PINN neural network-based sliding bearing lubrication clearance prediction method

Abstract

The invention belongs to the technical field of aero-engine design, and provides a sliding bearing lubrication gap prediction method based on a PINN neural network, and the method comprises the steps: generating a training data set of the PINN neural network, constructing the PINN neural network, employing a reverse mechanism of the neural network, calculating a partial differential operator through automatic differential, and carrying out the prediction of the lubrication gap of a sliding bearing. Customizing a dynamic pressure lubrication Reynolds equation into a loss function in a deep learning framework; and a prediction data set of the neural network model is generated, the trained PINN model and weight parameters are loaded, construction of a prediction model is completed, and an oil film pressure distribution curved surface is generated. According to the method, the accuracy of oil film pressure distribution calculation is remarkably improved, and meanwhile, the speed of numerical calculation can be remarkably increased.

Description

Technical Field

[0001] This invention belongs to the field of aero-engine design technology, and relates to a method for predicting design parameters by using numerical calculation of key and important characteristics of equipment and artificial intelligence. Specifically, it relates to a method for predicting the lubrication clearance of sliding bearings based on PINN neural networks. Background Technology

[0002] Sliding bearings have a relatively simple structure and installation method. The shaft diameter and bearing bush have surface contact, resulting in good load-bearing capacity. They operate smoothly and with low noise at high speeds, making them widely used in oil pumps. To reduce wear and friction loss on the bearing bush surface, it is desirable for the sliding bearing to operate in a hydrodynamic lubrication state after the oil pump reaches its rated operating speed. At this point, a lubricating oil film of a certain thickness and pressure is formed between the shaft diameter and bearing bush, preventing direct contact. To achieve this, calculating and verifying the minimum oil film thickness required for the rotating bearing under a certain load, i.e., the lubrication clearance, is extremely important.

[0003] To determine whether a bearing is under hydrodynamic lubrication, it is necessary to calculate the oil film pressure distribution. Traditional numerical methods use the finite difference method to solve the two-dimensional Reynolds partial differential equation. The core principle of this method is to use finite difference approximations of differentials. However, this method suffers from unavoidable errors, namely, the discarding of higher-order truncation errors. Furthermore, most current literature only studies the solution of oil film pressure distribution, with limited research on solving for the minimum lubrication clearance from the oil film bearing capacity. Inverse solving involves repeatedly solving for the oil film pressure distribution under different eccentricities, and each pressure distribution iteration requires more nested finite difference calculations, thus resulting in low efficiency for inverse solving using the finite difference method. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a method for predicting the lubrication clearance of sliding bearings based on a PINN neural network. This method rapidly predicts the lubrication clearance value of sliding bearings and is more efficient and accurate than traditional numerical calculation methods.

[0005] The technical solution of the present invention is as follows: A method for predicting the lubrication clearance of a sliding bearing based on a PINN neural network includes the following steps: S1, in a two-dimensional coordinate system, with the sliding bearing axial direction Zhou Xiang Eccentricity ε, radius to width ratio Based on the base data, the training dataset for the PINN neural network is generated by sampling with different strategies, random shuffling, and combination. S2, construct an NN neural network with 4 input layer nodes, 1 output layer node, and at least two hidden layers in between; S3 utilizes the inverse mechanism of neural networks, employs automatic differentiation to calculate partial differential operators, and customizes the Reynolds equation for hydrodynamic lubrication as a loss function within a deep learning framework: S4, initialize the parameters of the neural network, use the adaptive optimization algorithm Adam to minimize the loss function in the equation, and save the PINN network and weight parameters when the network training reaches the termination condition. S5 collects structural parameters including the width B, radius r, and radial clearance c between the shaft and the bearing of the sliding bearing, as well as operating parameters including the bearing linear velocity U, the external load Fw, and the dynamic viscosity coefficient eta of the lubricating medium, and generates a prediction dataset for the neural network model according to S1. S6: Load the PINN model and weight parameters trained in S4 to complete the construction of the prediction model; S7, predefine the initial value of the eccentricity ε; S8, the prediction model quickly generates the oil film pressure distribution surface, and the oil film bearing capacity under the current eccentricity is obtained by integrating the pressure surface. ; S9, Determine the oil film bearing capacity If the external load Fw meets the termination condition, the eccentricity ε is adjusted using the relaxation method, and S7~S9 are repeated until the termination condition is met; otherwise, S10 is performed. S10 determines whether the bearing can operate normally under the specified load.

[0006] Furthermore, in S2, the activation function for the hidden layer is Tanh(); the activation function Softplus() is added to the output layer to ensure that the network output is not less than 0; the Reynolds boundary conditions are:

[0007] In the formula, The coordinates are unquantized in the circumferential direction, with values ​​in the range [0, 2]. ]; Due to import pressure, This refers to the oil film pressure.

[0008] Furthermore, in S2, hard constraints are added to the network structure of the NN neural network, including: Solution domain constraints:

[0009] Correction formula:

[0010] In the formula: Due to import pressure, For network output; Values ​​at the boundary; This refers to the oil film pressure.

[0011] Furthermore, in S3, the loss function is:

[0012] In the formula: , The thickness is a dimensionless oil film. This refers to the oil film pressure.

[0013] Furthermore, in S3, due to the existence of Reynolds boundary conditions, the coordinates at the points after the oil film ruptures... , , All are 0, among which The existence of these terms prevents the loss function from ever approaching 0. Setting a mask tells the neural network model to ignore these locations. The mask is defined as Mask = (p < 0.001) ∩ ( <0.001) ∩ ( > The loss function is corrected using masked_fill_.

[0014] Furthermore, in S8, the calculation formula is:

[0015]

[0016]

[0017] Among them, Fb subscript and These represent the axial oil film bearing capacity and the circumferential oil film bearing capacity, respectively.

[0018] Furthermore, in S9, the termination condition is... .

[0019] Furthermore, in S10, the determination method is as follows: take the minimum value of the two-dimensional space oil film thickness and the allowable oil film thickness [h], so that the bearing operates under a fully fluid lubrication state, and the minimum oil film thickness h min satisfy:

[0020] In the formula: , , respectively, represent the surface finish of the shaft and bearing bore; s is the safety factor; L is the bearing span; E is the elastic model of the shaft material; J is the bending coefficient of the shaft section; B is the bearing width.

[0021] The beneficial effects of the technical solution are: 1. The present invention provides a method for predicting the lubrication clearance of sliding bearings based on PINN neural network. In the PINN network model, partial differential equations are used as physical constraints, which significantly improves the accuracy of oil film pressure distribution calculation and also significantly improves the speed of numerical calculation.

[0022] 2. This invention utilizes the backpropagation mechanism of PINN, which has a built-in automatic differentiation function, to avoid truncation error. It can quickly predict the oil film pressure distribution under different bearing structural parameters and operating parameters with only one training. It is suitable for multi-round iterative problems of solving the minimum lubrication clearance by backpropagation of oil film distribution, which greatly improves the iteration efficiency. Attached Figure Description

[0023] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a flowchart of the training and prediction process for the PINN neural network.

[0025] Figure 2 This is a schematic diagram showing the axis position and gap shape.

[0026] Figure 3 This is a schematic diagram of the overall framework of a neural network.

[0027] Figure 4 This is a schematic diagram of the loss curve during the training process.

[0028] Figure 5 This is a schematic diagram of the eccentricity change curve during the prediction process.

[0029] Figure 6 The oil film pressure distribution cloud map when the oil film bearing capacity and external load are balanced. Detailed Implementation

[0030] This section describes embodiments of the present invention, used to explain and illustrate the technical solutions of the present invention. Unless otherwise specified, the embodiments and features described herein can be combined with each other.

[0031] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating directions or positional relationships, are given in the accompanying drawings and are used only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or device referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include more than one of those features. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0032] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integrated connections; they can refer to mechanical connections or point connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0033] Example 1: In a fully fluid lubrication state, when the shaft diameter is in an eccentric position, the two components converge into a wedge shape. The rotation of the shaft diameter generates hydrodynamic force in the lubricating film to support the load on the shaft diameter. See the working state diagram. Figure 2 .

[0034] S1: Generate the training dataset, with values ​​ranging from... ∈[0,1]、 ∈[0,2pi], ε∈[0.1,0.9], ∈[0.25,0.9], with the number of values ​​N1=41, N2=101, N3=10, and N4=13 respectively, resulting in the final Cat dataset x, y, ε and Generate a tensor with size [538330,4].

[0035] S2: Construct a neural network model with layers = [4,64,64,64,64,64,1].

[0036] S3: Using automatic differentiation to calculate partial differential operators, the hydrodynamic lubrication Reynolds equation is customized as a loss function within a deep learning framework, and masking position conditions are set. See details. Figure 6Using mask_fikk_, the loss value at the condition is set to 1e-10. The overall framework of the neural network is shown below. Figure 3 .

[0037] S4: Train the PINN network using the adaptive optimization algorithm Adam and a learning rate of 0.001. See the loss curve below. Figure 4 The loss value gradually decreases and tends to 0.

[0038] S5: Collect the following parameters for the sliding bearing: width B=90mm, radius r=40, radial clearance c=0.08mm between shaft and bearing; bearing linear velocity U=12.57m / s, external load Fw=1000N; dynamic viscosity coefficient of lubricating medium eta=0.009pa·s, and generate the prediction dataset for the neural network model according to S1.

[0039] S6: Load the PINN model and weight parameters trained in S4 to complete the construction of the prediction model.

[0040] S7: The initial value of the eccentricity ε is predefined as 0.6.

[0041] S8: The prediction model quickly generates an oil film pressure distribution surface, and the oil film bearing capacity under the current eccentricity is obtained by integrating the pressure surface. .

[0042] S9: Relaxation iterations are performed on the eccentricity, with 33 iterations and a GPU computation time of 45 seconds (high computational efficiency; traditional difference methods require several hours of iteration computation time), to improve the oil film bearing capacity. The load Fw is balanced with the eccentricity deformation curve during the prediction process. Figure 5 The final oil film pressure distribution is shown in the figure. Figure 6 .

[0043] S10: The minimum oil film thickness of the sliding bearing is calculated to be 0.06mm. When designing the product, the clearance between the shaft and the bearing needs to be controlled above 0.06mm to avoid wear. At the same time, the existing design tolerance range can be checked based on the allowable oil film thickness.

[0044] Example 2: The method for predicting the lubrication clearance of sliding bearings based on PINN neural networks includes the following steps: S1: In a two-dimensional coordinate system, with the sliding bearing axial direction... Zhou Xiang Eccentricity ε, radius to width ratio Based on the base data, the training dataset for the PINN neural network is generated through sampling with different strategies, random shuffling, and combination.

[0045] Regarding different sampling strategies, specifically, for ∈[0,1] and ∈[0,2π] are sampled evenly, with the number of data points being N1 and N2 respectively; for ε and Uniformly distributed random sampling was performed, with the number of data points being N3 and N4 respectively; Regarding random shuffling, specifically, for the above... , The sample is shuffled with replacement, and the above ε and The copies are then copied to generate four sets of tensors with shape [N1*N2*N3*N4, 1]. Finally, the four tensors are combined into a tensor of shape [N1*N2*N3*N4, 4], which serves as the input sample for the PINN neural network.

[0046] S2: Construct an NN neural network with 4 input layer nodes, 1 output layer node, and several hidden layers in between.

[0047] The hidden layer uses the Tanh() activation function to ensure that the network output is limited to a reasonable range. The output layer adds the Softplus() activation function to ensure that the network output is not less than 0. The purpose is to allow the neural network to automatically find the boundary conditions for the natural rupture of the oil film, thereby satisfying the Reynolds boundary conditions. The Reynolds boundary conditions are as follows:

[0048] In the formula, The coordinates are unquantized in the circumferential direction, with values ​​in the range [0, 2]. ]; Oil film pressure; This is due to import pressure.

[0049] To ensure that the network output better meets the boundary constraints of the solution domain, hard constraints are added to the network structure.

[0050] Solution domain constraints:

[0051] Correction formula:

[0052] In the formula: For network output; Values ​​at the boundary; This refers to the oil film pressure.

[0053] S3: Utilizing the inverse mechanism of neural networks, partial differential operators are calculated using automatic differentiation. Within a deep learning framework, the Reynolds equation for hydrodynamic lubrication is customized as a loss function, as shown in the following equation:

[0054] In the formula: , The thickness is a dimensionless oil film.

[0055] Due to the existence of Reynolds boundary conditions, the coordinates at the points after the oil film ruptures are... , , All are 0, among which The existence of these terms prevents the loss function from ever approaching 0, so a mask is needed to tell the neural network model to ignore these positions.

[0056] The mask is defined as Mask = (p < 0.001) ∩ ( <0.001) ∩ ( > The loss function is corrected using masked_fill_.

[0057] S4: The parameters of the neural network are randomly initialized using the Xavier Normal scheme. The Adam adaptive optimization algorithm is used to minimize the loss function in the equation. When the network training reaches the termination condition, the PINN network and weight parameters are saved.

[0058] The termination condition is: or

[0059] S5: Collect structural parameters such as the width B, radius r, and radial clearance c between the shaft and the bearing (generally about two-thousandths of the radius) of the sliding bearing; operating parameters such as the bearing linear velocity U and the external load Fw; and the dynamic viscosity coefficient eta of the lubricating medium, and generate the prediction dataset of the neural network model according to S1.

[0060] S6: Load the PINN model and weight parameters trained in S4 to complete the construction of the prediction model.

[0061] S7: Predefine the initial value of the eccentricity ε. It is generally recommended that ε be taken near the midpoint of the [0,1] interval.

[0062] S8: The prediction model quickly generates an oil film pressure distribution surface, and the oil film bearing capacity under the current eccentricity is obtained by integrating the pressure surface. The calculation formula is:

[0063]

[0064]

[0065] S9: Determine the oil film's load-bearing capacity Check if the external load Fw meets the termination condition. If not, use the relaxation method to adjust the eccentricity ε and repeat S7~S9 until the termination condition is met; otherwise, proceed to S10.

[0066] Termination condition is

[0067] S10: To determine whether a bearing can work normally under a specified load, it is necessary to take the minimum value of the two-dimensional space oil film thickness and the allowable oil film thickness [h]. In order for the bearing to work in a fully fluid lubrication state, the minimum oil film thickness (i.e., lubrication clearance) satisfies the following formula.

[0068]

[0069] In the formula: , denoted as s, where s is the surface finish of the shaft and bearing bore; s is the safety factor; L is the bearing span; E is the elastic model of the shaft material; J is the bending coefficient of the shaft section; and B is the bearing width.

[0070] The above description is merely a specific embodiment of the present invention, providing a detailed description of the invention. Parts not covered herein are conventional techniques. However, the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the lubrication clearance of sliding bearings based on a PINN neural network, characterized in that, Includes the following steps: S1, in a two-dimensional coordinate system, with the sliding bearing axial direction Zhou Xiang Eccentricity ε, radius to width ratio Based on the base data, the training dataset for the PINN neural network is generated by sampling with different strategies, random shuffling, and combination. S2, construct an NN neural network with 4 input layer nodes, 1 output layer node, and at least two hidden layers in between; S3 utilizes the inverse mechanism of neural networks, employs automatic differentiation to calculate partial differential operators, and customizes the Reynolds equation for hydrodynamic lubrication as a loss function within a deep learning framework: S4, initialize the parameters of the neural network, use the adaptive optimization algorithm Adam to minimize the loss function in the equation, and save the PINN network and weight parameters when the network training reaches the termination condition. S5 collects structural parameters including the width B, radius r, and radius clearance c between the shaft and the bearing of the sliding bearing, as well as operating parameters including the bearing linear velocity U, the external load Fw, and the dynamic viscosity coefficient eta of the lubricating medium, and generates a prediction dataset for the neural network model according to S1. S6: Load the PINN model and weight parameters trained in S4 to complete the construction of the prediction model; S7, predefine the initial value of the eccentricity ε; S8, the prediction model quickly generates the oil film pressure distribution surface, and the oil film bearing capacity under the current eccentricity is obtained by integrating the pressure surface. ; S9, Determine the oil film bearing capacity If the external load Fw meets the termination condition, the eccentricity ε is adjusted using the relaxation method, and S7~S9 are repeated until the termination condition is met; otherwise, S10 is performed. S10 determines whether the bearing can operate normally under the specified load.

2. The method for predicting the lubrication clearance of a sliding bearing based on a PINN neural network according to claim 1, characterized in that, In S2, the activation function for the hidden layer is Tanh(); the activation function Softplus() is added to the output layer to ensure that the network output is not less than 0; the Reynolds boundary conditions are: In the formula, The coordinates are unquantized in the circumferential direction, with values ​​in the range [0, 2]. ]; Due to import pressure, This refers to the oil film pressure.

3. The method for predicting the lubrication clearance of a sliding bearing based on a PINN neural network according to claim 1, characterized in that, In S2, hard constraints are added to the network structure of the NN neural network, including: Solution domain constraints: Correction formula: In the formula: Due to import pressure, For network output; Values ​​at the boundary; This refers to the oil film pressure.

4. The method for predicting the lubrication clearance of a sliding bearing based on a PINN neural network according to claim 1, characterized in that, In S3, the loss function is: In the formula: , The thickness is a dimensionless oil film. This refers to the oil film pressure.

5. The method for predicting the lubrication clearance of a sliding bearing based on a PINN neural network according to claim 1, characterized in that, In S3, due to the existence of Reynolds boundary conditions, the coordinates at the points after the oil film ruptures are... , , All are 0, of which The existence of these terms prevents the loss function from ever approaching 0. Setting a mask tells the neural network model to ignore these locations. The mask is defined as Mask = (P < 0.001) ∩ ( <0.001) ∩ ( > The loss function correction uses masked_fill_. This refers to the oil film pressure.

6. The method for predicting the lubrication clearance of a sliding bearing based on a PINN neural network according to claim 1, characterized in that, In S8, the calculation formula is: Among them, Fb subscript and These represent the axial oil film bearing capacity and the circumferential oil film bearing capacity, respectively. This refers to the oil film pressure.

7. The method for predicting the lubrication clearance of a sliding bearing based on a PINN neural network according to claim 6, characterized in that, In S9, the termination condition is .

8. The method for predicting the lubrication clearance of a sliding bearing based on a PINN neural network according to claim 1, characterized in that, In S10, the determination method is as follows: take the minimum value of the two-dimensional space oil film thickness and the allowable oil film thickness [h], so that the bearing works in a fully fluid lubrication state, and the minimum oil film thickness h min satisfy: In the formula: , , respectively, represent the surface finish of the shaft and bearing bore; s is the safety factor; L is the bearing span; E is the elastic model of the shaft material; J is the bending coefficient of the shaft section; B is the bearing width.

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