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<p>Accurate prediction of surface micro-topography in 5-axis CNC milling is essential for achieving high-quality finishes in aerospace, biomedical, and precision engineering components. Traditional simulation methods like the Classical Z-Map often suffer from high computational cost and limited applicability to freeform surfaces. This paper presents RMAP, a fast and vectorized algorithm that enhances the Classical Z-Map by projecting cutter edge points in a locally transformed coordinate system aligned with the surface normal. The method supports arbitrary machining strategies exported from CAM software and is compatible with both ideal and realistic cutter edge geometries. Simulations were performed on a hyperbolic paraboloid surface using tool paths generated in NX CAM and validated experimentally on aluminum. RMAP achieved speedups up to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_16013_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(100\times\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>100</mn> <mo>×</mo> </mrow> </math></EquationSource> </InlineEquation> compared to Classical Z-Map, with relative errors below <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_16013_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(6\text{\%}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>6</mn> <mtext>\%</mtext> </mrow> </math></EquationSource> </InlineEquation> for key areal experimental parameters <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_16013_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({S}_{a}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>a</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_16013_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({S}_{q}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation>. Notably, simulations incorporating realistic cutter edge imperfections, modeled with a stochastic distribution, accurately reproduced short-wavelength directional features observed in experimental measurements. The algorithm proved robust across multiple strategies, including 3-axis and 5-axis configurations with variable feed rates. By maintaining accuracy on complex freeform geometries and significantly reducing computation times, RMAP enables reliable and scalable topography simulation.</p>

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Efficient topography simulation for freeform surfaces in 5-axis CNC milling

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Yasser Zekalmi,
  • José Antonio Albajez,
  • María José Oliveros,
  • Sergio Aguado

摘要

Accurate prediction of surface micro-topography in 5-axis CNC milling is essential for achieving high-quality finishes in aerospace, biomedical, and precision engineering components. Traditional simulation methods like the Classical Z-Map often suffer from high computational cost and limited applicability to freeform surfaces. This paper presents RMAP, a fast and vectorized algorithm that enhances the Classical Z-Map by projecting cutter edge points in a locally transformed coordinate system aligned with the surface normal. The method supports arbitrary machining strategies exported from CAM software and is compatible with both ideal and realistic cutter edge geometries. Simulations were performed on a hyperbolic paraboloid surface using tool paths generated in NX CAM and validated experimentally on aluminum. RMAP achieved speedups up to \(100\times\) 100 × compared to Classical Z-Map, with relative errors below \(6\text{\%}\) 6 \% for key areal experimental parameters \({S}_{a}\) S a and \({S}_{q}\) S q . Notably, simulations incorporating realistic cutter edge imperfections, modeled with a stochastic distribution, accurately reproduced short-wavelength directional features observed in experimental measurements. The algorithm proved robust across multiple strategies, including 3-axis and 5-axis configurations with variable feed rates. By maintaining accuracy on complex freeform geometries and significantly reducing computation times, RMAP enables reliable and scalable topography simulation.