What is the formula for the temperature rise in the design of field windings?

The temperature rise in the design of field windings, like those in electric motors or generators, can be estimated using the formula derived from the principle of energy balance and Ohm’s and Joule’s laws. The basic equation used to calculate the temperature rise ((ΔT)) in degrees Celsius is based on the power loss ((P)) in the winding, the thermal resistance ((R_{th})) of the system, and sometimes the cooling method employed. The simplified formula is:

[ΔT = P times R_{th}]

Where:

– (ΔT) is the temperature rise in degrees Celsius (°C),

– (P) is the power loss in the winding in watts (W), which can be calculated as (I^2R) (where (I) is the current through the winding in amperes (A), and (R) is the resistance of the winding in ohms ((Ω))),

– (R_{th}) is the thermal resistance of the system from the winding to its cooling medium in °C/W.

This thermal resistance encompasses the path from the winding through the insulation, any structural material, and eventually to the air or cooling medium. It takes into account the efficiency of heat removal through various cooling methods, such as natural convection, forced air, or liquid cooling.

In more detailed designs, additional factors can complicate this equation, such as the specific heat capacity of the materials,