Dynamics Analysis and Modeling of Rubber Belt in Large Mine Belt Conveyors

Transcription

1 Sensors & Transducers Vol. 8 Issue 0 Ocober 04 pp. 0-8 Sensors & Transducers 04 by IFSA Publshng S. L. hp:// Dynamcs Analyss and Modelng of Rubber Bel n Large Mne Bel Conveyors Gao Yang College of Mecharonc Engneerng Befang Unversy of Naonales Chna Tel.: Receved: 9 July 04 /Acceped: 30 Sepember 04 /Publshed: 3 Ocober 04 Absrac: Rubber bel no only s one of he key componens of bel conveyor bu also affecs he overall performance of he core par. Research on dynamcs analyss of large conveyor no only helps o mprove he relably and desgn level bu also can gude he raonal selecon of conveyor safey facor and effecvely reduce he cos of he conveyor bel. Based on unque vscoelasc properes of bel conveyor was smplfed as one-dmensonal vscoelasc rod n hs sudy and hen a dscree elemen model of conveyor sysems was esablshed. The knec equaons of each dscree un was derved usng knec energy poenal energy of drvng segmen bearng segmen and reurn segmen and equaon of energy dsspaon and Lagrange equaon. Based on Wlson-θ algorhm he knec equaon of DT307-ype ST000's conveyor bel was solved by usng Malab o wre compuer programs. Research on he change rule of conveyor dsplacemen velocy acceleraon and dynamc enson durng he boo process revealed he workng mechansm of nonlnear vscoelasc whch lay he heorecal foundaon for dynamc performance opmzaon of large bel conveyor. The calculaon resuls were used o opmze desgn and analyss of conveyor sysem he resul showed ha could reduce he drven enson peaks abou % save 5 % of overall manufacurng cos whch brng consderable profs for enerprses. Copyrgh 04 IFSA Publshng S. L. Keywords: Bel conveyor Rubber bel Dscree elemen model Dynamcs analyss.. Inroducon The mos mporan queson of large mnng bel conveyor sysem s how o choose desgn sandards ha mee he acual needs o desgn fully funconal relable sysems o mee he acual needs of he projec. The bgges dfference of selecon of desgn sandards was from a dfferen calculaon of runnng ressance and dynamc performance desgn. Too small runnng ressance wll cause ha he sysem canno operae properly bu oo much wll resul n wased power only he rgh runnng ressance calculaon can selec he mach power and conveyor bel. Somemes he dynamc enson peaks of large mne bel conveyor a work was several mes or even dozens of mes durng normal operaon If was sll desgned n accordance wh he sac sandards he performance and relably of he conveyor sysem can be ensured only by choosng a larger safey facor. Clearly here s a conradcon whch a large safey facor would ncrease he manufacurng cos of he conveyor and wase nvesmen []. Conveyor bel s he bearng componen of whole large bel conveyor and s nvesmens are generally accouned for 30 %-50 % of he machne [ 3] somemes even more. Raonal calculaon and allocaon of dynamc enson s he premse of choosng he rgh conveyor bel bu also one of he mos effecve means o save manufacurng cos. Conveyor bel no only s one of he key componens 0 hp://

2 Sensors & Transducers Vol. 8 Issue 0 Ocober 04 pp. 0-8 of bel conveyor bu also affecs he overall performance of he core par. Is dynamc characerscs research s he prmary queson of conveyor desgn and manufacurng. Mos of he radonal conveyor desgns use he sac mehod wh a larger safey facor o compensae dynamc performance for he sarup operaon and brakng process. However large capacy hgh effcency and long dsance conveyor s composed by a rubber layer and he core wre or fabrc rope no only has sac characerscs bu also has comple dynamc characerscs. The specfc manfesaons was nonlnear characerscs of sress and sran hyseress characerscs creep properes relaaon properes dynamc modulus of elascy herefore has obvous feaures of dynamc vscoelasc properes. In engneerng applcaons he mechancal relaonshp of he conveyor can be epressed usng combnaons of an deal elasc model (deal sprng) and he deal vscous (damper) model. In 96 Malng and Verlng worked n Unversy of Hannover Germany suded he vscoelasc of bel and he frs used no he knec analyss of he conveyor bel and proposed he vscoelasc model of conveyor bel. Then Vog model Fg. (a) has been wdely used paralleled he vscosy and he elasc elemens whch can reflec response of he maeral o sress bu do no smulae a good response of he bel o he nsananeous sran [4]. Mawell model Fg. (b) was n seres wh he vscosy and he elasc elemen can smulae he response of he maeral o he sran bu no he responses o he sress. In 984 Nordell frs proposed a four parameer vscoelasc model [5] furher mprove he analyss accuracy of he model. S. N. Ganerwala [6] used Fourer ransform dynamcs analyss mehod o deermne he dynamc mechancal properes of lnear and nonlnear vscoelasc maeral. Based on he above analyss he Vog model or Mawell models canno descrp he real vscoelasc of conveyor bel. Accordng o he vscoelascy heory he conveyor bel can be smplfed as a more comple vscoelasc model formed from more sprngs and dampers hrough seres or parallel and can be more close o he real mechancal properes of he maeral bu he ncreased number of componens and he compley of model wll cause he compley of he mechancal equaon of conveyor model. In addon he programmng and solvng calculaon was comple he boundary condons are comple and unceran and he applcaon of comple model s lmed whch s no conducve o solvng and calculaon of he conveyor bel model bu also grealy lms applcaon of comple rheologcal model n engneerng pracce. These problems make ha modelng analyss and research of he conveyor Dynamc has been one hospo conen of conveyor echnology and heorecal research. Based on he above problems vscoelasc properes of conveyor wll be smplfed no onedmensonal elasc rod compose dscree elemen model wll be bul based on Vog and Mawell model. The knec equaons of each dscree uns was derved usng knec energy poenal energy of drvng segmen bearng segmen and reurn segmen and equaon of energy dsspaon and LaGrange equaon. Based on Wlson-θ algorhm he knec equaon of DT307-ype ST000's conveyor bel was solved by usng Malab o wre compuer programs. Research on he change rule of conveyor dsplacemen velocy acceleraon and dynamc enson durng he boo process reveals he workng mechansm of nonlnear vscoelasc and conrols dynamc enson peak of conveyor bel n he sae of moon. I wll lay he heorecal foundaon for dynamc performance opmzaon of large bel conveyor and provde relable desgn bass for he desgners. I has ceran heorecal and praccal sgnfcance for desgners o reduce desgn safey facor of rubber bel preven breakng choose a reasonable rollers reduce sysem power consumpon and spare pars and save nvesmen [7 8]. (a) Vog model (b) Mawell model Fg.. Comparson of wo vscoelasc model.. Dscree Modelng of Conveyor Sysem.. Dscree Modelng of Conveyor Sysem Dynamc characerscs of he conveyor bel has obvous vscoelasc characerscs whle was n non-seady condons he speed acceleraon dsplacemen and dynamc enson of each pon n he rubber bel have dynamc feaures namely was he funcon of me. Dynamc characerscs a low speed shor dsance and a small volume of he conveyor bel s no obvous (even under ceran condons can be gnored) can be analyzed drecly usng rgd body dynamcs mehod. For hghspeed long-dsance and large-scale overloaded

3 Sensors & Transducers Vol. 8 Issue 0 Ocober 04 pp. 0-8 mnng conveyor bel hs dynamc characersc wll be a very sgnfcan mpac on he performance and relably of he conveyor sysem and can be analyzed hrough he esablshmen of conveyor dynamcs model. Esablshng Knec model s o buld he approprae vscoelasc model bu rubber bel sysems ncludng rubber bel as well as loadng and unloadng manner of ranspored maerals. The physcal characerscs self (such as elasc modulus and vscosy coeffcen) he physcal properes of maerals (such as specfc gravy angle of repose he dsrbuon coeffcen ec.) and shock of loadng and unloadng poson have an mpac on dynamc characerscs of he conveyor whch canno be accuraely descrbed by he model of he esng conveyor. The ransmsson and supporng rollers and conveyor dlers makes conveyor occurs comple deformaon whch belongs o he caegory of shell deformaon heory. Takng no accoun he engneerng praccal desgn and applcaon he conveyor bel was seen as a onedmensonal vscoelasc rod fully mees he engneerng requremens. Jus as shown n Fg. he conveyor bel n hs sudy wll be consdered as one-dmensonal vscoelasc conveyor rod he coordnae sysem whose orgnal poson was seen as he orgn and he dynamc model was esablshed and we assumed ha he drecon of he conveyor bel enson s posve and conracon drecon s negave. The connuous qualy of endless conveyor bel was dvded no several uns each oher was conneced wh no qualy vscous componen and elasc componen namely uses dscree sysem o appromae he connuous sysem [9]. Meanwhle he conveyor sysem s dvded no ypcal hree uns was he drve roller head un bearng un and reurn segmen un from rgh o lef. Numbered was from he head of he orgnal poson he number agans he ranspor drecon are j j +... n so he oal number of uns was n = + j. Consderng he mpac of ensonng devce and vbraon on he rubber bel he dsplacemen and velocy generaed by enson force and vbraon was dsrbued evenly o boh sdes of he ensonng rollers conveyor bel... Knec Equaon of Conveyor Un Takng bearng secon as solaon he equaons of knec energy T he poenal energy U and energy dsspaon D of he un body can be wren whch s composed an equaon sysem (). ìï T = m + m + m ï íu = k - + k - ïd= c ïî where m ( ) c ( ) () s he -h un mass; k s he sffness c s he dampng coeffcen coeffcen of -h un; of -h un; s he dsplacemen of -h un. Accordng o Lagrange equaon [7] he formula () can be obaned. d T T U D + + = Q () d q q q q where (= ) The correspondng paral dervave was conduced for equaons () and he resul was subsued no equaon () he formula (3) was obaned. m k + k + k k+ c + c + c c = w + (3) where w s he suffered ressance of -h un. Smlarly he equaon of drvng drum head un and reurn segmen un can be wren as formula (4). J m+ knn + ( k+ kn) k R (4) c + c + c c = F + F w n n n d d where F d F d are he drvng forces of he drvng drum respecvely; J s he roaon nera of drvng drum; R s he radus of drvng drum. m k + k + k k j j j j j j j j j+ c + c + c c = w j j j j j+ j (5) Fg.. Conveyor sysem dscree elemen model. Accordng o he above dervaon he dynamc equaon group for each dvded un was bul (6).

4 Sensors & Transducers Vol. 8 Issue 0 Ocober 04 pp. 0-8 J m+ knn + ( k+ kn) k cn n + ( cn + c) c = Fd+ Fd w R m k + ( k + k) k+ c + ( c + c) c + = w m j j kj j + ( kj + kj) j k j j+ cj + ( cj + cj) c j j+ = wj m n n kn n + ( kn + kn) n k n cn n + ( cn + cn) n c n = wn (6) Solvng equaons group (6) was convered no a mar form: [ M]{ X} + [ C]{ X } + [ K]{ X} = { F() } (7) where [ M ] s he mass mar of n uns; [ C ] s he dampng coeffcen of N uns; [ K ] s he sffness X s he acceleraon column vecor; { X } s he speed column vecor; { X } s he dsplacemen column vecor; { F () } s he eernal force column vecor. Meanwhle he dynamc enson equaon of any n un s as follows: coeffcen mar of N uns; { X } { } () = () () + () () F k + c + (8) Solvng equaons group (7) and (8) he dsplacemen he speed he acceleraon and he dynamc enson F () of a un a any me can be obaned. 3. Knec Equaon Algorhm 3.. Boundary Condons and Inal Condons Before solvng he dynamc equaons of conveyor bel he boundary condons and nal work condons also need o be deermned. Takng DT307 ype as an eample uses a hammer-ype ensonng devce. For lj s hammer dsplacemen r r are he dsplacemen of separaon pon chemoas pon of enson roller respecvely S S + are enson of boh sdes of he drum G lj s gravy of hammer g s gravaonal acceleraon hen he boundary condons beween hammer rollers and conveyor can be obaned: () () () () = / lj r r lj = r r / S + S+ = Glj + r() r() / g (9) When When n = () = n() () = () () + = () = n() ;. () + = When he conveyor sarup he nal enson s for = n. F 0 Inal condons: when he conveyor sarup = 0; A he end of brakng = = () = 0 () = 0 where = n. In addon corporae engneer provded reasonable boundary condons for he runnng ressance roller loadng and unloadng and preenson accordng o he conveyor workng condons so ha he conveyor bel was close o he acual workng condons. 3.. Knec Equaon Algorhm Usng sep-by-sep negraon mehod above heorecal dervaon can be calculaed by he program. The man dea of sep-by-sep negraon mehod s o dscree response me hsory n he me doman and dfferenal equaon wll be dscree no equaon for he momen and he speed and acceleraon a any a momen s lnear combnaon wh all he dsplacemen a adjacen me hen moon dfferenal equaon of sysem can be convered o a dscree-me algebrac equaon group conssed of dsplacemen. Sepwse numercal negraon for he dfferenal equaons of coupled sysem can oban any response on he dscree me. Wlson-θ mehod s an mplc negraon mehod wdely used o conduc dscree process and as long as θ s greaer han.37 no maer wha value he sep Δ s he algorhm s uncondonally sable. Durng he sarup and brakng process he equvalen elasc modulus changes wh enson of he conveyor bel so ha runnng ressance has dreconal whch make dynamc equaons of he conveyor bel o be a nonlnear equaon of a varable dampng varable sffness and varable load so s numercal calculaon can be used wh uncondonally sable Wlson-θ mehod. Wlson-θ mehod assumed ha he change of acceleraon s lnearly n [] () whn he [ + θδ ]( θ ) me nerval. 3

5 Sensors & Transducers Vol. 8 Issue 0 Ocober 04 pp. 0-8 If τ s he me varable snce me hen 0 τ θδ he acceleraon can be obaned whn hs range under he assumpon of lnear acceleraon was shown n Formula 0. τ ( + τ + θδ ) (0) θδ {} = {} + {} {} Afer wo negral he formula () and () can be obaned: τ ( + τ + θδ ) () θδ {} = {} + {} τ + {} {} 3 τ 6θΔ {} = {} + {} τ + {} τ + {} {} + τ + θδ () If τ = θδ he nsananeous speed (3) and dsplacemen (4) a + θδ me can be obaned from he above wo equaons. θδ ( +Δ θ +Δ θ ) (3) {} = {} + {} {} θδ 6 {} = {} + θδ {} + {} {} +Δ θ +Δ θ (4) Accordng o he above wo formulas he acceleraon formula (5) and velocy formula (6) a + θδ me can be epressed by dsplacemen means. 6 6 = ( ) {} {} +Δ θ +Δ θ θ Δ θδ (5) {} {} {} 3 θδ {} = ({} {} ) {} {} +Δ θ +Δ θ θδ (6) So he momenum equaon a + θδ me s formula (7): { } = [ ]{ } + [ ]{ } = { F} [ M] C K + θδ + θδ + θδ + θδ (7) where he meanngs of [ M ] [ C ] [ K ] are he F same as n he formula (7) { } + θδ s eernal force column vecor can be epressed usng formula (8). { F} { F} θ { F} { F} = + (8) +Δ θ +Δ Combned he formula (5) (6) (7) and (8) o solve he solvng equaon of { } +Δ θ can be obaned (9). where { } { F} [ Kˆ ] = ˆ (9) + θδ +Δ θ 3 6 Kˆ = K + C M θ + Δ θ Δ (0) { Fˆ } { } θ { } { } +Δ θ 6 6 {} {} {} = F + F F + M +Δ + + θ Δ θδ 3 θδ + C {} + {} + {} θδ () Afer obanng he nsananeous dsplacemen { } +Δ θ a me of + θδ { } can be +Δ θ obaned combnng formula (5). If τ =Δ n formula (0) hen formula () can be obaned combnng formula (9) = 3 ( ) {} + {} +Δ θ +Δ θ θ Δ θ Δ θ () {} {} {} Smlarly τ =Δ combned formula (0) wh formula () and () hen Δ ( + τ + θδ ) (3) {} = {} + {} {} Δ 6 {} = {} +Δ {} + {} {} +Δ θ +Δ θ So one-sep negraon s compleed Compuer Solvng of Knec Equaon (4) Based on heorecal analyss n secon 3. and Wlson-θ gradual negraon mehod provded n he leraure [0] he seps and procedures for solvng knec equaons of dscree elemen model are shown n Table. The compuer program bo of Wlson-θ mehod was showed n Fg. 3 he correspondng compuer program can be wren o calculae he dynamc characerscs of he conveyor bel n knec model a any me whch lay he foundaon for subsequen analyss. 4

6 Sensors & Transducers Vol. 8 Issue 0 Ocober 04 pp. 0-8 Table. Compuer solvng procedures of Wlson-θ gradual negraon mehod. No. Solvng procedures Inal calculaon. Form mass mar [M] dampng mar [C] and sffness mar [K]. Inpu{ 0 } { 0 } { 0 }.3 Selec me sep Δ forθ =.4 Calculae negraon consan: a0 = 6/( θδ ) a = 3/ θδ a = a a3 = θδ / a = a / θ 4 0 a = a / θ 5 a6 = 3/ θ a7 =Δ / a8 =Δ /6.4 Form effecve sffness mar ˆK.5 Pu ˆK : Kˆ a M a C = + + [ K] 0 as a rangle decomposon: Kˆ = [ L][ D][ L] T Calculae for ncremen of each me Calculae payload a+ θδ :. { Fˆ } = { F} + θ { F} { F} + [ M]( a + a + θ Δ {} +Δ θ + ) + C ( a{} + {} + a3{} ) { } { 0 }. Calculae dsplacemen a θ.3 = { Fˆ} +Δ θ +Δ θ + θδ me = a + a + a + Δ : Kˆ { } Calculae acceleraon velocy and dsplacemen a { } { } { } 4 { } { } + θδ + θδ 5 6 { } = { } + a ( 7 { } + { } ) +Δ θ +Δ θ { } = { } +Δ { } + a { } + { } 8 ( ) +Δ θ +Δ θ Fg. 3. Compuer program bo of Wlson-θ mehod. 4. Analyss of Compung Resul Takng flame-reardan seel cord conveyor bel ST000 of DT307-ype conveyor bel desgned and produced by Nnga Tand Norhwes Coal Machnery Co. Ld as an eample dynamc enson dsplacemen velocy and acceleraon curves of conveyor bel was calculaed a any me usng Wlson-θ program shown n Fg. 3. Load sarup process of large mnng conveyor bel s a very unsable condon he enson force of conveyor bel wll reach a mamum n he sarup process he nensve dynamc research on sarup process s very mporan. The curve n Fg. 4 s he enson force of he dfferen poson durng he boo process. A he frs 5 s enson force of each poson has dramac flucuaons and he flucuaon range of he drve un s greaer han he bearng un reurn un has a small flucuaon range and mnmum enson force. In nsan sarup he dynamc enson of drve un can be up o KN afer 50 s he enson ends o drve 5

7 Sensors & Transducers Vol. 8 Issue 0 Ocober 04 pp. 0-8 around KN n a sable sae. The reason for enson of drve un rsng faser s manly due o unreasonable sar-up mode a shorer sar-up me and oher facors caused a greaer enson peaks. Seng a suffcenly long me selecng conrollable way o sar opmzng sarup curve and ncreasng he pre-sar delay can reduce he acceleraon peak smooh acceleraon changes o effecvely reduce sarer enson of he conveyor and ncrease runnng smooh of he bel. The speed of conveyor n he 0 s rse rapdly hen gradually approach o desgn speed 5 m/s and connue o flucuae n he vcny hen reached he desgn speed afer 60 s. From he velocy curve Fg. 5 he speed change beween drve un he bearng un and reurn un has a me lag whch showed ha he sress wave gradually ransfer from he drve un o reurn un and he change s nonlnear. flucuaon ends o zero and hen he enson of he bel wll reach a sable value. In he acual desgn and use should be possble o ensure ha he sarng process acceleraon curve s genly and whou muaon he peak of acceleraon s small n order o mee projec needs. The dsplacemen curve of dfferen un conveyor s showed n Fg. 7. Fg. 6. The acceleraon curve. Fg. 4. Tenson curve of conveyor bel. Fg. 7. The dsplacemen curve. Fg. 5. Speed of conveyor bel. Whn he 0 s afer sarng he acceleraon change of conveyor s more severe Fg. 6 bu wh he ncrease of sar me he acceleraon peak decreases when was abou 50 s he acceleraon In large capacy hgh effcency long dsance conveyor desgn and selecon he majory of domesc manufacurers use rgd heorecal o analyss conveyor bel develop compuaonal mehods and desgn specfcaons. On hs bass he manufacurers always mulples approprae facor o mee he engneerng requremens on he seleced safey facor (usually abou 0-5) accordng on her own desgn eperence. Ths safey facor based on a sac desgn s generally hgher and he choce of conservave because he drven enson of conveyor bel canno accuraely analyzed and calculaed durng sarup and brakng process. The above dynamc analyss shows ha he speed acceleraon or dynamc enson have he mos dramac flucuaons n he former 0 s and has he greaes mpac on 6

8 Sensors & Transducers Vol. 8 Issue 0 Ocober 04 pp. 0-8 he enre conveyor bel conveyor. Usng a conrolled sof-sar echnology and power equalzaon can effecvely reduce moor sarng power and enson and reduce flucuaon caused by he speed and acceleraon. Applcaon of he above resuls npung he mamum dynamc enson and desgn power parameers Fg. 8 he resul can be calculaed by he bel conveyor desgn calculaon sofware programmed by Nnga Tand Norhwes Coal Machnery Co. Ld. Fg. 8(a). A varey of logc was ncorporaed no he sofware no only can adap o a varey of dfferen ypes of ppe conveyor and can auomacally deermne he arrangemen of he bel conveyor such as V ype an-v ype N ype and W ype whch has some nellgence. The calculaon can be compleed n a shor me bass s relably has been esed hrough a lo of engneerng applcaon and was acceped by he user. In addon he sofware has he characersc of user-frendly and smple operaon and npung he nal desgn parameers can complee desgn checkng and oher compung asks. Accordng o he resuls he drawngs 3 D modelng vrual assembly and smulaon nerference checkng proofreadng and oher desgn work can be o compleed by he desgner Fg. 8(b) whch grealy save desgn me of bel conveyor. Meanwhle can carry on he relably opmzaon desgn for he key componens of he conveyor such as he rack russ rollers ec. qualy opmzaon desgn and vbraon modal sress and sran analyss Fg. 8(c). If mees he desgn goals you can follow he approprae procedures o produce componen manufacurng and oher work. Nnga Tand Norhwes Coal Machnery Co. Ld. opmzed he desgn of DT307-ype bel conveyor and adjused he dynamc conrol sraegy he nal desgn safey facor decreased from o 7 and he cos of manufacurng machne reduced 5 %. Meanwhle mproves dynamc conrol precson of he conrol sysem and he enson reduced by abou % whch make a consderable prof for manufacurng enerprses. Fg. 8. Opmzed desgn skech of bel conveyor. 5. Conclusons Applcaon of drven vscous properes of conveyor bel he dscree dynamc model and he correspondng dynamcal equaons of conveyor sysem was bul. Then a compuer negrang program was wren n Wlson-θ mehod and was used o solve he knec of equaon mne conveyor and s dynamc analyss was carred ou. Takng flame-reardan seel cord conveyor bel ST000 an eample look for solvng dynamcs o verfy he relably of heory he resul showed objecvely refleced he acual work of conveyor bel. The conveyor sysem was dscree no a number of uns and dynamc analyss s carred on a he dfferen me domans and he neracon mechansm of each un n he movemen and force he process was ndeph suded. The resuls show ha he sarup speed acceleraon had a bg nfluence on dynamc enson of he rubber bel and were closely relaed wh me and sze ha he enson peaks appeared. The above fndngs provded he correspondng heorecal bass for he relevan people o desgn and opmze bel conveyor sysem. Under he condons of meeng he acual needs of he projec ransporaon desgn enson s reduced by appromaely % han before manufacurng cos of he DT307-ype conveyor machne saved abou 5 % whch brng consderable profs for enerprses. Acknowledgemens Ths work was suppored by Key laboraory of chemcal echnology of The Sae Ehnc Affars Commsson (0SY0). Meanwhle we hank boundary condons and he performance parameers of conveyer bel provded by Nnga Tand Norhwes Coal Machnery Co. Ld. 7

9 Sensors & Transducers Vol. 8 Issue 0 Ocober 04 pp. 0-8 References []. Zhang Shrong Xa Xaohua Modelng and energy effcency opmzaon of bel conveyors Appled Energy Vol. 88 Issue 9 0 pp []. A. Harrson Bel conveyor research Bulk Solds Handlng Vol. Issue 00 pp [3]. Zhang Zunjng Wang Su Type DT II(A) bel conveyor drawngs manual for desgnng Meallurgcal Indusry Press Bejng 000. [4]. Zhang Yong Theory hermo-vscoelascy Tanjn Unversy Press Tanjn 00. [5]. L. K. Nordell Z. P. Cozda Trsen bel sresses durng sarng and soppng: elasc response smulaon n long conveyor bels Bulk Solds Handlng Vol. 4 Issue 984 pp [6]. S. N. Ganerwala Fourer ransform mechancal analyss for deermnng he nonlnear vscoelasc properes of polymers Polymer Engneerng and Scence Vol. 7 Issue 987 pp [7]. G. Fedorko V. Molnár J. Žvčák M. Dovca N. Husáková Falure analyss of ele rubber conveyor bel damaged by dynamc wear Engneerng Falure Analyss Vol. 8 Issue 3 03 pp [8]. Zhang Weje Zhao Xjng e al Dynamc model analyss of conveyer bel Coal Mne Machnery Vol. 9 Issue pp [9]. Pao Lanang Research on he key desgn echnologes of long-dsance bel conveyor wh horzonal curves Ph.D. Thess Jln Unversy Jln 00. [0]. K. J. Bahe E. L. Wlson Numercal Mehods n Fne Elemen Analyss Prence Hall Copyrgh Inernaonal Frequency Sensor Assocaon (IFSA) Publshng S. L. All rghs reserved. (hp:// 8