#### Basic parameters of motor windings

##### 1. Mechanical angle and electrical angle

When the motor windings are distributed in the core slots, they must be embedded and connected according to a certain rule to output symmetrical sinusoidal alternating current or generate a rotating magnetic field. In addition to being related to some other parameters, we also need to use the concept of electrical cost to reflect the law of the relative positions between each coil and winding. From mechanics, we know that a circle can be divided into 360°, and this 360° is what we usually call the mechanical angle. In electrical engineering, the angle unit for measuring electromagnetic relations is called electrical angle, which divides each cycle of sinusoidal alternating current into 360° on the horizontal axis, that is, when the conductor space passes through a pair of magnetic poles, the electromagnetic angle changes by 360°. Therefore, the relationship between electrical angle and mechanical angle in the motor is: electrical angle α = pole pair number xP x360°. For example, for a two-pole motor, the pole pair number p = 1, then the electrical angle is equal to the mechanical angle, for a four-pole motor, p = 2, then there are two pairs of magnetic poles in one circumference of the motor, and the corresponding electrical angle is 2×360° = 720°. And so on.

##### 2. Pole pitch (τ)

The pole pitch of the winding refers to the distance of each magnetic pole on the circumferential surface of the core. It usually refers to the slot spacing between the centers of two adjacent magnetic poles of the motor core. The stator core is calculated by the slot spacing of the inner air gap surface; the rotor is calculated by the slot spacing of the outer air gap surface of the core. There are usually two ways to express the pole pitch, one is to express it in length; the other is to express it in the number of slots. It is customary to express it in the number of slots. Generally, the pole pitch is τ=Z1/2p.

##### 3. Pitch (y)

The number of core slots occupied by the two sides of each coil element of the motor winding is called the pitch, also known as the span. When the pitch of the coil element is equal to the pole pitch, it is a full-pitch winding, y=τ; when the pitch of the coil element is less than the pole pitch, it is called a short-pitch winding, y＜τ; and when the pitch of the coil element is greater than the pole pitch, it is called a long-pitch winding y＞τ. Since short-pitch windings have many advantages such as shorter ends, less electromagnetic wire material, and higher power factor, short-pitch windings are used without exception in the more commonly used double-layer windings.

##### 4. Winding coefficient

The winding coefficient refers to the product of the short-distance coefficient and the distribution coefficient of the AC distributed winding, that is,

Kdp1=Kd1Kp1.

##### 5. Slot angle (α)

The electrical angle between two adjacent slots of the motor core is called the slot angle, usually represented by a, that is,

α=total electrical angle/z1=p×360°/z1

##### 6. Phase belt

The phase belt refers to the area occupied by each phase winding at each magnetic pole, usually expressed in electrical angles or the number of slots. If the winding of a three-phase motor under each pair of magnetic poles is divided into six areas, there are three under each pole. Since the slot angle α=360°P/Z, if the motor has 4 poles and 24 slots, the width of each phase and each area is qα=Z/6P*360P/Z=60°, and the winding embedded in this distribution is called a 60° phase belt winding. Due to the obvious advantages of the 60° continuous phase belt winding, this winding is used in most three-phase motors.

##### 7. Number of slots per pole per phase (q)

The number of slots per pole per phase refers to the number of slots occupied by each phase winding in each magnetic pole, and the number of coils to be wound in each pole per phase winding is determined based on it. That is,

q=Z/2Pm

Z: number of core slots; 2P: number of motor poles; m: number of motor phases.

Calculation result, if q is an integer, it is called integer slot winding; if q is a fraction, it is called fractional slot winding.

##### 8. Number of conductors per slot

The number of conductors per slot of the motor winding should be an integer, and the number of conductors per slot of the double-layer winding should also be an even integer. The number of conductors per slot of the wound rotor winding is determined by its open circuit voltage. The number of conductors per slot of the wound rotor of a medium-sized motor must be equal to 2. The number of conductors per slot of the stator winding can be calculated by the following formula:

NS1=NΦ1m1a1/Z1

NS1: number of conductors per slot of the stator winding;

NΦ1: number of conductors per slot calculated according to the air gap flux density;

m1: number of phases of the stator winding;

a1: number of parallel branches of the stator winding;

Z1: number of stator slots.

##### 9. Number of conductors in series per phase

The number of conductors in series per phase refers to the number of turns of the bus in series for each phase winding in the motor. However, the number of turns of the bus in series is related to the number of parallel branches in each phase winding. If the number of parallel branches of the motor is 1-way connection, then all the turns of the series wires of the coils under each pole of the motor should be added to become the number of turns of the bus in the phase winding. If there are multiple parallel branches in each phase winding of the motor, that is, the motor is 2-way connection, 3-way connection, etc., then the number of conductors in series per phase can only be based on the number of turns of the wires in series in one of the windings. Because the number of turns of the series wires in each branch in the phase winding is the same, it is impossible to increase the number of turns of the series wires after connecting them in parallel to form the phase winding.

##### 10. Total number of coils

The windings in the motor are composed of coils of various sizes and shapes. Since each coil has two component sides embedded in the core slot, that is to say, each coil must be embedded in two slots. In a single-layer winding, since only one coil element side is embedded in each slot, the total number of coils is only equal to half of the total number of slots; in a double-layer winding, since two coil element sides are embedded in the upper and lower layers of each slot, its total number of coils is equal to the number of core slots.