GB2031659A - Pole changing induction electrical machines - Google Patents

Abstract

An induction electrical machine has a ferromagnetic core with a number of slots wound with concentric coils. In each of two phases A and B the coils have the same number of turns. Each slot contains 0, n or 2n conductors of phase A; and O, krn or 2krn conductors of phase B; where 2n is the number of turns in a phase A coil, 2krn the number of turns in a phase B coil, and kr the winding ratio of B to A. The coils are variably interconnected in two or preferably three different ways to give two or three different pole numbers. At one pole number, preferably the highest or lowest of three pole numbers, the coils produce a two-phase winding, Fig. 11a, whereas at the or each other pole number coils from the two phases are used equally and combined as a single phase winding, Figs. 11b, 11c (Fig. 11c not shown). <IMAGE>

Description

SPECIFICATION Induction electrical machine This invention relates to induction electrical machines, and more particularly to those in which the number of poles can be changed, for example to produce different motor speeds.

Pole-changing induction motors, providing two or three alternative pole numbers, and corresponding running speeds in reverse ratio to the pole-numbers, are well-known and widely used in practice. Best known are motors employing a Dahlanderwinding.

However, a new method called pole amplitude modulation (P.A.M.) has been devised and developed successfully in recent years to provide a step change in the number of poles and consequently in the speeds of the motor; see for example U.K. Patent Specification 900600. However, there are several difficulties in normal P.A.M. techniques when applied to small single-phase induction motors.

In British Patent 966576, in order to start and run the motor at the desired pole number, it is required to wind the machine as a three phase motor. When the machine runs up to speed, then one of the three phase-windings (which is connected to the supply via a capacitor) is open-circuited and the motor runs as a pure single-phase machine. Alternatively, the machine can be wound as a three phase motor and run as a permanent capacitor single phase motor.

However, as can be shown mathematically, the principles of P.A.M. cannot be applied satisfactorily to a true two-phase machine (which a permanent capacitor motor resembles), and the harmonic content of such motors would be high. Broadway in Patent Specification No. 1267924 applied the principle of P.A.M. to single-phase motors with concentric coils using an auxiliary winding for starting, but he pointed out that the harmonic content in his motor was rather high and he had to arrange his windings sinusoidally on the stator. Such a compromise however, is difficult to achieve if one requires more than two speeds from the motor. Moreover, the starting torque for such single-phase P.A.M. motors would be low owing to the large harmonic content and they would not be suitable for driving compressors and other loads which require a reasonable starting torque.In addition, this method requires either symmetrical or assymmetrical modulation to the winding, depending on the ratio of modulated pole number to the unmodulated pole number. This is a rather inconvenient restriction for motors having more than two speeds.

If a single-phase P.A.M. motor which is wound as a three-phase motor is to be run at a pole number which is three or a multiple of three, the principles of P.A.M. as described in British Patent 900600 cannot be applied directly. The principle of assymmetrical winding as described in British Patent 926101 can be employed, but this obviously would involve complicated switching. Alternatively, one could distribute the winding non-uniformly as described in British Patent 986384, but this requires a large number of slots, which is not suitable for small single-phase motors.

The present invention provides an induction electrical machine having a ferromagnetic core with a number of slots and wound with concentric coils which, in each phase, have equal numbers of turns, each slot containing 0, n or 2n conductors of phase A and 0, krn or 2k,n conductors of phase B wherein 2n is the number of turns in a coil of phase A, 2krn is the number of turns in a coil of phase B, and kr is the winding ratio between phases B and A, and means for interconnecting the coils in two or three different ways to produce respectively two orthree different pole numbers, the coils at a first pole number producing a two-phase winding, the or each other pole number using coils from the phases equally and combined as a single phase winding.

There are preferably three different pole numbers provided. It is preferred in most cases that the twophase operation is at the lowest or the highest of three alternative pole numbers; being for example the highest pole number where the anticipated use forthe motor will require a relatively high starting torque, as in driving some compressors and pumps, but otherwise being the lowest pole number where the highest current is drawn at the highest motor speeds (i.e. at the lowest pole number).

Motors of the present invention differ from prior art P.A.M. motors in various respects. Firstly, they are wound for two-phase operation at one pole number and single phase operation at the or each alternative pole number. Atthetwo-phase pole number the motor may be designed to operate as a permanent capacitor motor, as a capacitor startinduction run motor, or as a capacitor start-capacitor run motor. As distinct from Broadway's Patent No.

1267924, the coils of both of the original two phases are used and combined to form a single phase winding at the or each other pole number. This makes maximum use ofthewindings at these pole numbers. Moreover, as will be seen from the examples described below, the design approach of the present invention generally allows greater flexibility to the designer and greater freedom to choose a good winding to suit the motor requirements at the different pole numbers. Although, in some cases, the resulting winding will reflect something of the mathematical principles of P.A.M., the design approach is different, as will be seen below, and therefore not subject to the restrictions usually associated with P.A.M. (The distinction between the present invention and prior art P.A.M. techniques is described in mathematical terms at the end of this Specification).In the present invention there is in theory no restriction on the ratio of the pole numbers, nor on which of them is the 2-phase pole number. In the prior art of Krishnamurthy and Rajaraman (Proceedings of the Institution of Electrical Engineers, Vol. 112, No. 6, June 1965) the middle pole number is 2-phase and the other two pole numbers are an equal number of poles on either side of the middle number. There has also been a tendency on the part of Krishnamurthy and Rajaraman to assume that the 2-phase pole number must have an odd number of pole pairs per modulating wave, and that the modulating waves must be mutuallydisplaced around the machine axis by +90 (on the scale kO, where k = the number of modulating waves per revolution and e = mechanical degrees) or as near as possible thereto.But no such restric tions apply to the present invention. Rajaraman has applied the principle of P.A.M. to produce multispeed induction motors with concentric coils and without any restriction on pole ratio combinations, but he requires the omission of coils at one or other speed, and as a result 32 terminal leads are needed for a 3-speed motor.

In order that the present invention may be more clearly understood, the design procedure will be generally described and specifically illustrated with reference to the accompanying drawings.

The design will normally start with a given stator having a certain number of slots and a required set of alternative pole numbers. It may also be required that a particular one of these pole numbers be the starting pole number (i.e. for 2-phase operation).

The next stage is to draw a set of square wave diagrams for the different pole numbers. Each pole of a square wave will occupy s/2p slots of the stator (or an integral number adjacent thereto, for example if it is a non-integer or sometimes if it is an odd number), wherein s is the total number of stator slots and p is the number of pole pairs at that pole number. If the number of flots in a pole is an odd number, then one of the slots will be empty or two of the slots will be only half full or the number of coils per pole will be unequal. This is in fact no disadvantage since empty slots are common in concentric coil windings and can prouce a better m.m.f. Also it allows greater freedom to the designer to fit the coils into the appropriate pole space, as will be seen below.

It is assumed that all the coils of a particular phase have the same number of turns, and normally only one side of one coil will occupy a slot. However, one side of a coil may be separated into two equal parts and assigned to different (usually adjacent) slots.

Thus, if each coil of phase A comprises 2n turns and if each coil of phase B comprises 2krn turns, a slot may contain 0, n, krn,2n, (kr+1)n or 2krn turns.

The object is to assing the coils to the slots so that the ampere-conductors at the different pole numbers as nearly as possible follow the respective square wave configurations. It will be apparent that, since the current in the opposite sides of a coil flows in opposite directions, the sides of every coil have to occupy opposite poles at all of the alternative pole number unless ampere conductor neutralisation can be effected at pole boundaries as a result of a slot containing conductors from different coils.

It is generally preferable to start by assigning the coils for the 2-phase pole number, since there will normally be equal numbers of coils in the two phases and they will be similarly arranged so as to produce a 2-phase winding. The choice of arrangement of the coils at the 2-phase pole number is of course influenced by the requirement that the coils, with suitable reconnection between them will fit the square waves of the other pole numbers. Usually there will be more than one possible arrangement of the coils to suit the different pole numbers, and in this case it is for the designer to select the one which gives the best performance for the particular motor requirements. In particular, analysis of the harmon ics and calculation of the ratio of flux densities bet ween the difference pole numbers will be helpful in making the correct choice.Moreover, the existence of an undesirably high harmonic with one coil arrangement can indicate how to try and modify that arrangement to reduce or eliminate that harmonic.

The following specific examples will help to make the procedure clearer. In the first three examples kr = 1 and in the final example kr,; In the first example, the stator has 36 slots and three speeds are required at p = 2,3 and 4 pole pairs respectively, the 2-phase operation being at p = 2. Three square waves corresponding to the three pole numbers are then drawn, one under another, on the scale of the stator, as shown in Fig. 1(a), (b) and (c) respectively.

The value of s/2p for 4 poles is 9 slots, which when divided by two gives a non-integer. In order to assign conductors of phase A and phase B coils equally to each pole, either one slot must be empty or two slots half-filled or the number of conductors under each pole must be unequal. In the present case one slot is left empty; or in more general terms there will be four empty slots around the stator. The location of these empty slots is a matter of choice for the designer, and gives rise to various possible coil arrangements.

One possible arrangement of the conductors is shown in Figs. 2(a), (b) and (c) for the three pole numbers. The convention used in this diagram is that solid lines represent conductors of phase A coils and the broken lines of phase B coils. The lines are all of the same length, representing 2n conductors in a slot. The lines are drawn above and below an imaginary central datum to represent the two directions of current flow. The empty slots have been selected as slots 5, 18, 23 and 36.This corresponds to positions between adjacent poles in the 6- and 8-pole waveforms of Figs. (b) and 1(c), resulting in uniform 4-coil sides per pole in the 8-pole configuration of Fig. 2(c), but reduction of two poles from 6 coil sides to 4 coil sides in the 6-pole configuration of 2(b). In the 4-pole arrangement of Fig. 2(a) the four empty slots appear in two of the poles, but it should be remembered that since this is in 2-phase operation, the fundamental component of the square wave is continuously moving around the stator (i.e.

along the datum), so that this merely shows the situation at one particular instant.

It may not be apparent at first sight that Fig. 2 represents a concentric coil winding, but Fig. 3 shows the layout of the coils in this arrangement, again with phase A coils shown in solid lines and phase B coils in broken lines. Table 1 below shows the phase angle between phase A and phase B, the harmonic content of the m.m.f. wave at different pole numbers, the flux density ratio between different pole numbers (e.g. B6/B4 is the flux density ratio between the 6-pole and 4-pole configurations), and the winding factors for the winding arrangement of Fig. 2.

TABLE 1 Conductor sequence Phase A 2 2 2 2 PhaseB 2 2 2 2 Phase relationship between A and B 89.6 at 4 poles Harmonic content for 4 poles 4 poles 100.0% unmodulated. 8 poles 8.2% (Phase A) 12 poles 5.7% 16 poles 9.6% 20 poles 4.7% 24 poles 5.0 /O 28 poles 3.8% 44 poles 2.4% Winding factor: 0.886 48 poles 2.5% Harmonic content for 6 poles 2 poles 49.1% modulated. 6 poles 100.0% (PhaseAandB) 10 poles 6.2% 14 poles 7.7% 18 poles 8.5% 26 poles 3.4% 30 poles 2.1% 42 poles 1.5% Winding factor: 0.692 46 poles 1.9% B6/B4 0.96 Harmonic content for 8 poles 4 poles 23.0% modulated. 8 poles 100.0% (PhaseAandB) 12 poles 10.3% 20 poles 2.4% 24 poles 9.0 /O 28 poles 5.0 /O 32 poles 2.4% 40 poles 1.9% 44 poles 3.2% 48 poles 4.5% 60 poles 2.1% 64 poles 12.5% 80 poles 10.0% Winding factor: 0.698 96 poles 2.2% B8/B4 1.27 Figs. 4(a), (b) and (c) show an alternative arrangement to fit the waveforms of Fig. 1, and Fig. 5 shows the coil layout. In this case, one side of some of the coils has been separated into two equal parts and assigned to separate slots, so that those slots carry 2n conductors made up from n conductors from a phase A coil and n conductors from a phase B coil.

The result is that in the 6-pole configuration adjacent poles are spaced apart either by an empty slot or by a slot in which the turns from separate coils neutralise each other. This gives a better m.m.f., since the transition between adjacent poles is not so sharp. It will be appa rent that the 8 pole m.m.f. will be the same as for the winding of Fig. 2. The detailed analysis is given in Table 2.

TABLE2 Conductor sequence Phase A 2 1 1 -2 -2 Phase B -2 -2 1 1 2 Phase relationship between A and B 85.5 at 4 poles Harmonic content for 4 poles 4 poles 100.0% unmodulated. 8 poles 9.4% (Phase A) 12 poles 4.9% 16 poles 7.2% 20 poles 4.0 /O 24 poles 4.2% 28 poles 3.1% 36 poles 3.2% 44 poles 2.0% Winding factor: 0.856 48 poles 2.1% Harmonic content for 6 poles 2 poles 46.6% modulated. 6 poles 100.0% (Phase A and B in series) 10 poles 11.3% 14 poles 3.4% 18 poles 4.5% 22 poles 4.P/o 34 poles 1.9 h 38 poles 1.7% Winding factor: 0.660 50 poles 2.1% B6/B4 0.973 Harmonic content for 8 poles 4 poles 23.0% modulated. 8poles 100.0% (Phase A and B in series) 12 poles 10.3% 20 poles 2.4% 24 poles 9.0% 28 poles 5.0% 32 poles 2.4% 40 poles 1.9% 44 poles 3.2% Winding factor: 0.698 48 poles 4.5% B8/B4 1.226 Athird possible winding for this stator is shown in Fig. 6 and its harmonic analysis in Table 3.

TABLE3 Conductor sequence: Phase A 211-2-2-2-1-121121 1-2-2-2-1-1211 Phase B- -1 -1 -2 1 1 2 2 2-1 -1 -2 -1 -1 -2 1 1 2 2 2 -1 -1 -2 Phase relationship between phases A and B at4 poles 98.0 Harmonic content for 4 poles 4 poles 100.0% unmodulated. 8 poles 7.0 h (Phase A) 12 poles 6.4% 16 poles 5.6% 20 poles 1.8% 24 poles 3.6 h 28 poles 2.6 h 32 poles 2.0% 36 poles 1.6% 40 poles 1.6% 44 poles 1.6% Winding factor: 0.862 48 poles 1.8% Harmonic content for 6 poles 2 poles 51.6% modulated. 6 poles 100.0% (Phases Aand B) 10 poles 9.4% 14 poles 6.1% 22 poles 2.7% 26 poles1.7% 30 poles 5.4% Winding factor: 0.627 42 poles 3.8% B6/B4 1.031 Harmonic content for 8 poles 4 poles 18.6% modulated. 8 poles 100.0% (PhasesAand B) 12 poles 10.9% 16 poles 6.4% 20 poles 2.4% 24 poles 9.5% 32 poles 6.6% 40 poles 5.3% Winding factor: 0.661 48 poles 4.7% B8/B4 1.304 The harmonic analysis of these windings (and also the winding factors) of these different winding arrangements are reasonably good and compare favourably with conventional concentric coil P.A.M.

motors which give only two speeds.

As a second example, a 54-slot stator is to have 6-, 8- and 10-pole alternative pole numbers, with 2-phase operation, at 6 poles. The square wave diagrams are shown in Figs. 7(a), (b) and (c), and one possible winding arrangement is shown in Figs. 8(a), (b) and (c). The harmonic analysis of the winding arrangement of Fig. 8 is shown in Table 4.

TABLE4 Conductor sequence: as shown in Fig. 8.

Phase relationship between A and B at 6 poles = 84.8 Harmonic content for 6 poles 2 poles 12.0% unmodulated. 6 poles 100.0% (Phase A) 10 poles 10.2% 14 poles 4.9% 18 poles 8.5% 22 poles 2.1% 26 poles 1.5% 38 poles 2.4% 46 poles 2.0 h Winding factor: 0.868 90 poles 1.7% Harmonic content for 8 poles 4 poles 18.1% modulated. 8 poles 100.0% (Phase A and B) 12 poles 13.7% 16 poles 2.8% 20 poles 4.2% 24 poles 9.2% 32 poles 2.2% 36 poles 3.5% 40 poles 2.7% 44 poles 1.6% 48 poles 2.6% 52 poles 3.9% 56 poles 3.7% 60 poles 2.1% 68 poles 1.6% Winding factor: 0.611 72 poles 1.7% B8/B6 0.95 Harmonic content for 10 poles 2 poles 47.1% modulated. (Phases A and B) 6 poles 48.0% 10 poles 100.0% 14 poles 7.9% 18 poles 1.9% 22 poles 2.8% 26 poles 5.8% 30 poles 12.5% 34 poles 4.9% 42 poles 3.4% 46 poles 3.3% 50 poles 5.1% 54 poles 6.5% 58 poles 4.4% 62 poles 2.4% 66 poles 2.1% Winding factor: 0.598 98 poles 10.2% B10/B6 1.21 As a third example, the 54-slot stator is to have 6,8 and 12 poles with 2-phase operation at 6 poles. The square wave diagrams (not shown) are drawn up as before, and one possible winding arrangement is shown in Figs. 9(a), (b) and (c) and its harmonic analysis is shown in Table 5.

TABLE 5 Conductor sequence: Phase A 211-1-1-2 PhaseB 211-1-1-2 Phase relationship between phases A and B at 6 poles 90 Harmonic content for 6 poles 6 poles 100.0% unmodulated. 18 poles 8.3% (Phase A) 42 poles 3.3% 66 poles 2.1% 90 poles 1.P/o 102 poles 5.9 h 114 poles 5.3% 210 poles 2.9% Winding factor: 0.870 222 poles 2.P/o Harmonic content for 8 pole 4 poles 9.6% modulated. 8 poles 100.0% (PhasesAand B) 12 poles 2.8% 16 poles 11.6% 20 poles 6.P/o 24 poles 7.5% 28 poles 2.4% 32 poles 1.5% 40 poles 2.8% 44 poles 4.4% 48 poles 3.0% 52 poles 2.3% 56 poles 2.1% 60 poles 2.4% 64 poles 3.0 h 68 poles 1.6to 84 poles 2.1% Winding factor: 0.605 88 poles 1.5% B8/B6 0.958 Harmonic content for 12 pole 12 poles 100.0% modulated. 24 poles 3.2% (Phases A and B) 36 poles 10.2% 48 poles 3.pro 60 poles 3.0 /O 96 poles 12.5% 120 poles 10.0% 144 poles 2.5% 180 poles 2.0% 204 poles 5.9% Winding factor: 0.709 228 poles 5.3sub B1 2/B6 1.227 There are cases where it is desirable that the number of conductors in phase B should differ from that in phase A (i.e. kr/ 1) to achieve a better performance. In orderto obtain good utilisation of slot space it is required that the slots should be filled up as far as possible by conductors of phases A and B.

The "empty slot" effect is then obtained by neutralisation.

To illustrate this case, an example is considered of a 36-slot statorwhich is required to produce 4,6 and 8 poles, with 2-phase operation at4 poles. A possible winding arrangement is shown in Figs. 13(a), (b) and (c) with the corresponding winding layout in Fig.

13(d). (This example also serves to illustrate the case where s/2p is a non-integer and the number of conductors under adjacent poles is unequal).

The harmonic analysis for the above arrangement is shown in Table 6. In all three connections about 90% of all the slot spaces are filled with active conductors which compares favourably with conventional single- or multi-speed induction motors.

TABLE 6 Conductor sequence: As shown in Fig. 13.

Phase relationship between phases A and B at4 poles = 89.1 Kre = number of effective conductors in phase B number of effective conductors in phase A = actual number of conductors in phase B x winding factor of phase B actual number of conductors in phase Ax winding factor of phase A = 1.2 Harmonic contentfor4 poles 4 poles 100.0% unmodulated. 12 poles 10.9% (Phase A) 20 poles 3.8% 28 poles 2.0% 60 poles 2.2% 68 poles 5.9% 76 poles 5.3% Winding factor: 0.898 84 poles 1.6% Harmonic content for 6 poles 2 poles 52.0% modulated. 6 poles 100.0% (PhasesAandB) 10 poles 6.3% 14 poles 8.1% 18 poles 8.6% 26 poles 3.4% 30 poles 2.1% 42 poles 1.5% 46 poles 1.9% 54 poles 2.9% 58 poles 1.9% Winding factor: 0.615 66 poles 9.1% B6/B4 0.995 Harmonic content for 8 poles 4 poles 23.2% modulated. 8 poles 100.0% (PhasesAand B) 12 poles 10.4% 16 poles 4.5% 20 poles 2.5% 24 poles 9.0 /O 28 poles 5.0 /O 32 poles 2.4% 40 poles 1.9% 44 poles 3.2% 48 poles 4.5% 60 poles 2.1% 64 poles 12.5% Winding factor: 0.621 80 poles 10.0% B8/B4 1.310 It should be noted that the winding factor of concentric coil windings is generally higher than for double layer windings. This is because the distribution factor in concentric coil windings is generally higherthan that of double layerwindings. However, owing to the absence of chording, the harmonic content of concentric coil windings is not as good as that of double layer windings.However, as the number of slots per pole increases, there is a greater possibility of having some of the slots of a concentric coil motor empty or half full. By locating the best position for the empty slots or neutralised slots from the square wave pattern, one should be able to improve the m.m.f. waveform of the concentric coil motor. This is actually the case for the 36 slot motor shown in Figs.

1 to 6 and in Fig. 13. The way of grouping the concentric coils according to a square wave pattern is quite flexible, as is shown in Figs. 3, 5 and 6 and 13(d), where the winding distributions are completely different even though the number of slots and the three alternative speeds are identical. However, it is easier to group the coils according to a square wave pattern rather than a sinusoidal pattern, especially if the number cf alternative pole pairs is three instead of two. Theoretically, the m.m.f. should be improved if the coils are grouped sinusoidally since the former is the integral of the latter, but as reported by Broadway in U.K.Patent No. 1267924 he has to make a compromise between the two different alternative pole numbers, and as a result, the m.m.f.'s reported by him for the two speeds are no better than those shown in Tables 1,2 and 3 for three speeds using the procedure of the present invention.

One of the necessary requirements for polechanging in motors is the provision of relatively simple switching connections, and it will assist in understanding the simplicity of the switching connections possible in the present invention by con sideringtwo of the possible switching circuits for a 36-slot concentric coil motor wound as shown in Fig.

10(a) and whose coils have been grouped as shown in Fig. 10(b). In Fig. 10(a) n and 2n conductors in a slot are represented as "1" and "2" respectively, and the minus sign indicates current flowing in the direction opposite to that in the other conductors without the minus sign. In Fig. 10(b), each group represents a group of concentric coils in the slot numbers indicated. The groups are designated with letters; XV being used instead of AB to avoid confusion with phase A and phase B designations.

Fig. 11 shows circuit connections and the corresponding switch requirements for a series - series series connection in a 3 speed change-pole motor with starting torque at p, pole pairs. Note than 14 terminals from the motor and 19 independent circuits in the rotary switch are required. Fig. (a) to (c) shows the interconnection of the coil groups to pro duce the different pole numbers. In Fig. (a) the motor is run as a permanent capacitor motor at that pole number.

Fig. (d) shows the required connections on a 3-way 8-pole rotary switch; the letters referring to the relevant ends of the coil groups. "AIC" desig nates the current supply line, "N" designates the neutral line, "C/P" designates the capacitor, and "C/S" designates a normally open centrifugal switch on the rotor which closes when the motor is running slightly below the minimum speed it is designed for.

It is seen in Fig. 11 that if there is one path for each of phases A and B, then 14 leads are required to come out from the motor, and the leads should be con nected to a 3-way 8-pole switch as shown in Fig.

11(d).

If the rotary switch is turned to position 1 of Fig.

11(d), it is clear that E would be connected te D, C to Y,FtoG,HRtoneutral,StoL, MtoJ,Pviaa capacitor to K, and XQ to the supply. This connection provides 4-poles with a 2-phase power supply, the coil connections being given in Fig. 11(d).

Similarly, if the switch is turned to either position 2 or3, the motor will become a single phase motor using all the coils. However, if the motor is initially stationary, then no current could flow in all the coils since the centrifugal switch is open. If, on the other hand, the switch has been turned into position 2 or 3 from position 1, then the centrifugal switch would be closed and the motor would slow down to the new speed. In other words, it is if and only if the motor is running at a reasonably high speed that one can switch the motor from 2-phase to single phase.

Furthermore, by means of this simple switching connection, one can avoid applying the mains voltage to the pure single phase motor while it is at a standstill, thus eliminating the situation when the motor is drawing excessive current while it is not trying to rotate at all. Note that the centrifugal switch in this motor is different from orthodox centrifugal switches since the former is normally open, whereas in conventional motors they are normally closed.

Figs. 12(a), (b) and (c) show interconnections of coils at respectively 4 poles, 6 poles and 8 poles when there are two parallel paths in each of phases A and B. In this case only 12 leads have to be brought out from the motor, and a 3-way 8-pole rotary switch will again be required to accomplish all the switching requirements, as shown in Fig. 12(d).

If a dual speed motor is specified instead of a triple speed motor, it is possible to simplify the switch arrangement considerably. In general, six terminals are required to be brought out from the windings of a dual speed motor with series-series connection.

Fig. 18 shows circuit connections and switch requirements for series-series connections in a change-pole motor with starting torque at one pole number. Note that 6 terminals from the motor and 7 independent circuits in the rotary switch are required.

Furthermore, the number of terminals required for series (unmodulated)-parallel (modulated) con nected is five only. Fig. 19 shows circuit connections and switch requirements for series-parallel connections in a change-pole motor with starting torque at one pole number. Note that 5 terminals from the motor and 6 independent circuits in the rotary switch are required. In Fig. 19(a) the motor is run as a per manent capacitor motor at this pole number.

The switching arrangements described above relate specifically to the permanent capacitor motor.

For someone knowledgeable in single phase inducrtion motors it would be a straightforward task to modify these switching arrangements to cater for capacitor start-induction run motors and capacitor start-capacitor run motors.

It is, of course, possible to accomplish all the switching requirements by electronic means rather than using mechanical switches as described here.

The present invention therefore provides a pole changing induction motor having an armature wound to provide polyphase operation on starting the motor at a first pole number and switching means operable for reconnecting coils or groups of coils of the winding to produce single-phase operation at one or more alternative pole numbers, the switching means incorporating a switch which connects the single-phase winding or windings with the current supply, the switch being responsive to the speed of the motor so that it closes only when the motor speed reaches a predetermined level, whereby operation of the switching means to select a said alternative pole number will not result in the supply of current to the single-phase winding if the motor speed is below said level.

MA THEMA TICAL ANALYSIS In conventional P.A.M. motors, it is customary to representthe m.m.f. of a 2-phase machine by two sinusoidal waves mutually displaced by 90 electrical degrees. For a p pole-pair machine, the m.m.f. of the two phases are: Ao = m.m.f of phase A = K1 sin pe (1) Ir B = m.m.f. of phase B = K2 sin(pO ±) 2 = K2 cos pe (2) If the amplitudes K1 and K2 are space modulated by two sinusoidal waves, the resultant m.m.f. for each phase would be:: Av = 2 C1 sin pO sin(ke+a) = C1 [cos((p-k)O-a) - cos((p+k)O+a)] (3)

where K1 = 2 C1 sin(k0+a) K2 = 2 C2 sin(k(3+b) k = number of modulating cycles Ir a and bare constants taken to be 0 and-, 2 respectively by Krishnamurthy and Rajaraman.

C1 and C2 are both equal to C in Krishnamurthy and Rajaraman's machines.

Adding equations (3) and (4) gives A" = Be = + 2 C cos(p-k)O (5) Subtracting equation (4) from (3) gives AoBo = -2Ccos(p+k)O (6) The above logic was used by Krishnamurthy and Rajaraman to produce a 3-speed motor. They have pointed out, however, that it is not possible to apply the above logic to the case where p = 2 and k = 1 since the two modulating waves cannot be displaced from each other by 90 degrees on the scale of k.

Referring to the top layer of a 24 slot, unmodulated 4 pole, double layer stator, as shown in Fig. 14, should make the points clear.

It is obvious from Figs. 14(a) and 14(b) that the modulating wave for phase A is a square wave as shown in Fig. 14(c). The modulating wave for phase B could, however, be either the square wave in Fig.

14(d) or Fig. 14(e). Consequently, the modulating waves are rather ill-defined when the original number of pole pairs per modulating pole pair is even, and the simple theory first proposed by Krishnamurthy and Rajaraman is not applicable. To overcome the difficulties of such pole combinations, Krishnamurthy has proposed using assymmetrical modulation, but this requires the omission of coils and the harmonic content is high.

A more detailed analysis indicates that the above restriction does not apply, and in particular, a and b are not necessarily 90 degrees (on the scale of kO) apart. In fact, for p1 = 2, p2 = 3 where p1 and p2 are the unmodulated and modulated pole-pair number respectively, a and b should not be 90 degrees apart.

The following analysis should make the points clear.

Fig. 15(a) shows a 4 pole m.m.f. which is to be modulated by a single square wave (k = 1) as shown in Fig. 15(b). If the origin of the modulating square wave and that of the 4 pole m.m.f. are displaced by "a" radians, half of the original m.m.f. will be reversed as shown in Fig. 15(c). Since there cannot be an abrupt change in m.m.f., the actual m.m.f. will be as shown in Fig. 15(d).

In general, the Fourier coefficient for a 2-pole m.m.f. which is modulated by one complete cycle (k = 1) of modulation can be found as follows: In phase component =

if n = odd p = odd = 4 sin p(#-a)sin n a nIr ifn = even p = even = 0 2 2 if n = odd p = even = --- cos(p+n)a + --- cos (p+n)# (p-n)# 4 (p - n)a - - sin p(#-a) sin n a n# 2 2 ifn=even p=odd = --- cos(p+n)a + --- cos (p+n)# (p-n)# (p-n)a where n is the order of harmonic on the scale of mechanical degrees. The subscript A in n refers to phase A of a two-phase winding.

Similarly, the out of phase component for the m.m.f. shown in Fig. 15(d) can be found in a similar manner.

Out of phase component =

4 if n = odd p = odd = - - sinp(ir-a)cosna n# ifn=even p=even = 0 2 2 ifn=even p=odd = - sin(p+n)a+ (p+n)# (p-n)# sin(p-n)a 2 2 ifn = odd p=even = - ---- sin(p+n)a + - sin (p+n)# (p-n)# 4 (p-n)a - - sin p(ir-a)cos n a n# Likewise, the Fourier coefficient for phase B is found to be: : = = In phase component A = - -cos p(r-b)sin nb n# n = odd p = even = 0 n = even p = even 2 = --- sin(p+n)b+ (p+n)# 2 4 sin-(p-n)b- -cos (p-n)# n# p(ir-b)sin nb n = odd p = even 2 2 = ---- sin(p+n)b + (p+n)# (p-n)# sin(p-n)b n = even p = odd b8n= Out of phase component = - - cos p(7r-b) cos nb n# n = odd p = odd = 0 n = even p = even 2 2 = + cos(p+n)b - --- (p+n)# (p-n)# cos(p-n)b n = even p = odd 2 2 = + --- cos(p+n)b (p+n)# (p-n)# 4 cos(p-n)b- - cos p(7r-b) n7r cos nb n=odd p=even The resultant Fourier coefficient when phase B is subtracted from phase A is: In phase component = Ran = aAn-KieaBn (7) Out of phase component = Rbn = bAn-KrebBn (8) where Ran and Rbn are the resultant Fourier coefficients for the nth harmonic, and Kr, = number of effective conductors in phase B KwB Kr number of effective conductors in phase A KwA actual number of conductors in phase B where Kr = actual number of conductors in phase A KWA, KWB are winding factors for phases A and B respectively.

If one wants to modulate a 4 pole m.m.f. to give 6 poles, one should put Ra1 = Rbl = 0 in equations (7) and (8) in order to eliminate the 2 pole subharmonic.

In general, it is impossibleto solve equations (7) and (8) analytically, but it is possible to solve the above two equations numerically by computer.

The solution for p = 2, n = 1, Kre = lisa = 81.7 and b = 143.3 .

In the case of the 4 pole, 24 slot machine, the values chosen are a = 82.5 (Fig. 14(f)) and b = 142.5 , and it can be shown that the 2 pole component has been eliminated all together in the resultant m.m.f.

In the case of the 4 pole, 36 slot machine, as shown in Fig. 16, the values chosen are a = 75 and b = 135 (Fig. 16(b)).

Note that according to equations (7) and (8), it is not possible for one to eliminate the two pole subharmonic for p = 2 if a = 0 and b = 90 . This conclusion is of course more realistic than those deduced from the simple theory of Krishnamurthy and Rajaraman.

In the case of p = 2, n = 1, Kr, = 1.2, the solution is a = 77.1", b = 139.8 .

Likewise, it is possible to apply the more elaborate theory to any pole number combinations without any of the restrictions imposed by Krishnamurthy and Rajaraman.

In the case of concentric coil windings, it might not be possible for one to apply the modulating waves at the correct values of a's and b's. As a result, the unwanted pole number does appear in the resultant m.m.f. This, however, is not due only to the wrong values of a's and b's, but is due mainly to the absence of chording in concentric coils. Neverthe less, by choosing the correct value of relative dis placement for a and b (in the case of p1 = 2, p2 = 3, the relative displacement is 61.6 degrees for Kr, = 1 and is 62.7 degrees for Kr, = 1.2. They are obviously about 60 degrees), it is possible for one to reduce the unwanted pole number.

There are certain cases when one could not apply the modulating waves with the required length. For example, if the unmodulated pole pair number is 3, and k = 2, then it is obvious that the modulating waves need to be unsymmetrical as shown in Fig.

17, since some half-cycles of the modulating wave would cover 2 pole lengths while the other halfcycles will cover 1 pole length only. In such cases, it is obvious that some subharmonics will be generated, buttheyareofcourse not detrimental to the performance of the motor.

APPENDIX In order to demonstrate the practicality of the proposed technique, this appendix gives the test results of the triple-speed winding whose harmonic contents are listed in Table 1.

A conventional 36 slot, single-phase motor frame was used to accommodate the triple-speed winding.

In its standard form, this stator is wound as a threephase, 6-pole motor giving an output power of 250W. Each of the 44 bars in the rotor is skewed by 2 bars.

The rated performance figures for the triple speed 4/6/8 pole motor with the permanent capacitor in the 4-pole connection is as given in Table Al.

4-pole 6-pole 8-pole Output power 450W 120W 70W Speed 1415 rev/min 930 rev/min 700 rev/min Efficiency 69.156 51;6% 27.6,"3 Power Factor 0.836 0.521 0.456 Current 3.89 A 2.23 2.78 A Starting torque 69.55 Full - - load torque

Table Al Rated performance figures of the 4/6/8 pole motor at an operating voltage of 200V. Furthermore, the complete range of torque versus speed characteristics is as shown in Fig. 20. Note that the test was carried out at a phase voltage of 180V in order to avoid overheating of the motor.

This motor is suitable for fan driving duties in which the torque increases with the square of the operating speed.

Claims (4)

1. An induction electrical machine having afer- romagnetic core with a number of slots and wound with concentric coils which, in each of two phases A and B, have equal numbers of turns, each slot containing 0, n or 2n conductors of phase A and 0, k,n or 2krn conductors of phase B wherein 2n is the number of turns in a coil of phase A, 2krn is the number of turns in a coil of phase B, and k, is the winding ratio between phases B and A, and means for interconnecting the coils in two or three different ways to produce respectively two orthree different pole numbers, the coils at a first pole number producing a two-phase winding, the or each other pole number using coils from the two phases equally and combined as a single phase winding.

2. An induction electrical machine according to claim 1 wherein three different pole numbers are provided.

3. An induction electrical machine according to claim 2 wherein the two-phase operation is at the lowest or highest of the three alternative pole num bers.

4. An induction electrical machine having a fer romagnetic core wound with concentric coils sub stantially as described herein with reference to the accompanying drawings.