A solution for finite journal bearings by using physics-informed neural networks with both soft and hard constrains

Abstract

Purpose The purpose of this study is to solve the Reynolds equation for finite journal bearings by using the physics-informed neural networks (PINNs) method. As a meshless method, it is unnecessary to use big data to train the neural networks, but to satisfy the Reynolds equation and the corresponding boundary conditions by using the known physics information. Design/methodology/approach Here, the boundary conditions are enforced through the loss function firstly, i.e. the soft constrain method. After this, an equation was constructed to build a surrogate model for satisfying the corresponding boundary conditions naturally, i.e. the hard constrain method. Findings For the soft one, in brief, the pressure results agree well with existing results, apart from the ones on the boundaries. While for the hard one, it can be noted that the discrepancies on the boundaries are reduced significantly. Originality/value The PINNs method is used to solve the Reynolds equation for finite journal bearings, and the error values on the boundaries for the results of the soft constrain method are improved by using the hard constrain method. Therefore, the hard constraint maybe also a good option when the pressure results on the boundaries are emphasized. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2023-0045/

Physics-Informed Machine Learning—An Emerging Trend in Tribology

“…Xi et al [70] investigated the application of PINNs to predict the pressure distribution of a finite journal bearing and compared the results when employing soft or hard constraints for the boundary conditions (see Figures 8a and 8b, respectively). The models were implemented in the Python library, DeepXDE, whereby the ANN consisted of three hidden layers with 20 neurons each, and tanh was used as the activation function.…”

“…Using PINN to solve the 1D Reynolds BVP to predict the pressure distribution in a fluid-lubricated linear converging slider 2021 [64] Using PINN to solve the 2D Reynolds equation to predict the pressure and film thickness distribution considering load balance in a fluid-lubricated linear converging slider 2023 [66] Using supervised, semi-supervised, and unsupervised PINN to solve the 2D Reynolds equation to predict the pressure and film thickness distribution considering load balance and eccentricity in a gas-lubricated journal bearing 2022 [68] Using PINN to solve the 2D Reynolds equation to predict the behavior of fluid-lubricated journal as well as two-lobe bearings 2023 [69] Using PINN with soft and hard constraints to solve the 2D Reynolds equation to predict the pressure distribution in fluid-lubricated journal bearings at fixed eccentricity with constant and variable viscosity 2023 [70] Using PINN to solve the 2D Reynolds equation to predict the pressure and fractional film content distribution in fluid-lubricated journal bearings at fixed and variable eccentricity considering cavitation 2023 [71] Using PINN to solve the 2D Reynolds equation to predict the pressure and fractional film content distribution in fluid-lubricated journal bearings at fixed eccentricity considering cavitation 2023 [72] Wear and damage prediction Using semi PINN to find regression fitting parameters for Archard's wear law based upon small data from fretting wear experiments 2015 [77] Using hybrid PINN to predict wind turbine bearing fatigue based upon a physics-informed bearing damage model as well as data-driven grease degradation approach 2020 [78] Using physics-informed CNN with preceding threshold model for rolling bearing fault detection 2021 [79] Using physics-informed residual network for rolling bearing fault detection 2023 [80] Using PIML framework consisting of piecewise fitting, a hybrid physics-informed data-driven model, and meta-learning to predict tool wear 2022 [81] As such, PINNs have been employed for lubrication prediction by solving the Reynolds differential equation. Starting with the 1D Reynolds equation for a converging slider, in only two years, the complexity has already been tremendously increased, now covering the 2D Reynolds equation, journal bearings with load balance and variable eccentricity, and cavitation effects.…”