Face-centred design approach for modelling and predicting areal surface roughness in freeform surface milling of stavax ESR
Keywords:
Freeform surfaces, Face centered composite design, Ball nose milling, Stavax, ANOVA, Areal surface roughnessAbstract
Freeform surfaces have become a major element in high precision industrial design, such as moulds and dies. These sculptured surfaces are characterised by non-uniform and aesthetic features requiring high-quality surface finishing. Therefore, minimising surface roughness becomes critical, especially when machining Stavax, a well-known material, in moulds and dies. This study aims to optimise 3-axis CNC ball nose milling parameters, namely spindle speed (vc), feed rate (fz), and depth of cut (ap), in minimising areal surface roughness on the B-Spline tensor product of the Stavax freeform profile. A total of 17 experimental runs were designed using a face-centred composite approach (FCD) under the response surface methodology (RSM). Areal surface roughness data were captured via Alicona InfiniteFocus and then evaluated by MountainsLab in compliance with ISO 25178. ANOVA validation indicated a highly reliable predictive model, characterised by an R2 of 0.9680, an adjusted R2 of 0.9268, and a predicted R2 of 0.8762 with the difference less than 0.2. This study also developed the FCD mathematical model for factors influencing the roughness.
Downloads
References
P. N. Linh, T. N. Tan, V. D. Toan, and T. D. Nguyen, ‘Multi-Objective Optimization of Finishing Milling of C45 Steel using Factorial Design’, Eng. Technol. Appl. Sci. Res., vol. 14, no. 6, pp. 18199–18204, 2024, doi: 10.48084/etasr.8017.
F. Marin, A. Fagali De Souza, H. Da Silva Gaspar, A. Calleja-Ochoa, and L. N. López De Lacalle, ‘Topography simulation of free-form surface ball-end milling through partial discretization of linearised toolpaths’, Eng. Sci. Technol. Int. J., vol. 55, p. 101757, 2024, doi: 10.1016/j.jestch.2024.101757.
S. Maeng, H. Ito, Y. Kakinuma, and S. Min, ‘Study on Cutting Force and Tool Wear in Machining of Die Materials with Textured PCD Tools Under Ultrasonic Elliptical Vibration’, Int. J. Precis. Eng. Manuf.-Green Technol., vol. 10, no. 1, pp. 35–44, 2023, doi: 10.1007/s40684-022-00416-0.
M. F. M. Rashid, M. H. A. Bakar, M. F. Mamat, N. A. Rosli, N. A. Wahab, and S. G. Herawan, ‘Optimization of Cutting Parameters for Surface Roughness and Microscopy Analysis in Machining Hardened High Thermal Conductivity 150 (htcs-150) Steel’, Malays. J. Microsc., vol. 20, no. 2, pp. 133–144, 2024.
D. Masato and S. K. Kim, ‘Global Workforce Challenges for the Mold Making and Engineering Industry’, Sustainability, vol. 16, no. 1, p. 346, 2023, doi: 10.3390/su16010346.
A. Yıldız, L. Uğur, and İ. E. Parlak, ‘Optimization of the Cutting Parameters Affecting the Turning of AISI 52100 Bearing Steel Using the Box-Behnken Experimental Design Method’, Appl. Sci., vol. 13, no. 1, p. 3, 2022, doi: 10.3390/app13010003.
J. Lee, C. Yeo, K. C. Bae, and D. Mun, ‘Replacing NURBS surfaces with analytic surfaces based on isocurve characteristics in B-rep models’, J. Comput. Des. Eng., vol. 12, no. 8, pp. 78–106, 2025, doi: 10.1093/jcde/qwaf063.
S. Samreen, M. Sarfraz, and A. Mohamed, ‘A quadratic trigonometric B-Spline as an alternate to cubic B-spline’, Alex. Eng. J., vol. 61, no. 12, pp. 11433–11443, 2022, doi: 10.1016/j.aej.2022.05.006.
Y. Yan, G. He, C. Yao, S. Wang, and Z. Tan, ‘A precision reconstruction method based on refined and adjusted multilevel T-spline for complex surface manufacturing’, J. Manuf. Process., vol. 153, pp. 531–546, 2025, doi: 10.1016/j.jmapro.2025.08.070.
C. Harmening and R. Butzer, ‘Improving the approximation quality of tensor product B-spline surfaces by local parameterization’, J. Appl. Geod., vol. 18, no. 4, pp. 575–596, 2024, doi: 10.1515/jag-2023-0071.
P. Cong, D. Zhou, W. Li, and M. Deng, ‘Structural optimization of mining decanter centrifuge based on response surface method and multi-objective genetic algorithm’, Chem. Eng. Process. - Process Intensif., vol. 212, p. 110276, 2025, doi: 10.1016/j.cep.2025.110276.
Y. T. Wibowo, N. Siswanto, and M. Suef, ‘Response surface methodology approach in achieving multi-response setup optimization in the machining process’, Salud Cienc. Tecnol., vol. 2, p. 190, 2022, doi: 10.56294/saludcyt2022190.
N. Szpisják-Gulyás, A. N. Al-Tayawi, Zs. H. Horváth, Zs. László, Sz. Kertész, and C. Hodúr, ‘Methods for experimental design, central composite design and the Box–Behnken design, to optimise operational parameters: A review’, Acta Aliment., vol. 52, no. 4, pp. 521–537, 2023, doi: 10.1556/066.2023.00235.
C. Lu and J. Shi, ‘Relative density and surface roughness prediction for Inconel 718 by selective laser melting: central composite design and multi-objective optimization’, Int. J. Adv. Manuf. Technol., vol. 119, no. 5–6, pp. 3931–3949, 2022, doi: 10.1007/s00170-021-08388-2.
M. Ben Said, E. Ftoutou, I. Hajjaji, A. Benkhalifa, and M. Trigui, ‘Experimental investigations of tooth pitch variation and cutting parameters on areal surface texture in flat end milling of Fe–Ni alloy Supra50’, Int. J. Adv. Manuf. Technol., vol. 139, no. 9–10, pp. 5009–5023, 2025, doi: 10.1007/s00170-025-16210-6.
B. He, S. Ding, and Z. Shi, ‘A comparison between profile and areal surface roughness parameters’, Metrol. Meas. Syst., pp. 413–438, 2021, doi: 10.24425/mms.2021.137133.
M. Raza, Z. Alam, and A. D. Udai, ‘ISO Standardized Form Removal and Filtering of Surface Texture for Areal Surface Roughness Measurement Using Zygo Mx’, MAPAN, vol. 40, no. 4, pp. 937–942, 2025, doi: 10.1007/s12647-025-00844-8.
I. Malkorra et al., ‘Numerical modelling of the drag finishing process at a macroscopic scale to optimize surface roughness improvement on additively manufactured (SLM) Inconel 718 parts’, Procedia CIRP, vol. 108, pp. 648–653, 2022, doi: 10.1016/j.procir.2022.01.002.
J. Kalisz, K. Żak, S. Wojciechowski, M. K. Gupta, and G. M. Krolczyk, ‘Technological and tribological aspects of milling-burnishing process of complex surfaces’, Tribol. Int., vol. 155, p. 106770, 2021, doi: 10.1016/j.triboint.2020.106770.
R. Adhikari, G. Bolar, R. Shanmugam, and U. Koklu, ‘Machinability and surface integrity investigation during helical hole milling in AZ31 magnesium alloy’, Int. J. Lightweight Mater. Manuf., vol. 6, no. 2, pp. 149–164, 2023, doi: 10.1016/j.ijlmm.2022.09.006.
Muhamad Afiq Azwan Yusni, N. K. Kamardin, A. F. Zubair, and A. S. Mohd Rodzi, ‘The Effects Of Taguchi Method And Anova In Optimizing Parameters For Enhancing Power Optimization For Electrical Discharge’, J. Mek., 2025, doi: 10.11113/jm.v48.563.
A. F. Zubair and M. S. Abu Mansor, ‘Embedding firefly algorithm in optimization of CAPP turning machining parameters for cutting tool selections’, Comput. Ind. Eng., vol. 135, pp. 317–325, 2019, doi: 10.1016/j.cie.2019.06.006.
Y. Yang and X. Wei, ‘Optimization of Process Parameters for Surface Roughness and Milling Power of AL7075 CNC Milling Based on a Hybrid Multi-Objective Particle Swarm Optimization Integrating Whale Optimization Algorithm’, Integrating Mater. Manuf. Innov., vol. 14, no. 3, pp. 401–424, 2025, doi: 10.1007/s40192-025-00412-7.
Assab, ‘Stavax ESR (2024)’. [Online]. Available: https://www.assab.com/app/uploads/sites/199/2024/05/Stavax_ESR_PH-EN.pdf
Z. Xie et al., ‘The manufacturing process and influencing factors for curved aspheric-microlens arrays by Slow Tool Servo Machining’, J. Manuf. Process., vol. 125, pp. 217–225, 2024, doi: 10.1016/j.jmapro.2024.07.032.
Y. Sun, Z. He, C. Fu, Z. Xie, B. Zhang, and H. Liu, ‘Surface modeling and influencing factors for microlens array by slow tool servo machining’, J. Manuf. Process., vol. 102, pp. 365–374, 2023, doi: 10.1016/j.jmapro.2023.07.037.
W. Ji, H. Shang, B. Li, H. Yang, and Z. Li, ‘Effects of tool orientation and surface curvature on tool wear in ball end milling of 17-4PH stainless steel’, Int. J. Adv. Manuf. Technol., vol. 135, no. 11–12, pp. 5595–5613, 2024, doi: 10.1007/s00170-024-14836-6.
L. L. Duan, G. Y. Yang, D. C. Hao, F. Huang, J. Xing, and K. X. Liu, ‘Tribological and Mechanical Properties of Nanocrystalline TiN, TiAlN, and TiSiN PVD Coatings’, Strength Mater., vol. 55, no. 4, pp. 822–833, 2023, doi: 10.1007/s11223-023-00573-w.
N. Geier and C. Pereszlai, ‘Analysis of characteristics of surface roughness of machined CFRP composites’, Period. Polytech. Mech. Eng., vol. 64, no. 1, pp. 67–80, 2020, doi: 10.3311/PPme.14436.
T. Pavol, J. Holubjak, V. Bechný, M. Novák, A. Czán, and T. Czánová, ‘Surface Analysis and Digitization of Components Manufactured by SLM and ADAM Additive Technologies’, Manuf. Technol., vol. 23, no. 1, pp. 127–134, 2023, doi: 10.21062/mft.2023.008.
A. Pereira, M. Fenollera, T. Prado, and M. Wieczorowski, ‘Effect of Surface Texture on the Structural Adhesive Joining Properties of Aluminum 7075 and TEPEX®’, Materials, vol. 15, no. 3, 2022, doi: 10.3390/ma15030887.
M. Vanrusselt, H. Haitjema, R. Leach, and P. De Groot, ‘International comparison of flatness deviation in areal surface topography measurements’, CIRP Ann., vol. 71, no. 1, pp. 453–456, 2022, doi: 10.1016/j.cirp.2022.04.030.
M. K N, B. Hosamani, Nagaraju, V. Kemminje, V. R. Raju, and Nagahanumaiah, ‘An investigation into the surface integrity and cutting force characteristics in titanium alloy end milling using soluble oil and MQL as coolants’, Results Surf. Interfaces, vol. 17, p. 100341, 2024, doi: 10.1016/j.rsurfi.2024.100341.
J. Wang, C. Zhang, F. Jiao, and Y. Cao, ‘Parameters optimization for 2.5D needled Cf/SiC in longitudinal torsional ultrasonic-assisted laser milling on PSO-BP-PSO’, CIRP J. Manuf. Sci. Technol., vol. 58, pp. 87–106, 2025, doi: 10.1016/j.cirpj.2025.02.002.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Mohd Faizal Yasak, Ahmad Faiz Zubair, Mohd Fauzi Ismail, Muhammad Akmal Mohd Zakaria

This work is licensed under a Creative Commons Attribution 4.0 International License.






