DESIGN OF MACHINES AND STRUCTURES

Transcription

1 HU ISSN n rnt HU ISSN onlne DESIGN OF MACHINES AND SRUCURES A Publcaton of te Unverty of Mkolc Volume 5, Number (05) Mkolc Unverty Pre 05

2 EDIORIAL BOARD Á. DÖBRÖCZÖNI Inttute of Macne and Product Degn Edtor n Cef Unverty of Mkolc H-355 Mkolc-Egyetemváro, Hungary macda@un-mkolc.u Á. AKÁCS Inttute of Macne and Product Degn Atant Edtor Unverty of Mkolc H-355 Mkolc-Egyetemváro, Hungary takac.agne@un-mkolc.u R. CERMAK Deartment of Macne Degn Unverty of Wet Boema Unverztní 8, 3064 Plzen Czec Reublc rcermak@kk.zcu.cz B. M. SHCHOKIN Conultant at Magna Internatonal oronto bory.cokn@ymatco.ca W. EICHLSEDER Inttut für Allgemenen Macnenbau Montanunvertät Leoben, Franz-Joef Str. 8, 8700 Leoben, Öterrec wlfrd.ecleder@note.unleoben.ac.at S. VAJNA Inttut für Macnenkontrukton, Otto-von-Guercke-Unvertät Magdeburg, Unvertät Platz, 3906 MAGDEBURG, Deutcland vajna@mb.un-magdeburg.de P. HORÁK Deartment of Macne and Product Degn Budaet Unverty of ecnology and Economc orak.eter@gt3.bme.u H- Budaet, Műegyetem rk. 9. MG. é. I. em. 5. K. JÁRMAI Inttute of Materal Handlng and Logtc Unverty of Mkolc H-355 Mkolc-Egyetemváro, Hungary altjar@un-mkolc.u L. KAMONDI Inttute of Macne and Product Degn Unverty of Mkolc H-355 Mkolc-Egyetemváro, Hungary mackl@un-mkolc.u GY. PAKÓ Deartment of Macne ool Unverty of Mkolc H-355 Mkolc-Egyetemváro, Hungary atko@un-mkolc.u J. PÉER Inttute of Macne and Product Degn Unverty of Mkolc H-355 Mkolc-Egyetemváro, Hungary macj@un-mkolc.u

3 CONENS Floran, Pavel: Modellng of Motocycle and ter Comonent... 5 Herbt, Dánel akác, Ágne: Degnng Pram etng Equment... 3 Nagy, Gergő Sák, Bettna Szója, Attla Szánta, Itván Jalkanen, Jarmo Mattla, Jarno Rentola, Mara Puká, bor: Branc Saker Degnng Project... 7 Nagy, Józef: Flow n Callary ube Sarka, Ferenc Döbröczön, Ádám Szlágy, Attla: Meaurng Metod to Determne te Vbraton Damng Beavour of Metallc Foam akác, Ágne: On Degn Metodology... 55

4

5 Degn of Macne and Structure, Vol. 5, No. (05). 5. MODELLING OF MOORCYCLES AND HEIR COMPONENS PAVEL FLORIAN Unverty of Wet Boema Unverztn 8, Plen Czec Reublc floran@kk.zcu.cz Abtract: One of te am of te aer to develo a matematcal model of a motorcycle ung Lagrange equaton; te model verfed tank to ADAMS. Reult of multbody mulaton are ued a nut for boundary condton of frame FEM mulaton and followng toology otmzaton wc reult n modfcaton of te frame degn. Keyword: Multbody ytem, motorcycle dynamc, FEM, toology otmzaton. Introducton Degn of a motorcycle frame a comlcated tak. e frame a to wttand gnfcant dynamc force wtout falure. e mot relable metod to acqure neceary data an exerment. However, n cae tere no exermental data multbody modellng arguably te bet way to obtan te needed nformaton. At te ont wen force and load are know tey can be aled n FEM mulaton. oology otmzaton te lat te n te roce tat el to fnd te tffet tructure oble takng nto account a contrant of lmted volume of materal tat can be ued.. Matematcal model.. Nonlnear model of a motorcycle Frt te of te oluton roce to develo a nonlnear matematcal model of a motorcycle. A lanar 5-degre-of-freedom model wa rooed wt followng generalzed coordnate: x frame orzontal tranlaton; y frame tranlaton; φ frame tc angle; y 3 front aembly vertcal tranlaton; y 4 rear aembly vertcal tranlaton. A ceme of te model contanng generalzed coordnate a well a oter arameter own n Fgure. e generalzed coordnate are ncluded n vector q a own n (). q = [x, y, φ, y 3, y 4 ] () Lagrange equaton () were ued to develo equaton of moton of te ytem. d dt ( E k ) E k + E + R = Q q q q q ()

6 6 Pavel Floran Were E k, E and R rereent knetc energy functon, otental energy functon and Rayleg daton functon of te ytem. Eac one of tem lted a te equaton below. Fgure. Sceme of te model E k = {mx + Iφ + my + m 3red [ d dt (y + a 3 n φ y 3 )] co φ + m 4red [ d dt (y a 4 n φ y 4 co φ )] E k = [k 3 (l 03 y + a 3 n φ y 3 ) + k co φ 4 (l 04 y a 3 n φ y 4 ) ] co φ R = {b 3 [ d dt (y + a 3 n φ y 3 )] + b co φ 4 [ d dt (y a 3 n φ y 4 )] } co φ } (3) (4) (5) After conductng artal dervatve accordng to () a ma matrx M, a tffne matrx K and a damng matrx B can be develoed a own below.

7 Modellng of Motorcycle and ter Comonent 7 K = m m M = 0 0 I m 3red 0 [ m 4red ] k 3 + k 4 (k 3 a 3 k 4 a 4 ) n φ φ k 3 k 4 0 (k 3 a 3 k 4 a 4 ) co φ (k 3 a 3 k 4 a 4 ) n φ φ k 3 a 3 co φ k 4 a 4 co φ 0 k 3 k 3 a 3 n φ φ k 3 0 k 4 a 4 n φ 0 k [ 4 0 k φ 4 ] b 3 + b 4 (b 3 a 3 b 4 a 4 ) co φ b 3 b 4 B = 0 (b 3 a 3 b 4 a 4 ) co φ (b 3 a 3 ba 4 ) co φ b 3 a 3 co φ b 4 a 4 co φ 0 b 3 b 3 a 3 co φ b 3 0 [ 0 b 4 b 4 a 4 n φ 0 b 4 ] (6) (7) (8) e tffne matrx and te damng matrx are bot not contant and deend on te generalzed coordnate φ wc mean te ytem nonlnear and rovde more accurate reult a dlacement ncreae. However, t alo lace requrement on te ntegraton metod of te moton equaton telf... yre contact model Interacton between tyre and road a gnfcant ource of force tat act on te frame. In t cae longtudnal drvng and brakng force are neglected and te key tak to obtan normal contact force. A tated revouly te wole model lanar terefore lateral cornerng force are not taken nto account eter. e model of te tyre contact own n Fgure. Fgure. yre contact model

8 8 Pavel Floran Let aume tat te locaton of tyre centre n known at any tme. In cae tat any ont of road urface cloer to te tyre centre tan tyre radu a contact reure exertng on te tyre can be calculated a k = k c (9) Were k [N m ] decrbe tffne caractertc of te tyre and c te dfference between te tyre radu and te dtance. Dfferental normal force can be obtaned accordng to (0). dn = k cd (0) Dfferental d relate to tyre arc. Dfferental normal force alway erendcular to te road urface. For our roblem t crucal to determne t comonent n orzontal and vertcal drecton. can be accomled by ung dervatve of road functon a decrbed n te followng equaton. dn x = k c n (arctan droad dx ) dx () dn y = k c co (arctan droad dx ) dx () In order to determne te comonent of te actual normal force, ntegraton conducted a te very lat te. x(s neu )+r neu (3) N x = dn x x(s neu ) r neu y(s neu )+r neu (4) N y = dn x y(s neu ) r neu e tyre contact model rooed above baed on elatc contact model. yre ytere effect can be taken nto conderaton a well aumng damng force ave mlar caracter to normal contact force a tated n te followng equaton. N b = c N b k k k (5) e varable from revou equaton relate to tyre deformaton rate.

9 Modellng of Motorcycle and ter Comonent 9 3. Numercal ntegraton of te equaton of moton Once we acqured te force actng on tyre we can roceed to oluton roce of te moton equaton wt MALAB. Set of 5 nonlnear ordnary dfferental equaton ummed u n te (6). Mq (t) + Bq (t) + Kq (t) = f n (q,q,t) (6) Contant average acceleraton ntegraton metod wa ued due to t relatve mlcty and numercal tablty. metod redctor-corrector baed a te ytem n queton nonlnear. A road functon wa degned ung modfed n functon to rereent an obtacle, wc uoed to caue a lo of contact between te tyre and te road. In t way a jum of a motorcycle can be mulated. egt [mm] Fgure 3. Road rofle 40 frame 30 acceleraton [m*-] tme Fgure 4. Frame acceleraton reult Acceleraton reult are own n te fgure below. In Fgure 4 tere are acceleraton reult of te frame. e ntal tee ncreae relate to te begnnng of te obtacle. A te acceleraton dro to aroxmately -0 m t mean tat te tyre lot contact wt urface. e eak value occur after landng reacng 36 m. Acceleraton reult of front and rear aembly n Fgure 5 can be exlaned n a mlar way.

10 0 Pavel Floran front aembly rear aembly 50 acceleraton [m*-] tme 4. Model verfcaton Fgure 5. Front and rear aembly acceleraton reult e matematcal model tat wa develoed rovde reaonable reult; owever, furter verfcaton neceary. In order to do o, ADAMS/VI-Motorcycle module wa ued to comare reult. In Fgure 6 tere a motorcycle model n VI- Motorcycle nterface runnng over an obtacle defned n te ame a n te MALAB model. Fgure 6. VI-Motorcycle model In Fgure 7 tere are acceleraton reult of front aembly n ADAMS and MALAB. In t mulaton tyre damng roerte were neglected n MALAB, wc exlan te key dfference between bot curve.

11 Modellng of Motorcycle and ter Comonent 5. FEM Smulaton Fgure 7. Front aembly acceleraton reult e lat te tat conclude t aer a FEM mulaton followed by a toology otmzaton. Boundary condton tat are neceary for te mulaton were obtaned n te revou te. A t can be een n Fgure 8 te frame an oen tubular frame, wc mean an engne lay major role n overall tffne. Engne tffne roerte were determned earately and tee effect were exreed by D CBUSH element n te wole model. oology otmzaton enabled degn modfcaton reultng n tffne ncreae by 33% wle avng 00g n wegt. Lower overall value of tre were alo aceved tank to toology otmzaton. Fgure 8. CAD, FEM and oology otmzaton model

12 Pavel Floran 6. Summary Fgure 9. FEM reult after toology otmzaton Degn of a racng motorcycle frame a comlcated tak. Wtout revou exerence exermental data multbody modellng arguably te only way to obtan boundary condton for FEM mulaton. Nevertele, to decrbe motorcycle beavour and exertng force roerly a large number of mulaton would be neceary. erefore te data acqured n t aer are more uted to comare degn alternatve ntead of exact FE modellng. oology otmzaton a owerful tool allowng ortenng te wole degn roce n order to fnd otmal oluton. 7. Reference [] DUPAL, J.: Výočtové metody mecanky. Učební text. ZČU FAV, 004. [] COSSALER, V.: Motorcycle Dynamc. Lulu Pre, London, 006. [3] FOALE,.: Motorcycle Handlng and Ca Degn, te art and cence. San, 00.

13 Degn of Macne and Structure, Vol. 5, No. (05) DESIGNING PRAM ESING EQUIPMEN DÁNIEL HERBS ÁGNES AKÁCS Unverty of Mkolc, H-355 Mkolc-Egyetemváro, Hungary takac.agne@un-mkolc.u Abtract: e brt of a cld te bgget comleton n one lfe a due to te bologcal functon one can forward ter genetc value by conceton, later moralty n educaton. Human lfe a great value, tu we can ay te vecle carryng te baby or toddler ould be afe and relable. e artcle ow te conderaton of equment tat utable for tetng te adult andle. Keyword: ram, load tet, degnng conderaton, envronmental awarene. e oeratve tandard and te coen tet e erfect oeraton of a cld ram guaranteed by tetng n lne wt te arorate tandard of MSZ EN e durablty tet agant te lftngreng tre of te andguard of te adult andold a been coen out of a great number of tet. e tandard defne an otmal ram contructon wt arorate ze and renforcement ont, a well a te tet wegt ut n te ram. For a ram orter tan 800mm two dfferent tet wegt can be ued, one of tem tet wegt A, wc (9+0.0/0) kg, te oter tet wegt B, wc weg (5+0.0/0) kg. For ram longer tan 800 mm tet wegt F aled, wc weg (3+0.0/0) kg. e andold can be reed wt te maxmum trengt u to 450N, t way reng te rear tructural element of te ram a far a te front weel are condered u to te front weel 0±0mm. Lftng te load of te reed tructure mean lftng te rear weel onto te egt of 0±0mm. e cycle own n te frt aage ould be reeated 3000 tme, wt (5±) cycle number er mnute. ae of te tet to tudy durablty wle crong a ardoulder. e econd ae can be decrbed by a more mle cycle durng wc by rang te andold and lftng te rear weel te tructure move u untl tey reac te egt of 0±0mm. Full reure move onto te frt weel of te ram. After tat come lettng te weel down, n a more careful way, tat makng te ram lower. e econd ae of te tet a 7000 cycle, te cycle number er mnute a been te ame a t wa n te frt tak (5±). All n all, te tet tude te durablty of te ram troug te adult andolder. A ram ae te tet only f t urvve 0,000 cycle wtout any erou damage.

14 4 Dánel Herbt Ágne akác. Summary of degnng e frt te after te atent and egmented market reearc wa followed by te concetualed degnng roce, n wc dfferent form of oluton aeared from te abtract functon analy to exact functon tructure. Studyng te dfferent veron of oluton accordng to te ytem of owng otve value wt Coeland value analyng metod, te otmal veron aeared wc gave gudelne for te later degnng roce. Imortant ecurty and materal uage retrcton and requrement were condered, wc could nfluence te formng of contructon, ayng attenton to te mortance of te envronmentally frendly degn of te equment, and afe uage. For te formng of te contructon we needed to make clear te force requrement of movng te ram at gven arametre. Durng te tudy t force mean a erodcal load on te element of te tetng equment, t way we need zng for fatgue, wc can be done by te Soderberg rocedure. Frt, te rocedure for te general cae wa decrbed, wc later wa ued for te art of te clam devce. Wt te el of zng rocedure te clam devce wa otmed wt a fnte element oftware. 3. Degn conderaton Conderaton refer to everal feld, for examle, te regulaton of 6/008 (VIII. 30.) NFGM, wc a regulaton for te afety requrement and mantenance of macne. Producton of te tock Ung te roduct Raw materal extracton Product roducton Wate management Fgure. Lfe-cycle of a roduct-materal [] It mortant to aroac degnng from envronmentally frendly erec-tve a envronment reource are lmted and ter uage take lace n an rreonble way. In te reent cae crcumtance comng from te lfe cycle of te equment domnate. Raw materal ould be ealy acceble from trade, t way energy reource are mnmzed a raw materal are roduced n bulk, or te tool art made more effcently tan t could be at ome.

15 Degnng Pram etng Equment 5 We ave to ue art tat make te tructure more mle (e.g. functon contracton), t way te requred number of element could be decreaed. e raw materal art alo ould be roduced wt mnmal envronment load, or at leat te recyclng of te raw materal ould be eay. e element ued n te devce ould be relaceable, or at leat recyclable. way we can ncreae te lfean of te devce and te raw materal, o tere le materal wll be needed to extract. At aembly or at untng certan art nto bgger unt docable tecnologe ould be ued tecnologe takng nto conderaton te oblty tat t can be ued for oter tet, a well a for oble relacement of tool. Secal tool tat ave to be manufactured ould not be needed for te aembly of te equment. Safety element ould be ued, wc revent te falure of art manufactured wt bgger envronmental load. 4. Alcaton of conderaton e uort tructure of te equment could be made of alumnum rofle, wt a rofle ae from any oter market, or general teel n te arorate form. In te cae of alurofle, fttng element to eac oter take lace troug ntce and flexble nut wt corner element and wtcng element avalable wt rofle. Untng a workng element and t coure of element moved by t can mean functon untng (lke a neumatc actuator). e effort for te mot mle way of formng te number of art can be decreang te number of art. For examle, n te cae of an alurofle te eet under te ram could be laced on te wall of ntce of te alurofle, and t enoug to te tem n te end. 5. Outlook onto te ue of materal uage It can be tated tat raw materal are of great mortance n any degned equment or macne. We uually cooe te materal accordng to ter mecancal roerte tat are neceary for te aect of functon comleton; owever, tere are oter trend, wc lead to maller envronmental load. Certanly we ave to ay attenton n te cae of materal to dfferent effect carrer troug wc roceng rocedure we ould take over to aceve te arorate geometry and ze. We can fnd a lot of cart and gra about te exendture of certan materal, for examle, te cart of energy need of te Autodek wc wa worked out for te economcal lannng. In te cart te load of certan materal grou comared wt te exendture on energy. (Fgure, tt://manufacturngtoolbox.tyead.com/my-blog/0/0/)

16 6 Dánel Herbt Ágne akác 6. Acknowledgement Fgure. Energy necety dagram reearc wa uorted by te Euroean Unon and te State of Hungary, cofnanced by te Euroean Socal Fund n te framework of ÁMOP-4..4.A/-/ Natonal Excellence Program. 7. Reference [] LUROPP, C. LAGERSED, J.: EcoDegn and e en Golden Rule: generc advce for mergng envronmental aect nto roduct develoment. Journal of Cleaner Producton, 006, Elever. [] OO, K. WOOD, K.: Product Degn ecnque n Revere Engneerng and New Product Develoment. Prentce Hall, 008. [3] PAHL, G. BEIZ, W.: Engneerng Degn A Sytematc Aroac. Srnger Verlag, London, 005. [4] MAZINOVA, I.: Degner and Sutanablty. Degn of Macne and Structure, Vol. 5, Nr., Mkolc Unverty Pre, Mkolc, 05.

17 Degn of Macne and Structure, Vol. 5, No. (05) BRANCH SHAKER DESIGNING PROJEC GERGŐ NAGY BEINA SPISÁK AILA SZÓJA ISVÁN SZÁNAI JARMO JALKANEN JARNO MAILA MARIA RENOLA IBOR PUSKÁS Unverty of Mkolc, Deartment of Macne and Product Degn 355 Mkolc-Egyetemváro JAMK Unverty of Aled Scence PO BOX 07, FI-400 Jyväkylä, Fnland nagy.gergo@caeffler.com Abtract: In t aer a new and tool degnng roject wll be rereented. e background of te roject an nternatonal co-oeraton between JAMK Unverty of Aled Scence from Fnland and Unverty of Mkolc. e man tak wa created by Robert Boc Power ool Ltd. to degn a multfunctonal battery oerated garden and tool. For te more effectve work wa organzed two mxed grou from Hungaran and Fnn tudent. e cometton between te grou mulate te real lfe, were te comane ave to create better roduct tan te oter. Keyword: and tool, branc aker, roject lannng. Introducton e frt and mot mortant tak lke n every roject wa defnng te role of te member. It wa neceary to fnd te utable oton for te member n te roject. e mot mortant role were marketng, qualty, urcang, degnng and te engneerng de (Fgure ). Project manager Itván Szánta Marketng Bernadett Sák Qualty bor Puká Purcang Jarno Mattla Degnng Mara Rentola Jarmo Jalkanen Engneerng Attla Szója Gergő Nagy Fgure. Poton of te member Project manager wa Itván Szánta, e leaded te team. He wa reonble for fnng te roject. Every team member got te agnment from m. He uerved everybody work, organzed te meetng and ent te udate reort to te uervor. Marketng eron wa Bernadett Sák. Her mot mortant job wa to kee contact wt te otental cutomer and ma te comettve roduct.

18 8 G. Nagy B. Sák A. Szója I. Szánta J. Jalkanen J. Mattla M. Rentola. Puká Qualty man wa bor Puká. H tak wa to overee tat te coong of te art were rgt and economc. He oberved tat every art of te contructon atfy te requrement of te cutomer, o e revewed toe dea tat were not rgt. He made te connecton between te engneer and te marketng eron. Purcang wa Jarno Mattla job. He andled to fnd te rgt comonent, and got nformaton about t cot. On to of tat, e created a cotng table. From t, e could calculate a comettve rce for te roduct. Purcang and marketng eron worked togeter to fnd out te rce cutomer are wllng to ay. Indutral degner and mecancal engneer ad two dfferent knd of tak, but ter job were connected. Attla Szója and Gergő Nagy were te mecancal engneer and Mara Rentola, Jarmo Jalkanen were te ndutral degner. Engneer degned certan art of te roduct, lke te motor, battery etc. Indutral degner made te conceton of te oue for tee tool art, wc are ergonomc and comfortable for te cutomer.. Frt te of te roject Collectng dea In te frt te tere wa te ardet tak to fgure out a new tool. For t, te roject member tarted brantormng on wat knd of work eole can do n te garden. ee work are e.g.: gra cuttng, branc akng, leave collectng, lantng, dggng, frut collectng, cleanng garden table and car, root removng and o on. After tat, te grou tarted to tnk about wat knd of tool not on te market yet. It wa known te Boc roduct are good at gra cuttng and edge trmmng, o te roject concentrated on te lantng, dggng, frut collectng and root removng work. From tee knd of gardenng job tree oble tool were magned for future degn. ee tool are: eed feeder, weed remover and branc aker. o fnd te bet tool t wa neceary to comare tee tool n dfferent aect lke ow often ued, mlar roduct n te market, wegt, ze, oble rce of te roduct. e team tougt tat eole are able to ue te branc aker to ake many dfferent frut down from te tree and tey can ue t for leave akng a well. e grou dd not fnd uc branc aker tool on te market tat oerated wt battery, a well a t aker tecnque ued n more tool and macne for arvetng, o n t tool could work alo. e branc aker ad o many advantage a t wa coen to degn. 3. Degnng te tool 3.. Degnng te aker ead Searcng for atent of dfferent ead tye very mortant tak, becaue tealng anybody dea not correct. However, te earcng ueful, becaue we can ue te old, forgotten dea to degn a new macne.

19 Branc Saker Degnng Project 9 Fgure. Fxed ead (frt 3D model) Many conceton were created durng degn. For examle: fxed-, adjutable-, andle oerated-, automatc ead. All of tee were analyed, and te mot utable wa coen. e coen ead a fxed ze (Fgure ). not adjutable. Peole can grab brance under te ze of te ead mout. If te nternal ze of te mout 40 mm, tan man can grab a branc tat a a dameter of 40 mm, or maller. Some meaurement were made to defne te average branc dameter and aker force tan te concluon were decrbed. e nternal ze of te mout can be maxmum 60 mm. Larger mout unneceary. e ead art materal a trong teel or alumnum alloy. Part a flexble deot. It materal rubber. ead can be one art wt te rod, or t can be connectable to te rod n ont, art 3. Dfferent workng tuaton were examned and te fxed ead wa coen. Peole can grab te branc wt t tye of ead and t work on oter tool too. It degn eaer tan te oter. 3.. Fnte element analy of te ead It an mortant exerce becaue t could mulate te workng tuaton and te grou can otmze te crtcal art. We made te analy more tme. wo materal were coen, an alumnum alloy and ABS latc materal. e reult of te analy were comared wt te materal roerte. e mot mortant tng were te deformaton, and te equvalent tre n te materal of te ead. e analy wa made n Any 4 and Sold work. Fgure 3. Fnte element analy of te ead

20 0 G. Nagy B. Sák A. Szója I. Szánta J. Jalkanen J. Mattla M. Rentola. Puká Platc materal ceaer and lgter tan alumnum, but t trengt would not be enoug, jut wt larger ze, tat wy te materal of te ead a to be alumnum alloy. Reult of te analy owed, te form of te ead not te otmal. It wa neceary to make an otmzaton. e get tre value were n te nner corner of te mout. It wa neceary to aly bgger radu n t corner. So te loadng dtrbute evenly n te ead. e oter reaon wa te ncer form. It look retter wt te modfed ae (Fgure 4). Fgure 4. New degn of te ead 3.3. Connecton between te ead and te arm of te tranmon tool multfunctonal. Frt functon branc akng; econd one branc cuttng. It neceary to cange te ead and te aw on t macne. Our grou ad to create an adater to te arm of te tranmon. adater able to fx te ead or te jgaw fxer adater. Fgure 5. Adater for fxng te ead and jgaw adater Fgure 6. Saker ead and jgaw blade wt te adater

21 Branc Saker Degnng Project 3.4. Rod connecton Our grou found ome atent for rod connecton. ere were connectable and telecoc too. Druan Franco ad a great dea. He nvented te telecoc rod connecton for agrcultural tool on te 0 t June 995. It laed, o we could ue t u free. A mlar oluton wa aled n cae of te branc aker. connecton tye oerate a follow. ere an outer tube and tere a treaded connecton element fxed n t tube. ere an nner tube wt clong element. ere a taered clamng element next to te treaded element. ere a gr on tee art wt an nternally treaded element. If we turn te gr n one drecton, we can releae te clamng, o we can ull te nner tube to full lengt. If we turn te gr revere, we can make te clamng, o te nner tube fxed n tat oton (Fgure 7). Fgure 7. Rod connecton n cae of branc aker Fnte element analy alo mortant n cae of te rod. It wa neceary to run dynamc analy becaue akng and cuttng load cange n tme. Fgure 8. Fnte element analy of te rod ere are two fxed uort on te rod, becaue te cutomer grab te tool wt two and. e oton of te electrcal and tool durng te work not orzontal, but 45 angle to te ground. ere not only one load, but tere are two. ee load cange n tme. One of tem te wegt of te motor and te ead; t about 0 N. load at te end of te rod and t ont toward te ground. e oter load te aker force. It n drecton of te rod. e aker force about 00 N,

22 G. Nagy B. Sák A. Szója I. Szánta J. Jalkanen J. Mattla M. Rentola. Puká but t not te maxmal. We ave to make analy wt overload. Overload 500 N. It mulate f te cutomer grab te branc wt t tool and ull t. e tandard eart gravty alo take t effect. Fgure 9. Full lengt of te rod wt ock aborber Fgure 9 ow te rod degn. e wegt of te rod wtout te ock aborber,77 kg Sock Aborber Unt Fgure 0. Sock-aborber unt It wa neceary to create a unt tat reduce vbraton of te branc akng. It obvou, tat vbraton armful for uman body, o vbraton aborbng wa an mortant art of engneerng degn. Inde and outde dameter were mortant, becaue te vbraton aborber nvolved te bottom of te rod. erefore, tere oung for te tube. oue cylndrcal. Snce t neceary to uort te rod, te oue a 75 mm uort ole. In te oue tere an extra lace for te ock aborber. e damer under te rod. Sock aborber cont of tree man art. One of tem te lcon cylnder tat reonble for aborbng.

23 Branc Saker Degnng Project 3 due to te fact, tat lcon a bg caablty for ae deformaton. Oter two art are crew, one for te rod and one for te oue fxng. Sock reducng roce mle. Wen te motor tart and te aker workng, tere g vbraton n te entre rod. erefore, vbraton caue deformaton n te lcon art of damer. Slcon ollow, o tere enoug ace for deformaton (Fgure 0) Motor coong and movement converon e man art of te tool te motor. art reonble for ow ard te tool can u and ull te branc and ow muc tme te tool work. A quck alternate movement wa needed to te branc aker tat wy a movement converter art ad to take lace nto te tool tat cange te motor rotaton to alternate movng. e eaet way for t tranmon wa a coule of gear and an arm art, were te bgger gear an eccentrc gear (Fgure ). Fgure. Motor and gear for alternate movng It wa neceary to determne ow large force needed for te akng and ow long te cutomer would lke to ue te tool n one tme. Baed on marketng urvey uer do not lan to work wt te tool above one an our at once. Meaurement owed tat a 50 N force enoug to move tnner branc. Etmatng te workng tme of te tool wa created n ScLab rogram, were more factor were needed to defne revouly. It wa very mortant to defne te ma movng by te motor. e ma of te rod would wegt too muc for te motor to move tat wy te motor oue at te to of te rod, o n t cae te motor a to move jut te ma of te ead and arm art. Oter eental element of te tool were te tranmon of te gear and te eccentrcty. ee number were taken from a Boc edge trmmer arameter. e trd factor wa te motor tat wa coen for bg tall torque, bg no load eed and a utable battery caacty.

24 4 G. Nagy B. Sák A. Szója I. Szánta J. Jalkanen J. Mattla M. Rentola. Puká e rogram teted te degned tool accordng to tee coen arameter and we found tat te tool can work between 0 30 mnute f te akng force between N. Conequently f we ave two battery ack we could reac te 60 mnute workng tme wt te tool. 4. FMEA Falure mode and effect analyng Rk analy tool are ued to dentfy oble rk of te roce or a target. It ow n wat way te roduct doe not fulfl cutomer requrement and wat are te effect of te rk to te cutomer. Degn FMEA a great tool to el degnng and qualty eronnel to detect te get rk of te new roduct before te roce a gone too far. way t eaer to take note of te bgget ue wen you are degnng te roduct and you do not ave to make bg crtcal cange later. It mortant to fnd out all te rk tat are armful or dangerou to te fnal uer of te roduct. Durng engneerng degn of te roduct you mut ay attenton to all of tee rk and fgure out te bet oluton to revent tee armful tng to come true n te fnal roduct. At te begnnng of t roject-fmea our grou tarted to lt all dfferent knd of rk from a many dfferent aect a oble. Grou wanted to fnd rk tat eecally concern about uer afety and atfacton of ung te roduct. Lted rk were collected to an Excel temlate. After t te rk were valuated from 0 accordng to tree dfferent factor: everty (SEV), occurrence (OCC) and detecton (DE). After valung te rk tee tree factor were multled togeter to get te Rk Prorty Number (RPN= 000). Grou wanted to kee te RPN below 00 to enure tat te rk low enoug becaue mot of te rk concerned about uer afety. Hget rk tat were found and needed acton were te akng of te tool, wegt of te tool, rotecton agant water and accdental tartng of te roduct. Sakng can be reduced by ant-vbraton oluton n andle and rod connecton. For te wegt of te tool t mortant to ue lgt materal. Water roofng neceary for t tool becaue t ued outde and t can get n touc wt water. Accdental tartng of te roduct can be mnmzed wt two-button tart. 5. Purcang ere wa one man tak for urcang. Calculate te fnal roduct rce wt materal coong, wc atfy te qualty requrement. Bede t wa decded tat gro margn roft a to be over 40%. Calculatng materal cot wa a lttle ard becaue dtrbutor do not alway ow rce for materal n webte. After nvetgaton, t wa te bet way to ue Albaba.com for earcng te materal and rce. At t ont we could only ue materal cot becaue we dd not know te ng cot. Becaue of tat rce, wc are ued n calculaton, are a bt ger tan n dtrbutor te. Excel table ued for materal cot calculaton and wegt of te roduct calculaton alo. A art of t table can be een n able.

25 Part Branc Saker Degnng Project 5 able Purcang cart Quantty Prce/ece ( ) otal rce ( ) Ma (kg) Battery cell *0,5 5 0,38 Battery oung 0,5 0,5 0,08 Lower oue,, 0,3 Lower rod 4 4 Uer rod 4 4 0,8 Motor,65,65 0, otal materal cot er roduct: 59, total ma: 6 kg 5.. Labour cot Labour cot er roduct needed to know alo for te total manufacturng rce. Formula : x = (w ) (d ), were x labor cot er roduct, w montly wage, eole er ft, d workng day er mont and roduct er ft. Value wc were ued: 500 montly wage 7 eole er ft,7 workng day er mont 000 roduct er ft Wt tee value labour cot er roduct only 0, Market rce Formula for gro margn roft g = (t m)/t, were g gro margn roft, m manufacturng rce and t total market rce. Convertng t formula to t form t = m/( g). For manufacturng rce um from labor cot and materal cot are ued and t Gro margn roft 40%. Wt tee value market rce Becaue t muc lower rce tan comettve roduct, 5 te fnal market rce for our roduct. 6. Marketng 6.. Smlar roduct At te begnnng of te roject, marketng job wa to fnd mlar roduct. It wa neceary becaue t way we were able to collect dea for our tool. On te nternet, tere were ome tem, wc ad te ame functon to ake te brance. ey were comared n dfferent aect. ree out of fve work wt fuel, wc make te tool exenve, but te effectvene of tem very good. ey are eavy o te ung of tem ard for elderly eole. e oter two tem work wt battery and electrcty. At te end of te rod tere a rake wc moveable. ee one are

26 6 G. Nagy B. Sák A. Szója I. Szánta J. Jalkanen J. Mattla M. Rentola. Puká ued only for olve akng. ey are lgt o tey can be ued ealy. We tred to combne tee tool. 6.. Survey Anoter mortant job of te marketng eron wa to kee contact wt te otental cutomer. So e made a urvey. Makng a quetonnare a bac tak of a roduct degn, a we can meaure te future cutomer need. Wt a quetonnare, we are able to collect large number of anonymou revew. It ealy roceed, and we can make tattcal analy of te data. However, we ave to ay attenton, becaue f te queton not roerly rovded, ten a roblem may are later Makng te urvey We ad to make a ort, eental urvey. Many queton were collected, wc ould be aked from te cutomer. e mot mortant queton were coen. at ow we got te followng one:. Wat your gender?. Wat your age? 3. Wc your country? 4. Do you ave frut tree or bue at ome? 5. Wat knd of frut tree/ tree do you ave? 6. How do you arvet your frut tree? 7. Would you ue a tool tat el you ake te frut down? 8. If you ave a frut aker tool wt cuttng ead would you ue t for branc cuttng? 9. Would you ue t branc aker tool to ake te leave down? 0. How muc tme would you ue t branc aker tool for one occaon?. How muc would you ay for a tree aker?. How mortant would be for you te wegt of te tool? 3. How mortant would be for you te ae of te tool? 4. How mortant would be for you te ze of lace takng of te tool? ere are two dfferent knd of queton. It can be een tat te frt tree queton are ordnary one. It mortant to know, wo te anwerer, becaue wt t t can be redcted, wo are te future uer. ere were ecfc queton too; ere we aked mortant tng about our tool. ey were needed becaue t way we could conclude, wc are te mot relevant tng of our tool. It wa neceary to know wat knd of tree te future uer ave, becaue t way we could etmate ow muc force needed to move a branc of te gven tree. Our job wa to make a multfuncton tool. Our dea wa to ue t for branc cuttng bede te branc akng. From all of tee te mot mortant, f te cutomer wll ue t tool. Anoter one ow muc te uer would ay for t.

27 Branc Saker Degnng Project Some reult of te urvey on dagram How do you collect te frut from te tree/bu? From te tree Sake te tree Wat tll fall How do you collect te frut from te tree/bu? Wat tll fall Sake te tree From te tree Fgure. Frut collectng metod How mortant te... Wegt of te tool Aearance of te tool Sace t occue wen not ued Fgure 3. Imortance of aect ( not mortant, 5 mortant,) How muc would you ay for a tree aker? How muc would you ay for a tree aker? Fgure 4. Sellng rce

28 8 G. Nagy B. Sák A. Szója I. Szánta J. Jalkanen J. Mattla M. Rentola. Puká 7. Qualty Qualty manager overaw every art of te tool: ow muc afe tey are, are tey atfy te cutomer requrement, etc. at wy qualty manager ket connecton between marketng manager and engneerng degner. Durng te roject t wa uggeted by te qualty tat battery ould be bult from ltum on cell ntead of buyng a battery rack, becaue t way ceaer and could be more ergonomc. Anoter uggeton wa te frequency canger tat el to control te velocty of te ead and te fxed ead conceton tat more affordable and relable tan te adjutable ead. It wa gven t for rod materal and defned te maxmum wegt of te tool. Determne te maxmum lengt of te oened and cloed tool wa mortant for carryng te tool and baed on te quetonnare te rce of te tool wa calculated. 8. Summary e tool wa named Boc Pyton, t could be a good name becaue te cutomer can memorze ealy and t refer tat our tool trong. Everybody from our grou tuded new tecnc on ow to work n a grou. All of te member got a lot of exerence durng roject workng, ow to buld-u a roject, lannng te te of te roject, execute te agnment and tee exerence could be aled n te future work. Becaue of tee lot of exerence we would lke to ay tank to te uervor, wo made t roject realed. We got a bunc of uggeton and el o tank for ter work and entuam. Our grou made te wole 3D model of t tool n t roject work and fnally you can ee ome cture from te Boc Pyton. Fgure 5. Boc Pyton wt jgaw blade

29 Branc Saker Degnng Project 9 9. Reference Fgure 6. Boc Pyton wt aker ead [] ZSÁRY, Á.: Géelemek I II. ankönyvkadó, Budaet, 989. [] ERPLÁN, Z.: Géelemek I II. Nemzet ankönyvkadó, Budaet. [3] PÉER, J.: Gétervezé alaja. Mkolc Egyetem Kadó, Mkolc, 008. [4] KAMONDI, L. SARKA, F. AKÁCS, Á.: Fejlezté-módzertan meretek. Elektronku jegyzet. ÁMOP //a , Mkolc, 0. [5] tt://

30 Degn of Macne and Structure, Vol. 5, No. (05) FLOW IN CAPILLARY UBE JÓZSEF NAGY Electrolux Leel Kft. H-500 Jázberény, Fémnyomó u.. Abtract: In t tudy, I owed te equaton tat decrbe te teady tate flow n te callary n a way tat no dtncton ould be made accordng to weter tere a one or a two-ae flow. due to te fact tat te entaly artal dervatve n te equaton are reared by numercal calculaton. In cae of teady tate flow I owed te trottlng effect on callary flow, a well a ow to calculate (numercally) te ze of te unagnable callary flow, and te entaly and denty of te flud wc come nto te evaorator Keyword: callary, numercal mulaton, teady tate flow. Introducton In te coolng ytem of te oueold refrgerator te mot common exanon devce te callary tube. e callary tube control te amount of refrgerant flowng from te condener to te evaorator. e callary tube a an exanon devce ued wdely due to t low cot and relable oeraton (no movng art). e callary tube a a tructural comonent of te coolng ytem one of te mlet comonent, but t more dffcult to undertand t ycal functon and to decrbe t matematcally. Fgure. eoretcal coolng cycle n log()- dagram

31 Flow n Callary ube 3 Coolng devce develoer determne te alcable callary dameter and lengt troug exerment and tet. In general, tey ecfy te o-called callary ar flow rate. mean tat tey ecfy te amount of outgong ntrogen volumetrc flow n cae of a 6 bar nlet and bar outlet reure rato.. value uually gven n ltre/mnute. Callary tube are uually made of coer or alumnum. er external dameter,85 mm and te nternal dameter range 0,57; 0,63; 0,70; 0,76 mm (0,05; 0,05; 0,075; 0,030 ). ey elect from t nner dameter range, and et te dfferent ar flow rate value by rearng te lengt of te callary tube to te roer value. Fgure ow a teoretcal coolng cycle n a log()- dagram. (Uually t knd of dagram ued to decrbe coolng cycle.) In t fgure ont 3 te end of te condener and ont 4 te front of te evaorator. ee two ont are connected by te callary tube. In te teoretcal coolng cycle t aumed tat te refrgerant flow from te condener to te evaorator at a contant entaly (wt a o called trottlng tate cange). In ractce, te callary tube and te ucton tube, wc latter connect te evaorator to te comreor, are counter flow eat excanger. (It furter comlcate te decrton of te oeraton of te callary.) Fgure ow t layout. e total lengt of te callary, te lengt of t before te eat excanger, te lengt of te eat excanger, te lengt of te callary after te eat excanger wc n te nulatng PUR foam. ecton, terefore, we can take adabatc. Fgure. Structure of eat excanger We know wat reure (temerature) and denty te medum a wc enter te callare, but we do not know t quantty. (Wat te ma flow rate?) We do not know te denty (te amount of team) and te entaly of te flud, wc ext te callary and enter te evaorator. mortant to recognze o tat we can tell wat long evaorator needed (or wat te ze of t urface) for te enterng amount of refrgerant to evaorate.

32 3 Józef Nagy. Equaton decrbng te flow Ung te nomnaton of Fgure 3 te followng equaton can be recrbed. Contnuty equaton w w 0 () t x x Equaton of moton (Euler Equaton of moton) w w w w w g n () t x x D Energy equaton w w 4k w w w k wg n (3) t x t t x D Equaton of tate ermal equaton of tate, (4) Calorc equaton of tate, (5), (6) Fgure 3. Elementary ecton of e wt markng Equaton for teady-tate flow In cae of equaton of te tatonary (tme contant) flow te artal dervatve of te tme t daear. e equaton are a follow.

33 Contnuty equaton t mean tat Flow n Callary ube 33 w x 0, Equaton of moton (Euler Equaton of moton) w w w w g n x x D Energy equaton (7) w G Con. (8) w w w w g n x x D G w 4k w x x Dw w x x Equaton of tate are not canged. G g n 4k k D w G k g n Swtcng over from dfferental to dfference n equaton (0) and () we get te followng equaton: G Gdw d g dx D n (3) w 4k d k g n dx (4) DG. G Gw g n x (5) D w 4k k DG at te ame tme baed on equaton (8) we know tat G w. g n x (9) (0) () () (6) (7) Fgure 4. Net wt equal cale nterval

34 34 Józef Nagy u, equaton (5) and (6) can be wrtten a follow (Fgure 4): x g G D w w G n (8) x g DG k w w k n 4 (9) akng relaton (7) nto account and after rearrangng (8) and (9) we get n G Gw x g G D (0) n 4 k G w x g DG k () exreon. At te ame tme, alo te calorc tate equaton mut be atfed.e.,. () Equaton () and () all be equal, te reure ( +), calculated from relaton (0), mut be olved numercally concernng te denty (ρ +). It a to be olved n cae of all te elementary ecton of e (Δx) under a gven ma flow (G). mean tat an mlct equaton wt g comutatonal demand a to be olved n cae of all te elementary ecton of e. We reent anoter oton, wc make te calculaton exlct (and fater). o do t refer to equaton (3) and (4), and baed on relaton (7) exre dw: d G Gd G d dw. () Subttutng relaton (3) nto equaton (3) and (4), we get te followng: d G dx g G D d n () d G dx g DG k d k 3 n 4 (3) In addton to te ndeendent varable dx te unknown varable are d, d and te dρ. We ave tree unknown and two equaton. e equaton of tate of flud mng. Let make te equaton of tate of te flud known numercally n = (, ρ) form. From t d can be exreed a follow: d d d (4) Subttutng formula (6) nto equaton (5), we get te followng relaton: d G dx g DG k d k 3 n 4. (5)

35 Flow n Callary ube 35 From equaton (4) and (7) we get te elemental denty cange 3 n n 4 G G dx g G D dx g DG k d k. (6) Swtcng over to dfference, te denty cange, te reure cange and te entaly cange can be calculated a follow: 3 n n 4 k G G x g G D x g DG k, (9) G x g G D n, (30) k G x g DG k 3 n 4. (3) Knowng t te followng can be calculated:, (3), (33). (34) Fgure 5. Net wt varable cale nterval If we take Δ a ndeendent varable, ten we get te followng relaton for Δx (Fgure 5) baed on equaton (9) and (30): k g DG k g G D G G x n 4 n. (35)

36 36 Józef Nagy Δx calculated from exreon (35) mut be met te 0 x (36) condton. e borderlne cae 0 x met wen 0 G (37) equalty fulflled. o analye t relaton let ue te followng baed on exreon (8) w G, (38) furtermore, we know te reure, te entaly and te entroy a functon of temerature and denty baed on equaton (4), (5) and (6). u, we can wrte tat d d d, (39) d d d, (40) d d d. (4) In equaton (37) coeffcent and can be exreed a follow, knowng tat d d d d d d d d d (4) and relaton (4) true at any dρ and at any d, o, (43). (44) Exreng coeffcent and from relaton (43) and (44)

37 Flow n Callary ube 37, (45), (46) and ubttutng tem nto equaton (37) we get 0 w. (47) Wrte te frt law of termodynamc n te d d d (48) form and ung relaton (39), (40) and (4), we can wrte d d d d d d. (49) Equaton (49) mut be fulflled at eac dρ and d, terefore, (50). (5) Exreng artal dervatve and from equaton (50) and (5):, (5), (53) and ubttutng tem nto equaton (47) 0 w, (54)

38 38 Józef Nagy 0 w, (55) 0 w, (56) 0 0 w w. (57) It follow tat a w, (58).e. a w (59) were te eed of ound a. In relaton (58) te econd equalty can be rovded a follow. Wrte down te reure a te functon of entroy and denty,.e. = (, ρ), o n t cae d d d. (60) Ung relaton (39) and (4) d d d d d, (6), (6). (63)

39 Flow n Callary ube 39 In ummary te Δx = 0 atfed f te eed equal to te eed of ound. In addton, te condton Δx = 0 at locaton x L mut be met. Wen Δx = 0 (but now let turn back to dfferental and ung relaton dx = 0), ten equaton (0) a follow: d dw (64) G, and relaton () d wdw 0. (65) Rearrangng t and relacng d by relaton (48) and relacng dw by exreon (64) we can wrte d w d d 0 G (66). It follow tat, were Δx = 0, tere te cange n te entroy alo become zero (d = 0),.e., te entroy reace t maxmum. Entroy defned by: q d (67) f te q 0, ten te d 0,.e. te entroy cannot be reduced. If at gven ma flow te eed of flow reace te eed of ound at locaton x < L (t not oble), ten te callary not able to let tat ma flow rate flow troug, but only a maller ma flow rate were te eed of flow reace te eed of ound at locaton x = L. enomenon called trottlng. At te gven ma flow rate m te reure can be calculated were te velocty reace te eed of ound namely by te teratve oluton of relaton m G w a, (68) A. If te reultng reure le tan te evaoraton reure ( e), ten no trottlng occur. However, f te reure value ger tan te evaoraton reure, ten trottlng occur, wc mean tat te callary not caable of tranmttng t flow rate. u, te flow rate a to be determned (alo n an teratve way) o tat equalty w = a can meet at lace x = L. e reultng ma flow mut redefne te reure at wc te velocty reace te eed of ound. e teraton a to be carred out, a long a relaton (68) and equalty w = a multaneouly atfe at lace x = L. So t can determne numercally te callary ma flow rate. 3. Numercal metod e frt te to determne Δ. o do t, we frt need to calculate te reure value were at a gven ma flow te rate of flow reace te eed of ound. If

40 40 Józef Nagy c e t reure lower tan te evaoraton reure, ten n, f t greater, c ten n. o determne reure we mut know te eed of ound, a a functon of te reure and te denty. e bae of te numercal determnaton of te eed of ound gven by equaton (63). (Detal below.) Now let uoe tat we were able to determne Δ. u, te next te te calculaton of Δx baed on relaton (35). e determnaton of coeffcent n equaton (35) are te followng.. Numercal determnaton of e bae of te numercal determnaton of gve equaton(45). So we trace back to te numercal determnaton of and. Accordng to equaton (4) and (5) we know te reure and te entaly a a functon of te denty and temerature. Here we aume te numercal knowledge of tee functon. Baed on Fgure 6 te numercal artal dervatve can be reared by te followng formula: (69) (70) Fgure 6. Numercal determnaton of artal dervatve

41 Flow n Callary ube 4 Smlarly to relaton (69) and (70) we could alo et, but te reure and te entaly are known a a functon of temerature and denty o t arorate to ntroduce artal dervatve of tee varable. Fgure 7 and Fgure 8 ow functon () ρ and () ρ n cae of obutene (R600a). Fgure 7. () = Contant Fgure 8. () = Contant. Numercal determnaton of Lke n te revou ont, ere we alo trace t back to te artal dervatve of te temerature and denty. tracng back oble accordng to relaton (46). In addton to te foregong, ere are alo te entaly and reure artal dervatve of denty at a contant temerature. Numercal determnaton of tem oble accordng to te aroxmate relaton (7, 7). Fgure 7 and Fgure 8 ow te functon (ρ) and (ρ) n cae of te obutene (R600a) (7), (7). Fgure 9. () = Contant Fgure 0. () = Contant

42 4 Józef Nagy 3. e frcton factor defned n te functon of te Reynold-number. Dw DG For two-ae n te calculaton of Reynold-number Re te dynamc vcoty condered below accordng to relaton [3] x g xg (73) g f. Deendng on te value of te Reynold number e frcton factor can be calculated a follow accordng to [7]: f Re 30, ten n te context of lamnar flow 64 (74) Re, f 30 < Re 0 5, ten 0,5 0,364 Re (75) accordng to te Blau equaton, f 0 5 < Re < 0 8, ten 0,37 0,003 0, Re (76) accordng to Nkurade. 4. Defnton of te eat tranfer coeffcent k e eat tranfer coeffcent of te nner cylndrcal wall urface a to be calculated accordng to te followng equaton [5]: k 4 b Dk D ln D b cő D D,3 Nu k were D b k, D can be calculated. For a ae te Nuelt-number calculated accordng to te Dttu Boelterequaton 0,8 0,3 Nu 0,03 Re Pr, (78) For two-ae [7]: were (m: mxture) Nu b D f Pr c. 0,8 3 0,06 Re m Pr f k k,, (77) (79) (80)

43 Flow n Callary ube 43 Re g f g f f m Dw. (8) 5. Determnaton of te artal dervatve for te calculaton of te eed of ound We alo trace t back to te artal dervatve of te temerature and denty, accordng to relaton. (8) can be calculated baed on te (7), and baed on te aroxmaton (70). Smlarly, te mng artal dervatve can be determned ung exreon (83, 84) and wt te el of Fgure and Fgure , (83) (84) Fgure. () = Contant Fgure. () = Contant 4. Reult Knowng te tate urface of te flud accordng to relaton (4), (5) and (6) we can calculate te reure, te denty, te entaly and te velocty a a functon of locaton. In addton, we can calculate ow muc ma flow te gven geometry

44 44 Józef Nagy callary caable to tranmt troug knowng te reure, denty and entaly of te enterng flud. If te flud ntrogen, ten te callary arflow rate can be determned by calculaton, a well a te lengt of te callary needed to aceve te dered arflow rate at a elected nde dameter of te e. Fgure ow a teoretcal coolng cycle n log()- cart. It teoretcal, becaue te callary flow aume a contant entaly (between ont 3 and 4) and te comreor ree te refrgerant nto te condener at contant entroy (between ont and ). tudy doe not deal wt te comreor. tudy deal wt te flow between ont 3 and 4, and we are artcularly ntereted n te flow around ont 4. Let' take a look at ow to develo te flow n te callary tube under te followng aumton: e nner dameter of te callary 0,7 mm, t total lengt (L) 800 mm, te lengt before te eat excanger (L ) 380 mm, te lengt of te eat excanger (L ) 330 mm. e temerature of te refrgerant (R600a) n te condener 40 C, and t a aturated lqud. e temerature of te flud n te evaorator 4 C. On te lengt before te eat excanger (L ) te callary tube n contact wt te tatc ambent ar, avng a temerature of 5 C. On te eat excanger ecton te ar temerature vare lnearly between 0 C and +0 C around te callary. Fgure 3. e reure n callary a a functon of te entaly

45 Flow n Callary ube 45 After te eat excanger, te callary n te nulatng foam (PU foam). ecton condered to be adabatc. e reultng reure n te callary marked on Fgure 3 wt a tck red curve (between ont 3 and 4) n a log()- cart. It can be een tat te callary reure ger at end tan te reure n te evaorator (ont 4). alo mean tat trottlng occur. e callary caable of tranmttng a,78593 kg/ ma flow under te above condton. e reure 0,06859 MPa at te end of te callary, wc correond to a 0,3048 C flud. Fgure 4. (x) and (x) n te callary Fgure 5. (x), w(x) and a(x) n te callary

46 46 Józef Nagy 5. Summary In t tudy, I owed te equaton tat decrbe te teady tate flow n te callary n a way tat no dtncton ould be made accordng to weter tere a one or a two-ae flow. due to te fact tat te entaly artal dervatve n te equaton are reared by numercal calculaton. In cae of teady tate flow I owed te trottlng effect on callary flow, a well a ow to calculate (numercally) te ze of te unagnable callary flow, and te entaly and denty of te flud wc come nto te evaorator. Wt tat I ave anwered te queton aked n te frt art. 6. Reference [] CZIBERE, bor: Vezetée őátvtel. Mkolc Egyetem Kadó, Mkolc, 998. [] JAKAB, Zoltán: Komrezoro űté I II. Magyar Medrnt Szakkadó Kft. [3] JAKAB, Zoltán: Háztartá űtőbútorok é komfort légűtők.. javított kadá. Hűtő- é Klímatecnka Vállalkozáok Szövetége, 006. [4] GAÁL, Ferenc: Kűtőgéek. Műzak Könyvkadó, 97. [5] HOLMAN, J. P.: Heat tranfer. 7t Edton n SI Unt. McGrow-Hll Book Comany, 99. [6] ULLRICH, Han-Jürgen: Hűtőtecnka I. Soó é ára Hűtőtecnka Rt., 999. [7] ARORA, C. P.: Refrgeraton and ar condtonng. 3rd edton. ata McGraw Hll Educaton Prvate Lmted, 00. [8] REYNOLDS, W. C.: ermodynamc roerte n SI gra, table, and comutatonal equaton for 40 ubtance. Deartment of Macancal Engneerng Stanford Unverty, 979. [9] CARLSLAW, H. S. JAEGER, J. C.: Conducton of eat n old. nd edton. Oxford Unverty Pre, 959. [0] SZABÓ, Szlárd: Erő- é munkagéek. Előadávázlat. [] SZABÓ, Szlárd: Gázdnamka. Előadávázlat. [] KALMÁR, L. BARANYI, L.: Hő- é áramlátan feladatok numerku modellezée. Szakmérnök jegyzet. Mkolc Egyetem, Mkolc, 006. [3] HUHN, J. WOLF, J.: Kétfázú áramlá. Gáz-folyadék rendzerek. Műzak Könyvkadó, Budaet, 978. [4] GARBAI, L. DEZSŐ, Gy.: Áramlá energetka cővezetékrendzerekben. Műzak Könyvkadó, Budaet, 986. [5] VIDA, Gy.: Műzak őtan. ankönyvkadó, Budaet, 99. [6] ZHANG, C. L. DING, G. L.: Aroxmate analytc oluton of adabatc callary tube. Internatonal Journal of Refrgeraton, 004 (7), 7 4. [7] CZIBERE, bor: Áramlátan. ankönyvkadó, Budaet, 990.

47 Degn of Macne and Structure, Vol. 5, No. (05) MEASURING MEHOD O DEERMINE HE VIBRAION DAMPING BEHAVIOUR OF MEALLIC FOAMS FERENC SARKA ÁDÁM DÖBRÖCZÖNI AILA SZILÁGYI Unverty of Mkolc, H-355 Mkolc-Egyetemváro, Hungary macf@un-mkolc.u Abtract: In t aer te autor decrbe a meaurng metod to determne te vbraton damng beavour of te metallc foam and try to determne wc damng model good to decrbe te beavour of metallc foam (Coulomb damng or vcou damng). Keyword: metallc foam, vbraton damng, damng model. Introducton e tecnologcal develoment brougt cloe to aval metallc foam for degner n ndutral ue. Many Hungaran nttuton are manufacturng and workng wt metallc foam uc a te Unverty of Mkolc and te Bay Zoltán Nonroft Ltd. n Mkolc, or n Budaet te Budaet Unverty of ecnology and Economc. e name metallc foam ndcate uc a old metallc materal, wc a more tan 90% oroty (ome manufacturer roduce metal foam le tan 90% oroty). e denty of t knd of materal le by one order of magntude. Metallc foam a everal roerte tat make t ue derable n engneerng. ee roerte are energy-aborbng, eat conducton, damng, ound-aborbng and flterng ablte. Metallc foam ave two tye; te oen-cell and cloed-cell one. Mot of te cae te materal of te metallc foam alumnum-alloy but metallc foam alo can be created from oter materal (teel, coer, lver and ttan) [], []. Many reearce were carred out to determne ycal, cemcal and mecancal roerte of metallc foam. Proerte of metallc foam deend on te ze of te cell, te tckne of te wall (brdge) between te cell and te ae of te cell f te materal te ame. Wt te ue of te modfed rato between te old metal denty and te foam metal denty, we can aroxmately determne foam materal roerte. e comutatonal equaton equaton (). P k 0 0 P were, P: a knd of roerty, ρ: denty, 0: ndex for metal, wtout ndex 0 for metal foam, n, k: can be coen accordng to able, arameter from meaurement. n Lterature ort-oken n te ont of vew of te damng beavour of metallc foam. About te damng beavour of old metal many lterature ubl data uc a logartmcal decrement or Ler damng rato [3], [4]. ()

48 48 Ferenc Sarka Ádám Döbröczön Attla Szlágy at would be obvou to ue equaton () to determne te damng caablty of metallc foam. e damng caablty of metallc foam wore tan for te old metal materal wll be te reult f we make te calculaton. would be te oote of toe tatement tat underlne te gnfcant vbraton damng caablty of metallc foam. We can determne tat equaton () cannot ue for determne vbraton damng caablty of metallc foam. able k and n factor to determne arameter of metal foam Proerty k n R (Ωm).6.85 λ (W/mK).6.85 E (GPa) σ (MPa) Lterature ort-oken n te ont of vew of te damng beavour of metallc foam. About te damng beavour of old metal many lterature ubl data uc a logartmcal decrement or Ler damng rato [3], [4]. Fgure. Nature and te enveloe of Coulomb damng Fgure. Nature and te enveloe of vcou damng

49 Meaurng Metod to Determne te Vbraton Damng Beavour of Metallc Foam 49 at would be obvou to ue equaton () to determne te damng caablty of metallc foam. e damng caablty of metallc foam wore tan for te old metal materal wll be te reult f we make te calculaton. would be te oote of toe tatement tat underlne te gnfcant vbraton damng caablty of metallc foam. We can determne tat equaton () cannot ue for determne vbraton damng caablty of metallc foam. Vbraton damng beavour of old metal materal can be decrbed wt a vcou damng model (Fgure ). It quetonable weter we can ue or not te ame damng model for metallc foam. Next cater wll be decrbed a meaurement, wc can el to determne te vbraton damng beavour of metallc foam and te value of logartmcal decrement. aer ntroduce te next te of te reearc ntroduced n [].. Sae of te amle and te layout of te meaurement We made beam wt rectangular cro-ecton from te metallc foam materal. e beam wa made from a greater metallc foam late wt a mllng macne. Fgure 3. e metallc foam beam e dmenon of te metallc foam beam: 35.5 mm x 7 mm x 300 mm, wegt 9 g (Fgure 3). We fatened a wegt to one of te end of te beam wt a crew fatenng (t gned wt m0 n Fgure 6), n t way et u te amle (Fgure 4). Fgure 4. e amle

50 50 Ferenc Sarka Ádám Döbröczön Attla Szlágy We fatened te free end of te aembled amle wt a fxed uort (Fgure 5). Fgure 5. Faten of te amle We laced load to te amle wt anoter wegt, wt a el of a fng lne (gned wt m n Fgure 6). After cuttng te fng lne wc eld te (m) wegt we meaured te dlacement of te free end of te beam. e dlacement wa meaured wt a laer dlacement meter (gned wt L n Fgure 6). e ketc of te meaurement can be een n Fgure 6, and real meaurng n Fgure 7. Metallc foam beam L m 0 m Fgure 6. Sketc of te meaurement Fgure 7. Real envronment of te meaurement