Digital twin technology puts forward higher requirements on the real-time performance of simulations. In order to realize the online simulation of the heat treatment process, a transient temperature field-microstructure field coupling calculation method based on the reduced-order model was constructed. This mathematical model was applied to the online simulation of the end-quenching treatment of 42CrMo steel with complex time-varying water spray. The results show that the utilization of a 10th-order reduced-order model diminishes the total computation time from 1 h to 3.4 s, with a reduction in storage requirements by a factor of 610. The calculation accuracy of the reduced-order model is 99.2%, which satisfies the requirements of real-time online simulation. A framework for the heat treatment digital twin system has been proposed and an online simulation platform for end-quenching treatment was developed. The single-step calculation time for the proposed platform is 0.4 s. The online simulation temperature is basically consistent with the measured temperature results. This work provides novel avenues for fast calculation and real-time control of the heat treatment process.
Gong et al. (2026) studied this question.