Bearing temperature prediction method based on physical information neural network

Abstract

The application discloses a bearing temperature prediction method based on a physical information neural network, comprising: acquiring bearing working condition parameters and groove temperature measured data; constructing a physical information neural network to output bearing temperature field prediction values; constructing a total loss function, including a data loss term and a physical loss term based on a force balance equation; in the training process, inputting the temperature field prediction values into a thermal-mechanical coupling closed loop calculation module, sequentially performing thermal induced pre-tightening amount calculation, contact load solving and contact thermal resistance calculation, and feeding back the contact thermal resistance to the temperature field prediction to form a two-way coupling closed loop of 'temperature deformation load thermal resistance temperature'. The application deeply integrates a mechanical analytical model and deep learning, takes force balance residuals as physical constraints, significantly improves the accuracy, robustness and physical consistency of joint solving of bearing temperature and contact load, and provides reliable technical support for online monitoring and life assessment of high-end equipment bearings.

Description

Technical Field

[0001] This invention belongs to the field of rotating machinery condition monitoring and thermo-mechanical coupling analysis technology, specifically involving a bearing temperature prediction method based on physical information neural network. It is particularly suitable for temperature field prediction and thermo-mechanical coupling state assessment of rolling bearings in high-end equipment such as aero-engines, gas turbines, and high-speed precision machine tools under complex thermo-mechanical conditions. Background Technology

[0002] As a fundamental component for load-bearing and transmission in rotating machinery, the operating state of rolling bearings directly determines the service performance and safety boundaries of the entire equipment. With the development of high-end equipment towards higher speeds, heavier loads, and greater integration, the service conditions faced by bearings are becoming increasingly demanding. The thermo-mechanical coupling effect between frictional heat generation and contact loads has become a bottleneck restricting the accuracy of bearing life prediction and reliability assessment. Accurately predicting the temperature field distribution and dynamic evolution of contact loads during bearing operation is crucial for early fault warning, optimizing lubrication strategies, and improving system reliability.

[0003] Currently, the methods for predicting bearing temperature and assessing its thermo-mechanical condition mainly have the following technical limitations.

[0004] (1) Monitoring systems based on a single physical quantity are limited by their sensing capabilities. Existing condition monitoring systems based on single physical quantities such as vibration and temperature are limited by the sparse distribution of sensors and signal attenuation, and can usually only obtain surface temperature information of limited locations such as the outer ring of the bearing or the bearing housing. Such methods are difficult to see the evolution of the thermal state inside the contact area between the rolling elements and the raceway, and cannot provide mechanistic predictions of early damage precursors such as lubrication failure and contact micro-welding.

[0005] (2) Numerical simulation based on the finite element method is inefficient. Although the finite element method can characterize the spatial distribution of contact stress and temperature field, its multi-physics field alternating iteration calculation framework makes it take several hours to solve a single working condition, and it is heavily dependent on boundary parameters such as contact thermal conductivity and friction coefficient that are difficult to obtain accurately, which severely limits its practicality in engineering real-time analysis and online monitoring scenarios.

[0006] (3) Purely data-driven deep learning models lack physical consistency and generalization ability. In recent years, deep learning-based temperature prediction methods (such as BP neural networks, GA-BP neural networks, etc.) have shown certain advantages in pattern recognition and trend extrapolation. However, these models deviate from the basic physical laws such as Hertz contact mechanics, thermoelastic deformation, and energy conservation. When encountering working conditions outside the coverage of training data (such as transient impact, sudden load, variable speed, etc.), purely data-driven models are prone to producing prediction results that violate physical laws, and their generalization ability and engineering reliability are difficult to meet the needs of high-end equipment. In addition, existing methods are disconnected from the complex thermo-mechanical coupling mechanism inside the bearing, and cannot achieve simultaneous solution of temperature field and contact load distribution.

[0007] Therefore, there is an urgent need for a thermo-mechanical coupling analysis method that can deeply integrate physical laws and data-driven capabilities to achieve high-precision and high-efficiency joint solution of bearing temperature field and contact load, and has strong generalization ability, in order to solve the problems of poor prediction accuracy, long calculation time and lack of physical consistency of existing technologies under dynamic and variable working conditions. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide a bearing temperature prediction method based on physical information neural network. By deeply integrating mechanical analytical model and deep learning, a thermo-mechanical closed-loop coupled architecture is constructed. With Hertz contact mechanics and force balance equation as constraints, a high-precision and highly generalized joint solution and state assessment of the temperature field and contact load distribution of high-speed heavy-duty bearings is achieved.

[0009] To achieve the above objectives, the present invention provides the following technical solution: A bearing temperature prediction method based on a physical information neural network includes the following steps: Step 1: Obtain the structural parameters, operating parameters, and measured data from the temperature sensor located in the bearing race groove. The operating parameters include time variables, rotational speed, axial load, and radial load. Step 2: Construct a physical information neural network. The physical information neural network takes the operating parameters and measured groove temperature data as input feature vectors and outputs discrete node prediction values ​​of the bearing temperature field. Step 3: Construct a thermo-mechanical coupling closed-loop model and a total loss function. The total loss function includes a data loss term and a physical loss term. The data loss term represents the deviation between the predicted temperature field value and the measured groove temperature value. The physical loss term is constructed based on the force balance equation and is used to constrain the temperature field prediction value output by the neural network to satisfy the internal mechanical balance law of the bearing. Step 4: Train the physical information neural network using the total loss function and update the network parameters; Step 5: Input the real-time collected operating parameters and groove temperature data into the trained physical information neural network, and output the current bearing temperature field distribution prediction result; During the training or prediction process of the physical information neural network, the predicted temperature field value is input into the thermo-mechanical coupling closed-loop model, and the calculation of thermal preload, contact load solution and contact thermal resistance are executed in sequence. The calculated contact thermal resistance is then fed back to the temperature field prediction as a heat conduction boundary condition, forming a two-way coupling closed loop of "temperature → deformation → load → thermal resistance → temperature".

[0010] Furthermore, the thermo-mechanical coupling closed-loop model includes a bearing rolling element angular position distribution model, which determines the position angular distribution of each rolling element relative to the direction of external radial load based on the parity of the total number of bearing rolling elements. If the total number of rolling elements is even, then the angular position distribution is as follows: If the total number of rolling elements is odd, then the angular position distribution is as follows: in: For the first The angular position of each rolling element relative to the direction of the load; The angle representing the direction of the external radial load is the angle between the load line and the zero-position reference line. For the set of scroll body indices; This represents the total number of rolling elements.

[0011] Furthermore, the thermo-mechanical coupling closed-loop model includes a ring local stiffness correction model based on the groove effect, and the method for constructing the ring local stiffness correction model is as follows: The local equivalent thickness of the raceway after the effect of the groove is calculated using the Gaussian attenuation function: in: For the first The equivalent thickness of the ferrule at the corresponding position of each rolling element; The nominal thickness of the ring; For the first The depth parameter of each trench characterizes the amount of material removed; For the first The location of the center corner of the trench; The standard deviation of Gaussian decay; This represents the total number of trenches; The moment of inertia of the ring section is calculated based on the local equivalent thickness of the ring: in: For the first The moment of inertia of the cross section at the corresponding position of each rolling element; This refers to the effective width of the ring; This is the cross-sectional shape correction factor; Calculate the local bending stiffness of the collar: in: For the first Local stiffness of the raceway at each rolling element; The elastic modulus of the ring material; The characteristic length of the trench.

[0012] Furthermore, in the aforementioned thermo-mechanical coupling closed-loop model, the contact stiffness and the local stiffness of the collar are considered as a series spring system, resulting in the comprehensive contact stiffness, expressed as: in: For the first Local stiffness of the raceway at each rolling element; The contact stiffness between a single rolling element and the raceway is calculated based on the Lundberg-Palmgren line contact theory.

[0013] Furthermore, in the thermo-mechanical coupling closed-loop model, the calculation method for the thermally induced preload is as follows: Based on the theory of linear thermal expansion, calculate the radial thermal expansion of the inner ring and the radial thermal expansion of the outer ring: in: and These are the radial thermal expansion of the inner ring and the radial thermal expansion of the outer ring, respectively. and These are the raceway radii for the inner and outer rings, respectively. and The first The inner and outer ring node temperatures corresponding to each rolling element; For ambient reference temperature; The coefficient of linear thermal expansion of the ring material; The calculated thermal preload amount is as follows: in: For the first The thermal preload at each rolling element is positive, indicating a decrease in clearance, and negative, indicating an increase in clearance. This refers to the outer contact angle.

[0014] Furthermore, in the aforementioned thermo-mechanical coupling closed-loop model, the contact load is solved using a gradient descent-based load balance iterative algorithm. The method is as follows: Constructed with unknown inner radial displacement and axial displacement Force balance loss function for variables: in: The force balance loss function; For the first Normal contact load of each rolling element; For the first The angular position of each rolling element relative to the direction of the load; Outer contact angle; and These are external radial load and axial load, respectively; This represents the total number of rolling elements; The inner radial displacement is updated iteratively using the gradient descent method. and axial displacement Until the force balance loss function converges; based on the converged inner radial displacement and axial displacement Calculate the normal approximation of each rolling element: in: No. Thermal preload at each rolling element; Obtain the normal contact load: in: For comprehensive contact stiffness.

[0015] Furthermore, in the aforementioned thermo-mechanical coupling closed-loop model, the contact thermal resistance is calculated based on Hertz contact theory, using the following method: Calculate the half-width of the contact ellipse: The contact thermal resistance is obtained as follows: in: For the first Contact thermal resistance of each rolling element; For the first The contact ellipse half-width of the rolling element; For the first Normal contact load of each rolling element; It is the equivalent elastic constant; The overall curvature of the contact body; This is the effective contact length of the rolling element.

[0016] Furthermore, the physical information neural network adopts a fully connected deep neural network. In the fully connected deep neural network, the number of neurons in the input layer corresponds to the dimension of the input feature vector, the hidden layer of the network adopts the ReLU activation function, and the number of neurons in the output layer of the network corresponds to the number of discrete nodes in the temperature field. The input feature vector of the physical information neural network is represented as follows: in: The input feature vector; It is a time variable; For the first Temperature measurements at each trench , This represents the total number of trenches; and These are external radial load and axial load, respectively; The physical information neural network outputs a predicted temperature field value, expressed as follows: in: These are predicted values ​​for the temperature field. Let j be the predicted temperature value for the j-th temperature field node. , This represents the number of nodes in the temperature field.

[0017] Furthermore, the total loss function is expressed as: in: For data loss; For physical loss; This refers to the physical loss weighting coefficient; The data loss is the mean square error between the predicted temperature field value and the actual sensor value, expressed as: in: This represents the number of training samples; This represents the number of nodes in the temperature field. For the first The first sample Predicted temperature values ​​for each node; For the first The first sample The actual temperature label of each node; The physical loss is a quadratic penalty term for the force balance residual, expressed as: in: For the first Force balance loss of each sample.

[0018] The beneficial effects of this invention are as follows: This invention presents a bearing temperature prediction method based on a physical information neural network. By constructing a loss function that integrates physical constraints of force balance and establishing a bidirectional coupled closed loop of "temperature → deformation → load → thermal resistance → temperature", it achieves high-precision joint solution of the bearing's thermal-mechanical state. The technical effects are as follows: it effectively overcomes the shortcomings of pure data-driven models, such as poor generalization ability and easy violation of physical laws, and significantly improves the prediction robustness and physical consistency under unknown working conditions such as sudden loads and transient impacts. At the same time, compared with the traditional finite element method, the inference speed is greatly improved, which can meet the needs of online real-time monitoring and provide reliable technical support for the health assessment and intelligent operation and maintenance of bearings in high-end equipment. Attached Figure Description

[0019] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration: Figure 1 This is a flowchart of the bearing temperature prediction method based on physical information neural network of the present invention. Detailed Implementation

[0020] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0021] This invention aims to propose a bearing temperature prediction method based on a physical information neural network. It constructs a closed-loop coupled deep learning architecture of "temperature field prediction - thermoelastic deformation - load redistribution - contact thermal resistance feedback". Using Hertz contact mechanics and force balance equations as physical constraints, it achieves joint learning of physical laws and the coupling relationship of multiple physical fields by embedding the iterative solution process into the forward propagation fusion mechanism of the neural network. This enables accurate solution and state assessment of bearing contact load distribution and temperature field evolution under high-speed heavy-load conditions.

[0022] Specifically, such as Figure 1 As shown in the figure, the bearing temperature prediction method based on physical information neural network in this embodiment includes the following steps.

[0023] Step 1: Obtain the structural parameters, operating parameters, and measured data from the temperature sensor located in the bearing race groove. The operating parameters include time variables, rotational speed, axial load, and radial load.

[0024] Step 2: Construct a physical information neural network. The physical information neural network takes the operating parameters and measured groove temperature data as input feature vectors and outputs discrete node prediction values ​​of the bearing temperature field.

[0025] Step 3: Construct a thermo-mechanical coupling closed-loop model and a total loss function. The total loss function includes a data loss term and a physical loss term. The data loss term represents the deviation between the predicted temperature field value and the measured groove temperature value. The physical loss term is constructed based on the force balance equation and is used to constrain the temperature field prediction value output by the neural network to satisfy the internal mechanical balance law of the bearing.

[0026] Step 4: Train the physical information neural network using the total loss function and update the network parameters.

[0027] Step 5: Input the real-time collected operating parameters and groove temperature data into the trained physical information neural network, and output the current bearing temperature field distribution prediction result.

[0028] During the training or prediction process of the physical information neural network, the predicted temperature field value is input into the thermo-mechanical coupling closed-loop model, and the calculation of thermal preload, contact load solution and contact thermal resistance are executed in sequence. The calculated contact thermal resistance is then fed back to the temperature field prediction as a heat conduction boundary condition, forming a two-way coupling closed loop of "temperature → deformation → load → thermal resistance → temperature".

[0029] I. Thermo-mechanical coupling closed-loop model.

[0030] 1.1 Bearing rolling element angular position distribution model.

[0031] In this embodiment, the thermo-mechanical coupling closed-loop model includes a bearing rolling element angular position distribution model. The bearing rolling element angular position distribution model determines the position angular distribution of each rolling element relative to the direction of external radial load based on the parity of the total number of bearing rolling elements.

[0032] Define the set of scroll body indices ,in: This represents the total number of rolling elements. (The first...) angular position of each rolling element Determined based on the symmetry condition of the bearing area.

[0033] For a rolling element number that is even ( For bearings with an even number of bearings, the angular position distribution is as follows: For an odd number of rolling elements ( For bearings with an odd number of bearings, a half-cycle offset needs to be considered to ensure the symmetry of the load-bearing area. The angular position distribution is as follows: in: , for the first The angular position of each rolling element relative to the direction of the load; The angle representing the direction of the external radial load is the angle between the load line and the zero-position reference line. For the set of scroll body indices; This represents the total number of rolling elements.

[0034] Define the discrete node set of the temperature field ,in: This refers to the temperature of the inner node. This represents the temperature of the corresponding node on the outer ring.

[0035] 1.2. Local stiffness correction model for rings based on groove effect.

[0036] To capture the influence of local structures such as grooves and recesses on the stiffness of bearing races, a local stiffness correction model for the races considering the groove effect needs to be established. The presence of grooves reduces the effective local thickness of the races, thereby causing changes in the moment of inertia and bending stiffness of the cross section. Specifically, in this embodiment, the thermo-mechanical coupling closed-loop model includes a local stiffness correction model for the races based on the groove effect. The method for constructing the local stiffness correction model for the races is as follows.

[0037] For bearing rings with multiple grooves, the groove angle set is defined as follows: ,in: This represents the total number of trenches; For the first The center corner of the trench.

[0038] (1) Calculate the local equivalent thickness of the ring.

[0039] At the trench angle At this location, the effective thickness of the collar decreases due to material removal. The Gaussian decay function is used to describe the effect of the trench on the thickness of the surrounding area, and the local equivalent thickness of the collar is calculated: in: For the first The equivalent thickness of the ferrule at the corresponding position of each rolling element; The nominal thickness of the ring (area unaffected by the groove); For the first The depth parameter of each trench characterizes the amount of material removed; For the first The location of the center corner of the trench; The standard deviation of Gaussian attenuation characterizes the spatial extent of the groove's influence and is related to the rolling element spacing. ; This represents the total number of trenches.

[0040] This Gaussian weighted model reflects the smooth transition effect of the trench on the stiffness of the surrounding area, avoiding numerical instability caused by abrupt boundary changes.

[0041] (2) Calculate the moment of inertia of the ring section.

[0042] Considering the formula for the bending moment of inertia of a rectangular cross-section, an empirical correction factor is introduced to account for actual cross-sectional shape deviations, and the moment of inertia of the collar section is calculated based on the local equivalent thickness of the collar: in: For the first The moment of inertia of the cross section at the corresponding position of each rolling element; This refers to the effective width of the ring; This is a cross-sectional shape correction factor, taking into account that the actual trench cross-section is not an ideal rectangle. In this embodiment, .

[0043] (3) Calculate the local bending stiffness of the collar.

[0044] Based on the cantilever beam model from the mechanics of materials, the local bending stiffness of the collar is: in: For the first Local stiffness of the raceway at each rolling element; The elastic modulus of the ring material; The characteristic length of the groove represents the extension dimension of the groove along the circumference of the collar.

[0045] 1.3 Hertz contact stiffness and integrated contact stiffness model.

[0046] Based on the Lundberg-Palmgren line contact theory, the contact stiffness between a single rolling element and the raceway is derived from the relationship between the elastic approximation and the load: in: The effective contact length of the rolling element; Outer contact angle; Inner contact angle; For flange contact angle; , representing the load distribution factor, characterizes the load distribution relationship between the inner and outer rings, and .

[0047] In the thermo-mechanical coupling closed-loop model, the contact stiffness and the local stiffness of the collar are considered as a series spring system, resulting in the comprehensive contact stiffness. , represented as: in: For the first Local stiffness of the raceway at each rolling element; The contact stiffness between a single rolling element and the raceway is calculated based on the Lundberg-Palmgren line contact theory.

[0048] This series model ensures that the overall stiffness is dominated by the more flexible element, that is... This conforms to the basic laws of structural mechanics.

[0049] 1.4. Preload coupling model based on thermal expansion deformation.

[0050] Temperature field changes cause thermal expansion of the bearing rings, altering the radial clearance between the rolling elements and raceways, and consequently affecting the contact load distribution. A mapping relationship between the temperature field and preload is established to achieve bidirectional thermo-mechanical coupling. Specifically, the calculation method for thermally induced preload in the thermo-mechanical coupling closed-loop model is as follows.

[0051] (1) Calculate the radial thermal expansion of the inner and outer rings.

[0052] According to the theory of linear thermal expansion, the inner and outer rings undergo radial displacement under the influence of temperature rise. The radial thermal expansion of the inner ring and the radial thermal expansion of the outer ring are calculated as follows: in: and These are the radial thermal expansion of the inner ring and the radial thermal expansion of the outer ring, respectively. and These are the raceway radii of the inner and outer rings, respectively. , , and These are the raceway diameters of the inner and outer rings, respectively. and The first The inner and outer ring node temperatures corresponding to each rolling element; For ambient reference temperature; is the coefficient of linear thermal expansion of the ring material.

[0053] (2) Calculate the change in thermal preload.

[0054] The projection component of the thermal expansion difference between the inner and outer rings in the contact angle direction of the outer ring constitutes the radial clearance change, from which the thermal preload is calculated. in: For the first The thermal preload at each rolling element is positive, indicating a decrease in clearance, and negative, indicating an increase in clearance. This refers to the outer contact angle.

[0055] This model compresses temperature field information into boundary condition changes in contact analysis, realizing a unidirectional coupling entry point from the thermal field to the force field.

[0056] 1.5 Iterative solution of load balance based on gradient descent.

[0057] Under external load, the inner ring undergoes radial displacement. and axial displacement Different normal approximations are generated at each rolling element, requiring the establishment of load balance equations to solve for the unknown displacements. In the thermo-mechanical coupled closed-loop model of this embodiment, a gradient descent-based load balance iterative algorithm is used to solve for the contact load, as follows.

[0058] (1) Calculate the normal approach of each rolling element.

[0059] No. The total normal approximation of the rolling element and the inner and outer rings is composed of the geometric projection of the inner ring displacement and the thermal preload: Considering that the rolling element can only withstand normal compressive loads, a non-negative constraint is adopted: in: No. Thermal preload at each rolling element; For the first The total normal approximation of the rolling element and the inner and outer rings.

[0060] (2) Calculate the normal contact load of each rolling element.

[0061] Based on the Hertz line contact load-deformation relationship, the first The normal contact load of each rolling element is: in: For comprehensive contact stiffness.

[0062] (3) Establish the radial and axial force balance equations.

[0063] The external load is balanced by the components of the contact forces of all rolling elements: in: and These are the external radial load and the axial load, respectively.

[0064] (4) Construct the loss function and solve it iteratively. The force balance equations are transformed into an optimization problem, and a model is constructed with the unknown inner radial displacement. and axial displacement Force balance loss function for variables: in: The force balance loss function; For the first Normal contact load of each rolling element; For the first The angular position of each rolling element relative to the direction of the load; Outer contact angle; and These are external radial load and axial load, respectively; This represents the total number of rolling elements.

[0065] The unknown inner radial displacement is updated iteratively using the gradient descent method. and axial displacement The learning rate is Iterate until convergence, maximum number of iterations : After convergence, the radial displacement of the inner ring is obtained. and axial displacement Substituting the values, we can obtain the final contact load of each rolling element. .

[0066] 1.6 Calculation of contact state based on Hertz contact theory.

[0067] In the thermo-mechanical coupling closed-loop model of this embodiment, the contact thermal resistance is calculated based on Hertz contact theory, as follows.

[0068] (1) Calculate the half-width of the contact ellipse.

[0069] For line contact (rolling element-raceway contact), the Hertz contact half-width is: in: For the first The contact ellipse half-width of the rolling element; For the first Normal contact load of each rolling element; It is the equivalent elastic constant, and , Poisson's ratio of the material; For the overall curvature of the contact body, the following can be considered for roller-raceway contact: ; This is the effective contact length of the rolling element.

[0070] (2) Calculate the contact thermal resistance.

[0071] in: For the first The contact thermal resistance of each rolling element is a parameter that feeds back the mechanical calculation results to the thermal analysis module.

[0072] II. Physical Information Neural Networks

[0073] (1) Definition of network input features.

[0074] Define network input vector This includes time variables, trench temperature characteristics, and operating parameters. Specifically, the physical information neural network outputs the predicted temperature field value, expressed as: in: The input feature vector; It is a time variable used to characterize the temporal evolution of the temperature field; For the first Temperature measurements at each trench , This represents the total number of trenches; and These are external radial load and axial load, respectively; This refers to the bearing speed.

[0075] (2) Neural network architecture design.

[0076] Building a fully connected deep neural network The structure is as follows: Input layer: Each neuron corresponds to a dimension of the input feature; Hidden layer 1: 128 neurons, activation function ; Hidden layer 2: 128 neurons, activation function ; Output layer: Each neuron corresponds to a discrete node temperature value in the temperature field.

[0077] In this embodiment, the temperature field prediction value output by the physical information neural network is expressed as: in: These are predicted values ​​for the temperature field. Let j be the predicted temperature value for the j-th temperature field node. , This represents the number of nodes in the temperature field.

[0078] (3) Two-way coupled closed-loop calculation process.

[0079] Predicting temperature fields using neural networks Enter the calculation of thermally induced preload in Section 1.4. Then, the contact problem is solved in Section 1.5. Then, the contact thermal resistance is calculated in Section 1.6. Contact thermal resistance, as a boundary condition for heat conduction, further influences the temperature field distribution, forming a complete closed-loop coupling of "temperature → deformation → load → thermal resistance → temperature".

[0080] III. Construction of the total loss function.

[0081] The total loss function includes a data fitting term and a physical constraint term.

[0082] (1) Data loss: The mean square error between the predicted temperature field value and the actual sensor value, expressed as: in: This represents the number of training samples; This represents the number of nodes in the temperature field. For the first The first sample Predicted temperature values ​​for each node; For the first The first sample The actual temperature label of each node.

[0083] (2) Physical loss: The second-order penalty term of the force balance residual, expressed as: in: For the first Force balance loss of each sample.

[0084] (3) The total loss function is expressed as: in: For data loss; For physical loss; This is the physical loss weighting coefficient, used to balance the strength of data fitting and physical constraints.

[0085] In other embodiments of this example, the network architecture of the physical information neural network can employ a residual network to improve the gradient flow and training stability of deep networks. Alternatively, the network architecture of the physical information neural network can employ a neural network incorporating an attention mechanism to capture the weights of the non-uniform influence of different trench temperature characteristics on the temperature field distribution, thereby obtaining stronger feature representation and generalization capabilities under complex and variable working conditions.

[0086] This embodiment addresses the problems of low computational efficiency and poor generalization ability of traditional methods in the thermo-mechanical analysis of high-speed heavy-duty bearings, which are caused by the tight coupling of multiple physics fields, complex spatiotemporal correlation of contact states, and limited measured data on internal temperature and load. To solve these problems, a bearing temperature prediction method based on a physical information neural network is proposed. This method effectively integrates a mechanical iterative solution model based on thermoelastic deformation and Hertz contact theory with a deep learning-based temperature field prediction network. Using force balance residuals as physical constraints to guide network training, it significantly improves the accuracy, robustness, and physical consistency of the joint solution of bearing contact load distribution and temperature field, providing reliable technical support for online health monitoring and remaining life assessment of bearings in high-end equipment.

[0087] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A bearing temperature prediction method based on a physical information neural network, characterized in that: Includes the following steps: Step 1: Obtain the structural parameters, operating parameters, and measured data from the temperature sensor located in the bearing race groove. The operating parameters include time variables, rotational speed, axial load, and radial load. Step 2: Construct a physical information neural network. The physical information neural network takes the operating parameters and measured groove temperature data as input feature vectors and outputs discrete node prediction values ​​of the bearing temperature field. Step 3: Construct a thermo-mechanical coupling closed-loop model and a total loss function. The total loss function includes a data loss term and a physical loss term. The data loss term represents the deviation between the predicted temperature field value and the measured groove temperature value. The physical loss term is constructed based on the force balance equation and is used to constrain the temperature field prediction value output by the neural network to satisfy the internal mechanical balance law of the bearing. Step 4: Train the physical information neural network using the total loss function and update the network parameters; Step 5: Input the real-time collected operating parameters and groove temperature data into the trained physical information neural network, and output the current bearing temperature field distribution prediction result; During the training or prediction process of the physical information neural network, the predicted temperature field value is input into the thermo-mechanical coupling closed-loop model, and the calculation of thermal preload, contact load solution and contact thermal resistance are executed in sequence. The calculated contact thermal resistance is then fed back to the temperature field prediction as a heat conduction boundary condition, forming a two-way coupling closed loop.

2. The bearing temperature prediction method based on physical information neural network according to claim 1, characterized in that: The thermo-mechanical coupling closed-loop model includes a bearing rolling element angular position distribution model, which determines the position angular distribution of each rolling element relative to the direction of external radial load based on the parity of the total number of bearing rolling elements. If the total number of rolling elements is even, then the angular position distribution is as follows: If the total number of rolling elements is odd, then the angular position distribution is as follows: in: For the first The angular position of each rolling element relative to the direction of the load; The angle representing the direction of the external radial load is the angle between the load line and the zero-position reference line. For the set of scroll body indices; This represents the total number of rolling elements.

3. The bearing temperature prediction method based on physical information neural network according to claim 1, characterized in that: The thermo-mechanical coupling closed-loop model includes a ring local stiffness correction model based on the groove effect. The method for constructing the ring local stiffness correction model is as follows: The local equivalent thickness of the raceway after the effect of the groove is calculated using the Gaussian attenuation function: in: For the first The equivalent thickness of the ferrule at the corresponding position of each rolling element; The nominal thickness of the ring; For the first The depth parameter of each trench characterizes the amount of material removed; For the first The location of the center corner of the trench; This represents the total number of trenches; The moment of inertia of the ring section is calculated based on the local equivalent thickness of the ring: in: For the first The moment of inertia of the cross section at the corresponding position of each rolling element; This refers to the effective width of the ring; This is the cross-sectional shape correction factor; Calculate the local bending stiffness of the collar: in: For the first Local stiffness of the raceway at each rolling element; The elastic modulus of the ring material; The characteristic length of the trench.

4. The bearing temperature prediction method based on physical information neural network according to claim 1, characterized in that: In the aforementioned thermo-mechanical coupling closed-loop model, the contact stiffness and the local stiffness of the collar are considered as a series spring system, resulting in the comprehensive contact stiffness, expressed as: in: For the first Local stiffness of the raceway at each rolling element; The contact stiffness between a single rolling element and the raceway is calculated based on the Lundberg-Palmgren line contact theory.

5. The bearing temperature prediction method based on physical information neural network according to claim 1, characterized in that: In the thermo-mechanical coupling closed-loop model, the calculation method for the thermally induced preload is as follows: Based on the theory of linear thermal expansion, calculate the radial thermal expansion of the inner ring and the radial thermal expansion of the outer ring: in: and These are the radial thermal expansion of the inner ring and the radial thermal expansion of the outer ring, respectively. and These are the raceway radii for the inner and outer rings, respectively. and The first The inner and outer ring node temperatures corresponding to each rolling element; For ambient reference temperature; The coefficient of linear thermal expansion of the ring material; The calculated thermal preload amount is as follows: in: For the first The thermal preload at each rolling element is positive, indicating a decrease in clearance, and negative, indicating an increase in clearance. This refers to the outer contact angle.

6. The bearing temperature prediction method based on physical information neural network according to claim 1, characterized in that: In the aforementioned thermo-mechanical coupling closed-loop model, the contact load is solved using a gradient descent-based load balance iterative algorithm. The method is as follows: Constructed with unknown inner radial displacement and axial displacement Force balance loss function for variables: in: The force balance loss function; For the first Normal contact load of each rolling element; For the first The angular position of each rolling element relative to the direction of the load; Outer contact angle; and These are external radial load and axial load, respectively; This represents the total number of rolling elements; The inner radial displacement is updated iteratively using the gradient descent method. and axial displacement Until the force balance loss function converges: in: and The first Iteration step and the The inner radial displacement of the iteration step; and The first Iteration step and the The axial displacement of the inner circle in the iteration step; Based on the converged inner radial displacement and axial displacement Calculate the normal approximation of each rolling element: in: No. Thermal preload at each rolling element; Obtain the normal contact load: in: For comprehensive contact stiffness.

7. The bearing temperature prediction method based on physical information neural network according to claim 1, characterized in that: In the aforementioned thermo-mechanical coupling closed-loop model, the contact thermal resistance is calculated based on Hertz contact theory, using the following method: Calculate the half-width of the contact ellipse: The contact thermal resistance is obtained as follows: in: For the first Contact thermal resistance of each rolling element; For the first The contact ellipse half-width of the rolling element; For the first Normal contact load of each rolling element; It is the equivalent elastic constant; The overall curvature of the contact body; This is the effective contact length of the rolling element.

8. The bearing temperature prediction method based on a physical information neural network according to any one of claims 1-7, characterized in that: The physical information neural network adopts a fully connected deep neural network. In the fully connected deep neural network, the number of neurons in the input layer corresponds to the dimension of the input feature vector, the network hidden layer adopts the ReLU activation function, and the number of neurons in the network output layer corresponds to the number of discrete nodes in the temperature field. The input feature vector of the physical information neural network is represented as follows: in: The input feature vector; It is a time variable; For the first Temperature measurements at each trench , This represents the total number of trenches; and These are external radial load and axial load, respectively; The physical information neural network outputs a predicted temperature field value, expressed as follows: in: These are predicted values ​​for the temperature field. Let j be the predicted temperature value for the j-th temperature field node. , This represents the number of nodes in the temperature field.

9. The bearing temperature prediction method based on a physical information neural network according to any one of claims 1-7, characterized in that: The total loss function is expressed as: in: For data loss; For physical loss; This refers to the physical loss weighting coefficient; The data loss is the mean square error between the predicted temperature field value and the actual sensor value, expressed as: in: This represents the number of training samples; This represents the number of nodes in the temperature field. For the first The first sample Predicted temperature values ​​for each node; For the first The first sample The actual temperature label of each node; The physical loss is a quadratic penalty term for the force balance residual, expressed as: in: For the first Force balance loss of each sample.

10. The bearing temperature prediction method based on a physical information neural network according to any one of claims 1-7, characterized in that: The network architecture of the physical information neural network adopts a residual network or a neural network that incorporates an attention mechanism.

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