Investigation of Flexible Multi-Mode Harmonic Vibration for the Automatic Washing Process

Transcription

1 Inesigaion of Flexible Muli-Mode Hamonic Vibaion fo he Auomaic Washing Pocess JIAN-LONG KUO a, TSUNG-YU WANG b, a Depamen of Mechanical and Auomaion Engineeing, Naional Kaohsiung Fis Uniesiy of Science Technology, Nan-Tze, Kaohsiung 811, TAIWAN b Dep of Elecical Engineeing, Chang-Gung Uniesiy, Kwei-Shan, Tao-Yuan 333, TAIWAN JLKUO@CCMSNKFUSTEDUTW Absac: - This pape will discuss muli-mode ibaion fo he ibaion moo in he washing pocess Sinusoidal ibaion modes fo he speed seo command will be caefully designed fo he flexible conol Diffeen kinds of opeaing modes fo he possible auomaic pocess conol ae poided Thee basic and fie exended ibaion modes fo diffeen opeaion ae poposed Simulaion and expeimenal esuls will be compaed o eify he fomulaion This will make he washing pocess moe flexible, in ode o easily configue he seo conol Diffeing fom he conenional appoach o egulae he blade angle fo he ibaion moo mechanically, he muli-mode ibaion deeloped by he sofwae appoach is successfully poposed I is easy fo he washing pocess o be egulaed elecically insead of mechanical opeaing only I is belieed ha his pape will be beneficial o he auomaic washing pocess applicaion fo he washing machine Key-Wods: - Muli-mode, hamonic ibaion, Washing Pocess, Vibaion moo, Auomaion, Mechaonics 1 Inoducion Recenly, he ibaion moo has been playing an impoan ole in consume eleconic poducs o poide he equied ibaion Thee ae many eseach papes discussing he mechanical aspecs fo he ibaion moo Wu descibed how o educe acousic noise and ibaion in he swiched elucance moo die [1] By uilizing he pope daa collecion and analysis echniques [], he ue souce of he ibaion could be discoeed Seeal mehods [3] fo educing acousic noise emission wee sudied The emied noise is paiculaly song when he fequency of defomaion coincides wih ha of he naual mechanical esonance of he sao The elaionship beween hamonic cuens and mechanical ibaions in DC acion moos was delineaed in [4] I concludes ha he mechanical esonance of a moo a a ceain locomoie speed is a majo cause fo he excessie bush and commuao wea A digial signal pocesso (DSP) cad [5] was used o capue olage and cuen signal waefoms and o pecisely monio oo angula posiions fom a 1- bi absolue encode The ibaion moo can poide he equied ibaion opeaions, such as: sifing, mixing, fileing, coneying, and cenifugal Howee, he conenional appoach [6, 7] is always egulaed o poduce he cenifugal foce by manually adjusing he angle of he blade on he oo side Also, he scew has o be fimly ighened o peen he hazadous ejecion of he ibaing blades Fuhemoe, he conenional appoach canno also be implemened in on-line seo conol, when he ibaion needs o be immediaely changed following he command Theefoe, he conenional consan ibaion mode can no adequaely poide a moe flexible ibaion pocess I may no be suiable fo he auomaic pocess conol Noewohy, many paens wee poposed fo he cenifugal washing pocess [8-14] in he washing pocess applicaion, o poide a moe flexible washing pocess Howee, he conenional mechanical appoach is used o implemen he washing pocess Theefoe, he on-line ibaion conol can no be achieed when he cenifugal foce is ceaed by mechanical foce In his pape, he flexible ibaion pocess needs o be poided o mach diffeen washing equiemens ISSN: Issue, Volume 5, Febuay 8

2 Muli-Mode Vibaion and Cenifugal Foce Model Deiaion 1 Thee Basic Vibaion Modes Fo he washing pocess applicaion, he cenifugal foce ofen can be mechanically egulaed by seing he spanned angle of he eccenic oo The oo has o be econfigued manually Bu his migh cause difficuly in implemening he auomaic conol, especially in ems of eal ime conol This pape poposes an elecical egulaion o subsiue fo he conenional appoach Thee basic modes will be poposed o poide he equied flexible conol fo he washing pocess The washing pocess can opeae wih he help of a seo moo Thee basic ibaion modes ae poposed fo diffeen applicaions They ae: song, sof, and weak, ibaion modes as classified in Table 1 The epesenaion is depiced in Fig 1 The muli-mode ibaion can be deied fom he following basic expession: o F = ω ω, F ω = (1) ' If he M and R ae known, he squae of he speed command ω is jus like he cenifugal foce F Tha means ha squae of ω The he eccenic mass: M F is popoional o he ' R is defined as he adius of Fig 1 Poposed hee basic modes fo he flexible muli-mode hamonic ibaion pocess The cenifugal foce can be classified ino hee ypes, as in Fig 1 The elecical command can be sub-diided ino wo componens: he DC componen and AC componen The CSM and DSM modes ae defined in his pape If he speed command euns o zeo, his is called DSM, which has posiie and negaie command, alenaely If he speed command does no eun o zeo, his is called CSM, which has posiie command only If he speed command is opeaed unde full speed, hen he song ibaion mode is defined If he speed command is opeaed unde only half of he full speed, hen he sof ibaion mode is defined Song ibaion mode: This mode includes he DC componen only Also, he speed does no eun o zeo, which is called he coninuous speed mode (CSM) Sof ibaion mode: This mode includes boh of he DC and AC componens The AC sinusoidal componen could mach he naual fequency o poide he equied auxiliay cenifugal foce This mode is also called CSM mode Weak ibaion mode: This mode has only he AC componen This AC componen has he sinusoidal ibaion fequency Since he speed command will eun o zeo, hee will be zeo-cossing phenomena in such case This is called disconinuous speed mode (DSM) Thee modes can be on-line econfiguable by seing he paamees fo he conol sofwae Cenifugal Foce Analysis and Command Pogamming Muli-mode ibaion can be achieed by popely ω pogamming he speed command fo he pocess conol The genealized speed command can be defined as he specific em: ω = k1 + k sinω, () ISSN: Issue, Volume 5, Febuay 8

3 whee k1 is he DC bias command, and k is he sinusoidal command ω is he mino ibaion angula fequency The k1 dominaes he sengh of he cenifugal foce, he k is elaed o he mino ibaion mode The k can help he ibaion moo o einfoce he enie cenifugal foce by means of combining he majo and mino modes ogehe; heefoe, he moion would become mulimode ibaion If he speed command has he consan funcion, he cenifugal foce also emains consan ω F = k1 = k 1 (3) If he speed command has he sinusoidal funcion as follows: ω = k sinω F = ( k )(1 cosω)/ (4) The aboe expession shows ha he fequency of he cenifugal foce is double he fequency of he speed command Based on he aboe fomulaion, simple eificaion will be done by compaing he simulaed and expeimenal esuls in he nex secion 3 Definiions of Fequency Componens fo Muli-Mode Hamonic Vibaion By adjusing he adequae paamees: k 1, k and ω, he cenifugal foce no only keeps he oiginal mechanical ibaion popey, bu also poides he elecical ibaion popey due o k paamee As shown in Fig, he mechanical and elecical ibaion popeies ae specified in he following Caie fequency: The caie fequency ω implies ha he cenifugal foce opeaes unde he mechanical spindle fequency [15] The caie fequency and is magniude can be conolled by he DC bias command k 1, ie, he caie fequency is conolled o coincide wih he command k 1 Band 1 fo mino ibaion fequency: Band 1 is double he mino ibaion fequency ω, which can be conolled by jus only he sinusoidal command k Band fo mino ibaion fequency: By adjusing he condiions of k 1, k and ω, band will be eealed on he fequency domain, as shown in Fig 3 The command: k 1, k and ω can poduce a moe flexible cenifugal foce To poduce he obious Band effec, he mino ibaion angula fequency ω should be much smalle han he caie fequency ω 4 Vibaion Foce Analysis As shown in Fig 3(a), he washing ank is coupled wih he shaf of he seo moo Theefoe, he washing ank can be oaed wih he seo moo Assume ha he wae filled ino he washing ank has a consan mass The washing ank wih he wae will hae an ouwad cenifugal foce along he angenial diecion of he oue cicumfeence of he washing ank The cenifugal foce can be descibed by (1) In geneal, as shown in Fig 3(b), he foce is heoeically composed of x- and y- diecional foces [15] The cenifugal foce in he x-diecion is as follows, and he same expession can also be wien fo he y-diecion ) x sinθ sinω sin πf, and ) y cosθ cosω cosπf (5) Fig Fequency definiions fo he poposed muli-mode hamonic ibaion Fig 3 (a) he washing ank wih he wae and (b) he x- and y- diecional cenifugal foces ISSN: Issue, Volume 5, Febuay 8

4 The ω and f ae he ibaion angula and ibaion fequencies, especiely, whee ω is The synchonous wih he caie fequency ω cenifugal foce usually poides he moie foce in he washing pocess A oo song cenifugal foce migh damage he washed maeial in he washing pocess Fo he flexible ibaion seo conol, he cenifugal foce wih he genealized speed command can be defined as follows = ω = ( k1 + k sinω) (6) F Thee cases ae classified and discussed: Case 1: k 1, k F = ω = [(1/ ) k + MRk ' 1 ] + [ MRkk ' 1 ]sinω [(1/ ) MR ' k ]cos ω (7) I is a genealized case fo he ibaion Case : k 1, k = F = ω = ( k ) (8) 1 If he speed command is consan, hen he cenifugal foce is also consan Case 3: k 1 =, k F = ω = ( 1/ ) k (9) ( 1/ ) k cosω If he speed command is sinusoidal, hen he fequency of he cenifugal foce is double ha of he speed Meanwhile, o keep he ibaion smooh, i is suggesed ha he ω is he muliple of he ω, wih he elaion ω << ω Case is he consan case, which is he commonly-used case fo he ibaion moo in he washing pocess The following elaion can be deied: ) x sinθ sinω = ( k1 )sinω ( F ) = F cosθ y (1) cosω = ( k )cosω 1 Fo Case 3, a much moe complicaed elaion will be deied I is he sinusoidal speed command: ( F ) = F sinθ x = F sinω = ( 1/ ) k sinω ( 1/ ) k cosω sinω ) y cosθ cosω (11) = ( 1/ ) k cosω ( 1/ ) k cosω cosω I can be found ha hee ae poduc ems of he sinusoidal funcion Thee ae fequency componens: ω, ω + ω, ω ω in he sysem Fo Case 1, he deiaion can also be he same as in Case 3 I is a mixed mode fo Cases and 3: ) x sinθ sinω = [( 1/ ) k + MRk1 ]sinω + [ k1k]sinωsinω [( 1/ ) k ]cosω sinωsinω ) y cosθ cosω (1) = [( 1/ ) k + MRk1 ]cosω + [ k1k]sinω cosω [( 1/ ) k ]cosω sinω cosω I can be found ha hee ae poduc ems of he sinusoidal funcion Thee ae: ω, ω +ω, ω ω ω + ω and ω ω fequency componens in he sysem The fequency componens can be found unde his fomulaion, 5 Fie Exended Vibaion Modes fo he Washing Machine The aboe deiaion shows ha he cenifugal foce can be popely modeled unde he poposed fomulaion Moe fequency componens can be found I means ha he sinusoidal sof ibaion is smoohe han conenional shap ibaion In his pape, fie modes ae defined o poide he aious ibaion modes fo he diffeen auomaic applicaions as lised in Table ISSN: Issue, Volume 5, Febuay 8

5 Mode 1: Case wih highe k 1 and wihou k : Shap song ibaion, CSM mode Mode : Case wih lowe k 1 and wihou k : Shap sof ibaion, CSM mode Mode 3: Case 3 wihou k 1 : Weak ibaion, DSM mode Mode 4: Case 1 wih highe k 1 and wih k : Smooh song ibaion, CSM mode Mode 5: Case 1 wih lowe k 1 and wih k : Smooh sof ibaion, CSM mode Fie modes can be auomaically econfigued hough he elecical command in he auomaic conol sofwae insead of he conenional mechanical appoach 6 Applicaions fo Fie Exended Vibaion Modes A he pe-washing sage, he deegen should be unifomly sied ino he wae, so ha he washed maeial can be adequaely mixed wih he deegen A he washing sage, he flexible ibaion pocess will be poided fo diffeen wash maeials such as geneal and woolen clohes A he cenifugal dehydaion sage, he flexible ibaion pocess needs o be poided in ode o effeciely conol he ibaion The poposed mehod can poide a moe flexible washing pocess o fuhe incease he cleaning effec In his pape, an elecical appoach is suggesed fo a moe flexible ibaion pocess a each washing sage No blade is equied on he oo side Wih he elecical appoach, a moe flexible auomaic opeaion can be obained Again, some pecise washing pocesses equie he sof ibaion o aoid seee collision fo he clohes The sinusoidal sof ibaion can poide a moe igoous ibaion unde closed-loop seo conol A moe flexible ibaion pocess can be ealized o mee he equiemen of cusome-oiened design The oeall inesigaion in his pape is shown in Fig 4 An expeimenal pocedue simila o he one used in his pape had been poposed by Maienga [15] I poides he ime domain and fequency domain measuemens fo he pocess cuing foce in he x-, y- and z-diecions In his pape, he cenifugal foce, which is composed of wodimensional componens, can be discussed by conolling he sinusoidal speed command In ode o conenienly inesigae he ibaion mode sudy in his pape, a small size seo moo is used o analyze he equied ibaion pocess The Fig 4 Vibaion mode sudy fo he washing pocess associaed esuls can be fuhe applied o pacical washing pocess 3 Simulaion and Expeimenal Resuls The conenional cenifugal foce can be conolled by he eccenic mass, eccenic adius and oaing angula fequency By he conenional appoach, he pope eccenic mass and eccenic adius can be egulaed o poduce he adjusable cenifugal foce Howee, he conenional appoach canno be used while he moo is unning Fo a moe flexible opeaion, he elecical appoach can be used o achiee on-line egulaion by using pogammable angula fequency command The expeimenal seup is shown in Fig 5 The conol paamees of k 1, k and ω can be specified by he conolle The I/O conol cad will poduce he diing signal coesponding o he aboemenioned paamees o he inee die, in ode o fuhe acuae he seo moo Theefoe, he muli-mode hamonic ibaion pocess can heefoe be achieed When he washing ank is oaing, as shown in Fig 3 and Fig 5, he cenifugal foce will make he washing maeial moe ouwad along he angenial diecion of he washing ank In his pape, a foce gauge mee will be employed o measue he cenifugal foce The esing poins P and P1 indicaed he foces in x- and y-diecion will be fuhe measued ISSN: Issue, Volume 5, Febuay 8

6 Fig 5 Expeimenal seup Two 16-bi foce gauge mees ae used o measue he cenifugal foces (x- and y-diecion ensile foces) In his expeimenal seup, he cenifugal foces in x- and y-diecion will be measued a he same ime In his expeimenaion, he eccenic mass oaes on he oo side The muli-mode ibaion can be poduced by he pogammable conol paamees The conol paamees, including: k 1, k and ω will be caefully assigned o poduce he equied ibaion Theeby he poduced cenifugal foce can be moe flexible To clealy eeal he muli-mode ibaion effec, he expeimenal esuls will focus on hee main aspecs: measuemen in fequency domain, measuemen in ime domain, and foce ajecoy which is also poided fo associaed discussion The cenifugal foce is measued in SI unis 31 Measuemen in Fequency Domain The fequency domain analysis can eeal he specum disibuion fo he ibaion moion By pogamming he diffeen condiions fo he k 1, k and ω, he fequency domain analysis will show he specum disibuion fo diffeen ibaion modes 311 Mode 1 and Mode The fequency and magniude plo fo mode 1 is illusaed in Fig 6 These esuls exhibi he elaions of (6) and (1) The commanded caie fequency ω is equal o k 1 I shows he conenional mechanical ibaion fo mode 1 I can be concluded ha he main cenifugal foce will appea a he caie fequency because of he DC bias command k 1 ω If he ibaion moo has wo poles, he conesion elaion beween he oaing speed and he angula fequency can be expessed as: ω mode 1 o N mode 1 o =, (13) π 6 is he commanded caie whee ω mode 1, o fequency ω of mode 1 o mode N is he measued oaing speed wih he uni pm fo mode 1 o mode Fom he specum analysis in Fig 6, he main magniude can be found a aound 5Hz I is almos equal o he commanded caie fequency 56 Hz fo mode 1 The measued oaing speed is 336 pm Similaly, he caie fequency fo mode can also be eealed a he 3841 Hz unde he condiion of 35 pm, as shown in Fig 7 The x-and y-diecional cenifugal foces of mode 1 and mode can be expessed in he following foms: ) x mode1 ( k1) sinω mode1 = (14) ) x mode ( k1) sinω mode and ) y mode1 ( k1) cosω mode1 = (15) ) y mode ( k1) cosω mode Fom (14), he magniude fo mode 1 is almos double he magniude fo mode Fo example, efeing o Fig 6(b) and 7(b), he magniude aound 5Hz fo mode 1 is abou 9N, and he magniude aound 38Hz fo mode is abou 45N Similaly, Fom (15), and efeing o Fig 6(a) and 7(a), he magniude aound 5Hz fo mode 1 is almos 15 imes he magniude of aound 38Hz fo mode Fig 6 Magniude esus fequency fo mode 1, (a) he expeimenal esul of x-diecional cenifugal foce (F ), and (b) he expeimenal esul of y-diecional cenifugal foce (F ) x y Fig 7 Magniude esus fequency fo mode, (a) he expeimenal esul of x-diecional cenifugal foce (F ), and (b) he expeimenal esul of y-diecional cenifugal foce (F ) y x ISSN: Issue, Volume 5, Febuay 8

7 31 Mode 3 Fo mode 3, he magniude plo is measued in fequency domain, as shown in Fig 8 The specum shows no only he mechanical fequencies such as naual fequency [3], bu also elecical fequencies such as caie fequency and mino ibaion fequency, will also be shown Mode 3 is defined as he ibaion moion wihou k1 and wih appopiae sinusoidal command k Fom (6), (9) and (11), we obain ha he commanded caie fequency ω equals k sin ω Fo he specum, he caie fequency ω and he mino ibaion fequency ω ae specified as 3Hz and 8Hz, especiely Fig 8 shows he esuls of (11) By igonomeic ideniies, i can be concluded ha he fequency componens will be locaed a: ω, ω + ω, and ω ω Thei fequency componens include Band in fequency domain as shown in Fig 3 The mechanical fequency componen ω also occus because he sinusoidal signal k poduces he alenae cenifugal foce [3] 313 Mode 4 and Mode 5 Modes 4 and 5 eeal moe complicaed opeaion han modes 1, and 3 Fom (6), (7) and (1), we obain ha he commanded caie fequencyω equals k1+ ksinω Fo he specum in Fig 9, he caie fequency ω and he mino ibaion fequency ω ae specified as 48Hz and 1Hz, especiely In addiion, he caie fequency ω and he mino ibaion fequency ω ae specified as 373Hz and 1Hz especiely, in Fig 1 By (1), he hamonic fequencies include: ω, ω + ω, ω ω, ω + ω and ω ω Fig 8 Magniude esus fequency fo mode 3, (a) he expeimenal esul of x-diecional cenifugal foce (F ), and (b) he expeimenal x y esul of y-diecional cenifugal foce (F ) Fig 9 Magniude esus fequency fo mode 4, (a) he expeimenal esul of x-diecional cenifugal foce (F ), and (b) he expeimenal x y esul of y-diecional cenifugal foce (F ) Fig 1 Magniude esus fequency fo mode 5, (a) he expeimenal esul of x-diecional cenifugal foce (F ), and (b) he expeimenal x y esul of y-diecional cenifugal foce (F ) I can be concluded ha no only can he cenifugal foce hae he fequency componen of caie fequencyω, bu he ohe cenifugal foce componens can also be deemined hough he conol of mino ibaion fequency ω The analysis of fequency domain can poide he aluable daa fo addessing he adjusable hamonic ibaion fequency Refeing o Figs 9 and 1, he associaed magniude aenuaes apidly when he hamonic ibaion fequency is gadually moing fa away fom he cene of he caie fequency Fo example, he magniudes of he hamonic ibaion fequencies: ω + ω and ω ω ae aenuaed apidly when hey ae fa away fom he command caie fequency ω 3 Measuemen in Time Domain Fig 11(a) shows he ime domain compaison beween he simulaion esuls and he expeimenal esuls fo case wih k 1 and k = Mode 1 and mode can be exended fom Case As shown in Fig 11(a), he waefom is measued ISSN: Issue, Volume 5, Febuay 8

8 unde ha of mode 1 The diffeence beween mode 1 and mode is only in he ampliude The case 3 wih k 1 = and k is exhibied in Fig 11(b) The mode wihou he oaional ems k1 poduces only alenae cenifugal foce The mode can poide lowe ibaing effec, which is called he weak ibaion mode The waefom is composed of he mino ibaion fequency ω and he mino ibaion fequency ω As shown in Fig 11(b), he simulaion esul and he expeimenal esul can be fuhe compaed In case 1, he waefom is composed no only of he k 1, bu also he mino ibaion fequency ω poduced in each cycle synchonously The compaable waefoms fo simulaion and expeimenal esuls ae shown in Fig 11(c) The ampliude of he cenifugal foce ange is abou fom +1 o -1 N The paamee k 1 and mino ibaion fequency ω will affec he ampliude of he cenifugal foce, which was discussed in he peious secion (a) (b) (c) Fig 11 Expeimenal and simulaion esuls fo x-diecional cenifugal foce (F ) x ; (a) Case unde he es condiion ω =(π) 56 ad/s fo expeimen and ω =(π) 5 ad/s fo simulaion (b) Case 3 unde he condiions of ω =(π) 153 ad/s fo expeimen and ω =(π) 16 ad/s fo simulaion And (c) Case 1 unde he es condiions of ω =(π) 54 ad/s fo expeimen and ω =(π) 5 ad/s fo simulaion 33 Foce Tajecoy As shown in Fig 1, he foce ajecoies eeal he cues elaed o x-diecional and y-diecional cenifugal foce fo he poposed 5 modes The ajecoy fo mode 1 and mode foms a cicle because he angenial foces in he x-diecion and y-diecion hae he same waefom and ampliude The expeimenal and simulaion esuls mach Mode 3 is ploed o illusae he dependency on he pogammable sinusoidal signal The conex ajecoy is symmey along he hoizonal x-axis and eical y-axis The mino ibaion fequency dominaes he cuaue of his ajecoy The ajecoies fo mode 4 and mode 5 ae shown in he las wo sub-plos of Fig 1 The fis ajecoy anges fom 1 N o 1 N The second ajecoy anges fom 1 N o 1 N The hid one is like he cadioid cue since he mino hamonic fequency dominaes he ibaion modes The ajecoy can also coespond o he analysis in ime domain The expeimenal ajecoies fo mode 4 and mode 5 exhibi some diffeence fom he simulaion esuls because phase diffeence occus beween x-diecional and y- diecional cenifugal foces Howee, he ampliudes of he cues in he expeimenal esuls ae almos coinciden o he one in he simulaion esuls ISSN: Issue, Volume 5, Febuay 8

9 caie fequency: ω Theefoe, he ibaing esuls of modes 4 and 5 can be used o wash delicae clohes such as woolen clohes, fo alleiaing ibaion inensiy Some impoan conclusions summaized as follows: an auomaic sysem The poposed elecical appoach is moe inelligen fo such applicaions Conenional ibaion has only a single fequency caused by he eccenic oo sucue By using he elecical ibaion mode, he moo wih muli-modes can poide a moe flexible ibaion moion fo he washing pocess Such ibaion can offe sofe opeaion o peen seee collision The conenional ibaion which elies on DC command ype is he only special case in mode 1 The fie ibaion modes can be easily pogammed ino conol sofwae Theefoe, he auomaic washing pocess can be moe flexible, based on his appoach Fig 1 The foce ajecoies of x- and y-diecional cenifugal foce (F ) and x (F ) y 4 Discussion Mode 3 can poide he equied back-and-foh ibaion by conolling he mino ibaion fequency ω, and poduce abundan sufacan by conolling he paamee: k Theefoe, he washed maeial can essenially absob he sufacan Modes 4 and 5 can poduce a moe flexible ibaion compaed wih modes 1 and Tha is o say, hey ae he same caie fequency: ω and he same ampliude fo he wo kinds of ibaion Howee, hee is a sligh diffeence beween modes 4 and 5 and modes 1 and The hamonic ibaion is inoduced by he mino ibaion fequency: ω and k As shown in Fig 1, i indicaes ha he hamonic ibaion will be peiodically ibaed wih he caie fequency: ω, and poide he song and weak ibaion moions by egulaing he 5 Conclusion In his pape, aious applicable modes ae poided fo he washing pocess Thee basic and fie exended ibaion modes ae suggesed fo he associaed auomaic applicaion The poposed fomulaion has been eified in his pape by he expeimenal esuls The ibaion modes can be easily econfigued by pope seo conol o implemen he associaed funcion Based on he sofwae pogamming, he seo ibaion is easy o be implemened and ealized Flexible seo conol is poided o mee diffeen ibaion equiemens The flexibiliy can be enhanced based on he poposed appoach Though he deailed fomulaion, a pope sofwae-based muli-mode ibaion fo he ibaion moo has been successfully poposed o eplace conenional mechanical ibaion Acknowledgemens: Thanks o Jiann-De Lee and Yuan-Giey Eleconic Inc fo poiding he esing equipmen Financial suppo fom he Naional Science Council wih conac numbe NSC E is also appeciaed Thanks o Tzeng Tseng fo yping his aicle enhusiasically Refeences: [1] CY Wu and CPollock, Analysis and educion of ibaion and acousic noise in ISSN: Issue, Volume 5, Febuay 8

10 he swiched elucance die, IEEE Tans Indusy Applicaions, ol 31, pp 91-98, 1995 [] WR Finley, MM Hodowanec, and WG Hole, An analyical appoach o soling moo ibaion poblems, IEEE Tans Indusy Applicaions, ol 36, pp , [3] DE Cameon, JH Lang, and SD Umans, The oigin and educion of acousic noise in doubly salien aiable-elucance moos, IEEE Tans Indusy Applicaions, ol 8, pp , 199 [4] F Flindes, J Zhang, and W Oghanna, Inesigaion on excessie commuao and bush weas in DC acion machines, in IEEE Powe Eleconics and Die Sysems Conf, pp -5, 1999 [5] P Chanchaoensook and M F Rahman, Magneizaion and saic oque chaaceizaion of a fou-phase swiched elucance moo: expeimenal inesigaions, in IEEE Powe Eleconics and Die Sysems Conf, pp , 1 [6] H Banisla, G Guo, Inesigaion of he feasibiliy of acie balancing of had disk dies, Mechaonics, ol 14, pp , 4 [7] KWC Lai, AP Hui, and WJ Li, Nonconac bach mico-assembly by cenifugal foce, IEEE inenaional confeence on mico elecon, mechanical, pp , 4 [8] S Yasuaki, Y Hioshi, and Y Yasuhiko, Deelopmen of he Vibaion Conol Sysem G-Fall Balance fo a Dum ype Washe/Dye, Poc IEEE/ASME Inenaional Confeence on Adanced Inelligen Mechaonics, pp , 3 [9] SK Pak, Washing mehod fo washing machine, US Paen 69, Jan 6 [1] TR Smih, Twin Impelle Washing Machine, Biish Paen , Apil 197 [11] K Suou, Y Funada, M Iwaa, T Awaguchi, and K Nakagawa, Cenifugal Spin Oy Machine, Japan Paen 1395, Aug 1 [1] H Fujii, F Oa, Y Omua, and S Imai, Washing Machine, US Paen , Oc [13] N Taeishi, Rolle Washing Machine Due o Cenifugal Resin Remoal, Japan Paen , No 1994 [14] T Maeda, K Adachi, M Nakaya, and S Kumagai, Elecic Washe, Japan Paen , June 1994 [15] PT Maienga and KKB Hon, An Expeimenal Sudy of Cuing in High-Speed End Milling and Implicaions fo Dynamic Foce Modeling, ASME Jounal of Manufacuing Science and Engineeing, ol 17, pp 51-61, 5 ISSN: Issue, Volume 5, Febuay 8