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# DC Motors

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# DC Motors

Every motor generates heat, even when at zero speed, and this will lead to an increase of the motor temperature. Especially when running in continuous operation, there is a good change that a motor, which is perfectly capable of generating the needed output power, will heat up beyond its thermal limit and break down.

As explained in the previous section the thermal limit is indicated in the torque speed curve by the maximum continuous torque line. To generate such a line, a thermal model is used. This thermal model is also part of the dynamic model that is used in 20-sim. This section describes the thermal model of permanent magnets motors.

In standard brush DC motors the coils are part of the rotor. To create a thermal model, various components will be identified first.

## Heat Generation

Heat is generated in the motor at every place where energy is lost: coils, bearings, iron etc. Because the main source of energy loss is in the coils due to the coil resistance, we start at the coils. The coils act as a heat source and generate a heat flow equal to:

## Thermal Capacity

The rotor package, consisting of the coils and possibly iron and other material, will heat up due to the generated heat. The temperature increase depends on the generated heat dQ, the heat capacity of the rotor Ccoil and the transfer of heat to the stationary housing of the motor dQcoil-housing:

## Thermal Resistance

The heat flow from the coils to the housing dQcoil-housing depends on the temperature difference between the rotor and the housing and the thermal resistance Rcoil-housing :

Thermal Capacity

Like the rotor, the housing will also heat up. The temperature increase depends on the heat coming from the rotor dQrotor-stator, the heat capacity of the housing Chousing and the transfer of heat to the environment dQhousing-amb:

## Thermal Resistance

The heat flow from the stator to the environment stator dQhousing-amb depends on the temperature difference between the housing and the environment and the thermal resistance Rhousing-amb:

The thermal resistance Rhousing-amb depends on the motor mounting and external cooling. In most data sheets, a value for the thermal resistance can be found based on standard motor mounting.

## Environment

The environment is supposed to have a fixed temperature Tamb.