Numerical investigation of induction hardening of stationary cylindrical steel pins with convective quenching

This paper presents a comprehensive, fully-coupled Multi-physics finite element model for simulating the induction hardening process of stationary cylindrical steel pins, including subsequent convective cooling. The model integrates three interacting physics domains—electromagnetic induction, transient heat transfer, and metallurgical phase transformations—within an efficient two-dimensional axisymmetric formulation. Temperature-dependent material properties for all steel phases (ferrite, pearlite, austenite, martensite) and the surrounding air are implemented, and the formulation accounts for latent heat effects during phase changes. The framework employs a segregated solver approach, ensuring robust convergence between the strongly coupled electromagnetic, thermal, and phase transformation modules. The stationary configuration simplifies the computational approach while retaining high fidelity for industrial applications. The simulation predicts critical process outcomes such as transient temperature distributions, phase evolution, and the resulting spatially-graded hardness profile. It further evaluates the resultant residual stress distribution, providing insight into potential distortion and component performance. Furthermore, it serves as a predictive tool for optimizing key operational parameters, including induction coil current frequency and magnitude, heating time, and forced convective cooling intensity. Model predictions for case depth versus applied power show strong agreement with experimental measurements, validating the framework. The validated model demonstrates its utility as a virtual design platform, reducing the need for costly experimental trials. This integrated model provides a complete and practical computational framework for designing, analyzing, and optimizing stationary induction hardening processes to achieve targeted hardness depths, improve energy efficiency, and ensure consistent product quality in manufacturing.