RESEARCH PAPER
A surface quality analysis method for CNC milling based on an improved Z-Map algorithm
More details
Hide details
1
Logistics Engineering College, Shanghai Maritime University, Shanghai, 201306, China, China
2
School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, Jilin Province, China, China
3
Key Laboratory of CNC Equipment Reliability, Ministry of Education, Jilin University, Changchun 130025, Jilin Province, China, China
4
College of Robotics, Beijing Union University, Beijing, 100027, China
5
Beijing University of Technology, Beijing 100124, China, China
A – Conceptualization; B – Methodology; C – Software; D – Validation; E – Formal analysis; F – Investigation; G – Resources; H – Data curation; I – Writing – original draft; J – Writing – review & editing; K – Visualization; L – Supervision; M – Project administration; N – Funding acquisition
Submission date: 2025-12-09
Final revision date: 2026-05-25
Acceptance date: 2026-06-25
Online publication date: 2026-07-10
Corresponding author
Ziling Zhang
Logistics Engineering College, Shanghai Maritime University, Shanghai, 201306, China, China
KEYWORDS
TOPICS
ABSTRACT
Demands for superior surface quality in high-end components make precise analysis and reliable assessment critical. This paper presents an integrated method combining improved morphology simulation with an intelligent evaluation framework. Specifically, the Z-Map algorithm is enhanced by particle swarm optimization for efficient, high-precision surface topography simulation. The high-fidelity simulation data provides an effective database for training the subsequent intelligent prediction model. The simulated data then trains a radial basis function neural network (RBFNN) optimized by an improved butterfly optimization algorithm (IBOA) for roughness prediction, achieving over 99% accuracy. This model serves as a surrogate in Monte Carlo simulations for reliability analysis (IBOA-RBFNN-MC). Results show this approach outperforms benchmarks and aligns closely with experimental measurements, validating its accuracy for process optimization and quality control.
REFERENCES (44)
1.
Zhao B, Zhang S, Man J, Zhang Q, Chen Y. A modified normal contact stiffness model considering effect of surface topography. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 2015; 229(6): 677-688.
https://doi.org/10.1177/135065....
2.
Ait-Sadi H, Hemmouche L, Hattali L, Britah M, Lost A, Mesrati N. Effect of nanosilica additive particles on both friction and wear performance of mild steel/CuSn/SnBi multimaterial system. Tribology International 2015; 90: 372-385.
https://doi.org/10.1016/j.trib....
3.
Ghorbani M, Movahhedy M. Extraction of surface curvatures from tool path data and prediction of cutting forces in the finish milling of sculptured surfaces. Journal of Manufacturing Processes 2019; 45: 273-289.
https://doi.org/10.1016/j.jmap....
4.
Boz Y, Erdim H, Lazoglu I. A comparison of solid model and three-orthogonal dexelfield methods for cutter-workpiece engagement calculations in three- and five-axis virtual milling. International Journal of Advanced Manufacturing Technology 2015; 81(5-8): 811-823.
https://doi.org/10.1007/s00170....
5.
Zhang W-H, Tan G, Wan M, Gao T, Bassir DH. A New Algorithm for the Numerical Simulation of Machined Surface Topography in Multiaxis Ball-End Milling. Journal of Manufacturing Science and Engineering 2008; 130(1): 011003-1-011003-11.
https://doi.org/10.1115/1.2815....
6.
Chen H, Wang Q. Modelling and simulation of surface topography machined by peripheral milling considering tool radial runout and axial drift. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 2019; 233(12): 2227-2240.
https://doi.org/10.1177/095440....
7.
Teimouri R, Grabowski M, Kowalczyk M, Skoczypiec S. Simulation of surface roughness alternation in milling-burnishing sequence. Measurement 2023; 218: 1-17.
https://doi.org/10.1016/j.meas....
8.
Xu J, Zhang H, Sun Y. Swept surface-based approach to simulating surface topography in ball-end CNC milling. International Journal of Advanced Manufacturing Technology 2018; 98(1-4): 107-118.
https://doi.org/10.1007/s00170....
9.
Li S, Dong Y, Li Y, Li P, Yang Z, Landers R. Geometrical simulation and analysis of ball-end milling surface topography. International Journal of Advanced Manufacturing Technology 2019; 102(5-8): 1885-1900.
https://doi.org/10.1007/s00170....
10.
Xiao Y, Ge G, Zeng Z, Feng X, Du Z. An improved Z-MAP method based on the SQP algorithm for fast surface topography simulation of ball-end milling. International Journal of Advanced Manufacturing Technology 2023; 128(3-4): 1863-1878.
https://doi.org/10.1007/s00170....
11.
Zekalmi Y, Albajez JA, Aguado S, Oliveros MJ. New fast micro-topography estimation algorithms for 5 axis milling. Advances in Engineering Software 2025; 205: 103909.
https://doi.org/10.1016/j.adve....
12.
Guo Q, Liu Z, Jiang Y, Sun Y, Yang Z, Wang W, Zhao W, Okoye C. Topography prediction at boundaries between sub-regions in the 5-axis milling of Plexiglas based on dimension reduction method. Journal of Manufacturing Processes 2024; 131: 827-843.
https://doi.org/10.1016/j.jmap....
13.
Benardos P, Vosniakos G. Predicting surface roughness in machining: a review. International Journal of Machine Tools & Manufacture 2003; 43(8): 833-844.
https://doi.org/10.1016/S0890-....
14.
Salgado D, Alonso F, Cambero I, Marcelo A. In-process surface roughness prediction system using cutting vibrations in turning. International Journal of Advanced Manufacturing Technology 2009; 43(1-2): 40-51.
https://doi.org/10.1007/s00170....
15.
Duan C, Hao Q. Surface roughness prediction in high speed milling of 45 steel. Journal of Harbin Engineering University 2015; 36(9): 1229-1233.
https://doi.org/10.11990/jheu.... (In Chinese).
16.
Zhao M, Xue B, Li B, Zhu J, Song W. Ensemble learning with support vector machines algorithm for surface roughness prediction in longitudinal vibratory ultrasound-assisted grinding. Precision Engineering, Journal of the International Societies for Precision Engineering and Nanotechnology 2024; 88: 382-400.
https://doi.org/10.1016/j.prec....
17.
Xu L, Huang C, Niu J, Wang J, Liu H, Wang X. Prediction of cutting power and surface quality, and optimization of cutting parameters using new inference system in high-speed milling process. Advances in Manufacturing 2021; 9(3): 388-402.
https://doi.org/10.1007/s40436....
18.
Al-Ahmari A. Predictive machinability models for a selected hard material in turning operations. Journal of Materials Processing Technology 2007; 190(1-3): 305-311.
https://doi.org/10.1016/j.jmat....
19.
Zhang Y, Xiao G, Gao H, Zhu B, Huang Y, Li W. Roughness Prediction and Performance Analysis of Data-Driven Superalloy Belt Grinding. Frontiers in Materials 2022; 9: 765401.
https://doi.org/10.3389/fmats.....
20.
Peng B, Yan X, Du J. Surface quality prediction based on BP and RBF neural networks. Surface Technology 2020; 49(10): 324- 328+337.
https://doi.org/10.16490/j.cnk... (In Chinese).
21.
Zhu Y, Meng F, Dai Y, Guo H, Shi C, Li Z. Prediction of Cutting Surface Roughness of Compacted Graphite Iron (CGI) Based on Machine Learning Techniques. Iranian Journal of Science and Technology-Transactions of Mechanical Engineering 2025; 49(4): 1765-1772.
https://doi.org/10.1007/s40997....
22.
Zhan J, Zhou J, Xu Y, Chen J, Sun J. Research on ground surface roughness of cemented carbides with various grain sizes based on RBF neural network prediction. Rare Metals and Cemented Carbides 2022; 50(4): 87-93.
https://doi.org/10.19990/j.iss... (In Chinese).
23.
Li J. Study of surrogate model approximation and surrogate-enhanced structural reliability analysis. PhD thesis. Shanghai: Shanghai Jiao Tong University; 2013.
https://kns.cnki.net/kcms2/art... (In Chinese).
24.
Deng J. Structural reliability analysis for implicit performance function using radial basis function network. International Journal of Solids and Structures 2006; 43(11-12): 3255-3291.
https://doi.org/10.1016/j.ijso....
25.
Wang Q, Fang H. Reliability analysis of tunnels using an adaptive RBF and a first-order reliability method. Computers and Geotechnics 2018; 98: 144-152.
https://doi.org/10.1016/j.comp....
26.
Abbasianjahromi H, Shojaeikhah S. Structural Reliability Assessment of Steel Four-Bolt Unstiffened Extended End-Plate Connections Using Monte Carlo Simulation and Artificial Neural Networks. Iranian Journal of Science and Technology-Transactions of Civil Engineering 2021; 45(1): 111-123.
https://doi.org/10.1007/s40996....
27.
Barbosa M, Rade D. Kriging/FORM Reliability Analysis of Rotor-Bearing Systems. Journal of Vibration Engineering & Technologies 2022; 10(6): 2179-2201.
https://doi.org/10.1007/s42417....
28.
Luo C, Zhu SP, Keshtegar B, Macek W, Branco R, Meng D. Active Kriging-based conjugate first-order reliability method for highly efficient structural reliability analysis using resample strategy. Computer Methods in Applied Mechanics and Engineering 2024; 423: 116863.
https://doi.org/10.1016/j.cma.....
29.
Ding F, Wang Q, Zhang L, Wang C. Support vector machine for hydraulic support reliability prediction. Journal of Mechanical Strength 2017; 39(3): 603-607.
https://doi.org/10.16579/j.iss... (In Chinese).
30.
Chen JY, Feng YW, Teng D, Lu C, Fei CW. Support vector machine-based similarity selection method for structural transient reliability analysis. Reliability Engineering & System Safety 2022; 223: 108513.
https://doi.org/10.1016/j.ress....
31.
Schubert J. Managing inconsistent intelligence. In: Proceedings of the Third International Conference on Information Fusion ; Paris, France. Piscataway, NJ: IEEE; 2000. p. TUB4/10-TUB4/16.
https://doi.org/10.1109/IFIC.2....
33.
Jaberipour M, Khorram E, Karimi B. Particle swarm algorithm for solving systems of nonlinear equations. Computers & Mathematics with Applications 2011; 62(2): 566-576.
https://doi.org/10.1016/j.camw....
34.
Li F, Li Y, Li W, Wang B, Li Z. Surface roughness and surface morphology of milled carbon/epoxy composite surface. Surface Technology 2017; 46(9): 264-269.
https://doi.org/10.16490/j.cnk... (In Chinese).
35.
Arora S, Singh S. Butterfly optimization algorithm: a novel approach for global optimization. Soft Computing 2019; 23(3): 715-734.
https://doi.org/10.1007/s00500....
36.
Liu J, Ma Y, Li Y. Improved butterfly algorithm for multi-dimensional complex function optimization problem. Acta Electronica Sinica 2021; 49(6): 1068-1076.
https://doi.org/10.12263/DZXB.... (In Chinese).
37.
Gul N, Ahmed S, Elahi A, Kim S, Kim J. Optimal Cooperative Spectrum Sensing Based on Butterfly Optimization Algorithm. Computers, Materials & Continua 2022; 71(1): 369-387.
https://doi.org/10.32604/cmc.2....
38.
Tan L, Zainuddin Z, Ong P. Wavelet neural networks based solutions for elliptic partial differential equations with improved butterfly optimization algorithm training. Applied Soft Computing 2020; 95: 106518.
https://doi.org/10.1016/j.asoc....
39.
Sahoo AK, Panigrahi TK, Das SR, Behera A. Chaotic butterfly optimization algorithm applied to multi-objective economic and emission dispatch in modern power system. Recent Advances in Computer Science and Communications 2022; 15(2): 170-185.
https://doi.org/10.2174/266625....
40.
Gotkhindikar NN, Singh M, Kataria R. Optimized deep neural network strategy for best parametric selection in fused deposition modelling. International Journal on Interactive Design and Manufacturing 2024; 18(8): 5865-5874.
https://doi.org/10.1007/s12008....
42.
Freites A, Corbett P, Rongier G, Geiger S. Automated Classification of Well Test Responses in Naturally Fractured Reservoirs Using Unsupervised Machine Learning. Transport in Porous Media 2023; 147(3): 747-779.
https://doi.org/10.1007/s11242....
43.
Al Debeyan F, Madeyski L, Hall T, Bowes D. The impact of hard and easy negative training data on vulnerability prediction performance. Journal of Systems and Software 2024; 211: 112003.
https://doi.org/10.1016/j.jss.....
44.
Sekaninová M. Causes of Non-normality of Monitored Quality Characteristics in Process Capability Analysis. Quality Innovation Prosperity 2025; 29(3): 112-138.
https://doi.org/10.12776/qip.v....