Neuro-fuzzy optimization of cutting tool geometry in machining using Sugeno and Mamdani inference models

Abstract This study presents the design and validation of zero-order Sugeno and Mamdani fuzzy inference systems applied to the estimation of optimal cutting tool angles in machining processes. The input variables considered were the tool destruction energy (D) and the material’s specific cutting energy (U), while the output variables corresponded to the clearance angle ( $$\alpha _{\text {n}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mtext>n</mml:mtext> </mml:msub> </mml:math> ), rake angle ( $$\gamma _{\text {n}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mtext>n</mml:mtext> </mml:msub> </mml:math> ), and cutting-edge inclination angle ( $$\lambda _{\text {s}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>λ</mml:mi> <mml:mtext>s</mml:mtext> </mml:msub> </mml:math> ). Based on a real dataset of 81 experimental values, a synthetic database of 118,300 records was generated using an adaptive neuro-fuzzy inference system (ANFIS) trained via the backpropagation algorithm, achieving a reliability level of 85%. Both models were implemented in MATLAB using Gaussian membership functions with nine rules per output variable. The Sugeno model employed constant outputs, whereas the Mamdani model used linguistic labels. Validation was performed through the calculation of the cutting-edge angle ( $$\beta _{\text {n}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mtext>n</mml:mtext> </mml:msub> </mml:math> ), derived from $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> n and $$\gamma _{\text {n}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mtext>n</mml:mtext> </mml:msub> </mml:math> , by comparing the outputs of both systems. The normalized relative root mean square error (rMSE) was found to be below 6.5%, indicating a high level of agreement between the two models. The results demonstrate that fuzzy inference systems—particularly when integrated with neuro-fuzzy architectures like ANFIS—are effective tools for addressing geometric optimization problems in industrial environments characterized by uncertainty and complexity. It is concluded that this approach provides a robust and accurate alternative for computer-aided cutting tool design.