DC winding

Terminology and definitions

Concept

A DC winding is formed by as many individual coils as the number of slots of the machine. All these coils are identical except for an angular shift. Since the coils have an input slot and an output one, a slot will always have two coils wound inside it.

A key characteristic of a DC winding is that, unlike the 3-phase one, a coil is characterized (other than by its input and output slots) by the two commutator segments connected to it (one for the input side and a second for the output side). These commutator segments will connect the coil to the brushes and, therefore, to the DC source feeding the machine.

That means that two main variables are needed to fully identify a coil:

The throw – The coil pitch number of slot pitch between coil input and coil output.
The commutator pitch: the number of commutator segments between the segment connected to the coil input and the segment connected to the coil output.

Note: The graphic below gives an example of a reference coil with a throw 4 and a commutator pitch 1 This winding corresponds to a lap winding, simplex with progressive coil connection (see below).

Table 1. Example

1	Throw
2	Commutator pitch

These two parameters are not chosen randomly but to optimize the electromotive force. Two main types of winding exist: wave winding and lap winding.

Lap winding: The ends of one coil are connected to consecutive commutation segments (i.e., the commutator pitch absolute value is equal to 1 for simplex winding)
Wave winding: The ends of one coil are connected to commutator segments separated by an angular distance as close as two pole pitch as possible (for simplex winding)

For both winding types, the throw is usually as close as possible to a pole pitch.

Another two important concepts that define a DC winding and are applicable to both wave and lap windings are the plex and the coil connection.

The plex defines the number of commutator segments in contact with the same brush at a given time. It has a great influence on the number of parallel paths and, therefore, on the machine’s back EMF and the maximum current.
The coil connection can be progressive or regressive: In a progressive connection the commutator segments are connected following the same direction as the winding (i.e., commutator pitch is positive) while in a regressive connection the commutator segments are connected following the opposite direction as the winding (i.e., commutator pitch is negative).

Winding type

Table 2. Winding type – Graphical example

1	Lap winding example
2	Wave winding example

Plex

Table 3. Plex – Graphical examples for a lap progressive winding

1	Simplex winding
2	Duplex winding

Coil connection

Table 4. Coil connection – Graphical example for lap progressive and regressive winding

1	Progressive winding
2	Regressive winding

Winding Architecture – Outputs

Introduction

Output is quite like 3-phase winding, but some specific parameters arise when dealing with DC machine winding. For the sake of completeness, the parameters are listed in the tables below.

Characterization - Winding

Table 5. Characterization - Winding
Label	Tooltip, note, formula
No. poles	Number of rotor pole pairs =p. 2p = number of poles.
No. slots	Number of stator slots
No. Layers	Number of layers – For a DC winding it is always equal to 2
Winding type	The winding type: Lap or wave
Plex	The plex (simplex, duplex or triplex)
Coil connection	Connection type: Progressive or regressive Progressive connection: Commutator segments are connected following the same direction as winding (i.e., commutator pitch is positive). Regressive connection: Commutator segments are connected following the opposite direction as winding (i.e., commutator pitch is negative).
Commutator pitch	Number of commutator segments between the segment connected to the coil input and the segment connected to the coil output.
No. parallel paths	Number of parallel paths. For a wave winding it is equal to twice the plex. For a lap winding it is equal to number of poles * plex
Coil layout	Coil layout inside the slot – Full, Superimposed or Adjacent.
Throw (coil pitch)	Number of slot pitch between coil input and coil output.

Characterization - Coil

Table 6. Characterization - Coil
Label	Tooltip, note, formula
No. turns per coil	Number of turns per coil.
No. turns in series	Number of turns in series N_turns=N_coils/(2×P_paths ) Where Ncoils is the total number of coils and Ppaths the number of parallel paths
No. conductors	Total number of conductors N_coils=2×N_slots×Turns Where Ncoils is the total number of coils and Nslots is the number of slots and Turns is the number of turns per coil.

Lengths

Table 7. Lengths
Label	Tooltip, note, formula
Total conductor length	Total conductor length.
Mean turn length	Mean turn length.
Coil connection length	Additional length corresponding to the connections between coils and commutator segments.
Axial overall length	Axial overall length. Length between the two extremities of the winding i.e. between connection side and opposite connection side.

Areas in slot

Table 8. Areas in slot
Label	Tooltip, note, formula
Conductive area	Conductive area inside one slot. A_CondSlot=A_Cond×Turns Where Turns is the number of turns per coil.
Conductor conductive area	A_Cond=N_wires×A_wire This area allows to compute the current density.
Wire conductive area	Wire area (without insulation) = A_wire
Slot area	Slot area = A_slot
Insulation area	Insulation area inside one slot =A_InsulSlot One considers the slots of the machine where the number of coils is maximum.
Free area	A_Free= A_slot- A_CondSlot- A_InsulSlot

Fill factors

Table 9. Fill factors
Label	Tooltip, note, formula
Gross fill factor	Gross fill factor. Occupancy rate of the slot (conductive area only). (Conductor conductive area)/(Slot area)×100
Net fill factor	Net fill factor. Occupancy rate of the slot (conductive area + insulation area). (Conductor conductive area+insulation area)/(Slot area)×100

Resistances

Table 10. Resistances
Label	Tooltip, note, formula
Single coil resistance	Single coil resistance
Parallel path resistance	Resistance of one of the parallel paths
Total resistance	Total resistance of the machine at its terminals
Winding straight part resistance

End-winding resistance
Connection side end-winding resistance
Opposite connection side end-winding resistance

Note: The reference temperature is a user input parameter defined in the winding – X-Factor tab.

Note: The connection side end-winding resistance considers the additional length corresponding to the connection between coils and commutator segments.

Inductances

Table 11. Inductances
Label	Tooltip, note, formula
End winding	Total end winding inductance (including the two sides of the machine).
C.S. end winding	Connection side end winding inductance.
O.C.S. end winding	Opposite connection side end winding inductance.

Masses and costs

For additional information, refer to the sections dedicated to the coil and conductor settings and End-winding topology.

Table 12. Masses and costs
Label	Tooltip, note, formula
Total	Total winding mass.
Electric conductor	Conductive part mass.
Total insulation	Total winding insulation mass (wire + conductor + coil insulation + liner + phase separator).
Wire insulation	Wire insulation.
Conductor insulation	Conductor insulation.
Coil insulation	Coil insulation.
Liner insulation	Liner insulation.
Phase separator insulation	Phase separator insulation.
Impregnation insulation	Impregnation insulation
Wedge insulation	Wedge insulation, only when the slot topology contains a wedge