ZESZY TY N A U K O W E P O L IT E C H N IK I ŚLĄSK IEJ 1994
Seria: M E C H A N IK A z. 116 Nr kol. 1231
C tirad K R A T O C H V IL In stitu te o f M echanics o f Solids Technical U n iversity o f Brno
A N A L IZ A I SY M U L A C JA D Y N A M IC Z N Y C H W L A SN O SC I E L E K T R O M E C H A N IC Z N Y C H SY ST E M Ó W N A P Ę D O W Y C H ZE
SPR Z Ę Ż E N IA M I Z W R O T N Y M I
S treszczen ie. W referacie zajęto się problem em sym ulacji system ów napędow ych ze sprzężeniam i zw rotnym i. Symulacji organizacji strukturalnej dokonano za p o m o cą m odelu urządzenia napędowego jako całości, jak również przez w y liczen ie w ew nętrznych i zew nętrznych oddziaływ ań, m ających w pływ na reakcje pod system ów .
A N A L Y SIS A N D SIM U LATIO N O F D Y N A M IC A L P R O P E R T IE S OF IN T E R A C T IV E EL E C T R O M E C H A N IC A L D R IV E SY ST E M S Sum m ary. T h e paper deals w ith th e problem o f sim u latin g o f in teractive drive sy stem s. T he sim ulation o f th e structural arrangem ent is defined by a correct assessent of th e internal and external interaction s, influencing the reaction o f m od el sy stem s, and also the m odel o f the drive as a whole.
A N A L Y S E U N D SIM U LATIO N VON D Y N A M ISC H E N E L E K T R O M E C H A N ISC H E N E IG E N SC H A F T E N D E R
A N T R IE B S S Y S T E M E M IT R Ü C K K O P PL U N G E N
Zusam m enfaßung. D as R eferat behandelt das Problem der Sim ulation von A n trieb ssystem en m it Rückkopplungen. D ie Sim ulation der Strukturor
gan isation wurde m ittels des M odells einer als G anzes betrach teten A n trieb
seinrichtu ng sow ie durch Berechnung der inneren und äußeren E inw irkungen, w elche die R eaktionen von Su bsystem en beinflussen, durchgeführt.
1. IN T R O D U C T IO N
T h e o b jectiv e social need to bring th e design sector closer to th e needs of the operatin g con d ition s m akes it necessary to analyse a number of inform ations on possible future
144 C. Krotochvi'l
effects, on internal and extern al interaction s o f th e analysed sy stem , and last bu t not least to seek answ ers to qu estion s regarding the dyn am ic properties o f the sy s te m , and its reaction s to th e stan dard and break-dow n situ ation s. If possible, all th is sh ould be already acquired at th e sta g e of design.
In case o f d yn am ic analysis o f th e drive system s th ese requirem ents are com p licated by th e fact th a t w e have to do w ith a com plex d yn am ic sy stem , w hose basic structural parts have various p h ysical asp ects (m echanical, electronic, hydraulic, e tc .). E sp ecially, in th e case o f controlled drives, th ese interactive sy stem s are com bined w ith bassically m u lti-sta g e feedback su b sy stem s. M achine drive system s, in th e narrower tech n ical se
n se, contain as a rule: sy stem s o f driving m otors, transm ission s, th e w orking m achines, feedback and control sy stem s and inform ation transfer system s.
2. S P E C IA L P U R P O S E A N D PARTIALLY S T R U C T U R E D D Y N A M IC SY ST E M S
T h e answ ers to th e q u estion s regarding th e properties o f new m achine drives, and how th e y react on a num ber o f operatin g conditions, can b e acquired through exp erim en ts w ith m a th em a tica l m odels, defined on actual system s, e.g. [1], [2], [3). T h e n otin g
’’d yn am ic s y s te m ” has itse lf not yet been un ivically defined. We shall stick to th e definition of it according to Z A D E H [4], in sense w ith th e identification of th e actu al (prim ary) o b ject and o f th e a b stract (secondary) o b ject, represented by th e general d yn am ic sy stem , represented in th is case by a m athem atical m odel.
T h e basis o f th e su ccess o f experim en tin g w ith this m ath em atical m od el is a correct fu n ction al d efin ition o f th e sy stem , w ith sp ecial view to solving a concrete problem . T h e
’’fu n ction al d efin ition ” o f th e sy stem does not m ean that it is fully defined by its fu n ction s and m a n ifestation s only, on th e very contrary. We presum e, th a t all th ese fu n ction s have their bearers, th a t sh ould also b e com prehended as a black box. Therefore w e define at least th e app roxim ate degree o f structural com plexity, pow er o u tp u t and inform ative cap acity o f th e sy stem . T h u s th e system has a certain target and som e inform ative fu n ction s, on higher level som e control functions. In view o f th e fact th at th e actu al m odels o f m achine drives are o f varying com plexity, we have defined th e m otion "purpose- form ulation o f th e sy stem on th e actual o b jec t” [2]. We com prehend it in th e sen se th at som e sy stem elem en ts, sy stem links and properties m ay be a sm plified or even n eglected in co n n ectio n w ith th e concrete situ ation . Further, th e dyn am ic sy stem w ill alw ays be reagarded as ’’im p erfectly structu red ” . A ccording to th e concrete purpose we can create, if need b e, several structural qu alities. A t th at we can m ake even o f som e e xtrem e principles, fa cilia tin g th e descrip tion o f th e sta te o f the system in m arginal cases, e.g. in cases when th e p erm itted load level has been exceeded , in case of deform ation, breakdow n, etc.
A ll th is is don e to en ab le th e fun ctional definition o f the sy stem , to acquire th e basic d yn am ic ch aracteristics, principles o f configuration, param eters of fu n ction in g, and ev en tu a lly o f th e d evelop m en t o f com plex sy stem s that could be quantified, at least partially.
Analysis an d sim ulation of dynam ical properties.. 145
GB
M
..
m o to rC . . . co u p lin g
G B . a <D o cro X M f.
R U . . r o llin g u n it - L M O F
.
. m a in d is t r ib u t io n Cfro m «
A . 0 J L * :
RU RU RU RU
MDF
Û1
, ! [RUJ [RU
— 1q MDF q
v (l) j Fig. 1.
Rys. 1.
3. C O N C R E T E EX A M PLE
T h e schem e of th e drive of an experim ental w ire-drawing m ill we can see in Fig. 1. T h e task was to check th e dynam ic properties of th e drive as a whole, and th e specific dynam ic properties and behavior of th e m otor subsystem . Herq we face problem s in synchronizing th e revolutions of th e individual m otors on startin g th e run of th e mills, in idle ru n on entering th é mill by th e m aterial, and following problem s, on account of the purpose-form ulation of m ath em atic models are suitable.
R U ( r t o - l o o d )
. N
RU (working m o t io n )
Fig. 2. Rys. 2.
For exam ple, th e first problem , th e analysis of basic dynam ic properties of th e drive as a whole, can be solved w ith th e help of a m odel of a branched discrete system presented in th e Fig. 2. T h e m a th e m a tic m odel is a system of differential equations of m ovem ent (linear or linearized - th e couplings betw een m otors m ay have a nonlinear characteristic).
A nother problem to be faced is the detailed analysis of th e dynam ic system of the m otor subsystem . A su itab le purpose-m odel in this case is presented in Fig. 3. Technological p a rt is reduced on th e technological m om ent M T . Here we have to consider a controlled drive system s (th e to ta l speed is controlled).
It has been therefore necessary for each m otor to set up m odel com prising sub-m odels of a th y risto r converter for feeding th e arm atu re of the m otor of th e power regulator in a rm a tu re circuit an d m otor speed regulator [5]. T he possible ways of controlling the m otor subsystem have been defined in Fig.4.
146 C. Krotochvfl
SUBSYSTEM I . SUBSYSTEM I .
TACHO
MASTER (SLAVE)
, 4 ilr = = ± . . ñ i
kXL ' Jmi ---(TACHO) I I
j fc-iJfc-iJ 1T_J —
— - T ’ v m7 —
jlM ASTER) SLAVE
S L A V E R
— jrv%_ —
i + SLAVE
m t z
4e
F ig. 3.
Rys. 3.
Fig. 4.
Rys. 4.
T h e resu lts o f d yn am ic analysis o f th e train drive, acquired w ith th e help of descri
bed m o d els, can be found in [2] and [5]. O nly two exam ples com puter sim u lation s are d em on strated here. In order to suppress th e parasitic effects o f non-linear characteristic o f flexible couplings have been used. T h is has lead to th e lim itation o f parasitic affect only on th e b egin n in g o f th e sim u late rolling proces (see courses o f th e flexible m om ent M45 in th e train drive, w ith ou t clearance on the Fig. 5a and w ith clearance on th e Fig.
5b.
In th e conseq u en ce o f th e disengagem ent o f th e drive sy stem (clearance in th e m ech ani
cal co u p lin g s), thyristor converters m ay generate very com plicated parasitic com ponents.
T h en , th e clearan ce in th e flexible couplings, nam ely the size o f th e clearance, causes cha
nges in th e p aram eters o f the couplings. T h ese changes m ake rise to com p licated m otions - for ex a m p le phase p ortraits in coupling (2-5), see Fig. 6a,b,c, (a...very little clearan ce - sta te o f d eterm in istic chaos; b, c ... an increase o f the clearance in th e coupling).
A nalysis an d sim ulation of dynam ical properties. 147
Fig. 5.
Rys. 5.
a) C)
V 1Q'1
Fig. 6. Rys. 6.
4. CON CLU SIO N
T h e problem s connected w ith th e sim ulation of th e dynam ic properties of interactive m ovem ent system s contain, as an analysis of the properties of each complex system , certain m om ents of uncertainty, inconclusiveness and still have an open character. The developm ent of th e present level of scientific knowledge, however, m akes it im perative to follow th e problem ’s areas too, include certain disputed m om ents. We could m ention here e.g. th e form ulation of purpose - stru ctu red m athem atic models of drive system s. We also d em o n strated th e links betw een functional m anifestations of drive subm odels and their organized stru c tu re , arising in the process of discovering new release, new context.
148 0 . K rotochvil
Such a m eth o d ic approach to th e solution o f practical problem s can b e already d on e at th e sta g e o f designin g th e basic structural com ponents o f th e drive sy stem s.
R E F E R E N C E S
[1] K A L M A N ,R.: A lgebraic A sp e ct o f th e T heory o f D yn am ic S y stem s, in: D ifferential E q u ation s and D yn am ic S y stem s, A cadem e Press, N ew York 1967.
[2] K R A T O C H V IL ,C .: D igital S im ulation o f the D yn am ic P rop erties o f E lectrom ech a
n ical S y stem s D rive o f M achine, doct. th esis T U B rno 1990.
[3] V A N B R U S S E L ,H .,JA N K O V S K I,K.: M athem atical M odels for S y stem D yn am ics and C on troll, in: C om p uter Controlled M otion, H everlee, B elgium 1992.
[4] Z A D E H ,L .:T h e C oncent o f S ta te in S ystem Theory, in: V iew s on G eneral S y stem s T heory, W illey, N ew York 1964.
[5] K R A T O C H V L ,C . and others : Som e Problem s o f D yn am ic o f E lectrom echanical D rive S y stem s, R esearch R ep. N o M -7 /9 0 , Inst, of M ech. o f Solids T U B rno 1990.
R ecenzent: Prof. dr hab. in ż.E u gen iu sz Sw itoński W p ły n ęło do Redakcji w grudniu 1993 r.
Streszczenie
A n alizę dyn am ik i sy stem ó w napędow ych kom plikuje fakt, że oprócz zjawisk c zy sto m e
chanicznych m am y do czyn ien ia ze zjawiskam i elektronicznym i, hydraulicznym i i innym i.
D od atkow o, w przypadku napędów sterow anych, m usim y brać pod uw agę przep ływ info
rm acji w sy stem ie. O dpow iedzi n a w iele pytań d otyczących w łasności now ych urządzeń nap ęd ow ych , ich zachow ań w rozm aitych sytu acjach (na przykład aw aryjnych) m ożn a u zy
skać przez sym u lację nu m eryczną. W pracy przedstaw iony jest konkretny przykład ana
lizy d yn am icznej w alcarki do drutu, napędzanej czterem a silnikam i elek tryczn ym i. W zięto pod uw agę różn e m ożliw ości sterow ania silnikam i. Z am odelow ane nieliniow ości (lu zy ) w sprzęgłach generu ją chaos determ inistyczny, m ożliw y do zaobserw ow ania n a płaszczyznach fazow ych.
