Method and system for analyzing temperature field of rolling bearing

Abstract

The application discloses a kind of analysis methods and systems of rolling bearing temperature field, it is related to bearing temperature measurement field, comprising: using Latin supercube sampling method in each region of rolling bearing simplified model Set up sampling node that can evenly cover entire model space;According to convolutional neural network CNN, PINN heat transfer model for analyzing rolling bearing temperature field is constructed, and loss function of PINN heat transfer model;Using steady-state three-dimensional heat transfer equation integrates each heat transfer equation and heat source term, constructs the loss term of control equation;Collect the temperature of sampling point in different regions as temperature boundary condition, construct the loss term of boundary condition;Using the PINN heat transfer model of trained rolling bearing temperature field is obtained.

Description

TECHNICAL FIELD

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

[0002] As the main functional components of various rotating machinery, rolling bearings not only affect the operation efficiency of the machinery, but also directly relate to the operation precision, reliability and service life of the machinery. During the operation of rolling bearings, the internal temperature field of the rolling bearings has a significant impact on the thermal expansion of the bearing components and the state of the lubricant, thereby affecting the overall operation state of the rolling bearings, especially for rolling bearings in high-speed and high-precision machinery. Therefore, accurate analysis of the internal temperature field of the rolling bearings is an important basis for the optimization design and thermal compensation of the rolling bearings. The temperature field analysis of rolling bearings mainly adopts two ideas of theoretical model driving and data model driving. When evaluating the temperature field of rolling bearings by using a theoretical driving model, the model parameters such as non-stable heat source, multi-medium and multi-dimensional heat transfer parameters cannot be accurately defined. When analyzing the temperature field of rolling bearings by using a data-driven model, the temperature of a large number of important nodes such as the contact area of the rotating bearing components cannot be obtained. The above problems greatly hinder the accuracy of the temperature field analysis of rolling bearings.

[0003] In the prior art, one solution is to try to use experimentally determined temperature data to correct the theoretical model in reverse. However, when correcting the theoretical model, the model parameters such as the distribution ratio of the heat source, the thermal conductivity coefficient and the convective heat transfer coefficient are mainly adjusted by experience and manually, so that the temperature field data obtained by the model is not accurate. Therefore, how to accurately analyze the temperature field of rolling bearings is an important problem to be solved. SUMMARY

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

[0005] The embodiments of the present application provide a rolling bearing temperature field analysis method, which comprises the following steps:

[0006] A simplified model of the rolling bearing is constructed, and the simplified model of the rolling bearing is divided into multiple regions according to the heat transfer mode, and sampling nodes are set in each region;

[0007] According to the heat transfer equation describing the heat transfer mode between the multiple regions and the heat source term describing the friction heat generated between the rolling body and the raceway in the rolling bearing, a loss term of the control equation is constructed by using a steady-state three-dimensional heat transfer equation; the temperature of the sampling points in different regions is collected as the temperature boundary condition to construct a loss term of the boundary condition; and a loss function is constructed according to the loss term of the control equation and the loss term of the boundary condition;

[0008] According to the temperature data collected on the sampling nodes, the PINN heat transfer model is trained by using a loss function, and a PINN rolling bearing heat transfer model for obtaining a rolling bearing temperature field is obtained.

[0009] Further, the rolling bearing simplified model is divided into a plurality of regions, specifically including a heat source region, a rolling body-raceway contact heat conduction region, an outer ring-bearing seat heat conduction region, an inner ring bearing heat conduction region, and a rolling body and ring convective heat exchange region.

[0010] Further, the loss function is formulaed as:

[0011] ;

[0012] wherein, and are weight hyperparameters of each loss, and are a loss term of a control equation and a loss term of a boundary condition, respectively, is a loss function;

[0013] ;

[0014] ;

[0015] wherein, N is a total number of model sampling nodes, i and j are labels of the sampling nodes, represents a difference between a heat transfer partial differential equation model prediction result and a theoretical solution result; is a difference between a model prediction result of a temperature boundary condition and an actual measurement result, is a difference between a model prediction result of a heat flux density boundary condition and an actual measurement result, k is a thermal conductivity of a material at a sampling node, represents a gradient in one direction.

[0016] Further, the loss term of the control equation is constructed by using a steady-state three-dimensional heat transfer equation, specifically including:

[0017] ;

[0018] wherein, x, y, z are Cartesian coordinates of the collection nodes, respectively; T is a temperature value of the collection node; λ is a thermal conductivity; Q origin is a heat source term.

[0019] Further, the temperature of the sampling points in different regions is collected as the temperature boundary condition, and the specific steps include: collecting the temperature of the sampling points in different regions by the thermocouple sensor, the quantum dot sensor and the heat flow sensor as the boundary condition.

[0020] Further, the sampling nodes are set in each region, and the specific steps include: using the Latin hypercube sampling method to set the sampling nodes in each region of the simplified model of the rolling bearing, which can uniformly cover the entire model space.

[0021] The embodiment of the present application provides a rolling bearing temperature field analysis system, which comprises:

[0022] The region division module is used for constructing a simplified model of a rolling bearing, dividing the simplified model of the rolling bearing into multiple regions according to the heat transfer mode, and setting sampling nodes in each region.

[0023] The loss function construction module is used for constructing a loss term of a control equation by using a steady-state three-dimensional heat transfer equation according to a heat transfer equation describing the heat transfer mode between multiple regions and a heat source term describing the heat generated by friction between rolling bodies and raceways in the rolling bearing; collecting the temperature of the sampling points in different regions as a temperature boundary condition to construct a loss term of the boundary condition; and constructing a loss function according to the loss term of the control equation and the loss term of the boundary condition.

[0024] The temperature field analysis module is used for training a PINN heat transfer model by using the loss function according to the temperature data collected on the sampling nodes, so as to obtain a PINN rolling bearing heat transfer model used for obtaining the temperature field of the rolling bearing.

[0025] The embodiment of the present application provides a rolling bearing temperature field analysis method and system, and the beneficial effects thereof compared with the prior art are as follows:

[0026] The sampling nodes are set in each region of the simplified model of the rolling bearing; a loss term of a control equation is constructed by using a steady-state three-dimensional heat transfer equation according to a heat transfer equation describing the heat transfer mode between multiple regions and a heat source term describing the heat generated by friction between rolling bodies and raceways in the rolling bearing; the temperature of the sampling points in different regions is collected as a temperature boundary condition to construct a loss term of the boundary condition; a loss function is constructed according to the loss term of the control equation and the loss term of the boundary condition; and a PINN rolling bearing heat transfer model used for obtaining the temperature field of the rolling bearing is obtained by training a PINN heat transfer model according to the temperature data collected on the sampling nodes. The loss function comprises the loss term of the control equation and the loss term of the boundary condition, the loss term of the control equation is integrated with the heat transfer equation and the heat source term by using the steady-state three-dimensional heat transfer equation, the loss term of the boundary condition collects the temperature of the sampling points in different regions as the temperature boundary condition, so that the loss function can be self-adapted to the number and position of the set sampling nodes, thereby accurately analyzing the temperature field of the rolling bearing according to the required sampling nodes. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 A scheme flow chart of a rolling bearing temperature field analysis method provided by an embodiment of the present application is shown in the figure;

[0028] Figure 2 A rolling bearing simplified model and a region division diagram of a rolling bearing temperature field analysis method provided by an embodiment of the present application are shown in the figure;

[0029] Figure 3 Temperature field results of a 7008AC angular contact ball bearing under different working conditions of a rolling bearing temperature field analysis method provided by an embodiment of the present application, wherein (a) is an initial ambient temperature of 21℃ without forced heat dissipation, (b) is an initial ambient temperature of 21℃ with bearing circumferential and air forced heat dissipation, and (c) is an initial ambient temperature of 21℃ with bearing left side axial and air forced heat dissipation. DETAILED DESCRIPTION

[0030] In order to make the above objectives, characteristics and advantages of the present application more apparent and comprehensible, the specific embodiments of the present application are described in detail below with reference to the accompanying drawings. In the following description, a large number of specific details are set forth in order to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present application, so the present application is not limited by the specific embodiments disclosed below.

[0031] Reference Figure 1 The embodiment of the present application provides a rolling bearing temperature field analysis method, which comprises the following steps:

[0032] Step 1: Construct a rolling bearing simplified model, and divide the rolling bearing simplified model into multiple regions according to the heat transfer mode.

[0033] Step 2: Use the Latin hypercube sampling method to set sampling nodes in each region of the rolling bearing simplified model, which can uniformly cover the entire model space.

[0034] Step 3: According to the heat transfer equation describing the heat transfer mode between multiple regions and the heat source term describing the heat generated by the friction between the rolling body and the raceway in the rolling bearing, a loss term of the control equation is constructed by using the steady-state three-dimensional heat transfer equation; the temperature of the sampling point in different regions is collected as the temperature boundary condition to construct the loss term of the boundary condition; and the loss function is constructed according to the loss term of the control equation and the loss term of the boundary condition.

[0035] Step 4: According to the temperature data collected on the sampling nodes, the PINN heat transfer model is trained by using the loss function to obtain the PINN rolling bearing heat transfer model for obtaining the rolling bearing temperature field.

[0036] The specific implementation steps are as follows:

[0037] S1: Ignore the small geometric features such as modification, chamfer, clearance, etc. which have little effect on heat transfer, design the geometric parameters according to the rolling bearing assembly theory, and divide the model into regions according to the heat transfer mode. When dividing, define the contact area between the rolling body and the inner and outer rings as the composite medium (metal material-lubricating oil-metal material) heat conduction area, define the contact between the bearing inner ring and the shaft and the contact between the bearing outer ring and the bearing seat as the metal material heat conduction. Usually, the area where the rolling body, the bearing inner ring, the bearing outer ring and the air in the bearing cavity space are in contact is defined as air forced convection heat transfer, and the contact between the bearing inner ring, the bearing outer ring 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 bearing inner ring, the bearing outer ring and the air outside the bearing cavity space can also be defined as air forced convection heat transfer.

[0038] Finally, the model region can be divided into: heat source region, rolling body-raceway contact heat conduction region, outer sleeve ring-bearing seat heat conduction region, inner sleeve ring bearing heat conduction region, rolling body and sleeve ring convection heat transfer region, as shown in Figure 2 .

[0039] S2: The Latin supercube sampling method sets sampling nodes in each region of the above model, ensures that the sampling nodes uniformly cover the entire model space, and provides coordinate information for subsequent model boundary condition definition and bearing temperature field description.

[0040] S3: A PINN heat transfer model for analyzing the temperature field of rolling bearings is constructed based on Convolutional Neural Networks (CNN). The loss function of the constructed PINN heat transfer model is shown in equation (1).

[0041] The loss term of the neural network can be expressed as:

[0042] (1).

[0043] Wherein, and are the weight hyperparameters of each loss, , are the loss of the control equation and the loss of the boundary condition respectively, as shown in equations (2) and (3).

[0044] (2).

[0045] (3).

[0046] S4: According to Figure 2The region division of the rolling bearing interior shown is described by equations (4)~(7) to describe the heat transfer mode between components, wherein the bearing inner ring-shaft contact definition and the bearing outer ring-bearing seat contact definition are metal material heat conduction, the rolling element-inner and outer raceway contact definition is multi-medium composite heat conduction (including metal material heat conduction and lubricating oil convective heat transfer), and the rolling element, inner raceway, outer raceway and air contact are defined as natural convection heat transfer or forced convection heat transfer according to the actual working conditions.

[0047] (4).

[0048] (5).

[0049] (6).

[0050] (7).

[0051] wherein, is the heat flow of metal material heat conduction; is the lubricating oil convective heat transfer coefficient; is the air free convection heat transfer coefficient; is the air forced convection heat transfer coefficient; λ is the rolling element and bearing ring heat conduction coefficient; A is the rolling element and bearing contact heat conduction area; δ is the bearing ring heat conduction thickness; t 2- t 1 is the temperature difference of the rolling element or the bearing ring and the contact surface of different components; k l is the thermal conductivity of lubricating oil; x is the pitch diameter; P lr is the Prandtl number of lubricating oil; v is the 1 / 3 cage rotation speed; ν 0 is the kinematic viscosity of lubricating oil; R e is the Reynolds number; T - T a is the temperature difference of the rolling element or the bearing ring and the surrounding air; k α is the thermal conductivity of air; D h is the bearing seat outer ring diameter.

[0052] S5: The contact load and contact area of the rolling element on the inner and outer raceways are calculated according to the quasi-static model of the rolling bearing shown in equation (8) and the Hertz contact theory shown in equation (9), and then the friction heat generated by the contact load is calculated by equation (10). Finally, the contact area and friction heat generation are definedFigure 2 The area of ​​the heat source and the heat flow rate of the heat source are shown.

[0053] (8).

[0054] (9).

[0055] (10).

[0056] in, F x , F y , F z External load for rolling bearings; a , b The width of the elliptical contact area between the rolling element and the raceway; Q origin Heat is generated by friction between the rolling elements and the raceway; Q jo Let be the contact load between the j-th roller and the outer raceway; α o The contact angle between the roller and the outer raceway; φ j For the first j The position angle of each roller; n a and n b These are the major and minor semi-axes of the contact ellipse, which are dimensionless (1). η The combined elastic modulus of the contact between the rolling element and the raceway; The combined radius of curvature of the contact between the rolling element and the raceway; V c The relative sliding speed between the rolling element and the raceway; μ lu This is the equivalent coefficient of friction between the rolling element and the raceway; n r This represents the total number of rollers.

[0057] The above heat source calculation method is a localized heat source calculation method based on the rolling element-raceway contact state. In addition to this method, the heat generated by the entire bearing can also be calculated using empirical formulas or industry standards, and then distributed to each pair of rolling element-raceway contact pairs in a specific proportion.

[0058] S6: Combining the generated sampling node coordinates, the above heat transfer equations and heat source terms are integrated using the steady-state three-dimensional heat transfer equation shown in equation (11) to construct the loss term of the control equation (2).

[0059] (11).

[0060] in,x, y, z is the Cartesian coordinate of a certain point in the solution domain of the heat transfer model; T is the temperature value of a certain point in the solution domain; λ is the thermal conductivity; Q origin is the heat source term.

[0061] The heat transfer coefficients of different heat transfer modes shown in formulas (4) to (7) are used, combined with the contact interface form and heat transfer mode of different points in the model x, y, z ; the thermal conductivity in formula (11) is defined λ ; and the heat source term in formula (11) is defined using the heat generation shown in formula (10).

[0062] S7: As many as possible temperature boundary conditions of sampling points in different regions shown in formula (3) are collected by using thermocouple sensors, quantum dot sensors, heat flow sensors and the like, and wired and wireless transmission modes, and a loss term of the boundary condition of formula (3) is constructed. Figure 2

[0063] S8: An ADAM solver is used for model training, a Tanh activation function is used for the hidden layer, the learning rate is set to 1e -3 , the total number of samples is 90000, and after 10000 epochs, a rolling bearing heat transfer model based on PINN is finally obtained. Figure 3 is the temperature field result of 7008AC angular contact ball bearing under different working conditions obtained by using the constructed model.

[0064] The present application provides a new paradigm for a rolling bearing temperature field analysis method based on a physics-informed neural network (PINN), which can effectively integrate thermodynamic prior knowledge and various boundary conditions, construct a rolling bearing temperature field analysis model driven by theory and data fusion, fully utilize multi-dimensional numerical heat transfer theory and experimental data, and improve the accuracy of rolling bearing temperature field analysis. The temperature field analysis model proposed in the present application can adapt to different amounts and positions of temperature experimental data in a wide range of working conditions, thereby achieving higher analysis accuracy.

[0065] The present application has the advantages that a small amount of experimental test data can be used to realize accurate analysis of the internal temperature field of the rolling bearing. Compared with the rolling bearing temperature field analysis method based on finite elements, the accuracy of the analysis result of the present application depends less on the definition accuracy of a large number of complex heat transfer parameters in the theoretical heat transfer model. In addition, compared with the rolling bearing temperature field analysis method based on finite elements, the method proposed in the present application has a faster analysis speed.

[0066] ​The embodiment of the application provides a kind of analysis system of rolling bearing temperature field, comprising:

[0067] Regional division module is used to construct the simplified model of rolling bearing, and the simplified model of rolling bearing is divided into multiple regions according to heat transfer mode, and sampling node is set in each region.

[0068] Loss function construction module is used to construct loss term of control equation by using steady-state three-dimensional heat transfer equation according to heat transfer equation describing heat transfer mode between multiple regions and heat source term describing heat generation of friction between rolling body and raceway in rolling bearing;Temperature of sampling point in different regions is collected as temperature boundary condition, and loss term of boundary condition is constructed;Loss function is constructed according to loss term of control equation and loss term of boundary condition.

[0069] Temperature field analysis module is used to train PINN heat transfer model by using loss function according to temperature data collected on sampling node, and PINN rolling bearing heat transfer model for obtaining rolling bearing temperature field is obtained.

[0070] One specific implementation is as follows:

[0071] The embodiment discloses a kind of analysis methods of rolling bearing temperature field, and specific steps are as follows:

[0072] S1, according to the model of rolling bearing assembly theoretical design geometric parameter is constructed, and the model is divided into regions according to heat transfer mode, specifically related to heat source region, rolling body-raceway contact heat conduction region, outer ring-bear seat heat conduction region, inner ring bearing heat conduction region, rolling body and sleeve circle convection heat exchange region.

[0073] S2, Latin hypercube sampling method is used to set sampling node in each region of the above model, to ensure that sampling node uniformly covers the entire model space, to provide coordinate information for subsequent model definition boundary condition and describe bearing temperature field.

[0074] S3, PINN heat transfer model for analyzing rolling bearing temperature field is constructed based on convolutional neural network (CNN).

[0075] S4, according to the results of regional division, the heat transfer equation is used to describe the heat transfer mode between components.

[0076] S5, according to rolling bearing quasi-static model and Hertz contact theory, the contact load and contact area of rolling body and inner and outer raceway are calculated. The friction heat generated by contact load is calculated. The contact area and the friction heat generated define the heat source area and the heat source heat flow in the divided region.

[0077] S6, according to the coordinates of the sampling nodes, using the steady-state three-dimensional heat transfer equation to integrate the above various heat transfer equations and heat source terms, the loss term of the control equation is constructed. Using thermocouple sensors, quantum dot sensors, heat flow sensors and other sensors, and wired and wireless transmission methods, as many as possible, the temperature boundary conditions of the sampling points in different regions are collected to construct the loss term of the boundary conditions.

[0078] S7, using ADAM (adaptive moment estimation) solver, using Tanh activation function for model training in the hidden layer, learning rate is set to 1e -3 , the total number of samples is 90000, after 10000 epochs, the final rolling bearing heat transfer model based on PINN is obtained.

[0079] The above-described embodiments only express several embodiments of the present application, and the description is more specific and detailed, but it cannot be understood as limiting the scope of the patent. It should be noted that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method of analyzing a temperature field of a rolling bearing, characterized in that, The method comprises the following steps: A simplified model of the rolling bearing is constructed, the simplified model of the rolling bearing is divided into multiple regions according to heat transfer modes, and sampling nodes are set in each region; According to a heat transfer equation describing the heat transfer mode between the multiple regions and a heat source term describing the heat generated by friction between the rolling elements and the raceways in the rolling bearing, a loss term of a control equation is constructed by using a steady-state three-dimensional heat transfer equation; temperature of the sampling points in different regions is collected as a temperature boundary condition to construct a loss term of a boundary condition; and a loss function is constructed according to the loss term of the control equation and the loss term of the boundary condition; According to the temperature data collected at the sampling nodes, a PINN heat transfer model is trained by using the loss function to obtain a PINN rolling bearing heat transfer model for obtaining a temperature field of the rolling bearing; The loss function is as follows: ； wherein, and are weight hyperparameters for each loss, and are the loss terms for the control equation and the boundary condition, respectively, is the loss function; ； ； wherein, N is the total number of sampling nodes for the model, i and j are labels of the sampling nodes, represents the difference between the model prediction result of the heat transfer partial differential equation set and the theoretically solved result; is the difference between the model prediction result of the temperature boundary condition and the actual measurement result, is the difference between the model prediction result of the heat flow density boundary condition and the actual measurement result, k is the thermal conductivity of the material at the sampling node, represents the gradient in one direction; The loss term of the control equation constructed by using the steady-state three-dimensional heat transfer equation specifically includes: ； wherein, x, y, z are Cartesian coordinates of the acquisition nodes, respectively; T are temperature values of the acquisition nodes; λ is the thermal conductivity; Q origin is the heat source term.

2. A method of analyzing a temperature field of a rolling bearing according to claim 1, characterized in that, The simplified model of the rolling bearing is divided into multiple regions, and specifically includes: a heat source region, a rolling element-raceway contact heat conduction region, an outer ring-bearing seat heat conduction region, an inner ring-bearing heat conduction region, and a rolling element and ring convective heat exchange region.

3. A method of analyzing a temperature field of a rolling bearing according to claim 1, characterized in that, The temperature of the sampling points in different regions is collected as the temperature boundary condition, and specifically includes: The temperature of the sampling points in different regions is collected by a thermocouple sensor, a quantum dot sensor and a heat flow sensor as the boundary condition.

4. A method of analyzing a temperature field of a rolling bearing according to claim 1, characterized in that, The sampling nodes are set in each region, and specifically include: The Latin hypercube sampling method is used to set sampling nodes that can uniformly cover the entire model space in each region of the simplified model of the rolling bearing.

5. A system for analyzing a temperature field of a rolling bearing, characterized in that, It comprises: a region division module, configured to construct a simplified model of a rolling bearing, divide the simplified model of the rolling bearing into multiple regions according to heat transfer modes, and set sampling nodes in each region; a loss function construction module, configured to construct a loss term of a control equation by using a steady-state three-dimensional heat transfer equation according to a heat transfer equation describing the heat transfer mode between the multiple regions and a heat source term describing the heat generated by friction between the rolling elements and the raceways in the rolling bearing; collect temperature of the sampling points in different regions as a temperature boundary condition to construct a loss term of a boundary condition; and construct a loss function according to the loss term of the control equation and the loss term of the boundary condition; a temperature field analysis module, configured to train a PINN heat transfer model by using the loss function according to temperature data collected at the sampling nodes to obtain a PINN rolling bearing heat transfer model for obtaining a temperature field of the rolling bearing; The loss function is as follows: ； wherein, and are weight hyperparameters for each loss, and are the loss terms for the control equation and the boundary conditions, respectively, is the loss function; ； ； wherein, N is the total number of model sampling nodes, i and j are labels of the sampling nodes, represents a difference between a model prediction result of a heat transfer partial differential equation set and a theoretically solved result; is a difference between a model prediction result of a temperature boundary condition and an actually measured result, is a difference between a model prediction result of a heat flow density boundary condition and an actually measured result, k is a thermal conductivity of a material at the sampling node, represents a gradient in one direction; The loss term of the control equation constructed by using the steady-state three-dimensional heat transfer equation specifically includes: ； in,( x, y, z The coordinates of the data acquisition nodes are shown below. T The temperature value of the data acquisition node; λ Thermal conductivity; Q origin This is a heat source term.

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