Analysis of Tubular Linear Permanen Magne Moor for Drilling Appliaion Shujun Zhang, Lars Norum, Rober Nilssen Deparmen of Eleri Power Engineering Norwegian Universiy of Siene and Tehnology, Trondheim 7491 Norway Absra- Tubular linear permanen magne moor wih gas springs using for drilling appliaions is presened in his paper. This moor has he advanage of direly ransmiing eleri power o rok wihou gears. Mahemaial model wih hammering effe is esablished and dynami proess of osillaory moion is analyzed. Dynami response omparison of no load mode and load mode is done. Simulaion resuls show ha his moor is suiable for drilling appliaion. I. INTRODUCTION Tubular linear permanen magne moors are being inreasingly employed in many indusrial appliaions, suh as linear ompressor, elevaor door, and indusrial robo [1-3]. These moors have signifian advanages in erms of good dynami haraerisi, high effiieny, and opimal fore apabiliy. The osillaory moion of ubular linear permanen magne moors (TLPMMs is proposed in his paper. I an be effeively uilized in demanding offshore oil drilling appliaions. The proposed TLPMM wih wo gas springs is suied as linear hammer, espeially for hard rok drilling wih drilling fluid. This moor an direly ransfer power from eleri soure o rok wihou any mehanial equipmens like gears, bearings, driving shaf, and so on. The TLPMM used in his ase has been inrodued in [4, 5]. Eleromagnei fore and flu densiy analysis was given in [4]. This paper deals wih dynami analysis and omparison beween no load mode and full load mode and predis he performane for he drilling appliaion. Fig.1. Prooype of TLPMM oninuous hiing. Tha is o say, eah ollision an make more spae beween drill bi and rok. The whole sysem moves down a lile o over his spae suh ha ne ollision omes o he new surfae of rok a he appropriae poin. We define middle poin of he pison as he origin for asing and pison and hoose posiive direion for displaemen of asing and pison as shown in Fig.. Fig. 3 shows an equivalen irui of saor winding. II. DESCRIPTION OF TLPMM The onep of TLPMM is inrodued in [6]. Fig.1 shows he TLPMM prooype buil for drilling appliaion in offshore oil indusry. The moor onsiss of asing wih saor winding, pison wih permanen magnes, gas spring in eah end of he asing. The saor winding is around he asing made of fibre. The pison is an assembly of laminaed iron disks and permanen magnes. Gas springs sand a eah end of asing. The equivalen model of TLPMM is shown in Fig.. For he purpose of simplifiaion, we use equivalen spring and dampers denoe gas springs and he friions respeively. Therefore, we have wo mass-spring-damper subsysems wih same naural frequeny: one is pison-gas springs-damper subjeed o eleromagnei fore, anoher is asing-eernal spring-damper subjeed o he ne fore from pison-gas spring-damper subsysem and ouner fore from rok. The whole sysem has a onsan speed o rok in order o ge III. MATHEMATIC MODEL OF TLPMM By using linearizaion for gas springs, is haraerisi funion is gas f y k y. (1 es k es is equivalen siffness oeffiien. The pison is subjeed o hree fores shown in Fig. 4. Using Newon s seond law of moion, we an wrie he equaion in he verial direion as m y f f b y k y. ( p p nep e p es is pison veloiy relaive o asing, y y y p
y y bp y fe fnep Fig. 4. Fore analysis for pison v b y e k y Fig.. Equivalen model of TLPMM fnep y is R L us u emf d f Fig. 3. Equivalen eleri irui of saor winding y yp y y displaemen of pison, y p pison displaemen relaive o asing, displaemen of asing. Casing is subjeed o four fores shown in Fig. 5. Using Newon s seond law of moion, we obain he moion equaion in he verial direion as: m y fne f k y b y df nep e ke y is eernal spring fore, b y friion fore beween asing and surroundings, d f ouner fore 1 during ollision from rok due o ollision, d=. f 0 no ollision an be obained by applying law of onservaion of momenum in his ase. The eleromagnei fore fore equaion. fe (3 is obained from Lorenz is Fig. 5. Fore analysis for asing is urren in saor winding. 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 (5 d us is inpu volage of saor winding. uemf bak EMF in he saor winding due o relaive moion beween pison and saor winding. Using Faraday s Law, bak EMF is emf u Bly B DNy (6, Defining sae spae variable: 1 yp y p, 3 y, 4 y, 5 is and olleing (1 -(6, he sae spae model of TLPMM is e s f Bl i (4
0 1 0 0 0 0 0 bp b p BND 1 1 0 0 mp mp mp mp mp 0 0 0 0 0 1 0 3 3 us d k b 0 es p k b e b p BND f. (7 4 4 m m m m m m 5 5 1 BND BND R 0 0 0 L L L L In his ase, we assume ha: 1 he ompleely inelasi ollision ours, and he fore due o ollision is onsan during he period 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 p (8 f is onsan, p differene of momenum during ollision. afer before p m v m v (9 The ouner fore f in (3 an be obained from (8 and(9. IV. COLLISION ANALYSIS FOR TLPMM The TLPMM prooype parameers are shown in Table I. The inpu volage is sinusoidal volage. Peak value of inpu volage is 1V and frequeny of he inpu volage is he same as naural frequeny of mass-spring-damper sysem. Only ompleely inelasi ollision ours in simulaions. Therefore, he energy ransfer equaion is 1 1 1 1 m yb ke yb m y a ke ya Wol. (10 1 m y b is kinei energy sored in asing before 1 ollision, ke yb poenial energy sored in eernal spring 1 before ollision, m y kinei energy sored in asing a 1 afer ollision, ke ya poenial energy sored in eernal spring afer ollision, W ol energy ransferred o rok during ollision. The lef-hand side of (10 is he energy sored in he sysem before ollision. The righ-hand side of (10is he energy afer ollision. Only kinei energy is ransferred o rok during ollision. Poenial energy is kep in he sysem and has no dire onribuion o he ollision. The ideal ollision poin is o make y 0 b. And hen, all energy sored in sysem is kinei energy. So, he energy ransfer funion is 1 m y b Wol. (11 Therefore, he energy ransfer has he highes effiieny based on moion of asing. We define ha TLPMM operaes a full load mode if every ollision ours a his poin. TLPMM an operae a differen modes aording o differen ollision poin. By omparing he no load mode wih full load mode, he dynami proess of ollision is shown in Fig.6-Fig.10. A. Eleri power analysis The inpu power only overs losses and TLPMM behaves as an induive load in he no load mode shown in Fig.6- Fig.7. Collision, whih ours a ideal poin, inrodues he phase shif beween inpu volage and inpu urren ompared wih no load mode. Mos energy sored in TLPMM ransfers o rok during ollision. Eleri soure inpus power and TLPMM sores energy during he period beween wo ollisions. B. Casing moion analysis Casing osillaes a no load mode shown in Fig.8 (a. Rok ries o sop asing when he drill bi ouhes rok. Veloiy of asing dereases from he highes value o zero during ollision shown in Fig.8 (b. Kinei energy is ransferred o rok and rok ollapses. Collision ma a small spae beween drill bi and rok afer small roks ollapsed TABLE I TLPMM PROTOTYPE PARAMETERS Parameer Value Uni Flu densiy ( B 1. T Diameer of hamber( D 0.04 m Number of urns of saor winding( N 100 Period of ollision( T 0.005 s Mass of pison( mp 0.950 kg Mass of asing( m 1.100 kg Friion oeffiien beween pison and asing( bp 0.005 Friion oeffiien beween asing and 0.0001 surroundings( b Siffness oeffiien of equivalen spring( 4500 N/m Siffness oeffiien of eernal spring( ke 510.5 N/m Resisane of Coil.35 Induane of Coil 0.003 H
rok during ompleely inelasi ollision period and ollision inrodues he phase shif beween inpu volage and inpu urren. The power ransfer an our wih a high effiieny wihou gears. This moor an work as a linear hammer for drilling appliaion in oil indusrial. Fig.6. Inpu volage and inpu urren Fig.8. Casing moion analysis Fig.7. Losses and Insananeous inpu power go away. More kinei energy, more spae beween drill bi and rok. C. Fore analysis TLPMM omes ino seady sae in a shor period a no load mode beause i has small friion oeffiiens shown in Fig.9-Fig.10. The driving fore of pison is eleromagnei fore fe. The eleri soure inpus power by driving pison and asing. The driving fore of asing is ne fore fnep from mass-gas springs-damper. This ne fore inpus power o TLPMM by driving asing and ompressing eernal spring. Fig.9. Eleromagnei fore and veloiy of pison V. CONCLUSION Osillaory moion of ubular linear permanen magne synhronous moor is analyzed by using mahemai model wih hammering effe in his paper. Power ransfer proess analysis is done by omparing differen operaion modes. Simulaion resuls show ha eleri power is ransferred o Fig.10. Driving fore and veloiy of asing
REFERENCES [1] J. Wang,; Z. Lin, D. Howe, Analysis of a shor-sroke, single-phase, quasi-halbah magneised ubular permanen magne moor for linear ompressor appliaions, Eleri Power Appliaions, IET, Volume, Issue 3, Page(s:193 00, May 008 [] X. Liu, Y. Ye, Z. Zheng, Q. Lu, A novel ubular permanen magne linear synhronous moor used for elevaor door, Elerial Mahines and Sysems, 007. ICEMS. Inernaional Conferene on. Page(s:801 804,8-11 O. 007 [3] H. Lu, J. Zhu; Y. Guo, Z. Lin, A miniaure shor sroke ubular linear auaor and is onrol, Elerial Mahines and Sysems, 007. ICEMS. Inernaional Conferene on. Page(s:1680 1685, 8-11 O. 007 [4] R. B. Ummaneni, R. Nilssen, J.E. Brennvall, Fore Analysis in Design of High Power Linear Permanen Magne Auaor wih Gas Springs in Drilling Appliaions, Eleri Mahines & Drives Conferene, 007.IEMDC 07 IEMDC '07. IEEE Inernaional Volume,1, Page(s:85 88, 3-5 May 007 [5] S. Zhang, L. Norum, Modeling and Conrol for Tubular Linear Permanen Magne Synhronous Mahines wih Gas Springs in Drilling Appliaions, Elerial Mahines and Sysems, 008. ICEMS. Inernaional Conferene on. Page(s:968 971, 17-0 O. 008 [6] R. Ummaneni, J.E. Brennvall, R. Nilssen, Conep of linear permanen magne auaor wih gas springs in drilling appliaions, The Inernaional Conferene on Elerial Mahines and Sysems, 0-3 Nov. 006