Methodology to establish a hybrid model for prediction of cutting forces and chip thickness in orthogonal cutting condition close to broaching

  • Gorka Ortiz-de-ZarateEmail author
  • Andres Sela
  • Mikel Saez-de-Buruaga
  • Mikel Cuesta
  • Aitor Madariaga
  • Ainhara Garay
  • Pedro J. Arrazola


Broaching is a widely used finishing operation for the manufacturing of transmission gears which are commonly made of steel AISI 1045. Therefore, there is a high interest for industry to understand the metal cutting process and modeling could shed light on it. In the present work, an innovative methodology to establish a hybrid model based on the combination of empirical, numerical, and analytical approaches is presented. The hybrid model improves the cutting force, feed force, and chip thickness predictions when compared to the results obtained with the empirical, numerical, or analytical ones separately. The empirical model was developed by carrying out experimental tests under orthogonal condition close to broaching. The analytical method uses the Oxley law extended to the proposed flow stress model. DEFORM-2D software was used for the finite element model development with a specific subroutine for the constitutive model. The influence of each approach in the hybrid model was calculated based on a statistical analysis between experimental and model results. Moreover, to achieve better predictions in the numerical and analytical models, the material was characterized by static and dynamic compression tests to take into account strain softening and coupling between strain rate and temperature phenomena, not considered in the commonly used Johnson-Cook law. Furthermore, the hybrid model was validated with additional experimental tests, to demonstrate its validity in a wide range of cutting conditions. The relative error obtained with the hybrid model in force and chip thickness predictions were 6% and 12%, respectively, reducing more than three times the maximum error in comparison to any other approach.


Hybrid model AISI 1045 Machining Transmission gear Orthogonal cutting Broaching 


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The authors thank the Laboratory Technicians Denis Soriano and Erika Dominguez for their assistance in the realization of experimental tests and chip analysis.

Funding information

This study was funded by Basque and Spanish Government projects AEROBROCH (UE2016–07), SMAPRO (KK-2017/00021), MICROMAQUINTE (PI_2014_1_116), EMULATE (DP12015–67667-C3-3R), and in the grant for Education and Training of Research Staff (PRE_2017_1_0394).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of EngineeringMondragon UnibertsitateaMondragonSpain

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