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A Steepest Ascent Analysis Based on an Experimental Approach for the Hardening Process of a Steel Alloy

Author

Listed:
  • Paulo Eduardo García-Nava

    (Department of Industrial Engineering and Manufacturing, Autonomous University of Ciudad Juárez, Ciudad Juárez 32310, Mexico)

  • Gabriel Plascencia-Barrera

    (Department of Metallurgy and Structural Integrity, Research Center for Advanced Materials, Chihuahua 31136, Mexico)

  • Luis Alberto Rodríguez-Picón

    (Department of Industrial Engineering and Manufacturing, Autonomous University of Ciudad Juárez, Ciudad Juárez 32310, Mexico)

  • Roal Torres-Sánchez

    (Department of Metallurgy and Structural Integrity, Research Center for Advanced Materials, Chihuahua 31136, Mexico)

  • Rafael García-Martínez

    (Department of Mathematics, University of Sonora, Hermosillo 83000, Mexico)

Abstract

A significant number of alloyed metals applied for different purposes are currently available in industry. The hardness of a piece is an important parameter to consider. The tempering process is widely used to change a metal’s hardness, which is obtained using a hardness test. Once the response is obtained, a way to evaluate the system is by performing an analysis of variance to verify the significance of terms and obtain a regression equation to improve the response. The aim of this work is to illustrate the implementation of an experimental approach based on the steepest ascent method and stopping rules for optimization purposes by considering the hardening process of the steel alloy 4140. The regression coefficients obtained from an experimental design were used to build the steepest path of improvement. The Myers and Khuri stopping rule and the enhanced parabolic stopping rule were applied to determine the best value while individual experimentation is developed. The obtained results, discussion, and a conclusive analysis are disclosed in this document.

Suggested Citation

  • Paulo Eduardo García-Nava & Gabriel Plascencia-Barrera & Luis Alberto Rodríguez-Picón & Roal Torres-Sánchez & Rafael García-Martínez, 2024. "A Steepest Ascent Analysis Based on an Experimental Approach for the Hardening Process of a Steel Alloy," Mathematics, MDPI, vol. 12(22), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3563-:d:1521229
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