Sonoco Tube Testing

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    E N G I N E E R I N G P A P E R T U B E S T O I M P R O V E W I N D I N G P E R F O R M A N C E

    O F V A R I O U S M A T E R I A L S

    T e rr y G e r h ar d t, S e n i or Re se ar c h Fe l l ow, S on oc o Pr od u c ts Com p an y , M ad i son , W I

    Yan p i n g Q i u , S e n i or Pr o fe s s i on a l S c i e n t i s t , S on oc o Pr od u c ts Com p an y , M ad i son , WI

    Ch u c k Joh n son , Re se ar c h Assoc i a te , S on oc o Pr od u c ts Com p an y , M ad i son , W I

    Dav i d Rh od e s , T e c h n i c a l M an age r , S on oc o Pr od u c ts Com p an y , H ar tsv i l l e , S C

    A B S T R A C T

    O ve r th e p as t 10 ye ar s , S on oc o h as c on d u c te d fu n d am e n ta l , so l i d m e c h an i c s r e se ar c h

    c on c e r n i n g s tr uc tu r al b e h av i o r o f sp i r a l ly wou n d p ap e r tu b e s. T h e s c op e o f thi s p r ogr am h as

    inc luded exper imental , numer ical , and analyt ical mechanics approaches as documented in re ferences

    1 -7 ) . For r e c e n t n on - l in e ar f in i t e el e m e n t r e se ar ch , we h a ve u se d AB A Q U S an d d e ve l op e d u se r -

    def ined mater ia l subroutines . Th ese subroutines feature a propr ietary 3D const i tut ive mod e l for

    paperboard. Th e m ode l uses non -l inear stress-s train propert ies of So no co paperboard mea sured in 3

    pr inc ip le d irec t ions . A n im po r t a n t r e sea r ch ob je c t i ve i s t o deve l op i n n ova t i ve tube des i g n s tha t

    e n a b l e ou r c u s tome r s t o imp r o v e th e i r w i n d i n g o p er a t i o n s

    T o ac h i e ve th i s ob je c t i ve , we h ave

    d e ve l op e d se ve r a l p a te n te d te s t d e v i c e s th a t m e asu r e tu b e p r op e r t i e s fu n d am e n ta l to wi n d i n g

    appl icat ions . Tests to measure core radial s t i f fness on the ins ide and outs ide E c ) with respect to an

    external pressure and radial s trength have been deve loped. This paper descr ibes the tes t methods and

    p r e se n ts d a ta to ve r i fy m e c h an i c s r e se ar c h f in d i n gs b y wa y o f two c or e ap p l ic a t ion s . T h e se ar e

    e xam p l e s o f wh e r e c or e s we r e e n g i n e e r e d u s i n g m e c h an i c s t e c h n o l ogy to i m p r ove wi n d i n g

    c ap ab il ity : 1 ) d e ve l op m e n t o f an ex tr e m e l y h i gh E ~ c or e for wi n d i n g l ow fr ic t ion , c oa te d a l u m i n u m ,

    an d 2 ) c or e s for wi n d i n g te x t i l e yam s an d p o l ye th y l e n e s tr e tc h f il m b ase d on r ad ia l s t if fn e s s o f

    ins ide d iameter .

    N T R O D U C T I O N

    Son oco p roduces paper tubes for industr ia l pack aging us in g a sp iral w indin g process f igure 1) .

    Because paper i s an anisotropic mater ia l , the sp iral winding process y ie lds a general ly anisotropic

    structure . To com pl icate m atters , paper tubes are frequently loaded into the non-l inear s tress-s train

    region dur ing use . Over the past 10 years , we have deve loped several exper imental , numer ical , and

    an a l y ti c a l too l s to a i d e i n th e d e s i gn o f tu b e s to m e e t a wi d e var i e ty o f c u s tom e r r e q u i re m e n ts .

    E xp e r i m e n ta l m e c h a n i c s wor k a t S on oc o h as two c on c e n tra t i on s. T h e f ir st is to ge n e ra te

    m ate r ia l b e h av i or d a ta to c om p l i m e n t th e d e ve l op m e n t o f c on s t itu t i ve m od e l s . T h e s e c on d i s to

    m im ic loading con di t ions tubes are subjec ted to in the fie ld . The overal l goal i s to dev e lop a

    capabi l i ty to des ign tubes to meet spec i f ic requirements and to tes t for compl iance wi th those

    requirements .

    A n u m e r i ca l m e c h an i c s c ap ab i li ty h as b e e n d e v e l op e d for s itu a t ion s w h e r e t e s t in g an d an a l y t ic a l

    m o d e l s c an n ot p rov i d e a r eason ab l e f r am e wor k for p r od u c t d e s ign or u n d er s tan d i n g . Pr ob l e m s w i th

    c om p l e x b u c k l i n g an d c on tac t h ave b e e n su c c e s s fu l l y so l ve d . Pr opr ie tar y c on s t i tu t i ve m od e l s h ave

    b e e n i n c or p orate d in to A B A Q U S to an a l yze th e se p r ob l e m s .

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    Severa l ana ly t i ca l mo del s have been deve loped over the year s . Both l inear and non- l inear

    mod el s have been produced , inc lud ing a genera l 3D non- l inear paper model . W i th these model s and

    ABAQUS, many product conf igura t ions and load ing have been succes s fu l ly modeled .

    The ba lance o f th i s paper w i l l d is cus s the app l i ca t ion o f these t echnolog ies and capab i l it i es

    th rough two des ign cases .

    C O R E S F O R W I N D I N G C O A T E D A L U M I N U M P R O D U C T S

    Many researcher s have computed in te rna l s t r es ses in web mater i a l s wound around paper o r

    meta l cores. For exam ple Pfe i f f e r (8 ), Yagod a (9 ), Hakie l (10), and Wi l l e t t and Poesch (11) have

    cons idered ro ll s cons t ruc ted by cen te r wind ing . These a re typ ica l ly non l inear , one-d imen s iona l

    fo rmula t ions in the rad ia l d i r ec t ion o f the ro l l. Roi sum (12) p resen t s an ex ce l l en t r ev iew.

    In the pub l i shed wind ing m odel s , core o u t s ide d iam eter s t i ffnes s (E~) i s in t roduced th rough a

    boundary condi t ion . Gerhard t and Qiu (4 ) pub l i shed Ee fo r paper tubes . Data i s f rom measurements

    wi th s t r a in gauges on th ree- inch d iameter tubes . Analy t i ca l , numer ica l , and exper imenta l r esu l t s in

    th i sp ape r show tha t core s t i f fnes s va lues pub l i shed in the l i t e r atu re were incor rec t .

    Bern ie Bec ker o f AL CO A presen ted a pape r a t the four th 1WEB (13) descr ib ing h i s e f fo r ts to

    so lve wind ing prob lems as soc ia ted wi th two f a i lu re mode s , V-bu ck le and s ag co l l apse (13).

    F igures 2a and 2b i l lus tr a t e these f a i lu re modes . Becker , us ing W IN D ER l , es t ab l i shed an

    excep t iona l ly h igh Ec per formance r equ i r ement needed to so lve th i s p rob lem. F igures 3 and 4 show

    the e f f ec t o f increas ing tube E~ on r ad ia l and t angen t ia l s t res s in the woun d on a luminum . As Be cker

    i l lus t rates in f igure 9 (13) , theoret ical ly , the higher tube s t i f fness widens the process window for web

    tens ion control .

    For thi s wind ing app l i ca t ion , we deve loped and m anufac tured an ex t r em ely s t i f f paper tube to

    the des i r ed E l eve l. Tube des ign was accom pl i shed us ing a p ropr ie t a ry mul t i -g rade l inear -e last i c

    equa t ion to es t imate tube deformat ions und er ex te rna l p res sure . W i th th is model , Ec va lues o f

    var ious cons t ruc tions can be ca lcu la ted . Requi red inpu t s to the model inc lude e l as t i c mod ulus va lues

    for the pap er g rades und er co ns idera tion , Qiu , e t a l . (7 ) . Becker descr ibes the r esu l ts o f us ing the new

    core in (13).

    Large d iameter tubes , 406 .4 mm (16 inch) , a r e used fo r wind ing in the me ta l s indus try . An

    issue is that these are too large to tes t us ing our patente d radial crush tes ters (14) . Thus to ver i fy this

    des ign methodology , we deve lope d a t es t dev ice to d i r ec tly measure Ec .

    E ~ T e s t D e v i c e

    The l a rge- sca le t es t dev ice i s p ic tu red in F igure 5 . A tube i s in i t ia l ly mo unted as shown. The

    ent i re sect ion then s l ides into an extremely large pressure vessel . Dur ing the tes t , a i r pressure is

    increased in increment s to about 125 ps i . Dur ing pres sur i za t ion , the two arms shown ro ta te and

    sensor s mo unted on the ends measure ou t s ide d iameter deformat ion . Av erage ou t s ide d iam eter i s

    me asured a t s evera l d i f fe ren t p res sure l eve l s .

    1WIN DER V4.2, A proprietary winding analysis software package developed by the Web Handling Research Center,

    Oklahom a State University.

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    T yp ic a l d a t a c o l l e c t e d i s sh o w n in F igu r e 6 . B y d e f in i t i on ( 12 ) , t h e s lop e o f t h is l in e

    m u l t ip l i e d b y t u b e ou t s id e d iam e t e r i s t h e E ~ va lu e . N o t e t h e l i n e a r i t y o f h e p r e ss u r e - OD c h a n g e

    response. For t h i s t e s t an d t h e ID s t i f f n e s s t e s t t h a t f o l l ow s , w e an a lyz e ave r age d iam e t e r c h an ge s .

    D at a f r om b o t h te s t s sh ow a lin e ar r e sp on s e a t l ow p r e s su r e s .

    For O D p r e s su r e l oad in g o f t u b e s , th e f ir s t b u c k l in g m od e i s an ova l sh ap e . A s d i sc u s se d in

    t h e c