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

Mohammad Yaghoub Abdollahzadeh Jamalabadi

doi:10.59400/mea3942

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

Mohammad Yaghoub Abdollahzadeh Jamalabadi
Department of Marine Engineering, Chabahar Maritime University, Chabahar 99717-56499, Iran

Article ID: 3942

Keywords: induction hardening, Multiphysics modeling, phase transformation, axisymmetric formulation, convective cooling, finite element analysis, process optimization

Abstract

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.

Published

2026-01-15

How to Cite

Jamalabadi, M. Y. A. (2026). Numerical investigation of induction hardening of stationary cylindrical steel pins with convective quenching. Mechanical Engineering Advances, 4(1). https://doi.org/10.59400/mea3942

Download Citation

Issue

Vol. 4 No. 1 (2026)

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Dziatkiewicz G, Kuska K, Popiel R. Evolutionary Optimizing Process Parameters in the Induction Hardening of Rack Bar by Response Surface Methodology and Desirability Function Approach under Industrial Conditions. Materials. 2023; 16(17): 5791. doi: 10.3390/ma16175791

[2]Garois S, Daoud M, Chinesta F. Data-Driven Inverse Problem for Optimizing the Induction Hardening Process of C45 Spur-Gear. Metals. 2023; 13(5): 997. doi: 10.3390/met13050997

[3]Derouiche K, Garois S, Champaney V, et al. Data-Driven Modeling for Multiphysics Parametrized Problems-Application to Induction Hardening Process. Metals. 2021; 11(5): 738. doi: 10.3390/met11050738

[4]Dollhofer B, Dietrich S, Schulze V. Improvement of an Electromagnetic-Thermal-Mechanical Coupled Simulation for the Optimization of Complex Processes in Induction Hardening. arXiv preprint. 2024; doi: 10.14940/netsushori.64.ex66

[5]Jan J, MacKenzie DS. On the Development of Computational Fluid Dynamics Quenching Simulation Methodology for Effective Thermal Residual Stress Control. Journal of Materials Engineering and Performance. 2024; 33(8): 3986–4010. doi: 10.1007/s11665-023-09106-7

[6]Thakur AK, Das B, Chowdhury SG. A data-driven approach to model the martensitic transformation temperature in strain-induced metastable austenitic steels. Materials Today Communications. 2024; 39: 109016. doi: 10.1016/j.mtcomm.2024.109016

[7]Sun F, Mino Y, Ogawa T, et al. Evaluation of Austenite–Ferrite Phase Transformation in Carbon Steel Using Bayesian Optimized Cellular Automaton Simulation. Materials. 2023; 16(21): 6922. doi: 10.3390/ma16216922

[8]Fisk M, Lindgren L-E, Datchary W, et al. Modelling of induction hardening in low alloy steels. Finite Elements in Analysis and Design. 2018; 144: 61–75. doi: 10.1016/j.finel.2018.03.002

[9]Desisa D, Smalcerz A, Kotlan V, et al. Mathematical modelling of thermal stresses of induction surface hardening in axi-symmetric formulation. Surface and Coatings Technology. 2024; 479: 130516. doi: 10.1016/j.surfcoat.2024.130516

[10]Li H, Gai K, He L, et al. Non-isothermal phase-transformation kinetics model for evaluating the austenization of 55CrMo steel based on Johnson–Mehl–Avrami equation. Materials & Design. 2016; 92: 731–741. doi: 10.1016/j.matdes.2015.12.110

[11]Jamalabadi MYA. Revolutionizing Gear Performance: Cutting-Edge Heat Treatment Methods, Breakthrough Innovations, and Industry Standards for Superior Durability, Journal of Sustainable Engineering Green Technologies. 2025; 1(1): 1–66.

[12]Sharifi M, Amani E. Electromagnetic effects on the solidification of a metallic alloy droplet impacting onto a surface. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2024; 700: 134806. doi: 10.1016/j.colsurfa.2024.134806

[13]Amani E, Sharifi M. Metallic alloy droplet impact and solidification under an alternating magnetic field: Scaling laws and regime maps. International Journal of Thermal Sciences. 2025; 210: 109645. doi: 10.1016/j.ijthermalsci.2024.109645

[14]Sharifi M. Investigating the influence of magnetic field on heat transfer in turbulent ferromagnetic fluid over a backward-facing step. Physics of Fluids. 2024; 36(12): 125152. doi: 10.1063/5.0244293

[15]Rudnev V, Loveless D, Cook RL. Handbook of Induction Heating, 2nd ed. CRC Press; 2017. doi: 10.1201/9781315117485

[16]Hömberg D. A mathematical model for induction hardening including mechanical effects. Nonlinear Analysis: Real World Applications. 2004; 5(1): 55–90. doi: 10.1016/S1468-1218(03)00017-8

[17]Mühlbauer A. History of Induction Heating and Melting. Vulkan-Verlag GmbH; 2008.

[18]Coupard D, Palin-luc T, Bristiel P, et al. Residual stresses in surface induction hardening of steels: Comparison between experiment and simulation. Materials Science and Engineering: A. 2008; 487(1–2): 328–339. doi: 10.1016/j.msea.2007.10.047

[19]Hirao M, Ogi H. Electromagnetic Acoustic Transducers: Noncontacting Ultrasonic Measurements using EMATs. Springer; 2017. doi: 10.1007/978-4-431-56036-4

[20]Bhadeshia HKDH, Honeycombe RWK. Steels: Microstructure and Properties. Elsevier; 2017.

[21]Koistinen DP, Marburger RE. A general equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels. Acta Metallurgica. 1959; 7(1): 59–60. doi: 10.1016/0001-6160(59)90170-1

[22]Pinheiro PM, Junio JU, Gonçalves LAP, et al. Modeling and Simulation of the Induction Hardening Process: Evaluation of Gear Deformations and Parameter Optimization. Processes. 2024; 12(7): 1428. doi: 10.3390/pr12071428

[23]Toros S, Altinel K. Contribution of functionally graded material modelling on finite element simulation of rod end parts in automotive steering system. Journal of Mechanical Science and Technology. 2016; 30(7): 3137–3141. doi: 10.1007/s12206-016-0623-6

[24]Sjöström S. Interactions and constitutive models for calculating quench stresses in steel. Materials Science and Technology. 1985; 1(10): 823–829. doi: 10.1179/mst.1985.1.10.823

[25]Kabir H, Aghdam MM. A generalized 2D Bézier-based solution for stress analysis of notched epoxy resin plates reinforced with graphene nanoplatelets. Thin-Walled Structures. 2021; 169: 108484. doi: 10.1016/j.tws.2021.108484

[26]Wang Y, Gu Y, Liu J. A domain-decomposition generalized finite difference method for stress analysis in three-dimensional composite materials. Applied Mathematics Letters. 2020; 104: 106226. doi: 10.1016/j.aml.2020.106226

[27]Jamalabadi MYA. An Improvement of Port-Hamiltonian Model of Fluid Sloshing Coupled by Structure Motion. Water. 2018a; 10(12): 1721. doi: 10.3390/w10121721

[28]Induction Systems, Inc. Operator Instruction Manual Version 9. ProScan; n.d.

In order to improve thermal comfort of vehicle cab, reduce driver fatigue and further improve work efficiency, researches on thermal comfort of vehicle cab are summarized. Research background of thermal comfort for vehicle cab is analyzed. And then related research progress on thermal environment in vehicle cab is studied from aspect of time and space, and thermal environment inside and outside vehicle are compared. Affecting factors of thermal comfort in vehicle cab are discussed in depth, which conclude thermophysical parameters, human physiological factors, clothing thermal resistance and other secondary factors. And thermal comfort evaluation indexes are analyzed in depth. Evaluation methods of thermal comfort in uniform environment are analyzed, related experimental research and theoretical analysis are summarized, and it also points out some problems in thermal comfort of vehicle at this stage, and also gives corresponding solutions. The future trend of thermal comfort of vehicle cab is predicted. Analysis results can provide theoretical guidance for optimization design of air conditioning supply parameters and structural parameters, and has significant meaning of improving thermal comfort of vehicle cab.

This manuscript presents a sophisticated deep neural networks (DNNs)-driven adaptive control paradigm for concurrently regulating the attitude and suppressing structural oscillations of a flexible spacecraft in a fully three-dimensional domain. By leveraging Hamilton’s principle, the spacecraft’s motion is formulated as an infinite-dimensional dynamic model described by partial differential equations, capturing the subtle interactions between rigid-body rotational maneuvers and flexible panel deformations. In contrast to traditional schemes, the proposed control methodology integrates a DNNs module to compensate for uncertain actuator anomalies and external input disturbances in real time, thereby ensuring fault tolerance under arbitrary, potentially unbounded actuator malfunctions. A rigorously constructed Lyapunov-based stability analysis corroborates that the system’s energy, angular rates, and transverse deflections remain uniformly bounded and asymptotically converge to zero, even in the face of multiple actuator failures. This theoretical guarantee stems from the synergistic interplay between the network’s representational power and the adaptive control law’s robust learning capabilities. Extensive computational experiments demonstrate the efficacy of the developed framework in orchestrating high-precision attitude stabilization while simultaneously mitigating detrimental vibrations, showcasing the superior performance and resiliency of the proposed DNNs-infused control architecture.

This study focuses on the development of a cleaning robot, covering the three main aspects of mechanical design, circuit design, and software design. First, in the area of mechanical design, we created a structure capable of agile movement and efficient cleaning to ensure the robot can operate smoothly in various environments. Second, for circuit design, we developed a microcontroller-based control system to coordinate the operation of various components, including drive motors, sensors, and image recognition modules. Furthermore, in the software design aspect, we utilized YOLO (You Only Look Once) and OpenCV technologies to enable the robot to accurately identify and classify waste during the automatic cleaning process. Finally, we conducted practical cleaning experiments to verify the robot’s ability to recognize waste and the accuracy of waste classification. The experimental results show that the cleaning robot not only possesses the ability to recognize waste but also accurately classify it, demonstrating its potential for practical applications.