Abstract
The last decade has witnessed a surge of interest in artificial neural network in many different areas of scientific research. Despite the rapid expansion in the application of neural networks, few efforts have been carried out to introduce such a powerful tool into lubrication studies. Thus, this work aims to apply the physics-informed neural network (PINN) to the hydrodynamic lubrication analysis. The 2D Reynolds equation is solved. The PINN is a meshless method and does not require big data for network training compared with classical methods. Our results are consistent with those obtained by experiments and the finite element method. Hence, we envision that the PINN method will have great application potential in lubrication and bearing research.
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Abbreviations
- b :
-
Bias of neuron
- B :
-
Bearing width (m)
- C(w):
-
Loss during training
- h :
-
Film thickness (m)
- h 0 :
-
Outlet film thickness (m)
- H :
-
Dimensionless film thickness (H = h/ho)
- L :
-
Bearing length (m)
- N[X,Y]T :
-
Neural network
- N e :
-
Maximum allowable epoch number
- N L :
-
Layer number
- N n :
-
Neuron number of each layer
- p :
-
Pressure (Pa)
- P :
-
Dimensionless pressure (P = ph 20 /(UηL))
- U :
-
Sliding velocity (m/s)
- W :
-
Applied load (N)
- z :
-
Neuron output
- λ :
-
Working condition vector
- η :
-
Lubricant viscosity (Pa·s)
- θ :
-
Inclination
- ϕ(ξ):
-
Activation function
- w :
-
Weight of neuron
- Ω L :
-
Lubrication domain
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 51805310), the Scientific Research Startup Fund for Shenzhen High-caliber Personnel of SZPT (No. 6022310045k). Special thanks go to Prof. A. Almqvist for his valuable comments on the work.
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Authors and Affiliations
Contributions
YZ implemented the PINN codes and drafted the manuscript. LG conducted the experimental measurements and discussed about PINN. PLW contributed mainly on the discussion and presentation.
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Additional information
Yang ZHAO. He obtained his Ph.D. degree from both City University of Hong Kong and Xi’an Jiaotong University in 2019, and his B.S. degree from China University of Mining and Technology in 2013. He is currently a lecturer in Shenzhen Polytechnic. His research interests include lubrication, computational tribology, and interfacial phenomena.
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Zhao, Y., Guo, L. & Wong, P.P.L. Application of physics-informed neural network in the analysis of hydrodynamic lubrication. Friction 11, 1253–1264 (2023). https://doi.org/10.1007/s40544-022-0658-x
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DOI: https://doi.org/10.1007/s40544-022-0658-x