Proceeings of ICAD Worcester Jne 7-8, ICAD--4 THE VACUUM CLEANER AS A CASE STUDY FOR TEACHING CONCEPTUAL DESIGN Joan B. Rorígez joan.rorigez@altran.com Altran Calle Camezo, 8 Mari, Sain Efrén M. Benavies efren.moreno@m.es Deartment of Prolsion an Fli Mecanics Universia Politécnica e Mari Pza. Carenal Cisneros, 84, Mari, Sain ABSTRACT Tis aer is intene as an acaemic examle for teacing Axiomatic Design in a trimestral corse to engineering stents or ractitioners connecting wit te teory for te first time. Te roose examle is an alication of Axiomatic Design to te selection of te best filtering system for vacm-cleaning. Two ifferent ysical soltions are consiere for collecting an retaining te soli articles: first soltion is base on a filter meia wit a given oros size, an secon one is base on a searation e to te larger ensity of te articles. Pysical laws for bot cases are given an esign matrices are erive from tem. Finally, te axioms are se to gie te ecision making rocess an conclsions are given. Keywors: Axiomatic Design, qalitative analysis, qantitative analysis, ecation, esign matrix. INTRODUCTION / STATE OF THE ART Wen teacing Axiomatic Design to an aience tat faces te teory for te first time, one of te rincial objectives of te ecator is to make is stents feel te axioms an comreen teir imlications. A main asect tat makes Axiomatic Design sc a significant teory is its caacity to make exlicit te relations existing between te fnctional an te ysical omains, ointing te ones tat govern te otimal esigns [S, 99]. It is articlarly interesting to focs on ow te Ineenence Axiom, base on a qalitative statement: maintain te ineenence of te fnctional reqirements [S, 99], triggers a qantitative formlation base on te esign matrices. Accoring to te ators exerience, bot qalitative an qantitative efinitions of te Ineenence Axiom are often well nerstoo by te aience, wo at te beginning fins te main ifficlties in te formal efinition of te esign roblem, an later on, in te nerstaning of te imlications tat Axiom as in teir esign rotines. On te oter an, te Information Axiom is base on a qantitative formlation: minimize information content [S, 99]. Conseqently, its entire nerstaning reqires exloring its qalitative imlications in te esign rocess. Imortant efforts ave been mae in tis sense as resente by S [] or Benavies []. Fll comreension of te imlications erive from a qalitative alication of Axiom constittes a real callenge for te ecator an for all te engineers willing to acqire te ability of sing Axiomatic Design in teir own esign rocesses. As exose by Park [], esign ecation is more like a ilosoy. As a conseqence, in te framework of engineering, ilosoical concets giing creative rocess ave to be balance wit te accracy of engineering laws. Nakao an Nakagawa [] resent ow te correct efinition of te esign roblem els te acievement of innovative rocts wit a ge imact in te market. In tis sense, it is imortant to note tat te analysis of a articlar soltion exclsively from a qalitative oint of view may reslt in te loss of a goo roblem formlation. On te oter an, if only a qantitative aroac is roose, ractitioners an stents may get lost in te roblem efinition, reslting in te increase ifficlty for selecting an aeqate set of fnctional reqirements (FR). Batrst [4] resents some of te common roblems fon by engineers wen facing Axiomatic Design for te first time. In orer to commnicate te qalitative an qantitative imlications of te esign axioms, it is significant to select aeqate intitive examles tat col el stents an ractitioners to entirely nerstan an interiorize te teory. Te main rose of tis aer is to sggest te strctre of a lectre wic, base on te resoltion of a eagogical examle, wol el stents to comreen Axiomatic Design rinciles as ostlate by S [99; ]. Altog tis work focses mainly on te learning of te Ineenence Axiom an its imlications, it gives some interesting conclsions erive from te Information Axiom. To acieve tis objective, tis aer focses on te qalitative an qantitative analysis of te vacm cleaner filtering system as a case sty. First of all, a smmary of te lectre s strctre is resente. Next, te esign roblem of te vacm cleaner is solve; first qalitatively, an later on, qantitatively. In bot, te lectre s strctre is conceive in orer to illstrate te Axiomatic Design rinciles [S 99; ] witin te concrete examle. PROPOSED LECTURE S STRUCTURE Te lectre s strctre is base on te metoological stes escribe by S [99; ]. As a first ste in te ecation of Axiomatic Design rinciles, it is sitable to analyze an existing soltion from a qalitative ersective. Tanks to it, te stents ave te oortnity to come into contact wit basic esign roblem efinition, an articlarly, Coyrigt by ICAD
Te Vacm Cleaner as a Case Sty for Teacing Concetal Design Worcester Jne 7-8, wit two main imlications of te Ineenence Axiom: irect eenence (case by te formlation of nees wic reresent eqivalent concets) an inirect eenence (case by te syntesis of a ysical soltion tat coles te set of FRs). Once stents ave contacte qalitatively wit te imlications of te esign axioms, te qantitative formlation of te esign roblem can be sitably exose. Te roose strctre for te lectre is resente in te next sbsections.. QUALITATIVE ANALYSIS For analyzing an existing soltion from a qalitative ersective, we roose te following stes [Base on S, 99]:. Qalitative formlation of te esign roblem a. Callenge efinition b. Selection of te minimm nmber of ineenent FRs in a netral soltion environment c. Establisment of constraints. Descrition of te ysical soltion trog its main DPs. Writing of te esign matrix 4. Analysis wit te se of te Ineenence axiom 5. Introction to te Information Axiom in terms of robability of sccess 6. Proose ncole soltions an otline new callenges. QUANTITATIVE ANALYSIS For analyzing an existing soltion from a qantitative ersective, we roose te following stes [Base on S, 99]:. Qantitative formlation of te esign roblem a. Callenge efinition b. Selection of te minimm nmber of ineenent FRs in a netral soltion environment c. Establisment of constraints. Definition of FRs. Descrition of te existing soltion trog its main DPs a. Writing of te esign eqations (ysical laws) b. Ientification of DPs c. Establisment of new constraints erive from te DPs. Writing of te esign matrix 4. Analysis wit te se of te Ineenence Axiom 5. Introction to te Information Axiom in terms of robability of sccess 6. Selection of new DPs to acieve te otimal esign an otline new callenges. Te selection of te new DPs may imly te selection of a new ysical soltion. THE VACUUM CLEANER AS A CASE STUDY Accoring to S [99], te esign roblem efinition is erforme wen te callenge is exresse an te lists of FRs an constraints are establise. Becase te FRs ave to be state in a netral soltion environment, te roblem formlation as to be vali wen analyzing two ifferent soltions to te same esign roblem. For tat reason, since te metoological stes a, b an c are common for bot te qantitative an te qalitative aroaces; we will collect tem in te following block.. FORMULATION OF THE DESIGN PROBLEM.. CHALLENGE DEFINITION Analyze two ifferent tecnologies (oros filter an centrifgal searation) for filtering st articles wen vacm cleaning. Ientify teir main eenences an select te best soltion accoring to Axiomatic Design... SELECTION OF THE MINIMUM NUMBER OF INDEPENDENT FRS IN A SOLUTION NEUTRAL ENVIRONMENT Te minimm list of ineenent FRs for te first level of ierarcy can be settle as follows (becase te main objective of tis aer is focse on te FRs, te set of constraints will not be establise): FR: Clean- st articles FR: Retain st articles FR: Oerate for a long time At tis oint, stents mst realize tat te nees state in FR, FR an FR are fnctional reqirements becase tey reresent, in a soltion netral environment, ineenent concets. Te concet of irect ineenence is exlaine as a necessary conition for establising a correct set of FRs.. QUALITATIVE ANALYSIS.. DESCRIPTION OF THE POROUS FILTER SOLUTION THROUGH ITS MAIN DPS: Te main DPs tat satisfy in te oros filter soltion te aforementione list of FRs can be settle as follows: DP: Vacm DP: Filter size DP: Filter area.. WRITING OF THE DESIGN MATRIX: ANALYSIS WITH THE USE OF INDEPENDENCE AXIOM Wit te se of te Ineenence Axiom [S, 99], te esign matrix relating te establise sets of FRs an DPs can be written: Clean- st articles X X X Vacm Retain st articles X X X Filter ore size () Oerate a long time X X X Filter area Page: /8 Coyrigt by ICAD
Te Vacm Cleaner as a Case Sty for Teacing Concetal Design Worcester Jne 7-8,.. ANALYSIS WITH THE USE OF THE INDEPENDENCE AXIOM Te esign matrix (DM) makes exlicit ow te filtering system coles te fnctional reqirements (clean- st articles an retain st articles). Inee, te more articles tat are retaine, te more filter clog, an conseqently, te ower for vacming an cleaning- articles ecreases. For a articlar time of se, te conceive soltion generates a eenency between fnctional reqirements tat, rior to te obtaining of te ysical soltion, were ineenent...4 INTRODUCTION TO THE INFORMATION AXIOM IN TERMS OF PROBABILITY OF SUCCESS As state by S [S, ] in a cole esign, te variability of te DPs can generate a ecrease in te robability of sccess of satisfying te FRs (an terefore of satisfying client nees). In tis examle tis asect is visible wen te filter as to be remove an cange becase te vacm ower is not enog to clean- st articles...5 PROPOSING UNCOUPLED SOLUTIONS AND OUTLINE NEW CHALLENGES Te coling ientifie leas to te formlation of a new callenge: ow to retain st articles witot losing vacm ower an maximizing te time of se. Tere are ifferent soltions in te market tat solve tis eenency. One of tem is te one atente by Dyson: te centrifgal vacm cleaner base on cyclone tecnology. In tis soltion, te FR retain st articles is satisfie by a searation of te st articles wit te se of te centrifgal force. Tis soltion resons to te following new esign matrix. Clean- st articles X Vacm Retain st articles X X Cyclone () Oerate a long time X X X Container caacity In tis case, te DM sows a ecole esign. Inee, te filtering system for retaining st articles oes not affect te vacm ower, an conseqently, te fnctionality of cleaning- st articles. It s remarkable to note te ge effect tat tis new concet a in te market, sowing te ee imact tat te rection of te nmber of eenencies as into te acievement of more cometitive rocts. At tis oint it is sefl to ince te stents to tink abot te ineenency obtaine wit resect to te oros bag reqire for te conventional filter vacm cleaner. Aitionally, tey can be roose to tink in terms of robability of sccess, etermining wic of te soltions as a iger robability of satisfying FRs. FR: Clean- st articles: FR reresents te fnctionality of cleaning- articles, wic migt be reresente by te variable wic reresents te see of articles tat are cleane. FR: Retain st articles: min FR may be state as follows: searate all te articles tat ave a size bigger tan min. FR: Maximize oerational time: t max FR migt be state as te time in wic FRs are satisfie... DESCRIPTION OF THE POROUS FILTER SOLUTION THROUGH ITS MAIN DPS Writing of te esign eqations (ysical laws): In orer to obtain te ysical laws tat aly to te roblem, let s consier te following system as a simlification of te vacm cleaner we want to analyze: Figre. Soltion base on oros filter. were, = room, = tbe, = st container before filter, = filter, 4= st container after filter, an 5 = fan. Te ysical laws alying to tem for an ieal gas are collecte in Table. Table. Main ysical laws for filtering soltion. Zones See Pressre Entaly Mass flow m m A State eqation. QUANTITATIVE ANALYSIS.. DEFINITION OF FRS In orer to acieve te qantitative analysis, te set of FRs as to be efine in terms of te aroriate ysical variables: m m A Coyrigt by ICAD Page: /8
Te Vacm Cleaner as a Case Sty for Teacing Concetal Design Worcester Jne 7-8, 4 4 4 5 5 5 m 4 5 W m m 4 4 4 5 55 Assming an isentroic evoltion between -, -, an / / / /, 4-5, i.e.,, 5/ 4 5/ 4 ; an assming tat te variations of ensity are small, we can retain te first terms of Taylor exansion in orer to solve te system of eqations in terms of te FR selecte. Te following transfer eqations are ece (see aenix for etails): Design eqation for FR- W / A A A Design eqation for FR (4) Design eqation for FR t max Consiering te limit as te moment wen te wole filter is clogge: t max N N N m WA n WA n n A A A N Definition of DPs Te DPs tat erive from esign eqations are A,, an N W... WRITING OF THE DESIGN MATRIX FOR POROUS FILTER SOLUTION Accoring to te esign eqation (), none of te terms of te first row of te DM are zero, conseqently: ; ; ; ; W (6) A N Accoring to te esign eqation (4), te terms of te secon row of te DM are: W A N (7) 4 max () (5) Finally, analyzing te esign eqation (5) for FR, t t t t ; ; ; W (8) A N Tis reslts in te following esign matrix: W A N W start A t t t t t N W A N..4 ANALYSIS WITH THE USE OF THE INDEPENDENCE AXIOM As it can be observe trog te esign matrix, te soltion base on a filter for retaining st articles coles te FRs. Inee, e to te fact tat te nmber of te filter iminises wit time, an tat te mass flow as to be conserve trogot sections,,, te effective area of te filter A N iminises. 4 As a conseqence, te vacm ower (reresente by ) ecreases ring te oerational time. Tis coling is articlarly critical becase as it can be observe, even if te oter control arameters vary in orer to comensate tis coling, te iameter of te filter cannot be as big as esire, becase it wol imly te not acievement of FR:. min..5 INTRODUCTION TO THE INFORMATION AXIOM IN TERMS OF PROBABILITY OF SUCCESS As commente in te qalitative analysis, te coling generates a rogressive loss of vacm ower. Tis ecrease inces a smaller robability of sccess for satisfying FR: clean- st articles...6 SELECTION OF NEW DPS TO UNCOUPLE SOLUTIONS AND OUTLINE NEW CHALLENGES: CYCLONE BASED VACUUM CLEANER Axiomatic Design ientifies ow far esigns are from te otimal soltion. Terefore, it answers wy soltions become searate from te best esign, making exlicit teir critical oints [S, 99]. In tis articlar case, Axiomatic Design sows ow te ysical soltion base on a filter generates a cole esign. Te tenency inicate by DPs is tat in orer to eliminate te fnctional coling, te oros filter as to be remove, reqiring a new DP tat wol ncole te soltion. Te next sbsection analyses ow a ifferent ysical soltion ecoles te system...7 DESCRIPTION OF THE CYCLONE BASED SOLUTION THROUGH ITS MAIN DPS In orer to obtain te main DPs tat escribe te cyclone base soltion, let s consier te following system: (9) Page: 4/8 Coyrigt by ICAD
Te Vacm Cleaner as a Case Sty for Teacing Concetal Design Worcester Jne 7-8, x x c 4 4 R 4 () For large size articles or for low raial sees te following ineqality ols: Figre. Soltion base on centrifgal force. Writing of te esign eqations (ysical laws) Pysical laws are eqivalent to te ones exose reviosly, consiering tat in tis case, zone an are eqivalent. Table. Main ysical laws for centrifgal soltion. Zones See Pressre - 4 4 4 5 5 5 Entaly Mass flow m m A State eqation - m 4 5 W m m 4 4 4 5 55 Alying te laws reviosly exose an solving te system in terms of te FR selecte, an consiering tat in cyclone case A >> A we obtain: Design eqation for FR- m W A A () Design eqation for FR Te ifferential eqation tat escribes te raial islacement of a st article insie te cyclone is: 4 4 R xc Uner tis conition Eq. () yiels to: mx m R Tis eqation can be integrate to obtain: () () x t (4) R x t (5) R Te time sent by te article insie te cyclone is: RNc t (6) Taking into accont Eqs. (,, 4, 5 an 6), we can write te conition for neglecting te aeroynamic forces: N c R (7) c A article will escae from te cyclone towars te container if x, were reresents te iameter of te tbe (note tat A /4 ). Ts a article will reac te container if te following ineqality is satisfie: N R (8) c It is convenient to remark tat tis conition is easily satisfie, an ence, te FR is satisfie by all te articles tat ave a large size as state by Eq. (7). For articles wit a mc lower iameter tan tat, te aeroynamic force will become ominant an te raial velocity will become constant as state by: 4 x (9) c R o 4 x t () c R o c 6 () RNc Coyrigt by ICAD Page: 5/8
Te Vacm Cleaner as a Case Sty for Teacing Concetal Design Worcester Jne 7-8, Design eqation for FR t max Consiering te limit as te moment were te wole st container is fll: V 4 V tmax () m n n WA Definition of DPs Te DPs tat erive from esign eqations Eq. (, an ) are, A, Nc, R an W..8 WRITING OF THE DESIGN MATRIX FOR CYCLONE BASED SOLUTION Accoring to te esign eqations, te resltant esign matrix can be written as follows: ; ; W () R Nc A ; ; W (4) A R N t t t t t ; ; ; W A R Nc (5) Tis reslts in te following esign matrix: W W R (6) R Nc t Nc t t t A W A..9 ANALYSIS WITH THE USE OF INDEPENDENCE AXIOM As it can be observe, te soltion obtaine eliminates te main fnctional eenence tat was resent in te oros filter soltion. As it is erive from te esign matrix, in te cyclone base soltion vacming st articles oes not eenent on te system se to filter tem. As a conseqence, in te aforementione soltion te vacm ower oes not ecrease ring te oerational time. In tis case, te limit is imose by te volme of te st container, an not by te system se to searate articles. In tis sense, te qantitative analysis confirms te eenencies ientifie in te qalitative sty. As it can be note, in te qantitative analysis resente (for bot filter an cyclone base soltions) te nmber of DPs available is bigger tan te nmber of FRs. Particlarly, eac FR eens on more tan one an only one DP, concting to renant esigns in terms of te nmber of DPs, an generating cole or ecole esigns in terms of ineenency. c Tis sitation is to be execte wen te ysical laws tat allow esigners to acieve te qantitative sty of esigns are settle. In general, te nmber of DPs tat erive from te laws of ysics is mc bigger tan te minimal set of ineenent FRs. For tat reason, Axiomatic Design constittes a valable tool to minimize te imact tat a bigger nmber of DPs generates in te efinition of new esigns. By minimizing te eenencies between FRs an DPs an by selecting te aroriate DP tat maximizes te robability of sccess, Axiomatic Design teory kees te inerent comlexity of te ysical roblem minimal [L an S, 9]... PROPOSING UNCOUPLED SOLUTIONS AND OUTLINE NEW CHALLENGES Altog te main fnctional coling is solve wit te escribe soltion, at tis oint it is convenient to ince stents to tink abot ow tis soltion col be imrove. More secifically, stents can be aske to tink abot ow te obtaining of a non-renant esign col be acieve. For examle, tey can be aske for analyzing if te DPs col be combine in imensionless variables an mainly, wic of tem sol be fixe as constant vales. Aitionally, stents sol be invite to evalate eac erivative of te esign matrix, an articlarly, te relative weigt of eac term, concling wic terms sol be frozen an wat tenencies te DPs sol follow in orer to maximize ineenency an te robability of sccess. 4 CONCLUSION Tis aer rooses te strctre of a lectre wose rose is to introce stents an ractitioners te basics of Axiomatic Design trog te case sty of an existing roct wic resents ifferent configrations. Te aim is to examine weter te esign is otimal or not. Te case sty is solve bot qalitatively an qantitatively, an it sows ow te comliance or not wit te esign axioms introces a rationale tat certainly ientifies te critical oints were te syntetize soltions move away from te otimal. Tis ientification constittes a valable gie for esigners an ecision makers, even wen jst a qalitative sty can be concte, in orer to irect teir creativity into te otimal soltion, wat confers a recios tool to valiate esigns before investing resorces to evelo tem. In aition, it sows ow te accomlisment of te Axiom can lea to te accomlisment of te Axiom. 5 ACKNOWLEDGEMENTS Te ators wol like to tank Altran for its sort in te researc an eveloment of Axiomatic Design. Tis aer as been conceive in te framework of te roject Alication of Axiomatic Design in te resoltion of tecnical, strategic or innovation roblems, finance by te Sanis Ministry of Science an Innovation (MICINN) trog its rogram Torres Qeveo, an co-finance by te Eroean Social Fn. Page: 6/8 Coyrigt by ICAD
6 REFERENCES [] Batrst S., On learning an execting axiomatic esign in te engineering instry, Proceeings r International Conference on Axiomatic Design, ICAD 4, Seol, Jne - 4, 4. [] Benavies E.M., Avance Engineering Design: An integrate Aroac, Cambrige Wooea blising,. ISBN -8579-9- [] L S., S N.P., Comlexity in esign of tecnical systems, CIRP Annals Manfactring tecnology, 9. [4] Nakao M., Nakagawa S., A serb instrial esign as secial FRs or DPs tat go beyon te cstomer s imagination, Proceeings 6 t International Conference on Axiomatic Design, ICAD, Daejon, Marc -,. [5] Park G.J, Teacing axiomatic esign to stents an ractitioners, Proceeings 6 t International Conference on Axiomatic Design, ICAD, Daejon, Marc -,. [6] S N.P., Axiomatic Design: Avances an Alications, New York: Oxfor University Press,.ISBN -9-5466-7 [7] S N.P., Te Princiles of Design, New York: Oxfor University Press, 99. ISBN -9-5445-6 Te Vacm Cleaner as a Case Sty for Teacing Concetal Design Worcester Jne 7-8, Coyrigt by ICAD Page: 7/8
Te Vacm Cleaner as a Case Sty for Teacing Concetal Design Worcester Jne 7-8, APPENDIX LIST OF VARIABLES i Air see in zone i i Air ressre in zone i i Air entaly in zone i m Mass of te air m Flow mass of te air Heat caacity ratio of te air n Air ensity Dst articles ensity Dst articles iameter Nmber of st articles er volme nit Filter iameter N A A V W R N c x x x c Nmber of filter Poros filter area Tbe iameter Tbe area Dst container caacity Fan ower Rais of crvatre of cyclone Nmber of cyclone trns Raial acceleration insie cyclone Raial see insie cyclone Raial osition insie cyclone Drag coefficient PROCEDURE TO OBTAIN THE DESIGN EQUATIONS. Density resoltion in all te zones m A Incomressible regime. m ( ) A ( ) ( ) ( ) ( ) ( ) ( ) m N A Filter not clogge; incomressible regime. A ( ) NA 4 4 ( ) 4 ( ) ( ) ( ) 4 ( ) ( ) ( ) 4 A ( ) NA W 5 m. Obtaining of i an m as a fnction of DPs m W W W / 4 4 5 4 5 4 5 W / / A NA W W A A ( ) NA NA W m m A A NA W A m A NA m W / A A A NA Page: 8/8 Coyrigt by ICAD