An analysis of precise positioning scenarios of the electromechanical rotating system driven by a stepping motor

Transcription

1 SIRM h Inenaional Confeene on Vibaions in Roaing Mahines Magdebug Gemany.. Febuay An analysis of peise posiioning senaios of he eleomehanial oaing sysem diven by a sepping moo Robe Konowoi Andzej Pohane Agniesza Pęgowsa omasz Szol Insiue of Fundamenal ehnologial Reseah of he Polish Aademy of Sienes ul. A. Pawińsiego B -6 Wasaw Poland szol@ipp.pan.pl Fauly of Eleial Engineeing of he Wasaw Univesiy of ehnology Pl. Poliehnii -66 Wasaw Poland andzej.pohane@ee.pw.edu.pl Absa In he pape hee is invesigaed epeimenally and heoeially eleomehanial dynami ineaion beween he diving sepping moo and he diven laboaoy bel-anspoe sysem imiaing an opeaion of he oboi devie in he fom of woing ool-aie unde anslaional moion. he onsideed obje is popely equipped wih measuemen sysems enabling us a egisaion of sudied eleial and mehanial quaniies. he analyial onsideaions ae pefomed by means of he iui model of he elei moo and of he disee non-linea model of he mehanial sysem. In he invesigaed eamples vaious senaios of he woing ool-aie moion and posiioning by he bel-anspoe ae measued and simulaed whee in he all ases he elei uen onol of he diving moo has been applied. Inoduion he poblem of dynami ineaion beween seveal oaing sysems o-opeaing wih vaious elei mahines i.e. asynhonous and synhonous moos and geneaos as well as wih DC and sepping moos has been onsideed ill pesen by many auhos fo many yeas [-]. Majoiy of eseah in his field aied ou using moe o less advaned eleomehanial models have been foused on seady-sae opeaing ondiions of he invesigaed objes as e.g. in [-]. Bu he uenly obseved fas developmen of peise auiliay dives of mahines vehiles and aiafs as well as of oboi devies ommonly diven by elei moos equies deepe and deepe nowledge abou hei ansien opeaion popeies. Apa of a ealizaion of possibly peise moions suh faos as appopiaely sho duaions of posiioning imes elei powe onsumpion and dynami loadings imposed on he sysem moving elemens ae usually he mos impoan fom he engineeing paie poin of view. An inedependene of he menioned above faos assoiaed wih he onsideed poesses essenially follows fom dynami popeies of he diven mehanial sysem as well as fom oupu haaeisis and onol of he diving elei moo. he sepping moos ae ommonly nown soues of powe usually applied fo a possibly ea posiioning of seleed elemens of diven peise mehanial sysems. On he one hand in suh sysems an auay of posiioning essenially depends on eleial popeies and pope onol of he diving moo. Bu on he ohe hand his auay follows fom fleibiliy and dynami popeies of he diven obje. Hee beause he fleible mehanial sysems usually indiae a naual abiliy of vibaions ausing a fluuaion of he angula veloiy of he sepping moo oo he flows of elei uens in he moo windings beome affeed by hese mehanial osillaions whih esuls in addiional vaiable omponens of he diving eleomagnei oque geneaed by he sepping moo. Aoding o he above he eleial uen osillaions ae oupled wih mehanial vibaions of he diven obje. In ode o assue a possibly auae posiioning of elemens of he mehanial sysems diven by he sepping moos he phenomenon of eleomehanial ineaion beween he mehanial and eleial pas should be hooughly invesigaed heoeially and epeimenally. his poblem has been onsideed ill pesen by many auhos bu usually fom he viewpoin of modelling of he sepping moo. Majoiy of hem have applied he iui models of he sepping moo and he diven mehanial sysem was edued o only one igid body he mass momen of ineia of whih is added o ha of he moo oo as e.g. in [-8]. In [] one an find fundamenals of eleial modelling of he sepping moo. Pape ID-

2 he main age of invesigaions pefomed in [6-8] was a possibly he mos ea onol of he sepping moo opeaion in ode o assue a peise angula posiioning of he oo. Fo his pupose in [6] an influene of eleial paamees of he moo and is onolle has been sudied. In [78] vaious sepping moo onolles wee developed whee in [8] also highe hamoni omponens of he moo eleomagnei oque have been aen ino onsideaion fo an analysis of a possible esonane eiaion. Some inoduoy aemps o invesigaions of dynami ineaion beween he diving sepping moo and he diven mehanial sysem an be found in [9] and [] whee apa of iui models of he elei uni he ineial-viso-elasi popeies of he mehanial sysem have been aen ino onsideaion espeively in he fom of a suual diseeoninuous and disee model. In [9] hee was ealized one of he fis appoah o moe qualiaive analysis of he iui model of he sepping moo ineaing wih he osionally vibaing suual model of he geaed dive sysem whee all neessay geomeial and maeial paamees wee aen ino onsideaion. In ha pape in addiion o simulaion eamples of ansien and seady-sae opeaing ondiions also a qualiaive speal analysis of he eleial-o-mehanial esponse has been pefomed. In [] similaly as in [9] he volage-fequeny onol of he sepping moo was applied fo he heoeial eleomehanial model of a oboi devie. In he pape pesened hee hee is sudied a dynami ineaion beween he eal wo-phase hybid sepping moo and he eising eal mehanial laboaoy bel-anspoe sysem epesening a oboi devie haaeized by he moving ineial woing ool-aie unde anslaional moion. he main goal of his wo is o develop a possibly effeive and ea posiioning senaio of he ool-aie fom he viewpoin of a heoeial and epeimenal oaional dynami analysis of he onsideed obje. Desipion of he onsideed obje and measuemen sysems he eal obje of onsideaions is he above menioned laboaoy bel-anspoe sysem imiaing a oboi devie haaeized by he moving ineial woing ool-aie unde anslaional moion. A phoogaph of his mehanism is shown in Fig.. he anslaional moion of he ool-aie is ealized by he oohed bel spanned on wo olles of he adius. m. he aes of hese olles ae muually sepaaed by.7 m. he ool aie olley moves diely along he guideway made of he single Hepo onsuion beam wih a nominal lengh of 98 mm and a oss seion of 7 mm. his enie suue is suspended by an aluminium uss fame whih an be addiionally siffened by igid plae elemens in ode o assue possibly hoizonal movemen of he woing ool-aie i.e. wihou emaable veial defleions duing ess. his mehanism is diven by he double-phase sepping moo FLSH by means of he shaf segmen onneing he moo oo wih he lef-hand olle see Fig.. A shemai view of his enie obje is pesened in Fig.. Figue : he laboaoy bel-anspoe sysem diven by he sepping moo. Figue : Sheme of he laboaoy bel-anspoe sysem diven by he sepping moo. Pape ID-

3 A oaional speed of his moo an be hanged by means of he onolle USN-D8A and monioed using he oay enode AM mouned on he ale of he diving moo. Addiionally his enode enables he measuemen of he disane whih oveomes he moving mass duing esing. he ool-aie esing on he olley an be aeleaed and deeleaed duing epeimenal ess wih he ae up o of m/s. hese seings enable us o ge he maimum mass veloiy equal o m/s. Moe fundamenal paamees of his es-ig an be found in able. able : ehnial paamees of he es ig Paamee Value. maimum baing oque of he diving moo FLSH Nm. maimum uen of he onolle USN-D8A 7 A. veloiy ange of he moving mass - m/s. maimum aeleaion and deeleaion of he moving mass m/s. mass of he ool-aie wih he olley 7 g 6. disane beween he olle ales / olle adius.7 m /. m 7. maimum avel disane of he moving mass along he guideway.8 m 8. esoluion of he oay enode AM 8 p/ev 9. sampling of he measuemen ad NI USB-68 duing ess S/s. sensiiviy of aeleomee PCB 6B8 mv/m/s². mass of he anspoe bel A. g. longiudinal siffness of he anspoe bel A 768 N/m A anslaional moion of he ool-aie is onolled by means of he iaial aeleomee PCB 6B8 and using he oay apaiive enode AM. he aeleaion senso is mouned on he olley aying he moving ool-aie. I measues he anslaional aeleaion of he moving ool-aie duing ess. he measued aeleaion signal is fileed by Buewoh file. In he onsideed ase he file haaeisi of he h ode was used as well as he low-pass egion wih he Hz heshold value has been seleed. he fequeny esponse of he Buewoh file appoimaion funion is also ofen efeed o as maimally fla esponse beause he applied pass-band is designed o have a fequeny esponse whih is as fla as mahemaially possible in he u-off fequeny ange. his file is able o pass all fequeny signals in he uoff ange bu also o aenuae signals wih fequenies lowe han he u-off fequeny. his is he eason why suh a file has been applied. Duing ess also vaiable values of elei uens in he sepping moo windings an be egiseed. In ode o measue elei uens in boh phases of he moo windings ino eah of hem a esiso of esisane. ohm has been onneed in seies. Hee he egiseed volage dops aoss hese esisos beome aoding o Ohm s law he measues of uen values in a given phase of he sepping moo. In he measuemen sysem of he onsideed es ig pesened in Fig. all signals fom he iuis of he sepping moo powe supply fom he aeleomee and fom he apaiive enode ae eoded by he analog-digial onvee NI USB- 68 wih he sampling fequeny of S/s. he anslaional veloiy of he moving ool-aie and he moo oo oaional speed ae measued by means of he apaiive enode. A high esoluion of he enode eahing 8 poins pe evoluion maes i vey onvenien fo suh measuemens and fo eoding an angula speed fluuaion of he dive sysem oaing elemens. Upon a onveing his angula speed ino he anslaional one he anslaional veloiy of he moving ool-aie an be deemined. hen by means of he ime-inegaion of he anslaional veloiy he disane avelled by he ool-aie is obained. his disane enables us o speify a peise loaion of he moving ool-aie a he end of he pogammed moion. he applied laboaoy bel-anspoe sysem maes possible a peise posiioning of he woing oolaie moving wih vaious speeds and aeleaion aes. hus a pogammed posiioning poedue fo he woing ool-aie an be ealized by means of moions wih appopiae onsan aveage aeleaions and deeleaions and wih piee-wise onsan aveage anslaional veloiies. Pape ID-

4 Pape ID- Modelling of he eleomehanial sysem he obje of modelling is he abovemenioned bel-anspoe sysem diven by he sepping moo. his mehanism imiaes a oboi devie haaeized by he moving ineial woing ool-aie unde anslaional moion a suue of whih is shown in Figs. and. A dynami behaviou of his mehanial sysem an be desibed by he non-linea disee model of fou degees of feedom whih is pesened in Fig.. Figue : Physial model of he laboaoy bel-anspoe sysem. Moion of his model is govened by he following sysem of odinay diffeenial equaions: el d I [ ] sgn F I sgn F I sgn F m whee i i i ae espeively he oaional and anslaional ime-dependen genealized oodinaes desibing igid body- and vibaoy moion of he disee mehanial model I denoes he mass momen of ineia of he sepping moo oo I I ae he mass momens of ineia of he bel-anspoe olles of adius m is he mass of he ool-aie denoe espeively he osional siffness and maeial damping oeffiien of he shaf segmen onneing he moo oo wih he diving olle ae he onsan and ae he vaiable ool-aie posiion dependen longiudinal siffness and maeial damping oeffiien of he pe-ensiled bel beween he diving and diven olle beween he diving olle and he ool-aie and beween he ool-aie and diven olle espeively see Figs. and. he symbols e and d denoe he eleomagnei oque funion and he absolue oo-o-sao mehanial damping oeffiien. In his model hee is assumed ha he eading oques and he eading foe imposed espeively on he boh olles and on he ool-aie ae epessed as sums of slowly vaying omponens j epesening dy fiion effes in he dive sysem and of he squae funions of he uen oaional o anslaional speed F j ω j whee j and ω j j fo j ω j fo j and F j denoe he pope onsan oeffiiens. Hee fo he assumed popoional maeial damping in he sysem he onsan and vaiable bel longiudinal siffness and damping oeffiiens an be deemined by means of he following fomulae: l EA EA l EA i i i γ γ whee EA is he bel longiudinal oss-seional siffness l denoes he disane beween he olle ales see Figs. and able and γ is he onsan maeial loss fao. In he onsideed ase of he eleomehanial sysem govened by Eqs. and aoding e.g. o [9] he iui model of he wo-phase hybid sepping moo usually haaeized by he negligible fluuaion of he oo-o-sao eluane an be desibed by wo volage odinay diffeenial equaions of he fis ode: [ ] { } os sgn sin U R i Z U K d d d di L Φ [ ] { } d sin sgn os e f U R i Z U K d d d di L τ τ π Φ Φ

5 whee i i denoe he elei uens in boh moo phases L is he phase induane R denoes he esisane of he one phase K U is he moo volage onsan U is he maimal value of onol volage Z denoes he oo pole numbe and f e is he volage supply ommuaion fequeny. Hee in a ase of suffiienly good ommuaion ealized by means of a pope sepping moo onol he onol volage supply phase angle Φ should be followed by he moo oo elei angle Z. hen he eleomagnei oque geneaed by suh a double-phase sepping moo is epessed by he following fomula: el whee K denoes he sepping moo oque onsan. [ i sin Z i os Z ] K Numeial inepeaions of he elei uen onol of he sepping moo In he ase of he volage-fequeny onol of he sepping moo applied in [9] Equaions and wee ombined ogehe ino he fom of a one oupled sysem of odinay diffeenial equaions desibing eleomehanial oupling effes beween he diving elei moo and he diven mehanial sysem whee he vaiable onol volage U and he ommuaion fequeny f e played a ole of inpu quaniies. Sine he uen onol of he sepping moos seems o be moe onvenien in an engineeing paie as well as suh a onol onep has been applied in he onsideed eal obje i is neessay o desibe i mahemaially fo he aim of numeial simulaions. hus applying he uen onol appoah ime-hisoies of he elei uens i and i in he moo phases ae a pioi assumed in he following fom of hamoni funions: n π n π i ima os and i ima sin whee i ma is he maimal uen value in he moo phases denoes he numbe of oo mio-seps pe one full sep and n is he inege ime-dependen numbe of elei uen feeding impulses pe one mio-sep. hen by subsiuing ino he eleomagnei oque el an be epessed in he sinusoidal fom: n π el K ima sin Z 6 whee he agumen of he sine-funion is a diffeene beween he oo elei angle Z and he onol angle n-π/. Hee his eleomagnei oque mus always balane he sum of all ineial and passive eenal loadings imposed on he diven mehanial sysem moion of whih has been desibed by Eqs.. Moeove in he onsideed ase of he uen onol he eleomagnei oque el epessed by elaion 6 an be egaded as an eplii eenal eiaion soue in ode o obain a sysem ansien o seady-sae dynami esponse by means of a die inegaion of Eqs.. In his pape a pope deeminaion of funion el has been aied ou in wo alenaive ways fo he aim of ineasing a eliabiliy of epeed heoeial esuls. he fis way ealized by means of he oiginal auhos ompue ode edued o deeminaion of n fom he equaion of equilibium beween el desibed by 6 and he sum of all ineial and passive eenal loadings epessed by funions of aeleaions and veloiies oesponding o a given epeed moion senaio. In he ase of he seond way ealized using he MALAB- SIMULINK ommeial ode n was deemined on-line duing die inegaions of Eqs. whee he pedio-oeo appoah has been applied fo a uen aing of a oe sysem moion wih pogammed aveage aeleaions deeleaions and onsan veloiies following fom he assumed senaio. Posiioning senaios fo he bel anspoe sysem In he heoeial ompuaional eamples in [] he main age edued o posiioning of he mehanial sysem ino a given onfiguaion wihin an assumed ime of duaion by he use of volage-fequeny onol of he sepping moo. Hee beause of he eising limis of admissible aeleaions maimal oaional and anslaional veloiies and of he moo diving oque haaeizing he onsideed eal eleomehanial obje see able he invesigaed epeimenally and heoeially posiioning senaios had o be popely pogammed aoding o boundaies of hese paamees. hus in eah sudied ase he mowing ool-aie used o avel ealy he same disane.76 m o he given poin beween he olles wih vaious admissible aes of onsan aeleaions deeleaions and veloiies bu wih diffeen imes of duaion. Suh posiioning senaios have been analyzed fom he viewpoin of paial effiieny i.e. imes of duaion magniudes of mehanial vibaions and ineial loadings as well as of he onsumed elei enegy. Sine he ypial indusial onolle of he applied sepping moo enabled us ealizaions of sysem moions only wih onsan aveage aeleaions deeleaions and onsan aveage veloiies he epeimenally egiseed posiioning senaios wee edued o apezoidal and iangula modes. his means ha he ool-aie of he Pape ID-

6 laboaoy oboi devie was aeleaed fom is sandsill a he lef-hand side eeme bel loaion see Figs. and wihin he equied ime insan o he assumed onsan aveage anslaional veloiy and afe a given ime of avel duaion i has been deeleaed ba o a sandsill. Suh movemens wee ealized by means of he sepping moo uen onol. In Figs. and hee ae demonsaed ime-hisoies of he measued eleomehanial dynami esponses of he onsideed eal obje egiseed fo wo eemely diffeen posiioning senaios. In Fig. he esuls of he apezoidal mode ae pesened whee he ool-aie mass has been aeleaed wihin. s o he onsan aveage veloiy equal m/s and hen upon. s deeleaed o is sandsill in ode o oveome disane.76 m wihin.9 s. Figs. a and b show espeively he plos of mass veloiy and aeleaion. Fig. pesens he plo of mass avelled disane and in Fig. d ime-hisoies of he onol uens in boh moo phases ae depied by he bla and gey lines. In an idenial way in Fig. hee ae shown analogous measued esuls egiseed fo he iangula posiioning mode whee he oolaie mass was aeleaed wihin.86 s o he maimal admissible speed m/s and hen immediaely deeleaed o is sandsill. Hee he avelled disane.76 m has been oveome wihin.76 s only. Howeve Figs. 6 and 7 pesen analogous ime-hisoies of espeively he same quaniies deemined by means of numeial simulaions fo he idenial as above posiioning senaios. he bla lines in Figs. 6ab and 7ab oespond o he esuls obained by means of he menioned above uen onol appoah implemened in he auhos oiginal ompue ode and he plos denoed by he gey lines oespond o he esuls deemined using he uen onol saegy ealized by he pogam opeaing in he famewo MALAB-SIMULINK sofwae paage. hese heoeial esuls have been obained fo he abovemenioned paamees of he eal mehanial sysem lised in Seion and in able as well as fo paamees of he applied hybid fou-yle double-phase sepping moo FLSH haaeized by L mh R.8 Ω K.8 Nm/A and by he fundamenal sep angle.8 deg. ad whih means ha is oo has Z poles. he uen onol of he moo opeaion was ealized fo i ma 7 A and fo he ommonly used 8 oo mio-seps pe one full sep. he mass momen of ineia of he oohed bel has been unifomly edued o he aes of boh olles. I is o emphasize ha a vey good qualiaive and quaniaive ageemen beween he oesponding epeimenal and heoeial esuls have been obained paiulaly using he auhos oiginal ompue ode. Hee he egiseed muual disepanies beween he heoeial esuls obained using he wo menioned above simulaion appoahes ou mainly fo osillaion loal ampliude values. hese diffeenes ae aused by a a a b b d d Figue : Measued sysem esponse fo he Figue : Measued sysem esponse fo he apezoidal posiioning mode wih v ma m/s. iangula posiioning mode wih v ma m/s. 6 Pape ID-

7 a b d mass veloiy [m/s] mass ael.[m/s ] uens ii [A] avelled disane [m] ime [s] Figue 6: Simulaed sysem esponse fo he apezoidal posiioning mode wih v ma m/s. a b d mass ael.[m/s ] uens ii [A] mass veloiy [m/s] avelled disane [m] ime [s] Figue 7: Simulaed sysem esponse fo he iangula posiioning mode wih v ma m/s. some ind of numeial ineia obseved duing he on-line aing of he assumed moion senaios ealized by he MALAB-SIMULINK ommeial ode egadless applied lenghs of he die inegaion seps. Fuhemoe fo he aim of a bee eplanaion of popeies of he all measued esuls in Figs. 8 and 9 hee ae shown ime-hisoies of he simulaed eleomagnei oques geneaed by he sepping moo ogehe wih plos of he sysem esulan eenal eading oques edued o he moo oo ais and wih he dynami oques ansmied by he shaf segmen onneing he moo-oo wih he lef-hand olle see Figs. and. Hee Fig. 8 oesponds o he abovemenioned apezoidal posiioning senaio and Fig. 9 o he iangula one. In hese figues by he gey solid lines he eleomagnei oque ime-hisoies ae ploed by he bla lines hee ae depied he ime-hisoies of he shaf viso-elasi dynami oques and he bla dashed oespond o he eading oques. In he boh ases of he posiioning senaios i.e. he apezoidal and he iangula one he ime-hisoies of he eleomagnei moo oque ae haaeized by he low- and highfequeny fluuaing omponens. he lae of ahe seady-sae osillaion ampliudes is aused by he sepwise disoninuous haae of a ommuaion ealized by he uen onol wih he given numbe of mio-seps pe one full sep. Fom some auiliay numeial simulaions aied ou fo vaious equal o 6 and 6 i follows ha if he numbe of mio-seps ineases ampliudes of he eleomagnei oque highfequeny omponen end o zeo. In a onadisinion he low-fequeny moo oque omponen gadually deays wih ime. Bu hese ansien osillaions of elaively geae ampliudes vey signifianly influene also ime-hisoies of he ool-aie aeleaions and veloiies whih has been onfimed by epeimenal measuemens fo he boh onsideed posiioning senaios as shown in Figs. ab and ab. dyn. oques [Nm] ime [s] Figue 8: Simulaed dynami oques fo he apezoidal posiioning mode wih v ma m/s. dyn. oques [Nm] ime [s] Figue 9: Simulaed dynami oques fo he iangula posiioning mode wih v ma m/s. 7 Pape ID-

8 hese low-fequeny ansien vibaions indued afe eah apid hange of he pogammed aveage aeleaion in he famewo of he ealized posiioning senaio ae aused by he dynami ineaion beween he elei moo and he diven mehanial sysem. Hee similaly as in he ase of induion moos invesigaed in [] and [] he sudied fee-fee osional ain pesened in Figs. and beomes oaionally lamped by he sepping moo sao. Aoding o [] he oaional siffness of he eleomagnei sping onneing he moo oo wih he sao an be epessed as e Z K i ma. whee he symbols sanding on he igh-hand side have been aleady defined in Eqs. and. hen upon eigenfequeny analyses pefomed fo he undamped and lineaized mehanial sysem i.e. fo he assumed saionay posiions of he ool-aie l/ and l- see Fig. and fo he addiional lamping elasi em e sanding on he lef-hand side of Eq. he fis naual fequeny values ae equal o. Hz fo 9.89 Hz fo and 9.7 Hz fo posiion whee he naual fequenies oesponding o highe eigenmodes eeed 6 Hz. his esul fis well o all espeive ime hisoies pesened in Figs. ab ab 6ab 7ab as well as in Figs. 8 and 9. Fom a qualiaive ompaison of he boh onsideed senaios i follows ha he iangula one lass moe han wo imes shoe bu i equies sysem aeleaion o imes geae maimal veloiy han he iangula mode whih esuls in moe sevee ansien low-fequeny osillaions. Neveheless in he boh ases he ampliudes of ool-aie deeleaion a he end of movemen i.e. duing he final posiioning ae simila o eah ohe whih esuls in ompaable pea values of he ineial foes assoiaed wih baing of he moving ool-aie. hese popeies have been epeimenally and heoeially onfimed by he hid also apezoidal posiioning senaio whee he ool-aie was aeleaed o he maimal aveage onsan veloiy m/s wihin. s and upon. s deeleaed ba o a sandsill wihin ne. s. hus he enie posiioning poess lased.9 s whih is essenially shoe han in he ase of he pevious apezoidal mode and only. s longe han he iangula one. he ime-hisoy plos of he of he ool-aie veloiy aeleaion avelled disane and of he onol uens whih wee measued and simulaed using he boh mehods menioned in Seion ae pesened in Figs. and in an idenial way as in Figs. 6 and 7. Fom an analysis of he epeimenally and heoeially obained pos i follows ha his posiioning senaio is haaeized by simila qualiaive and quaniaive popeies as hose wo onsideed above. Fis of all afe eah apid hange of he aveage aeleaion also he sevee ansien osillaions of fequeny a. Hz ae indued. Moeove despie of only wo imes geae aveage maimal veloiy han in he ase of a a mass veloiy [m/s] b b mass ael. [m/s ] uens ii [A] avelled disane [m] d d ime [s] Figue : Measued sysem esponse fo he Figue : Simulaed sysem esponse fo he apezoidal posiioning mode wih v ma m/s. apezoidal posiioning mode wih v ma m/s. 8 Pape ID-

9 pevious apezoidal mode he enie mehanial sysem mus have been baed o a sandsill wih a ompaable aveage deeleaion as hose ealized befoe. Namely he deeleaion values neessay fo baing he moving ool-aie wee equal o.8 m/s in he ase of apezoidal mode wih v ma m/s.88 m/s fo he apezoidal mode wih v ma m/s and. m/s in he ase of iangula mode. his means ha duing ealizaions of all hese hee posiioning senaios ompaably high ineial foes a on he baed oolaie whih an negaively influene a peision of is moion. hus in ode o avoid disadvanages of hese all posiioning senaios onsideed above and o ahieve a possibly sho ime of ool-aie moion wihin he admissible speed ange - m/s see able he applied ill pesen sep-wise apid hanges of he sysem aveage aeleaions an be modified by an alenaive fluen one haaeized by a sinusoidal fom whih esuls in a osinusoidal vaiaion of he ool-aie aveage veloiy. Sine he sepping moo onolle applied hee enables us o ealize moions only wih onsan aveage aeleaions and veloiies suh poposed osinusoidal posiioning senaio has o be invesigaed heoeially. In Fig. hee ae shown oesponding esuls of simulaion fo he ool-aie oveoming he same avelled disane.76 m wihin.76 s and wih v ma m/s i.e. fo idenial paamees as in he ase of he iangula mode. Using he bla lines Figs. ab and pesen ime-hisoies of he ool-aie veloiy aeleaion and avelled disane espeively. Fo a ompaison in hese figues by means of he gey lines also he analogous ime-hisoies oesponding o he onsideed above iangula mode ae ploed. In an idenial way as in Figs. 8 and 9 fo he osinusoidal posiioning senaio hee ae depied ime-hisoies of he sepping moo eleomagnei oque gey line ogehe wih ime-hisoies of he dynami oque ansmied by he shaf segmen onneing he moo-oo wih he lef-hand olle bla solid line and of he esulan eenal eading oque aing on he enie mehanial sysem bla dashed line. Fo he aim of a bee demonsaion of diffeenes beween he all fou onsideed posiioning senaios as well as of emphasizing advanages of he poposed osinusoidal mode in Figs. e and f in he avelled disane domain hee ae espeively pesened plos of he ool-aie movemen ajeoies and of he baing foe hisoies. In hese figues he bla solid lines oespond o he osinusoidal posiioning senaio he gey lines o he iangula one and using he doed and dashed lines he plos oesponding o he apezoidal modes wih espeively v ma m/s and v ma m/s ae depied. Fom an analysis of suessive plos in Figs. a-f hee follow seveal advanages of he osinusoidal posiioning senaio in a ompaison wih he iangula and boh apezoidal ones. Fis of all he fluen jump-fee vaiaion of he aveage movemen aeleaion esuls in signifianly smalle ampliudes of he low-fequeny ansien vibaions as shown in Figs. ab. Moeove he oal ime of ool-aie un an be hee as sho as in he ase of he fases iangula mode. Alhough he osinusoidal posiioning senaio is ealized wih insananeously he geaes aveage aeleaions and veloiies of he moving ool-aie and of all sysem oaing pas see Figs. abe bu hei moions ae foed by he eleomagnei and dynami oques haaeized by smalle osillaion ampliudes and muh moe fluen vaiaion in ime as indiaed in Fig. d in a ompaison wih he analogous plos in Figs. 8 and 9. his feaue seems o be vey onvenien fom he viewpoin of maeial faigue unneessay noise geneaion and hea losses. Bu he geaes benefis a b mass veloiy [m/s] mass ael.[m/s ] avelled disane [m] d ime [s] f e dyn. oques [Nm] baing foe [N] mass veloiy [m/s] ime [s] avelled disane [m] Figue : Simulaed sysem esponse fo he osinusodal posiioning mode wih v ma m/s. 9 Pape ID-

10 assoiaed wih an appliaion of he poposed osinusoidal senaio seem o follow fom he smalles baing foes ouing a he ime insan of ool-aie posiioning a he age disane.76 m. he espeive plos in Fig. f indiae emaably he mildes baing foe fluuaion obseved in his ase whih eaes he bes ondiions fo possibly peise plaemens of mehanial sysem elemens o he given poin. Neveheless he insananeous bigge aveage aeleaions and veloiies assoiaed wih he osinusoidal senaio esul in he highes elei enegy onsumpion due o appopiaely geae eading foes and oques. he onsumed elei enegies alulaed using Eqs. fo he apezoidal modes wih v ma and v ma m/s as well as fo he iangula and osinusoidal ones wee espeively equal o and 7.6 Ws. Final emas In he pape hee was pefomed an epeimenal and heoeial invesigaion of an opeaion of a eal eleomehanial sysem in he fom of he laboaoy oboi ool-aie moved by he bel-anspoe sysem diven by he sepping moo. By means of his devie seveal senaios of he ool-aie posiioning wee analyzed using esuls of measuemens and numeial simulaions fo whih a vey good muual qualiaive and quaniaive ageemen has been obained. hese senaios onsised of sysem movemens haaeized by piee-wisely onsan as well as oninuously vaiable aveage aeleaions and veloiies. I uned ou ha apid hanges of hese aveage aeleaions and veloiies esuled in eiaion of sevee low-fequeny ansien osional and anslaional vibaions indued by he eleomehanial ineaion beween he diving moo and he diven sysem. Moeove hese osillaions supeimposed on he nominal moions wih high onsan aveage deeleaion aes duing ool-aie posiioning o he age poin wee assoiaed wih elaively lage baing foe fluuaions negaively influening a peise opeaion of he onsideed devie. Howeve ool-aie posiioning senaios haaeized by fluen oninuous vaiaions of sysem aveage aeleaions deeleaions and veloiies esuled in essenially smalle ansien low-fequeny vibaions and in signifianly lowe ampliudes of baing foes. hus suh movemen senaios seem o be paiulaly pomising fo pogammed peise opeaions of numeous esponsible eleomehanial devies. Anowledgemen he invesigaions suppoed by he Naional Siene Cene: Reseah Poje: UMO-//N/S8/9. Refeenes [] abesh A. and Iavani R. : On he appliaion of he omple oque oeffiiens mehod o he analysis of osional dynamis. IEEE ansaions on Enegy Convesion Vol. No. pp [] Repo A.-K. Rasilo P. and Aio A. 8: Dynami eleomagnei oque model and paamee esimaion fo a deep-ba induion mahine. Elei Powe Appliaions IE pp [] Xu K. Zhao C. Zhang J. and Guo C. : he appliaion of omple oque oeffiien mehod in muli-geneao sysem. Eleial Powe Sysems and Compues LNEE 99 X. Wan Ed. Spinge- Velag Belin Heidelbeg pp [] Szol. Konowoi R. Mihajłow M. and Pęgowsa A. : An invesigaion of he dynami eleomehanial oupling effes in mahine dive sysems diven by asynhonous moos. Mehanial Sysems and Signal Poessing 9 pp. 8. [] Sohoi R. 996: Eleial Mio-mahines. Eds. of he Wasaw Univesiy of ehnology Wasaw ISBN in Polish. [6] Liu X. and Zhao D. : he simulaion of sepping moo unde wo inds of ondiion. Poedia Engineeing pp [7] Jahani R. Chahandi Nejad H. Shayanfa H.A. and Zae A. : Posiioning onol of PM seppe moo based on ype- fuzzy obus onol. Inenaional Jounal on ehnial and Physial Poblems of Engineeing Issue Vol. No. pp [8] Wang-Hay sui K. Chow Cheung N. and Chi-Wah Yuen K. 9: Novel modeling and damping ehnique fo hybid seppe moo. IEEE ans. on Indusial Eleonis Vol. 6 No. pp. -. [9] Szol. and Pohane A. : Dynami invesigaions of eleomehanial oupling effes in he mehanism diven by he sepping moo. J. of heoeial and Applied Mehanis pp [] Szol. Mihajłow M. and Konowoi R. : On eleomehanial dynami oupling effes in he semi-aively onolled oaing mahine dive sysem diven by he induion moo. In Po. h In. Conf. on Vibaions in Roaing Mahines SIRM Belin 7 Febuay Pape ID-8. [] Pęgowsa A. Szol. Pohane A. and Konowoi R. : Modeling and dynami analysis of he peise eleomehanial sysems diven by he sepping moos. Advanes in Inelligen Sysems and Compuing Spinge Inenaional Publishing Swizeland Vol. 67 pp.. Pape ID-