RU2293424C2 - ASYMMETRIC THREE-PHASE FRACTIONAL-SLOT WINDING WITH 2p = 6c POLES PLACED IN z = 30c SLOTS - Google Patents

Abstract

FIELD: electrical and electromechanical engineering; three phase induction and synchronous machines including slip-ring induction motors.

SUBSTANCE: proposed asymmetric three-phase fractional-slot double-layer lap winding, m = 3-phase, m' = 3-band, with 2p = 6c poles in z = 30c slots and with slot number per pole per phase q = z/3p = 10/3 has 3pc coil groups 1G through 9G, with coil grouping 4 3 3 3 3 4 3 4 3 repeated c times. Novelty is that concentric windings have slot pitch y_pi = 8 - 2 (i - 1) and turn numbers (1 - x)w_c; for coils with i' = 1, 4 and turn number (1 + 1)w_c, for coil with i = 2 in four-coil groups 1G, 6G, 8G, slot pitches y'_pi = 7 - 2(i' - 1) and turn number (1 + x)w_c, for coils with i' = 2 in all three-coil groups turn number equals (1 - x)w_c, for coils with i' = 1 in coil groups 3G, 4G, and for coils with i' = 3 in coil groups 7G, 9G; for coil groups 2G, 5G with slot pitch y'_pi = 5 turn number equals (1 - x)w_c for coil with i' = 3 in coil group 2G, and for coil with i' = 1 in coil group 5G ; turn number in remaining coils of coil groups equals w_c, where c = 1, 2, 3 ...; i' = 1 - 4, and i' = 1 - 3 are coil numbers in coil groups starting from external one; 3w_c is turn number in slots completely filled with winding; x = 0.55.

EFFECT: reduced asymmetry and scatter ratios.

1 cl

Description

The invention relates to three-phase windings of electric machines of alternating current of asynchronous motors (HELL) and synchronous generators (SG).

Known two-layer loop m = 3-phase fractional windings are known, performed at 2p poles in z grooves from m′p coil groups with equal-step or concentric coils with an average pitch of grooves y _to ≈z / 2p, the number of grooves per pole and phase q = z / m′p = b + c / d, where m ′ = 2m = 6 or m ′ = m = 3 is the number of phase zones per pair of poles, c / d <1; according to symmetry conditions, the 2p / d ratios are integer, d / m are non-integer [Voldek A.I. Electric cars. L .: Energy, 1978, S. 392-394].

Grouping coils in groups of fractional asymmetric (d / m - integer) windings are given in rows and depend on c / d [Livshits-Garik M. Windings of AC machines. / Per. from English L .: SEI, 1959, p. 254], for example 4 3 3 3 3 4 3 4 3 for q = 10/3; Due to phase asymmetry, differential scattering increases.

The invention aims at reducing the asymmetry coefficients, differential scattering of an asymmetric m ′ = 3-zone winding at q = 10/3.

The solution of this problem is achieved by the fact that for m = 3-phase asymmetric fractional winding with 2p = 6s poles in z = 30s grooves, a two-layer m ′ = 3-zone with the number of grooves per pole and phase q = z / 3p = 10 / 3 of 3pc coil groups 1G ... 9G with a group of 4 3 3 3 3 4 3 4 3, repeated with time, concentric coils have steps along the grooves y _pi = 8-2 (i-1) with the number of turns (1 ) w _to coils with i = 1, 4 and (1 + x) w _to coils with i = 2 for groups of four-coil 1G, 6G, 8G, y ′ _pi = 7 - 2 (i′-1) with the number of turns (1 + x) w _to coils with i ′ = 2 for all three-coil groups with (1-x) w _to turns of coils with i ′ = 1 groups 3G, 4G and c i '= 3 groups 7G, 9G, and for groups 2G, 5G with y _P = 5 - (1-x) w _{to the} turns of the coil with i '= 3 in 2G and with i' = 1 in 5G with w _to the other coils of the groups, where = 1, 2, 3, ..., i = 1 ... 4 and i '= 1 ... 3 are the numbers of coils in the groups, starting from the outside, x = 0.55, and 2w _k is the number of turns of the grooves, completely filled with a winding.

Figure 1 shows a scan of the groove layers of the proposed winding with c = 1, 2p = 6, z = 30 with numbers 1 ... 30 from the bottom, 3p = 9 groups with numbers 1G ... 9G from above, alternating phase zones A-B -From the upper, XYZ lower layers and the blackened grooves contain (2) w _to turns at 2w _to turns in the remaining grooves, and the shifts of the axes of the groups are marked from the bottom, in Fig.2 a diagram of the shifts of the groups, their EMF of the phases E _A , E _B , E _C , relative to the axis of symmetry 8G; figure 3 and 4 on a triangular grid constructed polygons of the MDS winding for coils equal- (figure 3) and unequal (figure 4). The winding (figure 1) is connected with a series-consonant inclusion of groups: 1G, 4G, 7G in phase I; 2G, 5G, 8G in phase II; 3G, 6G, 9G in phase III with beginnings from 1G, 2G, 3G; phases can mate in Y and Δ. With c = 2, 3, ... the winding has 2p = 6s = 12, 18, ... poles, z = 30s = 60, 90, ... grooves and 3pc = 18, 27, ... groups.

при Е_г.м=2,6187034+х0,190983 для групп 3Г, 4Г, 7Г, 9Г трехкатушечных (малых). Диаграмма фиг.2 построена для 2р=6, z=30, α_п=360°/z=12° и углах сдвигов осей групп по фиг.1: 8Г→9Г=3,5α_пр=126°=120°+0,5α_п и 8Г→7Г=240°-0,5α_п; 8Г→1Г=7(36°)=252°=240°+α_п и 8Г→6Г=120°-α_П; 8Г→2Г=10,5(36°)=378°=360°+1,5α_п и 8Г→5Г=360°-1,5α_п; 8Г→3Г=13,5(36°)=120°+0,5α_п и 8Г→4Г=240°-0,5α_п, по которой: E_В=E_8Г(б)+2E_2Г(м)cos18°=8,05748+x0,50203 - вертикальный вектор, где для неконцентрических групп 2Г, 5Г-2x[cos1,5α_п-cos(1,5+3)α_п]=х0,726543; Е² _А=(2Е_4Г(м))²+Е² _4Г(б)-4Е_4Г(м)Е_1Г(б)cos(180°-18°) - по теореме косинусов и при х=0 - Е_A=Е_C=8,21842, угол γ на фиг.2 определяется по теореме синусов 2Е_4Г/sinγ=E_A/sin(162°), откуда γ=11,3545° и тогда углы сдвигов фазных ЭДС равны: φ_BA=φ_BC=120°-12°+γ=119,3545 и φ_AC=121,291°. По фазным ЭДС и углам сдвигов определяются линейные ЭДС а=Е_BA=b=Е_BC=14,0951, с=Е_AC=14,3264 и тогда по выражениям: S=а+b+с, А=(а²+b²+с²)/6,

K_нес%=(F/D)100 [Петров Г.Н. Электрические машины, ч.2. Асинхронные и синхронные машины. М.-Л.: ГЭИ, 1963, с.162] вычисляется коэффициент несимметрии К_нес%=4,49 % при К_об=(Е_АС+2Е_ВА)/

·30=0,81823 (x=0).For winding (1) groups EMF determined by the coefficients of shortening concentric coils K _yi = sin (90y _pi / τ _n) = sin (18 ° y _pi) with the pole pitch τ _p = z / 2p = 5; By _yi = (1-x) 0.587770 (y _pi = 8 & 2), (1 + x) 0.951057 (y _pi = 6) at E = 3.0777 _g.b-h0,22451 groups for chetyrehkatushechnyh (large), (1-x) 0.80902 (y ′ _pi = 7 or 3), (1 + x) 1.0

with E _gm = 2.6187034 + х0.190983 for groups 3G, 4G, 7G, 9G three-coil (small). Figure 2 is constructed for 2p = 6, z = 30, α _p = 360 ° / z = 12 ° and the angles of the axes of groups 1 shifts: 8G 9G → = 3,5α _n p = 126 ° = 120 ° + 0.5α _p and 8G → 7G = 240 ° -0.5α _p ; 8G → 1G = 7 (36 °) = 252 ° = 240 ° + α _p and 8G → 6G = 120 ° -α _P ; 8G → 2G = 10.5 (36 °) = 378 ° = 360 ° + 1.5α _p and 8G → 5G = 360 ° -1.5α _p ; 8G → 3G = 13.5 (36 °) = 120 ° + 0.5α _p and 8G → 4G = 240 ° -0.5α _p , according to which: E _B = E _{8G (b)} + 2E _{2G (m)} cos18 ° = 8.05748 + x 0.50203 is a vertical vector, where for non-concentric groups 2G, 5G-2x [cos1.5α _n -cos (1.5 + 3) α _n ] = x0.726543; Е ² _А = (2Е _{4Г (m)} ) ² + Е ² _{4Г (b)} -4Е 4Г _(m) Е _{1Г (b)} cos (180 ° -18 °) - by the cosine theorem and for х = 0 - Е _A E = _C = 8,21842, the angle γ in Figure 2 is determined by the sine theorem 2E _4D / sinγ = E _A / sin (162 °), where γ = 11.3545 °, and then shifts the phase angles of emf are: φ _BA = φ _BC = 120 ° -12 ° + γ = 119.3545 and φ _AC = 121.291 °. From the phase EMF and shift angles, the linear EMF a = E _BA = b = E _BC = 14.0951, c = E _AC = 14.3264, and then by the expressions: S = a + b + c, A = (a ² + b ² + c ² ) / 6,

K _carried% = (F / D) 100 [Petrov G.N. Electric cars, part 2. Asynchronous and synchronous machines. M.-L.: SEI, 1963, p. 162], the asymmetry coefficient K _ns% = 4.49% is calculated at K _rev = (E _AC + 2E _VA ) /

30 = 0.81823 (x = 0).

(z-3x)=0,87385 и z=30-3x=28,5 - эквивалентное число полностью заполненных обмоткой пазов, т.е. она имеет больший К_об и меньший К_нес% (в 4,49/0,294=15,3 раза).Similarly, for the unequal winding of FIG. 1, at x = 0.5: E _B = 8.3085, E _A = E _C = 8.2982, γ = 11.6597 °, φ _VA = φ _BC = 119.6597 ° , φ _AC = 120.6806 °, a = E _BA = b = E _BC = 14.3571, c = E _AC = 14.4219, K _carried% = 0.294, K _rev = (E _AC + 2E _VA )

(z-3x) = 0.87385 and z = 30-3x = 28.5 is the equivalent number of grooves completely filled by the winding, i.e. it has a larger K _about and a smaller K _carried% (4.49 / 0.294 = 15.3 times).

From the MDS polygons of Figs. 3, 4 (with unit current vectors of phase zones A-Z-B-X-C-Y in the center) according to a triangular grid and the relations

the differential scattering coefficient σ _D% is determined, which characterizes the quality of the winding by the harmonic composition of the MDS with the square of the average radius j = 1 ... z of the groove points R ² _d , the radius R _{o of the} circle for the main harmonic [Popov V. Determination and optimization of the parameters of three-phase windings along the MDS polygons // Electricity, 1997, No. 9, p. 53-55]:

According to (1) - (2): at x = 0, K _rev = 0.81823 - R ² _d = 228/30, R _o = 30 · 0.81823 / 3π and σ _D% = 12.04; when x = 0.5 and K _r = 0.87385 - R ² _d = 226.5 / 30, R _o = 28.5 · 0.87385 / 3π, σ _D% = 8.13%, i.e. σ _D% decreases by 12.04 / 8.13 = 1.48 times. Given the changes in K _about , K _carried% , σ _{d%, the} winding of Fig. 1 with x = 0.5 has a high efficiency K _eff = (0.87385 / 0.81823) (4.490 / 0.29) (12.04 / 8.13) (28.5 / 30) = 23.0, and with optimal x = x _opt = 0.55, the parameters improve: K _about = 0.87992, K _carried = 0.236, σ _D% = 7.93 and K _eff = 29.4.

The proposed m = 3-zone winding, in comparison with m = 6-zone at z = 30, 2p = 6, q = z / 6p = 5/3, for _P = 4, grouping 2 1 2 1 2 2 2 2 1, K _about = 0.8971, K _carried% = 1.310, σ _D% = 7.93, has a reduced K _carried (1.31 / 0.24 = 5.5) with half as many groups.

Its application allows to reduce additional losses in the rotor and magnetic noise in the blood pressure with short-circuit rotor, improve the shape of the voltage curve in the SG.

Claims (1)

Three-phase asymmetric fractional winding at 2p = 6s poles in z = 30s grooves, performed by a two-layer m = 3-zone with the number of grooves per pole and phase q = z / 3p = 10/3 of 3pc coil groups 1G ... 9G with a group 4 3 3 3 3 4 3 4 3 repeated with times, characterized in that the concentric coils have _groove steps y _pi = 8-2 (i-1) and the number of turns (1-x) w _k for coils with i ′ = 1.4 and the number of turns (1 + x) w _k for a coil with i = 2 in four-coil groups _{1Г, 6Г, 8Г, groove} steps y ′ _пi = 7-2 (i′-1) and the number of turns (1 + x) w _k for a coil with i ′ = 2 in all three-coil groups, the number of turns (1-x) w _k for coils with i ′ = 1 in a coil groups of 3G, 4G and for coils with i ′ = 3 in the coil groups of 7G, 9G, and for coil groups of 2G, 5G with a pitch in the grooves of _n = 5, the number of turns is equal to (1) w _to for the coil with i ′ = 3 in the 2G coil group and for a coil with i ′ = 1 in the 5G coil group, while the number of turns in the remaining coils of the coil groups is w _k , where c = 1, 2, 3, ...; i ′ = 1 ... 4 and i ′ = 1 ... 3 are the numbers of coils in the coil groups, starting with the outer one; 2w _to - the number of turns in the grooves, completely filled with a winding, x = 0.55.

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