# Motor Winding Calculations

Electric motors are essential devices used in a broad range of industries to convert electrical energy into mechanical energy. These motors generate rotational force due to the interaction between the motor’s magnetic field and electric current in the motor winding.

As simple as the electric motor’s function might seem, a lot of effort goes into designing and specifying these motors for several applications. One of the critical areas that engineers must consider when designing motors is the winding. Wrongly specifying the motor winding wire types, materials, and dimensions are major causes of poor motor performance.

This article presents valuable information about motor windings as well as a few motor winding calculations that designers must know.

The stator of an electric motor with copper windings

## What is Motor Winding?

Motor windings in electric motors are insulated wires wrapped around a magnetic core (usually laminated soft iron). These wires provide a path for electric current to flow and create the magnetic field to spin the motor's rotor.

## Motor Winding Materials: A Key to Improving the Performance of Electric Motors

Today, there exist so many types of motor winding materials that it can be overwhelming to find the ideal one for a particular application. As a rule, there’s no perfect material for motor windings: the right choice will depend on the designer’s budget, electrical conductivity, density, and flexibility requirements.

Here are some of the most desirable motor winding materials today:

### Motor Winding Material #1: Copper

Copper is the most common material used for motor winding construction. This is primarily due to its high electrical conductivity ( 5.96 x 107 S/m) and relatively low cost. Designers typically use copper with a very thin enamel coating since it prevents short circuits from occurring and extends the longevity and efficiency of the wire.

However, a major challenge with copper as a motor winding material is its high density (8.96 g/cm3). It might not be the ideal material choice for applications requiring lightweight materials, such as aircraft and electric vehicles.

### Motor Winding Material #2: Aluminum

Aluminum is another popular material used for motor winding design. With a density of 2.7 g/cm3 (almost one-third the density of copper), aluminum is a better choice in applications where lightweight materials are essential.

However, aluminum has a lower electrical conductivity (3.69 x 107 S/m) than copper . Designers will have to compensate for this lower conductivity by using an aluminum wire with a larger cross-section than an equivalent copper wire to offer the same conductance and power outputs. This means that windings made with aluminum wires would typically have a greater volume than an equivalent copper wire motor.

### Motor Winding Material #3: Silver

Wires made of silver offer greater electrical conductivity than copper and aluminum winding wires. However, silver wires don’t come off the line cheap: the cost of a silver wire is substantially higher than an equivalent copper or aluminum wire.

### Motor Winding Material #4: Carbon Nanotubes

Carbon nanotube fibers and yarns are gaining popularity in the electric motor industry; they are poised to replace copper and aluminum winding wires in the coming years. These fibers are more flexible and stronger than copper wires. They are also lighter (about nine times lighter) than an equivalent copper wire.

But these are not the only positives of using carbon nanotubes as motor winding materials.

In a study at the Lappeenranta University of Technology (LUT) in Finland, the research team created an electric motor prototype that used woven carbon nanotube fibers as the motor winding material. Their results indicated that designers could reduce the Joule losses in the motor windings to half of the present-day machines only by replacing copper with carbon nanotube fibers.

## Some Key Motor Winding Calculations

The stators used in electric motors are cylindrical, with slots shaped like wedges. The number of slots depends on how many phases of power are provided to the coil windings. For example, a simple AC single-phase motor typically has four slots containing two pairs of coil windings. In contrast, a three-phase motor typically features six slots containing three pairs of coil windings.

One of the major ways designers can maximize the torque output in a motor is by maximizing the amount of wire inserted into each slot.

Here are some essential motor winding calculations that designers should consider.

Slot Fill: is the measure of the total cross-section area of materials going into the slot. These materials include the motor winding wire, wedges, and liners, among others. It is expressed as:

Where:

Aw=Total cross-section area of the motor winding wire (including the wire insulation)

Am=Total cross-section area of all the insulating materials

As=Total cross-section area of the bare slot

Slot Fill Factor: is the ratio of the cross-section occupied by the copper wire inside the stator to the total available area in the bare slot.

Theoretically, a “slot fill factor ” of 1 results in the maximum torque output of the motor. But it’s almost always impossible to build a motor that meets this requirement since motor winding wires leave gaps no matter how designers arrange them. The majority of motor designs today have a slot fill factor ranging between 0.6 and 0.70.

Motors with higher slot fill factors are usually more challenging and expensive to manufacture as designers require specialized tooling to create them.

## Conclusion

While this article provides helpful information about motor winding, there still exist many factors that engineers need to consider to design a motor successfully. For example, designers still have to specify the type of motor winding connection, mutual phase displacement, and type of single-phase winding, among others.

Engineers are advised to reach out to electric motor manufacturers to discuss their application requirements.