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

doi:10.1007/s11465-022-0688-0

Front. Mech. Eng.

2022, Vol. 17

Issue (3) : 32 https://doi.org/10.1007/s11465-022-0688-0

RESEARCH ARTICLE

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

Long BAI¹, Fei XU¹, Xiao CHEN¹, Xin SU², Fuyao LAI², Jianfeng XU¹(

)

¹. State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
². Southwest Institution of Electronic Technology, Chengdu 610036, China

Download: PDF(5620 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

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.

Keywords precision milling dimensional accuracy cutting force convolutional neural networks coherent noise

Corresponding Author(s): Jianfeng XU

About author: Tongcan Cui and Yizhe Hou contributed equally to this work.

Just Accepted Date: 27 April 2022 Issue Date: 14 October 2022

Cite this article:

Long BAI,Fei XU,Xiao CHEN, et al. A hybrid deep learning model for robust prediction of the dimensional accuracy in precision milling of thin-walled structural components[J]. Front. Mech. Eng., 2022, 17(3): 32.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-022-0688-0
https://academic.hep.com.cn/fme/EN/Y2022/V17/I3/32

Fig.1 Schematic of the workpiece showing three typical features of the structural component studied in this study: holes (top), slots (middle), and squares (top and bottom).

Tab.1 Design dimensions of the slots and squares of the workpiece. The holes are machined at the back surface of the workpiece, and their design diameters are 6 mm

Fig.2 Experimental setup adopted for cutting-force measurements during the milling experiment.

Tab.2 Diameter of holes d_hole, area (length×width) of the slots A_sl1, A_sl2, and area of the squares A_sq1, A_sq2, and A_sq3, measured using a CMM for the workpiece material 3A21 aluminum. The mean diameter of the four holes machined during the same experiment is listed

Fig.3 Schematic of the dimensional error measurement using a CMM.

Tab.3 Cutting parameters (spindle speed n_s, feed rate v_f, and depth of cut α_p) adopted for the experiments

Fig.4 Structure of the hybrid model for robust prediction of the dimensional accuracy.

Fig.5 Cutting-force data (in Y-direction) measured during Experiment 4 (Tables 2 and 3): (a) raw data and (b) data after pre-processing.

Fig.6 (a) Segmented cutting-force signal of Square 2 and (b) the corresponding GAF image. The results shown here were obtained from Experiment 5 (Table 3).

Fig.7 Structure of the GAF + CNN model adopted in this study.

Fig.8 A random realization of (a) the white Gaussian noise, and (b) the coherent noise. The standard deviation of noise is 2.5 in both examples.

Feature	Expression
Absolute mean (original signal)	$x m = ∑ i = 1 n \| x i \| n$
Variance (original signal)	$σ 2 = ∑ i = 1 n (x i − ∑ j = 1 n x j n) 2 n − 1$
Root mean square (original signal)	$x r m s = ∑ i = 1 n x i 2 n$
Absolute mean (upper envelope)	$x ~ m = ∑ i = 1 n \| x ~ i \| n$
Variance (upper envelope)	$σ ~ 2 = ∑ i = 1 n (x ~ i − ∑ j = 1 n x ~ j n) 2 n − 1$
Root mean square (upper envelope)	$x ~ r m s = ∑ i = 1 n x ~ i 2 n$

Tab.4 Time-domain features of the cutting-force signal considered in this study

Fig.9 (a) Illustration of the WPD of the third order [32], and (b) the distribution of energy in different frequency bands after WPD. s denotes the original time-domain signal, and LPF and HPF represent low-pass and high-pass filters, respectively. (b) Result of Square 1 obtained from the measurement shown in Fig. 5(b).

Fig.10 Scatter plot matrix which shows the pair-wise correlations between the different time-domain features (Table 4). The plots in the diagonal are the probability densities of the individual features.

Tab.5 Classification accuracy (mean value and standard deviation) obtained from the 10-fold cross validation

Fig.11 (a) Typical training processes of the proposed hybrid model for classification of squares, (b) slots, and (c) holes. The left and right columns show the results of the accuracy and loss, respectively. The validation accuracy is 93.83% for squares at epoch = 500, 89.36% for slots at epoch = 500, and 80.84% for holes at epoch = 200.

Tab.6 Classification accuracy (e_sq for squres, e_sl for slots, and e_h for holes) of different machine learning classifiers obtained from the test set

Fig.12 t-SNE visualization of the training samples: (a) squares, (b) slots, and (c) holes. The class labels 0, 1, and 2 correspond to “high precision,” “pass,” and “unqualified,” respectively.

Tab.7 Mean classification accuracy for the noise input data of squares obtained from 100 random noise realizations using different approaches

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
A_sl1, A_sl2	Areas of the machined slots
A_sq1, A_sq2, A_sq3	Areas of the machined squares
$b (l)$	Bias of the convolutional layer at the lth layer
d_hole	Diameter of the machined holes
e_sq, e_sl, e_h	Classification accuracy of squares, slots, and holes, respectively
f_l, f_h	Lower and higher cutoff frequencies of band-pass filter, respectively
f_s	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
n_s	Spindle speed
p, q	Pixel coordinates of the input image
r_i (i = 1,2,…,n)	Radius of the cutting-force signal at each time point in polar coordinate system
v_f	Feed rate
$w i, j (l)$	Weight of the convolutional layer at the lth layer
x_i (i = 1,2,…,n)	Cutting-force signal at each time point
x_m	Mean value of cutting-force signal
x_rms	Root-mean square value of cutting-force signal
$x ¯ i$ (i = 1,2,…,n)	Normalized cutting-force signal at each time point
$x ~ i$ (i = 1,2,…,n)	Upper envelope of cutting-force signal at each time point
$x ~ m$	Mean value of the upper envelope of cutting-force signal
$x ~ r m s$	Root mean square value of the upper envelope of cutting-force signal
x	Cutting-force vector
x_filt	Cutting-force vector obtained using a band-pass filter
x_noise	Cutting-force noise vector
x_recons	Reconstructed cutting-force vector
α_p	Depth of cut
φ_i (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
σ_n	Standard deviation of noise
$σ ~$	Standard deviation of the upper envelope of cutting-force signal

1	C Hodonou, M Balazinski, M Brochu, C Mascle. 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 https://doi.org/10.1007/s00170-019-03613-5
2	V Palazzi, W J Su, R Bahr, S Bittolo-Bon, F Alimenti, P Mezzanotte, L Valentini, M M Tentzeris, L Roselli. 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 https://doi.org/10.1109/TCPMT.2019.2919187
3	D H Huo, K Cheng, F Wardle. 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 https://doi.org/10.1007/s00170-009-2128-2
4	R Bian, N He, L Li, Z B Zhan, Q Wu, Z Y Shi. 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 https://doi.org/10.1007/s00170-013-5494-8
5	Z B Zhan, N He, L Li, R Shrestha, J Y Liu, S L Wang. Precision milling of tungsten carbide with micro PCD milling tool. The International Journal of Advanced Manufacturing Technology, 2015, 77(9–12): 2095–2103 https://doi.org/10.1007/s00170-014-6632-7
6	S J Wang, S To, C Y Chan, C F Cheung, W B Lee. 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 https://doi.org/10.1007/s00170-010-2613-7
7	S Li, K P Zhu. In-situ tool wear area evaluation in micro milling with considering the influence of cutting force. Mechanical Systems and Signal Processing, 2021, 161: 107971 https://doi.org/10.1016/j.ymssp.2021.107971
8	Z L Zhu, D Buck, X L Guo, P X Cao, J X Wang. Cutting performance in the helical milling of stone-plastic composite with diamond tools. CIRP Journal of Manufacturing Science and Technology, 2020, 31: 119–129 https://doi.org/10.1016/j.cirpj.2020.10.005
9	X L Guo, J X Wang, D Buck, Z L Zhu, M Ekevad. 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 https://doi.org/10.1007/s00170-021-06991-x
10	X Y Wang, C Z Huang, B Zou, G L Liu, H T Zhu, J Wang. Experimental study of surface integrity and fatigue life in the face milling of Inconel 718. Frontiers of Mechanical Engineering, 2018, 13(2): 243–250 https://doi.org/10.1007/s11465-018-0479-9
11	C L Wang, P F Ding, X Z Huang, T H Gao, C Y Li, C Zhang. Reliability sensitivity analysis of ball-end milling accuracy. The International Journal of Advanced Manufacturing Technology, 2021, 112(7–8): 2051–2064 https://doi.org/10.1007/s00170-020-06334-2
12	A Agarwal, K A Desai. Predictive framework for cutting force induced cylindricity error estimation in end milling of thin-walled components. Precision Engineering, 2020, 66: 209–219 https://doi.org/10.1016/j.precisioneng.2020.07.007
13	W Y Sun, M Luo, D H Zhang. 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 https://doi.org/10.1007/s00170-020-05153-9
14	Z X Zhang, M Luo, K Tang, D H Zhang. 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 https://doi.org/10.1016/j.jmapro.2020.09.079
15	Z Q Yao, C Fan, Z Zhang, D H Zhang, M Luo. Position-varying surface roughness prediction method considering compensated acceleration in milling of thin-walled workpiece. Frontiers of Mechanical Engineering, 2021, 16(4): 855–867 https://doi.org/10.1007/s11465-021-0649-z
16	Z L Zhang, Y Qi, Q Cheng, Z F Liu, Z Q Tao, L G Cai. Machining accuracy reliability during the peripheral milling process of thin-walled components. Robotics and Computer-Integrated Manufacturing, 2019, 59: 222–234 https://doi.org/10.1016/j.rcim.2019.04.002
17	Y Altintas. Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design. 2nd ed. Cambridge: Cambridge University Press, 2012
18	E J A Armarego, N P Deshpande. Computerized end-milling force predictions with cutting models allowing for eccentricity and cutter deflections. CIRP Annals-Manufacturing Technology, 1991, 40(1): 25–29 https://doi.org/10.1016/S0007-8506(07)61926-X
19	M Kaymakci, Z M Kilic, Y Altintas. Unified cutting force model for turning, boring, drilling and milling operations. International Journal of Machine Tools and Manufacture, 2012, 54–55: 34–45 https://doi.org/10.1016/j.ijmachtools.2011.12.008
20	E Ducroux, G Fromentin, F Viprey, D Prat, A D’Acunto. 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 https://doi.org/10.1016/j.jmapro.2020.12.042
21	X J Li, Y Y Zhang, X M Sun. Numerical analysis for rock cutting force prediction in the tunnel boring process. International Journal of Rock Mechanics and Mining Sciences, 2021, 144: 104696 https://doi.org/10.1016/j.ijrmms.2021.104696
22	C W Shan, M H Zhang, Y Yang, S N Zhang, M Luo. A dynamic cutting force model for transverse orthogonal cutting of unidirectional carbon/carbon composites considering fiber distribution. Composite Structures, 2020, 251: 112668 https://doi.org/10.1016/j.compstruct.2020.112668
23	T Fu, J B Zhao, W J Liu. 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 https://doi.org/10.1007/s11465-012-0338-z
24	Z Y Jia, X H Lu, H Gu, F X Ruan, S Y Liang. Deflection prediction of micro-milling Inconel 718 thin-walled parts. Journal of Materials Processing Technology, 2021, 291: 117003 https://doi.org/10.1016/j.jmatprotec.2020.117003
25	G Wu, G X Li, W C Pan, X Wang, S L Ding. 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 https://doi.org/10.1007/s00170-020-05346-2
26	H Manikandan, T C Bera. Modelling of dimensional and geometric error prediction in turning of thin-walled components. Precision Engineering, 2021, 72: 382–396 https://doi.org/10.1016/j.precisioneng.2021.05.013
27	M X Yuan, X B Wang, L Jiao, J Yi, S N Liu. 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 https://doi.org/10.1007/s00170-017-0474-z
28	G Baiocco, S Genna, C Leone, N Ucciardello. 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 https://doi.org/10.1007/s00170-021-06857-2
29	I Goodfellow, Y Bengio, A Courville. Deep Learning. Cambridge: MIT Press, 2016
30	J J Xie, P Y Zhao, P C Hu, Y Yin, H C Zhou, J H Chen, J Z Yang. 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 https://doi.org/10.1007/s00170-021-06902-0
31	J Pan, J A Libera, N H Paulson, M Stan. Flame stability analysis of flame spray pyrolysis by artificial intelligence. International Journal of Advanced Manufacturing Technology, 2021, 114(7–8): 2215–2228 https://doi.org/10.1007/s00170-021-06884-z
32	X Zhang, T Huang, B Wu, Y M Hu, S Huang, Q Zhou, X Zhang. Multi-model ensemble deep learning method for intelligent fault diagnosis with high-dimensional samples. Frontiers of Mechanical Engineering, 2021, 16(2): 340–352 https://doi.org/10.1007/s11465-021-0629-3
33	Z G Wang, T Oates. 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	A Krizhevsky, I Sutskever, G E Hinton. ImageNet classification with deep convolutional neural networks. Communications of the ACM, 2017, 60(6): 84–90 https://doi.org/10.1145/3065386
35	A V Oppenheim, A S Willsky, S H Nawab. Signals and Systems. 2nd ed. New Jersey: Prentice-Hall, Inc., 1997
36	N V Chawla, K W Bowyer, L O Hall, W P Kegelmeyer. SMOTE: synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 2002, 16: 321–357 https://doi.org/10.1613/jair.953
37	F Huang, D S Liu, X C Tan, J Wang, Y P Chen, B B He. Explorations of the implementation of a parallel IDW interpolation algorithm in a Linux cluster-based parallel GIS. Computers & Geosciences, 2011, 37(4): 426–434 https://doi.org/10.1016/j.cageo.2010.05.024
38	D B Percival, A T Walden. Wavelet Methods for Time Series Analysis. Cambridge: Cambridge University Press, 2006
39	Z D Zheng, S Washington. On selecting an optimal wavelet for detecting singularities in traffic and vehicular data. Transportation Research Part C: Emerging Technologies, 2012, 25: 18–33 https://doi.org/10.1016/j.trc.2012.03.006
40	T Cover, P Hart. Nearest neighbor pattern classification. IEEE Transactions on Information Theory, 1967, 13(1): 21–27 https://doi.org/10.1109/TIT.1967.1053964
41	T Hastie, R Tibshirani, J Friedman. The Elements of Statistical Learning. New York: Springer, 2009 https://doi.org/10.1007/978-0-387-84858-7
42	C C Chang, C J Lin. LIBSVM: a library for support vector machines. ACM Transactions on Intelligent Systems and Technology, 2011, 2(3): 1–27 https://doi.org/10.1145/1961189.1961199
43	L Breiman. Random forests. Machine Learning, 2001, 45(1): 5–32 https://doi.org/10.1023/A:1010933404324
44	L van der Maaten, G Hinton. Visualizing data using t-SNE. Journal of Machine Learning Research, 2008, 9(11): 2579–2605

[1]	A. DAVOUDINEJAD, P. PARENTI, M. ANNONI. 3D finite element prediction of chip flow, burr formation, and cutting forces in micro end-milling of aluminum 6061-T6[J]. Front. Mech. Eng., 2017, 12(2): 203-214.
[2]	Angelos P. MARKOPOULOS,Ioannis K. SAVVOPOULOS,Nikolaos E. KARKALOS,Dimitrios E. MANOLAKOS. Molecular dynamics modeling of a single diamond abrasive grain in grinding[J]. Front. Mech. Eng., 2015, 10(2): 168-175.
[3]	Zhaoxu QI,Bin LI,Liangshan XIONG. Improved analytical model for residual stress prediction in orthogonal cutting[J]. Front. Mech. Eng., 2014, 9(3): 249-256.
[4]	Surinder Kumar GILL, Meenu GUPTA, P. S. SATSANGI. Prediction of cutting forces in machining of unidirectional glass fiber reinforced plastics composite[J]. Front Mech Eng, 2013, 8(2): 187-200.
[5]	Genghuang HE, Xianli LIU, Fugang YAN. Research on the dynamic mechanical characteristics and turning tool life under the conditions of excessively heavy-duty turning[J]. Front Mech Eng, 2012, 7(3): 329-334.
[6]	LI Xiwen, YANG Shuzi, YANG Mingjin, XIE Shouyong. Cutting Force Model for a Small-diameter Helical Milling Cutter[J]. Front. Mech. Eng., 2007, 2(3): 272-277.

Viewed

Full text

Abstract

Cited

Shared

Discussed