Multi-domain Unified Modeling of High Speed Motorized Spindle Water Cooling System Based on Modelica

Transcription

1 Int'l Conf. Modling, Sim. and Vis. Mthods MSV' Multi-domain Unifid Modling of High Spd Motorid Spindl Watr Cooling Sstm Basd on Modlica Chao Ni, Zhihua Li, Huii Zng School of Mchanical Enginring, Hanghou Diani Univrsit, Hanghou , Zhjiang, China Abstract: To build a modl with high accurac and bttr rusabl abilit for th high spd motorid spindl watr cooling sstm (HSMS-WCS), a multi-domain unifid modling mthod basd on Modlica was proposd. Aftr obtaining th coupling block diagram basd on th analsis of th HSMS-WCS, thrmal analsis of th high spd motorid spindl (HSMS) wr applid to calculat its hat powr and hat transfr powr. Thn a multi-domain unifid modl basd on Modlica for th HSMS-WCS was finall built. Furthr mor, influncs of th cooling sstm initial tmpratur and its channl sction axial si to th spindl tmpratur ris wr discussd rspctivl. Rsults show that th proposd modl can bttr rflct th complx coupling rlationship btwn th subsstms of th HSMS-WCS and gt a good simulation rsults. Kwords: watr cooling sstm; multi-domain unifid modling; coupling rlations 1 Introduction HSMS has bn widl usd in high grad CNC machin tools. As th cor componnt of th machin tool, its working prformanc has an important ffct on th machining accurac. Usuall spindl motor is built in th HSMS, so its hat dissipation condition is poor. Du to th significant importanc of rasonabl spindl tmpratur ris[1-], it is ncssar to carr out a comprhnsiv analsis on th HSMS-WCS and build its modl to provid a usful rfrnc for th lattr optimiation dsign. Th modling mthod for th HSMS-WCS is of grat significanc, scholars had mad lots of rsarchs on it. It can b roughl dividd into two catgoris: th first was just for on singl fild and much attntion was paid to this catgor. Chn t al. [3] had a 3D simulation and analsis of th xprimnt b Anss CFX and thn undrtook a comparison for th tmpratur ris of th spindl undr th conditions of diffrnt working conditions and nvironmnt tmpratur. H t al. [4] had usd finit lmnt mthod to charactri th hat distribution of th HSMS and th final analsis showd that tmpratur ris could b significantl rducd with th application of cooling sstm. Rui t al. [5] had studid th diffrnt cooling ffcts for th HSMS-WCS undr various working conditions with th us of orthogonal tst mthod and thn obtaind th rlationship btwn th coolant flow rat and spindl tmpratur ris. Th waknss of th first catgor was basd on th fact that dnamic prformancs of th HSMS-WCS wr dcidd b th coupling rlations of diffrnt subsstms. If th natural coupling rlations btwn ach subsstm wr sparatd, that ma lad to low prcision and can not rflct th corrction of th modl. Th scond catgor was that diffrnt subsstms of collaborativ simulation wr ralid through th intrfac tchnolog btwn diffrnt softwar, but it can rsult in poor coupling rlations as a rsult of th difficult with achiving a samlss data transfr dspit th fact that it can solv th problm to som xtnt. Such kinds of paprs ar as followsford motor compan had utilid ADAMS and Xmath to acquir th simulation modl of Vhicl attitud control sstm[6]; Viston compan using ADAMS and MATLAB softwar to dvlop torqu controllr[7]tc. Such abov mthods nd to b rbuilt whn th modl was locall modifid and th similar modl can not b usd bfor, which mad th modl lss fficint. This is th problm of poor rusabl abilit for th modl.

2 10 Int'l Conf. Modling, Sim. and Vis. Mthods MSV'16 In summar, it is still to b improvd in modl prcision and rusabl abilit. In this papr, a multi-domain unifid modling mthod basd on Modlica[8] was prsntd. This languag is a kind of multi-domain unifid modling languag basd on quations, in which all th modls ar stablishd b on languag, so that th coupling btwn th subsstms can b ralid and th modling fficinc is high. B using th MWorks[9] softwar basd on Modlica languag, th samlss connction btwn th subsstms of th HSMS-WCS can b rachd and th problms causd b th intgration of diffrnt softwar can b ovrcom. At last, a multi-domain unifid modl was obtaind with high accurac and bttr rusabl abilit, which is an innovativ mthod. Channl structur and coupling subsstm, but also subjctd to th impact of othr subsstms that hav th coupling rlations. Thrfor th global coupling analsis of th HSMS-WCS should b carrid out bfor building a multi-domain unifid modl. Firstl, ach subsstm that influncs th HSMS-WCS should b clarl dfind; Thn th global coupling rlations of th HSMS-WCS was dcomposd into svral subsstms which hav local coupling rlations, so that ach subsstm can indpndntl accomplish thir phsical functions; Aftr that, th coupling paramtrs and th phsical rlationship wr discussd btwn th subsstms. At th nd, all th subsstms wr connctd b a spcific intrfac to form a global coupling block diagram. It is givn in Fig.. Cooling sstm analsis.1 Structur of cooling channl Spindl sstm Baring sstm Spindl motor built in th HSMS with spiral cooling channl was prsntd in this papr. Th built-in motor is locatd in th middl of th watr cooling sstm and th powr loss is convrtd into hat to hat this ara. Cooling sstm of th HSMS gnrall adopts th circulating watr containing additiv, corrsponding to th piplin and tmpratur control dvic. Th coolant circulats in th spiral cooling channl that is a rctangular slot. Its cross sctional ara can b xprssd as A. Structur of th cooling channl is as shown in Fig.1. Control sstm Snsor sstm Fig. Global coupling block diagram of th HSMS-WCS As shown in Fig., th HSMS-WCS is involvd in multipl subsstms such as mchanical sstm, control sstm, thrmal sstm and so on, which is a multi-domain modling problm. 3 Thrmal analsis for th HSMS Without taking into account th production of cutting hat from th machining procss, spindl sstm mainl includs two kinds of hat sourcs. Th formr is from th spindl motor and th lattr is from th spindl barings. 3.1 Hating powr of th spindl motor Fig.1 Structur of th cooling channl. Coupling analsis Prformanc of th HSMS-WCS is not onl dtrmind b svral input paramtrs of singl Th hating of th spindl motor is drivd from th powr loss of motor, which mainl includs mchanical loss and lctrical loss Mchanical loss Mchanical loss is causd b th friction loss btwn th rotor and air whn th rotor is running at

3 Int'l Conf. Modling, Sim. and Vis. Mthods MSV' high spd. It is dfind as: (1) pm cc 1 D L pm is mchanical loss w, c is th 1 that is M M M (4) M m f Fd (5) cofficint of flow rsistanc, c is air dnsit rpm, 3 kg / m, is rotor angular vlocit D and L ar th diamtr and lngth of rotor rspctivl m Elctrical loss Th lctrical loss is mainl from th loss btwn th stator coil and rotor, which can b computd as: L P I R I c () S p is lctrical loss w, currnt A, I is stator coil c is lctrical conductivit of coil, total lngth of th coil m, coil m. L is S is sctional ara of th 3. Hating powr of th spindl baring Hating powr of th angular contact ball barings is mainl from loss du to baring friction torqu, which can b calculatd as: pf baring M (3) p f is hating powr of th spindl w, is rotor angular vlocit total friction torqu Nmm. rpm, M is Th baring friction torqu is mainl composd of two parts. On is th torqu th othr is th torqu M du to applid load and M du to viscosit of lubricant, M is load friction torqu Nmm, factor rlatd to th baring tp and load, f is a F is baring prloadn, d is man diamtr of th baringmm. m 3 M f v n d v n (6) m, 000 M f d v n (7) m, 000 M Nmmis viscous friction torqu of th angular contact ball barings, it is gnratd b th rlativ friction among th rolling lmnts of th baring, th cag, and th lubricant, baring tp and lubrication mthod, viscosit of th lubricant mm f is a factor rlatd to / v is kinmatic s, n is th baring angular vlocitrpm,whn vn 000, formula (6) can b usd and vn 000, formula (7) can b usd. 3.3 Convctiv hat transfr of coolant In addition to th influncs of ths two hating powrs, th HSMS-WCS prformancs ar also affctd b th hat convction of cooling sstm. In ordr to mak th rsarch procss simpl and clar, som ncssar simplification and assumptions can b mad. (1) Th main rsarch objct was th cooling sstm, so th rotor, baring and othr parts wr simplifid; () It was assumd that th hating powr producd b th spindl motor and spindl barings was forcd to tak awa through th hat convction, furthr mor, th surrounding natural convction and thrmal radiation was ngligibl. (3) Coolant can not b comprssd and th phsical proprtis ar constant. Thr is no phas chang

4 104 Int'l Conf. Modling, Sim. and Vis. Mthods MSV'16 and it is a continuous bod Convctiv hat transfr cofficint of cooling sstm Cooling sstm uss coolant for cooling, in which th avrag spd of th coolant can b xprssd as follows: vw uw (8) A v w is unit flow rat of coolant l/ s, A is cross sctional ara of th cooling channl m. Convctiv hat transfr cofficint of cooling sstm can b writtn as: a NK u v v (9) dv Nu is Nusslt numbr, Kv is hat conductivit of coolant w/ m k, dv is diamtr of cooling channl m Convctiv hat transfr powr of cooling sstm Th convctiv hat transfr powr of cooling sstm can b calculatd b th convctiv hat transfr cofficint, which can b stablishd as: p a A( t t ) (10) v v v cofficint w/ m 0 av is convctiv hat transfr k, A is cross sctional ara of th cooling channl m, tv is spindl intrnal multi-domain unifid modl for th HSMS-WCS basd on th Mworks softwar was built. Subsstms of th HSMS-WCS includ spindl motor hating modl, baring hating modl, cooling sstm convction modl and PID control modl. Th final multi-domain unifid modl was built on th sam softwar and connctd b a spcific intrfac. 4.1 PID control modl Th tmpratur ris of spindl must b controlld within a rasonabl rang, othrwis it will affct spindl machining accurac. In this papr, PID control sstm was adoptd to control th tmpratur ris. PID control quation is as follows: ukp t tdtt d t 1 t 0 d T (11) i dt t is th input signal, it is dfind as: t NT NT (1) d t is th input signal, oprating tmpratur, tmpratur, K p, T i, Td NTd is th dsird NT is th actual oprating ar th control paramtrs. Th working procss of PID controllr was brifl as follows: Th tmpratur snsor dtctd th actual oprating tmpratur. Through fdback, th input signal was transmittd to th PID controllr. Th adjustd currnt signal was output to th cooling sstm modl aftr tratmnt, which mad th tmpratur ris in a rasonabl valu. PID control modl basd on Modlica is shown in Figur.3. tmpratur k, t0 is initial tmpratur of coolant k. 4 Multi-domain unifid modling of th HSMS-WCS Considring th complx coupling rlations, a Fig.3 PID control modl 4. Hating powr modl and convctiv hat transfr powr modl

5 Int'l Conf. Modling, Sim. and Vis. Mthods MSV' Th hating powr modl of th HSMS-WCS consistd of two parts: on for th spindl motor and th othr for th spindl barings, which can b built in Mworks b mathmatical modl rspctivl. Convctiv hat transfr powr modl was also modlld b its mathmatical modl whos function is to tak th hat awa. Aftr th two modls wr finishd, a coupling modl basd on Modlica was built, which is shown in Figur. 4. Figur.4 Coupling modl 4.3 Intgratd modl of th HSMS-WCS Using Modlica languag to construct modls at Mworks platform, ach sub-modl is indpndnt of ach othr on dscribing th phsical charactristics and mathmatical rlations. In ordr to nsur th rusabl abilit of sub-modls, ach sub-modl has its own input and output connctors to input paramtrs and communicat with othr sub-modls. Manwhil, a sub-modl can b composd of othr sub-modls and componnts b packaging, which is th multi-lvl modling mthod. In this papr, th hating powr modl, convctiv hat transfr powr modl and control modl wr packagd rspctivl and thn connctd b spcific intrfac. Thrfor th multi-lvl modling mthod has th advantags of clarl organid, bttr rusabl abilit and high modling fficinc tc. Th procss of intgratd modling was as follows: At first, th tmpratur snsor modl obtaind th actual oprating tmpratur of spindl sstm and thn th signal diffrnc btwn NTd and NT was fd back to th PID control modl. Finall NT can rach a rasonabl valu whn th output currnt control signal was transmittd to th PID control modl. B packaging and conncting all of th sub-modls at Mworks, th intgratd modl was obtaind and shown in Figur.5. Figur.5 Intgratd modl of th HSMS-WCS 5 Simulation analsis of th HSMS-WCS Tpicall, th HSMS-WCS can rach th cooling ffct b controlling th rat of coolant flow, but such kinds of rsarchs ar mor. Prvious rsarchs [10-11]

6 106 Int'l Conf. Modling, Sim. and Vis. Mthods MSV'16 indicatd that: th tmpratur ris of spindl dos not mak significant chang whn coolant flow rat incrass to a crtain thrshold, thrfor th mthod ma not rach th dsird goal in somtims. Basd on th abov, this papr had xplord th othr two factors affcting th tmpratur ris of spindl. 5.1 Th factor of initial tmpratur t 0 To invstigat th ffcts on th spindl tmpratur ris, paramtrs rlatd to th initial tmpratur wr input to th proposd modl undr th conditions of kping th spindl angular vlocit and coolant flow unchangd. At th sam tim, anothr two traditional modls including Anss mthod and Simulink mthod wr usd to compar. Finall, th simulation rsults ar as shown in Figur. 6. spindl tmpratur ris dcrass with graduall dcrasing th initial tmpratur; () whn compard to anothr two traditional modls, th prsntd modl can acquird th similar simulation rsults. This can nsur that th modl built b multi-domain unifid modling mthod is right. Furthr mor, it has a bttr rusabl abilit whn compard to th modl b Anss and can mak it mor fficint to build a simulat modl. Simulink mthod has th difficult to achiv a samlss data transfr. This waknss can lad to a low prcision for th modl built. Whil th proposd mthod is basd on Modlica languag, it can rach th samlss connction btwn th subsstms, nsuring a high accurac modl. 5. Th factor of channl sction axial si L Not onl is th spindl tmpratur ris rlatd with coolant initial tmpratur, but also associatd with th channl sction axial si L. Similar to th mthod abov 5.1, th rlatd initial paramtrs kp constant and th channl sction axial si L changd without changing th chang cross-sctional ara A. Th channl sction axial si L is shown in Tabl 1 and th final simulation rsult is as shown in Figur.7. Figur.6 Initial tmpratur ffct on th spindl tmpratur ris Figur.6 can b obtaind: (1) th spindl tmpratur ris is influncd b th initial tmpratur and th Tabl 1 Channl sction axial sil (mm) Channl sction axial si L Figur.7 shows that channl sction axial si L has influnc on th spindl tmpratur ris and th spindl tmpratur ris dcrass with graduall incrasing th channl sction axial si L. 6Conclusions Figur.7 Channl sction axial si ffct on th spindl tmpratur ris Whn constructing modl of th HSMS-WCS, it was gnrall dividd into two catgoris. On is th modling mthod for on singl fild and th othr is th mthod for multi-domain intgration. It is not suitabl to us th first catgor, bcaus it sparats th natural

7 Int'l Conf. Modling, Sim. and Vis. Mthods MSV' coupling rlationships btwn subsstms, which can not rflct th complx coupling rlations. Th scond catgor ma lad to problms such as poor coupling rlations and low prcision dspit th fact that it can rali multi-domain unifid modling for multipl subsstms to som xtnt. A multi-domain unifid modling mthod basd on Modlica was prsntd in this papr. At first, th complx coupling rlations among subsstms of th HSMS-WCS wr anald and th coupling block diagram was obtaind; thn th thrmal analsis of th HSMS was carrid out. Basd on this, a multi-domain unifid modl of th HSMS-WCS was built and th simulation rsults wr anald. Th final rsults show that th mthod basd on Modlica can ffctivl ovrcom th problms brought b th prvious mthod and mak th modl mor accurat and suitabl for th modling and simulation of complx mchanical and lctrical products. Acknowldgmnts This stud was supportd b National Natural Scinc Foundation of China (Grant No ). Rfrncs [1] Moorth, R.S.; Raja, V.P.: An improvd analtical modl for prdiction of hat gnration in angular contact ball baring. Arabian Journal for Scinc and Enginring.39(11), (014) [] Bian, W.; Wang, Z.H.; Yuan, J.T.: Thrmo-mchanical analsis of angular contact ball baring. Journal of Mchanical Scinc and Tchnolog. 30(1), (015) [3] Chn, W.H.; H, Q.C.; H, Q.: Simulation and Exprimntal Analsis for High- spd Spindl with Watr- cooling Sstm. China Mchanical Enginring. 1(5), (010) [4] H, Q.; Zhang, Y.; Y, J.: Thrmal charactristics of high spd motorid spindl with hlical watr cooling channl. Rcnt Patnts on Mchanical Enginring. 5(1), (01) [5] Rui, Z.Y.; Chn, T.; Li, C.L.: Simulation analsis for watr cooling sstm of high-spd motorid spindl basd on CFX. Machin ToolHdraulics. 4(7), 4-8 (014) [6] BMS. Co-simulation boosts vhicl dsign fficinc at ford. Computr Aidd Enginr, 1999, 18(7):8-9. [7] C.S. Liu, V. Monkaba, t al. Co-simulation of Viston drivlin torqu bias controls. Adams Usr Confrnc 001-North Amrica, Dtroit, USA, 001:48. [8] Zhao, J.J.; Ding, J.W; Zhou, F.L.: Modlica and its mchanism of multi-domain unifid modling and simulation. Journal of Sstm Simulation. 18(), (006) [9] Wu, Y.Z.; Wu, M.F; Chn, Y.P.: Stud on th hbrid modling platform basd on Modlica languag for complx machinr sstm. 17(), (006) [10] Zhang, J.F.; Fng, P. F.; Chn, C.; Yu, D.W.: A mthod for thrmal prformanc modling and simulation of machin tools. Th Intrnational Journal of Advancd Manufacturing Tchnolog. 68(5), (013) [11] Yang, S.Y.; Gao, X.H.; Liu, X.X.: Simulation on solid-fluid coupld hat transfr of watr cooling sstm in high-spd lctro-spindl. Machin ToolHdraulics. 39(11), (011)