Although it is difficult to understand the temperatures of each part in a real machine, the temperatures of each of these parts can be obtained with ease through simulations, and changes to characteristics due to increases in temperature can also be taken into account. As methods of analysis that account for the increases in temperature for each part, there exists the method of coupled analysis via magnetic field analysis and thermal analysis, as well as the method of performing magnetic field analysis that uses thermal equivalent circuits. Detailed evaluations that obtain temperature distribution are possible for coupled analysis. While the evaluation of temperature distribution is not possible when using thermal equivalent circuits, magnetic field analysis that accounts for temperature increases can be performed at high speeds with ease.
In this example, magnetic field analysis is performed using a thermal equivalent circuit, and changes in average torque due to magnet demagnetization are confirmed.
Thermal Equivalent Circuit
The coil temperature, magnet temperature, external case temperature, and copper loss during initial temperature and during thermal equilibrium are shown in Table 1.
From Fig. 2 it is understood that heat is transferred from the magnet to the external case via the rotor core and the shaft, then dissipated to the ambient air. The magnet and heat dissipation path temperatures are as per Table 1; the ambient air is 20 deg C, the external case temperature is 134.5 deg C, and the magnet temperature is 136.1 deg C. Because the difference in temperature between the external case and the magnet is small, it can therefore be determined that the cause of the rise in temperature for the magnet is mainly the small heat dissipation that occurs from the external case to the ambient air.
It is understood from Table 1 that copper loss also increases in accordance with the rise in coil temperature. In this analysis there are no changes in current due to temperature because drive occurs with a specified current. Specifically, the temperature increases the coil electric resistance and copper loss.
Part Temperature, Copper Loss
Temperature history until coil and magnet temperatures of a thermal equilibrium are achieved is shown in Fig. 2, and copper loss history is shown in Fig. 3.
In terms of analysis flow, first a transient response magnetic field analysis is performed, followed by the calculation of time averaged loss. Temperatures during steady states from when that heat is being generated are next obtained from average loss.
The combination of magnetic field analysis and thermal equivalent circuit calculations constitutes a single coupled step, corresponding to one step in Fig. 2 and Fig. 3. Because coil resistance is updated when temperatures increase, transient response magnetic field analysis is performed again, time averaged loss is calculated, and the temperature steady state value of each part is obtained. A state of thermal equilibrium is obtained by repeating these steps. In this example, a process of ten steps is performed until reaching a state of thermal equilibrium.
It is understood from Fig. 2 and Fig. 3 that coil resistance changes due to temperature, and that changes in copper loss also occur.
It is understood that average torque decreases during thermal equilibrium. As mentioned previously, there are no changes in current due to temperature. It can therefore be determined that the decrease in average torque is due to the thermal demagnetization of the magnet.