Mike Howell
EASA Technical Support Specialist

For those who work almost exclu­sively with lap or concentric wound three-phase stators, wave wound rotor connections can be a challenge. This is especially true if connection data gets lost or if an existing winding con­nection is damaged during a failure. In these cases, it is useful to have a practical method for laying out a valid connection diagram.

Why use wave windings?
Both lap and wave rotor windings are used in wound-rotor induction machines. It is fairly common to see lap windings in smaller, random wound rotors. However, for larger form-wound rotors, wave windings are almost always employed and it is worthwhile to mention a couple of the reasons why. The apparent (centrifu­gal) force exerted on a rotating object such as a rotor winding is proportional to its mass, radius (of gyration), and the square of its speed of rotation as shown below.
F ∝ m·r·n²
where:
F    is the force
m    is the mass
r    is the radius of gyration
n    is the speed, rpm

The magnitude of this force increas­es greatly with machine size. For a lap winding, the additional conductor ma­terial required to make pole jumpers can be significant. With a wave wind­ing, these pole jumpers are eliminated and the connections that are required can typically be more symmetrically distributed. This leads to a winding that can be more easily braced and an overall rotor assembly that can be more easily balanced.

Before getting started
The procedure included here is applicable to many machines, but it is conditional as follows. The number of slots per pole per phase (SPP) must be an integer or an integer + ½. SPP examples are provided below. If this condition is violated, contact EASA’s Technical Support Department for assistance.
SPP = Q / (M·P)
where
SPP    is the number of slots per pole per phase
Q    is the number of rotor slots
P    is the number of poles
M    is the number of phases

Like all three-phase windings, wave wound rotors are connected ei­ther wye or delta and most have either 1 or 2 circuits per phase. Additionally, most form wound rotor slots will have 2 layers with 1 conductor per layer. If there is uncertainty about the winding data, it can be verified by using EASA’s “AC Motor Verification & Redesign” program. For this purpose, only the air gap flux density and current den­sity should be evaluated. If the stator winding data is available, the air gap flux density of the rotor and stator windings can be compared and should be close to one another (+/- 10%).

WAVE basics + procedure
As with most types of windings, there are multiple ways to configure wave windings and achieve practically the same performance. For simplic­ity and efficiency, this procedure will only use the progressive-retrogressive method. For reasons that will become apparent later, this method is also called the long-pitch, short-pitch (LP-SP) method.

Some important terms for wave windings are demonstrated graphi­cally in Figure 1. The back pitch (BP) is the same as the coil pitch or span for a lap winding. As such, it is expressed in the same fashion with examples for a 36 slot, 4-pole, and full-pitch coil be­ing “slot 1 to 10” or “9 teeth spanned.” The front pitch (FP) is where coil ends are connected on the lead end. For example, one front pitch connection is shown in Figure 1 and it is connecting the lower conductor in slot 10 to the upper conductor in slot 19. This is a front pitch of slot 1 to 10 or 9 teeth spanned. The required back pitch and front pitch can easily be determined once the slots per pole per phase (SPP) is known.

For SPP = integer (e.g., 3, 4, 5)
back pitch (BP) = 3·SPP
front pitch (FP) = back pitch
For SPP = integer + ½ 
(e.g., 3.5, 4.5, 5.5)
back pitch (BP) = (3·SPP) + ½
front pitch (FP) = back pitch – 1

One complete coil series for a 4-pole wave winding is shown in Figure 1. In the completed winding, there will be two coil parts per phase connected by a jumper. The jumper is called a reversing jumper because the first coil part progresses clockwise as shown in Figure 1 while the second part pro­gresses counter clockwise. In an LP-SP winding, the first part is progressive and the second part is retrogres­sive. When SPP = integer, the number of coil series per part = SPP. When SPP = integer + ½, one part has SPP + ½ coil series and the other has SPP – ½ coil series. 

For the LP-SP method, all coils will have the same back pitch and most of the coils will have the same front pitch. However, due to the connections, a small num­ber of coils will have a long front pitch (LP) equal to the normal front pitch + 1. Also, another small group will have a short front pitch (SP) equal to the normal front pitch – 1. The number of LP and SP coils can be determined if SPP is known.
For SPP = integer (e.g., 3, 4, 5)
LP count = SPP – 1 coils
SP count = SPP – 1 coils
For SPP = integer + ½ 
(e.g., 3.5, 4.5, 5.5)
LP count = SPP – 1 ½ coils
SP count = SPP – ½ coils

For this method, we will identify the start of the first phase as A1. With the number of slots (Q) known and using a clockwise numbering scheme, it is not necessary to diagram every connection.

The connections for each phase will be in an identical pattern such that knowing the starting location of the first phase and the connection pattern is sufficient information for correctly connecting the rotor. We will arbitrarily use a clockwise phase sequence of A – C – B.

Each phase will have four leads iden­tified by phase and number (e.g., A₁, A₂, A₃, A₄ for phase A). The phase connection pattern required for the LP-SP method where SPP = integer is shown in Figure 2 using phase A as an example. For SPP = integer + ½, the proper connection pattern is provided in Figure 3. For phases B and C, the first phase leads B₁ and C₁ will be determined by cal­culating the number of normal front pitch coils between the end of one phase and the beginning of the next.

The number of normal front pitch coils (NP) between the end of each phase and the beginning of the next (i.e., A₄ → C₁, C₄ → B₁, B₄ → A₁) can be calculated as a function of the number of poles (P), slots (Q) and SPP. We will call these values Z_AC, Z_CB and Z_BA and we will look at two distinct cases based on the number of poles.

1. When the number of poles (P) is not 6 or a multiple of 6  (e.g., 12, 18, 24,  30…), the phases can be equally distributed 120° mechanically. In this case, 
Z_AC = Z_CB = Z_BA = Q/3 – 4·SPP
where
Z        is the number of NP coils between phases
Q        is the number of rotor slots
SPP    is the number of slots per pole per phase

2. When the number of poles (P) is 6 or a multiple of 6 (e.g., 6, 12, 18, 24…), the phases can­not be equally distributed 120° mechanically. In these cases,

Z_AC = (P-6) · SPP
Z_CB = (P-6) · SPP
Z_BA = P·SPP
Note that when the number of poles is 6, Z_AC and Z_CB are 0.    

More than 2 conductors per slot
Up to this point, we have not ad­dressed cases where there are more than 2 conductors per slot. One conductor can be made of multiple parallel strands but they all will termi­nate in the same clip. If there are more than 2 conductors per slot, the number of clips will be increased as if there were more slots with 2 conductors per slot. For example, an 8-pole rotor with 48 slots and 2 conductors in each layer (4 conductors per slot) has the same number of coils and clips as an 8-pole rotor with 96 slots and 1 conductor in each layer (2 conductors per slot). To compare this construction with a lap winding, a top conductor connected to a bottom conductor one back pitch over is the same as one turn. Thus, when there are additional conductors per layer, there is essentially a multi-turn coil with the number of turns equal to the number of conductors per layer.

For the purposes of applying this connection procedure, one can pro­ceed by using a substitute number of slots (Q₁) for Q and a substitute number of slots per pole per phase (SPP₁) for SPP.
Q₁ = Q·N
SPP₁ = SPP·N
where
Q₁    is the substitute number of rotor slots
Q    is the number of rotor slots
N    is the number of conductors per layer
SPP₁    is the substitute number slots per pole per phase
SPP    is the number of slots per pole per phase

External connections
The LP-SP diagrams in Figure 2 and Figure 3 show that each phase will have up to four accessible points. In the diagrams, phase A is used as an example and the four points iden­tified as A₁, A₂, A₃ and A₄. In these diagrams, A₁ and A₂ are the start and finish of the first winding part while A₃ and A₄ are the start and finish of the second winding part. And, in those diagrams, A₂ and A₃ are connected with the reversing jumper (J) which places the two winding parts for phase A in series.

Figure 4 provides the external connections possible for the LP-SP method described thus far. With each phase having two winding parts with four accessible points, the available connections are no different than a standard three-phase stator: 1Y, 1∆, 2Y and 2∆.

In the case of the two-circuit connec­tions, the reversing jumper is simply omitted. The two-circuit connections also present the same potential issues as parallel circuit connections with three-phase stators. Most importantly, both parallel branches of the phase must have the same number of turns in series to produce a balanced wind­ing. This means when SPP = integer + ½ (e.g., 3.5, 4.5, 5.5), a two-circuit connection cannot be made by sim­ply accessing the two winding parts where the reversing jumper is omit­ted. This is not to say that a two-circuit connection is impossible when SPP = integer + ½; just that it requires different and more complex internal connections which are beyond the scope of this article.

Example – poles not 6 or multiple of 6
For an example, let’s look at an LP-SP connection for a rotor with 48 slots, 8 poles, 2 conductors per slot (1 conduc­tor per layer) and a 1Y connection. The working diagram provided in Figure 5 is sufficient information for complet­ing the rotor connection. Refer back to Figure 2 for the generic diagram.

1. The number of slots per pole per phase is: SPP = Q / (M·P) = 48 / (3·8) = 2
2. The back pitch is: BP = 3·SPP = 6 = Slot 1 to 7
3. The front pitch is: FP = BP = 6
4. The long front pitch coil quantity and pitch are: LP = SPP – 1 = 1 with FP of 1 to 8
5. The short front pitch coil quantity and pitch are: SP = SPP – 1 = 1 with FP of 1 to 6
6. The normal front pitch coil quantity between bottom leads is: 2· SPP = 2·2 = 4
7. The normal front pitch coil quantity between phases is: Q/3 - 4·SPP = 48/3 - 4·2 = 8
8. The beginning slot number for phase A is: A₁ = 1

Example: poles exactly 6
For this example, let’s look at an LP-SP connection for a rotor with 63 slots, 6 poles, 2 conduc­tors per slot (1 conductor per layer) and a 1Y connection. The working diagram provided in Figure 6 is sufficient information for completing the rotor connec­tion. Refer back to Figure 3 for the generic diagram.

1. The number of slots per pole per phase is: SPP = Q / (M·P) = 63 / (3·6) = 3.5
2. The back pitch is: BP = 3·SPP + ½ = 11 = Slot 1 to 12
3. The front pitch is: FP = BP – 1 = 10
4. The long front pitch coil quantity and pitch are: LP = SPP – 1 ½ = 2 with FP of 1 to 12
5. The short front pitch coil quantity and pitch are: SP = SPP – ½ = 3 with FP of 1 to 10
6. The normal front pitch coil quantity between bot­tom leads is: 2· SPP = 2·3.5 = 7
7. The normal front pitch coil quantity between phases is: Z_AC = 0, Z_CB = 0, Z_BA = 6·3.5 = 21
8. The beginning slot number for phase A is: A₁ = 1

Example: poles greater than 6 and a multiple of 6
For this example, let’s look at an LP-SP connection for a rotor with 72 slots, 12 poles, 2 conductors per slot (1 conductor per layer) and a 1Y connec­tion. The working diagram provided in Figure 7 is sufficient information for completing the rotor connection. Refer back to Figure 2 for the generic diagram.

1. The number of slots per pole per phase is: SPP = Q / (M·P) = 72 / (3·12) = 2
2. The back pitch is: BP = 3·SPP = 6 = Slot 1 to 7
3. The front pitch is: FP = BP = 6
4. The long front pitch coil quantity and pitch are: LP = SPP – 1 = 1 with FP of 1 to 8
5. The short front pitch coil quantity and pitch are: SP = SPP – 1 = 1 with FP of 1 to 6
6. The normal front pitch coil quan­tity between bottom leads is: 2· SPP = 2·2 = 4
7. The normal front pitch coil quan­tity between phases is: Z_AC = (P-6)·SPP = 12, Z_CB = (P-6)·SPP = 12, Z_BA = P·SPP = 24 
8. The beginning slot number for phase A is: A₁ = 1

Additional Information
This procedure is based on methods provided by Dr. Michael Liwschitz-Garik in his 1950 book, Winding Alternating-Current Machines, which would be a valuable addition to any service center’s library. Search the second-hand book sites to grab a copy while they can still be found. It has a wealth of information and with excep­tion to changes due to improvements in insulation technology, it is all relevant today. The author of this article is cer­tainly grateful to a mentor, Jim Oliver, for a copy given some years ago. 

AVAILABLE IN SPANISH

Categories: AC motors, Rotors, Wound rotors, Wound rotor motors

Tags: Wound rotor

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