A method and system for analyzing lubrication performance of a sliding bearing

Abstract

The application discloses a sliding bearing lubrication performance analysis method and system, and belongs to the technical field of sliding bearing lubrication. First, according to the geometric parameters and working condition parameters of the sliding bearing, a dimensionless Reynolds equation and its boundary conditions are established. Then, a physical information neural network model is constructed with spatial coordinates as input and oil film pressure as output. The augmented Lagrange method is used to construct a loss function, and the boundary conditions are taken as constraint terms with adaptive weights. Then, a transfer learning strategy is used, the network parameters under the trained working condition are taken as the initial value, and the solution of different working conditions is accelerated. After training, the pressure distribution is output, and the oil film carrying capacity, friction force and friction coefficient are calculated. The application can realize rapid and accurate analysis of the lubrication performance of the sliding bearing, and significantly improve the prediction accuracy and calculation efficiency of the pressure field.

Description

Technical Field

[0001] This invention relates to the field of sliding bearing lubrication, and in particular to a method and system for analyzing the lubrication performance of sliding bearings. Background Technology

[0002] Sliding bearings reduce friction and wear, increase load-bearing capacity, and improve the overall performance of mechanical systems by forming a lubricating oil film in the friction pair clearance. In engineering, traditional numerical methods such as the finite difference method and the finite volume method are often used to solve the Reynolds equation to obtain the oil film pressure distribution and lubrication performance indicators.

[0003] However, traditional numerical methods often require repeatedly establishing and solving models for different working conditions when dealing with uncertain problems, high-dimensional problems, and optimization design problems, resulting in a large amount of computation.

[0004] In recent years, with the rapid development of machine learning, physical information neural networks (PINs) have shown potential as a meshless framework for solving tribological problems, but they also have some shortcomings. For example, the invention patent with publication number CN121479945A discloses a method for predicting the lubrication clearance of sliding bearings based on a PSN. It adopts the soft constraint strategy of standard PSNs, encoding the control equations and boundary conditions as weighted penalty terms into the loss function. The difference in gradient magnitude between different loss components can easily lead to optimization imbalance, resulting in the boundary conditions not being accurately satisfied or training divergence.

[0005] In bearing design and lubrication analysis, the physical information neural network (PIN) needs to be repeatedly used to solve problems due to changes in bearing parameters and operating conditions, resulting in low efficiency from training from scratch each time. For example, the invention patent with publication number CN117057265A discloses a flow field prediction method based on transfer learning and discrete physical information neural networks. It uses transfer learning for flow field prediction in the PSN, but the transfer learning strategy of this patent freezes the time step sequence, which is not suitable for multi-condition scenarios (such as changes in geometric parameters and operating parameters) of sliding bearings. In addition, the existing technology has not yet systematically integrated solutions for the unique boundary conditions and multi-condition characteristics of sliding bearing lubrication problems.

[0006] Based on the above, there is an urgent need for a rapid analysis method for the lubrication performance of sliding bearings that is computationally efficient and accurate. Summary of the Invention

[0007] The purpose of this invention is to provide a method and system for analyzing the lubrication performance of sliding bearings. By adaptively adjusting the boundary condition constraint weights using the augmented Lagrangian method and combining it with a working condition adaptive transfer learning strategy, high-precision and high-efficiency lubrication performance analysis can be achieved.

[0008] To achieve the above objectives, the present invention provides a method and system for analyzing the lubrication performance of sliding bearings, comprising the following steps: Step 1: Based on the geometric parameters and operating parameters of the sliding bearing, establish the dimensionless Reynolds equation describing the lubrication behavior of the bearing and determine its boundary conditions. Step 2: Construct a physical information neural network model with spatial coordinates as input and oil film pressure as output; Step 3: Construct a loss function using the augmented Lagrange method. The loss function includes Lagrange multipliers and a penalty term. During training, the Lagrange multipliers are updated to adaptively adjust the weights of the boundary condition constraint terms. Step 4: Use the transfer learning method, with the pre-trained model weights as the initial values, and freeze some of the hidden layer parameters of the physical information neural network model; Step 5: After training is completed, output the oil film pressure distribution and calculate the lubrication performance index based on the oil film pressure distribution.

[0009] Preferably, in step 1, the geometric parameters include the bearing diameter. Bearing length Bearing radial clearance Operating parameters include bearing rotational angular velocity. Lubricant viscosity eccentricity ,load .

[0010] Preferably, in step 1, the dimensionless Reynolds equation is: ; in, Dimensionless pressure; The thickness is dimensionless. The dimensionless dynamic viscosity of the oil film; These are the transformed axial and circumferential coordinates.

[0011] Preferably, in step 2, the physical information neural network model is a fully connected neural network, including an input layer, multiple hidden layers, and an output layer; the activation function is a hyperbolic tangent function or others.

[0012] Preferably, in step 3, the loss function is: ; in, For neural network parameters; For Lagrange multipliers; This is the penalty coefficient; The residuals of the Reynolds equation; For boundary errors; For the first Lagrange multipliers corresponding to each boundary condition point; This represents the total number of boundary condition sampling points; For the neural network in the first Predicted pressure values ​​at each boundary point; For the first Boundary conditions at each boundary point; During training, the Lagrange multipliers are updated according to the following rules: ; in, The learning rate of the Lagrange multiplier; For Lagrange multipliers The gradient; and The first Second and third The updated Lagrange multiplier values ​​in the next iteration.

[0013] Preferably, the Reynolds equation residuals Represented as: ; Boundary error Represented as: ; in, The total number of internal points; and The first Dimensionless coordinates of the internal collocation points; For the neural network in the first Predicted pressure values ​​at each internal alignment point; For the first The dimensionless film thickness at each internal collocation point.

[0014] Preferably, in step 4, the parameters of the neural network under the trained working condition are loaded as initial values ​​for training the new working condition, and the parameters of the shallow neuron nodes are frozen, and only the parameters of the last hidden layer are trained.

[0015] Preferably, in step 5, the lubrication performance indicators include oil film bearing capacity, friction force, and friction coefficient; the dimensionless pressure predicted by the physical information neural network is restored to a dimensional pressure, and the oil film bearing capacity is obtained by integrating it on the bearing surface; the shear stress is calculated from the pressure gradient, and the oil film friction force is obtained by integrating it on the bearing surface.

[0016] The present invention also provides a sliding bearing lubrication performance analysis system for implementing the above-mentioned sliding bearing lubrication performance analysis method, comprising: Parameter acquisition module: used to acquire the geometric parameters and operating parameters of the sliding bearing; Lubrication Model Building Module: Used to establish the dimensionless Reynolds equation and its boundary conditions that describe the lubrication behavior of sliding bearings; Neural Network Building Module: Used to build a physical information neural network model with spatial coordinates as input and oil film pressure as output; Loss function construction module: used to construct the loss function based on the augmented Lagrange method and update the Lagrange multipliers during training to adaptively adjust the weights of the boundary condition constraint terms; Training module: Used to train the physical information neural network model; Transfer learning module: used to transfer network parameters between different operating conditions and freeze some hidden layer parameters; Output module: Used to output oil film pressure distribution and calculate lubrication performance parameters.

[0017] Therefore, the sliding bearing lubrication performance analysis method and system of the present invention have the following beneficial effects: (1) The augmented Lagrange method is used to construct the loss function. By dynamically updating the Lagrange multipliers, the weight of the boundary condition constraint term is adaptively adjusted during the training process. This effectively avoids the gradient imbalance problem between different loss components, so that the boundary conditions can be accurately satisfied. At the same time, the residual of the control equation is fully reduced, thereby significantly improving the prediction accuracy of the oil film pressure field and the stability of the training process.

[0018] (2) The transfer learning strategy is adopted, the weights of the physical information neural network model under the trained working conditions are used as the initial values, and some hidden layer parameters are frozen according to the difference type between the new working conditions and the pre-trained working conditions, so as to reduce the cost of repeated training and improve the efficiency of multi-working condition analysis.

[0019] (3) After training, the present invention outputs the oil film pressure distribution and calculates the lubrication performance indicators such as oil film bearing capacity, friction force and friction coefficient based on the pressure distribution by area integral. It can be directly used for the load capacity assessment of sliding bearings, friction power consumption calculation and design parameter optimization, forming a complete closed loop from solution to performance evaluation, providing directly usable data support for engineering practice.

[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0021] Figure 1 This is a flowchart of a sliding bearing lubrication performance analysis method according to an embodiment of the present invention; Figure 2 This is a physical information neural network framework for lubrication analysis of sliding bearings in an embodiment of the present invention; Figure 3This is a diagram showing the oil film pressure distribution predicted by a physical information neural network under different aspect ratios and eccentricities in an embodiment of the present invention, wherein (a) is , The predicted pressure distribution at time (b) is as follows: , The predicted pressure distribution at time (c) is , The predicted pressure distribution at time (d) is , The predicted pressure distribution at time (e) is , The predicted pressure distribution at time (f) is , Pressure distribution prediction results at that time; Figure 4 The diagram shows a performance comparison of the physical information neural network with and without transfer learning in this embodiment of the invention. (a) represents the prediction pressure, (b) represents the pressure comparison between the physical information neural network and the finite difference method at x=0, and (c) represents the iterative loss diagram of the physical information neural network. Detailed Implementation

[0022] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0024] Example 1 This embodiment provides a method for analyzing the lubrication performance of sliding bearings, such as... Figure 1 As shown, it includes the following steps: Step 1) Input basic parameters: The geometric and operating parameters of the sliding bearing are determined based on engineering experience. The geometric parameters include the bearing diameter. Bearing length Bearing clearance Operating parameters include speed. Lubricant dynamic viscosity eccentricity and load .

[0025] Step 2) Establish the dimensionless Reynolds equation: The dimensionless Reynolds equation describing the hydrodynamic behavior of the thin lubricating film between the journal and the bearing bushing is expressed as: ; in, Dimensionless pressure; The thickness is dimensionless. , For film thickness; The dimensionless dynamic viscosity of the oil film; axial coordinates dimensionless form ( ), Circumferential coordinates dimensionless form ( ), Where is the bearing radius.

[0026] The dimensionless film thickness equation is: ; Boundary condition: The pressure at both ends of the axial direction is zero, that is... The circumferential direction satisfies the periodic boundary condition, that is... .

[0027] Step 3) Construct a physical information neural network: like Figure 2 The diagram shows the physical information neural network framework used for lubrication analysis of sliding bearings in this embodiment. A fully connected neural network is established, with the following network structure: Input layer: 2 nodes, corresponding to the transformed spatial coordinates ; Hidden layers: 3 layers, 32 neurons per layer, activation function is hyperbolic tangent function. ; Output layer: 1 node, corresponding to dimensionless pressure .

[0028] Step 4) Construct the loss function: The loss function is constructed based on the augmented Lagrange method. First, collocation points are selected within the computational domain: these internal collocation points are collected using Hammersley sequences. Each point; boundary points (including corresponding points of the axial end boundary and the circumferential periodic boundary) are collected uniformly. One point.

[0029] Define the Reynolds equation residual : ; The partial derivatives are calculated automatically by the neural network.

[0030] Define boundary error : ; in, The total number of internal points; and The first Dimensionless coordinates of the internal collocation points; For the neural network in the first Predicted pressure values ​​at each internal alignment point; For the first The dimensionless film thickness at each internal collocation point.

[0031] The augmented Lagrange loss function is: ; in, For neural network parameters; For Lagrange multipliers; This is the penalty coefficient; The residuals of the Reynolds equation; For boundary errors; For the first Lagrange multipliers corresponding to each boundary condition point; This represents the total number of boundary condition sampling points; For the neural network in the first Predicted pressure values ​​at each boundary point; For the first Boundary conditions at each boundary point.

[0032] In this embodiment, the initial Lagrange multipliers All are set to 0, penalty coefficient Set it to 100.

[0033] Step 5) Training the network: The Adam gradient descent algorithm is used to update the parameters of the neural network. Lagrange multipliers. learning rate Set to 1, neural network parameters learning rate Set to 0.0005. During training, the neural network parameters and Lagrange multipliers are updated in each iteration, with a total training iteration count of 50,000. During the next training session, the Lagrange multipliers and neural network parameters The update is as follows: ; .

[0034] Step 6) Output pressure distribution and lubrication performance indicators: After training, forward propagation is performed on a uniform grid of 36,000 points (100 points along the axis and 360 points along the circumference in this embodiment) within the solution domain to obtain the dimensionless pressure distribution. .

[0035] Restoring dimensional pressure : , ;in, For reference pressure.

[0036] Calculate oil film bearing capacity : ; in, and These represent the true solution domain and the solution domain after unquantization, respectively; This embodiment uses Gauss-Legend de Gauss numerical integration for calculation.

[0037] Friction force was calculated using the Couette shear model. : ; Among them, shear stress , , Represents the film thickness along the circumferential coordinate. The distribution of frictional force. The integration method for frictional force is the same as that for bearing force, both involving surface integrals over the corresponding field.

[0038] coefficient of friction Friction Ratio to bearing capacity: .

[0039] like Figure 3 The figure shows the oil film pressure distribution predicted by the physical information neural network under different aspect ratios and eccentricities. Figure 3 It shows the aspect ratio and eccentricity The pressure distribution prediction results are presented under six different combinations. Comparing the calculation results of this embodiment with those of the finite difference method (200×100 grids), the maximum relative error is 1.2%, verifying the accuracy of this method.

[0040] Step 7) Transfer learning accelerates multi-condition analysis: With aspect ratio eccentricity As a baseline, train the network until convergence according to steps 1) to 6), and save the network weights. .

[0041] Set target operating condition: length-to-diameter ratio eccentricity (Only the eccentricity changes, while the geometric parameters remain the same).

[0042] For the target operating condition, perform the following operations: Construct a physical information neural network with the same structure as in step 3); Loading the network parameters of the baseline load condition As initial values ​​for the network; Construct the loss function (in the film thickness equation corresponding to the target operating condition) according to step 4). ); Train the network according to step 5), but freeze the parameters of the first two hidden layers and only train the parameters of the last layer; (Step 6) Output the pressure distribution and calculate the performance indicators.

[0043] like Figure 4 The figure shows a performance comparison of the physical information neural network with and without transfer learning in this embodiment. Figure 4 The medians (a) and (b) are the predicted stress distributions after 20,000 training cycles without and with transfer learning, respectively, and both are in good agreement with the finite difference reference solution. Figure 4 (c) shows the loss curve during training. The results indicate that after using transfer learning, the network reaches a loss value comparable to training from scratch for 50,000 steps in approximately 8,000 steps, reducing the number of training rounds by 84% and resulting in a lower final loss value (transfer learning: Training from scratch: This study verified the significant acceleration effect and accuracy improvement of transfer learning in the multi-condition analysis of sliding bearings.

[0044] Example 2 This invention provides a sliding bearing lubrication performance analysis system for performing the method described in Example 1. The system includes the following functional modules: Parameter acquisition module: Used to acquire the geometric parameters and operating parameters of the sliding bearing. In this embodiment, this module provides a graphical user interface to receive user input. , , , , , and It includes parameters such as [parameter name], and supports batch reading from files.

[0045] Lubrication Model Construction Module: Used to construct the dimensionless Reynolds equation and its boundary conditions. This module automatically generates the film thickness function based on data provided by the parameter acquisition module. Define the computational domain And set zero pressure at the axial end and circumferential periodic boundary conditions.

[0046] Neural Network Construction Module: Used to construct a physical information neural network model with spatial coordinates as input and oil film pressure as output. This module builds a fully connected network according to the structure in step 3) and supports saving / loading weights.

[0047] Loss function construction module: This module constructs the loss function based on the augmented Lagrange multiplier method and updates the Lagrange multipliers during training to adaptively adjust the weights of the boundary condition constraint terms. This module calculates the loss function according to the formulas in steps 4) and 5). and maintain the multiplier vector Set the update step count.

[0048] Training module: Used to train the physical information neural network model. This module uses the Adam optimizer to iteratively optimize the network parameters and Lagrange multipliers according to the update rule in step five, and records the loss curve during training.

[0049] Transfer learning module: Used to transfer network parameters between different operating conditions and freeze some hidden layer parameters. In this embodiment, for the target operating condition... This module freezes the parameters of the first two hidden layers.

[0050] Output module: This module outputs the pressure distribution and calculates lubrication performance parameters. After training, it generates a pressure contour map, calculates the load-bearing capacity, friction force, and coefficient of friction, and outputs the results in the form of charts and numerical reports.

[0051] The modules described above are interconnected via a data bus and work together. The system can be deployed on a general-purpose computer equipped with an NVIDIA GPU.

[0052] Therefore, this invention provides a method and system for analyzing the lubrication performance of sliding bearings. First, a dimensionless Reynolds equation and boundary conditions are established, constructing a physical information neural network model with spatial coordinates as input and oil film pressure as output. Then, an augmented Lagrange method is used to construct a loss function, and the boundary constraint weights are adaptively adjusted by dynamically updating the Lagrange multipliers, effectively solving the gradient imbalance problem under soft constraint strategies and improving the accuracy of pressure field prediction and training stability. Next, a transfer learning strategy is employed, using the pre-trained model weights as initial values ​​and freezing some hidden layer parameters according to the type of operating condition change, significantly reducing the computational cost of repeated training under multiple operating conditions, reducing the number of training iterations by more than 80%. Finally, the pressure distribution is output, and lubrication performance indicators such as bearing capacity, friction force, and friction coefficient are calculated, forming a complete analysis process. It significantly improves the efficiency of multi-operating condition analysis while ensuring solution accuracy, requires no mesh generation, and can be widely applied to the lubrication performance evaluation, parameter optimization, and rapid design of sliding bearings, exhibiting outstanding substantive features and significant progress.

[0053] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for analyzing the lubrication performance of a sliding bearing, characterized in that, Includes the following steps: Step 1: Based on the geometric parameters and operating parameters of the sliding bearing, establish the dimensionless Reynolds equation describing the lubrication behavior of the bearing and determine its boundary conditions. Step 2: Construct a physical information neural network model with spatial coordinates as input and oil film pressure as output; Step 3: Construct a loss function using the augmented Lagrange method. The loss function includes Lagrange multipliers and a penalty term. During training, the Lagrange multipliers are updated to adaptively adjust the weights of the boundary condition constraint terms. Step 4: Use the transfer learning method, with the pre-trained model weights as the initial values, and freeze some of the hidden layer parameters of the physical information neural network model; Step 5: After training is completed, output the oil film pressure distribution and calculate the lubrication performance index based on the oil film pressure distribution.

2. The method for analyzing the lubrication performance of a sliding bearing according to claim 1, characterized in that: In step 1, the geometric parameters include the bearing diameter. Bearing length Bearing radial clearance Operating parameters include bearing rotational angular velocity. Lubricant viscosity eccentricity ,load .

3. The method for analyzing the lubrication performance of a sliding bearing according to claim 2, characterized in that, In step 1, the dimensionless Reynolds equation is: ； in, Dimensionless pressure; The thickness is dimensionless. The dimensionless dynamic viscosity of the oil film; These are the transformed axial and circumferential coordinates.

4. The method for analyzing the lubrication performance of a sliding bearing according to claim 3, characterized in that: In step 2, the physical information neural network model is a fully connected neural network, including an input layer, multiple hidden layers, and an output layer.

5. The method for analyzing the lubrication performance of a sliding bearing according to claim 4, characterized in that, In step 3, the loss function is: ； in, For neural network parameters; For Lagrange multipliers; This is the penalty coefficient; The residuals of the Reynolds equation; For boundary errors; For the first Lagrange multipliers corresponding to each boundary condition point; This represents the total number of boundary condition sampling points; For the neural network in the first Predicted pressure values ​​at each boundary point; For the first Boundary conditions at each boundary point; During training, the Lagrange multipliers are updated iteratively according to the following rules: ； in, The learning rate of the Lagrange multiplier; For Lagrange multipliers The gradient; and The first Second and third The updated Lagrange multiplier values ​​in the next iteration.

6. The method for analyzing the lubrication performance of a sliding bearing according to claim 5, characterized in that: Reynolds equation residuals Represented as: ； Boundary error Represented as: ； in, The total number of internal points; and The first Dimensionless coordinates of the internal collocation points; For the neural network in the first Predicted pressure values ​​at each internal alignment point; For the first The dimensionless film thickness at each internal collocation point.

7. The method for analyzing the lubrication performance of a sliding bearing according to claim 6, characterized in that: In step 4, the parameters of the neural network under the trained conditions are loaded as initial values ​​for training the new conditions, and the parameters of some hidden layers are frozen as needed.

8. The method for analyzing the lubrication performance of a sliding bearing according to claim 7, characterized in that: In step 5, the lubrication performance indicators include oil film bearing capacity, friction force, and friction coefficient; the dimensionless pressure predicted by the physical information neural network is restored to a dimensional pressure, and the oil film bearing capacity is obtained by integrating it on the bearing surface; the shear stress is calculated from the pressure gradient, and the oil film friction force is obtained by integrating it on the bearing surface.

9. A sliding bearing lubrication performance analysis system, used to implement the sliding bearing lubrication performance analysis method according to any one of claims 1-8, characterized in that, include: Parameter acquisition module: used to acquire the geometric parameters and operating parameters of the sliding bearing; Lubrication Model Building Module: Used to establish the dimensionless Reynolds equation and its boundary conditions that describe the lubrication behavior of sliding bearings; Neural Network Building Module: Used to build a physical information neural network model with spatial coordinates as input and oil film pressure as output; Loss function construction module: used to construct the loss function based on the augmented Lagrange method and update the Lagrange multipliers during training to adaptively adjust the weights of the boundary condition constraint terms; Training module: Used to train the physical information neural network model; Transfer learning module: used to transfer network parameters between different operating conditions and freeze some hidden layer parameters; Output module: Used to output oil film pressure distribution and calculate lubrication performance parameters.

Images