A hybrid deep learning model for robust prediction of the dimensional accuracy in precision milling of thin-walled structural components

Abstract

The use of artificial intelligence to process sensor data and predict the dimensional accuracy of machined parts is of great interest to the manufacturing community and can facilitate the intelligent production of many key engineering components. In this study, we develop a predictive model of the dimensional accuracy for precision milling of thin-walled structural components. The aim is to classify three typical features of a structural component—squares, slots, and holes—into various categories based on their dimensional errors (i.e., “high precision,” “pass,” and “unqualified”). Two different types of classification schemes have been considered in this study: those that perform feature extraction by using the convolutional neural networks and those based on an explicit feature extraction procedure. The classification accuracy of the popular machine learning methods has been evaluated in comparison with the proposed deep learning model. Based on the experimental data collected during the milling experiments, the proposed model proved to be capable of predicting dimensional accuracy using cutting parameters (i.e., “static features”) and cutting-force data (i.e., “dynamic features”). The average classification accuracy obtained using the proposed deep learning model was 9.55% higher than the best machine learning algorithm considered in this paper. Moreover, the robustness of the hybrid model has been studied by considering the white Gaussian and coherent noises. Hence, the proposed hybrid model provides an efficient way of fusing different sources of process data and can be adopted for prediction of the machining quality in noisy environments.

Key words： precision milling; dimensional accuracy; cutting force; convolutional neural networks; coherent noise

Nomenclature

Abbreviations
BN	Batch normalization
CMM	Coordinate measuring machine
CNN	Convolutional neural network
GAF	Gramian angular field
IDW	Inverse distance weighting
KNN	k-nearest neighbor
LDA	Linear discriminant analysis
QDA	Quadratic discriminant analysis
RF	Random forest
SVM	Support vector machine
t-SNE	t-distributed stochastic neighbor embedding
WPD	Wavelet packet decomposition
Variables
Asl1, Asl2	Areas of the machined slots
Asq1, Asq2, Asq3	Areas of the machined squares
b^{(l)}	Bias of the convolutional layer at the lth layer
dhole	Diameter of the machined holes
esq, esl, eh	Classification accuracy of squares, slots, and holes, respectively
fl, fh	Lower and higher cutoff frequencies of band-pass filter, respectively
fs	Sampling frequency of cutting-force signal
g_{p,q}^{(l)}	Pixel value of the input image at the lth layer
G	Gramian angular field image
ns	Spindle speed
p, q	Pixel coordinates of the input image
ri (i = 1,2,…,n)	Radius of the cutting-force signal at each time point in polar coordinate system
vf	Feed rate
w_{i,j}^{(l)}	Weight of the convolutional layer at the lth layer
xi (i = 1,2,…,n)	Cutting-force signal at each time point
xm	Mean value of cutting-force signal
xrms	Root-mean square value of cutting-force signal
{\overline{x}}_i (i = 1,2,…,n)	Normalized cutting-force signal at each time point
{\tilde{x}}_i (i = 1,2,…,n)	Upper envelope of cutting-force signal at each time point
{\tilde{x}}_{\mathrm{m}}	Mean value of the upper envelope of cutting-force signal
{\tilde{x}}_{\mathrm{r}\mathrm{m}\mathrm{s}}	Root mean square value of the upper envelope of cutting-force signal
x	Cutting-force vector
xfilt	Cutting-force vector obtained using a band-pass filter
xnoise	Cutting-force noise vector
xrecons	Reconstructed cutting-force vector
αp	Depth of cut
φi (i = 1,2,…,n)	Angle of the cutting-force signal at each time point in polar coordinate system
σ	Standard deviation of cutting-force signal
σn	Standard deviation of noise
\tilde{\sigma }	Standard deviation of the upper envelope of cutting-force signal

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52005205). The authors declare that they have no known conflicts of interest that could have appeared to influence the work reported in this paper.

References

1 HodonouC, Balazinski M, BrochuM, MascleC. Material-design-process selection methodology for aircraft structural components: application to additive vs subtractive manufacturing processes. The International Journal of Advanced Manufacturing Technology, 2019, 103(1–4): 1509–1517

2 Palazzi V, Su W J, Bahr R, Bittolo-Bon S, Alimenti F, Mezzanotte P, Valentini L, Tentzeris M M, Roselli L. 3-D-printing-based selective-ink-deposition technique enabling complex antenna and RF structures for 5G applications up to 6 GHz. IEEE Transactions on Components, Packaging and Manufacturing Technology, 2019, 9(7): 1434–1447

3 HuoD H, Cheng K, WardleF. Design of a five-axis ultra-precision micro-milling machine—UltraMill. Part 1: holistic design approach, design considerations and specifications. The International Journal of Advanced Manufacturing Technology, 2010, 47(9–12): 867–877

4 BianR, He N, LiL, ZhanZ B, WuQ, ShiZ Y. Precision milling of high volume fraction SiCp/Al composites with monocrystalline diamond end mill. The International Journal of Advanced Manufacturing Technology, 2014, 71(1–4): 411–419

5 ZhanZ B, He N, LiL, ShresthaR, LiuJ Y, WangS L. Precision milling of tungsten carbide with micro PCD milling tool. The International Journal of Advanced Manufacturing Technology, 2015, 77(9–12): 2095–2103

6 WangS J, To S, ChanC Y, CheungC F, LeeW B. A study of the cutting-induced heating effect on the machined surface in ultra-precision raster milling of 6061 Al alloy. The International Journal of Advanced Manufacturing Technology, 2010, 51(1–4): 69–78

7 Li S, Zhu K P. In-situ tool wear area evaluation in micro milling with considering the influence of cutting force. Mechanical Systems and Signal Processing, 2021, 161: 107971

8 Zhu Z L, Buck D, Guo X L, Cao P X, Wang J X. Cutting performance in the helical milling of stone-plastic composite with diamond tools. CIRP Journal of Manufacturing Science and Technology, 2020, 31: 119–129

9 GuoX L, Wang J X, BuckD, ZhuZ L, EkevadM. Cutting forces and cutting quality in the up-milling of solid wood using ceramic cutting tools. The International Journal of Advanced Manufacturing Technology, 2021, 114(5–6): 1575–1584

10 Wang X Y, Huang C Z, Zou B, Liu G L, Zhu H T, Wang J. Experimental study of surface integrity and fatigue life in the face milling of Inconel 718. Frontiers of Mechanical Engineering, 2018, 13(2): 243–250

11 WangC L, Ding P F, HuangX Z, GaoT H, LiC Y, ZhangC. Reliability sensitivity analysis of ball-end milling accuracy. The International Journal of Advanced Manufacturing Technology, 2021, 112(7–8): 2051–2064

12 Agarwal A, Desai K A. Predictive framework for cutting force induced cylindricity error estimation in end milling of thin-walled components. Precision Engineering, 2020, 66: 209–219

13 SunW Y, Luo M, ZhangD H. Machining vibration monitoring based on dynamic clamping force measuring in thin-walled components milling. The International Journal of Advanced Manufacturing Technology, 2020, 107(5–6): 2211–2226

14 Zhang Z X, Luo M, Tang K, Zhang D H. A new in-processes active control method for reducing the residual stresses induced deformation of thin-walled parts. Journal of Manufacturing Processes, 2020, 59: 316–325

15 Yao Z Q, Fan C, Zhang Z, Zhang D H, Luo M. Position-varying surface roughness prediction method considering compensated acceleration in milling of thin-walled workpiece. Frontiers of Mechanical Engineering, 2021, 16(4): 855–867

16 Zhang Z L, Qi Y, Cheng Q, Liu Z F, Tao Z Q, Cai L G. Machining accuracy reliability during the peripheral milling process of thin-walled components. Robotics and Computer-Integrated Manufacturing, 2019, 59: 222–234

17 AltintasY. Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design. 2nd ed. Cambridge: Cambridge University Press, 2012

18 Armarego E J A, Deshpande N P. Computerized end-milling force predictions with cutting models allowing for eccentricity and cutter deflections. CIRP Annals-Manufacturing Technology, 1991, 40(1): 25–29

19 KaymakciM, Kilic Z M, AltintasY. Unified cutting force model for turning, boring, drilling and milling operations. International Journal of Machine Tools and Manufacture, 2012, 54–55: 34–45

20 Ducroux E, Fromentin G, Viprey F, Prat D, D’Acunto A. New mechanistic cutting force model for milling additive manufactured Inconel 718 considering effects of tool wear evolution and actual tool geometry. Journal of Manufacturing Processes, 2021, 64: 67–80

21 Li X J, Zhang Y Y, Sun X M. Numerical analysis for rock cutting force prediction in the tunnel boring process. International Journal of Rock Mechanics and Mining Sciences, 2021, 144: 104696

22 Shan C W, Zhang M H, Yang Y, Zhang S N, Luo M. A dynamic cutting force model for transverse orthogonal cutting of unidirectional carbon/carbon composites considering fiber distribution. Composite Structures, 2020, 251: 112668

23 Fu T, Zhao J B, Liu W J. Multi-objective optimization of cutting parameters in high-speed milling based on grey relational analysis coupled with principal component analysis. Frontiers of Mechanical Engineering, 2012, 7(4): 445–452

24 Jia Z Y, Lu X H, Gu H, Ruan F X, Liang S Y. Deflection prediction of micro-milling Inconel 718 thin-walled parts. Journal of Materials Processing Technology, 2021, 291: 117003

25 WuG, LiG X, PanW C, Wang X, DingS L. A prediction model for the milling of thin-wall parts considering thermal-mechanical coupling and tool wear. The International Journal of Advanced Manufacturing Technology, 2020, 107(11–12): 4645–4659

26 Manikandan H, Bera T C. Modelling of dimensional and geometric error prediction in turning of thin-walled components. Precision Engineering, 2021, 72: 382–396

27 YuanM X, Wang X B, JiaoL, YiJ, LiuS N. Prediction of dimension error based on the deflection of cutting tool in micro ball-end milling. The International Journal of Advanced Manufacturing Technology, 2017, 93(1–4): 825–837

28 BaioccoG, Genna S, LeoneC, UcciardelloN. Prediction of laser drilled hole geometries from linear cutting operation by way of artificial neural networks. The International Journal of Advanced Manufacturing Technology, 2021, 114(5–6): 1685–1695

29 GoodfellowI, Bengio Y, CourvilleA. Deep Learning. Cambridge: MIT Press, 2016

30 XieJ J, Zhao P Y, HuP C, YinY, ZhouH C, ChenJ H, Yang J Z. Multi-objective feed rate optimization of three-axis rough milling based on artificial neural network. The International Journal of Advanced Manufacturing Technology, 2021, 114(5–6): 1323–1339

31 Pan J, Libera J A, Paulson N H, Stan M. Flame stability analysis of flame spray pyrolysis by artificial intelligence. International Journal of Advanced Manufacturing Technology, 2021, 114(7–8): 2215–2228

32 Zhang X, Huang T, Wu B, Hu Y M, Huang S, Zhou Q, Zhang X. Multi-model ensemble deep learning method for intelligent fault diagnosis with high-dimensional samples. Frontiers of Mechanical Engineering, 2021, 16(2): 340–352

33 Wang Z G, Oates T. Imaging time-series to improve classification and imputation. In: Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI 2015). Buenos Aires: AAAI Press, 2015, 3939–3945

34 Krizhevsky A, Sutskever I, Hinton G E. ImageNet classification with deep convolutional neural networks. Communications of the ACM, 2017, 60(6): 84–90

35 OppenheimA V, WillskyA S, NawabS H. Signals and Systems. 2nd ed. New Jersey: Prentice-Hall, Inc., 1997

36 Chawla N V, Bowyer K W, Hall L O, Kegelmeyer W P. SMOTE: synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 2002, 16: 321–357

37 Huang F, Liu D S, Tan X C, Wang J, Chen Y P, He B B. Explorations of the implementation of a parallel IDW interpolation algorithm in a Linux cluster-based parallel GIS. Computers & Geosciences, 2011, 37(4): 426–434

38 PercivalD B, Walden A T. Wavelet Methods for Time Series Analysis. Cambridge: Cambridge University Press, 2006

39 Zheng Z D, Washington S. On selecting an optimal wavelet for detecting singularities in traffic and vehicular data. Transportation Research Part C: Emerging Technologies, 2012, 25: 18–33

40 Cover T, Hart P. Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 1967, 13(1): 21–27

41 HastieT, Tibshirani R, FriedmanJ. The Elements of Statistical Learning. New York: Springer, 2009

42 Chang C C, Lin C J. LIBSVM: a library for support vector machines. ACM Transactions on Intelligent Systems and Technology, 2011, 2(3): 1–27

43 Breiman L. Random forests. Machine Learning, 2001, 45(1): 5–32

44 van der Maaten L, Hinton G. Visualizing data using t-SNE. Journal of Machine Learning Research, 2008, 9(11): 2579–2605