<p>The primary standard for precision machining involves the production of parts that adhere to the necessary surface quality requirements for optimal tribological performance. The surface assessment in accordance with ISO 13115 (DIN 4776) is a crucial aspect of the methodologies used to assess and validate these requirements. This study seeks to merge a methodology that combines Taguchi’s <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_{16}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>16</mn> </msub> </math></EquationSource> </InlineEquation> design of experiments (DOE), analysis of variance (ANOVA), artificial neural networks (ANN), and the multi-objective dragonfly algorithm (MODA) to ascertain the influence of cutting parameters (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(V_{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(f\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>f</mi> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(ap\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">ap</mi> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(r_{\varepsilon }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>r</mi> <mi>ε</mi> </msub> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(X_{r}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>) on the bearing area curve parameters (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(R_{pk}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mrow> <mi mathvariant="italic">pk</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(R_{k}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(R_{vk}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mrow> <mi mathvariant="italic">vk</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(Mr1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mi>r</mi> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(Mr2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mi>r</mi> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>). Turning operations are conducted using medium-carbon steel C45 and uncoated carbide inserts. Unlike previous studies that have treated BAC parameters, ANN, or RSM individually, the novelty of this work lies in the integration of Taguchi’s <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(L_{16}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>16</mn> </msub> </math></EquationSource> </InlineEquation> with ANN modeling and MODA optimization. ANOVA results indicate that feed rate (<InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(f\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>f</mi> </math></EquationSource> </InlineEquation>) and cutting speed (<InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(V_{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>) are typically the most significant variables. Moreover, the models developed account for a substantial portion of the variability observed in the experimental data, with <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(R^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>R</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> values exceeding 95% for all responses. Ultimately, the MODA algorithm identifies the optimal conditions as follows: maximum <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(V_{c}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation> (420&#xa0;m/min), minimum <InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(f\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>f</mi> </math></EquationSource> </InlineEquation> (0.031&#xa0;mm/rev), maximum <InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(ap\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">ap</mi> </mrow> </math></EquationSource> </InlineEquation> (0.4&#xa0;mm), minimum <InlineEquation ID="IEq19"> <EquationSource Format="TEX">\(r_{\varepsilon }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>r</mi> <mi>ε</mi> </msub> </math></EquationSource> </InlineEquation> (0.4&#xa0;mm), and minimum <InlineEquation ID="IEq20"> <EquationSource Format="TEX">\(X_{r}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation> (45°). This shows that the simultaneous improvement of the five responses led to <InlineEquation ID="IEq21"> <EquationSource Format="TEX">\(R_{pk}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mrow> <mi mathvariant="italic">pk</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>&#xa0;=&#xa0;1.27&#xa0;µm, <InlineEquation ID="IEq22"> <EquationSource Format="TEX">\(R_{k}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> = 1.54&#xa0;µm, <InlineEquation ID="IEq23"> <EquationSource Format="TEX">\(R_{vk}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mrow> <mi mathvariant="italic">vk</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>&#xa0;=&#xa0;1.09&#xa0;µm, <InlineEquation ID="IEq24"> <EquationSource Format="TEX">\(Mr1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mi>r</mi> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;=&#xa0;5.68%, and <InlineEquation ID="IEq25"> <EquationSource Format="TEX">\(Mr2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mi>r</mi> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>&#xa0;=&#xa0;91.74%.</p> Graphical Abstract <p></p>

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Statistical analysis and multi-response optimization based on ANN-MODA for bearing area curve criteria (BAC) in dry turning of C45 steel

  • Amine Hamdi,
  • Hammoudi Abderazek,
  • Sidi Mohammed Merghache

摘要

The primary standard for precision machining involves the production of parts that adhere to the necessary surface quality requirements for optimal tribological performance. The surface assessment in accordance with ISO 13115 (DIN 4776) is a crucial aspect of the methodologies used to assess and validate these requirements. This study seeks to merge a methodology that combines Taguchi’s \(L_{16}\) L 16 design of experiments (DOE), analysis of variance (ANOVA), artificial neural networks (ANN), and the multi-objective dragonfly algorithm (MODA) to ascertain the influence of cutting parameters ( \(V_{c}\) V c , \(f\) f , \(ap\) ap , \(r_{\varepsilon }\) r ε , and \(X_{r}\) X r ) on the bearing area curve parameters ( \(R_{pk}\) R pk , \(R_{k}\) R k , \(R_{vk}\) R vk , \(Mr1\) M r 1 , and \(Mr2\) M r 2 ). Turning operations are conducted using medium-carbon steel C45 and uncoated carbide inserts. Unlike previous studies that have treated BAC parameters, ANN, or RSM individually, the novelty of this work lies in the integration of Taguchi’s \(L_{16}\) L 16 with ANN modeling and MODA optimization. ANOVA results indicate that feed rate ( \(f\) f ) and cutting speed ( \(V_{c}\) V c ) are typically the most significant variables. Moreover, the models developed account for a substantial portion of the variability observed in the experimental data, with \(R^{2}\) R 2 values exceeding 95% for all responses. Ultimately, the MODA algorithm identifies the optimal conditions as follows: maximum \(V_{c}\) V c (420 m/min), minimum \(f\) f (0.031 mm/rev), maximum \(ap\) ap (0.4 mm), minimum \(r_{\varepsilon }\) r ε (0.4 mm), and minimum \(X_{r}\) X r (45°). This shows that the simultaneous improvement of the five responses led to \(R_{pk}\) R pk  = 1.27 µm, \(R_{k}\) R k  = 1.54 µm, \(R_{vk}\) R vk  = 1.09 µm, \(Mr1\) M r 1  = 5.68%, and \(Mr2\) M r 2  = 91.74%.

Graphical Abstract