# Winding factor

The winding factor for a specific winding expresses the ratio of flux linked by that winding compared to flux that would have been linked by a single-layer full-pitch non-skewed integer-slot winding with the same number of turns and one single slot per pole per phase. The torque of an electric motor is proportional to the fundamental winding factor.

The winding factors are often expressed for each space harmonic. If a winding factor is referred to without reference to a harmonic number, the fundamental winding factor is addressed. In the Emetor winding calculator, both the fundamental winding factor as well as the winding factor harmonics are calculated.

The winding factor $k_w$ can generally be expressed as the product of three factors, the pitch factor $k_p$ (sometimes also called coil-span or chording factor), the breath coefficient or distribution factor $k_d$, and the skew factor $k_s$: $$k_w=k_p\cdot k_d\cdot k_s$$

The pitch factor $k_p$ reflects the fact that windings are often not fully pitched, i.e. the individual turns are reduced in order to decrease the length of the end-turns and do not cover a full pole-pitch (also called chorded).
Example:
2-pole 6-slot winding with coil span of 3 slot pitches (i.e. full pitch): $k_p=1.0$
2-pole 6-slot winding with coil span of 2 slot pitches: $k_p=0.866$
2-pole 6-slot winding with coil span of 1 slot pitch: $k_p=0.5$

The distribution factor $k_d$ reflects the fact that the winding coils of each phase are distributed in a number of slots. Since the emf induced in different slots are not in phase, their phasor sum is less than their numerical sum.
Example:
2-pole 6-slot winding with 1 slot per pole per phase: $k_d=1.0$
2-pole 12-slot winding with 2 slots per pole per phase: $k_d=0.966$
2-pole 18-slot winding with 3 slots per pole per phase: $k_d=0.96$
2-pole 24-slot winding with 4 slots per pole per phase: $k_d=0.958$
2-pole winding with an infinite number of slots per pole per phase: $k_d=0.955$

The skew factor $k_s$ reflects the fact that the winding is angularly twisted, which results in an angular spread and reduced emf.
Especially squirrel-cage induction motors have their rotor bars skewed by one slot-pitch in order to reduce the winding factor harmonics introduced by the slotting of the stator.

According to our definition of winding factor (The winding factor for a specific winding expresses the ratio of flux linked by that winding compared to flux that would have been linked by a single-layer full-pitch non-skewed integer-slot winding with the same number of turns and one single slot per pole per phase.), the winding factor of these single-layer full-pitch non-skewed integer-slot windings with one single slot per pole per phase must be 1.0!
Examples of winding layouts that have a winding factor of 1.0:
Single-layer 2-pole 6-slot integer-slot winding.
Single-layer 4-pole 12-slot integer-slot winding.
Single-layer 6-pole 18-slot integer-slot winding.
Single-layer 8-pole 24-slot integer-slot winding.