Abstract
Thermal error modeling (TEM) is essential for preserving machining accuracy and enhancing the reliability of electric spindle systems. However, the major challenges in TEM lie in the limited or unavailable labeled thermal error samples due to the difficulties in data acquisition, as well as the problem of large distribution discrepancy between training and testing data under variable working conditions. Recently, digital twin (DT) has emerged as a promising tool in intelligent manufacturing. The DT model of the electric spindle can simulate system thermal behavior data that closely resembles real working conditions, providing a remarkable opportunity for TEM. Additionally, deep transfer learning (DTL) leverages existing knowledge to minimize data distribution discrepancies, bridging the gap between virtual and real data, and ultimately enhancing the generalization and adaptation ability of the model. Thus, this paper proposes a DT-assisted DTL method for TEM of electric spindles. Firstly, the DT model for the electric spindle is built by establishing a high-fidelity simulation model based on the physical system’s thermal behavior mechanism. Furthermore, temperature field information for all interested working conditions can be simulated from the constructed DT model. Subsequently, the distance-guided domain adversarial network (DGDAN) is developed, with data generated by the DT model constructed as the training data in the source domain, while partially collected data from the physical system is used as the target domain for training. To validate the effectiveness of the proposed method, a case study is conducted using datasets from both the DT model and the physical system. The experimental results demonstrate that the proposed method successfully achieves TEM in scenarios where the thermal error data is limited or unavailable from the physical system, and the goodness of fit is higher than the state-of-the-art methods by 11.73%.
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Data availability
The data that support the findings of this study are available from the corresponding author upon request.
Abbreviations
- TEM:
-
Thermal error modeling
- DT(s):
-
Digital twin(s)
- DL:
-
Deep learning
- DTL:
-
Deep transfer learning
- DA:
-
Domain adaptation
- MMD:
-
Max mean discrepancy
- CNN(s):
-
Convolutional neural network(s)
- GRU:
-
Gate recurrent unit
- LSTM:
-
Long short-term memory
- ST-CLSTM:
-
Spatial–temporal-convolutional long short-term memory
- LSSVM:
-
Least squares support vector machine
- AO:
-
Aquila optimizer
- PSO:
-
Particle swarm optimization
- GAN:
-
Generative adversarial network
- GRL:
-
Gradient reversal layer
- SGD:
-
Stochastic gradient descent
- CAD:
-
Computer aided design
- C-ATLSTM:
-
Convolutional attention long short-term memory
- ReLU:
-
Rectified linear unit
- RKHS:
-
Reproducing kernel Hilbert space
- PC:
-
Personal computer
- C-LSTMN:
-
Convolutional long short-term memory network
- DGDAN:
-
Distance-guided domain adversarial network
- RMSE:
-
Root mean squared error
- MAPE:
-
Mean absolute percentage error
- \(R^{2}\) :
-
Goodness of Fit
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Acknowledgements
This work was supported by the State Administration of Science, Technology and Industry for National Defense, PRC under Grant No. JCKY2020209B005, the National Natural Science Foundation of China under Grant U20A6004 & 52205101, Guangdong Basic and Applied Basic Research Foundation under Grant 2021A1515110708, Guangzhou Basic and Applied Basic Research Foundation under Grant 202201010615, Science and Technology Major Project of Hubei Province under Grant 2021AAA003.
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Ma, S., Leng, J., Zheng, P. et al. A digital twin-assisted deep transfer learning method towards intelligent thermal error modeling of electric spindles. J Intell Manuf (2024). https://doi.org/10.1007/s10845-023-02283-1
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DOI: https://doi.org/10.1007/s10845-023-02283-1