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Prediction and control of surface roughness for the milling of Al/SiC metal matrix composites based on neural networks

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Abstract

In recent years, there has been a significant increase in the utilization of Al/SiC particulate composite materials in engineering fields, and the demand for accurate machining of such composite materials has grown accordingly. In this paper, a feed-forward multi-layered artificial neural network (ANN) roughness prediction model, using the Levenberg-Marquardt backpropagation training algorithm, is proposed to investigate the mathematical relationship between cutting parameters and average surface roughness during milling Al/SiC particulate composite materials. Milling experiments were conducted on a computer numerical control (CNC) milling machine with polycrystalline diamond (PCD) tools to acquire data for training the ANN roughness prediction model. Four cutting parameters were considered in these experiments: cutting speed, depth of cut, feed rate, and volume fraction of SiC. These parameters were also used as inputs for the ANN roughness prediction model. The output of the model was the average surface roughness of the machined workpiece. A successfully trained ANN roughness prediction model could predict the corresponding average surface roughness based on given cutting parameters, with a 2.08% mean relative error. Moreover, a roughness control model that could accurately determine the corresponding cutting parameters for a specific desired roughness with a 2.91% mean relative error was developed based on the ANN roughness prediction model. Finally, a more reliable and readable analysis of the influence of each parameter on roughness or the interaction between different parameters was conducted with the help of the ANN prediction model.

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Abbreviations

ANN:

Artificial neural network

CNC:

Computer numerical control

PCD:

Polycrystalline diamond

MMC:

Metal matrix composite

\(V_{\text{c}}\) :

Cutting speed

\(F_{\text{r}}\) :

Feed rate

\(D_{\text{c}}\) :

Depth of cut

\(\varphi_{\text{SiC}}\) :

Volume fraction of SiC

\(o_{m}^{k}\) :

Output of the mth neuron in the layer under consideration

\(o_{n}^{k - 1}\) :

Output of the nth neuron in the preceding layer

\(w_{mn}\) :

Weight value of the connection between the mth neuron in the layer under consideration and the nth neuron in the preceding layer

\(b_{m}^{k}\) :

Bias value for the mth neuron in the layer under consideration

\(f_{\text{activation}}\) :

Activation function

\(R_{{{\text{a}}\_{\text{predicted}}}}\) :

Output roughness value by the prediction model

\(R_{{{\text{a}}\_{\text{target}}}}\) :

Real roughness value of the milled surface

\(E_{i}\) :

Error between \(R_{{{\text{a}}\_{\text{predicted}}\_i}}\) and \(R_{{{\text{a}}\_{\text{target}}\_i}}\) for the ith input vector

\(S_{i}\) :

Squared error between \(R_{{{\text{a}}\_{\text{predicted}}\_i}}\) and \(R_{{{\text{a}}\_{\text{target}}\_i}}\) for the ith input vector

\(\varvec{W}_{\text{bnew}}\) :

New weights-bias matrix which consists of all weights and biases updated over \(\varvec{W}_{\text{bold}}\) after the ith input vector used for training

\(\varvec{W}_{\text{bold}}\) :

Old weights-bias matrix which consists of all weights and biases

\(\varvec{J}\) :

Jacobian matrix

\(P\) :

Number of elements in weights-bias matrix

\(\varvec{I}\) :

Unit matrix

\(\mu\) :

Adaptive factor

\(P_{\text{model}}\) :

Roughness prediction model

\(E_{\text{t}}\) :

Tolerable error

ANOVA:

Analysis of variance

BUE:

Built-up edge

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Acknowledgements

This work was supported by the National High Technology Research and Development Plan of China (Grant No. 2015AA043505), the Equipment Advanced Research Funds (Grant No. 61402100401), the Equipment Advanced Research Key Laboratory Funds (Grant No. 6142804180106) and Shenzhen Fundamental Research Funds (Grant No. JCYJ20180508151910775).

Author information

Authors and Affiliations

  1. Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, Shenzhen, 518055, Guangdong, People’s Republic of China

    Guo Zhou & Xiao-Hao Wang

  2. Shenzhen International Graduate School, Tsinghua University, Shenzhen, 518055, Guangdong, People’s Republic of China

    Chao Xu, Yuan Ma, Xiao-Hao Wang, Ping-Fa Feng & Min Zhang

  3. Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, People’s Republic of China

    Chao Xu, Yuan Ma & Ping-Fa Feng

Authors
  1. Guo Zhou
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  2. Chao Xu
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  3. Yuan Ma
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  4. Xiao-Hao Wang
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  5. Ping-Fa Feng
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  6. Min Zhang
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Corresponding author

Correspondence to Min Zhang.

Appendix

Appendix

See Tables 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, and 23.

Table 12 Trained weights of connections between neurons in the input and hidden layer of Model 1
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Table 13 Weights of connections between neurons in the hidden and output layer of Model 1
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Table 14 Biases of neurons in the hidden layer of Model 1
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Table 15 Biases of neurons in the output layer of Model 1
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Table 16 Trained weights and biases of connections between neurons in the input and hidden layer of Model 2
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Table 17 Weights of connections between neurons in the hidden and output layer of Model 2
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Table 18 Biases of neurons in the hidden layer of Model 2
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Table 19 Biases of neurons in the output layer of Model 2
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Table 20 Trained weights and biases of connections between neurons in the input and hidden layer of Model 3
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Table 21 Weights of connections between neurons in the hidden and output layer of Model 3
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Table 22 Biases of neurons in the hidden layer of Model 3
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Table 23 Biases of neurons in the output layer of Model 3
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Zhou, G., Xu, C., Ma, Y. et al. Prediction and control of surface roughness for the milling of Al/SiC metal matrix composites based on neural networks. Adv. Manuf. 8, 486–507 (2020). https://doi.org/10.1007/s40436-020-00326-x

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  • DOI: https://doi.org/10.1007/s40436-020-00326-x

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