In general, prototyping and testing high-frequency induction hardening equipment requires a great deal of time and money, and is sometimes accompanied by danger. Moreover, in addition to the complex phenomenon called induction heating, material properties also change greatly due to heating exceeding the Curie point, making it difficult to estimate the heating state. For this reason, simulation based on finite element analysis which can handle detailed phenomena is useful.
Moreover, when the hardening is performed, uniform heating is desirable, but there are significant factors to consider such as the shape and arrangement of heating coils and the adjustment of current frequency and amount. When there are many design variables or items to evaluate, applying automatic computation using an optimization function for simulation can greatly reduce the workload.
In this example, the design of a coil used for the high-frequency induction hardening of gears is carried out using an optimization function.
Coil Design Variables
The coil has 2 turns. The distance CPosition from the center of the gear height-wise to the bottom of the upper coil turn and the coil width CWidth are design variables (Fig. 1). In addition, the input current is also a design variable.
The temperature measurement points are shown in Fig. 2, and the following three items are defined for the evaluation functions (Fig. 3) used in the coil optimization design.
- Input current minimization
- Minimization of the standard deviation Tdev of temperature Ti taken from the measurement points (Fig. 2) around target temperature TR
- Minimization of the bias Tbias of temperature Ti taken from the measurement points (Fig. 2) from target temperature TR
Pareto Solution by Multi-Objective Optimization
Optimization processing of a multi-objective genetic algorithm with a population size of 10 and number of generations at 10 was performed. The obtained evaluation function values are shown in Fig. 4 and Fig. 5.
Evaluating the initial design plan with the input current and standard deviation of the temperature shows good agreement with the Pareto curve, but when evaluated with the temperature bias and standard deviation of the temperature, it can be seen that there is poor agreement with the Pareto curve.
Fig. 6 shows the temperature distribution for the design on the Pareto curve. For (1) where emphasis was placed on the standard deviation of the temperature, the uniformity of the temperature was improved, but for (2) where emphasis was placed on reduction of current input, insufficient heating became conspicuous. Furthermore, for (3) which emphasizes temperature bias, it can be confirmed that the average temperature of the whole gear is high.