INVESTIGATIONS OF THE FORCED TORSIONAL VIBRATIONS IN THE SAW UNIT OF A KIND OF WOOD SHAPERS, USED IN THE WOOD PRODUCTION

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1 INNOAION IN OODORKIN INDUSRY AND ENINEERIN DESIN / ): 6 69 INESIAIONS OF E FORCED ORSIONAL IRAIONS IN E SA UNI OF A KIND OF OOD SAPERS USED IN E OOD PRODUCION eo ukov alenn Slavov eo Kovaev Unvesy of Foesy Klmen Odsk lvd 797 Sofa ulaa e-mal: eov@av Unvesy of Cemal enoloy and ealluy Sofa e-mal: valslav@av ASRAC e poposed sudy pesens a numeal nvesaon of e foed osonal vaons n e wood sape s saw un aused y e vaale momens on e dve ele moo and e wood sape s saw e nfluene on e vaons of e lades nume of e saw w eally wok s nvesaed s esea s done on e ase of a onee meanmaemaal model fo nvesaon of e osonal vaons of a wood sape s saw developed y e auos e man feaues n e onsuon of s knd of wood sapes ae endeed an aoun n s model e nvesaon`s esuls an e used as a ase fo makn some onee and well-founded eommendaons onenn e opeaon of ese manes ese eommendaons ae mpoan fo nease of elaly of e wood sapes as well as e auay and ualy of e poduon Key wods: wood sapes modeln osonal vaons INRODUCION Dsoven and nvesaon of e auses fo onae of e nensve osonal vaon of e wood sapes eues undesandn e essene of e dynam poesses n em wen mane woks I s neessay o ondu puposeful sudes n w e mane an e onsdeed as a meanal van sysem w known aaess of s ndvdual elemens Amoue 6) Fo s pupose fsly s neessay o ave meanal-maemaal modeln and omposn of euaons desn e vaon of e elemens of e wood sape ell-aeed esea an e done y solvn ese euaons n dffeen ondons Some eommendaons fo e onsuon s desn and e wok emes of e mane ae fomed on e ase aev a al ) e knd of wood sapes a ae ommonly used n e pae of foesy ndusy Flpov 977) ae examned n e poposed sudy F sows e eneal vew and F a seme of s ype of wood sapes Oeskov 997) e mane ody s maked w s e ele moo e el dve w an e a wede el o a ed el e spndle w e eans e ao w mose one 6 e wok ale 7 wood sape s saw

INESIAIONSS OF E FORCED ORSIONAL IRAIONS IN 6

sape Some speal feaues n e modeln of woodwokn

ukov a al ) Some numeal nvesaons of e naual

made Some ased eommendaons fo e avodane of

Paally s onneed w e nease of elaly of e manee

oal of s sudy s o make a numeal nvesaon off e

o e vaale momens on e dve ele moo and on e

on e osonal vaons of e lades nume of e saw w

adeuae mean-maemaal model fo nvesaon of e

auos e model pesens feauess n e onsuon of a

mean-maemaal model fo nvesaon of e dynamall

elas elemens φ = ae e anles of e oaon off e

saf e el and e spndle ae aken no aoun e elasy

and s onee of e spndle w Nm/ad) e elasyy lnea

ae с and с N/m) e dampn oeffens ae maked w

sown oo Fue : ean-ma aemaal model e neessay

2 INESIAIONSS OF E FORCED ORSIONAL IRAIONS IN 6 Fue : ood sape eneal vew Fue : Seme of e wood sape Some speal feaues n e modeln of woodwokn manes ae examnedd n pevous woks of e auos ukov a al ) Some numeal nvesaons of e naual feuenes and mode sapes of e wood sapes ae made Some ased eommendaons fo e avodane of esonan emes ae fomed on e asss of s sudy Paally s onneed w e nease of elaly of e manee as well as w e auay and ualy of e poduon e oal of s sudy s o make a numeal nvesaon off e foed osonal vaons n e wood sape s saw un due o e vaale momens on e dve ele moo and on e wood sape ss saw e man am s o sudy e nfluene on e osonal vaons of e lades nume of e saw w eally wok e nvesaon s done on e ase of an adeuae mean-maemaal model fo nvesaon of e osonal vaons of e wood sapess developedd y e auos e model pesens feauess n e onsuon of a knd of wood sapes ECANIC-AEAICAL ODEL A mean-maemaal model fo nvesaon of e dynamall poesses and vaons n e wood sape s saw un s ul y e auos e model s sownn on e f s model nludes fou dsee mass onneed w ee massless elas elemens φ = ae e anles of e oaon off e oespondn oo e elasy oeffens of e ele moo s saf e el and e spndle ae aken no aoun e elasy e anula oeffen of e ele moo s saf s maked w and s onee of e spndle w Nm/ad) e elasyy lnea oeffens of e wo pas of e el eween e el pulle ae с and с N/m) e dampn oeffens ae maked w and espeve ndes e appled momens on e dsks ae sown oo Fue : ean-ma aemaal model e neessay edued masss nea momens k m ) ae endeed n aoun f ): eyy ae J e masss nea momen of e ele moo s oo J

3 INESIAIONS OF E FORCED ORSIONAL IRAIONS IN 6 e mass nea momen of e el pulle on e ele moo s saf J e mass nea momen of e el pulle on e spndle J e mass nea momen of e wood sape s saw w ue ao Some oe symols on f ae: d d damees of e ele moo s saf and spndle m) l l ompun len of e ele moo s saf and spndle m) adus of e el pulles on e ele moo s saf and spndle m) modulus of sean e nvesaon of e osonal vaons of e wood sape s saw un d EK E d wee ae e enealzed oodnaes E K and E P ae espevely e kne and e poenal eney of e mulody sysems F s dsspave funon Q s e veo of e enealzed foes e veo of e enealzed eues fomulaon and soluon of e dffeenal euaons w dese ese poesses eefoe e poy of e max means s used Anelov and Slavov ) e mean-maemaal model s done y usn e appled ennee poam aemaa) An alom fo fomulaon of e maxes w dese e popees of e meanal sysem s developed e dffeenal euaons w dese e vaons ae dedued y usn e Laane s meod K EP F Q ) eney of e fou as odes e ele moo s oo e el pulle on e ele moo s saf e el pulle on e spndle wood sape s saw) y analoy e poenal eney of e meanal sysem s oaned as a sum of e poenal enees eeved fom e defomaons of e oodnaes s ele moo s saf e el and e spndle e kne eney of e meanal sysem s oaned as a sum of e kne EK J J J J E P ) e dsspave funon s F ) e veo of e enealzed loads Q ) nludes all osonal momens appled on wee: М s e momen of e ele e oos I s moo М and М momens of e el

4 66 EORI UKO ALENIN SLAO EORI KOACE pulles fom e neaon w e el М e momen of e wood sape s saw w s fomed wen e mane woks s meod supposes eevn a sysem of paame lnea dffeenal euaons w dese e small foed osonal vaons of e saw un ey ae Q C ) e max w aaeze e mass-neal popees of e meanal sysem numeal values ae ven n km ) e elas popees ad m N ) and e dampn popees ad s m N ) ae 6 7 J J J J E a a j K j j 6) E j P j j C C 7) F j j j 8) e eneal soluons of e sysem of dffeenal euaons ) n e amonous appeaane of dsun foes and nal ondons = ) = ) wen n max fom ae

5 INESIAIONS OF E FORCED ORSIONAL IRAIONS IN 67 } Re{ sn )] ) ) [ os )] ) ) [ ) k n k e k k k e e Q 9) wee: R R L L R L s e modal max e max of e manay pa of e naual veos of e dampn sysem p naual values w v u naual veos elave dampn oeffen dampn oeffen feueny of fee dampn vaon w e manay pa of e naual veo aused y dampenn sysem v naual modes and naual feuenes of e non dampn sysem e developed meanal - maemaal model allows ondun a nume of sudes of e foed osonal vaons n e wood sape s saw un Foed vaons due o e vaale momens on e dve ele moo and on e wood sape s saw ae nvesaed n s sudy e unavodale devaon of e oe sape of e sao and e unalane of e oo lead o e ouene of a vaale osonal momen on e ele moo s momen s modeln as o s onsan pa ae added wo omponens a ave e ype sn ω and sn ω wee ω s e feueny of oaon of e oo and ae e ampludes espevely) e modeln of e vaale momen of e wood sape s saw demand sudous analyss of e man feaues of e saw s wok e nvesaons ondun y e auos sow a s momen an e ven as o e onenaed saw s momen s added a vaale omponen P s omponen of e momen s z P P sn ) wee: М P s e amplude of e vaale omponen of e momen z e lades nume of e saw w eally wok ω e feueny of oaon of e sape saw Numeal nvesaons ae ondued fo ee dffeen wok emes of e wood sape s saw In e fs ase s aeped a all sx lades of e saw ake pa n e saw poess т е z = 6 u paally only a pa of e saw s lades wok eause ee ae some nauaes n e saw s poduon e assemly and e ue ndn wo ases ae nvesaed n s sudy wen e eally wokn lades of

6 68 EORI UKO ALENIN SLAO EORI KOACE e saw ae ee e z = and wen ey ae wo e z = e momens and on pulleys fom e neaon w e el ae aken no onsdeaon ale : Daa RESULS e daa of e wood sape w ae neessay fo e nvesaons ae ven n e ale d damee of e ele moo s saf mm) 8 d damee of e spndle mm) adus of e el pulle mm) 9 adus of e el pulle mm) l dsane eween e el pulle and e ele moo mm) l dsane eween e sape saw and e el pulle mm) 6 М momen of e ele moo Nm) М addonal momen of e ele moo Nm) М addonal momen of e ele moo Nm) М momen of e el pulle Nm) М momen of e el pulle Nm) М momen of e sape saw Nm) М P addonal momen of e sape saw Nm) ω feueny of oaon s - ) ω feueny of oaon of e sape saw s - ) e ondued nvesaons sow a e nfluene of e lades nume of e saw w eally wok on e foed osonal vaons of e dve ele moo and of e el pulle on e ele moo s saf s slly u s nfluene s snfanly on e seond el pulle and s e on e sape s saw e aps a llusae e foed osonal vaons of ese wo elemens wen all sx lades of e saw ake pa n e saw poess ae sown n f and f e espeve aps a llusae vaons wen ee lades wok ae sown n f 6 and f 7 F 8 and f 9 llusae vaons wen wo lades wok 6 8 s 6 8 s Fue : Fue :

7 INESIAIONS OF E FORCED ORSIONAL IRAIONS IN s 6 8 s Fue 6: Fue 7: 6 8 s 6 8 s Fue 8: Fue 9: Some deduons follow fom fues aove e maxmal ampludes of e foed osonal vaons of seond el pulle nease wen e lades nume of e saw w eally wok deease e neasn of e maxmal ampludes of e foed osonal vaons of e sape s saw s e oweve e neasn of e ampludes of e snle amons s sonly dffeenly e analyss of e oaned esuls sows a e lades nume of e saw w eally wok as a de nfluene on e vaons of e sape s saw s fa efles on e auay and ualy of mane s wok CONCLUSION e sudy pesens e esuls of e mplemenaon of numeal nvesaons w onal meanal maemaal model of e osonal vaons of e wood sape s saw un e foed osonal vaons due o e vaale momens on e dve ele moo and on e wood sape s saw ae examned e nfluene on e vaons of e lades nume of e saw w eally wok s nvesaed e ondued analyss of e oaned esuls sows a e lades nume of e saw w eally wok as a de nfluene on e vaons of e sape s saw un s nfluene as moe weak effe on e vaons of e seond el pulle u s effe on e vaons of e sape s saw s e e neasn of e level of e vaons nevaly makes e auay and ualy of e poduon wose e eommendaons o supevson and onol of e assemly and e enal sae of e saw s lades ae mposed us uaanees e ualy of e poduon

8 7 EORI UKO ALENIN SLAO EORI KOACE REFERENCES Amoue F 6) Fundamenals of ulody Dynams eoy and Applaons käuse oson Anelov I Slavov R ) ook of polems ax means - Dynams Avanad Pma Sofa aev Nkolov C Anelov ) eanal maemaal modeln n spae of a s foed vaons aused y e oad s ouness Senf Jounal "eans of anes" yeas XX vol ssue 99 ana pp 9 Flpov 977) oodwokn manes Sofa Oeskov P 997) oodwokn manes Sofa 6 ukov Z oev Slavov ) osonal aons n e Saw Un of a Knd of Cula Saws Numeal Invesaons of e Naual Feuenes and ode Sapes Poeedns of Papes 8 Inenaonal Sene Confeene Cp and Cpless oodwokn Poesses Zvolen pp wwwmaemaaom

MATHEMATICAL MODEL OF THE DUMMY NECK INCLUDED IN A FRONTAL IMPACT TESTING SYSTEM

MATHEMATICAL MODEL OF THE DUMMY NECK INCLUDED IN A FRONTAL IMPACT TESTING SYSTEM he h Inenaonal onfeene Advaned opose Maeals Enneen OMA 8- Oobe Basov Roana MAHEMAIAL MODEL O HE DUMMY NEK INLUDED IN A RONAL IMPA ESIN SYSEM unel Sefana Popa Daos-Lauenu apan Vasle Unves of aova aova ROMANIA