Thermal resistance

The relationship between the heat generated in the motor, particularly the winding, and the surrounding temperature is expressed using a coefficient known as thermal resistance, here denoted Θ. We assume that heat is first transferred from the winding to the housing. When thermal equilibrium has been attained, assuming that the difference of the temperatures of the winding and housing, denoted Z_w and Z_h respectively, is proportional to the amount of heat generated per second P (i.e., thermal loss in the winding, units in W), we have

Z_w－Z_h=Θ_whP

The heat is then released from the housing to the surrounding air, which can be expressed using the thermal resistance Θ_ha between the housing and surrounding air and denoting the ambient temperature by Z_a, as follows.

Z_h－Z_a=Θ_haP

Combining the two expressions, the relation between the winding temperature and ambient temperature is obtained as follows.

Z_w－Z_a=(Θ_wh＋Θ_ha)P or Z=(Θ_wh＋Θ_hb)P＋Z_a

where
Θ_ha＝thermal resistance between the housing and surrounding air or oil (liquid)
Θ_wh＝thermal resistance between the winding and housing