Oscillatory Motion Application of Tubular Linear Permanent Magnet Machine

Transcription

1 Osillaory Moion Aliaion of Tubular Linear Permanen Magne Mahine Absra-Tubular linear ermanen magne mahine wih gas srings using for drilling aliaions is resened. This mahine has he advanage of direly ransmiing eleri ower o rok wihou gears. In his aer, mahemaial model wih hammering effe is esablished and dynami roess of osillaory moion is analyzed. Simulaion resuls show ha his mahine is suiable for drilling aliaion. Shujun Zhang, Lars Norum, Rober Nilssen Dearmen of Eleri Power Engineering Norwegian Universiy of Siene and Tehnology Shujun.Zhang@elkraf.nnu.no I. INTRODUCTION Tubular linear ermanen magne mahines are being inreasingly emloyed in many indusrial aliaions, suh as linear omressor, elevaor door, and indusrial robo [1]- [3]. These mahines have signifian advanages in erms of good dynami haraerisi, high effiieny, and oimal fore aabiliy. The osillaory moion of ubular linear ermanen magne mahines (TLPMMs) is roosed in his aer. I an be effeively uilized in demanding drilling aliaions for offshore oil indusrial. The roosed TLPMM wih wo gas srings is used as linear hammer, eseially for hard rok drilling wih drilling fluid. This mahine an direly ransmi ower from eleri soure o rok wihou mehanial equimens like gears, bearings, driving shaf, and so on. The TLPMM used in his ase has been inrodued in [4], [5]. This aer deals wih dynami analysis of osillaory moion wih hammering effe. II. TOPOLOGY OF TLPMSM Fig.1 shows he TLPMM rooye buil for drilling aliaion in offshore oil indusry. Main ars of TLPMM are lised as follows: a) Shaf: I is used o hold he whole drilling sysem inluding eernal sring, asing and he omonens inside asing; b) Eernal sring: Shaf is onneed wih asing by using he eernal sring. I is a key ar of mass-sring-damer sysem. Here, mass, sring and damer are mass of asing, eernal sring and friion beween asing and surroundings reseively; ) Casing: Casing rovides boh a frame for saor winding and a lubriae surfae for ison. I has wo ends whih are used o seal he whole uni; d) Permanen magne: hey are made u of many laminaes of ermanen magne and used o rovide he magnei field for saor winding; e) Iron: I is a ar of magnei irui; f) Saor winding: I is an engine oil for he whole sysem. I ushes ison when he saor winding is arrying urren; Fig.1. Tubular linear ermanen magne mahine g) Gas srings: The sysem has wo idenial gas srings. They are imoran ars for inner mass-sring-damer sysem. Here, mass, sring and damer are mass of ison, gas srings and friion beween ison and asing reseively. Inner srings are u in he hambers for keeing ison in he ener osiion; h) Drill bi: I is a ar of asing and used o hi rok. Rok under he drill bi ollases if he energy from asing o rok is big enough. The equivalen model of TLPMM is shown in Fig.. For he urose of simlifiaion, we use damers and equivalen sring o denoe he friions and ombinaion of gas srings and inner srings reseively. Therefore, we have wo masssring-damer subsysems wih same naural frequeny: one is ison-gas srings-damer subjeed o eleromagnei fore, anoher is asing-eernal sring-damer subjeed o he ne fore from ison-gas sring-damer subsysem and ouner fore from rok. The whole sysem has a onsan seed o rok in order o ge oninuous hiing. Tha is o say, eah ollision an make more sae beween drill bi and rok. The whole sysem moves down a lile o over his sae suh ha ne ollision will ome o he new surfae of rok a he aroriae oin. We define middle oin of he ison as he origin for asing and ison and hoose osiive direion for dislaemen of asing and ison as shown in Fig.. Fig.3 shows an equivalen irui of saor winding. The bak EMF will ome abou when he relaive movemen beween ison and asing ours.

2 v Fig.4. Charaerisi urve of gas srings Fig.. Equivalen model of ubular linear ermanen magne mahine is R us u emf Fig.3. Equivalen eleri irui III. MATHEMATICAL MODEL For he urose of simlifiaion of analysis, he assumions are as follow: Temeraure effes are negligible. No leakages beween wo gas hambers. Comleely inelasi ollision ours beween drill bi and rok. Negleing graviy. Flu densiy is onsan and eleromagnei fore is only he funion of urren. Sai friion and oulomb friion are negleed. Visous friion is only aken ino onsideraion. Gas sring has he haraerisi of PV Consan. Aually, gas srings are nonlinear omonens shown in Fig.4. The haraerisi equaion is y g y g fgas y A. (1) yg y yg y A is ross-seion of gas hamber, iniial ressure of gas srings, yg lengh of eah hamber, and y dislaemen of ison from he origin. Gas srings an be aken as linear omonens when he sroke lengh of ison is small enough omared wih he lengh of gas sring. Therefore, he blue line hrough oeraing oin A and B in Fig.4 is used o model he gas srings in his ase. The haraerisi funion is fgas y y. () is equivalen siffness oeffiien. k es L The ison is subjeed o hree fores shown in Fig.5: 1) eleromagnei fore; and ) friion fore beween ison and asing; and 3) sring fore. Using Newon s seond law of moion, we an wrie he equaion in he verial direion as m y fne feb y y. (3) y y y is ison veloiy relaive o asing, y y y ison dislaemen relaive o asing, y dislaemen of ison, y dislaemen of asing. Casing is subjeed o four fores shown in Fig.6: 1) ouner fore from ison-gas sring-damer subsysem; and ) friion fore beween asing and surroundings; and 3) eernal sring fore; and 4) fore from rok due o ollision. Using Newon s seond law of moion, we obain he moion equaion in he verial direion as: m y fne fne ke y b y d f is eernal sring fore, b y ke y friion fore beween asing and surroundings, d f a ouner fore 1 during ollision from rok due o ollision, d. noollision The eleromagnei fore is obained from Lorenz fore equaion. is e s fe (4) f Bl i (5) is urren in saor winding. y y b y fne fe Fig.5. Fore analysis for ison

3 b y y d f fne e Fig.6. Fore analysis for asing k y By using Kirhhoff s volage law (KVL) for he irui in Fig.3, he volage equaion is obained as follows: dis us Ris L uemf (6) d u bak us is inu volage of saor winding. emf EMF in he saor winding due o relaive moion beween ison and saor winding. Using Faraday s Law, bak EMF is u Bly B DNy. (7) emf 1 y, y, 4 y, 5 is Defining sae sae variable:, 3 y and olleing ()- (7), he sae sae model of TLPMM is 1 b b BND 1 1 m m m m m us d k b es k b e b BND f. (8) 4 4 m m m m m m BND BND R L L L L In his ase, we assume ha: 1) he omleely inelasi ollision ours; and ) he fore due o ollision is onsan during he eriod of ollision. The law of onservaion of momenum gives: if he ne eernal fore aing on a sysem is zero, hen he momenum of he sysem is onsan. We use i in his ase. f d f T (9) f is onsan, differene of momenum during ollision. m vafer m vbefore (1) The ouner fore f in (8) an be obained by using (9) and (1). IV. DYNAMIC PROCESS ANALYSIS The inu volage is sinusoidal volage. Is amliude is 1V and frequeny of he inu volage is he same as naural frequeny of ison-gas sring-damer sysem for simulaions. Only omleely inelasi ollision ours in simulaion. Therefore, he energy ransfer equaion is m yb ke yb m ya ke ya W ol 1 m y b is kinei energy sored in asing before 1 ollision, ke yb oenial energy sored in eernal sring 1 before ollision, m y kinei energy sored in asing a 1 afer ollision, ke ya oenial energy sored in eernal sring afer ollision, W ol energy ransferred o rok during ollision. The lef-hand side of (11) is he energy sored in he sysem before ollision. The righ-hand side of (11)is he energy afer ollision. Only kinei energy is ransferred o rok during ollision. Poenial energy is ke in he sysem and has no dire onribuion o he ollision. The shaf mus move o he aroriae oin in order o ge effiien energy ransfer. The ideal ollision oin is o make yb. And hen, all energy sored in sysem is kinei energy. So, he energy ransfer funion is 1 m y b Wol. (1). (11) Therefore, he energy ransfer has he highes effiieny based on moion of asing. Simulaion resuls are shown in Fig.7-Fig.9 for he ideal ollision oin. Eah eriod is divided ino hree hases shown in Fig.7-Fig.9 aording o he moion of asing:

4 Fig.7. Veloiy and dislaemen of asing beween drill bi and he surfae of rok shown in Fig.7 (b). The hanges influene of veloiy and dislaemen of asing is inrodued o veloiy and dislaemen of ison relaive o asing shown in Fig.8 when omared wih no load oeraion. Therefore, bak EMF and urren hange aording o (6) and (7) shown in Fig.9. Main ar of energy sored in asing is ransferred o rok. Fraional ar energy is resored in eernal sring for he sake of small dislaemen of asing during his eriod. TLPMM is drawing energy from eleri soure. Phase : Drill bi sos a he insan of 1 and kees on ouhing on he surfae of rok from 1 o beause asing is subjeed o he ne fore from mass-gas srings-damer subsysem, whih is in he downward direion and bigger han zero. Relaive veloiy and dislaemen of ison equals o is absolue values beause of sandsill asing. Pison omes ino normal moion wihou influene from asing. Bak EMF and urren are shown in Fig.9. TLPMM is drawing energy from eleri soure and does no ouu energy ee for overing losses. Phase 3: Drill bi oeraes a free osillaion mode from o 3. The whole sysem draws energy from eleri soure. The inu energy during his eriod is divided ino wo ars: one main ar is sored in he sysem rearing for ne ollision; anoher ar is overing he losses. V. TESTING BENCH The esing benh is shown in Fig. 1 and measuremens of TLPMM rooye arameers are shown in Table I. Resisane and induane are measured a 5Hz from Fluke PM636. Fig.8. Relaive veloiy and dislaemen of ison Fig.9. Inu volage, bak EMF and urren in saor winding Phase 1: Collision ours a he insan of and lass from o 1. During his eriod, veloiy of asing dereases from highes value o zero shown in Fig.7 (a) beause ouner fore f due o ollision as on asing. Drill bi ma more sae Fig. 1. Tesing benh for rooye

5 TABLE I TLPMM PROTOTYPE PARAMETERS Parameer Value Uni Flu densiy around saor winding ( B ) *.4 T Diameer of hamber( D ) **.476 m Number of urns of saor winding ( N ) 157 Period of ollision * ( T ).5 s Mass of ison( m ) ** 1.68 kg Mass of asing( m ) ** 5.14 kg Friion oeffiien beween ison and asing ( b ).5 Friion oeffiien beween asing and surroundings( b ).1 Siffness oeffiien of equivalen sring( k ) *** es 7.93*1 4 N/m Siffness oeffiien of eernal sring( k.578*1 4 N/m ) e Resisane of Coil( R ) 1. Induane of Coil( L ).119 H * esimaion ** measuremen *** siffness oeffiien of gas srings is roorional o he sroke lengh of ison shown in Fig.4. Masses of ison and asing are measured from weighomeer. Siffness oeffiiens of srings is measured by using F k y F is fore, y is dislaemen. If wo mass-sringdamer subsysems have same frequeny he maimum sroke lengh of asing is obained. Bu frequeny of mass-gas sring-damer subsysem is roorional o sroke lengh of ison in Fig.4. There is a onradiion beween leakage of gas and friion of ison. We have o omromise beween leakage and friion. Therefore, he osillaory frequeny varies from Hz o 45Hz. VI. CONCLUSION Osillaory moion of ubular linear ermanen magne synhronous mahine is analyzed by using mahemai model wih hammering effe in his aer. More eerimenal resuls will be given in fuure work. Simulaion resuls show ha eleri ower is ransmied o rok during omleely inelasi ollision eriod. The ower ransfer an our wih a high effiieny wihou gears. This mahine an work as a linear hammer for drilling aliaion in oil indusrial. REFERENCES [1] J. Wang,; Z. Lin, D. Howe, Analysis of a shor-sroke, single-hase, quasi-halbah magneised ubular ermanen magne moor for linear omressor aliaions, Eleri Power Aliaions, IET, Volume, Issue 3, Page(s):193, May 8 [] X. Liu, Y. Ye, Z. Zheng, Q. Lu, A novel ubular ermanen magne linear synhronous moor used for elevaor door, Elerial Mahines and Sysems, 7. ICEMS. Inernaional Conferene on. Page(s):81 84,8-11 O. 7 [3] H. Lu, J. Zhu; Y. Guo, Z. Lin, A miniaure shor sroke ubular linear auaor and is onrol, Elerial Mahines and Sysems, 7. ICEMS. Inernaional Conferene on. Page(s): , 8-11 O. 7 [4] R. B. Ummaneni, R. Nilssen, J.E. Brennvall, Fore Analysis in Design of High Power Linear Permanen Magne Auaor wih Gas Srings in Drilling Aliaions, Eleri Mahines & Drives Conferene, 7.IEMDC 7 IEMDC '7. IEEE Inernaional Volume,1, Page(s):85 88, 3-5 May 7. (13) [5] S. Zhang, L. Norum, Modeling and Conrol for Tubular Linear Permanen Magne Synhronous Mahines wih Gas Srings in Drilling Aliaions, Elerial Mahines and Sysems, 8. ICEMS. Inernaional Conferene on. Page(s): , 17- O. 8