Analysis method and system of rolling bearing temperature field

Abstract

The invention discloses a rolling bearing temperature field analysis method and system, and relates to the field of bearing temperature measurement, and the method comprises the steps: employing a Latin hypercube sampling method to set sampling nodes which can uniformly cover the whole model space in each region of a rolling bearing simplified model; according to a convolutional neural network CNN, constructing a PINN heat transfer model used for analyzing the temperature field of the rolling bearing and a loss function of the PINN heat transfer model; integrating each heat transfer equation and the heat source item by using a steady-state three-dimensional heat transfer equation, and constructing a loss item of the control equation; collecting temperatures of sampling points in different areas as temperature boundary conditions, and constructing loss items of the boundary conditions; and obtaining a rolling bearing temperature field by using the trained PINN heat transfer model. The method can accurately analyze the temperature field of the rolling bearing.

Description

Technical Field

[0001] The present invention relates to the field of bearing temperature measurement, and in particular to a rolling bearing temperature field analysis method and system. Background Art

[0002] Rolling bearings, as key functional components of various rotating machinery, not only impact the efficiency of the machinery but also directly influence its precision, reliability, and lifespan. During operation, the internal temperature field of a rolling bearing significantly influences the thermal expansion of the bearing components and the state of the lubricant, further impacting the overall operating state of the rolling bearing. This is particularly true for rolling bearings used in high-speed, high-precision machinery. Therefore, accurate analysis of the internal temperature field of rolling bearings is crucial for optimizing their design and thermal compensation. Rolling bearing temperature field analysis primarily employs theoretical model-driven and data-driven approaches. Theoretical model-driven approaches to evaluating rolling bearing temperature fields present challenges in accurately defining model parameters, such as non-stationary heat sources and multi-media and multi-dimensional heat transfer parameters. Data-driven models, on the other hand, present challenges in accurately capturing the temperatures of numerous critical nodes, such as rotating bearing components and contact zones. These challenges significantly hinder the accuracy of rolling bearing temperature field analysis.

[0003] One existing approach is to use experimentally measured temperature data to inversely modify theoretical models. However, this modification relies heavily on empirical adjustments to model parameters such as the heat source distribution ratio, thermal conductivity, and convective heat transfer coefficient, resulting in inaccurate temperature field data. Therefore, accurately analyzing the rolling bearing temperature field is a critical issue that needs to be addressed. Summary of the Invention

[0004] The embodiments of the present invention provide a method and system for analyzing the temperature field of a rolling bearing, which can solve the problem in the prior art that the temperature field of a rolling bearing cannot be accurately analyzed.

[0005] An embodiment of the present invention provides a method for analyzing the temperature field of a rolling bearing, comprising the following steps: Construct a simplified rolling bearing model, divide the model into multiple regions based on the heat transfer method, and set sampling nodes in each region; Based on the heat transfer equation describing the heat transfer between multiple regions and the heat source term describing the heat generated by friction between the rolling elements and raceways in the rolling bearing, the steady-state three-dimensional heat transfer equation is used to construct the loss term of the control equation. The temperatures of sampling points in different regions are collected as temperature boundary conditions to construct the loss term of the boundary conditions. A loss function is constructed based on the loss term of the control equation and the loss term of the boundary conditions. According to the temperature data collected on the sampling nodes, the PINN heat transfer model is trained using the loss function to obtain the PINN rolling bearing heat transfer model for obtaining the rolling bearing temperature field.

[0006] Furthermore, the simplified rolling bearing model is divided into multiple areas, specifically including: heat source area, rolling element-raceway contact heat conduction area, outer ring-bearing seat heat conduction area, inner ring bearing heat conduction area, rolling element and ring convection heat transfer area.

[0007] Furthermore, the loss function is formulated as follows: ; in, and is the weight hyperparameter of each loss, and are the loss terms of the control equation and the boundary condition, respectively. is the loss function; ; ; in, N is the total number of model sampling nodes, i and j are the labels of the sampling nodes, It represents the difference between the predicted results of the heat transfer partial differential equations model and the theoretical solution results; is the difference between the model prediction result and the actual measurement result of the temperature boundary condition, is the difference between the model prediction result and the actual measurement result of the heat flux boundary condition, k is the thermal conductivity of the material at the sampling node, Represents the gradient along a direction.

[0008] Furthermore, the steady-state three-dimensional heat transfer equation is used to construct the loss term of the control equation, specifically including: ; in,( x,y,z ) are the Cartesian coordinates of the acquisition nodes respectively; T is the temperature value of the acquisition node; λ is thermal conductivity; Q origin is the heat source term.

[0009] Furthermore, the collecting of the temperatures of the sampling points in different regions as temperature boundary conditions specifically includes the following steps: collecting the temperatures of the sampling points in different regions as boundary conditions by using thermocouple sensors, quantum dot sensors and heat flow sensors.

[0010] Furthermore, setting sampling nodes in each region specifically includes: using a Latin hypercube sampling method to set sampling nodes in each region of the rolling bearing simplified model that can evenly cover the entire model space.

[0011] An embodiment of the present invention provides a rolling bearing temperature field analysis system, comprising: The region division module is used to construct a simplified model of the rolling bearing, divide the simplified model of the rolling bearing into multiple regions according to the heat transfer method, and set sampling nodes in each region; The loss function construction module is used to construct the loss term of the control equation using the steady-state three-dimensional heat transfer equation based on the heat transfer equation describing the heat transfer mode between multiple regions and the heat source term describing the heat generated by friction between the rolling elements and raceways in the rolling bearing. The module collects the temperatures of sampling points in different regions as temperature boundary conditions and constructs the loss term of the boundary conditions. The module also constructs the loss function based on the loss term of the control equation and the loss term of the boundary conditions. The temperature field analysis module is used to train the PINN heat transfer model using a loss function based on the temperature data collected on the sampling nodes, and obtain the PINN rolling bearing heat transfer model for obtaining the rolling bearing temperature field.

[0012] The embodiments of the present invention provide a method and system for analyzing the temperature field of a rolling bearing. Compared with the prior art, the method and system have the following beneficial effects: Sampling nodes are set within each region of the simplified rolling bearing model. Based on the heat transfer equation describing the heat transfer between multiple regions and the heat source term describing the frictional heat generated between the rolling elements and raceways within the rolling bearing, the steady-state three-dimensional heat transfer equation is used to construct the loss term of the governing equation. The temperatures of the sampling points in different regions are collected as temperature boundary conditions, and the loss term of the boundary condition is constructed. A loss function is constructed based on the loss terms of the governing equation and the boundary condition. Based on the temperature data collected at the sampling nodes, the PINN heat transfer model is trained using the loss function to obtain the PINN rolling bearing heat transfer model used to obtain the rolling bearing temperature field. The loss function includes the loss term of the governing equation and the loss term of the boundary condition. The loss term of the governing equation integrates the heat transfer equation and the heat source term using the steady-state three-dimensional heat transfer equation, while the loss term of the boundary condition collects the temperatures of the sampling points in different regions as temperature boundary conditions. This allows the loss function to adapt to the number and location of the set sampling nodes, accurately analyzing the rolling bearing temperature field based on the desired sampling nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 A flowchart of a method for analyzing the temperature field of a rolling bearing provided by an embodiment of the present invention; Figure 2 A simplified rolling bearing model and a regional division diagram for a rolling bearing temperature field analysis method provided by an embodiment of the present invention; Figure 3 The temperature field results of a 7008AC angular contact ball bearing under different working conditions for a rolling bearing temperature field analysis method provided by an embodiment of the present invention, where (a) is an initial ambient temperature of 21°C with no forced heat dissipation, (b) is an initial ambient temperature of 21°C with forced heat dissipation in the circumferential direction of the bearing and air, and (c) is an initial ambient temperature of 21°C with forced heat dissipation in the axial direction of the bearing on the left side and air. DETAILED DESCRIPTION

[0014] To make the above-mentioned objects, features, and advantages of the present invention more readily apparent, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. The following description sets forth numerous specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art may make similar modifications without departing from the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0015] See also Figure 1 , an embodiment of the present invention provides a method for analyzing the temperature field of a rolling bearing, comprising the following steps: Step 1: Construct a simplified model of the rolling bearing and divide the simplified model into multiple areas based on the heat transfer method.

[0016] Step 2: Use the Latin hypercube sampling method to set sampling nodes that can evenly cover the entire model space in each area of the rolling bearing simplified model.

[0017] Step 3: Based on the heat transfer equation that describes the heat transfer mode between multiple regions and the heat source term that describes the heat generated by friction between the rolling elements and raceways in the rolling bearing, the steady-state three-dimensional heat transfer equation is used to construct the loss term of the control equation; the temperatures of the sampling points in different regions are collected as temperature boundary conditions to construct the loss term of the boundary conditions; and the loss function is constructed based on the loss term of the control equation and the loss term of the boundary conditions.

[0018] Step 4: Based on the temperature data collected at the sampling nodes, the PINN heat transfer model is trained using the loss function to obtain the PINN rolling bearing heat transfer model for obtaining the rolling bearing temperature field.

[0019] The specific implementation steps are as follows: S1: Ignoring minor geometric features such as shaping, chamfering, and clearance that have little effect on heat transfer, the model is constructed based on the geometric parameters designed according to the rolling bearing assembly theory, and the model is divided into regions according to the heat transfer method. When dividing, the contact area between the rolling element and the inner and outer rings is defined as the composite medium (metal material-lubricant-metal material) heat conduction area, and the contact between the inner ring of the bearing and the shaft, and the contact between the outer ring of the bearing and the bearing seat are defined as metal material heat conduction. Usually, the area where the rolling element, the inner ring of the bearing, and the outer ring of the bearing contact the air within the bearing cavity space is defined as air forced convection heat transfer, and the contact between the inner ring of the bearing and the outer ring of the bearing and the air outside the bearing cavity space is defined as air free convection heat transfer. When the bearing is equipped with auxiliary heat dissipation equipment such as a blower, the contact between the inner ring of the bearing and the outer ring of the bearing and the air outside the bearing cavity space can also be defined as air forced convection heat transfer.

[0020] Finally, the model area can be divided into: heat source area, rolling element-raceway contact heat conduction area, outer ring-bearing seat heat conduction area, inner ring bearing heat conduction area, rolling element and ring convection heat transfer area, such as Figure 2 shown.

[0021] S2: The Latin hypercube sampling method sets sampling nodes in each area of the above model to ensure that the sampling nodes evenly cover the entire model space, providing coordinate information for defining boundary conditions and describing the bearing temperature field in subsequent models.

[0022] S3: Based on Convolutional Neural Networks (CNN), a PINN heat transfer model is constructed to analyze the temperature field of rolling bearings. The loss function of the constructed PINN heat transfer model is shown in Equation (1).

[0023] The loss term of the neural network can be expressed as: (1).

[0024] in, and is the weight hyperparameter of each loss, 、 are the loss of the control equation and the loss of the boundary conditions, as shown in Equations (2) and (3), respectively.

[0025] (2).

[0026] (3).

[0027] S4: According to Figure 2The area division inside the rolling bearing is shown in the figure, and the heat transfer mode between components is described using equations (4) to (7). The contact between the inner ring of the bearing and the shaft and the contact between the outer ring of the bearing and the bearing seat are defined as metal material heat conduction, the contact between the rolling element and the inner and outer raceways is defined as multi-media composite heat conduction (including metal material heat conduction and lubricating oil convection heat transfer), and the contact between the rolling element, inner raceway, outer raceway and air is defined as natural convection heat transfer or forced convection heat transfer according to the actual working conditions.

[0028] (4).

[0029] (5).

[0030] (6).

[0031] (7).

[0032] in, The heat flow rate of heat conduction of metal materials; is the lubricating oil convective heat transfer coefficient; is the free convection heat transfer coefficient of air; is the air forced convection heat transfer coefficient; λ is the thermal conductivity of rolling elements and bearing rings; A The heat conduction area between the rolling element and the bearing; δ is the thermal conductivity thickness of the bearing ring; t 2- t 1 is the temperature difference between the rolling element or bearing ring and the contact surface of different components; k l is the thermal conductivity of the lubricating oil; x is the pitch diameter; P lr is the Prandtl number of the lubricating oil; v 1 / 3 of the cage speed; ν 0 is the kinematic viscosity of the lubricating oil; R e is the Reynolds number; T - T a The temperature difference between the rolling element or bearing ring and the surrounding air; k α is the thermal conductivity of air; D h Bearing housing outer ring diameter.

[0033] S5: Based on the pseudo-static model of the rolling bearing shown in formula (8) and the Hertz contact theory shown in formula (9), the contact load and contact area between the rolling element and the inner and outer raceways are calculated, and then the frictional heat generated corresponding to the contact load is calculated using formula (10). Finally, based on the above contact area and frictional heat generated, the definition Figure 2 The heat source area and heat source heat flow are shown.

[0034] (8).

[0035] (9).

[0036] (10).

[0037] in, F x , F y , F z is the external load of the rolling bearing; a , b is the half-width of the rolling element-raceway elliptical contact area; Q origin The heat generated by the rolling element-raceway friction; Q jo is the contact load between the jth roller and the outer raceway; α o is the contact angle between the roller and the outer raceway; φ j For the j Position angle of each roller; n a and n b are the major and minor semi-axes of the contact ellipse with dimension 1, respectively; η is the comprehensive elastic modulus of contact between rolling element and raceway; is the comprehensive curvature radius of contact between the rolling element and the raceway; V c is the relative sliding speed between the rolling element and the raceway; μ lu is the equivalent friction coefficient between the rolling element and the raceway; n r is the total number of rollers.

[0038] The above heat source calculation method is a localized heat source calculation method based on the rolling element-raceway contact state. Alternatively, empirical formulas or industry standards can be used to calculate the heat generated by the entire bearing and then distribute it to each rolling element-raceway contact pair according to a specific ratio.

[0039] S6: Combined with the generated sampling node coordinates, the steady-state three-dimensional heat transfer equation shown in Equation (11) is used to integrate the above heat transfer equations and the heat source term to construct the loss term of the control equation of Equation (2).

[0040] (11).

[0041] in, x, y, z Find the Cartesian coordinates of a point in the domain for a heat transfer model; T To find the temperature value of a point in the solution domain; λ is thermal conductivity; Q origin is the heat source term.

[0042] Using the heat transfer coefficients of different heat transfer modes shown in formulas (4) to (7), combined with different models x,y,z The contact interface form and heat transfer mode at the coordinates define the thermal conductivity in formula (11) λ ; Using the heat generated by equation (10), define the heat source term in (11).

[0043] S7: Use sensors such as thermocouple sensors, quantum dot sensors, heat flow sensors, and wired and wireless transmission methods to collect as much data as possible. Figure 2 The temperature boundary conditions of the sampling points in different regions are shown to construct the loss term of the boundary conditions of Equation (3).

[0044] S8: Use ADAM solver, the hidden layer uses Tanh activation function for model training, and the learning rate is set to 1e -3 ,The total number of samples is 90,000. After 10,000 epochs, the PINN-based rolling bearing heat transfer model is finally obtained. Figure 3 The temperature field results of 7008AC angular contact ball bearing under different working conditions were obtained by analyzing the constructed model.

[0045] This paper, based on Physics-Informed Neural Networks (PINN), provides a new paradigm for rolling bearing temperature field analysis. It effectively integrates thermodynamic prior knowledge with various boundary conditions to construct a theory-data fusion-driven rolling bearing temperature field analysis model. This model leverages multidimensional numerical heat transfer theory and experimental data to improve the accuracy of rolling bearing temperature field analysis. The proposed temperature field analysis model adapts to varying amounts and locations of temperature experimental data across a wide range of operating conditions, achieving higher analysis accuracy.

[0046] The present invention also offers the advantage of enabling precise analysis of the internal temperature field of rolling bearings using a small amount of experimental test data. Compared to finite element-based rolling bearing temperature field analysis methods, the accuracy of the analysis results from this method is less dependent on the accuracy of the definitions of numerous and complex heat transfer parameters in the theoretical heat transfer model. Furthermore, compared to finite element-based rolling bearing temperature field analysis methods, the method proposed in this invention offers faster analysis speeds.

[0047] An embodiment of the present invention provides a rolling bearing temperature field analysis system, comprising: The region division module is used to construct a simplified model of a rolling bearing, divide the simplified model of the rolling bearing into multiple regions according to the heat transfer method, and set sampling nodes in each region.

[0048] The loss function construction module is used to construct the loss term of the control equation using the steady-state three-dimensional heat transfer equation based on the heat transfer equation describing the heat transfer mode between multiple regions and the heat source term describing the heat generated by friction between the rolling elements and raceways in the rolling bearing; collect the temperatures of the sampling points in different regions as temperature boundary conditions to construct the loss term of the boundary conditions; and construct a loss function based on the loss term of the control equation and the loss term of the boundary conditions.

[0049] The temperature field analysis module is used to train the PINN heat transfer model using a loss function based on the temperature data collected on the sampling nodes, and obtain the PINN rolling bearing heat transfer model for obtaining the rolling bearing temperature field.

[0050] A specific embodiment is as follows: This embodiment discloses a method for analyzing the temperature field of a rolling bearing, and the specific steps are as follows: S1. Construct a model based on the theoretical design of geometric parameters of rolling bearing components, and divide the model into regions according to the heat transfer method, specifically involving the heat source area, rolling element-raceway contact heat conduction area, outer ring-bearing seat heat conduction area, inner ring bearing heat conduction area, and rolling element and ring convection heat transfer area.

[0051] S2. Use the Latin hypercube sampling method to set sampling nodes in each area of the above model to ensure that the sampling nodes evenly cover the entire model space and provide coordinate information for defining boundary conditions and describing the bearing temperature field in subsequent models.

[0052] S3. Based on the convolutional neural network (CNN), a PINN heat transfer model is constructed to analyze the temperature field of rolling bearings.

[0053] S4. Based on the zone division results, use the heat transfer equation to describe the heat transfer mode between components.

[0054] S5. Calculate the contact load and contact area between the rolling element and the inner and outer raceways based on the pseudo-static model of the rolling bearing and Hertz contact theory. Calculate the frictional heat generated corresponding to the contact load. The contact area and frictional heat generation define the heat source area and heat flux within the region demarcated.

[0055] S6. Based on the coordinates of the sampling nodes, use the steady-state three-dimensional heat transfer equation to integrate the above heat transfer equations and the heat source term to construct the loss term of the control equation. Utilize sensors such as thermocouples, quantum dot sensors, and heat flux sensors, as well as wired and wireless transmission methods, to collect temperature boundary conditions at as many sampling points in different regions as possible and construct the loss term for the boundary conditions.

[0056] S7, using the ADAM (Adaptive Moment Estimation) solver, the hidden layer uses the Tanh activation function for model training, and the learning rate is set to 1e -3 , the total number of samples is 90,000. After 10,000 epochs, the rolling bearing heat transfer model based on PINN is finally obtained.

[0057] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A method for analyzing the temperature field of a rolling bearing, characterized in that: The following steps are involved: Construct a simplified rolling bearing model, divide the model into multiple regions based on the heat transfer method, and set sampling nodes in each region; Based on the heat transfer equation describing the heat transfer between multiple regions and the heat source term describing the heat generated by friction between the rolling elements and raceways in the rolling bearing, the steady-state three-dimensional heat transfer equation is used to construct the loss term of the control equation. The temperatures of sampling points in different regions are collected as temperature boundary conditions to construct the loss term of the boundary conditions. A loss function is constructed based on the loss term of the control equation and the loss term of the boundary conditions. According to the temperature data collected on the sampling nodes, the PINN heat transfer model is trained using the loss function to obtain the PINN rolling bearing heat transfer model for obtaining the rolling bearing temperature field.

2. The method for analyzing the temperature field of a rolling bearing according to claim 1, wherein: The simplified rolling bearing model is divided into multiple areas, specifically including: Heat source area, rolling element-raceway contact heat conduction area, outer ring-bearing seat heat conduction area, inner ring bearing heat conduction area, rolling element and ring convection heat transfer area.

3. The method for analyzing the temperature field of a rolling bearing according to claim 1, wherein: The loss function is formulated as follows: ； in, and is the weight hyperparameter of each loss, and are the loss terms of the control equation and the boundary condition, respectively. is the loss function; ； ； in, N is the total number of model sampling nodes, i and j are the labels of the sampling nodes, It represents the difference between the predicted results of the heat transfer partial differential equations model and the theoretical solution results; is the difference between the model prediction result and the actual measurement result of the temperature boundary condition, is the difference between the model prediction result and the actual measurement result of the heat flux boundary condition, k is the thermal conductivity of the material at the sampling node, Represents the gradient along a direction.

4. The method for analyzing the temperature field of a rolling bearing according to claim 1, wherein: The loss term of the control equation constructed by using the steady-state three-dimensional heat transfer equation specifically includes: ； in,( x,y,z ) are the Cartesian coordinates of the acquisition nodes respectively; T is the temperature value of the acquisition node; λ is thermal conductivity; Q origin is the heat source term.

5. The method for analyzing the temperature field of a rolling bearing according to claim 1, wherein: The collecting of the temperatures of the sampling points in different areas as temperature boundary conditions specifically includes: The temperatures of sampling points in different areas are collected as boundary conditions through thermocouple sensors, quantum dot sensors and heat flow sensors.

6. The method for analyzing the temperature field of a rolling bearing according to claim 1, wherein: The setting of sampling nodes in each area specifically includes: The Latin hypercube sampling method is used to set sampling nodes that can evenly cover the entire model space in each region of the rolling bearing simplified model.

7. A rolling bearing temperature field analysis system, characterized in that: include: The region division module is used to construct a simplified model of the rolling bearing, divide the simplified model of the rolling bearing into multiple regions according to the heat transfer method, and set sampling nodes in each region; The loss function construction module is used to construct the loss term of the control equation using the steady-state three-dimensional heat transfer equation based on the heat transfer equation describing the heat transfer mode between multiple regions and the heat source term describing the heat generated by friction between the rolling elements and raceways in the rolling bearing. The module collects the temperatures of sampling points in different regions as temperature boundary conditions and constructs the loss term of the boundary conditions. The module also constructs the loss function based on the loss term of the control equation and the loss term of the boundary conditions. The temperature field analysis module is used to train the PINN heat transfer model using a loss function based on the temperature data collected on the sampling nodes, and obtain the PINN rolling bearing heat transfer model for obtaining the rolling bearing temperature field.

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