. Me|u dodacima za pobolj{anje lahko}e obrade formiranjem nemetalnih uklju~aka u livu (kako jendostavnih, tako i sloènih), apsorpcijom na povr{inu uklju~aka sulfida i oksida, kao i formiranjem izoliranih ostrva u osnovnoj masi (~ije se dimenzi e kre}u od 0,08 – 0,15µm) i dalje se koriste sumpor, fosfor, olovo, selen i telur. Istraìvanje i eksperimenti koje smo napravili i koji se odnose na pobolj{anje lako}e obrade imali su za cilj odre|ivanje tehnologije dodavanja sumpora na takav na~in da stepen asimilacije ne bude vi{e od 10% druga~iji od jednog punjenja do drugog. Eksperimenti su ura|eni u elektro-~eli~ani opremljenom pe}ima od 50t.

j

,, r

.

Klju~ne rije~i: ~elik, elektro ~eli~ana, dodaci, stepen asimilacije sumpora, mehani~ke osobine

IMPROVEMENT OF STEEL PROCESSING FOR METAL CONSTRUCTIONS – INDUSTRIAL RESEARCH AND

EXPERIMENTS

Prof. Eng. Teodor Hepuţ, Dr. es Sc., Prof. Eng. Isidor Prejban, Dr. es Sc., Lect. Eng. Imre Kiss, Lect. Eng. Camelia Bretotean-Pinca, Dr. es Sc., University “Politehnica” – Timişoara, Faculty of Engineering – Hunedoara, Romania

SUMMARY As these steels are meant for parts that work in conditions of shock, wear and fatigue they imply supplementary restrictions as to the means to be used in order to improve easiness of their processing. The additives that are favourable in case of cut-processing are to be accepted only to the extent to which their quantity, shape and distribution does not significantly affect the resilience resistance to fatigue the cross sectional mechanic characte istics, their cementing capability and hardening capacity, etc. Among the additives used in view of improving the easiness of the processing by inclusion forming (both simple and complex), by absorption on the sulphide and oxide inclusion surface, as well as by formation of isolated islands in the base mass (their dimensions ranging between 0 08 – 0.15µm) sulphur, phosphorous, lead, selenium and tellurium continue to be used. The research and experiments that have been carried out related to improvement of the processing easiness aimed at determining a technology of sulphur addition in such a manner that the assimilation degree should not be more than 10% different from one charge to another. The experiments have been conducted at an electric steel plant equipped with 50t furnaces.

Keywords: steel, electric steel plant, additives, sulphur assimilation degree, mechanical properties and characteristics

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1. UVOD

Jedan od najsloènijih problema koje je ma{inogradnja postavila pred metalurgiju jeste izrada metalnih materijala koji imaju ve}u sposobnost rezanja, ve}i u~inak, a istovremeno i uslove povr{ine koje odgovaraju tom cilju, u zavisnosti od budu}e upotrebe takvog proizvoda. Usljed razli~itosti uslova kori{tenja ~elika i stalne potrebe za pove}anjem u~inka koriste}i automatske alatke s intenzivnijim reìmom rezanja, opseg vrsta ~elika dobre mogu}nosti obrade se sada ekstrapolira uglavnom na sljede}e vrste ~elika: meki ~elik, za male komade s normalnim mehani~kim naponom, ~elik za ma{inogradnju, za komade izloène velikim optere}enjima, za nehr|aju}i ~elik i brzorezni ~elik. Vrstama ~elika za ma{inogradnju, odnosno komade izloène velikom optere}enju, radu pod udarom, te uslovima habanja i zamora potrebne su dodatne restrikcije kad je u pitanju na~in koji se koristi za pobolj{anje sposobnosti rezanja. Zbog toga }e prisustvo uklju~aka u livu biti prihvatljivo samo ako njegova koli~ina, oblik i distribucija ne utje~u na otpor na udar, zamor, mehani~ke osobine popre~nog presjeka, cementiranje i sposobnost otvrdnjavanja. Meki I exstra meki (extra-soft) ~elici, koje karakteri{e velika ìlavost, obra|uju se na nezadovoljavaju}i na~in rezanjem, zato {to formiranju strugotine, a njihovom uklanjanju s povr{ine rezanja prethodi zna~ajna deformacija i otvrdnjavanje feritne osnovne mase, {to ima negativan utjecaj na habanje alatki. Ovaj aspekt se moè rije{iti pozitivno za obradljivost rezanjem tako {to }e se smanjiti ìlavost feritne matrice ili prekidanjem njenog kontituiteta. Ono {to obi~no slijedi nakon toga jeste dodavanje u ~elik elemenata koji formiraju ili neabrazivne, nemetalne uklju~ke u livu (prekidanje kontinuiteta feritne strukture), ili se rastvaraju u feritu. Me|u legiraju}im elementima koji se koriste za pobolj{anje mogu}nosti obrade, sklonih formiranju neabrazivnih, nemetalnih uklju~aka u livu s osobinama podmazivanja u strukturi ~elika nalaze se sumpor, olovo, telur I selenium, u kontroliranim koli~inama, koje su obi~no manje od sadràja elemenata za legiranje u mekom ~eliku za automate. Obi~no se sumpor dodaje automatskim ~elicima u koli~ini do 0,04%. Dodavanje ve}eg sadràja, do 0,08% nije uobi~ajeno, zato {to je rast mogu}nosti obrade niì u pore|enju s pove}anim pote{ko}ama u fazama izrade i plasti~ne deformacije takvih ~elika. Crvena krtost je nagla{ena pri vrijednostima odnosa Mn / S manja od 1,7. U slu~aju ~elika namijenjenih za proizvodnju navrtaka, gdje je hladno sabijanje uklju~eno kao tehni~ka procedura, sadràj sumpora je smanjen do 0,08…0,12%.

1. INTRODUCTION

One of the most complex problems arisen by engineering machine-building industry to the metallurgy is the manufacturing of metallic materials with a better cutting capacity, a greater output and, at the same time, a surface condition suitable for that aim, depending on subsequent utilisation of the respective product. Due to diversity of steel utilisation conditions, along with a permanent need to increase output using automatic machine tools with heavy duty cutting regime, the range of the steel grades with good workability is now extrapolated mostly on the following steel grades: soft steel, for small pieces with normal mechanical stress, steel for engineering machine-building, for heavily stressed pieces, stainless steel and high-speed steel. The machine-building steel grades for heavy-duty pieces, working in shock, wear and fatigue conditions, need additional restrictions, regarding the means used for improving the cutting capacity. Therefore, presence of inclusions for the cutting processes will be accepted only if their amount, form and distribution do not affect resilience, fatigue strength, mechanical proprieties in the cross section, cementing and hardness capacities. Soft and extra-soft steels, characterised by high ductility, are processed unsatisfactorily through cutting, because the chip formation and its removal from the cutting area is proceeded by considerable deformation and hardening of the ferrite base mass, which negatively affects the wear of the tools. This aspect can be resolved in favour of the cutting workability by diminishing ductility of the ferrite die or by interrupting its continuity. Introducing into the steel elements, which either form non-abrasive, non-metallic inclusions (interrupting the continuity of ferrite structure), or dissolve in the ferrite, thus hardening it, usually succeeds this. Among the alloying elements used for improving workability, susceptible of forming non-abrasive, non-metallic inclusions with lubricating properties in the structure of steel, are sulphur, lead, tellurium and selenium, in controlled quantities, which are usually smaller than the content of alloying elements in automatic soft steel. Normally, sulphur is added to automatic steels up to approximately 0.04%. Adding higher contents, up to 0.08% is not a practice, because growth of workability is lower compared to increased difficulties in the phases of elaboration and plastic deformation of such steels. Thus, the red brittleness is stressed at values of the Mn / S ratio below 1.7. In the case of steels destined for production of screw nuts, where the cold upsetting is included as a technical procedure, the sulphur content is reduced to 0.08…0.12%.

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Kad je u pitanju sadràj sumpora ovih ~elika ({to je ispitano u toku eksperimenata), bili su to standardizirane vrste ~elika s 0,08…0,15% ili ~ak 0,25%. Obi~no se smatra da sadràj sumpora od 0,04 do 0,07% ima najmanji utjecaj na pove}anje vrijednosti mehani~kih osobina. Za stepen mogu}nosti obrade i mehani~ke osobine, obim je izabran kompromisom. Vrijedi zapamtiti da mnogo potrebnih hemijskih sastava vrsta ~elika garantira minimalni nivo sadràja sumpora (pribli`no 0,02%) za vrste ~elika s normalnim sadràjem ~elika (maksimalno 0,045%). Upotreba ovih vrsta ~elika s kontroliranim sadràjem sumpora (0,02…0,045%) pomaè pri pobolj{anju proizvodnih povr{ina ~elika pri maloj brzini rezanja. Pri istom sadràju sumpora u ~eliku, sastav, a posebno oblik i distribucija sulfida ({to zavisi o razradi, dezoksidaciji i ljevanju) ima snaàn utjecaj na mogu}nost obrade rezanjem. Op}epriznato je to da sulfidna pje{~ana gnijezda u livu tipa I (kuglasta) se vi{e koriste nego ona tipa II, s intergranularnom ili eutekti~nom distribucijom. Industrijski i laboratorijski eksperimenti koji se odnose na odre|ivanje kvantitativnih korelacija izme|u mogu}nosti obrade ~elika i osobina sulfidnih nemetalnih uklju~aka u livu (KZMnS), koji osiguravaju tu osobinu, predstavljeni su u tabeli 1. Srednja vrijednost KZMnS je odre|ena putem mjernog standarda sa sedam ocjena (ocjena 0 za fina sulfidna pje{~ana gnijezda, odnosno, ocjena 6 za gruba gnijezda), nakon mikroskopskog ispitivanja povr{ine metalografi~kog uzorka, pove}anu 200 puta.

Regarding the sulphur content of these steel grades (which has been inspected during the experiments), there were standardised steel grades with 0.08…0.15% or even 0.25%. Usually, it is considered that the 0.04 to 0.07% sulphur ranges has got the lowest impact on the decrease of the values of mechanical properties. A compromise range has been chosen for the workability level and mechanical properties. It is worth to remember that many required chemical compositions of steel grades guarantee the minimum limit of sulphur content (approximately 0.02%) for the steel grades with normal sulphur content (maximum 0.045%). The use of these steel grades with controlled sulphur content (0.02…0.045%) helps improve steel product surfaces at low cutting speed. At the same sulphur content in steel, the composition and especially the shape and distribution of sulphides (which depends on elaboration, deoxidation and casting) have a strong impact on the cutting workability. It is generally admitted that the sulphide’s inclusions of type I (globular) are preferred over those of type II, with intergranular or eutectic distribution. Industrial and laboratory experiments regarding the determination of quantitative correlations between this steel’s workability and the characteristics of the sulphide inclusions (KZMnS), which assure this property, are presented in table 1. The mean value of the KZMnS has been established through a graduated standard with seven scores (score 0 for fine sulphide inclusions and respectively, score 6 for the rough inclusion), after microscope examination of the metallo-graphic specimen surface, at an x 200 magnifying.

Tabela 1. Korelacija izme|u KZMnS i mogu}nosti obrade ~elika Table 1. The Correlation between KZMnS and the Workability of Steel

KZMnS

Granice-Limits Srednja vrijednost

Mean Value

Pona{anje pri obradi Behaviour at Machining

3,0 2,75 Slabo-Weak

3,0…3,5 3,25 Srednje-Medium

3,5…4,0 3,75 Dobro-Proper

4,0…4,5 4,25 Odgovaraju}e-Adequate

4,5 4,75 Izuzetno-Exceptional

Legiranje sumporom ~ini dodavanje sumpora ili ferosumpora u liva~kom loncu ili pe}i, zajedno sa feromanganom i silikonmanganom za dezoksidaciju. Mogu}e je dodati samo sumpor, pakovan u papirnim vre}icama, me|utim u tom slu~aju je asimilacija sumpora manja, a {irenje je jako veliko.

Adding sulphur or ferro-sulphur makes the sulphur alloying in steel ladle or in furnace, together with the ferromanganese and silicon-manganese for deoxidation. It is possible to add only sulphur, packed in paper bags, but in this case sulphur assimilation is lower and the spread is very high.

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Kod legiranja sumporom, tako|er je mogu}e koristiti neka hemijska jedinjenja sumpora (naprimjer: èljezni sulfid, mangan sulfid ili natrijum sulfid), ali se i u ovim slu~ajevima javljaju isti problemi kao i s direktnim dodavanjem sumpora. Moderno rje{enje za dodavanje sumpora je upotreba punjene ìce.

For sulphur alloying, it is also possible to use some of the sulphur chemical compounds (for example: iron sulphide, manganese sulphide or sodium sulphide), but in these cases the same problems appear as with the direct addition of sulphur. A modern solution for the sulphur addition is the use of filled wire.

2. EKSPERIMENTI I REZULTATI Eksperimenti su ra|eni u elektro ~eli~ani, opremljenoj elektro lu~nim pe}ima, kapaciteta 50 tona, a ~elik je ljevan u ingote kapaciteta 3,5 t. Izabrane su sljede}e radne verzije: I. Ponovno sumporisanje kori{tenjem komada

~istog sumpora; II. Ponovno sumporisanje kori{tenjem gvozdenog

sulfida; III. Ponovno sumporisanje kori{tenjem ferrosumpora

s 29,03% sumpora; IV. Ponovno sumporisanje kori{tenjem ìce punjene

sumporom. Eksperimentirano je sa svim verzijama obrade, kori{tenjem ~elika 33MoCr11, s kona~nim sadràjem sumpora od 0,04%.

2.1. Verzija I Sumpor je dodat u liva~ki lonac, prije izljeva, u papirnim vre}icama. U eksperimentima je kori{teno 8 (osam) razli~itih temperatura, gdje je stepen asimilacije sumpora varirao izme|u 12…58%. Smatra se da su razlozi velikoj varijaciji asimilacije sumpora sljede}i: ▪ relativno niska ta~ka topljenja (1120C) i paljenja (2500C) ~ini koli~inu sumpora te{kom za kontroliranje, te ona onda gori dok dno liva~kog lonca ne bude prekriveno slojem ~elika dubine najmanje 150 mm; ▪ neujedna~eno mje{anje malih komada sumpora s ~eli~nom smjesom, od kojih neki ostaju na povr{ini smjese mnogo duè vremena i sagorijevaju zbog atmosferskog oksigena. Velika varijacija stepena asimilacije sumpora uzrokovala je veliku varijaciju sadràja sumpora u ~eliku, te, u mnogo slu~ajeva, vrijednosti nisu mogle biti unutar odre|enog obima vrijednosti.

2.2. Verzija II Eksperiment je vr{en dodavanjem grudvica gvozdenog pirita dobivenih iz rudnika Băiţa – Haţeg (u okolini Hunedoara), ~iji je srednji sadràj sumpora 45%, a srednji sadràj mangana 3,3%. @eljezni sulfid pluta na povr{ini smjese, me|utim, u pore|enju s ~istim sumporom, djelimi~no je uronjen u ~eli~ni rastop, te je stepen asimilacije izme|u 32…61%, {to je stabilnije u odnosu na prvu verziju.

2. EXPERIMENTS AND RESULTS The experiments have been made at an electric steel plant, equipped with electric-arc furnaces, with the capacity of 50 tones and the steel was cast in ingots of 3.5 tone capacity. We have chosen the following working versions: I. The re-sulphuring using lumps of pure sulphur; II. The re-sulphuring using iron sulphide; III. The re-sulphuring using ferro-sulphur with

29.03% sulphur; IV. The re-sulphuring using wire filled with pure

sulphur. All the working versions have been experimented using the steel grade 33MoCr11 with the sulphur final content of 0.04%.

2.1. Version I Sulphur was added into the steel ladle, before tapping, bagged in paper bags. For experiments we used 8 (eight) heats with the sulphur assimilation degree varying within 12…58%. It is believed that a wide variation of the sulphur assimilation degree is due to the following reasons: ▪ relatively low melting point (1120C) and ignition point (2500C) make the sulphur amount uncontrollable, which then burns until the ladle bottom is covered with a steel layer having at least 150 mm deep; ▪ non-uniform mixing of small sulphur pieces with steel bath, some of them remaining a much longer period of time on the bath surface and burning due to the atmospheric oxygen. Wide variation of the sulphur assimilation degree caused a wide variation of the steel sulphur content and, many times, the values could not be within the imposed range.

2.2. Version II We experimented here the addition of pyrite lumps proceeded from the mine area Băiţa – Haţeg (vicinity of Hunedoara), whose medium sulphur content is 45% and medium manganese content 3.3%. Iron sulphide is floating on the bath surface, however, compared with pure sulphur, it is partly dipped into the steel bath and, thus, the assimilation degree was within the range from 32…61%, which is more stable compared to the first version.

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2.3. Verzija III U ovom slu~aju, ponovna sumporizacija je realizirana uz pomo} ferosumpora, proizvedenog na Ma{inskom fakultetu Hunedoara, u indukcionoj pe}i (kapaciteta 100 kg), koriste}i stari ugljeni~ni ~elik i ~isti sumpor (iz koksare) kao metalno punjenje, sa sadràjem sumpora izme|u 99,2…99,6%, livenog u ingote od 25 kg. [to je manja teìna ingota, to je ve}a hemijska homogenost. Sadràj ferosumpora je varirao unutar malog opsega (28,42…29,64%). Eksperimentirano se pri dvanaest razli~itih temperatura, stepen asimilacije sumpora se kretao izme|u 64…86%. Mada je stepen asimilacije varirao unutar {irokog opsega, hemijski sastav ~elika i odnos Mn/S nametnut da bi se izbjegla drobljivost bili su unutar standardnog opsega.

2.4. Verzija IV Dodavanje punjene ìce je moderno rje{enje za dezoksidaciju i legiranje (naravno samo ako se moè posti}i odgovaraju}a granulacija materijala za punjenje ìce). Punjena ìca pre~nika 15 mm proizvedena je u Buzău (Rumanija). Ma{ina za uranjanje punjene ìce ima dva kanala, φ 15 and φ 13 mm. Brzina uranjanja je bila 4 m/min. Za punjenje ìce kori{ten je sumpor. Stepen asimilacije za 15 razli~itih temperatura je bio izme|u 89…93%, {to je omogu}ilo da hemijski sastav ~elika bude unutar standardnih vrijednosti. To osigurava strogu kontrolu hemijskog sastava, s pozitivnim utjecajem na mogu}nost obrade materijala, na kvalitet povr{ine obra|enog proizvoda i, naravno, na pona{anje u toku rada i radni vijek reznog alata. Stepen varijacije asimilacije sumpora, za analizirane verzije, moè se vidjeti u tabeli 2.

2.3. Version III In this case, the re-sulphuring was realised with ferro-sulphur, produced at the Engineering Faculty of Hunedoara, inside an induction furnace (100 kg capacity), using carbon steel scrap and pure sulphur (from the cocking plant) as metal charge, with the sulphur content within 99.2…99.6%, cast in ingots of 25 kg. The smaller the ingot weight, the greater is the chemical homogenity. The sulphur content of ferro-sulphur varied within a small range (28.42…29.64%). Twelve different heats have been experimented, the sulphur assimilation degree being within 64…86%. Although the assimilation degree varied within a wide range, the chemical composition of steel and the Mn/S ratio imposed for avoiding the friability were within the standardised range.

2.4. Version IV The addition of the deoxidisation and alloying material filled wire is a modern solution for deoxidisation and alloying (of course, only if the respective materials can be brought to a suitable granulation for filling the wire). The filled wire 15 mm in diameter was produced at Buzău (Romania). The machine for dipping the filled wire has two channels, φ 15 and φ 13 mm. The dipping speed was 4 m/minute. For filling the wire, pure sulphur was used. The assimilation degree for 15 heats was within 89…93%, which allowed the chemical composition of the steel to be within the standardised ranges. This assures rigorous control of the chemical composition, with positive effects on the workability of the material, on the surface quality of the processed products and, of course, on the operation behaviour and the working life of the cutting tool. The variation of the sulphur assimilation degree, for the analysed versions, can be seen in the Table 2.

3. ZAKLJU^CI Nakon eksperimenata do{lo se do sljede}ih zaklju~aka: ▪ da bi se pobolj{ala mogu}nost obrade ma{inskog ~elika, mogu se koristiti razli~ite vrste ~elika; ▪ gledaju}i na prethodno navedene verzije, vidi se da se najbolji rezultati postiù upotrebom ìce punjene sumporom; ▪ ve}i tro{kovi proizvodnje punjene ìce se kompenziraju pove}anjem kvalitete ~elika, mogu}nosti obrade proizvoda produènjem vijeka trajanja alatki za rezanje.

3. CONCLUSIONS After the experiments, the following conclusions have been reached: ▪ to improve workability of the engineering, machine building steel, different steel grades can be used; ▪ looking at the above-mentioned versions, it can be observed that the best results are obtained using sulphur filled wire; ▪ greater costs for production of the filled wire are compensated for by increasing the steel quality, the workability of the products and the working life of the cutting tools.

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Tabela 2. Stepen asimilacije sumpora na osnovu eksperimenata Table 2. Sulphur Assimilation Degree According to the Experiments

Stepen asimilacije sumpora, [ % / verzija ] Sulphur Assimilation Degree [ % / verzija ]

Broj eksperimenta verzija

Number of experiments version

Verzija I Version I

Verzija II Version II

Verzija III Version III

Verzija IV Version IV

1 12,34 32,67 64,28 89,31 2 17,65 50,36 69,48 90,32 3 45,29 46,39 71,65 89,54 4 39,56 57,12 73,69 92,98 5 26,86 56,89 85,95 91,16 6 54,38 60,95 84,13 89,67 7 48,35 - 82,26 91,98 8 57,97 - 83,45 92,47 9 - - 81,97 90,75 10 - - 83,15 89,72 11 - - 84,37 92,59 12 - - 85,16 91,68 13 - - - 90,83 14 - - - 90,64 15 - - - 91,24

4. LITERATURA: [1] Al. Rău: “Elaborarea oţelurilor” (The steel

elaboration), Technique Editor–Bucureşti, 1963 [2] Al. Rău, D. Cosma, Gh. Ilin: “Elaborarea

oţelurilor în cuptoare electrice cu arc” (Steel making in electric arc furnaces), Technique Editor – Bucureşti, 1967

[3] V. Brabie, C. Bratu, I. Chira: “Tehnologia elaborării şi turnării oţelului”, (The elaborating and casting technology of steel), Didactic and Pedagogic Editor – Bucureşti, 1979

[4] S. Vacu, and others: “Elaborarea oţelurilor aliate”

(The elaborating of the alloyed steels), Technique Editor – Bucureşti, 1983

Slika 1. - Figure 1 Slika 2. - Figure 2.

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Ma{instvo 3(7), 165 – 174, (2003) A.Gigovi},...: METALNE PJENE

METALNE PJENE

Gigovi} Almaida, dipl.ing., asistent, Fakultet za metalurgiju i materijale, Travni~ka cesta 1, 72 000 Zenica, Bosna i Hercegovina, e-mail:[email protected] Mr. Avdu{inovi} Hasan, dipl.ing., asistent, Fakultet za metalurgiju i materijale, Travni~ka cesta 1, 72 000 Zenica, Bosna i Hercegovina, e-mail:[email protected]

REZIME Metalne pjene su vrsta materijala sa ekstremno niskom gusto}om i izvanrednom kombinacijom mehani~kih, elektri~nih, termi~kih, i akusti~nih osobina. U ovom radu su predstavljene i opisane razli~ite metode za proizvodnju metalnih pjena. Tako|e su predstavljene osobine i neke mogu}e primjene metalnih pjena.

Klju~ne rije~i: metalna pjena, }elijski materijal, na~ini proizvodnje, pjenjenje, osobina, primjena

METAL FOAMS

Gigovic Almaida, B.Sc., Assistant, Faculty of Metallurgy and Materials. Travnicka cesta 1, 72000 Zenica, B&H, e-mail:[email protected] Avdusinovic Hasan, M. Sc. assistant, Faculty of Metallurgy and Materials. Travnicka cesta 1, 72000 Zenica, B&H, e-mail:[email protected] SUMMARY

Metal foams are a class of materials with extremely low densities and an outstanding combination of mechanical, electrical, thermal, and acoustic properties. In this paper, various methods for producing such foams are presented and discussed. The properties and some possible applications for metallic foams a e presented too. r

Key words: metal foam, cellular material, production methods, foaming, property, application

1. UVOD Danas u svakodnevnom ìvotu je {iroko rasprostranjena upotreba }elijskih materijala i oni se koriste za, izolaciju, konstruiranje, za filtriranje i mnoge druge aplikacije. Za visoko porozne materijale je poznato da imaju visoku krutost kombinovanu sa veoma niskom specifi~nom teìnom. To je razlog {to se ~esto materijali koji se nalaze u prirodi (npr.drvo i kosti) koriste kao konstrukcioni materijali. înjenica da ~ak i metali i metalne legure se mogu proizvoditi kao ~vrste }elije ili metalne pjene nije tako dobro poznata kao mogu~nost pjenjenja tradicionalnijih konstrukcionih materijala kao {to su polimeri, keramike ili staklo. Metalne pjene nude interesantnu perspektivu zbog kombinacije osobina koje su povezane sa osobinama metala s jedne strane i poroznom strukturom s druge strane. U posljednjih 40 godina izvode se brojni poku{aji pjenjenja metala ili proizvodnje porozne metalne strukture, ali metode su trpjele zbog relativno visoke cijene i proizvodnje pjenastog materijala lo{eg kvaliteta.

1. INTRODUCTION Cellular materials are widespread in everyday life and are used for cushioning, insulating, constructing, filtering purposes and many other aplications. It is well known that porous materials have high stiffness combined with a very low specific weight. For this reason cellular materials frequently occur in nature as constructional materials (e.g. wood and bones). The fact that even metals and metallic alloys can be produced as cellular solids or metal foams is not as well known as the possibility to foam more traditional engineering materials such as polymers, ceramics or glass. Metallic foams offer interesting perspectives due to the combination of properties which are related to the metallic character on the one and to the porous structure on the other hand. In the past 40 years many attempts have been undertaken to foam metals or to produce porous metallic structures but the methods suffered from relatively high costs and produced only a poor quality foam material.

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Zadnjih deset godina postoje pobolj{anja tako da su nam danas na raspolaganju razli~ite metode za proizvodnju metalnih pjena. Ne postoji jasna i op}enito prihva}ena definicija za izraz “pjena”. Prvo treba postaviti razliku izme|u te~nih i ~vrstih pjena. Te~na pjena je fina disperzija plinskih mjehuri}a u te~nom. Hla|enjem te~ne pjene ispod ta~ke topljenja osnovnog materijala dobije se te~na pjena koja je potom, jasno, ~vrsta pjena. U kontekstu metalnih pjena se op}enito misli na ~vrste metalne pjene. Upotreba rije~i “~vrsta pjena” mo`e se ograni~iti na materijale koji su primarno bili u te~nom stanju. Me|utim, uobi~ajeno je da druge porozne strukture, kao {to je sinterovani metalni prah se ~esto tako|e zovu “pjene”, iako nikad nisu bile u te~nom stanju. Dakle ~esto se pro{iruje upotreba rije~i “pjena” na porozne metalne strukture koje u stvari nisu pjene, ali li~e pjenama uzimaju}i u obzir njihovu visoku poroznost, unutarnju strukturu ~vrstog materijala i njihovu nepravilnu strukturu [1].

In the last ten years there have been improvements so that nowdays various methods for producing metallic foams are available. There is not clear-cut and generally accepted definition of the term «foam». First of all, one has to distinguish between liquid and solid foams. Liquid foam is a fine dispersion of gas bubbles in a liquid. Cooling down liquid foam below the melting point of the respective material yields frozen liquid foam which is then clearly solid foam. What is generally meant in the context of metallic foams are in general solid metallic foams. One could restrict the use of the word «solid foam» to materials which originally were in the liquid state. However, customarily other porous structures such as sintered metal powders are often also called «foams» although they never were in liquid state. Therefore, one often extends the use of the word «foam» to porous metal structures, which are not actually foams but resemble foams in respect to their high porosity, inter-connectivity of the solid material and their irregular structure [1].

2. PROCES PJENJENJA Proces pjenjenja je prili~no komplikovan zato {to u toku pjenjenja nema vremena za dostizanje termodinami~ke ravnote`e. Pjena koja se {iri je kompleksna smjesa plinova, te~ne i ~vrste faze. Razli~iti stepeni evolucije pjene su pokazani na slici 1. Prvi stepen je formiranje pora: iznad temperature rastvaranja agensa koji se ubacuje, gas koji se {iri akumulira se u malim {upljinama u polaznom materijalu, pore se formiraju kako se polazni materijal {iri. Ako se ~vrsti polazni materijal pravi od kompaktiranog praha, uvijek }e postojati dovoljan broj ostataka pora ili oksida koji mogu dijelovati kao centri nukleacije [3].

2. FOAMING PROCESS The foaming process is rather complicated because at no time during foaming is thermodynamic equilibrium reached. The expanding foam is a complex mixture of gaseous, liquid and solid phases. The various stages of foam evolution are shown in Figure 1. The first stage is pore formation: above the decomposition temperature of the blowing agent the evolving gas accumulates in tiny voids in the precursor material, forming a pore as pressure increases. If the solid precursor material is made by compacting powder, there will always be a sufficient number of residual pores or oxide filaments which can act as centres of (heterogeneous) nucleation [3].

Figure 1. Stages of foaming, [2] Slika 1. Faze pjenjenja, [2]

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Dalje pove}anje temperature pove}ava pritisak plina i smanjuje ~vrsto}u metala, koja prakti~no nestaje na ta~ki topljenja: rast pore po~inje i pore se propagiraju plinom koji se {iri. Rast mo`da nije izotropski zato {to tekstura u ~vrstom je nastala na osnovu prirode polaznog materijala. Te~na pjena je nestabilna tako da proces pjenjenja zavr{ava sa kolapsom i dijelimi~nim propadanjem strukture.

Increasing the temperature further increases the gas pressure and reduces the strength of the metal, which practically vanishes at the melting point: pore growth begins and the pores are inflated by the evolving gas. Growth may not be isotropic because of textures in the solid, which originate from the nature of the precursor material. Liquid foam is essentially unstable so that the foaming process ends with collapse and a partial destruction of the structure.

3. NAÎNI PROIZVODNJE Razli~iti na~ini proizvodnje mogu se klasificirati kao: pjene koje se dobijaju iz talina, iz praha, raspr{avanjem i nano{enjem slika 2. Svaka proizvodna metoda pokriva karakteristi~na podru~ja gusto}e, veli~ine }elija i rasporeda }elija. Postoje metode adekvatne za proizvodnju velikih plo~a i blokova. Druge metode su pogodnije za proizvodnju pjenastih dijelova komplikovanijeg oblika. Izme|u svih metoda postoje bar neke koje su jeftinije. Ovo je pogotovo istina za pjene koje su dobijene iz talina ili praha. Uprkos razli~itim metodama proizvodnje postoje samo dva razli~ita na~ina da se obrazuje poroznost: samo-formiranje ili predoblikovanje. U prvom slu~aju, poroznost se obrazovala u samo-evoluacionom procesu koji uklju~uje fizi~ke principe. Metode gdje se poroznost obrazuje pomo}u mjehuri}a plina je samo-formiranje. U slu~aju predoblikovanja, struktura koja se dobije je odre|ena kalupom za oblikovanje }elija.

3.1. Pjenjenje taline uvo|enjem plina (Hydro/Alcan)

Prva metoda pjenjenja aluminija i legura aluminija se eksploati{e u Hydro Aluminium u Norve{koj i Cymat Aluminium Corporation u Kanadi. Saglasno s ovim procesom, {ematski opisanim na slici 3., ~estice silicij-karbida, aluminijum oksida, ili magnezij oksida se koriste da bi se pobolj{ala viskoznost taline. Stoga, prvi korak uklju~uje pripremanje taline aluminija koja sadrì jednu od ovih supstanci, ~ine}i je kompozitom sa metalnim matriksom (MMC). Ovaj korak navodno zahtijeva sloèniju tehniku mje{anja da bi se osigurala jednolika distribucija ~estica. Mogu se koristiti razli~ite legure aluminija. Talina se pjeni u drugom koraku pri uvo|enju plina (zraka, du{ika, argona) unutar taline pomo}u specijalno dizajniranih rotiraju}ih propelera ili vibriraju}ih ubrizgiva~a. Oni stvaraju veoma fine mjehuri}e plina u talini i distribuiraju ih jednoliko. Rezultiraju}a viskozna smjesa mjehuri}a i metalne taline pliva na povr{ini gdje se pretvara u sasvim suhu te~nu pjenu kako se te~ni metal isu{uje.

3. PRODUCTION METHODS The variety of different production methods can be classified: foams made from melts, from powders, by sputtering and by deposition Figure 2. Each production method covers a characteristic range of density, cell size, and cell topology. There are methods adequate for producing large panels and blocks. Other methods are more suitable for small complex shaped foam parts. Among all methods there are at least some which are cheap. This is especially true for foams made from melts or powders. Despite of the variety of production methods there are only two different strategies to generate porosity: self-formation or pre-design. In the former case, the porosity forms in a self-evolution process according to physical principles. Methods where the porosity is generated by gas bubbles are self-forming. In the case of pre-design, the resulting structure is determined by a cell-forming mold.

3.1. Foaming of Melts by Gas Injection (Hydro/Alcan)

The first method of foaming aluminum and aluminum alloys is being exploited by Hydro Aluminium in Norway and by Cymat Aluminium Corporation in Canada. According to this process, described schematically in Figure 3, silicon-carbide, aluminum-oxide, or magnesium-oxide particles are used to enhance the viscosity of the melt. Therefore, the first step comprises the preparation of an aluminum melt containing one of these substances, making it a metal-matrix composite (MMC). This step reportedly requires sophisticated mixing techniques to ensure a uniform distribution of particles. A variety of aluminum alloys can be used. The melt is foamed in a second step by injecting gases (air, nitrogen, argon) into it using specially designed rotating impellers or vibrating nozzles. These generate very fine gas bubbles in the melt and distribute them uniformly. The resultant viscous mixture of bubbles and metal melt floats up to the surface of the liquid where it turns into a fairly dry liquid foam as the liquid metal drains out.

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Precursor/polazni materijal

Stabilization/Stabilizacija

Gas Source/Izvor plina

Foaming/Pjenjenje

Names/Nazivi

Alporas

InstantaneousIstovremeno

Blowing AgentAgens za produvavanje

Oxidation in MeltOksidacija u talini

"Hydro/Alcan"


External Gas SourceVanjski izvor plina

Formgrip/Foamcast

Delayed/Naknadno


Added CeramicsDodatak stabilizatora

Gasar


Dissolved GasOtopljeni plin

Natural ViscosityPrirodna viskoznost

MeltTalina

Foaminal/Alulight

Delayed/Naknadno


Resident OxidesZaostali oksidi

PowderPrah

Metal foamsMetalne pjene

Figure 2. A family tree of metal foams, [4] Slika 2. Postupci dobijanja metalnih pjena, [4]

Figure 3. The foam casting process employed by Cymat for producing flat panels consists of melting and holding furnaces, the foaming box, and foaming equipment, and a twin-belt caster, [2]

Slika 3. Proces livenja pjene u Cymat kompaniji za proizvodnju ravnih plo~a sastoji se od pe}i za topljenje i ~uvanje, posude za pjenjenje i opreme za pjenjenje, i beskona~no duge trake, [2]

Zbog kerami~kih ~estica u talini, pjena je relativno stabilna. Ona se moè skidati sa povr{ine (tj. beskrajnom trakom) i potom se hladi i solidificira. ^vrsta pjena koja se dobije je, u principu, duìne koja se èli, {irine koliko to dozvoljava posuda koja sadrì te~ni metal, i obi~no debljine 10 cm. dio ~estica za oja~avanje se obi~no kre}e od 10% do 20% gdje je srednja veli~ina ~estice od 5�m do 20�m. Izbor veli~ine ~estice i sadràj odre|uje se empirijski. Gusto}a aluminijski pjena proizvedenih na ovaj na~in iznosi od 0,069g/cm3 do 0,54g/cm3, srednja veli~ina ~estice iznosi od 25mm do 3mm, i debljina od 50�m do 85�m. Srednja veli~ina }elije je inverzno vezana i sa srednjom debljinom zida }elije i sa gusto}om i moè se regulisati protokom plina, brzinom propelera, frekvencijom vibriranja duvnice, i drugim parametrima.

Because ceramic particles are in the melt, the foam is relatively stable. It can be pulled off the liquid surface (e.g. with a conveyor belt) and is then allowed to cool down and solidify. The resulting solid foam is, in principle, as long as desired, as wide as the vessel containing the liquid metal allows it, and typically 10 cm thick. The volume fraction of the reinforcing particls typically ranges from 10% to 20% with a mean particle size from 5�m to 20�m The choice of particle size and content has been caried out empirically. The density of aluminium foams produced this way range from 0.069 g/cm3 to 0.54 g/cm3, average pore sizes from 25 mm down to 3mm, and wall thicknesses from 50�m to 85�m. The average cell size is inversely related both to the average cell wall thickness and to the density and can be influenced by adjusting the gas flow, the impeller speed, nozzle vibration frequency, and other parameters.

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Prednosti procesa direktnog pjenjenja su sposobnost kontinuirane proizvodnje velike koli~ine pjene i postizanje niske gusto}e. MMC pjene su, me|utim, jeftinije od drugih }elijskih metalnih materijala. Mogu}i nedostatak procesa direktnog pjenjenja je kona~na potreba za rezanjem pjene, }ime se otvaraju }elije.

Advantages of the direct-foaming process include the capability for continuous production of a large volume of foam and the low densities that can be achieved. MMC foams are, therefore, probably less expensive than other cellular metallic materials. A possible disadvantage of the direct-foaming process is the eventual necessity for cutting the foam, thereby opening the cells.

3.2 Pjenjenje taline agensom koji produvava (Alporas)

Drugi na~in za direktno pjenjenje taline je dodavanje agensa koji se produvava u talinu umjesto uvo|enja plina. Toplota prouzrokuje razlaganje agensa koji se produvava i osloba|anje plina, koji potom pokre}e proces pjenjenja (slika 4.). Shinko Wire Company, Amagasaky, Japan proizvodi pjene na ovaj na~in od 1986 godine sa proizvodnjom od 1.000 kg na dan. U prvom koraku, oko 1,5 mase% kalcij metala se dodaje u talinu aluminija na 680˚C. Talina se mije{a nekoliko minuta, u toku kojih se njena viskoznost kontinuirano pove}ava do faktora pet zbog formiranja kalcij oksida (CaO), kalcij aluminij oksida (CaAl2O4), ili ~ak intermetalne faze Al4Ca, koji zgu{njavaju te~ni metal. Nakon {to je viskoznost dostigla èljenu vrijednost dodaje se titanij hidrid (TiH4), obi~no oko 1,6mase%, koji sluì kao agens i koji treba osloboditi vodik u vreloj viskoznoj te~nosti. Talina potom po~inje polako da se {iri i postepeno ispunjava posudu. Pjenjenje se odvija na konstantnom pritisku. Nakon hla|enja posude ispod ta~ke topljenja legure, te~na pjena prelazi u ~vrstu alumijsku pjenu i moè se vaditi iz kalupa za dalju obradu. Proces pjenjenja moè trajati najmanje 15 minuta za tipi~nu kupku (2,050 mm x 650 mm x 450 mm3). Pjena dobijena na ovaj na~in pod imenom Alporas je izgleda najhomogenija aluminijska pjena koja se trenutno moè dobiti. Empirijski odnos postoji ne samo izme|u srednjeg pre~nika }elije i viskoznosti taline nego i izme|u kona~ne gustine pjene i viskoznosti. Tipi~ne gusto}e nakon obrezivanja stranica livenog pjenastog bloka su izme|u 0,18 g/cm3 i 0,24g/cm3, sa srednjom veli~inom pora koja se kre}e od 2mm do 10mm.

3.3. Eutekti~ka solidifikacija ~vrsto-plin (Gasar)

Metod razvijen prije deset godina koristi ~injenicu da neki te~ni metali obrazuju eutekti~ki sistem sa plinom vodika. Ako jedan od ovih metala se topi u atmosferi vodika pod pritiskom (do 50 atmosfera), rezultat je homogena talina ispunjena vodikom.

3.2. Foaming of Melts with Blowing Agents (Alporas)

The second way for foaming melts directly is by adding a blowing agent to the melt instead of injecting gas into it. Heat causes the blowing agent to decompose and release gas, which then propels the foaming process (Figure 4). Shinko Wire Company, Amagasaky, Japan, has been producing foams in this way since 1986 with production volumes reportedly up to 1,000 kg per day. In the first step, about 1.5wt.% calcium metal is added to an aluminum melt at 680˚C. The melt is stirred for several minutes, during which its viscosity continuously increases because of the formation of calcium oxide (CaO), calcium aluminum oxide (CaAl2O4), or perhaps even Al4Ca intermetallics, which thicken the liquid metal. After the viscosity has reached the desired value, titnium hydride (TiH2) is added (typically 1.6wt.%), serving as a blowing agent by releasing hydrogen gas in the hot viscous liquid. The melt soon starts to expand slowly and gradually fills the foaming vessel. The foaming takes place at constant pressure. After cooling the vessel below the melting point of the alloy, the liquid foam turns into solid aluminum foam and can be taken out of the mold for further processing. The entire foaming process can last 15 minutes for a typical batch (2,050mmX650mmX450mm3). The foams produced in this way - trade name Alporas - seem to be the most homogenous aluminum foams currently available. An empirical relationship exists not only between average cell diameter and the viscosity of the melt but also between the final foam density and viscosity. Typical densities after cutting off the sides of the cast foam blocks are between 0.18 g/cm3 and 0.24 g/cm3, with the average pore size ranging from 2mm to 10mm.

3.3. Solid-Gas Eutectic Solidification (Gasar)

A method developed about a decade ago exploits the fact that some liquid metals form a eutectic system with hydrogen gas. If one of these metals is melted in a hydrogen atmosphere under high pressure (up to 50atms), the result is a homogeneous melt charged with hydrogen.

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Figure 4. Manufacturing process for Alporas Foams, [2]

Slika 4. Proces proizvodnje Alporas pjena, [2] Ako se temperatura sniàva, talina }e kona~no pretrpjeti eutekti~ku tranziciju do heterogenog dvofaznog sistema (~vrsto-plin). Ako sastav sistema je dovoljno blizu eutekti~koj koncentraciji, na jednoj temperaturi }e se javiti reakcija segregacije. Kako talina solidificira, pore plina precipitiraju i ostaju u metalu. Rezultiraju}a morfologija pora je uveliko odre|ena: sadràjem vodika, pritiskom preko taline, pravcem i brzinom uklanjanja toplote, te hemijskim sastavom taline. Op}enito, formiraju se uveliko izduène pore orjentisane u pravcu solidifikacije. Pre~nik pore se kre}e od 10�m do 10mm, duìna pore od 100�m do 300mm, i poroznost od 5% do 75%. Raspodjela veli~ine pora nije jednolika zbog istovremenog rasta malih i velikih pora i sjedinjavanja. Pore mogu biti koni~ne ili ~ak valovite. Rije~ «gasar» je uzeta da bi uputila na porozni materijal dobijen eutekti~kom solidifikacijom ~vrsto-plin. Ona je ruski akronim koji zna~i «oja~an-plinom).

3.4. Pjenjenje pra{kastog kompakta (Foaminal/Alulight)

Pjenasti metal tako|e se moè pripremiti iz metalnog praha. Proces proizvodnje po~inje sa mje{anjem metalnih prahova, elementarnih metalnih prahova, legiranih metalnih prahova, ili mje{avine metalnog praha sa agensom koji produvava, nakon ~ega se smjesa kompaktira do date gusto}e, polufinalnog proizvoda (slika 5). Kompakcija se postiè kori{tenjem bilo koje tehnike u kojoj se agens koji produvava uvodi u metalni matriks bez ikakvih zabiljeènih ostataka otvorene poroznosti. Primjeri ovakvih metoda za kompakciju su jednoaksijalna ili izostati~ko sabijanje, istiskivanje ili valjanje praha. Polazni materijal mora biti proizveden veoma pa`ljivo zbog ostataka poroznosti ili drugih defekata {to }e dovesti do slabijih rezultata u budu}oj obradi.

If the temperature is lowered, the melt will eventually undergo a eutectic transition to a heterogeneous two-phase system (solid+gas). If the composition of the system is sufficiently close to the eutectic concentration, a segregation reaction will occur at one temperature. As the melt is solidified, gas pores precipitate and are entrapped in the metal. The resulting pore morphologies are largely determined by the hydrogen content, the pressure over the melt, by the direction and the rate of heat removal, and by the chemical composition of the melt. Generally, largely elongated pores oriented in the direction of solidification are formed. Pore diameters range from 10�m to 10mm, pore lengths from 100�m to 300 mm, and porosity from 5% to 75%. The pore size distribution is non-uniform because of concurrent growth of small and large pores and coalescence. Pores may be conical or even corrugated. The word “gasar” was coined to refer to the porous materials formed by solid-gas eutectic solidification. “Gasar” is a Russian acronym meaning «gas-reinforced».

3.4. Foaming of Powder Compacts (Foaminal/Alulight)

Foamed metals can also be prepared from metal powder. The production process begins with mixing the metal powders-elementary metal powders, alloy powders, or metal powder blends-with a blowing agent, after which the mix is compacted to yield a dense, semi-finished product (Figure 5). The compaction can be achieved using any technique in which the blowing agent is embedded into the metal matrix without any notable residual open porosity. Examples of such compaction methods are uniaxial or isostatic compression, rod extrusion, or powder rolling. The precursor has to be manufactured very carefully because residual porosity or other defects will lead to poor results in further processing.

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Slijede}i korak je termi~ki tretman na temperaturama blizu ta~ke topljenja osnovnog materijala. Agens koji se {iri, koji je homogeno raspore|en unutar gustog metalnog matriksa, razla`e se i osloba|a plin koji primorava polazni materijal da se {iri, obrazuju}i visoko poroznu strukturu. Vrijeme potrebno za potpuno {irenje zavisi od temperature i veli~ine polaznog materijala i kre}e se od nekoliko sekundi do nekoliko minuta. Metoda nije ograni~ena na aluminij i njegove legure; kalaj, cink, mesing, olovo, zlato i neki drugi metali i legure mogu se tako|e pjeniti sa odgovaraju}im agensom koji se {iri i parametrima procesa. Ako komad polaznog materijala se pjeni u pe}i, rezultat }e biti komad metalne pjene sa nedefinisanim oblikom bez ograni~enja za {irenje. Dijelovi komplikovanog oblika mogu se proizvoditi uvo|enjem pjene koja je u fazi {irenja iz rezervoara unutar odgovaraju}eg kalupa. Ovo je u~injeno smje{tanjem polaznog materijala unutar {upljeg kalupa i {irenjem istog uslijed zagrijavanja, oblikuju se near-net shape komadi sa zatvorenom spolja{nom povr{inom i jezgrom koje je visoko porozno. Metoda topljenja pra{kastog kompakta je u maloj mjeri komercijalna u Njema~kim kompanijama Schunk (Giessen) i Honsel (Meschede) i Austrijskim kompa-nijama Alulight (Ranshofen) i Neuman Alufoam (Marktl). Imena «Foam-in-Al» i «Alulight» su uzeta za ove pjene.

Thethe agedengasformfor sizesecrestleadalsoproIf furnwithlimipreby closComthe mosmaSchAusNeuand

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Figure 5. Powder metallurgical process for foamed metals production, [2]

Slika 5. Proces pra{kaste metalurgije za proizvodnju pjenastih metala, [2]

next step is heat treatment at temperatures near melting point of the matrix material. The blowing nt, which is homogenously distributed within the se metallic matrix, decomposes and the released forces the melting precursor material expand, ing its highly porous structure. The time needed full expansion depends on the temperature and of the precursor and ranges from a few onds to several minutes. The method is not ricted to aluminum and its alloys; tin, zinc, brass, , gold, and some other metals and alloys can be foamed with appropriate blowing agents and cess parameters. a piece of precursor material is foamed in a ace, the result will be a lump of metal foam an undefined shape unless the expansion is ted. This can be avoided by inserting the cursor material into a hollow mold and expanding it heating, creating near-net shaped parts with a ed outer skin and highly porous cellular core. plicated parts can be manufactured by injecting still-expanding foam from reservoir into suitable

lds. The powder-compact melting method is in ll-scale commercial by the German companies unk(Giessen) and Honsel (Meschede) and the trian companies Alulight (Ranshofen) and man Alufoam (Marktl). The names «Foam-in-Al» «Alulight» have been coined for these foams.


3.5. Pjenjenje ingota koji sadrè agens koji se {iri (Formgrip/Foamcast)

Proces topljenja kompaktiranog praha je nedavno modifikovano uvo|enjem ~estica titanij hidrida unutar taline aluminija umjesto praha da bi se pripremio polazni materijal koji se moè pjeniti. Da bi se izbjeglo prerano {irenje vodika talina se mora ili brzo hladiti ispod njene ta~ke topljenja nakon mje{anja ili agens koji se {iri mora se pasivizirati da bi se onemogu~ilo njegovo {irenje prije solidifikacije. Prva tehnika, nazvana «Foamcast» se izvodila u ma{ini za livenje u kalupe, gdje se pra{kasti hidrid ubacivao unutar kalupa uporedo sa talinom. Koristile su se obi~ne legure za livenje kao {to je A356 bez kerami~kih dodataka. Liveni komad koji se dobio imao je prakti~nu gusto}u i mogao se pjeniti pretapanjem analogno metodi na bazi praha koja je predhodno opisana. Me|utim, izaziva se homogena raspodijela TiH2 praha u kalupu. Drugi spomenuti na~in zahtijeva da TiH2 prah se podvrgava termi~kom tretmanu tako obrazuju}i oksidnu povr{inu na svakoj ~estici i odlaè razlaganje. Prahovi se potom dodaju u talinu i nakon mje{anja mogu se hladiti na uporednim malim brzinama. Koriste se taline koje sadrè silicij karbide da bi se postigla stabilnost pjena. Na proces pjenjenja se moè utijecati mjenjanjem brzina zagrijavanja i kona~nim temperaturama pjenjenja, tako dozvoljavaju}i proizvodnju struktura sa razli~itim porama. Proces se zove «Formgrip», {to je akronim za pjenjenje oja~anog metala uslijed osloba|anja plina u polaznom materijalu [4].

3.5. Foaming of Ingots Containing Blowing Agents (Formgrip/Foamcast)

The powder-compact melting process has recently been modified by incorporating titanium-hydride particles directly into an aluminum melt instead of using powders to prepare a foamable precursor material. To avoid premature hydrogen evolution the melt has to be either quickly cooled down below its melting point after mixing or the blowing agent has to be passivated to prevent it from releasing gas before solidification The former technique, named “Foamcast”, was carried out in a die-casting machine, when the powdered hydride was injected into the die simultaneously with the melt. Normal casting alloys such as A356 without ceramic additives were used. The resulting cast part was virtually dense and could be foamed by re-melting in analogy to the powder-based method described previously. However, achieving a homogenous distribution of TiH2 powders in the die is challenging. The latter route requires that TiH2 powders be subjected to a cycle of heat treatments that form an oxide barrier on each particle and delay decomposition. The powders are then added to a melt and can be cooled at comparatively slow rates after stirring. Melts containing silicon carbide are used to obtain stable foams. The foaming process can be influenced by varying heating rates and final foaming temperatures, thus allowing the production of a variety of different pore structures. The process has been named “Formgrip”, which is an acronym of foaming of reinforced metals by gas release in precursor [4].

4. OSOBINE I PRIMJENA Mehani~ke i fizi~ke osobine metalnih pjena su blisko povezane sa njihovom }elijskom strukturom (otvorenom ili zatvorenom) i relativnom gusto}om. I jedno i drugo jako zavise od postupka proizvodnje i proizvodnih parametara. Va`no je napomenuti da specifi~ne mehani~ke i fizi~ke osobine }elijskih metala se uvijek lo{ije u pore|enju sa osobinama njima pripadaju}ih kompaktnih materijala. To vrijedi za za module elasti~nosti, ~vrsto}a i sposobnost apsorbcije energije tako|e. Zbog toga upotreba }elijskih materijala moè biti jedino efikasna ako se koriste odre|ene konstrukcione osobine. Najo~iglednija osobina koja je rezultat }elijske strukture je mala masa. Slijede}i efekat }elija je pove}anje momenta inercije zbog odvojenih masa. Kao rezultat }elijske strukture vidi se visoka specifi~na krutost vezivanja i ~vrsto}a koje se mogu dalje pobolj{ati konstrukcijom sendvi~a gdje su dvije guste povr{ine odvojene pjenastim jezgrom.

4. PROPERTIES AND DERIVED APPLICATIONS

Mechanical and physical properties of metal foams are intimately related to their cellular structure (open or closed) and relative density. Both are strongly dependent on the production method and the production parameters. It is important to notice that the specific mechanical and physical properties of cellular metals always compare badly with their bulk properties. This is true for the elastic modules, the strength and also the energy absorption ability. That is, the use of cellular materials can only be efficient if the structural properties are explicity used. The most obvious property resulting from the cellular structure is the lightness. A further effect of the cells is to increase the moment of inertia due to mass separation. As a result cellular structures show a high specific bending stiffness and strength which can be further improwed by a sandwich construction with two dense face sheets separated by a foam core.

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Suprotno gustim materijalima }elijski materijali mjenjaju njihovu gusto}u kad se deformi{u. [to je deformacija duè elasti~na to je homogenije raspore|ena. Reìm plasti~nosti se opisuje uzastopnim propadanjem }elija koje se nalaze vezane u nizu. Dokle god postoje preostale primarne }elije napon ostaje na niskom ili pribli`no konstantnom nivou. Ovo pona{anje dozvoljava apsorbciju energije na niskom nivou napona. ]elijske strukture mogu tako|e pomo}i apsorbciji energije zvuka. Jedan vaàn mehanizam rasipanja za generiranu energiju u zvu~nom talasu su gubici trenja kad plin prolazi od jedne do druge }elije. Tj.,da bi bili dobri za apsorbciju zvuka, }elije moraju biti povezane jedna s drugom. ]elijske strukture tako|e se mogu koristiti za termi~ko upravljanje. S jedne strane }elijska konstrukcija vodi veoma niskoj termi~koj provodnosti koja se moè iskoristiti za termi~ku izolaciju. S druge strane visoka termi~ka provodnost materijala }elijskog zida kombinovana sa visokom unutra{njom povr{inom su idealne za izmjenjiva~e toplote.Karakteristi~ne osobine, primjena a i kona~ni oblik proizvoda su prikazani u Tabeli 1, [2]. Va`no je podvu}i da najve}i potencijal }elijskih metala je u njihovoj izvanrednoj kombinaciji osobina, tj., skoro uvijek postoje bolja rje{enja ako se misli samo na jednu osobinu. Ako mora biti zadovoljeno vi{e od jedne osobine, apsorbcija zvuka i termi~ka stabilnost, isti~e se prednost metalnih pjena.

5. ZAKLJU~CI ]elijski materijali nude veliki potencijal za industrijsku primjenu. Pored toga, osim cijene postoje brojna tehni~ka pobolj{anja neophodna da bi se dobila {ira upotreba. Jedna va`na ta~ka je homogenost. Ako je pjena nehomogena rasipanje mehani~kih osobina je jako visoko. Posebno vaàn efekat nehomogenosti je drasti~an pad sposobnosti apsorbcije energije. Homogenost nije jednak problem za sve na~ine proizvodnje. Posebne metode bazirane na statisti~kom procesu samo-formiranja ~esto podlijeè lo{oj homogenosti. Op}enit izazov je ~injenica da mehani~ke osobine metalnih pjena veoma ~esto ostaju daleko iza njihovih teoretskih mogu}nosti. Mnogi defekti odgovorni za inferiorno izvo|enje su ve} identifikovani i poznat je na~in njihovog izbjegavanja. Mnoge aplikacije zahtijevaju da je }elijska struktura okruèna gustim povr{inskim slojem da bi je u~inilo pogodnom za visoko optere}ene konstrukcione komponente.

In contrast to dense materials cellular materials change their density when they are deformed. As long as the deformation is elastic it is homogenously distributed. The plastic regime is characterized by a successive collapse of cells localized in bands. While there are non-collapsed cells left the stress remains at a low and nearly constant level. This behavior allows energy absorbtion at a low stress level. Cellular structures can also help to absorb sound energy. One important dissipation mechanism for the energy stored in a sound wave are friction losses when gas flows from one to another cell. That is, in order to be a good sound absorber the cells have to be connected with each other. The cellular structures can also be used for thermal management On the one hand the cellular construction leads to a very low thermal conductivity which can be utilized for thermal insulation. On the other hand the high thermal conductivity of the cell wall material (metals) combined with the high internal surface are ideal for compact heat exchangers. The outstanding properties and the derived applications are listed in Table 1, [2]. It is important to emphasize that the greatest potential of cellular metals is seen in their extraordinary combination of properties. That is, there are almost always better solutions to meet a single demand. If more than one property must be satisfied at once, e.g., sound absorption and thermal stability, the advantages of metal foams emerge. Table 1 also indicates the product form required by the application [4].

5. CONCLUSION Cellular metals offer a large potential for industrial application. Nevertheless, besides the costs there are a lot of technical improvements necessary in order to gain more widespread use. One important points is the homogeneity. If the foam is inhomogenous the scatter in the mechanical properties is very high. A particularly important effect of inhomogeneity is a drastic drop of the energy absorbtion efficiency. Homogeneity is not equally a problem for all production routes. Especially methods based on a statistical self-forming process often suffer from a bad homogeneity. A general challenge is the fact that the mechanical properties of metal foams very often stay far behind their theoretical possibilities. Many defects responsible for the inferior performance have already been identified. How to avoid them is less clear at the moment. Many applications require the cellular structure to be surrounded by a dense surface layer in order to make them suitable

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[iroka je i upotreba kompleksnih aluminijskih pjenastih dijelova kao trajnih jezgara u aluminijskim odlivcima ili jednostavno da bi se izbjegla penetracija vlage. ]elije vidljive strukture sa zatvorenim }elijama su u stvarnosti ~esto spojene jedna sa drugom malim pukotinama, {to nije ne zanemarivo i jo{ se razmatra.

for highly loaded structural components, to use complex foamed aluminum parts as permanent cores in aluminum castings or simply to avoid the penetration of moisture. Since the cells of apparently closed-cell structure are in reality often connected with each other by small cracks, this is not trivial and still a matter of research.

Table 1. Characteristic properties, resulting aplications, and necessary product forms for metal foams, [2] Tabela 1. Karakteristi~ne osobine, primjena i neophodan oblik proizvoda za metalne pjene, [2]

Property Osobine

Application Primjena

Product form Oblik proizvoda

-High specific bending stiffness and strength -Visoka specifi~na krutost vezivanja i ~vrsto}a

-Stiff and super light-weight panels for transport and architecture -Krute i super lagane plo~e za transport i arhitekturu

-Shaped parts - Oblikovani dijelovi -(Sandwich) panels - (Sendvi}) plo~e -3d-shaped (sandwich) panels -3d-oblikovane (sendvi}) plo~e

-Isotropic absorbtion of impact energy at a nearly constant low stress level -Izotropska apsorbcija udarne energije na skoro konstantno niskom nivou napona

-Impact energy absorbtion components in cars -Apsorbcija udarne energije u automobilskim dijelovima -Packaging -- Pakovanje -Blast protection - Za{tita od strujanja

-Shaped parts -Oblikovani dijelovi -Large panels -Velike plo~e

-Good sound absorption, electromagnetic shielding, and vibration damping -Dobra apsorpcija zvuka, elektromagnetska za{tita i prigu{ivanje vibracija

-Self-supporting wall panels -Samopodr`avaju}e zidne plo}e -Housing for electronic devices -Ku}i{ta za elektronske ure|aje -Machine casing for sound absorption -Obloge ure|aja za apsorbciju zvuka -Soundproof walls along railway tracks and roads -Zvu~ne izolacije du` `eljeznica i puteva

-Large panels -Velike plo~e -Sandwich panels -Plo~e u obliku sendvi~a

-High thermal stability and low thermal conductivity -Visoka termi~ka stabilnost i niska termi~ka provodnost

-Heat shields -Toplotne za{tite

-Large panels -Velike plo~e

-Decorative, non-combustible, weather resistant -Dekorativne, ne zapaljive, otporne na vanjske uticaje

-Furniture -Namje{taj -Wall panels -Zidne plo~e

-Large panels -Velike plo~e -Shaped parts -Oblikovani dijelovi

-Light-weight -Mala masa

-Sand core replacement -Zamjena za pje{}ana jezgra -Floating structures -Konstrukcije koje plove

-Complex shaped parts with a dense surface skin -Dijelovi kompleksnog oblika sa gustim povr{inskim dijelom

-High inner surface -Visoka unutra{nja povr{ina

-Compact heat exchangers -Kompaktni izmjenjiva~i toplote -Catalyst support - Katalizatori -Cyrogenic applications -Kriogenska primjena

-Complex open-cell parts -Dijelovi kompleksnog oblika sa otvorenim porama

6. LITERATURA-REFERENCES [1] J. Banhart, J. Baumeister, “Production methods

for metallic foams”, Porous and Cellular Materials for Structural Applications, MRS/ Materials Reserch Society, Warrendale, Pennsylvania, 1998

[2] C. Körer, R.F.Singer, “Processing of Metal

Foams-Challenges and Opportunities”,

Advanced Engineering Materials No.4 (2000) 2, 159-165

[3] J. Banhart, “Foam Metal: The Recipe”,

Europhysics news, january/february 1999, 17-20 [4] J. Banhart, “Manufacturing Routes for Metallic

Foams”, JOM, decembre 2000, 22-27

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