Question 6.AE.10: For a totally enclosed fan-cooled motor [48–50] the surface ......
For a totally enclosed fan-cooled motor [48–50] the surface of the external frame dissipates the heat. The ribs are located along the axis of the machine where the hot air is removed by a fan. Test results show [49,50] that the stator end windings have about the same temperature as the slot-embedded part of the stator winding. This result permits us to assume that the end winding does not dissipate heat (e.g., radiates and removes heat by convection) to the surrounding air inside the end bells of the motor, and the heat developed by the stator winding is completely transferred to the stator core. The stator iron loss is then added to the stator copper loss and the resultant heat is transferred to the stator frame via the small air gap between core and frame from which it is removed by the fan through radiation and convection. A second assumption refers to the heat of the rotor winding. It is assumed that this heat is transferred to the stator. This means that the temperature of the rotor is higher than that of the stator. The temperature of the hottest spot in the stator determines the class of winding insulation. It is assumed that this point is residing in the stator winding inside a stator slot. The temperature of the hot spot consists of the following temperature drops:
• temperature drop across stator winding insulation, \Delta T_i
• temperature drop across stator back iron (yoke), \Delta T_{y1}
• temperature drop across the small air gap between the stator back iron and the frame of the motor, \Delta T_g
• difference between the temperature of the frame and the ambient temperature of the air, \Delta T_f.
The temperature rise of the stator winding is therefore
\Delta T=\Delta T_i+\Delta T_y1+\Delta T_g+\Delta T_f (E6.10-1)
The thermal network of the motor is shown in Fig. E6.10.1, where R_i is the thermal conductivity resistance of the stator slot insulation,R_{y1} is the thermal conductivity resistance of the stator back iron or yoke, R_g is the thermal conductivity resistance of the small air gap between the stator core and the frame of the motor, R_f is the thermal radiation/convection resistance of the outside of the stator frame and the moving air, P_{cu1} is the stator ohmic (copper) loss, P_{Al2} is the rotor ohmic (aluminum) loss, P_{t1} is the stator teeth (iron-core) loss, P_{y1} is the stator yoke (iron-core) loss, and P_{mech} is the friction (bearing, windage) loss.
From Fig. E6.10.1 one notes that the stator ohmic loss generates a temperature drop across the slot insulation (\Delta T_i ).Thetemperature drop acrossthe stator backiron or yoke (\Delta T_{y1}) is produced by the sum of the stator and rotor ohmic losses, stator teeth loss, and half of the stator back iron loss. The calculation of \Delta T_{y1} is based on half of the stator back iron loss because this loss is assumed to be generated uniformly throughout the stator back iron; therefore, the stator back iron loss generated radially through the stator back iron varies from zero to P_{y1} from the inner to the outer surfaces of the stator back iron, respectively.
The temperature drop acrossthe small air gap between stator back iron andthe frame (\Delta T_g) is produced by the sum of the ohmic and the iron-core losses of the motor. Finally,the total losses cause a temperature drop from the motor frame to the moving air (\Delta T_f ).
The temperature difference between the stator winding and the iron core (across the stator winding insulation) is
\Delta T_i=P_{a u 1} \frac{\beta_i}{\lambda_i \cdot S_i} (E6.10-2)
where β_i is the thickness of stator slot insulation, λ_i is the thermal conductivity (W/m°C) of stator slot insulation, and S_i is the total surface area of (all) stator slots.
The temperature drop across the stator back iron can be expressed as
\Delta T_{y1}=\left(P_{c u 1}+\frac{1}{2} P_{y1}+P_{t 1}+P_{s p 1}+P_{A l 2}+P_{s p 2}\right) \frac{h_{y1}}{\lambda_c \cdot S_{y 1}} (E6.10-3a)
where h_{y1} is the radial height of stator back iron, λ_c is the thermal conductivity (W/m°C) of the stator laminations, S_{y1} is the cross-sectional area of the stator core at the radial middle of the back iron, P_{sp1} is the surface and pulsation loss caused by stator teeth (note that these losses are very small and have been neglected in Fig. E6.10.1), and P_{sp2} is the surface and pulsation loss caused by rotor teeth (note that these losses are very small and have been neglected in Fig. E6.10.1).
The temperature difference across the small air gap between the stator back iron and the frame can be expressed as
\Delta T_\delta=\Delta T_g=\left(P_{cu1}+P_{y1}+P_{t 1}+P_{s p 1}+P_{A 12}+P_{s p 2}\right) \frac{\beta_\delta}{\lambda_\delta \cdot S_\delta} (E6.10-3b)
where β_δ is the air gap length between stator back iron and frame, λ_δ is the thermal conductivity (W/m°C) of the airgap, S_δ is the outside surface of stator core, P_{sp1} is the surface and pulsation loss caused by stator teeth (note that these losses are very small and have been neglected in Fig. E6.10.1), and P_{sp2} is the surface and pulsation loss caused by rotor teeth (note that these losses are very small and have been neglected in Fig. E6.10.1). The heat of the motor is dissipated to the air at ambient temperature through the end bells of the motor frameto the stationary air, and throughthe cylindrical frame surface containing the cooling ribs (which increase the frame surface) to the moving air. The temperature difference between the outer surface of the frame and the ambient temperature is
\Delta T_f=\frac{\sum P}{\alpha_o S_o+\alpha_v S_V} (E6.10-4)
where ΣP represents total losses of the motor, α_o is the surface thermal coefficient (W/m² °C) for dissipating the heat from the surface of the frame to the stationary air (near end bells), α_v is the surface thermal coefficient (W/m² °C) for dissipating the heat from the surface of the frame to the moving air (near cylindrical frame), So is the surface area in contact with stationary air, and S-v is the surface area in contact with moving air.
The relation between α_o\ and\ α_v is given by
\alpha_v=\alpha_o\left(1+k_v \sqrt{v}\right) (E6.10-5)
where k_v is a coefficient, and v is the air velocity (m/s).