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
Loss is expressed by heat source components. Heat sources are copper loss and the eddy current loss of magnets.
Coil temperature calculated with the thermal equivalent circuit is fed back into coil components. Coil components retain temperature dependency in resistance values, and copper loss values are updated. The feedback of coil temperature and updates to copper loss are repeated, and part temperatures during thermal equilibrium are obtained.
Magnets demagnetize due to heat generation from eddy current loss, in addition to heat transmitted from the coils through parts and air gaps.
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. In this analysis, there are no changes in current due to temperature because drive occurs with a specified current. Therefore, the decrease in average torque is due to thermal demagnetization of the magnet.