letnik/volume 52 - {t./no. 5/06 - str./pp. 267-338 Ljubljana, maj/May 2006, zvezek/issue 493 STROJNIŠKI VESTNIK JOURNAL OF MECHANICAL ENGINEERING cena 800 SIT 770039 248001 ISSN 0039-2480 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 267 Vsebina - Contents Vsebina - Contents Strojniški vestnik - Journal of Mechanical Engineering letnik - volume 52, (2006), številka - number 5 Ljubljana, maj - May 2006 ISSN 0039-2480 Izhaja mesečno - Published monthly Razprave Papers Lerher, T., Potrč, I.: Načrtovanje in optimiranje Lerher, T., Potrč, I.: The Design and Optimization of avtomatiziranih regalnih skladiščnih sistemov 268 Automated Storage and Retrieval Systems Leskovar, M., Končar, B., Cizelj, L.: Simuliranje Leskovar, M., Končar, B., Cizelj, L.: Simulation of a eksplozije pare v reaktorski votlini s splošnim Reactor Cavity Steam Explosion with a General programom za računsko dinamiko tekočin 292 Purpose Computational Fluid Dynamics Code Kulvietiene, R., Kulvietis, G., Tumasoniene, I.: Kulvietiene, R, Kulvietis, G, Tumasoniene, I.: A Simbolno-številčno analiziranje nihanj Symbolic-Numeric Vibrations Analysis of sistemov z velikimo številom stopenj prostosti 309 Systems with Many Degrees of Freedom Štubna, I., Trnik, A.: Popravni količniki za izračun Štubna, I., Trnik, A.: Correction Coefficients for Cal- Youngoveg amodula iz resonančnega culating the Young’s Modulus from the Reso- upogibnega nihanja 317 nant Flexural Vibration Drev, D., Panjan, J.: Teoretične in eksperimentalne Drev, D., Panjan, J.: Theoretical and Experimental osnove za izdelavo mehanskih izolacijskih Foundations for the Manufacturing of pen 323 Mechanical Insulation Foams Osebne vesti Personal Events Doktorati, magisteriji in diplome 335 Doctor’s, Master’s and Diploma Degrees Navodila avtorjem 337 Instructions for Authors Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 UDK - UDC 621.86:658.78 Izvirni znanstveni članek - Original scientific paper (1.01) Načrtovanje in optimiranje avtomatiziranih regalnih skladiščnih sistemov The Design and Optimization of Automated Storage and Retrieval Systems Tone Lerher - Iztok Potrč (Fakulteta za strojništvo, Maribor) V predloženem prispevku je predstavljen model za načrtovanje in optimiranje avtomatiziranih regalnih skladiščnih sistemov za delo v enem in več hodnikih. Zaradi zahtevanega pogoja o tehnično zelo zmogljivem in stroškovno sprejemljivem skladiščnem sistemu, predstavljajo namensko funkcijo v računskem modelu načrtovanja najmanjši skupni stroški. Namenska funkcija združuje elemente statičnega in dinamičnega dela skladiščnega sistema ter investicijske in obratovalne stroške skladišča. Zaradi nelinearnosti, večparametričnosti in diskretne oblike namenske funkcije smo za optimizacijo projektnih spremenljivk uporabili metodo genetskih algoritmov. Prikazana je analiza izbranega regalnega skladiščnega sistema, pri dveh različnih sistemih regalnega dvigala za delo v enem in več hodnikih. Ugotovili smo, da so stroškovno optimalne rešitve skladišč nahajajo v področju visokih in dolgih skladiščnih regalih, kar vpliva na zmanjšanje števila regalnih hodnikov in števila regalnih dvigal ter skupno na celotne stroške skladišča. Rezultati analize so pokazali, da je izbira posameznega sistema regalnega dvigala, za delo v enem ali več hodnikih, izrazito odvisna od zahtevane pretočne zmogljivosti skladišča. Predloženi model predstavlja uporabno in prilagodljivo orodje za načrtovanje skladiščnih sistemov ter izbiro posameznega sistema regalnega dvigala za delo v enem ali več hodnikih v postopku načrtovanja regalnih skladiščnih sistemov. © 2006 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: sistemi skladiščni, skladišča avtomatizirana, načrtovanje, optimiranje) In this paper a model for the design and optimization of an automated storage-and-retrieval system for single- and multi-aisle systems is presented. Because of the required conditions, i.e., that the warehouse should be technically highly efficient and that it should be designed at reasonable expense, the objective function is represented by minimum total costs. The objective function combines elements of the static and dynamic parts of the warehouse, the investment, and the operational costs of the warehouse. Due to the nonlinear, multi-variable and discrete shape of the objective function, the method of genetics algorithms was used for the optimization process of the decision variables. An analysis of the chosen automated warehouse with two types of the single- and multi-aisle automated storage and retrieval systems is presented. It was established that the optimum solutions regarding total costs of the warehouse can be found in the area of high and long storage racks. Consequently, this influences the reduction of the number of picking aisles and the number of storage and retrieval machines. The results of the analysis show that the choice of a type of single- or multi-aisle system depends crucially on the required throughput capacity of the warehouse. The presented model is a very useful and flexible tool for choosing a particular type of single- or multi-aisle system when designing automated warehousing systems. © 2006 Journal of Mechanical Engineering. All rights reserved. (Keywords: storage systems, automated warehousing systems, design, optimization) 0 UVOD 0 INTRODUCTION Skladišča s svojim osnovnim namenom so nujno potrebna za zvezno in optimalno delovanje tako proizvodnih kakor tudi oskrbnih postopkov. Žal The key feature of a warehouse is the absolute necessity for the continuous and optimum operation of the production and distribution processes. 268 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 so bili v preteklosti skladiščni, transportni in pretovorni postopki močno zapostavljeni, kar se še dandanes izkazuje v razmeroma nizki stopnji avtomatizacije v primerjavi s stanjem v proizvodnji. Skladišča so potrebna iz številnih razlogov, ki jih lahko razporedimo v naslednje skupine [1]: (i) neusklajen dotok in odtok blaga zaradi neustrezne dinamike v proizvodnji in porabi, (ii) prevzemanje blaga številnih izdelovalcev za izdelavo kombiniranih odprem, (iii) izvedba dnevne preskrbe blaga v proizvodnji in dostavi, (iv) izvedba dodatnih dejavnosti, kakor so pakiranje, končna montaža itn. Skladišča predstavljajo blagovno-tehnični del gospodarjenja z blagom ter glede na zapostavljenost v preteklosti predstavljajo priložnost pri zmanjšanju skupnih stroškov pri načrtovanju in obratovanju skladišča. V prispevku so predstavljena avtomatizirana skladišča, ki jih imenujejo tudi avtomatizirani regalni skladiščni sistemi (ARSS). V zadnjih desetletjih se izdatno povečuje delež ARSS, ki omogočajo doseganje večjih zmogljivosti v primerjavi z običajnimi skladišči. Razmišljanja o uporabi ARSS segajo že desetletja nazaj, ko je leta 1962 podjetje Demag izdelalo prvi ARSS [2]. Omenjeni ARSS je bilo prvo visoko regalno skladišče višine 20 metrov in je zaznamoval novo obdobje v razvoju transportno-skladiščne tehnike. ARSS so v osnovi sestavljeni iz skladiščnih regalov (SR), regalnega dvigala (RD), zveznih transporterjev, vhodne in izhodne (V/I) lokacije skladišča in računalniškega sistema za vodenje in organizacijo skladiščne dejavnosti. Glavne prednosti v primerjavi z običajnimi sistemi skladišč se izkazujejo z: (i) veliko pretočno zmogljivostjo skladišča Pf, (ii) velikim izkoristkom zalogovnega skladišča Q, (iii) veliko zanesljivostjo in večjim nadzorom skladiščnega postopka, (iv) izboljšanimi varnostnimi razmerami in (v) zmanjšanjem poškodb ter izgube blaga. Zaradi njihove tehnološke popolnosti in popolne avtomatizacije sistema, zahtevajo velike investicijske stroške. Prav tako so ARSS, pri katerih RD oskrbuje samo pripadajoč regalni hodnik, neprilagodljivi glede na morebitno spremembo pretočne zmogljivosti skladišča. Uspešnost izvedbe ARSS je odvisna predvsem od preudarnega in učinkovitega postopka načrtovanja, da bo izpolnjen glavni pogoj o tehnično zelo zmogljivem sistemu, ob predpostavki o optimalnih investicijskih in obratovalnih stroških skladišča. Zmogljivost ARSS je v največji meri odvisna od zmogljivosti transportno-skladiščnega Unfortunately, in the past, warehousing, transport systems and transferring processes were neglected, and this nowadays shows itself in a relatively low degree of automation in comparison with the production process. Warehouses are needed for the following reasons [1]: (i) an imbalance in the flow and outflow of goods due to the inappropriate dynamics of production and consumption, (ii) taking goods from numerous producers for the production of combined shipments, (iii) the realization of the daily supply of goods in the production and distribution, (iv) the realization of additional activities, such as packaging, final assembly, etc. Warehouses represent a technical part of dealing with goods. Since they were neglected in the past, they represent an opportunity to reduce total costs relating to the design and operation processes. In this study, automated warehouses, also named automated storage and retrieval systems (ASRS), are presented. In the past few decades, the share of ASRS, which in comparison with conventional warehouses provides a higher level of technological efficiency, has increased. The use of the ASRS already received consideration decades ago, when in 1962 the company Demag created the first ASAR [2]. The aforementioned ASRS was the first high-bay warehouse measuring 20 meters in height, which marked the beginning of a new era in the development of material handling equipment in Europe. The ASRS consists of storage racks (SRs), a storage and retrieval machine (SR machine), accumulating conveyors, an input and output location (I/O location) and a computer system for managing and organizing the activities in the warehouse. In comparison with conventional warehousing systems, the key advantages of the ASRS are: (i) high throughput capacity Pf, (ii) high warehouse volume Q (rack capacity), (iii) high reliability and better control of the warehousing process, (iv) improved safety conditions and (v) a decrease in the amount of damage and the loss of goods. Due to advanced technology and the complete automation of the system, the ASRS demands extensive investment. Additionally, those ASRSs where the SR machine operates only in the single picking aisle are rather inflexible as far as a possible change of the throughput capacity of the warehouse is concerned. The success of the ASRS largely depends on a careful and efficient design process, whereby the basic condition that the system is technically highly efficient must be fulfilled, along with the condition of optimum investment and the operational costs of the warehouse. The efficiency of the ASRS mainly depends on the efficiency of the material Načrtovanje in optimiranje avtomatiziranih regalnih - The Design and Optimization of Automated Storage 269 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 sredstva in vrste transportno-skladiščne enote TSE. V tipičnem ARSS samostojno RD oskrbuje samo pripadajoči regalni hodnik, kar imenujemo sistem RD za delo v enem hodniku. V primeru zahteve po manjši pretočni zmogljivosti in večji prilagodljivosti skladišča, uporabimo sistem RD za delo v več hodnikih ([4] do [6]). V omenjenem sistemu RD z uporabo pomičnega vozička, ki zagotavlja vožnjo v prečnem hodniku, oskrbuje več regalnih hodnikov. Ker zahteva RD tudi do 40 % [3] vrednosti celotne investicije ARSS, je izbira sistema RD za delo v enem in več hodnikih eno izmed ključnih vprašanj pri načrtovanju skladišč. Zmogljivost ARSS je odvisna tudi od geometrijske oblike SR in ustrezne skladiščne strategije. Načrtovanje in optimiranje skladiščnih sistemov (ne nujno ARSS) so v preteklosti obravnavali številni avtorji. Ena izmed prvih objav s področja optimizacije skladišča je delo Basana in sodelavcev [7], ki so analizirali optimalne izmere skladišča pri izbrani zalogovni velikosti skladišča v odvisnosti od različnih skladiščnih strategij. Karasawa in sodelavci [8] so predstavili model za načrtovanje ARSS. V njihovem delu je namenska funkcija definirana kot nelinearna in večparametrična ter se sestoji iz treh glavnih spremenljivk: (i) števila RD, (ii) dolžine SR in (iii) višine SR; ter nespremenljivih vrednosti: stroškov za nakup zemljišča, stroškov za izdelavo skladiščne zgradbe, stroškov za nakup regalne konstrukcije in stroškov za nakup regalnih dvigal. Pomanjkljivost modela [8] je, da se navezuje samo na sistem RD za delo v enem hodniku in skladiščno opravilo enojnega delovnega kroga. Ashayeri in sodelavci [9] so predstavili model načrtovanja ARSS, ki omogoča določitev glavnih vplivnih parametrov pri načrtovanju skladišč. V nasprotju s Karasawo in sodelavci [8], so avtorji upoštevali skladiščno opravilo dvojnega delovnega kroga. Bafna in sodelavci [10] ter Perry in sodelavci [11] so pri načrtovanju skladiščuporabili kombinacijo analitičnega modela in sistema diskretnih numeričnih simulacij. Pri tem so Perry in sodelavci [11] uporabili posebno iskalno metodo za določitev optimalnih rešitev ARSS, ki so jo vključili v simulacijski model ARSS. Za merilo zmogljivosti sistema so uporabili pretočno zmogljivost skladišča, v odvisnosti od števila RD ter števila delovnih mest. Načrtovanje skladišč z upoštevanjem vpliva skladiščno-upravljalne strategije sta predstavila Rosenblatt in Roll [12]. Pri opisu skupnih stroškov sta upoštevala, da so le-ti odvisni od: (i) stroškov za izgradnjo handling equipment and the type of transport unit load (TUL). In a typical ASAR, the SR machine independently operates only in the single picking aisle, which is called a single-aisle ASRS. In the case of smaller throughput capacities and higher flexibility of the warehouse, the multi-aisle ASRS is used ([4] to [6]). In the above-mentioned system, the SR machine serves several picking aisles with the help of the aisle transferring vehicle, which ensures driving in the cross aisle. Since the SR machine takes up to 40% [3] of the entire investment of the ASRS, the choice between a single- and multi-aisle ASRS is of key importance for the design of the automated warehouse. The efficiency of the ASRS is also dependent on the layout of the SR and the appropriate storage strategy. The design of warehouses (not necessarily ASRS) has been studied in the past by several authors. One of the first publications on the subject of optimizing warehouses is the work of Basan et al. [7], who analyzed the optimum dimensions of the warehouse, considering the chosen volume of the warehouse and the dependence on various storage strategies. Karasawa et al. [8] presented a design model of the ASRS. In their work, the objective function is defined as non-linear and multi-variable, consisting of three main variables: (i) the number of SR machines, (ii) the length of the SR and (iii) the height of the SR; and also of constant values: the cost of buying the land, the cost of building the warehouse, the cost of buying the SR construction and the cost of buying the SR machines. The main disadvantage of this model [8] is that it refers only to the single-aisle ASRS and the warehousing operation of the single command cycle (SC). Ashayeri et al. [9] presented a design model of the ASRS that enables the determination of the main influential parameters when designing warehouses. Unlike Karasawa et al. [8], they considered the warehousing operation of the dual command cycle (DC). Bafna et al. [10] and Perry et al. [11] used a combination of an analytical model and a system of discrete event simulations when designing the warehouse. Perry et al. [11] used a special search method to determine the optimum solutions for the ASRS, which they have included in the simulation model of the ASRS. As a measure of the efficiency of the system, they used the throughput capacity of the warehouse, with its dependence on the number of SR machines and the number of workplaces. The design of warehouses with regard to the influence of the storage policy was presented by Rosenblatt 270 Lerher T. - Potrč I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 skladiščne zgradbe, (ii) stroškov za nakup skladiščne opreme, (iii) stroškov, ki nastanejo zaradi preobremenitve skladiščnega sistema (trenutno pomanjkanje skladiščnega prostora) ter (iv) stroškov, ki so odvisni od posamezne skladiščno-upravljalne strategije. Poglobljen pregled s področja načrtovanja in upravljanja regalnih skladiščnih sistemov je predstavil Rouwenhorst s sodelavci [13], in sicer v obliki metodologije za načrtovanje skladiščnih sistemov. Postopek načrtovanja je predstavljen s strukturiranim postopkom, ki pri sprejemanju odločitev upošteva strateško, taktično in opravilno raven odločanja. Večina opisanih modelov načrtovanja se navezuje na sistem RD za delo v enem hodniku ([8] do [11]). Razlika med omenjenimi postopki in modeli se zrcali v stroških, ki so vključeni v namensko funkcijo, v izbiri projektnih spremenljivk ter v uporabi optimizacijskih tehnik. Veliko manj je bilo storjeno za druge tipe skladišč, predvsem za sisteme, pri katerih je število RD (S) manjše ali enako od števila regalnih hodnikov (R) (pogoj S < R) ([3] in [14]). Zaradi tega smo v model načrtovanja vključili izpopolnjene analitične modele za določitev zmogljivosti sistema RD za delo v več hodnikih ([2] in [15]). Zahteva po zelo zmogljivih skladiščih in najmanjših investicijskih in obratovalnih stroških skladišča je bila vodilo pri razvoju in izdelavi namenske funkcije najmanjši skupni stroški (NSS -Min. TC). Zaradi nelinearnosti, diskretne oblike in večparametričnosti namenske funkcije NSS [3] smo za optimizacijo projektnih spremenljivk uporabili postopek genetskih algoritmov ([16] in [17]). Rezultat modela načrtovanja regalnih skladiščnih sistemov je določitev tehnično zelo zmogljivega ARSS, ob pogoju o najmanjših investicijskih in obratovalnih stroških skladišča. 1 NAČRTOVANJE AVTOMATIZIRANIH REGALNIH SKLADIŠČNIH SISTEMOV Model načrtovanja ARSS temelji na strukturiranem postopku [13], pri čemer moramo upoštevati vse parametre, ki vplivajo na zalogovno velikost skladišča Q, pretočno zmogljivost skladišča Pf ter investicijske in obratovalne stroške skladišča. Pri razvoju in izdelavi modela načrtovanja smo upoštevali predloge in priporočila preostalih avtorjev ([3], [8], [12] in [18] do [22]). Na sliki 1 je predstavljen algoritem poteka modela načrtovanja ARSS z and Roll [12]. When describing total costs, the authors took into account: (i) the cost of building the warehouse, (ii) the cost of buying the storage equipment, (iii) the costs arising from overloading the warehousing system (a temporary shortage of storage space) and (iv) the costs that depend on a particular storage policy. An in-depth overview of the area of designing and controlling warehouses was presented by Rouwenhorst et al. [13] in the form of the methodology of designing warehousing systems. The design process is presented with a structured approach, which takes into account the strategic, tactical and operational level of decision making. The majority of described models refer only to the single-aisle ASAR ([8] to [11]). The difference between the discussed approaches and models lies in the costs included in the objective function, the decision on considered project variables and the use of optimization techniques. Less has been done for other types of warehouses, especially for systems where the number of SR machines (S) is less than or equal to the number of picking aisles (R) (the condition S < R) ([3] and [14]). Therefore, our newly proposed analytical travel-time models for the efficiency determination of multi-aisle ASRS have been included in our design model ([2] and [15]). The requirement for a highly efficient warehouse and minimum investment and operational costs of the warehouse was the guidance for how to develop and create the objective function minimum total costs (Min. TC). Due to the non-linear, discrete and multi-variable objective function Min. TC [3], the method of genetics algorithms ([16] and [17]) to optimize the project variables have been applied. The result of the model for designing warehouses is the determination of the technologically highly efficient ASRS under the condition that investment and operational costs of the warehouse are minimized. 1 DESIGNING AUTOMATED STORAGE AND RETRIEVAL SYSTEMS The model for designing the ASRS is based on the structured approach [13], where all the parameters influencing the warehouse volume Q (rack capacity), the throughput capacity Pf, the investment, and the maintenance costs have to be taken into account. When developing and creating the design model, propositions and references from other authors were considered ([3], [8], [12] and [18] to [22]). Figure 1 shows the algorithm of the design model of the Načrtovanje in optimiranje avtomatiziranih regalnih - The Design and Optimization of Automated Storage 271 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 naslednjimi glavnimi moduli: . Načrtovanje skladiščne cone, ki obsega izbiro palete in določitev osnovne transportno-skladiščne enote (TSE). Na podlagi izbrane TSE lahko določimo regalno okno (RO), ki je temelj za postavitev SR. V okviru določitve SR izberemo regalne stranice in regalne veznike, ki skupno sestavljajo regalno konstrukcijo. Vrsto regalne konstrukcije izberemo v odvisnosti od teže TSE ter njihove razporeditve v vodoravni smeri x in v navpični smeri y. Na podlagi zahtevane Q skladišča, geometrijske oblike skladiščnega objekta ter oblike SR določimo obliko skladiščne cone. . Načrtovanje transportne cone in določitev zmogljivosti skladišča, ki obsega izbiro osnovnega transportno-skladiščnega sredstva. Izbira se izvede glede na geometrijsko obliko SR in zahtevano Pf skladišča. V odvisnosti od zahtevane Pf skladišča izbiramo med sistemom: (i) RD za delo v enem hodniku ter (ii) RD za delo v več hodnikih. Za premik TSE do skladiščne cone imamo na voljo transportne viličarje ali zvezne transporterje. V odvisnosti od kombinacije transportno-skladiščnih sredstev določimo zmogljivost skladišča in izmere transportne cone. . Določitev skupnih stroškov, ki se deli na: (i) stroške za statični del skladišča, (ii) stroške za dinamični del skladišča in (iii) stroške za obratovanje skladiščnega sistema v izbranem časovnem obdobju. . Oblikovanje namenske funkcije in optimizacija parametrov namenske funkcije Min. TC, ki predstavlja kombinacijo projektnih spremenljivk, opravilnih parametrov in skupnih stroškov ARSS ter temelji na optimizacijski metodi z genetskimi algoritmi [16] in [17]. Cilj optimizacije NSS (Min. TC) je določiti takšno različico ARSS, da bo izpolnjen pogoj o tehnično zelo zmogljivem in stroškovno optimalnem ARSS. Novost v modelu načrtovanja je uporaba pogoja, da je število RD lahko manjše od števila regalnih hodnikov (S < R). Karasawa in sodelavci [8], Ashayeri in sodelavci [9], Azadivar [23] so v svojih modelih uporabili pogoj (S = R). Glede na dejstvo, da je RD najdražji element v ARSS (približno 40 % celotne investicije [3]), smo v model načrtovanja vključili uporabo RD s pomičnim vozičkom [2], ki se navezuje na pogoj, S < R. Bistvo omenjenega sistema se kaže v veliki prilagodljivosti glede na morebitno povečanje Q in Pf skladišča ter v izrazito manjših ASRS, including the following main modules: . Design of the storage zone, which includes the choice of the palette and the determination of the basic transport unit load (TUL). On the basis of the chosen TUL, the storage compartment, which forms the basis for setting up the SR, can be determined. When determining the SR upright frames and rack beams, which together form a storage rack structure, have been chosen. The type of storage-rack structure is selected in accordance with the weight of the TUL and their arrangement in the horizontal x and vertical y directions. On the basis of the required Q of the warehouse, the geometry of the warehouse and the form of SR and the form of the storage zone, have been determined. • Design of the transport zone and the determination of the efficiency of the warehouse, which covers the choice of basic material handling equipment The choice is made according to the geometrical form of the SR and the required Pf of the warehouse. Due to the throughput capacity Pf, two systems of handling equipment are possible: (i) the single-aisle system; (ii) the multi-aisle system. Lift trucks and conveyors are used for manipulating the TUL to the storage-rack zone. Depending on the combination of the material handling equipment and the warehouse volume Q, the dimensions of the transport zone can be determined. . Determination of the total costs, which is divided into: (i) costs of the static part of the warehouse, (ii) costs of the dynamic part of the warehouse and (iii) costs of operating the warehousing system in a selected time period. . Design of the objective function and optimization of the parameters of the objective function min TC., which presents a combination of project variables, operational variables and overall costs of the ASRS, and are based on the optimization method of genetics algorithms [16], [17]. The aim of the optimization of the decision variables in Min. TC is to define the cost-optimal solution for the ASRS, considering the conditions of technically high and economically optimal solution for the ASRS. An innovation in the design model is the application of the condition that the number of SR machines is lower than or equal to the number of picking aisles (S < R). Karasawa et al. [8], Ashayeri et al. [9], Azadivar [23] have applied the condition (S = R) to their models. Given that the SR machine is the most expensive element in the ASRS (taking up approximately 40% of the entire investment [3]), the utilization of aisle transferring storage and retrieval machine, which refers to the condition S < R, has been included in the design model [2]. The essential element of the above-mentioned 272 Lerher T. - Potrč I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 Načrtovanje skladišč ne cone Design of the storage Qi Načrtovanje transportne eorte I Vsilil ol'lhc transport pfi>=pf Določitev skupnih stroškov Determination of the total cost______ Namenska funkcija NSS Objective function Min. TC I/biru jviIl-Ll- in osnovne [ S] . The selection of the palette and basic TUL. Oblikovanje osnovnega regalnega okna. The design of the basic storage compartment. Izbira regalnih stranic in regalnih veznikov. The selection of upright frames and rack beams. Določitev oblike skladiščnega rcgala in Qi skladišča The design of storage rack structure and the rack capacity Qi Izbira sistema RD za delo v enem ali vec hodnikih. The selection of the single-or mulli-aisle AS/RS, Izbira transportnega viličarja ali zveznega transporterja. The selection of the lift truck or accumulating conveyor. Določitev pretočne zmogljivosti P/i skladišča. The definition of the throughput capacity Pfi of the warehouse. Določitev cone za komisioniranje blaga. The design of order-picking zone. Določitev stroškov za statični del skladišča. The definition of cost for static part of the warehousc. Dol oči lev stroškov /a dinamični del skladišča. The definition of cost for dynamic part of the warehouse. Določitev operativnih stroškov za skladiščni sistem v izbranem časovnem obdobju. The definition of operational cost for the warehouse defined in time. OPTIMIZACIJA GA OPTIMIZATION GA Omejitve Con si rants Kadar je število izvedenih generacij enako predpisanim, predstavlja rešitev optimizacije stroškovno optimalna varianta ARSS. When the number of conducted generations equals the prescribed number, the solution of the optimization process represents the best economical design of AS/RS. Najboljše rešitve ARSS, ocenjene z namensko funkcijo The best solutions of ASRS, valued with the Min. TC of generation ;;, follow in the next generation n+L Stroškovno optimalna varianta ARSS The most economical design of ASRS Sl. 1. Algoritem poteka modela načrtovanja ARSS Fig. 1. The algorithm of the design model of the ASRS investicijskih stroških v primerjavi s sistemom RD za delo v enem hodniku. Enak pogoj, S < R, sta v svojem modelu načrtovanja predstavila Rosenblatt in Roll [3] v okviru kombiniranega analitičnega in simulacijskega postopka za načrtovanje ARSS. V njunem modelu je Pf skladišča za pogoj, S < R, določena s simulacijo modela ARSS, ki nato zagotavlja vnos glavnih podatkov v analitično-optimizacijski model načrtovanja. Model načrtovanja [3] tako temelji na interakciji med simulacijami ARSS (diskretni sistem) in analitičnim system reflects in a high degree of flexibility regarding a possible increase of Q and Pf of the warehouse and in smaller investment costs in comparison with the single-aisle ASRS. The same S < R condition was set out by Rosenblatt and Roll [3] in their combined analytical and simulation approach to designing the ASRS. In their model, the Pf of the warehouse is determined under the S ' i t0 2a ^<- - Sl. 2. Tloris avtomatiziranega regalnega skladiščnega sistema Fig. 2. The layout of the automated warehouse 274 Lerher T. - Potrč I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 na vsaki strani regalnega hodnika po eden SR. V/I lokacija skladišča je nameščena na spodnjem, skrajno levem robu regalnega skladišča (sl. 2). . Število RD S je lahko manjše ali enako R (S: mz ,:,,,.................. :<]' m x '¦¦ • ", 276 Lerher T. - Potrč I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 N je projektna spremenljivka; b2, b6, b7, b9 [mm] predstavljajo varnostni dodatek za višino RO, višino regalnega nosilca, odmik regalnega okna od tal in varnostni dodatek za višino skladišča; C [€/m2] je strošek postavitve sten skladiščnega objekta (sl. 2 in 3). . Investicija za postavitev strehe skladiščne zgradbe I : N is the decision variable; b2, b6, b7, b9 [mm] indicate the safety addition to the height of the storage compartment, the height of rack beams, the deviation of the storage compartment from the floor and a safety addition to the height of the warehouse; C3 [€/mf] is the cost of building the walls of the warehouse (Figs. 2 and 3). . The investment in building the roof of the warehouse I4: I4=[((w-n + (n + 1)-b1+b4)Nx+b5+b10+b20) + LTZ-(R-WRD + Y-g + (R-)b8)-C4 (4), C4 [€/m2] pomeni strošek za postavitev strehe skladiščne zgradbe (sl. 2 in 3). C4 [€/mf] indicates the cost of building the roof of the warehouse (Figures 2 and 3). 2) Transportna in skladiščna sredstva . Investicija za nakup regalnih stranic I: 2) Storage and material-handling equipment . The investment in buying upright frames I: I5=((Nx+1)-2Y)-C5 (5), C5 [€/m] pomeni strošek za nakup regalnih stranic. . Investicija za nakup regalnih veznikov in dodatek za ojačitev regalne konstrukcije I6: C5 [€/m] indicates the cost of buying upright frames. . The investment in buying rack beams and an addition to the reinforcement of the storage-rack structure I6: ((((Nx+1)-2Y)-C5)+(Nx-Ny-2Y-Lv)C6) PD 100 (6), L [mm] je dolžina regalnega veznika (nosila); PD pomeni dodatek za ojačitev skladiščnih regalov; C6 [€/m] pomeni strošek za nakup regalnih veznikov. . Investicija za nakup prevzemnih miz I7 in montažo regalne konstrukcije I8: L [mm] is the length of the rack beam; PD indicates an addition to the reinforcement of storage racks, C6 [€/m] indicates the cost of buying rack beams. . The investment in buying buffers I7 and the assembly of the storage-rack structure I8: (7), I7=2R- C7 C7 [€] pomeni strošek za nakup prevzemnih miz, C C [€] indicates the cost of buying buffers and C8 [€] [€] pomeni strošek montaže. the cost of assembly. . Investicija za požarno varnost I9 in klimatske * The investment in fire-safety I8 and air zahteve I10: conditioning I9 equipment: I9=((Nx-Ny)-3-2)-C9 (L war ' Hwar ' Wwar ) ' C10 9 (8), C9 [€/PM] pomeni strošek požarne varnosti, C [€/ m3] pa strošek prezračevanja. . Investicija za transportni I11 in regalni viličar I12: C9 [€/PM] indicates the cost of fire safety and C10 [€/ m3] the cost of air ventilation. . The investment in lift truck I1 and reach trucks I1 : 1 = S C I = S C 12 RV 12 (9), STV pomeni število transportnih viličarjev (spremenljivka); SRV pomeni število regalnih viličarjev (spremenljivka); C11 [€] pomeni strošek za nakup transportnega viličarja; C12 [€] strošek za nakup regalnega viličarja. STV indicates the number of lift trucks (variable), SRV indicates the number of reach trucks (variable); C11 [€] indicates the cost of buying a lift truck; C12 [€] indicates the cost of buying a reach truck. Načrtovanje in optimiranje avtomatiziranih regalnih - The Design and Optimization of Automated Storage 277 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 . Investicija za RD za delo v enem hodniku I1: . The investment in the single-aisle ASRS I1 : 1 = C 4- T I 3 S Rd ^n^*-TZ C 14 (10), . Investicija za RD za delo v več hodnikih I: . The investment in the multi-aisle ASRS I14: I14 = C13 'SRD +(LtZ 'C14 )'R | WW SRD pomeni število RD (spremenljivka); LTZ [mm] je dolžina skladiščne cone; WWAR [mm] je širina skladišča; C13 [€] pomeni strošek za nakup RD; C14 [€] pa strošek regalnega hodnika; C15 [€] pomeni strošek prečnega hodnika. Za uskladiščenje in odpremo TSE v regalnem skladišču (vožnja v regalnih hodnikih) so namenjena samo regalna dvigala in regalni viličarji. Transportni viličarji se uporabljajo v izbirnemu in distribucijskemu delu skladišča. . Investicija za zvezni transporter I15: I15 =C16 + 2-R-C17 C16 [€] pomeni strošek zveznega transporterja (krmilni sistemi, krmilni program); C17 [€] pa strošek preusmeritvenega elementa. 3) Obratovanje ARSS . Stroški vzdrževanja regalnega skladiščnega sistema CVZD: 2g + SR C (11), SRD indicates the number of SR machines (decision variable); LTZ [mm] is the length of the transport zone; WWAR [mm] is the width of the warehouse; C13 [€] indicates the cost of buying the SR machine; C14 [€] indicates the cost of the picking aisle; C15 [€] indicates the cost of the cross aisle. For the storage and retrieval operation of the TUL in the high-bay warehouse (routing in the picking aisles), only the SR machines and reach trucks are used. Lift trucks are used in the order picking and distribution area. . The investment in the accumulating conveyor I15: (12), C16 [€] indicates the cost of the accumulating conveyor (the controls, the control system); C17 [€] indicates the cost of the diverted element. 3) Operating the ASRS . Costs of maintaining the automated storage and retrieval system CVZD: C P(%)-C13-S (13), . Metoda neto sedanje vrednosti NPV - diskontni stroški obratovanja, ki predvidevajo določeno dobo trajanja ARSS i in diskontno stopnjo r: . The method of net present value NPV - discount operational costs that assume a certain life expectancy of the ASRS i and the discount rate r NPV=Tj(( P(%)C13-S)+COD ) 1+ r i () (14), P(%) pomeni delež vrednosti RD za vzdrževanje; S pomeni število transportno-skladiščnih sredstev; COD je strošek osebnega dohodka za viličariste, ki delajo s transportnimi in regalnimi viličarji; r je diskontna stopnja; T je predvidena doba trajanja obratovanja ARSS. i Namenska funkcija NSS je vsota stroškov za postavitev skladiščnega objekta, nabavo vseh transportnih in skladiščnih sredstev ter stroškov obratovanja za načrtovano dobo trajanja skladišča. V namenski funkciji pomenijo stroški nespremenljivo vrednost in se v odvisnosti od geometrijske oblike skladišča ne spreminjajo. Namenska funkcija NSS ima naslednjo obliko: P (%) indicates the share of the value of the SR machine for maintenance; S indicates the number of pieces of material-handling equipment; COD is the cost of personal income for operators working with lift trucks and reach trucks; r is the discount rate; Ti is the anticipated life expectancy of the operation of the ASRS. The objective function Min. TC refers to all the costs of building the warehouse, purchasing the material-handling equipment and the costs of operating the warehouse within the expected operational time period. In the objective function, the costs indicate the constant value and do not change depending on the geometry of the warehouse. The objective function Min. TC has the following form: 278 Lerher T. - Potrč I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 .Namenska funkcija NSS .The objective function Min. TC Min. TC = I1 + I2 + I3 + I4 + I5 + I6 + I7 + I8 + I9 + I10 I11 + I12 + I13 + I14 + I15 + NPV (15). Pri optimizaciji projektnih spremenljivk S, R, Y, N, N v namenski funkciji NSS moramo upoštevati določene omejitve, ki se nanašajo na (1) geometrijske omejitve skladišča, (2) najmanjšo zahtevano Q skladišča in (3) število RD je lahko manjše ali enako številu regalnih hodnikov (S(h + b2+b6)-N+b7+b9<1e6 (16). (17). (18). 2) Izračunana Q skladišča mora biti enaka ali večja zahtevani Q skladišča: 2) The calculated Qi of the warehouse must be equal to or higher than the required Q of the warehouse: 2-3-Nx-N-R>Q (19). 3) Število RD je lahko manjše ali enako številu regalnih hodnikov (S (iii) ARSS za delo v enem hodniku (GA – generacija 1) (iii) The single-aisle ASRS (GA – generation 1) (ii) ARSS za delo v več hodnikih (GA - generacija 100) (ii) The multi-aisle ASRS (GA - generation 100) (vi) ARSS za delo v enem hodniku (GA – generacija 100) (vi) The single-aisle ASRS (GA – generation 100) Sl. 4. Diagrami celotnih stroškov sistemov RD za delo v enem in več hodnikih Fig. 4. The total costs of the single- and multi-aisle ASRS 282 Lerher T. - Potrč I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 GA prav tako prišel do rešitve, vendar bi za rešitev porabil več časa. V diagramih na slikah 4i in 4iii lahko vidimo, da tvori GA za obe različici transportno-skladiščnega sredstva (RD za delo v enem hodniku in RD za delo v več hodnikih) izbrano število naključnih različic ARSS. Skladiščne različice, ki ne ustrezajo predpisanim omejitvam, definiranim pri optimizaciji projektnih spremenljivk S, R, Y, N in N v namenski funkciji NSS, so izbrisane in na diagramih niso prikazane. Število naključno izbranih različic ARSS je tako enako velikosti populacije n ali v večini primerov manjše od n. Zaradi naključnega izbire množice ARSS, ki pomenijo nadaljnjo osnovo za optimizacijo, so vrednosti skupnih stroškov v namenski funkciji NSS največje prav v generaciji n = 1, kar velja za obe različici transportno-skladiščnega sredstva. V diagramih (slika 4i in 4iii) lahko vidimo, da skladiščne različice, označene s potemnjenimi simboli, pomenijo stroškovno najugodnejše rešitve ARSS. Večina najugodnejših rešitev je v področju večjega števila RO v vodoravni smeri x in v navpični smeri y, kar pomeni, da imajo omenjene rešitve ARSS na podlagi metode izbire z razvrščanjem veliko verjetnost, da bodo vključene v naslednjo generacijo. Na podlagi predpisanih razvojnih in genetskih operatorjev se izvedejo naslednje generacije n = (1 - 100), pri čemer je vsaka generacija boljša ali pa vsaj njej enaka. V diagramih na sliki 4ii in 4iv so prikazani rezultati optimizacije projektnih spremenljivk pri generaciji n = 100. Opazimo lahko, da je število različic ARSS v generaciji n = 100 manjše kakor v primerjavi z generacijo n = 1, kar nakazuje na pravilno delovanje GA. Stroškovno optimalna rešitev ARSS se navezuje na ARSS z N = 28 RO v vodoravni x in N = 13 RO v navpični smeri y, za obe različici transportno-skladiščnega sredstva (v diagramu 4ii in 4iv označena s potemnjenim simbolom). Vidimo lahko, da so skupni stroški najmanjši (optimalni) pri sorazmerno visokem Ny = 13 in dolgem Nx = 28 SR (glede na podane geometrijske omejitve e skladišča) za obe izvedbi transportno-skladiščnih sredstev. Predstavljeno odvisnost lahko komentiramo z dejstvom, da imamo v primeru velikega SR (>> N in >> N), veliko zalogovno velikost Q, pri manjšem številu SR ter zato majhno širino skladišča < W. Slednje ima za posledico manjše potrebno število transportno-skladiščnih sredstev S (še posebej očitno pri sistemu RD za delo v enem hodniku), kar ima velik vpliv na celotno investicijo skladišča. also arrive at a solution, but it would take more time to do so. The diagrams in Figures 4i and 4iii show that the GA forms a chosen number of random designs of the ASRS for both types of the single- and multi-aisle ASRS. Warehouses that do not follow the required constraints, defined at the optimization of the decision variables S, R, Y , N x, N y in the Min. TC, are deleted and not considered in the next generations. The number of randomly chosen designs of the ASRS is the same as the size of the population n or in most cases smaller than n. Because of the random selection of the number of ASRS, which present a further basis for the optimization, the values of the total costs in the Min. TC are the highest in the generation n = 1, which holds true for both types of the single- and multi-aisle ASRS. The diagrams ion Figures 4i and 4iii illustrate that warehouse designs, marked with darkened symbols, present the most economical designs of the ASRS. The majority of the most economical designs lies in the area of a large number of storage compartments in the horizontal direction x and the vertical direction y. Accordingly, the above-mentioned designs of the ASRS have a strong likelihood of being included in the next generation on the basis of the selection method with ranging. Based on the specified evolutionary and genetics operators, the next generations n = (1 – 100) are carried out, whereby each generation is better or at least equally good. The diagrams in Figures 4ii and 4iv show the results of the optimization of the decision variables with the generation n =100. It can be seen that the number of designs of the ASRS in the generation n = 100 is smaller than in the generation n = 1, which indicates the correct operation of the GA. The most economical design of the ASRS refers to the ASRS with Nx = 28 storage compartments in the horizontal x and Ny = 13 storage compartments in the vertical direction y, for both types of storage systems (in diagrams 4ii and 4iv, marked with a darkened symbol). It can be seen that the total costs are minimum (optimum) at a relatively high Ny = 13 and long Nx = 28 storage racks (with regard to the given geometrical constraints ei of the warehouse) for both variants of the single- and multi-aisle ASRS. One can comment on the presented dependence that in the case of a large SR (>> Nx and >> Ny ) we have a large storage volume Q, a small number of SR and consequently a small width of the warehouse < W. The latter takes the consequence of a lower number of necessary numbers of SR machines S (apparently obvious with the single-aisle ASRS), which has a significant influence on the entire investment in the warehouse. Načrtovanje in optimiranje avtomatiziranih regalnih - The Design and Optimization of Automated Storage 283 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 V odvisnosti od S lahko vidimo, da pri uporabi sistema RD za delo v enem hodniku potrebujemo 7 RD, medtem ko pri uporabi sistema RD za delo v več hodnikih potrebujemo le 4 RD. Čeprav omogoča ARSS s sistemom RD za delo v več hodnikih samo uporabo 4 RD, je znesek investicije za določen primer ARSS [2] (Q = 15 000 TSE in Pf = 140 TSE/h), približno enak za oba ARSS (3,626 • 103€ - slika 4ii in 3,800 • 103€ - slika 4iv). Vrednost RD za delo v več hodnikih je za približno 60 % večja od vrednosti RD za delo v enem hodniku prav zaradi dodatnih elementov (pomični voziček za vožnjo v prečnem hodniku, dodatna vodila, stikala, obsežnejše krmiljenje itn), ki omogočajo izvedbo skladiščnega opravila. Odločitev o uporabi posameznega sistema RD je v največji meri odvisna od zahtevane Pf skladišča. V nadaljevanju bo zato prikazana primerjava učinkovitosti (v odvisnosti od NSS) sistema RD za delo v enem in več hodnikih pri različnih Pf skladišča. 2.1 Učinkovitost sistemov regalnega dvigala za delo v enem in več hodnikih V primeru zahteve naročnikov skladišč po izdelavi ARSS se lahko odločamo med sistemoma RD za delo v enem ali več hodnikih. Kateri od sistemov RD se v določenem položaju najbolje obnese, je odvisno predvsem od zahtevane Pf skladišča. V analizi smo uporabili ARSS z zalogovno velikostjo Q = 15000 TSE, pri katerem smo spreminjali zahtevano pretočno zmogljivost skladišča v mejah od Pf = 60 do 160 TSE/h, glede na naslednje projektne omejitve: LWAR (e = 0 - e = 100) m, širina skladišča WW (e = 0 - e = 200) m in višina skladišča HR (e5 = 0 - e = 20) m. Opravilni parametri, transportno-skladiščna sredstva in stroški se navezujejo na ARSS [2] in so podrobneje predstavljeni v poglavju 3. Rezultati analize v preglednici 1 in na sliki 5, predstavljajo stroškovno optimalne različic ARSS, dobljene z optimizacijo projektnih spremenljivk S, R, Y, N in N v namenski funkciji NSS pri generaciji n = 100. y . Primerjava učinkovitosti sistemov RD za delo v enem in več hodnikih V preglednici 1 so prikazane različne izvedbe ARSS v odvisnosti od zahtevane Pf skladišča. Osnova za primerjavo sistemov RD predstavlja ARSS s sistemom RD za delo v enem hodniku z naslednjimi osnovnimi podatki: zalogovna velikost In dependence on the S, when applying the single-aisle ASRS we need 7 SR machines, whereas when applying the multi-aisle ASRS we need only 4 SR machines. Even though the multi-aisle ASRS requires the application of only 4 SR machines, the investment in the analysed ASRS [2] (Q = 15000 TUL and Pf = 140 TUL/h) is approximately the same for both types of the single- and multi-aisle ASRS (3.626- 10 € - diagram 4ii and 3.800103€- diagram 4iv). The cost of the SR machine for the multi-aisle system is approximately 60% higher than the cost of the SR machine for the single-aisle system due to additional elements (aisle transferring vehicle for traveling in the cross aisle, additional controls and switches, extensive control system, etc.) which make it possible to operate the warehouse. The decision on the application of a particular single- or multi-aisle system depends mainly on the required Pf of the warehouse. Consequently, in the following section a comparison between the single- and multi-aisle systems, with regard to various Pf of the warehouse, is presented. 2.1 The efficiency of the single- and multi-aisle ASRS When an order for the creation of the ASRS is placed, we can decide between the single-aisle and multi-aisle ASRS. Which of both systems is most suitable for a particular case depends largely on the required Pf of the warehouse. In the analysis the ASRS with the storage volume Q = 15000 TUL has been used. The required throughput capacity has been changed from Pf = 60 to 160 TUL/h, with regard to the following project constraints: the length of the warehouse LWA R (e = 0 - e = 100) m, the width of the warehouse WWAR (e = 0 - e = 200) m and the height of the warehouse HWAR (e = 0 - e = 20) m. Operational parameters, material handling equipment and costs refer to the ASRS [2] and are presented in detail in Section 3. The analysis results in Table 1 and Figure 5 present the most economical design of the ASRS, obtained from optimizing the decision variables S, R, Y N N in the Min. TC within the generation n = 100. x, y . Efficiency comparison between the single- and multi-aisle ASRS Table 1 shows different types of the ASRS depending on the required Pf of the warehouse. The basis for making the comparison between both systems is the single-aisle ASRS with the following data: storage volume of the warehouse Q = 15000 TUL, throughput 284 Lerher T. - Potrč I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 Preglednica 1: Primerjava sistema RD za delo v več hodnikih v odvisnosti od sistema RD za delo v enem hodniku Table 1. The comparison of the multi-aisle ASRS in dependence on the single-aisle ASRS Pf2 = 60 [TSE/h] [TUL/h] PRIMERJAVA ZMOGLJIVOSTI SKLADIŠČA COMPARISON OF THE WAREHOUSE EFFICIENCY Pf2 = 80 [TSE/h] [TUL/h] Pf3 = 100 [TSE/h] [TUL/h] Pf4 = 120 [TSE/h] [TUL/h] Pf5 = 140 [TSE/h] [TUL/h] Pf6 = 160 [TSE/h] [TUL/h] Q 15000 15000 15000 15000 15000 15000 R 7 7 7 7 7 7 S 2 3 3 4 4 5 Nx 28 28 28 28 28 28 Ny 13 13 13 13 13 13 n (%) NSS [€] Min. TCm 82 2,960 103 72,2 3,284 103 89 3,284 103 80 3,609 103 94 3,626 103 74 3,951 103 TC(g) Razlika v stroških [€] Differences in costs [e] r 3950000 3800000 3650000 3500000 3350000 3200000 3050000 2900000 P/=60 -840-103 -516-103 -516-103 191-103 174-103 151-103 ¦ /. —¦T I / X _"/ : RD s pomičnim vozičkom Multi-aisle AS/RS RD (klasično) Singlc-aislc AS/RS Vi 80 VI 1(10 VI 120 /y= no />/= 160 Pretočna zmogljivost Throughput capacity Sl. 5. Porazdelitev najmanjših skupnih stroškov v odvisnosti od Pf skladišča Fig. 5. Distribution of minimum total costs depending on the Pf of the warehouse skladišča Q = 15000 TSE, pretočna zmogljivost skladišča Pf = 160 TSE/h, število regalnih hodnikov R = 7, število RD S = 7, število SR Y = 14, število RO v vodoravni x smeri Nx = 28, število RO v navpični smeri y N = 13, najmanjši skupni stroški NSS = 3,800 • 104 Na sliki 5 je prikazana odvisnost zahtevane Pf skladišča glede na stroškovno optimalno izvedbo ARSS za oba sistema RD. Vidimo lahko, da je sistem capacity Pf = 160 TUL/h, the number of picking aisles R = 7, the number of SR machines S = 7, the number of SR Y = 14, the number of storage compartments in the horizontal direction N = 28, the number of storage compartments in the vertical direction Ny = 13, and the minimum overall costs Min. CS = 3.800-10€. The diagram in Figure 5 shows the dependence of the required Pf of the warehouse, with regard to the most economical design of the ASRS for Načrtovanje in optimiranje avtomatiziranih regalnih - The Design and Optimization of Automated Storage 285 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 RD za delo v več hodnikih smiselno uporabiti pri nižjih zmogljivostih skladišča << Pf saj je investicija skladišča neprimerno manjša kakor pri sistemu RD za delo v enem hodniku. V tem primeru je prispevek pri stroških v primerjavi s sistemom RD za delo v enem hodniku močno izrazit in znaša 840•103 € (Pf = 60 TSE/h). Z naraščanjem Pf skladišča se zmanjšuje tudi prispevek pri stroških in primernost uporabe sistema RD za delo v več hodnikih se zmanjšuje. V primeru zahtevane pretočne zmogljivosti nad vrednostjo Pf = 140 TSE/h je upravičenost omenjenega sistema RD že vprašljiva, saj je RD že močno obremenjeno (h = 94 %), prispevek pri stroških pa neizrazit. Opazimo lahko, da je investicija pri vrednosti Pf = 160 TSE/h za vrednost 151•103€večja v primerjavi s sistemom RD za delo v enem hodniku, saj je v ARSS treba zagotoviti že 5 RD. Prav tako pa so pri omenjeni pretočni zmogljivosti vprašljivi primernost uporabe in problem vodenja ter nadzora 5 RD pri 7 regalnih hodnikih. Analiza je bila izvedena za primer skladiščne strategije (i) naključnega uskladiščenja in (ii) naključne odpreme TSE, brez vpeljave skladiščnih con. Z uporabo izpopolnjenih strategij bi bila zmogljivost sistema RD za delo v več hodnikih neprimerno večja. Sklenemo lahko, da na splošno za (zahtevane) >> Pf pri uporabi klasične naključne skladiščne strategije, uporabimo sistem RD za delo v enem hodniku. Prav nasprotno velja v primeru sorazmerno << Pf pri katerih pride v poštev predvsem sistem RD za delo v več hodnikih. Večjo zmogljivost sistema RD za delo v več hodnikih lahko v največji meri dosežemo prav z uporabo učinkovitejše skladiščne strategije in vpeljave skladiščnih con ABC. 3 SKLEPI V tem prispevku je predstavljen izpopolnjen model načrtovanja ARSS. Zaradi vedno večje zahtevnosti skladišč in optimiranja skladiščnih virov, prehaja klasični postopek načrtovanja na višje in zahtevnejše stopnje, v obliki računalniško podprtega načrtovanja in optimiranja skladiščnih sistemov [13]. Model načrtovanja je tako zasnovan na sestavljenem postopku [13] in se navezuje na področje enoglobinskega regalnega skladiščnega sistema. Bistveni del v modelu načrtovanja je vpeljava in uporaba dveh različnih sistemov RD, in sicer (i) sistem RD za delo v enem ter (ii) sistem RD za delo v več hodnikih. V nasprotju s sistemom RD za delo v enem hodniku ([24] in [25]) so sistemi RD za delo v both systems. It can be seen that at low throughput capacities of the warehouse (<< Pf) it is reasonable to apply the multi-aisle ASRS, since the investment in the warehouse is much smaller than in the case of the single-aisle ASRS. In this case the difference in costs (840- 10 € - Pf = 60 TUL/h) is more significant in comparison with the single-aisle ASRS. With the rising of the Pf of the warehouse, the costs increase and also the appropriateness of applying the multi-aisle ASRS decreases. If the required throughput capacity is above Pf = 140 TUL/h, the application of the multi-aisle ASRS becomes rather questionable, since the SR machines are already overloaded (h = 94%) and the differences in costs are quite small. It can be seen that the investment within Pf = 160 TUL/h is larger for the value of 151103 € in comparison with the single-aisle ASRS, since 5 SR machines must be used in the ASRS. Additionally, in the above-mentioned Pf the application and the problem of the management and control of 5 SR machines at 7 picking aisles is rather questionable. The analysis has been carried out for the case of (i) random storage strategy and (ii) random retrieval strategy, without the introduction of the class-based storage. With the application of improved strategies, the efficiency of the multi-aisle ASRS would be much higher. It can be concluded that for the required >> Pf, with the application of the classical random strategy, we should generally apply the single-aisle ASRS. The opposite holds true for relatively << Pf, where especially the multi-aisle ASRS should be applied. A higher efficiency of the multi-aisle ASRS can be achieved by applying the most effective storage strategies and introducing a class-based ABC storage system. 3 CONCLUSIONS In this paper an improved design model of the ASRS is presented. Due to the great complexity and the difficult optimization of the warehouse, the conventional design process rises to higher and more demanding levels, in the form of the computer-aided design and optimization of warehousing systems [13]. The presented design model is based on the structured approach [13] and refers to the single deep-storage system with several picking aisles. The essential part of the design model is the application of two different systems: (i) the single-aisle ASRS and (ii) the multi-aisle ASRS. Unlike the single-aisle ASRS ([24] and [25]) the multi-aisle ASRS has not been investigated much in the literature 286 Lerher T. - Potrč I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 več hodnikih v literaturi veliko manj raziskani [22]. Zato smo v model načrtovanja vključili izpopolnjen analitični model za določitev zmogljivosti omenjenih sistemov [2]. Zaradi zahtev po stroškovno optimalni in hkrati tehnično zelo zmogljivi izvedbi skladišča, smo oblikovali namensko funkcijo Min. TC. Namenska funkcija je predstavljena z matematičnim modelom, ki vključuje projektne spremenljivke (S, R, Y, N, N), vse pomembne obratovalne in fizične parametre ter investicijske in obratovalne stroške [2]. Zaradi nelinearnosti namenske funkcije, njene diskretne oblike in predlaganih projektnih spremenljivk smo za optimizacijo projektnih spremenljivk v namenski funkciji NSS uporabili postopek genetskih algoritmov ([16] in [17]). Na temelju rezultatov optimizacije projektnih spremenljivk v namenski funkciji Min. TC in glede na določen em RD, lahko podamo naslednje glavne sklepe opravljene analize: Glede na vrednost skupnih stroškov (diagrami na slikah 4i, 4ii, 4iii in 4iv) v odvisnosti od števila RO v vodoravni smeri x in v navpični smeri y, lahko povzamemo, da je stroškovno optimalna različica ARSS (za oba sistema RD) dosežena pri visokem N = 13 RO in dolgem N = 28 RO skladiščnem regalu y Omenjena odvisnost se navezuje na določen ARSS in predpisane projektne omejitve skladišča e [2]. Ugotovitev lahko pojasnimo z dejstvom, da veliki SR omogočajo doseganje visoke Q skladišča, kar vpliva na manjše število hodnikov R in zato na manjšo površino skladišča. To ima za posledico manjše število RD < S (še posebej očitno pri sistemu RD za delo v enem hodniku), kar se izkazuje skozi celotne stroške investicije. V odvisnosti primerjave sistema RD za delo v enem in več hodnikih (sl. 5) opazimo izrazit vpliv Pf skladišča na znesek celotne investicije. Analiza je bila izvedena za določen ARSS z zalogovno velikostjo Q = 15000 TSE in pretočno zmogljivostjo, ki smo jo spreminjali v mejah od Pf = (60 do 160) TSE/h [2]. Splošna ugotovitev glede naraščanja zahtevane Pf skladišča je, da je za obravnavani ARSS, pri << Pf skladišča, primerno uporabiti sistem RD za delo v več hodnikih. V primeru uporabe sistema RD za delo v več hodnikih pri zahtevani Pf = 60 TSE/h, znaša odstopanje med sistemoma RD 840•103 €, kar narekuje nujno potrebo po vrednotenju obeh izvedb RD v postopku načrtovanja skladišč. Na sliki 5 lahko vidimo, da se znesek investicije v odvisnosti od zahtevane Pf skladišča povečuje diskretno in ustreza izbiri vse do vrednosti Pf = 140 TSE/h. Nad omenjeno [22]. Therefore, newly improved analytical travel-time models for the single- and multi-aisle systems have been included in the design model [2]. Due to requirements for the most economical design and at the same time technically highly efficient warehouse, the objective function Min. TC. has been formed. The objective function is represented by a mathematical model, which includes the decision variables (S, R, Y, N N), all the relevant operational and physical parameters, the investment and the operating costs [2]. Due to the non-linearity of the Min. TC, its discrete shape and proposed decision variables, the method of genetics algorithms has been applied ([16] and [17]) in order to optimize the decision variables. On the basis of the results of the optimization of the decision variables in the Min. TC and with regard to the single- and multi-aisle system, the following conclusions can be drawn. With regard to the total costs (the diagrams in Figures 4i, 4ii, 4iii, 4iv) in accordance with the number of storage compartments in the horizontal direction x and the vertical direction y, it can be concluded that the most economical design (for both types of the ASRS) is achieved with a high, (N = 13 storage compartments), and long (N = 28 storage compartments) storage rack. The above-mentioned dependence refers to the analysed ASRS and the prescribed project constraints e [2]. This finding can be explained with the fact that large SRs enable the achievement of a high warehouse volume of the warehouse, which influences a small number of picking aisles R and consequently a smaller width of the warehouse. Therefore, the number of SR machines is lower < S (particularly evident with the single-aisle ASRS), which shows in the overall costs of the investment. Depending on the comparison of the single-and multi-aisle ASRS (Figure 5), a significant influence of the Pf of the warehouse on the total costs of the investment can be seen. The analysis was carried out for the ASRS with the storage volume Q = 15000 TUL and throughput capacity that was changed within the limits of Pf = (60 to 160) TUL/h [2]. The general ascertainment regarding the increase of the required Pf of the warehouse is that for the particular ASRS, at << Pf of the warehouse, it is reasonable to apply the multi-aisle ASRS. If the multi-aisle ASRS is applied at the required Pf = 60 TUL/h, there is a deviation (of 840-103 Q between the two systems, which calls for of the need to evaluate both single- and multi-aisle systems in the design process. Figure 5 indicates that the investment according to the required Pf of the warehouse increases Načrtovanje in optimiranje avtomatiziranih regalnih - The Design and Optimization of Automated Storage 287 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 vrednostjo je smiselno izbrati sistem RD za delo v enem hodniku, saj je sistem RD za delo v več hodnikih že močno obremenjen in obsega že štiri RD pri sedmih regalnih hodnikih (S = 4, R = 7). Predstavljena odvisnost na sliki 5 ima zelo velik pomen pri načrtovanju skladišč in omogoča ustrezno izbiro sistema RD v odvisnosti od zalogovne velikosti Q in zahtevane pretočne zmogljivosti Pf skladišča. Zahvala Projekt razvoja orodja za načrtovanje in optimiranje avtomatiziranih regalnih skladiščnih sistemov je med drugimi v okviru projekta “Združitev kapacitet in razvoj znanja za realizacijo projektov visoko regalnih skladiš” podprlo in sofinanciralo podjetje Metalprim d.o.o. iz Maribora. Avtorja prispevka, bi se na tem mestu še posebej rada zahvalila vodstvu podjetja za vsestransko podporo in vzpodbudo pri nastanku znanstvenoraziskovalnega dela ter vsem sodelavcem na Fakulteti za strojništvo v Mariboru, ki so kakorkoli pripomogli k nastanku omenjenega dela. steadily and suits the choice up to the value Pf = 140 TUL/h. Above this value it is reasonable to choose the single-aisle ASRS, since the multi-aisle ASRS is already overloaded and encompasses four SR machines with seven picking aisles (S = 4, R = 7). The dependence shown in Figure 5 is extremely important when designing warehouses, since it enables the appropriate choice of the ASRS depending on the warehouse volume Q and the required throughput capacity Pf of the warehouse. Acknowledgments The project of the development of a tool for designing and optimizing ASRS has been among others supported and financed by the Metalprim d.o.o. company from Maribor. The authors of this paper would like to express special thanks to the management of this company for their complete support and encouragement for setting up this scientific and research project. Also, we would like to extend this thanks to all collaborators at the Faculty of Mechanical Engineering and others colleagues who have in any way contributed to this project. 4 OZNAKE 4 NOMENCLATURE Projektne spremenljivke število regalnih hodnikov število skladiščnih regalov število regalnih dvigal število regalnih oken v vodoravni smeri število regalnih oken v navpični smeri Operacijski parametri zalogovna velikost skladišča pretočna zmogljivost število TSE v regalnem oknu širina palete dolžina palete višina TSE število enojnih delovnih krogov število dvojnih delovnih krogov povprečni čas enojnega delovnega kroga povprečni čas dvojnega delovnega kroga R Y S Nx Ny Q Pf TSE/TUL TSE/h / TUL/h n w g h nSC nDC T(SC) s mm mm mm T(DC) s Decision variables the number of picking aisles the number of SR the number of S/R machines the number of storage compartments in the horizontal direction the number of storage compartments in the vertical direction Operational parameters warehouse volume (rack capacity) throughput capacity the number of TUL in storage compartment the width of the pallet the length of the pallet the height of the TUL the number of single command cycles the number of dual command cycles the average single command cycle time the average dual command cycle time 288 Lerher T. - Potrč I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 čas za delovno izmeno zmogljivost regalnega dvigala dolžina regalnega veznika (nosila) dodatek za ojačitev skladiščnih regalov dolžina regalnega okna višina regalnega okna globina regalnega okna dolžina skladiščnega regala višina skladiščnega regala dolžina transportne cone dolžina skladišča višina skladišča širina skladišča površina zemljišča za skladišče delež zazidanosti skladišča varnostni dodatek za širino regalnega okna varnostni dodatek za višino regalnega okna širina stebra debelina stebra višina regalnega nosila odmik regalnega okna od tal varnostni razmik med soležnimi regali varnostni dodatek za višino skladišča dodatek za širino palete na prevzemnem mestu dodatek na koncu skladišča Investicijski parametri strošek za nakup zemljišča strošek za postavitev temeljne plošče strošek za postavitev sten skladišča strošek za postavitev strehe skladišča strošek za nakup regalnih stranic strošek za nakup regalnih veznikov strošek za nakup prevzemnih miz strošek montaže strošek požarne varnosti strošek prezračevanja strošek za nakup transportnega viličarja strošek za nakup regalnega viličarja strošek za nakup regalnega dvigala strošek regalnega hodnika strošek prečnega hodnika strošek zveznega transporterja strošek preusmeritvenega elementa T n Lv PD Lro Hro Gro Lrs Hrs Ltz Lwar Hwar Wwar Pz Dz b1 b2 b4 b5 b6 b7 b8 b9 b10 b20 h mm % mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm mm C1 C €/m2 C3 €/m2 C4 €/m2 C5 €/m2 C6 €/m2 C7 € C8 € C9 € C € C11 € C12 C13 C14 C15 C16 C17 time for one shift the efficiency of the S/R machine the length of the rack beam the addition to the reinforcement of storage racks, the length of the storage compartment the height of the storage compartment the width of the storage compartment the length of the SR the height of the SR the length of the transport zone the length of the warehouse the height of the warehouse the width of the warehouse the surface of the land for the warehouse the share of the built warehouse the safety addition to the width of the storage compartment the safety addition to the height of the storage compartment the width of the upright frame, the thickness of the upright frame the height of rack beams the deviation of the storage compartment from the floor the safety spacing between racks that are placed close to each other the safety addition to the height of the warehouse the addition to the width of the palette at input buffer the addition to the end of the warehouse Investment cost parameters cost of buying the land cost of laying the foundations warehouse cost of building the walls of the cost of building the roof of the warehouse cost of buying upright frames cost of buying rack beams cost of buying buffers cost of the assembly cost of fire safety cost of air ventilation cost of buying a lift truck cost of buying a reach truck cost of buying S/R machine cost of the picking aisle cost of the cross aisle cost of the accumulating conveyor cost of the diverted element Načrtovanje in optimiranje avtomatiziranih regalnih - The Design and Optimization of Automated Storage 289 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 268-291 Parametri stroškov obratovanja delež vrednosti regalnega dvigala za vzdrževanje strošek osebnega dohodka za viličariste, ki delajo z transportnimi in regalnimi viličarji neto sedanja vrednost predvidena življenska doba obratovanja ARSS diskontna stopnja P Cod NPV Ti r % € let/years % Operational cost parameters the share of the value of the S/R machine for maintenance the cost of personal income for operators working with lift trucks and reach trucks net present value the anticipated life expectancy of the operation of the AS/RS the discount rate 5 LITERATURA 5 REFERENCES [1] Bartholdi, J. 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(1990) Travel time models considering the operating characteristics of the storage and retrieval machine, International Journal of Production Research, vol. 28, St. 10, str. 1779-1789. Naslov avtorjev: dr. Tone Lerher prof.dr. Iztok Potrč Univerza v Mariboru Fakulteta za strojništvo Smetanova 17 2000 Maribor tone.lerher@uni-mb.si iztok.potrc@uni-mb.si Authors‘ address: Dr. Tone Lerhet Prof.Dr. Iztok Potrč University of Maribor Faculty of Mechanical Eng. Smetanova 17 2000 Maribor, Slovenia tone.lerher@uni-mb.si iztok.potrc@uni-mb.si Prejeto: Received: 30.11.2005 Sprejeto: Accepted: 23.2.2006 Odprto za diskusijo: 1 leto Open for discussion: 1 year Načrtovanje in optimiranje avtomatiziranih regalnih - The Design and Optimization of Automated Storage 291 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 292-308 UDK - UDC 004.94:621.039.519:532.5 Izvirni znanstveni članek - Original scientific paper (1.01) Simuliranje eksplozije pare v reaktorski votlini s splošnim programom za računsko dinamiko tekočin Simulation of a Reactor Cavity Steam Explosion with a General Purpose Computational Fluid Dynamics Code Matjaž Leskovar - Boštjan Končar - Leon Cizelj (Institut “Jožef Stefan”, Ljubljana) Do eksplozije pare v reaktorski votlini lahko pride, če med hipotetično resno nezgodo v jedrski elektrarni popusti reaktorska posoda in se staljena sredica izlije v vodo, ki je v reaktorski votlini. Eksplozija pare je pojav medsebojnega delovanja goriva in hladiva pri katerem je časovna lestvica prenosa toplote s staljene sredice na vodo manjša od časovne lestvice za tlačno razbremenitev. To lahko povzroči tlačne udarne valove in kasneje, med raztezanjem pare, ki je pod visokim tlakom, nastanek izstrelkov, ki lahko poškodujejo okoliške objekte. Namen prispevka je predstaviti, kako je eksplozije pare mogoče obravnavati s splošnim programom za računsko dinamiko tekočin (RDT), podati vpogled v dogajanja med eksplozijo pare v reaktorski votlini tipičnega tlačnovodnega jedrskega reaktorja, in podati grobo oceno ogroženosti sten reaktorske votline in reaktorske posode ob eksploziji pare. Za dosego teh ciljev smo najprej razvili ustrezen namenski model eksplozije pare in nato opravili obsežno, primerno konzervativno parametrično analizo eksplozije pare v poplavljeni reaktorski votlini. Večfazni tok v reaktorski votlini med raztezanjem visokotlačne mešanice razpršene taline, kapljevite vode in vodne pare smo simulirali s programom CFX-5.7.1 za RDT, napetosti v stenah reaktorske votline pa s programom za simulacijo mehanike trdnin ABAQUS/ Explicit. © 2006 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: reaktorji jedrski, nezgode reaktorjev, eksplozija pare, votlina reaktorska, računska dinamika tekočin) A reactor cavity steam explosion might occur when, during a hypothetical severe reactor accident, the reactor vessel fails and the molten core pours into the water in the reactor cavity. A steam explosion is a fuel-coolant interaction process where the heat transfer from the melt to the water is so intense and rapid that the timescale for the heat transfer is shorter than the timescale for the pressure relief. This could lead to the formation of shock waves and the production of missiles at later times, during the expansion of the highly pressurized water vapour, which might endanger surrounding structures. The purpose of the paper is to demonstrate how steam explosions can be treated with a general purpose Computational Fluid Dynamics (CFD) code, to give an insight into the steam-explosion phenomenon in a typical Pressurized Water Reactor (PWR) cavity, and to provide a rough assessment of the vulnerabilities of cavity structures to steam explosions. To achieve this, a fit-for-purpose steam-explosion model was developed, followed by a comprehensive and reasonably conservative parametric steam-explosion study. The multiphase flow in the reactor cavity during the high-pressure pre-mixture expansion was simulated with the CFD code CFX-5.7.1 and the stresses in the reactor cavity walls were determined with the stress-analysis code ABAQUS/Explicit. © 2006 Journal of Mechanical Engineering. All rights reserved. (Keywords: nuclear reactor accident, steam explosion, reactor cavity, computational fluid dynamics) 0 UVOD 0 INTRODUCTION Eno od najpomembnejših nerešenih vprašanj One of the most important remaining issues in na področju taljenja sredice med hipotetično resno core-melt progression during a hypothetical severe 292 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 292-308 nezgodo v jedrski elektrarni je, kakšna je verjetnost nastanka eksplozije pare in kakšne so lahko njene posledice. Eksplozija pare se lahko razvije, ko pride staljena sredica v stik s hladilno vodo v reaktorski votlini. Eksplozija pare je pojav interakcije goriva in hladiva, pri katerem je časovna lestvica prenosa toplote s staljene sredice na vodo manj ša od časovne lestvice tlačne razbremenitve ([1] do [3]). To lahko povzroči tlačne udarne valove in kasneje med raztezanjem pare, ki je pod visokim tlakom, nastanek izstrelkov, ki lahko poškodujejo okoliške objekte. Eksplozija pare je zapleten, močno nelinearen, več-sestavinski in večfazen pojav, ki poteka na različnih krajevnih in časovnih lestvicah. Posledično je modeliranje eksplozij pare zelo zahtevno, negotovosti simuliranj resnih nezgod opravljenih z računalniškimi programi, ki temeljijo na modeliranju osnovnih pojavov eksplozije pare, pa so še vedno zelo velike. Zato je za oceno ogroženosti sten reaktorske votline in reaktorske posode med eksplozijo pare potreben parametričen postopek, ki zajame negotovosti razumevanja in modeliranja eksplozije pare. V ta namen smo razvili parametričen model eksplozije pare, ki ga je mogoče preprosto uporabiti in neposredno vključiti v splošne programe za računsko dinamiko tekočin (RDT). Glavni namen opravljene študije je predstaviti, kako je eksplozije pare mogoče obravnavati s splošnim programom za RDT, podati fizikalno sliko dogajanj med eksplozijo pare v reaktorski votlini tipičnega tlačnovodnega jedrskega reaktorja in podati grobo oceno ogroženosti sten reaktorske votline in reaktorske posode ob eksploziji pare. Eksplozijo pare smo modelirali kot raztezajočo se visokotlačno mešanico staljene sredice, kapljevite vode in vodne pare, ki je v delno poplavljeni reaktorski votlini. Podoben, vendar manj zahteven postopek so uporabili tudi v študiji eksplozije pare, ki je predstavljena v [4]. Večfazni tok med raztezanjem visokotlačne mešanice smo simulirali s programom CFX-5.7.1 za RDT [12], napetosti v stenah reaktorske votline pa s programom za simulacijo mehanike trdnin ABAQUS/Explicit [13]. 1.1 Model eksplozije pare Pri mešanju dveh kapljevin, pri katerih je temperatura ene kapljevine višja od temperature vrelišča druge, lahko pride do eksplozije pare. Potek accident in a nuclear power plant is the likelihood and the consequences of a steam explosion, which might occur when the hot core melt comes into contact with the coolant water. A steam explosion is a fuel-coolant interaction process where the heat transfer from the melt to the water is so intense and rapid that the timescale for the heat transfer is shorter than the timescale for the pressure relief ([1] to [3]). This could lead to the formation of shock waves and the production of missiles at later times, during the expansion of the highly pressurized water vapour, which might endanger surrounding structures. A steam explosion is a complex, highly nonlinear, coupled multi-component, multi-phase, multi-space-scale and multi-time-scale phenomenon. Consequently, the modelling of steam explosions is a difficult task and the uncertainties of reactor simulations performed with steam-explosion codes based on modelling fundamental steam explosion processes are still large. Therefore, for assessing the vulnerability of reactor-cavity structures to an ex-vessel steam explosion a parametric approach capturing the uncertainties in steam-explosion understanding and modelling is needed. For this purpose a comprehensive parametric steam-explosion model that can also be straightforwardly implemented in general purpose Computational Fluid Dynamics (CFD) codes was developed. The main purpose of the performed study was to present how steam explosions can be treated with a general purpose CFD code, to give an insight into the steam-explosion phenomenon in a typical Pressurized Water Reactor (PWR) cavity, and to provide a rough assessment of the vulnerabilities of cavity structures to steam explosions. The steam explosion was modelled as an expanding high-pressure pre-mixture of dispersed molten fuel, liquid water and vapour in the partially flooded reactor cavity. A similar, but less sophisticated, approach was also used in the steam-explosion study presented in [4]. The multiphase flow during the high-pressure pre-mixture expansion was simulated with the CFD code CFX-5.7.1 [12] and the stresses in the cavity walls were determined with the stress analysis code ABAQUS/Explicit [13]. 1.1 Steam Explosion Model Steam explosions are a subclass of what is called fuel-coolant interactions (FCI) in the safety studies of nuclear reactors. Based on the phenomena 1 OPIS MODELA 1 MODEL DESCRIPTION Simuliranje eksplozije pare v reaktorski votlini - Simulation of a Reactor Cavity Steam Explosion 293 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 292-308 Faza mešanja Faza sprožitve Faza širjenja Faza raztezanja Premixing phase Triggering phase Propagation phase Expansion phase talina goriva/ molten fuel J Sl. 1. Shema štirih zaporednih faz eksplozije pare Fig. 1. Schematic presentation of the four consecutive phases of the steam explosion eksplozije pare lahko glede na dogajanja razdelimo v štiri zaporedne faze: faza mešanja, faza sprožitve, faza širjenja in faza raztezanja (sl. 1). V fazi mešanja nastane območje, v katerem je staljena sredica grobo pomešana s hladilno vodo. Ker so delci taline obdani s plastjo pare, je prenos toplote s taline na vodo razmeroma majhen. V fazi sprožitve se eksplozija pare sproži. Sprožitveni dogodek je motnja, ki destabilizira plast pare okoli nekega delca taline, tako da pride do neposrednega stika med talino in vodo, ki privede do lokalnega povečanja prenosa toplote in povišanja tlaka ter fine fragmentacije delca. Med fazo širjenja pride do stopnjevanja eksplozije pare zaradi sklopitve potujočih tlačnih valov, fine fragmentacije delcev in prenosa toplote po sprožitvenem dogodku. Med fazo raztezanja se toplotna energija hladiva spreminja v mehansko energijo. Raztezanje visokotlačne mešanice razpršenega staljenega goriva, vode in vodne pare, ki povzroča odmikanje okoliških tekočin in tlačno obremenitev okoliških struktur, določa možen obseg škode, ki jo lahko povzroči eksplozija pare. Bolj izčrpen opis posameznih faz eksplozije pare je podan v [1] do [3]. Da bi lahko obravnavali eksplozijo pare s splošnim programom za RDT, smo razvili ustrezen parametrični model eksplozije pare. Za razliko od specializiranih programov za RDT za simulacijo eksplozij pare, pri katerih eksplozije pare modelirajo na mikroskali z osnovnimi povprečenimi ohranitvenimi enačbami večfaznega toka ([1], [2], [5] do [7]), v predstavljenem postopku eksplozijo pare modeliramo kot raztezajočo se visokotlačno mešanico razpršene taline goriva, kapljevite vode in vodne pare. Podoben postopek so uporabili tudi v študiji eksplozije pare, predstavljeni v [4], kjer so eksplozijo occurring during a steam explosion it can be divided into four consecutive phases: the premixing phase, the triggering phase, the propagation phase and the expansion phase (Fig. 1). In the pre-mixing phase a coarsely mixed region of molten corium and coolant water is formed. The melt and the water are separated by a vapour film, so the heat transfer between the melt and the water is relatively low. In the triggering phase the steam explosion is triggered. The triggering event is a disturbance that destabilizes the vapour film around a melt particle allowing liquid-liquid contact, which leads to locally enhanced heat transfer, pressurization and local fine fragmentation. During the propagation phase there is an escalation process resulting from the coupling between the pressure-wave propagation, the fine fragmentation, and the heat transfer after the triggering event. During the expansion phase the thermal energy of the coolant is converted into mechanical energy. The expansion of the high-pressure pre-mixture of dispersed molten fuel, water and vapour against the inertial constraints imposed by the surroundings determines the damage potential of the steam explosion. A more comprehensive description of the steam-explosion phases is presented in [1] to [3]. To be able to treat the steam explosion with a general purpose CFD code, an appropriate fit-for-pur-pose analytical model of the steam explosion was developed. In contrast to specialized steam-explosion CFD codes, where the steam explosion is modelled on a micro-scale using fundamental averaged multiphase flow conservation equations ([1], [2], [5] to [7]), in the presented approach the steam explosion is modelled reasonably simplified as an expanding high-pressure pre-mixture of dispersed molten fuel, liquid water and vapour. A similar approach was also used in the steam-explosion study presented in [4], where the steam 294 Leskovar M. - Končar B. - Cizelj L. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 292-308 pare obravnavali bolj preprosto kot raztezajoč visokotlačni parni mehur. V splošnem predlagani model eksplozije pare temelji na Hicks-Menziesovem termodinamičnem postopku [1], vendar poleg tega upošteva tudi zamisel mikrointerakcijskega območja [8]. Zamisel mikrointerakcijskega območja praktično pomeni, da med eksplozijo pri termični interakciji med delci taline in hladivom ne sodeluje celotno hladivo, ampak le tisto, ki se nahaja v okolici delcev taline. Na sliki 2 je shematično prikazan model eksplozije pare. Staljena sredica je označena s črno barvo in nadpisom cor, vodna para s svetlo sivo barvo in nadpisom vap in kapljevita voda s temno sivo barvo in nadpisom wat. Predpostavili smo, da si vse faze delijo isto hitrostno polje in isti tlak, kar je smiselna poenostavitev. V prikazani nadzorni prostornini je vsaka faza opisana s prostorninskim deležem faze a, prostornino V, gostoto r in temperaturo T. Mikrointerakcijsko explosion was treated less sophisticatedly as an expanding high-pressure vapour bubble. In general, the developed steam-explosion model is based on the Hicks-Menzies thermodynamic approach [1], taking into account the micro-interaction zone concept [8]. According to the micro-interaction zone concept not all the coolant thermally participates in the explosion, but only the coolant that is in the surrounding of the melt particles. In Figure 2 the steam-explosion model is schematically presented. The corium phase is denoted by the black colour and the superscript cor, the vapour phase by the light-grey colour and the superscript vap, and the liquid water phase with the dark-grey colour and the superscript wat. It was assumed that all the phases share the same velocity field and the same pressure, which is a reasonable simplification. In the presented control volume each phase is described with the phase volume fraction a, volume V, density r and temperature T. a) Faza mešanja (indeks 1) / Premixing phase (index 1) cor cor vap vap wat a,V a,V a ,V r1cor ,T1cor r1vap ,T1vap r1wat ,T1 b) Faza sprožitve in širjenja / Triggering and Propagation phase MI MI a ,V c) Konec faze širjenja in začetek faze raztezanja (indeks 2) / End of Propagation phase and Start of Expansion phase (index 2) d) Konec faze raztezanja (indeks 3) / End of Expansion phase (index 3) a3cor ,V3cor a3vap ,V3v r3cor ,T3cor r3vap ,T3v vap vap a 3wat ,V3wa r3wat ,T3wa Sl. 2. Shema modela eksplozije pare (črna - staljena sredica, svetlo siva - para, temno siva - kapljevita voda, pikčasta siva - kapljevita voda v mikrointerakcijski coni) Fig. 2. Schematic presentation of steam-explosion model (black - molten core, light grey - vapour, dark grey - liquid water, dotted grey - liquid water in micro-interaction zone) Simuliranje eksplozije pare v reaktorski votlini - Simulation of a Reactor Cavity Steam Explosion 295 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 292-308 območje je označeno s pikčasto sivo barvo in indeksom MI. V modelu smo predpostavili, da se ves prenos toplote med staljenim gorivom in hladivom dogodi v prvih treh fazah eksplozije pare in da se v fazi raztezanja proizvedena para, ki je pod visokim tlakom, razteza adiabatno. Opravljeno delo med predpostavljeno adiabatno fazo raztezanja A3 lahko izračunamo iz enačbe: vr p2(V2 vap ) k 4^3= 3 pdV = - Y V2vap k 1 kjer sta p2 in p3 tlaka na začetku in na koncu faze raztezanja, k pa razmerje med specifično toploto pare pri stalnem tlaku in pri stalni prostornini. Pomemben parameter eksplozije pare je energijski izkoristek eksplozije pare, ki ga merijo tudi pri preizkusih eksplozije pare, in pomeni razmerje med opravljenim mehanskim delom med eksplozijo in začetno notranjo energijo staljene sredice [1]. V našem modelu pomeni energijski izkoristek eksplozije pare h osnovo za izračun vseh preostalih parametrov eksplozije pare. Ko izberemo razmere med fazo mešanja, lahko tlak na začetku faze raztezanja p2 izračunamo iterativno z enačbo: The micro-interaction zone is denoted with the dotted grey colour and the index MI. In the model it was assumed that all the heat transfer from the molten fuel to the coolant occurs during the first three steam-explosion phases, and that during the expansion phase the generated vapour, which is at high pressure, adiabatically expands. The work performed during the presumed adiabatic expansion phase A23 can be calculated as: 1 Vk -1 p2V2 vap k -1 -1 (1), where p2 and p3 are the pressures at the start and the end of the expansion phase, and k is the ratio of the vapour specific heats at constant pressure and at constant volume. An important parameter of the steam explosion is the steam-explosion energy-conversion ratio, which is also quantified in steam-explosion experiments and reflects how much internal energy of the melt is transformed into the mechanical energy of the explosion [1]. In our model the steam-explosion energy-conversion ratio, h, was used as the basis for the calculation of all the other steam-explosion parameters. After the conditions during the pre-mixing phase are chosen, the pressure at the start of the expansion phase, p , can be calculated by iteratively solving the equation: p2 =h kjer so p3 tlak v zadrževalnem hramu, ccor specifična toplota sredice in Tsat temperatura nasičenja vode pri tlaku v zadrževalnem hramu. Prostorninski delež mikrointerakcijskega območja aMI, ki določa prostorninski delež pare na začetku faze raztezanja a2vap = aMI + a1vap, smo izbrali tako, da je bil tlak p2 na začetku faze raztezanja največji, pri čemer smo upoštevali fizikalno izvedljivost pojava. Zaradi predpostavke o adiabatnem raztezanju pare je mogoče gostoto mešanice med raztezanjem r2L3 izračunati le kot funkcijo tlaka: k -1) r1cora1cor ccor (T1cor -T1sat ) -1 (2), p2 where p3 is the containment pressure, ~ ,—-- ¦---------------< > 0,2 0,4 0,6 0,8 w Fig. 3. Tolerance for harmonic balance and small-parameter analytical methods 0 Simbolno-številčno analiziranje nihanj sistemov - A Symbolic-Numeric Vibrations Analysis of Systems 313 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 309-316 calculations, even with complex formulae and expressions. But often, a semi-analytical approach, combining the features of analytical and numerical computations, is the most desirable synthesis. This allows the analytical work to be pushed further, before the numerical computations start. For symbolic-numeric computation of the nonlinear oscillation multibody systems the VIBRAN computer algebra system was used. VIBRAN’s special procedure can generate optimized FORTRAN code from obtained analytical expressions, which can be directly used in programs for numerical analysis. Figure 4 illustrates the scheme of the proposed approach. Let us discuss the multibody system with s degrees of freedom. After good known perturbations the equations of motion can be rewritten in the matrix form: [A]{x} + [B]{x} + [C]{x} {H(x,x,t)} + {f(t)} (9), where: { f (t)} = { f0} +{ f1}sin(wt) +{ f2}cos(wt) +... {f(t)} - continuous periodical time function or expandable into a Fourier series, and vector H (x, x&,t) is the result from block 1. The solution of the above-mentioned system can be expressed using the harmonic balance method in the form: {x} ={D0}+{D1}sin(wt) +{D2}cos(wt) +... where {Di} are the unknown vectors that can be found from the nonlinear algebraic equations. Following the harmonic balance method ([6] and [15]) these equations for the first three vectors’ coefficients are: [U]{D} + {f(D)}={Q} (10), where fi are the coefficients of the function f(t) Fourier expansion. Analogously, the equations for other harmonics can be found using VIBRAN’s program, shown in block 4. The expressions of Hi and their required derivatives are expressed in closed form using computer algebra techniques with a FORTRAN code generation procedure. The programs’ structure is shown in Figure 4. Obviously, the matrix of coefficients [U] consists of independent sub-matrix blocks located at the main diagonal. Therefore, the linear part of the matrix equation decomposes into m separate systems (m is the number of harmonics in the solution vector) of size 2s and one system (corresponding to the zero harmonic) of size s. The obtained solution of these systems serves as an initial approximation for further computation. The Newton’s iteration formula claims: {E(Di)} + lE'(Di)]{Di+1 -Di} = { 0 } (11), where {E(D)} is the system of equations and [E’(D)] is the Jacobi matrix of the whole system (including the linear part as well). Substituting these two formulae the Newton iteration becomes ([U] + [f'(Di)]){Di +1} = [f '(Di)]{Di {f(Di)}+{Q} The iterations start with: [U]{A0} = {f} (12). (13). This linear matrix equation must be solved for every iteration step. This equation can be rewritten in the simple form ([U] + [f']){D} = {F} (14). It is not expedient to sum up the matrices [U] and [f] in advance, because they have quite different structures. Matrix [U], as was already mentioned, is block-banded, i.e., consists of separate sub-matrix blocks located at the main diagonal. The structure of matrix [f] depends on the type and location of nonlinear terms in the initial differential equation system, but it is always sparse and can possess nonzero elements far from the main diagonal. Thus, matrix [D] is not stored in the computer memory at all, and its every element is computed by a reference to the special subroutine. Matrix [f’] is stored in the main memory as a sparse matrix. Of course, such storage demands corresponding modifications to the solution algorithm itself. In many applications the solution of the differential equation system must be obtained in a specified domain of some varied parameters (frequency, stiffness, mass, etc.). Therefore, the program is designed in such a way that any parameter of the initial system can be varied with a regular or logarithmic step. Note that the analytical computation is performed only once, while the numerical calculations are repeated every time when the value of any parameter of the system is being changed. 314 Kulvietiene R. - Kulvietis G. - Tumasoniene I. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 309-316 The proposed symbolic-numeric method was tested for the dynamics of a double-head recording device with aerodynamic support [8]. The following equations describe the system behavior: & x&1 +k1x&1 +k2x&2 +k3x1 +u0 +u1x1 +u2x12 +u3x13 = f1(t ) & x&2 +k6x&1 +k7x&2 +k8x1+k9x2 = f2(t ) where: f1(t ) = k4 sint + k5 cost , f2 (t ) = k10 sint + k11 cost Analytical expressions obtained according to the VIBRAN program conclude the part of the analytical calculations. The analytical result for Hi in Equation (5) is: H0=k3*a10+u1*a10+.5*u2*a11**2+.5*u2*b 11**2+u2*a10**2+1.5*u3*a10*a11**2+1.5 *u3*a10*b11**2+u3*a10**3+u0 H1=a20*k9+k8*a10+u1*a10+.5*u2*a11**2 +.5*u2*b11**2+u2*a10**2+1.5*u3*a10*a1 1**2+1.5*u3*a10*b11**2+u3*a10**3+u0 H2=b21*w*k2+w*b11*k1+k3*a11+a11*u1+ 2*u2*a11*a10+.75*u3*a11**3+.75*u3*a11* b11**2+3*u3*a11*a10**2 H3=-a21*w*k2-w*a11*k1+k3*b11+b11*u1+2*u2*b11*a10+ .75*u3*a11**2*b11+.75*u3*b11**3+3*u3* b11*a10**2 H4=b21*w*k7+a21*k9+w*b11*k6+k8*a11+ a11*u1+2*u2*a11*a10+.75*u3*a11**3+.75 *u3*a11*b11**2+3*u3*a11*a10**2 H5=-a21*w*k7+b21*k9-w*a11*k6+k8*b11+b11*u1+2*u2*b11*a10+ .75*u3*a11**2*b11+.75*u3*b11**3+3*u3* b11*a10**2 The corresponding derivatives are very simple and there are only 25 nonzero terms: H23 = k1*w+1.5*u3*b11*a11 H26 = k2*w H31 = 2*u2*b11+6*u3*a10*b11 H32 = -k1*w+1.5*u3*b11*a11 H41 = 2*u2*a11+6*u3*a10*a11 H43 = k6*w+1.5*u3*b11*a11 H45 = k9 H46 = k7*w H51 = 2*u2*b11+6*u3*a10*b11 H52 = -k6*w+1.5*u3*b11*a11 H55 = -k7*w H56 = k9 Figure 4 illustrates the generated program code that could be directly used for numerical investigations. This code is very simple and contains only 89 floating-point product operations. B(2)=+O(10)+O(11)+Y5 ... END___________________________________ Fig. 4. A fragment of the code generated by VIBRAN 5 CONCLUSION On the basis of non-linear differential equations solved by a harmonic balance method and the synthesis of the VIBRAN analytical calculation system an investigation method for non-linear systems was created. This method combines the advantages of analytical calculation methods and computer algebra. They are compared on the principle of a symbolic-numerical calculation, where the analytical rearrangements are applied only to the nonlinear part of the system, and at the same time the linear part of the system could be easily solved in a numerical way. The proposed method provides smaller expressions for the analytical computation and allows the analysis of systems with greater order. SUBROUTINE ISRA01(A,O) IMPLICIT REAL(A-Z) DIMENSION A(20),O(60) u0 =A( 1) u3 =A( 2) u2 =A( 3) k3 =A( 4) ... O(17)=a11*a10*u3 O(19)=b11*a10*u3 O(20)=O(31)*b21 O(21)=O(29)*b1 ... END SUBROUTINE ISRA(A,B,O) DIMENSION A(20),B(42),O(60) Y1=+.5*O(3) Y2=+.5*O(4) Y3=+1. 5*O(6) ... Y26=+.75*O(13) Y27=+2.25*O(1) B(1)=+O(1)+O(2)+O(5)+O(8)+O(9)+Y1+Y2+Y3+Y4 Simbolno-številčno analiziranje nihanj sistemov - A Symbolic-Numeric Vibrations Analysis of Systems 315 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 309-316 The problem considered in this paper clearly de- proach is that it provides both quantitative and quali- monstrates the power of the symbolic-numeric per- tative results regarding the dynamic behavior of turbation method. An important feature of this ap- multibody systems. 6 REFERENCES [I] R. Lewandowski (1997) Computational formulation for periodic vibration of geometrically nonlinear structures, Part 1: Theoretical background, Int. J. Solids Structures, 34 (15) (1997) 1925-1947. [2] E.Riks (1984) Some computational aspects of the stability analysis of nonlinear structures, Computational Methods in Applied Mechanical Engineering, 47 (1984) 219-259. [3] D.M. Klymov, V.M. Rudenko (1989) Metody kompjuternoj algebry v zadačah mehaniki, Nauka, Moscow. [4] R. Kulvietiene, G. Kulvietis (1989) Analytical computation using microcomputers, LUSTI, Vilnius. [5] R. Kulvietiene, G. Kulvietis, J. Galkauskaite (1997) Computer algebra application to large nonlinear oscillation systems. Mechanine technologija, XXV, Kaunas, 126-130. [6] R. Kulvietiene, G. Kulvietis (1996) Symbolic solution of nonlinear oscillation system using harmonic balance method, Proc. of the 2nd European Nonlinear Oscillations Conference, Vol. 2, 1996, 109-112. [7] I.G. Malkin (1956) Some problems of the theory of nonlinear oscillations, Gostehizdat, Moscow. [8] R. Kulvietiene (1982) Dynamics of aerodynamically supported magnetic head in the recording device, Ph.D. Thesis, KTU, Kaunas. [9] F. San-Juan, A.Abad (2001) Algebraic and symbolic manipulation of poisson series. Journal of Symbolic Computation, 32 (5), (2001) 565-572. [10] A. Cepulkauskas, R. Kulvietiene, G. Kulvietis (2003) Computer algebra for analyzing the vibrations of nonlinear structures, Proc. CASA’2003, Lecture Notes in Computer Science, Vol. 2657, Springer-Verlag, Berlin Heidelberg New York, 747-753. [II] J.-C. Samin, P. Fisette (2003) Symbolic modeling of multibody systems, Kluwer Academic Publishers. [12] Gilsinn, David E. (1995) Constructing Galerkin’s approximations of invariant tori using MACSYMA. Nonlinear Dynamics 8 (2) (1995) 269-305. [13] N.N. Bogolyubov, JA. Mitropolskij (1995) Asymptotical methods in the theory of nonlinear oscillations. TTL, Moskva. [14] L. Pust, F Peterka, G. Stepan, G.R. Tomlinson, A. Tondl (1999) Nonlinear oscillations in machines and mechanisms theory. Mechanism and Machine Theory 34 (1999) 1237-1253. [15] C. Hayashi (1964) Nonlinear oscillations in physical systems. McGraw Hill, New York. Authors’ Address: Doc. Dr. Regina Kulvietiene Prof. Hab. Dr. Genadijus Kulvietis Inga Tumasoniene Vilnius Gediminas Technical University Department of Information Technologies rku@fm.vtu.lt gk@fm.vtu.lt tinga@gama.vtu.lt Sauletekio 11 Vilnius 2040, Lithuania Sprejeto: Odprto za diskusijo: 1 leto 23.2.2006 Accepted: Open for discussion: 1 year Kulvietiene R. - Kulvietis G. - Tumasoniene I. Prejeto: 7.11.2005 Received: 316 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 317-322 UDK - UDC 534.2:681.892 Kratki znanstveni prispevek - Short scientific paper (1.03) Popravni količniki za izračun Youngovega modula iz resonančnega upogibnega nihanja Correction Coefficients for Calculating the Young’s Modulus from the Resonant Flexural Vibration Igor Štubna - Anton Trnik (Constantine the Philosopher University, Nitra) Enostavna enačba, dobljena iz poenostavljene diferencialne enačbe upogibnega nihanja za primer z enakomernim prerezom, nam ne da točne vrednosti Youngovega modula oz. hitrosti zvoka, če je razmerje dolžine in premera (oz. dolžine in debeline) vzorca manjše od 20. Napako lahko odpravimo z množenjem izmerjene resonančne frekvence ali izračunanega Youngovega modula s popravnim količnikom. V prispevku predstavljamo nekaj enačb za popravne količnike in novo enačbo ter jih primerjamo z enačbami Ameriškega združenja za preizkušanje in materiale (American Society for Testing and Materials - ASTM). © 2006 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: nihanja upogibna, frekvence resonančne, moduli Youngovi, izračuni) A simple formula derived from the simplified differential equation of flexural vibration of a sample with a uniform cross-section does not give exact values for the Young s modulus or the velocity of sound if the ratio of the length to the diameter (or the length to the thickness) of the sample is less than 20. The error can be eliminated by multiplying the measured resonant frequency or the calculated Young’s modulus by a correction coefficient. Some formulae for the correction coefficients as well as a new formula are presented and compared with the ASTM formulae. © 2006 Journal of Mechanical Engineering. All rights reserved. (Keywords: flexural vibrations, resonant frequencies, Young’s modulus, calculations) 0 INTRODUCTION One of the best methods for determining the velocity of sound or the Young’s modulus of solids is based on the resonant flexural vibrating of a sample of a cylindrical or a prismatic shape. It is easy to excite this vibration, and its magnitude is sufficiently high. Its resonant frequency is less than the resonant frequency of a longitudinal vibration of a sample with the same length. These properties of the flexural vibration make it preferable for measuring the Young’s modulus or the velocity of sound. For measuring purposes the most suitable vibration is the vibration of a free-free sample because of the relative ease of fulfilling the boundary condition of the theoretical solution. A widely used method, which is also suitable for high temperatures, is based on Foster’s idea [1], later improved by Spinner and Tefft [2]. The solution for the three-dimensional form of the partial differential equation of flexural vibration is complex, but the mathematical approach can be simplified, and a reasonably exact solution can be obtained. For long samples the simplified partial differential equation of the flexural vibration can be used. This equation has the form [3]: L2y +c0i ^ y = 0 (1), d t dx where x and y are the coordinates of the mass element of the sample, t is time, c0 is the velocity of sound (i.e., the velocity of longitudinal wave propagation in the sample), i is the radius of inertion of the cross-section. For a sample with a circular cross-section, the radius of inertion is i = d /4 and for a sample with a rectangular cross-section it is i = d/-12, where d is the diameter of a cylindrical sample or the thickness of a prismatic sample in the direction of 317 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 317-322 the vibration. The frequency equation derived from Eq. (1) for the free-free sample is: cos(al) ch(al) = 1 (2), where l is length of the sample, a = w/(ic0) , w is a resonant angular frequency. The formulae for the velocity of sound c0 and the Young’s modulus E derived from Eq. (2) have the form: l 2 f c0 =K , E= d K l 2 f d r (3), where f is the resonant frequency r is the material density and the values of the constant K are: K = 1.12336 for a cylindrical sample and the fundamental resonant frequency K = 0.97286 for a prismatic sample and the fundamental resonant frequency K = 0.40752 for a cylindrical sample and the 1st overtone, K = 0.35292 for a prismatic sample and the 1st overtone. If a relatively short sample is used (with the ratio l/d < 20) it is necessary to take into account the influence of the shear forces and the rotary inertia. There are two possible ways to do this: 1) solving the complicated frequency equation derived from the partial differential equation accounting for these influences, 2) using the simple formula (3) and multiplying the calculated Young’s modulus (or measured resonant frequency) by a correction coefficient. Formulae for calculating the correction coefficients for the fundamental mode as well as for the first overtone of the flexural vibration of a cylindrical or a prismatic sample and comparisons of these coefficients are given in this paper. 1 CORRECTION COEFFICIENTS DERIVED FROM AN ALTERNATIVE EQUATION If the ratio of l/d > 20, the measured resonant frequency is in a good agreement with that calculated from Eq. (3). If the ratio of l/d < 20, the measured resonant frequency is less than the frequency calculated from Eq. (3) for the same sound velocity: the shorter the sample, the bigger the discrepancy between the theoretical and the measured frequencies. To avoid this disagreement, the effect of the shear forces and the rotary inertia has to be taken into account. This leads to Timoshenko’s equation [1] or to the alternative equation [4]: S y i-2d y ¦y + c 2i dt2 dx4 pi d4y d t2x2 (4). Here p = 2(1+ m) /k , where m is Poisson’s ratio, and k = 0.710. The frequency equation for the “free-free sample” derived from Eq. (4) is: 2RaRbPaPb[ch(al)cos(bl) -1]--[Rb2Pa2 - Ra2Pb2]sh(al)sin(bl) = 0 (5), where: Ra =R+a2 = R -b2 = Pa + a3 , Pb R = p(w / c0 )2 , P = (1+ p)(w /c0 )2 , = Pb -b3 , a = (w/c0)J-p/2 + ^p2/4 + (c0/iw)2 , b = (w/c0)l+p/2 + 4p2/4 + (c0/iw)2 . The frequency equation (5) is complex and can be solved only by a numerical method. This is the reason why correction coefficients are used. If the measured resonant frequency f is multiplied by the correction coefficient Q then the correct value of the velocity of sound (or the Young’s modulus) can be obtained from Eq. (3). Then Eq. (3) becomes: l 2 (Qf ) c0 =K , E= d K l 2 (Qf ) d r (6), where the coefficients K are the same as above. The correction coefficient Q was obtained from the resonant frequencies f(2) and f(5) computed using the numerical bisection method from the frequency equations (2) and (5) respectively. Then the correction coefficient is: Q = f (2) f (5) (7). The correction coefficients Q are dependent on the ratio of l/d as well as on Poisson’s ratio m, but the dependence between Q and m is weak. The values of Q could be considered constant for l/d > 6 and 0.15 < m < 0.4 (see Fig. 1 and 2). The values of Q were computed for the fundamental mode and l/d> 2.5, and for l/d > 5 for the 1st overtone. The tabulated coefficients Q for the fundamental mode of flexural vibration and the cylindrical and prismatic samples are shown in [5] and [6] and for the 1st overtone of the flexural vibration and cylindrical and prismatic samples in [7]. It is often more convenient to have correction coefficients in the form of a formula than atable. Therefore, the formula for calculating the correction coefficients was suggested [8]: 2 a 2 318 Stubna I. - Trnik A. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 317-322 Q=1 + 1- + — l/d [ju l/d l/d[ l/d For the fundamental mode and the prismatic sample: (8). Parameters A, B, C, D were obtained from a regression analysis of the correction coefficients listed in [5] to [7]. The values of the parameters A, B, C, D are in Tab. 1 and Tab. 2. 2 CORRECTION COEFFICIENTS DERIVED FROM TIMOSHENKO‘S EQUATION Timoshenko’s equation describes the flexural vibration of samples with a uniform cross-section with a sufficient precision [3]. Resonant frequencies predicted by the frequency equation derived from Timoshenko’s equation are in agreement with experimentally measured values. But this frequency equation is complex (even more than Eq. (5)) so correction coefficients together with the simple formula (3) are commonly used. The values of these coefficients calculated by Pickett are in table form in [9]. Pickett’s values served as the basis for the formulae of correction coefficients for the fundamental mode of flexural vibration ([9] to [13]). The application of Pickett’s coefficient T consists of its multiplication by the Young’s modulus calculated from the simple formula (3). For the fundamental mode and a cylindrical sample: T0p=1.000+6.585(d/l)2, if l/d>20 T0p=1 + 6.585(1 + 0.0752// + 0.8109//2)(/)2--0.868(d/l)4-8.340(1 + 0.2023// + 2.173//2)(d/l)4 (10). 1.000 + 6.338(1 + 0.1408// +1.536//2 )(d /l)2 if l/d<20 Then the correct value of the Young’s modulus is E = T0cE(3) or E = T0pE(3), where E(3) is calculated by Eq. (3). Another, complicated formula was proposed by Martinček [14]. The relationship T(M) or Q(M) is weak, and for l/d > 10 the correction coefficients can be considered independent of the Poisson’s ratio (see Fig. 1, Fig. 2). Therefore, a simpler formula for the correction coefficient can be used in such a case. For example, Acegorian and Chočian used: T =1+83(i / l)2 1370(i / l)4 125(i / l) (11), T0c=1.000 + 4.939(d/l)2, if ld > 20 T0c=1 + 4.939(1 + 0.0752// + 0.8109/u2)(d / l)2 -0.4883(d/l)4-4.691(1 + 0.2023// + 2. 173/j2)(d /l)4 1.000 + 4.754(1 + 0.1408// + 1.536/j2)(d /l) if l/d<20 Table 1. Parameters A, B, C, D for the fundamental mode 1 + 83.4(i/l) where i is a radius of inertia of the cross-section and l is the length of the sample [15]. 3 CORRECTION COEFFICIENTS FOR SAMPLE WITH CHAMFERED EDGES If the prismatic sample is not ideal but has chamfered or rounded edges an additional correction should be made. Correction factors F are in the range (9). of 1.0031 to 1.0287 for the chamfer size of 0.08 to 0.25 mm. If the density of the sample is determined from its weight and dimensions then the density correction is made by multiplying Young’s modulus by the factor P €(1.0011, 1.0105) for the same chamfer size. The Parameter B C D cross-section circular square 0.00002 2.5719 -0.14069 -2.43588 -0.00002 3.44347 -0.44952 -3.34228 Table 2. Parameters A, B, C, D for the 1st overtone Parameter B C D cross-section circular square 0.00131 -0.00249 7.44851 10.0605 3.56057 -7.076 4.50048 -2.02022 Popravni količniki za izračun - Correction Coefficients for Calculating 319 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 317-322 1.14 1.12 1.1 1.08 1.06 1.04 1.02 1 0.15 0.2 0.25 0.3 0.35 0.4 Poisson's ratio Fig. 1. Correction coefficients Q0p for the fundamental mode and prismatic sample. Graphs are (from the top) for: l/d = 5, 6, 7, 10, 15, 20 true Young’s modulus E = FPE0, where E0 is the Young’s modulus calculated for the ideal prismatic sample. The correction factors F and P as a function of the chamfer size were calculated by G. Quinn [16]. 4 COMPARISON OF THE CORRECTION COEFFICIENTS The correction coefficients calculated from Eq. (10) and Eq. (8) for the fundamental mode and a prismatic sample are shown in a graph in Fig. 3. The comparison of the coefficients Q could not be made because there is not a formula 1p for the correction coefficient for the 1st overtone and a prismatic sample in the ASTM standards ([10] to [13]), and correction coefficients for this case are not in [9]. An indirect verification of the correctness of the coefficients Q1p calculated from the formula (8) is in good agreement 1,3 1,25 1,2 1,15 1,1 1,05 1 1.25 1.2 1.15 1.1 1.05 1 0.15 0.2 0.25 0.3 0.35 0.4 Poisson's ratio Fig. 2. Correction coefficients Q1 for 1st overtone and cylindrical sample. Graphs are (from the top) for: l/d = 5, 6, 8, 10, 12, 15, 20 between resonant frequencies calculated from commonly accepted Timoshenko’s equation and Eq. (4), [4]. The graph of the correction coefficients Q1 calculated from Eq. (8) is in Fig. 6. The correction coefficients calculated from Eq. (9) and Eq. (8) for the fundamental mode and the cylindrical sample are in Fig. 4, and the correction coefficients for the 1st overtone and a cylindrical sample are plotted in Fig. 5. The coefficients T tabulated in [9] served as a basis for the comparison. As we can see in Fig. 3, 4 and 5, the correction coefficients calculated from Formula (8) show good agreement with those calculated with the help of Eq. (9) and Eq. (10), and with the coefficients presented in [9]. Acknowledgement This work was supported by grant VEGA 1/0279/03. 4 8 12 l/d 16 20 Fig. 3. Correction coefficients for prismatic sample and fundamental mode: line - T0p after ASTM, points - (Q0p)2 calculated from Eq. (8), m = 0.3 320 Štubna I. - Trnik A. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 317-322 1,25 1,2 1,15 1,1 -1,05- 1 4 8 12 16 20 l/d Fig. 4. Correction coefficients for cylindrical sample and fundamental mode: line - T0c after ASTM, points - (Q0c)2 calculated from Eq. (8), m = 0.3 1,7 1,6 1,5 1,4 1,3 1,2 1,1 1 4 8 12 l/d 16 20 Fig. 5. Correction coefficients for cylindrical sample and the1st overtone: line - T1c after ASTM, points - (Q1c)2 calculated from Eq. (8), m = 0.3 1,9 1,75 1,6 1,45 1,3 1,15 1 4 12 l/d 16 20 Fig. 6. Correction coefficients for prismatic sample and the 1st overtone: (Q )2 calculated from Eq. (8), m = 0.3 Popravni količniki za izračun - Correction Coefficients for Calculating 321 8 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 317-322 5 REFERENCES [I] Forster, F (1937) Ein neues Messverfahren zur Bestimmung des Elastizitatsmodulus und der Dampfung. Zeitschrift fur Metallkunde, 29, 1937, N2, pp. 109-113. [2] Spinner, S., Tefft, W.E. (1961) Method for determining mechanical resonance frequencies and for calculating elastic moduli from these frequencies. Am. Soc. Test. Mater. Proc., 61, 1961, pp. 1221-1230. [3] Timoshenko, S. P. (1955) Vibration problems in engineering. D. Van Nostrand Inc., New York. [4] Štubna, I., Majernik, V. (1998) An alternative equation of the flexural vibration. Acustica - Acta Acustica, 84, 1998, N6, 999-1001. [5] Štubna, I., Liška, M. (1999) Correction coefficients for calculation of Young’s modulus from resonant frequencies, I: Cylindrical sample. In: Proc. 4-th Inter. Conf. Theoretical and Experimental Problems of Material Engineering, Puchov [6] Štubna, I., Liška, M. (1999) Correction coefficients for calculation of Young’s modulus from resonant frequencies, II: Prismatic sample. In: Proc. Conf. DIDMATTECH 1999, Nitra, pp. 140-143. [7] Štubna, I., Liška, M., Malinarič, S. (2001) Correction coefficients for calculation of sound velocity from resonant frequencies, III: 1st Overtone In: Proc. Conf. DIDMATTECH 2000, Prešovskauniverzita, Prešov, pp. 419-422. [8] Štubna, I., Liška, M. (2001) Formula for correction coefficients for calculating Young’s modulus from resonant frequencies. Acustica - Acta Acustica, 87, 2001, N1, pp. 149-150. [9] Schreiber, E., Anderson, O.L., Soga, N. (1973) Elastic constants and their measurement. McGraw-Hill Book Co., New York. [10] ASTM C 1198-01 (2001) Standard test method for dynamic Young’s modulus, shear modulus and Poisson’s ratio for advanced ceramics by sonic resonance. (published in Standard Documents, Philadelphia USA). [II] ASTM C 848-88 (1999) Standard test method for dynamic Young’s modulus, shear modulus and Poisson’s ratio for ceramic whiteware by sonic resonance. (published in Standard Documents, Philadelphia USA). [12] ASTM C 1548-02 (2003) Standard test method for dynamic Young’s modulus, shear modulus and Poisson’s ratio of refractory materials by impulse excitation of vibration. (published in Standard Documents, Philadelphia USA). [13] ASTM C 1259-01 (2001) Standard test method for dynamic Young’s modulus, shear modulus and Poisson’s ratio for advanced ceramics by impulse excitation of vibration. (published in Standard Documents, Philadelphia USA). [14] Martinček, G. (1975) Teoria a metodika dynamickeho nedeštruktivneho skušania plosnych prvkov SAV, Bratislava. [15] Acegorian, ZA., Chočian, M.G. (1960) An investigation of strength of the stone materials. Zavodskaya Laboratoriya, 26, 1960, N11, pp. 98-100. [16] Quinn, G.D. (2000) Elastic modulus by resonance of rectangular prisms: Corrections for edge treatments. J. Amer. Ceram. Soc, 83, 2000, N2, pp. 317-320. Authors’ Address: DocDr. Igor Štubna Dr. Anton Trnik Constantine the Philosopher University Department of Physics A. Hlinku 1 949 01 Nitra, Slovakia istubna@ukf.sk Prejeto: Sprejeto: Odprto za diskusijo: 1 leto Received: 24.5.2005 Accepted: 23.2.2006 Open for discussion: 1 year 322 Stubna I. - Trnik A. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 UDK - UDC 699.86:62-404.8 Strokovni članek - Speciality paper (1.04) Teoretične in eksperimentalne osnove za izdelavo mehanskih izolacijskih pen Theoretical and Experimental Foundations for the Manufacturing of Mechanical Insulation Foams Darko Drev - Jože Panjan (Fakulteta za gradbeništvo in geodezijo, Ljubljana) V tem prispevku obravnavamo teoretične pogoje, ki so potrebni za izdelavo stabilne mehanske izolacijske pene. Poleg tega navajamo tudi stvarne predloge za izvedbo izdelave mehanske pene in nanosa na gradbene površine. Mehanska pena se oblikuje razmeroma preprosto, zagotovljeni morajo biti samo ustrezni pogoji. Izolacijske lastnosti dajo drobno porazdeljeni zračni mehurčki v izolacijski plasti. Podobne lastnosti imajo tudi različni izdelki iz penjenega betona in penjenega polistirena, ki pa se ne izdelujejo neposredno na gradbišču, temveč v proizvodnih obratih. Glavna zamisel pri tem je nastanek porozne mehanske pene na gradbišču in nanašanje le te na gradbene površine. Pena mora biti dovolj stabilna, da se lahko nanaša na gradbene površine in se tam tudi utrdi. © 2006 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: pene izolacijske, pene mehanske, stabilnost, lastnosti reološke) This paper deals with the theoretical conditions necessary for the formation of stable mechanical insulation foam. In addition to this it gives concrete proposals for the formation of mechanical foam and its application to surfaces in the field of civil engineering. Mechanical foam is formed relatively easily, provided suitable conditions are present. The insulating character is provided by finely distributed air bubbles in the insulation layer. Similar characteristics can be found in various products made of foamed concrete as well as foamed polystyrene, which are not manufactured on site but in manufacturing plants. The main objective is the formation of a porous mechanical foam on the construction site and its application onto construction elements. The foam must be stable enough to be applied to the construction surface and then solidify. © 2006 Journal of Mechanical Engineering. All rights reserved. (Keywords: insulating foams, mechanical foams, stability, rheological characteristics) 0 UVOD Na tržišču je velikoštevilo različnih izolacijskih gradbenih gradiv, ki se v glavnem izdelujejo v proizvodnih obratih v obliki plošč ali zidakov. S pripravljenimi izolacijskimi gradivi se oblagajo gradbene površine, v nekaterih primerih pa se lahko uporabljajo tovrstna gradiva namesto zidakov. V tem prispevku obravnavamo mehanizem nastajanja mehanske izolacijske pene ter postopek nanašanja na gradbene površine. Izhajamo z vidika, da ima gradivo z velikim številom majhnih zračnih mehurčkov zelo dobre izolacijske lastnosti. Podobne lastnosti imajo tudi različni izdelki iz penjenega betona, ki pa se ne izdelujejo neposredno na gradbišču, temveč v proizvodnih obratih, kjer se 0 INTRODUCTION A large number of insulating construction materials exist on the market. These materials are mostly manufactured in production plants in the form of plates and bricks/blocks. Confectional insulating materials are used for the cladding of construction surfaces and in some cases as a substitute for brick. This paper deals with the mechanism of forming mechanical insulating foam and the procedure of its application onto construction elements. We start from the basis that a material with a large number of small air bubbles has very good insulating characteristics. Various products made of foamed concrete posses similar characteristics. These are not manufactured on site but in production plants 323 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 pripravijo v obliki različnih zidakov in izolacijskih plošč. Tako kakor izdelki iz penjenega betona, se proizvajajo v industrijskih obratih tudi izolacijski materiali iz steklenih vlaken, penjenega polistirena, penjenega poliuretana itn. Ta izolacijska gradiva se vgradijo v obliki različnih pripravljenih kosov na fasade, stropove, tla in druge gradbene površine, kjer želimo povečati toplotno in zvočno izolacijo. Na takšne in podobne izolacijske materiale je treba nato nanesti ali pritrditi še pročelna gradiva za lepši videz in ustrezno mehansko trdnost (omet, pročelne obloge itn.). 1 MATERIALI IN METODE V kašasto snov, ki je sestavljena iz veziva, polnil, vode in drugih dodatkov, želimo vmešati čim večjo količino zraka. Mehanska pena je lahko stabilna le takrat, ko so mehurčki čim manjši, saj je pri tem vzgon najmanjši. Velikost mehurčka je odvisna od gostote razpršnine, površinske napetosti, specifične teže razpršnine, njene homogenosti (vrste gradiv) ter parametrov, ki so odvisni od nastavitve strojne opreme (tlak, vrtenje mešalne glave itn.). Zunanji tlak razpršnine na stene mehurčka in notranji tlak v mehurču morata biti v stabilnem ravnovesju: where they are confectionalized in the form of bricks and insulation plates. Likewise, insulation materials made of glass fibres, foamed polystyrene, foamed polyurethane, etc. are produced in production plants. These insulating materials are fitted in the form of standardised pieces on facades, ceilings, floors and other surfaces where we wish to increase the heat and sound insulation. After the application of these and similar insulating materials it is only necessary to apply or fasten the facade material for an improved appearance and adequate mechanical strength (mortar, facade cladding etc). 1 MATERIALS AND METHODS Our objective is to mix in an as much air as possible into a pasty material composed of binder, filler, water and other admixtures. The mechanical foam is stable only when the bubbles are as small as possible, since the corresponding buoyancy is then minimized. The size of the bubble depends on the density of the dispersion, its homogeneity and other parameters that vary with the settings of the mechanical equipment (pressure, rotation of the mixer etc.) The outer pressure of the dispersion on the wall of the bubble and the inner pressure in the bubble itself must be in stable equilibrium: 2g.Pm.M R rd .Re.T (1), pri tem morata biti vzgon in površinska napetost v the buoyancy and surface tension must be in ravnovesju: equilibrium: v.g.r = 2p . g . r (2) r =rd -rz (3). Na sliki 1 je prikazan nastanek mehurčka v Figure 1 presents the formation of a bubble razpršnini in sile, ki delujejo nanj pri stabilnih in the dispersion and the forces that act on it under pogojih. stable conditions. Pri stabilni mehanski peni je specifična teža In a stable mechanical foam the specific razpršnine enaka: weight of the dispersion equals: Re.T r d prostornina mehurčka je pri tem: the volume of the bubble is: 4 3 V= Pr 3 (4), ( 5), tlak v mehurčku mora biti v ravnovesju z vsoto the pressure inside the bubble must be in equilibrium atmosferskega tlaka in kritičnih tlakov na notranji in with the sum of the atmospheric pressure and critical 324 Drev D. - Panjan J. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 razprnina dispersion - fast Sl. 1. Shematski prikaz oblikovanja mehurčka mehanske pene Fig. 1. A schematic representation of the formation of a bubble of mechanical foam zunanji steni mehurčka: pressures on the inner and outer sides of the bubble wall: Pi = PA +PK + ( P K ) 1 (6), kritični tlak na notranji steni mehurčka je odvisen od the critical pressure on the inner wall of the bubble površinske napetosti in velikosti mehurčka: depends on the surface tension and the bubble size: () Pk2 2g (7), 2 r tlak v mehurčku je v ravnovesju z vsoto the pressure inside the bubble is in equilibrium with atmosferskega tlaka in pritiskov na zunanji in notranji the sum of the atmospheric pressure and the steni: pressures on the outer and inner walls: 2.g 2.g Pi=PA+ + =P A + 2. g . 11 + rr (8), za zelo tanke stene mehurčkov velja: for very thin walls: pri čemer je: Pi =PA where: 4.g r (9), (10) in velikost mehurčka je odvisna od površinske and the size of the bubble depends on the surface napetosti in razlike notranjega in atmosferskega tlaka: tension and the difference in the internal and atmospheric pressures: 4.g Pi -PA (11). Na sliki 2 so prikazani kritični pogoji, ki veljajo Figure 2 presents the critical conditions that za stabilno mehansko peno. V razpršnino je mogoče apply for a stable mechanical foam. Under given pri danih pogojih vmešati samo določeno količino circumstances only a specific amount of air can be Teoretične in eksperimentalne osnove - Theoretical and Experimental Foundations 325 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 \ P„ P \________________________________ Sl. 2. Kritični pogoji pri oblikovanju polimerne mehanske pene Fig. 2. Critical conditions in the formation of polymer mechanical foam zraka. Če dovedemo na stroj za oblikovanje mehanske pene večjo količino zraka od teoretično dovoljene, dobimo neenakomerno strukturo z velikimi mehurčki. Premajhna količina zraka pa povzroči nastanek debelih sten, večjo gostoto in slabše izolacijske značilnosti nanosa. Kritični pogoji: R = R« applied to a dispersion. In the event that a larger quantity of air, with regards to the theoretically permitted limit, is applied to the mechanical foam-forming machine, we get a non-homogenous structure with large bubbles. On the other hand an insufficient quantity of air causes the formation of thick walls, a larger density and poorer insulation characteristics of the coating. Critical conditions R = R„ ln m. (( p ) -pa ) M 2.g (12) (13). (PR) k Re.T.rd Re.T.rdPk Pri dviganju mehurčka mora biti vzgon večji od sil, ki In the event of the rising of the bubble the buoyancy držijo mehurček v razpršitvi: must be greater than the forces that hold the bubble in the suspension: 2.g.r 9 .hd 2 .(rd-rz) 3.hz+3.hd 3.hz+2.hd (14), pri tem sta gostota in površinska napetost razpršnine mnogo večji kakor pri zraku: rd >> rz pri takšnih pogojih je hitrost dviganja mehurčka: where the density and surface tension of the dispersion are greater than with the air: in / and d >> h under these conditions the velocity of the rising bubbles is: 2.g.r2 .rd 9. hd (15), kjer pomenijo: Indeksi: 1 = zrak + para 2 = tekočina (razpršnina) where the indexes and symbols mean: Indexes: 1 = air + steam 2 = fluid (dispersion) 326 Drev D. - Panjan J. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 3 = trdno r = na krivulji Simboli: rd = gostota polimerne razpršnine rz = gostota zraka u mehurčku V = prostornina r, r = polmer mehurčka Poo = tlak pare pri ravni površini (roo) P1 = notranji tlak P = tlak na konkavno ali konveksno površino P= atmosferski tlak rD = gostota pare Re = Reynoldsovo število v = hitrost dviganja mehurčka hd = viskoznost polimerne razpršnine hz = viskoznost zraka v mehurčku /= površinska napetost g = težnostni pospešek (9,81 m/s2 ) m = masa polimerne razpršnine 2 PREIZKUSNI DEL Mehansko izolacijsko peno bi lahko izdelovali neposredno na gradbišču z ustrezno strojno opremo. Za izdelavo mehanske pene bi lahko v načelu uporabili strojno opremo, ki se uporablja za oplemenitenje tekstila, ali pa posebej za to izdelane stroje. Ker gre za novost, še ni izdelane namenske strojne opreme za oblikovanje mehanske izolacijske pene v gradbeništvu. Pri praktičnih preizkusih se je zato uporabljala laboratorijska strojna oprema za oplemenitenje tekstila ter kuhinjski mešalnik za smetano. Strojno opremo razdelimo na dva dela: - strojno opremo za oblikovanje mehanske pene, - strojno opremo za nanos na gradbene površine. Nekaj mogočih sestav mehanske pene: - cement, voda, anorganski prah, stabilizator mehanske pene, pigmenti, drugi dodatki, - mavec, voda, stabilizator mehanske pene, pigmenti, drugi dodatki, - gašeno apno, voda, anorganski prah, stabilizator mehanske pene, pigmenti, drugi dodatki, - polimerno vezivo, voda, anorganski prah, stabilizator mehanske pene, pigmenti, drugi dodatki, - polimerno vezivo, voda, organski prah, stabilizator mehanske pene, pigmenti, drugi dodatki, - polimerno vezivo, voda, lesni prah, stabilizator mehanske pene, pigmenti, drugi dodatki, itn. 3 = solids r = on graph Symbols: rd = density of the polymer dispersion rz = density of the air in the bubble V = volume r, r = radius of the bubble Poo = steam pressure in the event of a flat surface (roo) P = internal pressure PR = pressure on a concave or convex surface P = atmospheric pressure rD = steam density Re = Reynolds number v = velocity of rising bubble hd = viscosity of the polymer dispersion = viscosity of the air inside the bubble hz = surface tension g = ground acceleration (9.81 m/s2 ) m = mass of the polymer dispersion 2 EXPERIMENTAL SECTION The mechanical foam could be produced on site with the appropriate mechanical equipment. In principle we could use the equipment employed in the upgrading of textiles or specially developed machinery. However, because this is an innovation, special, purposely constructed machines for the formation of mechanical foam in civil engineering do not exist. Therefore, in practise, mechanical laboratory equipment, such as that for the upgrading of textiles and kitchen food-mixers, is used. The mechanical equipment can be divided into two parts: - mechanical equipment for the formation of mechanical foam, - mechanical equipment for its placement on construction surfaces. Some of the possible compositions of the mechanical foam are as follows: - cement, water, inorganic dust, mechanical foam stabilisers, pigments, other additives, - gypsum, water, mechanical foam stabilisers, pigments, other additives, - lime, water, inorganic dust, mechanical foam stabilisers, pigments, other additives, - polymer binders, water, inorganic dust, mechanical foam stabilisers, pigments, other additives, - polymer binders, water, organic dust, mechanical foam stabilisers, pigments, other additives, - polymer binders, saw dust, mechanical foam stabilisers, pigments, other additives. Teoretične in eksperimentalne osnove - Theoretical and Experimental Foundations 327 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 Preglednica 1. Nekaj podatkov o snoveh, ki se uporabljajo v gradbeništvu (Pravilnik o toplotni zaščiti in učinkoviti rabi energije v stavbah (Ur.l. RS, št. 42/02)) Table 1. A few characteristics of the materials frequently used in civil engineering (Regulation regarding the efficient use of energy in buildings (Ur.l. RS, št. 42/02)) gradivo material apnena malta lime mortar cementna malta cement mortar cementna malta + lateks cement mortar + latex p kg/m3 1600 1050 0,81 10 2100 porolit porolit – clay blocks steklena pena glass foam 1900 1050 0,7 30 1,2 PS plošče (v kladah) PS plates (in blocks) penjeno steklo foamed glass klada iz celičnega betona, porobetona blocks of cell concrete, porous concrete 145 15 450 500 C J/kgK 1050 X W/mK 1,4 30 10-6 K-1 0,8 1,1 do/to 1,2 1200 920 0,52 4 840 1260 0,056 0,041 140 1100 0,06 ? 100000 25 0,5 0,8 6 860 860 0,14 0,15 3,5 4 Pravilnik o toplotni zaščiti in učinkoviti rabi energije v stavbah (Ur.l. RS, št. 42/02) ima v prilogi navedene snovne podatke o velikem število izolacijskih materialov, med katere bi lahko uvrstili tudi mehanske izolacijske pene, ki bi bile narejene po našem postopku. V preglednici 1 zato navajamo neaj skupin materialov, kamor bi lahko uvrstili izolacijske mehanske pene. The regulations regarding the efficient use of energy in buildings (Ur.l. RS, št. 42/02) specify the material characteristics for a large quantity of insulation materials, among which we could include mechanical insulation foams produced according to our procedure. Table 1 lists a few groups of materials where we could list insulation mechanical foams. 2.1 Mogoče tehnične rešitve oblikovanja in 2.1 Possible technical solutions for the formation nanašanja mehanske pene na gradbene površine and application of mechanical foam onto surfaces in civil engineering Tehnološki postopek lahko razdelimo na naslednje faze: - priprava razpršitve, - oblikovanje mehanske pene, - nanašanje mehanske pene na gradbeno površino. Priprava razpršitve Pri opisu se bomo omejili le na vodne razpršnine, čeprav so mogoče tudi druge razpršitve. Priprava razpršnine poteka: V vodo doziramo med mešanjem ustrezne deleže posameznih komponent (vezivo, polnilo, pigment, stabilizator mehanske pene, drugi dodatki). The technological procedure can be broken down into the following phases: - the preparation of the dispersion, - the formation of the mechanical foam, - the application of mechanical foam onto surfaces in civil engineering. The preparation of the dispersion Although other dispersions are possible we will limit the description of the procedure to water dispersions. The preparation of the dispersion includes: While stirring we mix in the required quantities of individual components (binder, filler, pigment, mechanical foam stabiliser, other admixtures). 328 Drev D. - Panjan J. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 Priprava razpršnine lahko poteka prekinjano ali zvezno. Pomembno je, da je zagotovljena ustrezna sestava razpršnine (deleži ustreznih komponent, homogenizacija). Če je v razpršitvi takšno vezivo, ki se zelo hitro utrdi (mavec, cement itn.), je treba zagotoviti takojšnjo obdelavo na stroju za nastanek mehanske pene in uporabo produkta na gradbeni površini, ki jo želimo izolirati ali dekorativno obdelati. Stabilizatorji mehanske pene in drugi dodatki za izboljšanje reoloških lastnosti se dodajajo glede na stvarne potrebe (nastanek pene, barva, utrjevanje itn.). Nastanek mehanske pene Iz pripravljene razpršnine, ki mora vsebovati predpisano sestavo in biti ustrezno homogenizirana, se lahko izdela mehanska pena. Za to pa morajo biti izpolnjeni pogoji, ki so navedeni v teoretičnem delu. Na sliki 3 je prikazana shema strojne opreme, ki se uporablja za nastanek mehanske polimerne pene za oplemenitenje tekstila. Ta shema vsebuje vse značilne sestavine, ki bi jih moral imeti namenski stroj za nastanek mehanske pene v gradbeništvu. Na dotoku v mešalno glavo priteka razpršnina, v katero želimo vmešati čim večjo količino zraka. Vmešavanje zraka poteka na mešalni glavi, kjer se mešata razpršnina in zrak. Količino razpršnine in zraka se lahko uravnava. Pri zraku je treba poleg količine uravnavati tudi tlak. Na iztoku iz stroja izstopa stabilna mehanska pena, ki se mora čimprej nanesti na ustrezno gradbeno površino. polimerna razpršnina polymer dispersion merilnik pretoka flow meter The preparation of the dispersion can be continuous or discontinuous. It is important that an adequate composition of the dispersion is guaranteed (parts of the individual components, homogeneity). If the dispersion contains fast-setting binders (gypsum, cement etc.) it is necessary to ensure immediate treatment in the machine for the formation of mechanical foam and use of the product on the surface we wish to insulate or decorate. Stabilisers of the mechanical foam and other additives for the improvement of its rheological characteristics are added according to specific needs. (formation of the foam, colour, hardening etc.). The formation of the mechanical foam Mechanical foam can be made from a prepared dispersion composed of the required ingredients, adequately homogenised. In this case all the conditions listed in the theoretical part must be fulfilled. Figure 3 presents a scheme of the mechanical equipment needed for the preparation of mechanical polymer foam used for the upgrading of textiles. This scheme includes all the characteristic components necessary for a purpose-built machine for the production of mechanical foam in the field of civil engineering. The dispersion into which we wish to mix a large as possible quantity of air flows into the mixing head. The admixing of the air takes place in the mixing head, where the dispersion and air are mixed. The quantity of dispersion and air can be regulated. When regulating the quantity of air its pressure is also regulated. On its outflow from the machine we obtain a stable mechanical foam, which has to be applied to the construction surface. mehanska polimerna pena mechanic polymer foam mešalna glava (rotor/stator) mixer (rotor/stator) tlak 6 do 8 bar pressure 6 to 8 bar Sl. 3. Shematski prikaz stroja za oblikovanje mehanske pene Fig. 3. A schematic drawing of the machine for the production of mechanical foam Teoretične in eksperimentalne osnove - Theoretical and Experimental Foundations 329 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 mehanska pena mechanic foam Sl. 4. Prikaz nanosa mehanske izolacijske pene na ravno steno Fig. 4. The application of mechanical insulation foam on a flat wall Nanašanje mehanske pene na gradbeno podlago Nastala mehanska pena se mora obnašati kot tekočina pri prenosu in nanašanju, nato pa kot trdna snov. Te značilne reološke lastnosti je treba upoštevati pri prenosnem sistemu (dovodni cevi) mehanske pene na mesto nanosa ter pri obliki nanašalne glave. Mogočih načinov nanašanja mehanske pene na gradbeno podlago je lahko več. Podajamo le eno izmed mogočih rešitev, ki je prikazana na sliki 4. Pri nanašalni glavi mora biti ustrezen distančnik, ki določa debelino nanosa. V stvarnem primeru je prikazan ta distančnik v obliki koleščka ob robu nanašalne glave. Z nastavitvijo stranskih koleščkov se lahko uravnava želen odmik od stene. S tem je določena tudi debelina nanosa mehanske izolacijske pene. 2.2 Primer oblikovanja mehanske pene iz vodne razpršnine polimernega veziva (poliakrilat), anorganskega polnila in dodatkov The application of mechanical foam onto surfaces The produced mechanical foam must behave as a fluid during both transport and placement, while its latter behaviour must be as a solid material. These typical rheological characteristics must be considered in the transport system (feeding hoses) of the mechanical foam to the placement surfaces as well as in the construction of the applicator. There are several ways of placing mechanical foam on surfaces in civil engineering. We present one of the possibilities in Figure 4. An appropriate spacer must be located on the applicator. Its purpose is to control the thickness of the placed layer. In this case the spacer is in the form of a guide wheel located at the edge of the applicator. By adjusting the wheels the distance from the wall can be regulated. This procedure determines the thickness of the layer of the mechanical insulation foam. 2.2 An example of the formation of mechanical foam from a water dispersion of polymer binder (polyacrilat), inorganic filler and admixtures Pogoji oblikovanja mehanske pene pri preizkusu so: The conditions of mechanical foam formation in the experiment are: 330 Drev D. - Panjan J. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 Polimerna razpršnina: rd = 1200 kg/m3 hd = 300 m Pa s Nastavitve na stroju za oblikovanje mehanske pene za oplemenitenje tekstila Mondomix: - zračni tlak: 4 bar - dotok polimerne razpršnine: 500 do 600 ml/min - dotok zraka: 0,5 l/min - vrtilna frekvenca mešalne glave: 1200 vrt./min - gostota mehanske pene: 180 do 220 g/l Izračun teoretične hitrosti gibanja mehurčka za določen preizkus: f pene/foam = f disp. + f Polymer dispersion: rd = 1200 kg/m3 hd = 300 m Pa s Settings on the machine for the production of mechanical foam for the upgrading of textiles Mondomix: - air pressure: 4 bar - intake of polymer dispersion: 500 to 600 ml/min - intake of air: 0.5 l/min - mixing head velocity: 1200 rpm - density of mechanical foam: 180 to 220 g/l Calculation of the velocity of the bubble for this concrete experiment: zraka/air (pri/at 1 bar) F P F 4bar 0,5 l l =-------.----= 2---- P0 0 1 bar min j pene 0,5 min +2 min 2,5 min teoretična gostota pene: r pene/foam disp. the theoretical density of the foam: 500 2,5 l =200 g/l pene/foam Dobljena gostota pene pri preizkusu: 180 do The achieved density of foam during the 220 g/l. experiment: 180 to 220 g/l. Hitrost dviganja mehurčkov: The velocity of the rising bubbles: v 2gr2 rd-rz 3hz+3hd 9hd m/s Izmerjena velikost por (z mikroskopom): r = pribl. 10-5 m 3hz + 2hd The measured size of the pores (using a microscope): r = approx. 10 5 m r2 >> r1 in / and v 2gr 9hd 2 'rd 2-9,812-(110-5m)2 1200 h2 >> h kg 1 9-300 m.Pa.s 8,7-10-10 m/s Izračunana hitrost je tako majhna, da se mehurčki praktično ne gibljejo. Mehanska pena je bila zato zelo stabilna. Takšno peno se lahko nanaša na podlago brez poškodbe njene strukture. Pri tem mora biti izbran ustrezen postopek nanašanja, pri katerem se ne poškoduje struktura pene. Na sliki 5 je prikazana fotografija toplotno utrjene obravnavane mehanske pene, posnete z elektronskim mikroskopom. S slike je razvidno, da se po utrditvi ni bistveno spremenila struktura mehanske pene. Količina zraka v nastali mehanski peni: The calculated velocity is so small that the bubbles are practically stationary. Therefore, the mechanical foam was very stable. Such a foam can be applied to a surface without damage to its structure. An appropriate application procedure must be chosen in order to prevent damage to the foam structure. Figure 5 presents a photograph of a hardened mechanical foam taken with an electron microscope. From the photograph it is evident that the hardening process did not have a significant influence on the mechanical foam’s structure. The quantity of air in the mechanical foam: Teoretične in eksperimentalne osnove - Theoretical and Experimental Foundations 331 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 Sl. 5. Fotografija mikroporozne mehanske pene na podlagi poliakrilatne razpršitve, povečava 190-krat Fig. 5. A photograph of the micro-porous mechanical foam on the basis of polyacril dispersion, enlargement 190 times Delež polimerne razpršnine: Delež zraka v mehanski peni: (%) The percentage of the polymer dispersion: 100 0,22 kg.100 18% r d 1, 2 kg l The percentage of air in the mechanical foam: (%) = 100% - 18% = 82% 3 REZULTATI IN RAZPRAVA Izolacijske mehanske pene so lahko ena izmed mogočih tehnoloških rešitev za dodatno toplotno zaščito stavb in okrasni zgornji sloj. Nastanek mehanske izolacijske pene je teoretično razmeroma preprost. Tudi nanos na gradbeno površino ne bi smel pomeniti prevelikega problema. Večje težave lahko nastanejo v primeru, kadar je čas utrjevanja bistveno počasnejši od časa stabilnosti mehanske pene. Če bi oblikovali mehansko peno iz gašenega apna, bi verjetno nastale težave s pravočasno utrditvijo strukture. Apno se namreč utrdi z vezavo CO iz zraka. Morda bi lahko oblikovali mehansko peno z dodatkom CO2. V tem primeru bi prišlo do hitrejše utrditve. Pri uporabi različnih cementov ali cementnih malt je mogoče laže uravnavati čas utrditve strukture mehanske izolacijske pene. To je glede na omejeno stabilnost mehanske pene zelo pomembno. Tudi mavec se zelo hitro utrdi. Problem pa lahko nastane pri oblikovanju stabilne mehanske pene. 3 RESULTS AND DISCUSSION Insulation mechanical foams can be one possible technological solution for the additional thermal protection of buildings as well as for decorative coatings. Theoretically, the formation of mechanical insulation foam is relatively simple. Its application onto surfaces in civil engineering should not pose any major problems. Larger problems could occur in the event that the hardening time is greater than the time the mechanical foam is stable. If we were to form mechanical foam from hydrated lime we would most likely have problems with timely hardening of its structure. Lime hardens by binding with CO2 from the air. Perhaps we could form a mechanical foam with the addition of CO2. In this case we could achieve a faster binding. With the use of various cements or cement mortars it is easier to regulate the hardening time of the mechanical insulation foam structure. Even gypsum hardens quickly. Problems can occur in the formation of a stable mechanical foam. The simplest way is the formation of mechanical foam 332 Drev D. - Panjan J. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 Najpreprostejše je oblikovanje mehanske pene pri vodni razpršnini na podlagi polimernih veziv, kar smo prikazali s praktičnim preizkusom. Preizkusi uporabe različnih anorganskih veziv so šele v začetni fazi, zato še nimamo ustreznih rezultatov. Ne glede na to, ali je vezivo anorganskega ali organskega porekla, velja enak mehanizem oblikovanja mehanske izolacijske pene. Tudi nanos na gradbeno površino se ne more bistveno razlikovati. Mehanska pena ima v vsakem primeru približno enake reološke lastnosti, ki jih je potrebno upoštevati. Penasto gradivo nastane tudi v zmesi vodnega stekla in alkohola. Po utrditvi pa je nastalo penasto gradivo zelo trdno. V primeru, da bi bila mehanska pena hidrofobna, bi imela tudi hidroizolacijske lastnosti. Hidrofobnost bi lahko zagotovili predvsem pri mehanskih penah na podlagi polimernih veziv. Če bi bilo vezivo na podlagi polisikolsanov ali fluorogljikov, bi dosegli zelo veliko hidrofobnost, polimerni material pa bi se razmeroma hitro utrdil na zraku. Poleg izbire ustreznih materialov je pomembna tudi strojna izvedba oblikovanja mehanske pene in sistem za nanašanje na gradbeno podlago. V tem prispevku podajamo le idejne rešitve, ki jih je treba v praksi preizkusiti in dograditi. Po nanosu na gradbeno podlago je treba utrjene materiale še testirati glede toplotno-izolacijskih zmožnosti in drugih fizikalnih in kemijskih lastnosti. S tem prispevkom želimo odpreti novo področje na področju izolacijskih in dekorativnih materialov v gradbeništvu, ki ga je treba šele razviti in preizkusiti v praksi. with a water dispersion made on the basis of polymer binders, as we showed in our practical test. Usage tests of various inorganic binders are still in the developing stage, so we do not have any results available. Regardless of the binder, be it of organic or inorganic origin, the mechanism of the mechanical insulation foam remains the same. Not even its application to construction surfaces can differ significantly. In all cases the mechanical foam has approximately the same rheological characteristics, which need to be considered. Foamy material also forms in mixtures of water glass and alcohol. After it hardens the formed foamy material is very hard. In the event that the mechanical foam would be hydrophobic it would also have hydro-insulation characteristics. Hydrophobic characteristics could be obtained mainly with mechanical foams on the basis of polymer binders. If the binder was based on polysicolsan or fluorine-carbons we could achieve good hydrophobic characteristics and the polymer material would harden relatively quickly in air. Apart from the choice of appropriate materials, the execution of the formation of mechanical foam as well as its application to surfaces in civil engineering are of great significance. This paper presents only the idea for the solution, which must be tested in practise and upgraded. After the application of the materials it is necessary to test the hardened materials with regards to their insulating capacities and other physical and chemical characteristics. The intention of this article is to open a new segment in the field of insulation and decorative materials in civil engineering. This segment must be developed and proven in practise. 4 LITERATURA 4 REFERENCES [1] A. J. Wilson (1989) Foams, physics, chemistry and structure. [2] JJ. Bikerman (1973) Foams. [3] J.F. Danielli, K.G.A. Pankhurst, A.C. Riddiford (1973) Recent progress in surfance science. [4] W. Bumbullis, Schaumfaigkeit. [5] Prospekti in navodila firm: Hansa, Mondomix, Stork, Pfersee, Bayer, Hoechst, itn. [6] D. Drev (2005) Izdelava mehanskih pen za izolacijo in njihova uporaba v gradbeništvu, Urad za intelektualno lastnino, patent št. 21557. [7] D. Drev (1997) Filtri za otprašivanje s mikroporoznim polimernim slojevima = Dust filtering with microporous polymer layers. Polimeri, 1997, 18, 5-6, str.: 228-232, Zagreb. [8] N. Thomas, S. Tait, T. Koyaguchi (1993) Mixing of stratified liquids by the motion of gas bublles with application to magma mixing, Earth Planet. Sc. Lett, 115, 161-175, 1993. [9] W.Miiller (2002) Mechanische Grundoperationen, Fachhochschule Dusseldorf. [10] K.G.Kornev, A.V.Neimark, A.N.Rozhkov (1999) Foam in porous: thermodynamic and hydrodynamic peculiars, Advences in Colloid and Interface Science, 82, 1999. Teoretične in eksperimentalne osnove - Theoretical and Experimental Foundations 333 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 323-334 Naslov avtorjev: dr. Darko Drev doc.dr. Jože Panjan Univerza v Ljubljani Fakulteta za gradbeništvo in geodezijo 1000 Ljubljana darko.drev@izvrs.si joze.panja@fgg.uni-lj.si Authors’ Address: Dr. Darko Drev DocDr. Jože Panjan University of Ljubljana Faculty of Civil Eng. and Gheodesy 1000 Ljubljana, Slovenia darko.drev@izvrs.si joze.panja@fgg.uni-lj.si Prejeto: Received: 20.9.2005 Sprejeto: Accepted: 23.2.2006 Odprto za diskusijo: 1 leto Open for discussion: 1 year 334 Drev D. - Panjan J. Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 335 Osebne vesti - Personal Events Osebne vesti - Personal Events Doktorati, magisteriji in diplome - Doctor’s, Master’s and Diploma Degrees DOKTORATI Na Fakulteti za strojništvo Univerze v Ljubljani sta z uspehom zagovarjala svoji doktorski disertaciji: dne 5. aprila 2006: mag. Damjan Klobčar, z naslovom: “Matematično modeliranje procesov pri reparaturnem varjenju orodij”; dne 5. aprila 2006: mag. Andrej Lešnjak, z naslovom: “Študij procesov navarjanja trdih plasti in njihovih lastnosti z elektroiskrnim postopkom”. Na Fakulteti za strojništvo Univerze v Mariboru so z uspehom zagovarjali svoje doktorske disertacije: dne 12. aprila 2006: mag. Primož Pogorevc, z naslovom: “Vpliv biodizelskega goriva na karakteristike vbrizganega curka”; dne 21. aprila 2006: mag. Jure Ravnik, z naslovom: “Metoda robnih elementov za hitrostno vrtinčno formulacijo simulacije velikih vrtincev” in mag. Zoran Žunič, z naslovom: “Mešana metoda robnih in končnih elementov za reševanje hitrostno vrtinčne formulacije Navier-Stokesovih enačb”. S tem so navedeni kandidati dosegli akademsko stopnjo doktorja znanosti. MAGISTERIJI Na Fakulteti za strojništvo Univerze v Ljubljani je z uspehom zagovarjal svoje magistrsko delo: dne 25. aprila 2006: Denis Giacomelli, z naslovom: “Inženirski informacijski sistem za podporo dinamičnih grozdnih struktur”. Na Fakulteti za strojništvo Univerze v Mariboru je z uspehom zagovarjal svoje magistrsko delo: dne 7. aprila 2006: Uroš Očko, z naslovom: “Metode za zagotavljanje celovitosti ležajnega obroča”. S tem sta navedena kandidata dosegla akademsko stopnjo magistra znanosti. DIPLOMIRALI SO Na Fakulteti za strojništvo Univerze v Ljubljani sta pridobila naziv univerzitetni diplomirani inženir strojništva: dne 25. aprila 2006: Miha ERJAVEC, Radoica GAVRANOVIČ. * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 13. aprila 2006: Luka ČIBEJ, Jernej DEMŠAR, Darko KRAJNC, Borut PUC; dne 14. aprila 2006: Emin DURAKOVIČ, Boris KRAŠEVEC, Janez OGRINC, Matej ERŽEN, Gregor ROMIH, Danjel ZOBEC. Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 20. aprila 2006: Aleš BRENCE, Albin FERLEŽ, UrošTRATNJEK. 335 lZEESSE SS ICIT&MPT 2007 atenal Processing Technologi M Industrijska orodja se lahko opišejo kot ena najpomembnejših vlečnih sil sodobnih proizvodnih tehnologij. Proizvodnja In gospodarstvo se danes opisujeta kot turbulentna, polna sprememb, konkurence, priložnosti in tveganj. Povsem enako velja tudi za področje orodjarstva in proizvodnje. Nove tehnologije predelave materialov in izdelave orodij, navidezna proizvtdnja, inteligentni sistemi, hitra proizvodnja orodij, orodja za prilagodljivo in proizvodnjo majhnih serij, upravljanje orodjarskih tehnologij, novi materiali in njihova obdelava, sočasni postopki in metode načrtovanja izdelkov,... na vseh teh področjih bodo potekale razprave med strokovnjaki, inženirji, raziskovalci in znanstveniki iz industrije, raziskovalnih ustanov ali univerz. Eden predpogojev za uspešno konferenco je gotovo kraj, zato vas vabimo na Bled, slovenski biser s čisto vodo in zrakom, obkrožen s temnimi gozdovi in visokimi belimi gorami. Za več informacij obiščite uradno spletno stran konference. Industrial tools can be described as one of the most important driving forces of modern manufacturing technologies. As nowadays the production and economy can be described as turbulent, full of changes, competition, opportunities and risks, the same is valid also for tool development and production. New material processing and tool manufacturing technologies, virtual manufacturing, intelligence systems, rapid tooling, tools for flexible and small quantity production, management of tool making, new materials and their treatments, concurrent processes and part (re)design methods,...all these topics will be discussed during the gathering of respected specialists, engineers, researchers and scientists coming from the industry, research institutions or academia. One of preconditions for having a successful conference is also the meeting place, therefore we invite you to Bled - a Slovene pearl with pure air and water, surrounded by dark forests and high white mountains. For more information please visit official website of the conference. Organizatorja /»"N ¦iafiiaff lyiiUniiiiim i ti n =m n mmMMkmwtUBUMk. 6 4611, E: icit@tecos.si, I: http://www.tecos.si/ici 13 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 337-338 Navodila avtorjem - Instructions for Authors Navodila avtorjem - Instructions for Authors Članki morajo vsebovati: - naslov, povzetek, besedilo članka in podnaslove slik v slovenskem in angleškem jeziku, - dvojezične preglednice in slike (diagrami, risbe ali fotografije), - seznam literature in - podatke o avtorjih. Strojniški vestnik izhaja od leta 1992 v dveh jezikih, tj. v slovenščini in angleščini, zato je obvezen prevod v angleščino. Obe besedili morata biti strokovno in jezikovno med seboj usklajeni. Članki naj bodo kratki in naj obsegajo približno 8 strani. Izjemoma so strokovni članki, na željo avtorja, lahko tudi samo v slovenščini, vsebovati pa morajo angleški povzetek. Za članke iz tujine (v primeru, da so vsi avtorji tujci) morajo prevod v slovenščino priskrbeti avtorji. 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Equations should be on a separate line in the main body of the text and marked on the right-hand side of the page with numbers in round brackets. 337 Strojniški vestnik - Journal of Mechanical Engineering 52(2006)5, 337-338 Enote in okrajšave V besedilu, preglednicah in slikah uporabljajte le standardne označbe in okrajšave SI. Simbole fizikalnih veličin v besedilu pišite poševno (kurzivno), (npr. v, T, n itn.). Simbole enot, ki sestojijo iz črk, pa pokončno (npr. ms1, K, min, mm itn.). Vse okrajšave naj bodo, ko se prvič pojavijo, napisane v celoti v slovenskem jeziku, npr. časovno spremenljiva geometrija (ČSG). Slike Slike morajo biti zaporedno oštevilčene in označene, v besedilu in podnaslovu, kot sl. 1, sl. 2 itn. Posnete naj bodo v ločljivosti, primerni za tisk, v kateremkoli od razširjenih formatov, npr. BMP, JPG, GIF. Diagrami in risbe morajo biti pripravljeni v vektorskem formatu. 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Fajdiga (2004) Measurement of the surface-temperature field in a fog lamp using resistance-based temperature detectors, Stroj. vestn. 2(2004), pp. 72-79. [2] Vesenjak, M., Ren Z. (2003) Dinamična simulacija deformiranja cestne varnostne ograje pri naletu vozila. Kuhljevi dnevi ’03, Zreče, 25.-26. september 2003. [3] Muhs, D. et al. (2003) Roloff/Matek Maschinenelemente - Tabellen, 16. Auflage. Vieweg Verlag, Wiesbaden. Podatki o avtorjih Članku priložite tudi podatke o avtorjih: imena, nazive, popolne poštne naslove in naslove elektronske pošte. SPREJEM ČLANKOV IN AVTORSKE PRAVICE Uredništvo Strojniškega vestnika si pridržuje pravico do odločanja o sprejemu članka za objavo, strokovno oceno recenzentov in morebitnem predlogu za krajšanje ali izpopolnitev ter terminološke in jezikovne korekture. Avtor mora predložiti pisno izjavo, da je besedilo njegovo izvirno delo in ni bilo v dani obliki še nikjer objavljeno. Z objavo preidejo avtorske pravice na Strojniški vestnik. Pri morebitnih kasnejših objavah mora biti SV naveden kot vir. Units and abbreviations Only standard SI symbols and abbreviations should be used in the text, tables and figures. Symbols for physical quantities in the text should be written in italics (e.g. v, T, n, etc.). Symbols for units that consist of letters should be in plain text (e.g. ms1, K, min, mm, etc.). All abbreviations should be spelt out in full on first appearance, e.g., variable time geometry (VTG). Figures Figures must be cited in consecutive numerical order in the text and referred to in both the text and the caption as Fig. 1, Fig. 2, etc. Pictures may be saved in resolution good enough for printing in any common format, e.g. BMP, GIF, JPG. However, graphs and line drawings sholud be prepared as vector images. When labelling axes, physical quantities, e.g. t, v, m, etc. should be used whenever possible to minimise the need to label the axes in two languages. Multi-curve graphs should have individual curves marked with a symbol, the meaning of the symbol should be explained in the figure caption. All figure captions must be bilingual Tables Tables must be cited in consecutive numerical order in the text and referred to in both the text and the caption as Table 1, Table 2, etc. The use of names for quantities in tables should be avoided if possible: corresponding symbols are preferred to minimise the need to use both Slovenian and English names. In addition to the physical quantity, e.g. t (in italics), units (normal text), should be added in new line without brackets. All table captions must be bilingual. The list of references References should be collected at the end of the paper in the following styles for journals, proceedings and books, respectively: [ 1 ] A. Wagner, I. Bajsič, M. Fajdiga (2004) Measurement of the surface-temperature field in a fog lamp using resistance-based temperature detectors, Stroj. vestn. 2(2004), pp. 72-79. [2] Vesenjak, M., Ren Z. (2003) Dinamična simulacija deformiranja cestne varnostne ograje pri naletu vozila. Kuhljevi dnevi ’03, Zreče, 25.-26. september 2003. [3] Muhs, D. et al. (2003) Roloff/Matek Maschinenelemente - Tabellen, 16. Auflage. Vieweg Verlag, Wiesbaden. Author information The information about the authors should be enclosed with the paper: names, complete postal and e-mail addresses. ACCEPTANCE OF PAPERS AND COPYRIGHT The Editorial Committee of the Journal of Mechanical Engineering reserves the right to decide whether a paper is acceptable for publication, obtain professional reviews for submitted papers, and if necessary, require changes to the content, length or language. Authors must also enclose a written statement that the paper is original unpublished work, and not under consideration for publication elsewhere. On publication, copyright for the paper shall pass to the Journal of Mechanical Engineering. The JME must be stated as a source in all later publications. 338 Navodila avtorjem - Instructions for Authors