A New Type of Capacitive Machine

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1 Enegy and Powe Engineeing, 015, 7, Published Online Febuay 015 in SciRes. A New Type of Capacitive achine Aie Shenkan, Saad Tapuchi, Dity Baiel Electical and Electonics Engineeing Depatent, Shaoon College of Engineeing, Bee Sheva, Isael Eail: tapuchi@sce.ac.il, ditba@sce.ac.il Received 3 Januay 015; accepted 10 Febuay 015; published 13 Febuay 015 Copyight 015 by authos and Scientific Reseach Publishing Inc. This wok is licensed unde the Ceative Coons Attibution Intenational License (CC BY). Abstact The pape poposes a new type of the synchonous capacitive achine opeated on a pinciple of the electic field effect. The poposed achine has salle size and lighte weight than the standad electoagnetic synchonous achines with the sae ated paaetes. Anothe ipotant advantage is a siple stuctue of the achine, which siplifies the poduction pocess and educes the costs of the oto. The pape also pesents extensive siulation esults of the poposed capacitive achine. The siulation esults show that the poposed achine is able to each the sae powe output as the electoagnetic achines. Keywods Capacitive achine, Electic Field, Toque, Synchonous achine 1. Intoduction Today, ost of the electical achines opeate on the pinciple of agnetic field effect at which the electic enegy is conveted into echanical enegy and vice vesa. The agnetic field is poduced by the cuent flowing in the stato and oto coils. On the othe hand, it is also possible to constuct the electical achines that opeate on the electic field pinciple, whee the electical enegy is stoed in an electic field [1]. It is known that the electic and the agnetic fields ae always linked to each othe and it is ipossible to sepaate the. Howeve, the electic field in the electoagnetic achines is uch weake than the agnetic field, and, pactically, is negligible. The electic achines opeated on the electic field pinciple would have echanical stuctue based on capacitos []-[4] while the echanical stuctue of the electoagnetic achines is based on the inductos. While the developent of the electoagnetic achines has eached the ost advanced state, the electic field achines (capacito achines) eained soehow ignoed. The eason is low electic peittivity-ε of ost dielectic ateials. Howeve, ecently, new dielectic ateials have been developed. These ateials possess elatively high electic peittivity of up to ε = 104. Theefoe, the capacito otos acquie an inteest again. How to cite this pape: Shenkan, A., Tapuchi, S. and Baiel, D. (015) A New Type of Capacitive achine. Enegy and Powe Engineeing, 7,

2 A. Shenkan et al. The geatest difficulty in the developent and poduction of capacitive achines is peventing fiction between the stato and oto plates which occus when the dielectic ateials ae solid. A coon ethod to pevent the fiction is to ensue an ai gap. Howeve, in the capacitive achine this ethod is not suitable because even sall ai gap diinishes the advantages of using dielectic ateial with high dielectic peittivity ε. One possible solution could be to use liquid electic ateials with low density and high values of ε. Anothe possible solution ight be changing the ai gap to plasa, which can be accoplished by using high voltage and a naow ai gap. The ain facto deteining the efficiency of electic powe echaniss fo enegy convesion is the density of the electic o agnetic enegy stoed in the electoagnetic o electic fields. The electoagnetic and electic field achines could be copaed fo the enegy point of view [5] [6]. The enegy density of the agnetic field in electoagnetic achines could be calculated by: w B = (1) µµ whee B is the agnetic flux density of the agnetic field, μ 0 is the agnetic peeability constant 7 ( µ 0 = 4π 10 H/ ) and µ is the agnetic peeability of the ai (in agnetic achines the pocess of enegy convesion occus within the ai gap between the oto and the stato so µ = 1 ). By using the feoagnetic ateials (paticulaly electic steel), the agnetic field of the electoagnetic achines can have agnetic flux density of B = Wb/. The density of the agnetic enegy would be (fo B = 1.4 Wb/ ): w = = W/ () 7 4π 10 The enegy density of the electic field in the electic achines could be calculated by: 1 we = εε oe (3) 1 whee ε 0 is the electic peittivity constant ( ε 0 = F/) and E is electic flux density of the electostatic field. Today s technology allows usage of vey stong electostatic fields, but because of low electic stength of ost insulating ateials, the electostatic field is pactically liited to - 0 V/. Theefoe, in the achine whose opeation is based on the electic field pinciple and in which the pocess of enegy convesion also takes place in the ai ( ε 7 = 1), the enegy density of the electic field, fo E = 10 V/, could be deteined by Equation (4): w e = = 450 W/ (4) Lately, new dielectic ateials have been developed, such as ceaics based on a paatitanite ba, which has 4 a elatively high electic peittivity of up to ε = 10 [F/]. In electic achines, whee the enegy convesion pocess takes place in the new dielectic ateials and not in the ai, the density of the electic enegy could be significantly inceased. 4 7 Fo electic peittivity of ε = 10, the obtained density of the electic enegy, fo E = 10 V/, would be: 0 ( ) ( ) w e = = W/ (5) Such a esult is even geate than the esult obtained with the electoagnetic achines, a fact that encouages developent of new electic achines based on the electic field effect. The electic field achines have seveal advantages upon the electoagnetic achines. The ain advantage is that the electic field achines ae uch salle in size and lighte in weight than the electoagnetic achines with the sae output paaetes. This could be explained by the fact that agnetic foce lines of any electoagnetic achine ae foed in a closed loop. The agnetic foce lines ae foed by the agnetic cicuit, built fo a vey heavy ateial like electic steel. The agnetic cicuit is used fo the powe tansfe, while the enegy convesion pocess takes place in the ai-gap itself (between the stato and the oto). The ai-gap 3

3 A. Shenkan et al. volue is elatively a sall pat of the volue of the whole achine. In the electic field achines, the powe lines of the electic field stat and end in electic chages, i.e. the oto and stato plates. The enegy convesion pocess takes place in the gap between the stato and oto, which takes up a sizable pat of the volue of the whole achine. Assuing that the specific enegy is equal fo both electic field and electoagnetic achines, the achines based on the electic field effect will be significantly salle. And since the dielectic ateials (e.g. ceaics and plastics) ae uch lighte than the feoagnetic ateials, the electic achines based on the electic field effect will be also lighte. As a esult of these two factos, the poduction of the achines based on the electic field effect will be cheape. Just like agnetic achines, the capacitive achines can be of two kinds, in dependence of the cuent/voltage used fo thei opeation: diect cuent (DC) achines with coutato o altenative cuent (AC) achines: synchonous o asynchonous. Section II shows how the sectoed capacito could be used as a pactical solution fo the DC capacitive achines. Section III pesents the poposed AC capacitive achine based on the sinusoidal capacito. Section IV pesents the siulation esults of the poposed capacitive achine. Section V pesents the conclusions of the pape.. The Sectoed Capacito as a Pactical Solution fo the DC Capacitive achines The siplest DC capacitive achine can be constucted fo a ound capacito having two o oe sectos, as shown in Figue 1. In this achine, two positively chaged otating sectos fo the oto and two negatively chaged static sectos fo the stato. In the position shown in Figue 1, the attactive foce between the stato and oto sectos establishes a oent, which otates the oto on a quate of a cicle until the sectos coincide. At the oent of a coincidence of the sectos, the applied voltage polaity is changed between the positively and negatively chaged sectos. In othe wods, this achine should be constucted with a coutate o (like egula DC achines). If the nube of plates will be inceased, the achine opeation will be soothe. In ode to ensue sooth opeation, at least thee couples of plates should be used. The toques of the capacitive achine could be calculated by diffeentiation of the enegy stoed in the electic field of the capacito [6]. In the case of angula oveent, the diffeentiation is pefoed by an angle α : ( α ) ( α ) V d C = dα whee C ( α ) is vaying capacitance of the capacito plates as function of the oto angle α and V is the voltage applied to the capacito plates (this foula is adequate when the capacito is connected to a powe souce). With the oveent of the oto, the capacitance between the oto and the stato vaies popotionally to the suface of coincidence between sectos. The suface of coincidence between the sectos is popotional to the oto angle α and could be calculated by: (6) Figue 1. DC capacitive achine constucted fo ound capacito with fou sectos. 33

4 A. Shenkan et al. s α = ρ (7) whee ρ is the adius of the plates. The capacitance of the ound capacito with fou sectos (two couples of plates) could be calculated by: ( ) εε 0ρ α C α = (8) d whee d is the distance between the plates. The axial toque of the capacitive achine with thee couples of plates could be calculated by substituting Equation (8) in Equation (6): εε 0ρ V α = (9) d ( ) Equation (9) shows that the oent of this capacitive achine is constant and independent of the oto angleα. The speed of capacitive otos is a function of the supplied powe and the nube of evolutions pe inute could be calculated by = 9.55 ( P). Fo exaple, fo the 130 W oto with insulating ateial which has 4 dielectic peittivity of ε = 10, two couples of plates, the distance between the plates d =, the adius of the plates ρ = 10 c and applied voltage V = 1 kv, the oent will be = 0.44 N. The oto speed will be n = 955 p. 3. The Poposed AC Capacitive achine Based on a Sinusoidal Capacito This pape poposes novel synchonous achine opeating on the pinciple of the electic field effect. The poposed achine is constucted fo a vaiable capacito having static and otating plates. The capacitance be haves as a sinusoidal function and depends on the plates oveent angle. The poposed sinusoidal capacito achine with otating plates (oto) above static plates (stato) is shown in Figue. The plates ae constucted in such a way that thei adius-vecto is dependent on the angle and thei ovelapping suface is a sinusoidal function of the angle. The stato plates ae constucted as standad sectos. This fo allows oe efficient usage of the plate s suface and as a esult, inceases the axiu capacity of the capacito. The vaiable suface of the plates is a function of the α angle and could be calculated by: 1 α S ( α) = ρ ( α) dα (10) 0 On the othe hand, the vaiable suface is sinusoidal and it could be also expessed as: 1 cos( α ) S( α ) = S (11) (a) Figue. (a) The poposed capacitive oto with two otating plates (oto) and two static plates (stato); (b) The poposed capacitive oto with fou otating plates (oto) and fou static plates (stato). (b) 34

5 A. Shenkan et al. whee S is the axiu ovelap suface of the capacito (when the plates of the stato and the oto ae fully ovelapped one above the othe). The vaiable suface vesus the otating angle α is shown in Figue 3. The adius of the capacito plates ρ( α ) could be calculated fo Equations (10) and (11): ( ) sin ( α) ρ α = (1) By using Equation (1), the diaete of the capacito plates could be obtained: S D = ρ = S (13) whee ρ is the axial adius of the otating plates. When the oto plates otates above the stato plates, the capacity of the achine vaies accoding to: ( α ) ( α) S ( α) 1 cos 1 cos = = (14) C C εε 0k d whee d is the distance between the static and the otating plates, ε is the elative electic peittivity of the insulating ateial between the plates, k is the nube of pais of the oto/stato plates and C is the axial capacitance of the achine with k couple of plates. The toque of the capacitive achine could be calculated by the diffeentiation of the enegy stoed in the electic field of the capacito. If the capacito is supplied by the voltage- u, the axial toque of the capacitive achine could be deteined by substituting Equation (14) into Equation (6): Cu ( α) = sinα (15) As it seen fo the Equation (15), if the poposed capacitive achine was supplied by a DC voltage souce, the aveage toque would be zeo. In ode to obtain efficient aveage toque (diffeent than zeo), the applied voltage should be an altenating voltage ( u = U sin ( ωt) ) and the angula speed of the oto should be equal to the angula fequency of the applied voltage. dα The angula velocity could be defined as ω =. Theefoe, the oto angle could be obtained by an integation of the angula velocity: dt δ α = ωt + (16) whee δ is the angle between the stating line ( α = 0 ) of the oto plate and the phase angle of the altenating voltage (see Figue 3(b)). The eaning of the angle δ could be also explained by using a coplex plane having Real and Iaginay axes. The altenating voltage applied to the sinusoidal capacito could be epesented by the otating vecto U, which otates with the angula velocity ω on the coplex plain. The capacito otating plates (oto) ae efeed to the zeo degee line. Theefoe, the δ angle is the angle between voltage vecto U and the oto axis. Figue 3. The vaiable suface of the capacito vesus the angle α. 35

6 A. Shenkan et al. The angula velocity of the oto could be obtained by: ω = ω k (17) whee k is the nube of pais of the oto/stato plates. The speed of the achine in evolutions pe inute (p) could be calculated accoding to the following foula: 60 f n = (18) k whee f is the fequency of the applied AC voltage. The toque of the poposed achine as a function of tie could be calculated by substituting the Equation (16) into the Equation (15): t ( ) sin ( ω ) sin ( ( ω δ ) ) t = CU t t+ (19) CU ( t) = ( 1 cos( ωt) ) sin ( ωt+ δ) (0) CU sinδ sin 4 = + ( ) sin ( ωt δ) The aveage toque, i.e., the effective toque, would be: t π d π 0 ( ω + δ) (1) 1 CU avg = ( t) t = sinδ () The eaning of the inus sign in the foula of toque is that the toque esists otion, i.e. that achine opeates in a geneato ode and the convesion is fo echanical enegy into electic enegy. In the geneato ode, the oto pecedes the altenating voltage (positive δ angle). In the oto ode, whee the δ angle is negative, the oto lags behind the altenating voltage. The geneato and the oto opeation odes ae shown in the toque diaga, Figue 4. The achine would develop axial toque when the angle δ would be equal to π : UC ax = (3) The obtained diaga is siila to the toque diaga of a synchonous achine. It can be seen fo the pesented analysis, that a otating field is not needed fo the capacitive achine opeation as fo the thee-phase electoagnetic achines, and that a capacito achine can also opeate as a single-phase achine. Thee ae no diffeences between the analysis of single-phase capacito oto and the thee-phase one. 4. Siulation of the Poposed AC Capacitive achine The poposed AC capacitive achine was siulated by using the atlab poga. The paaetes of the siu- k = 4, the axial ovelap suface of the oto and stato plates is lated achine ae: 4 couples of plates ( ) Figue 4. The toque diaga of the poposed capacitive achine. 36

7 A. Shenkan et al. 4 S = 50 c, electic peittivity of the dielectic ateial is ε = 10, the distance between the plates is d = 3. The applied AC voltage is U = 6 kv and the fequency is f = 50 Hz. The siulation esults fo δ = 30 (geneato ode) ae shown in Figue 5. It can be seen that the capacitance vaies in a sinusoidal shape: C ( α ) = 0 fo α = 0, π, π ; C ( α ) = 6 uf fo α = 0, 0.5π, 1.5π. The obtained aveage toque is negative 54 N (see Figue 5(a)). Theefoe, the achine opeates in the geneato ode. The spectu of the instantaneous toque has thee haonics: DC, 100 Hz and 00 Hz. This esult is logical because ( t ) consists of CU sinδ CU which is epesented by DC haonic, sin ( ωt + δ) which is epesented by 100 Hz CU sin ( 4ωt + δ ) haonic and which is epesented by 00 Hz haonic. The siulation esults fo δ = 0 ae shown in Figue 6. In this case, the achine opeates on the bounday of geneato and oto odes. The obtained aveage toque is zeo. The spectu of the instantaneous toque has CU sinδ 100 Hz and 00 Hz haonics. The DC haonic is zeo because = 0. The siulation esults fo δ = 30 ae shown in Figue 7. In this case, the achine opeates in the oto ode. The obtained aveage toque is 54 N. The atlab siulation esults could be validated by nueical calculations. The axial capacitance could be calculated by Equation (14): C 4 S = εε 0k = = 6 uf d (a) (b) Figue 5. The angle δ = 30 (geneato ode). (a) The siulated otating oto angle α (va- t ies fo zeo to π), vaying capacitance C ( α ), instantaneous toque of the achine ( ) and the aveage toque avg. (b) The spectu of the instantaneous toque. 37

8 A. Shenkan et al. (a) (b) Figue 6. The angle δ = 0 (bounday between the geneato and oto odes). (a) The siulated otating oto angle α (vaies fo zeo to π), vaying capacitance C ( α ), instantaneous toque of the achine ( t ) and the aveage toque Fo the case of δ = 30, the calculated aveage toque would be: Fo the case of δ = 30 avg; (b) The spectu of the instantaneous toque. ( ) ( ) CU avg = sinδ = 0.5 = 54 N, the calculated aveage toque would be: 6 3 ( 6 10 ) ( 6 10 ) ( 0.5) CU avg = sinδ = = 54 N In this case, the oto output powe would be: ω Pout = avg ω = avg = = 439 W k 4 The calculations show that the pesented siulation esults ae coect. 5. Conclusions The novel capacitive synchonous achine is poposed. The achine is opeating on the pinciple of the electic field. By using new ateials with high electic peittivity ε, the poposed achine is feasible fo the theoetical and the pactical points of view. The achine design is based on the sinusoidal capacito whose capacitance vaies accoding to a sinusoidal function. The poposed achine is actually electical synchonous achine with chaacteistics siila to those of the agnetic synchonous achines. 38

9 A. Shenkan et al. Figue 7. The angle δ = 30 (oto odes). The siulated otating oto angle α (vaies t fo zeo to π), vaying capacitance C ( α ), instantaneous toque of the achine ( ) and the aveage toque avg. Extensive siulation esults of the achine opeated in the oto and the geneato odes validate the theoetical analysis and show the pactical feasibility of the poposed achine. The poposed achine has a nube of advantages upon the conventional electic achines based on the agnetic inteaction. The ain advantage is that the electic field achines ae uch salle in size and lighte in weight than the electoagnetic achines with the sae output paaetes. Futheoe, the capacito oto has vey low inetial toque due to the low weight of the oto. This fact allows apid stating and stopping of the achine, as well as othe vaiations duing opeation. This featue could be highly ipotant in contol systes. Anothe advantage is the siple stuctue of a single-phase capacito oto. Refeences [1] ooe, A.D. (1973) Electostatics and Its Applications. John Wiley & Sons, [] Hojjat, Y., Dadkhah,., odabbeifa,. and Ghanbai,. (007) Electostatic Rotation of Plexiglas Disc Suppoted on Ai Beaing. 14th Intenational Confeence on echatonics and achine Vision in Pactice, Xiaen, 4-6 Decebe 007, [3] Santana-atín, F.J., ontoya, S.G.-A., onzón-veona, J.. and ontiel-nelson, J.A. (008) Analysis and odeling of an Electostatic Induction icooto. 18th Intenational Confeence on Electical achines, Vilaoua, 6-9 Septebe 008, 1-5. [4] Stanczl,., Saajlic, E., Fujita, H. and Yaahata, C. (011) odal Analysis and odeling of Fictionless Electostatic Rotay Steppe icooto. IEEE 4th Intenational Confeence on ico Electo echanical Systes (ES), Cancun, 3-7 Januay 011, [5] atsuzaki, K., atsuo, T. and ikuia, Y. (1994) Copaison of Electostatic and Electoagnetic otos Based on Fabication and Pefoance Citeia. Poceedings of 5th Intenational Syposiu on ico achine and Huan Science, Nagoya, -4 Octobe 1994, [6] Behjat, V. and Vahedi, A. (004) Study Toque Ripple of the Side Dive Electostatic icooto. 39th Intenational Univesities Powe Engineeing Confeence, Bistol, 8 Septebe 004,

10 A. Shenkan et al. Appendix: Exaple of Design of the Capacitive oto The poposed capacitive achine and the shape of the plates of both stato and oto ae shown in Figue 8. In ode to incease the oveall capacity of the oto, it is ade of a lage nube of plates, and the insulation between the plates is of a ateial with a high ε value. This ateial takes the fo of insulation washes. In ode to ensue a good contact between the plates of the otating oto and the insulation washes, idling togethe with the stato plate, and in ode to educe fiction, the lubicant should have also high ε value. 1 Stato plates; Insulating washe; 3 Roto plates; 4 oto shaft; 5 Suppots; 6 Bed plate; 7 Teinals; 8 Connecting lead of stato; 9, 1 Connecting lead of oto; 10 Bush; 11 Slip ings; 1 Fae housing. (a) (b) Figue 8. The poposed capacitive oto. 40

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