Face gear pair lubrication characteristic prediction method and device based on neural network model

Abstract

The invention belongs to the field of gear friction dynamics, and discloses a face gear pair lubrication characteristic prediction method and device based on a neural network model, and the method comprises the steps: inputting the characteristic parameters of a to-be-predicted face gear pair into a face gear pair lubrication characteristic prediction model, and outputting to obtain a face gear pair lubrication characteristic prediction result; the construction process of the face gear pair lubrication characteristic prediction model comprises the following steps: determining an input variable and an output variable of an artificial neural network model; sampling the input variables to obtain training sample input parameters; inputting the training sample input parameters into the non-Newtonian thermal elastohydrodynamic lubrication model to solve the output variables to obtain training sample output parameters; the training sample input parameters and the training sample output parameters are randomly divided, the artificial neural network model is trained and verified, and a face gear pair lubrication characteristic prediction model is obtained; the method can accurately reflect the lubrication characteristics of the face gear pair, and improves the accuracy and efficiency of the prediction result of the lubrication characteristics of the face gear pair.

Description

Technical Field

[0001] The present invention belongs to the technical field of gear friction dynamics, relates to the field of lubrication characteristic evaluation of face gear pairs, and in particular to a method and device for predicting lubrication characteristics of face gear pairs based on a neural network model. Background Art

[0002] A face gear pair is generally composed of a face gear and an involute gear, and the involute gear is called a pinion. The face gear pair has the advantages of compact structure, high transmission efficiency and low sensitivity to installation errors. It is used for power transmission between intersecting axes or crossing axes, and is particularly suitable for motion and power transmission under complex working conditions such as high speed and heavy load. It is widely used in aerospace, wind power transmission, vehicles and other fields. The high-speed and heavy-load working conditions in the above-mentioned fields put forward higher requirements on the friction dynamics performance of the face gear pair.

[0003] At present, the friction dynamics model is usually used to analyze the friction dynamics performance of face gear pairs. The friction dynamics model takes into account the mutual influence between the gear lubrication characteristics and the dynamic characteristics, and couples the elastohydrodynamic lubrication model and the dynamic model, so as to accurately evaluate the friction dynamics performance of the face gear pair. However, since the control equation group of the elastohydrodynamic lubrication model contains many nonlinear equations such as the Reynolds equation, film thickness equation, load equation and energy equation, the solution of the elastohydrodynamic lubrication model is not only very time-consuming but also very easy to fail to converge, which makes it difficult to solve the friction dynamics model efficiently and accurately, and thus it is impossible to quickly and accurately analyze the friction dynamics performance of the face gear pair. Summary of the invention

[0004] In response to the technical problems existing in the prior art, the present invention provides a method and device for predicting the lubrication characteristics of a face gear pair based on a neural network model, so as to solve the technical problems that the existing friction dynamics model is difficult to solve efficiently and accurately, and cannot quickly and accurately analyze the friction dynamics performance of the face gear pair.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is: The present invention provides a method for predicting lubrication characteristics of a face gear pair based on a neural network model, which is characterized by comprising: Obtain characteristic parameters of the gear pair to be predicted; Inputting characteristic parameters of the face gear pair to be predicted into the face gear pair lubrication characteristic prediction model, and outputting the face gear pair lubrication characteristic prediction result; The construction process of the face gear pair lubrication characteristics prediction model includes: Establish an artificial neural network model; determine the input variables and output variables of the artificial neural network model; wherein the input variables include the geometric parameters of the face gear pair, the material properties of the face gear pair, the lubricant properties and the operating characteristic parameters of the face gear pair; the output variables are the minimum oil film thickness, the center oil film thickness and the friction coefficient; sample the input variables to obtain the training sample input parameters; input the training sample input parameters into the non-Newtonian thermal elastic hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters; randomly divide the training sample input parameters and the training sample output parameters into a training set and a validation set, and use the training set and the validation set to train and validate the artificial neural network model to obtain a face gear pair lubrication characteristics prediction model.

[0006] Furthermore, the geometric parameters of the face gear pair include the equivalent radius of curvature and the ellipticity; the material properties of the face gear pair include the equivalent elastic modulus; the lubricant properties include atmospheric viscosity, room temperature viscosity-pressure coefficient, room temperature viscosity-temperature coefficient, specific heat capacity, thermal conductivity and Eyring characteristic shear stress; the operating characteristic parameters of the face gear pair include the pinion speed in the direction of the minor axis of the tooth contact ellipse, the pinion speed in the direction of the major axis of the tooth contact ellipse, the face gear speed in the direction of the minor axis of the tooth contact ellipse, the face gear speed in the direction of the major axis of the tooth contact ellipse and the normal load capacity.

[0007] Furthermore, the input variables are sampled to obtain the training sample input parameters, including: The Latin hypercube sampling method is used to sample the input variables and obtain the training sample input parameters.

[0008] Furthermore, the control equations of the non-Newtonian thermoelastic-hydrodynamic lubrication model include the non-Newtonian fluid constitutive model, the non-Newtonian thermoelastic-hydrodynamic Reynolds equation, the viscosity-pressure-temperature relationship, the density-pressure-temperature relationship, the film thickness equation, the force balance equation and the energy equation; The constitutive model of non-Newtonian fluid is as follows:

[0009]

[0010]

[0011] in, For lubricant along Flow velocity in the axial direction; For lubricant along Flow velocity in the axial direction; For along Shear stress in the axial direction; For along Shear stress in the axial direction; is the equivalent viscosity defined by the Eyring rheological model; is the apparent viscosity; is the hyperbolic sine function; is the Eyring characteristic shear stress, which is a constant; is an intermediate variable; for Axis direction; The non-Newtonian thermoelastic hydrodynamic Reynolds equation is as follows:

[0012]

[0013]

[0014]

[0015]

[0016] in, is the density of the lubricant; is the oil film thickness; is the oil film pressure; , , , as well as They are all intermediate variables that characterize the density of lubricants; For along The entrainment velocity in the axial direction; For along The entrainment velocity in the axial direction; for Pinion speed in axial direction; for Face gear speed in axial direction; for Pinion speed in axial direction; for Face gear speed in axial direction; , It is an intermediate variable that characterizes the viscosity of the lubricant; For the inner integral Axis direction integration variable.

[0017] Furthermore, the viscosity-pressure-temperature relationship is as follows:

[0018]

[0019]

[0020] in, is the initial viscosity of the lubricant at ambient temperature; is a constant; is the temperature field; is the ambient temperature; is the viscosity-pressure coefficient; is the viscosity-temperature coefficient; is the viscosity-pressure coefficient at room temperature; is the temperature viscosity coefficient at room temperature; The density-pressure-temperature relationship is as follows:

[0021] in, is the initial density of the lubricant at ambient temperature; is the density-temperature coefficient.

[0022] Furthermore, the film thickness equation is as follows:

[0023] in, is the rigid body displacement; is the tooth contact ellipse The equivalent radius of curvature in the axial direction; is the tooth contact ellipse The equivalent radius of curvature in the axial direction; is the equivalent elastic modulus; is the integration area; and The integral area Any point inside The horizontal and vertical coordinates of The force balance equation is as follows:

[0024] in, is the external load; The energy equation includes the energy equation of viscous fluid and the energy equation of solid; The energy equation for viscous fluid is as follows:

[0025] in, is the specific heat capacity of the lubricant, which is a constant; is the thermal conductivity of the lubricant, which is a constant; is the temperature field; The energy equation for a solid is as follows:

[0026]

[0027] in, is the specific heat capacity of the pinion; is the density of the pinion; is the heat transfer coefficient of the pinion; For small gear The coordinate system in the axis direction, The axis directions are in the same direction; is the specific heat capacity of the face gear; is the density of the face gear; is the heat transfer coefficient of the face gear; For face gear The coordinate system in the axis direction, The axes are in the same direction.

[0028] The present invention also provides a face gear pair lubrication characteristic prediction system based on a neural network model, comprising: A characteristic parameter acquisition module is used to acquire characteristic parameters of the face gear pair to be predicted; A performance prediction module, used for inputting characteristic parameters of the face gear pair to be predicted into the face gear pair lubrication characteristic prediction model, and outputting the prediction result of the face gear pair lubrication characteristic; The construction process of the face gear pair lubrication characteristics prediction model includes: Establish an artificial neural network model; determine the input variables and output variables of the artificial neural network model; wherein the input variables include the geometric parameters of the face gear pair, the material properties of the face gear pair, the lubricant properties and the operating characteristic parameters of the face gear pair; the output variables are the minimum oil film thickness, the center oil film thickness and the friction coefficient; sample the input variables to obtain the training sample input parameters; input the training sample input parameters into the non-Newtonian thermal elastic hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters; randomly divide the training sample input parameters and the training sample output parameters into a training set and a validation set, and use the training set and the validation set to train and validate the artificial neural network model to obtain a face gear pair lubrication characteristics prediction model.

[0029] The present invention also provides a device for predicting lubrication characteristics of a face gear pair based on a neural network model, comprising: a processor suitable for executing a computer program; A computer-readable storage medium having a computer program stored therein, wherein when the computer program is executed by the processor, the method for predicting lubrication characteristics of a face gear pair based on a neural network model is executed.

[0030] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the method for predicting the lubrication characteristics of a face gear pair based on a neural network model is implemented.

[0031] The present invention also provides a computer program product, which includes a computer program. When the computer program is executed by a processor, the method for predicting the lubrication characteristics of a face gear pair based on a neural network model is implemented.

[0032] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a method for predicting the lubrication characteristics of a face gear pair based on a neural network model. The characteristic parameters of the face gear pair to be predicted are obtained and input into the prediction model for the lubrication characteristics of the face gear pair. The prediction model for the lubrication characteristics of the face gear pair is trained and verified using training sample input data and training sample output parameters solved by a non-Newtonian thermal elastic-hydrodynamic lubrication model. The method can accurately reflect the lubrication characteristics of the face gear pair, improve the accuracy and efficiency of the prediction results of the lubrication characteristics of the face gear pair, and thus realize rapid and accurate analysis of the friction mechanical properties of the face gear pair. Among them, the output variables are solved by the non-Newtonian thermal elastic-hydrodynamic lubrication model, so that the lubrication state of the face gear pair under actual working conditions can be accurately obtained. The method of randomly dividing the training sample input parameters and the training sample output parameters into a training set and a verification set to train and verify the artificial neural network model helps to reduce the risk of overfitting of the model, enhance the generalization ability of the model, enable the model to better adapt to different face gear pairs and lubrication conditions, realize rapid evaluation of the lubrication performance of the face gear pair, and provide strong data support for the design and use of the face gear pair.

[0033] The lubrication characteristics prediction system for face gear pairs based on a neural network model, the lubrication characteristics prediction device for face gear pairs based on a neural network model, the computer-readable storage medium and the computer program product provided by the present invention have all the advantages of the above-mentioned lubrication characteristics prediction method for face gear pairs based on a neural network model. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0035] Figure 1 A flowchart of the method for predicting lubrication characteristics of a face gear pair based on a neural network model provided in Example 1; Figure 2It is a principle diagram of the tooth surface contact ellipse of the face gear pair in Example 1; Figure 3 This is a schematic diagram of the prediction results of the center film thickness of the face gear pair to be tested in Example 1; Figure 4 It is a schematic diagram of the prediction result of the minimum film thickness of the face gear pair to be tested in Example 1; Figure 5 It is a schematic diagram of the prediction result of the friction coefficient of the gear pair to be tested in Example 1; Figure 6 A structural block diagram of a face gear pair lubrication characteristic prediction system based on a neural network model provided in Example 2; Figure 7 This is a structural block diagram of the face gear pair lubrication characteristics prediction device based on the neural network model provided in Example 3. DETAILED DESCRIPTION

[0036] In order to make the technical problems, technical solutions and beneficial effects solved by this application clearer, the technical solutions in the embodiments of this application will be described clearly and completely in combination with the drawings in the embodiments of this application; obviously, the described embodiments are only part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0037] The present invention provides a method for predicting lubrication characteristics of a face gear pair based on a neural network model, comprising: The characteristic parameters of the face gear pair to be predicted are obtained; the characteristic parameters of the face gear pair to be predicted are input into the face gear pair lubrication characteristic prediction model, and the face gear pair lubrication characteristic prediction result is output.

[0038] The construction process of the face gear pair lubrication characteristics prediction model includes: Establish an artificial neural network model; determine the input variables and output variables of the artificial neural network model; sample the input variables to obtain the training sample input parameters; input the training sample input parameters into the non-Newtonian thermal elastic hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters. The training sample input parameters and the training sample output parameters are randomly divided into a training set and a validation set, and the training set and the validation set are used to train and validate the artificial neural network model to obtain the face gear pair lubrication characteristics prediction model.

[0039] In the present invention, the input variables include the geometric parameters of the face gear pair, the material properties of the face gear pair, the lubricant properties and the operating characteristic parameters of the face gear pair; the output variables are the minimum oil film thickness, the central oil film thickness and the friction coefficient; wherein, the geometric parameters of the face gear pair include the equivalent radius of curvature and the ellipticity; the material properties of the face gear pair include the equivalent elastic modulus; the lubricant properties include atmospheric viscosity, room temperature viscosity-pressure coefficient, room temperature viscosity-temperature coefficient, specific heat capacity, thermal conductivity and Eyring characteristic shear stress (Eyring characteristic shear stress is an important parameter to describe the plastic flow behavior of materials); the operating characteristic parameters of the face gear pair include the pinion speed in the direction of the minor axis of the tooth contact ellipse, the pinion speed in the direction of the major axis of the tooth contact ellipse, the face gear speed in the direction of the minor axis of the tooth contact ellipse, the face gear speed in the direction of the major axis of the tooth contact ellipse and the normal load capacity.

[0040] The present invention also provides a face gear pair lubrication characteristics prediction system based on a neural network model, comprising a characteristic parameter acquisition module and a performance prediction module; the characteristic parameter acquisition module is used to acquire the characteristic parameters of the face gear pair to be predicted; the performance prediction module is used to input the characteristic parameters of the face gear pair to be predicted into the face gear pair lubrication characteristics prediction model, and output the face gear pair lubrication characteristics prediction result.

[0041] The construction process of the face gear pair lubrication characteristics prediction model includes: Establish an artificial neural network model; determine the input variables and output variables of the artificial neural network model; sample the input variables to obtain the training sample input parameters; input the training sample input parameters into the non-Newtonian thermal elastic hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters. The training sample input parameters and the training sample output parameters are randomly divided into a training set and a validation set, and the training set and the validation set are used to train and validate the artificial neural network model to obtain the face gear pair lubrication characteristics prediction model.

[0042] In the present invention, by obtaining the characteristic parameters of the face gear pair to be predicted and inputting them into the face gear pair lubrication characteristics prediction model, the face gear pair lubrication characteristics prediction model is trained and verified using training sample input data and training sample output parameters solved by a non-Newtonian thermal elastic-hydrodynamic lubrication model. It can accurately reflect the lubrication characteristics of the face gear pair and improve the accuracy and efficiency of the face gear pair lubrication characteristics prediction results.

[0043] In the process of constructing the prediction model of the lubrication characteristics of face gear pairs, the output variables are solved by the non-Newtonian thermal elastic-hydrodynamic lubrication model, so that the lubrication state of the face gear pair under actual working conditions can be accurately obtained; the method of randomly dividing the training sample input parameters and the training sample output parameters into training sets and verification sets is used to train and verify the artificial neural network model, which helps to reduce the risk of model overfitting and enhance the generalization ability of the model, so that the model can better adapt to different face gear pairs and lubrication conditions, realize rapid evaluation of the lubrication performance of face gear pairs, and provide strong data support for designers.

[0044] Example 1 As attached Figure 1 As shown, this embodiment 1 provides a method for predicting lubrication characteristics of a face gear pair based on a neural network model, comprising the following steps: Step 1: construct a non-Newtonian thermal elastohydrodynamic lubrication model; wherein the non-Newtonian thermal elastohydrodynamic lubrication model is used to obtain the lubrication characteristics of the face gear pair during the transmission process.

[0045] It should be noted that under actual working conditions, in order to reduce friction, the face gear and pinion in the face gear pair realize transmission under lubrication conditions; specifically, the motion and torque in the face gear pair are transmitted from the tooth surface of the pinion to the tooth surface of the face gear through the lubricant; due to the elastic deformation of the tooth surface, the point contact between the tooth surface of the pinion and the tooth surface of the face gear is expanded to an elliptical contact, that is, a tooth surface contact ellipse is formed; using the non-Newtonian thermal elastic hydrodynamic lubrication model through numerical simulation, the lubrication characteristics of the face gear pair during transmission can be obtained efficiently and accurately, that is, the lubrication characteristics of the tooth surface contact ellipse area can be solved.

[0046] Specifically, the control equations of the non-Newtonian thermoelastic-hydrodynamic lubrication model include the non-Newtonian fluid constitutive model, the non-Newtonian thermoelastic-hydrodynamic Reynolds equation, the viscosity-pressure-temperature relationship, the density-pressure-temperature relationship, the film thickness equation, the force balance equation and the energy equation; by numerically solving the control equations of the non-Newtonian thermoelastic-hydrodynamic lubrication model, the lubrication characteristics of the tooth surface contact elliptical area can be obtained, thereby providing data for the training and verification of the artificial neural network model.

[0047] (1) Constitutive model of non-Newtonian fluid Considering the non-Newtonian fluid behavior of the lubricant, the non-Newtonian fluid constitutive model is used to describe the relationship between the viscosity and shear rate of the lubricant; a right-handed Cartesian coordinate system is established in the tooth surface contact ellipse area, as shown in the attached figure. Figure 2 As shown in the figure, the origin of the coordinate system is located at the center of the tooth surface contact ellipse. The minor axes of the contact ellipses of the shaft and tooth surface coincide with each other, and the coordinate system The major axis of the contact ellipse between the shaft and the tooth surface coincides with the major axis of the coordinate system. The axis is parallel to the normal direction of the tooth contact ellipse.

[0048] The constitutive model of non-Newtonian fluid is as follows:

[0049]

[0050]

[0051] in, For lubricant along Flow velocity in the axial direction; For lubricant along Flow velocity in the axial direction; For along Shear stress in the axial direction; For along Shear stress in the axial direction; is the equivalent viscosity defined by the Eyring rheological model (Eyring rheological model, a physical model based on quantum mechanics theory, used to describe the non-Newtonian nature of viscous flow of fluids); is the apparent viscosity; is the hyperbolic sine function; is the Eyring characteristic shear stress (Eyring characteristic shear stress is an important parameter to describe the plastic flow behavior of materials), which is a constant; is an intermediate variable; for Axis direction.

[0052] (2) Non-Newtonian thermoelastic hydrodynamic Reynolds equation Considering the non-Newtonian behavior and thermal effect of the lubricant, the steady-state non-Newtonian thermoelastic hydrodynamic Reynolds equation is established, and the non-Newtonian thermoelastic hydrodynamic Reynolds equation is obtained; among them, the non-Newtonian thermoelastic hydrodynamic Reynolds equation is as follows:

[0053]

[0054]

[0055]

[0056]

[0057] in, is the density of the lubricant; is the oil film thickness; is the oil film pressure; , , , as well as They are all intermediate variables that characterize the density of lubricants; For along The entrainment velocity in the axial direction; For along The entrainment velocity in the axial direction; for Pinion speed in axial direction; for Face gear speed in axial direction; for Pinion speed in axial direction; for Face gear speed in axial direction; , It is an intermediate variable that characterizes the viscosity of the lubricant; For the inner integral Axis direction integration variable.

[0058] (3) Viscosity-pressure-temperature relationship The apparent viscosity of the lubricant is described by the viscosity-pressure-temperature relationship; the viscosity-pressure-temperature relationship is as follows:

[0059]

[0060]

[0061] in, is the initial viscosity of the lubricant at ambient temperature; is a constant, ; is the temperature field; is the ambient temperature; is the viscosity-pressure coefficient; is the viscosity-temperature coefficient; is the viscosity-pressure coefficient at room temperature; is the temperature viscosity coefficient at room temperature.

[0062] (4) Density-pressure-temperature relationship The density of the lubricant is described by the density-pressure-temperature relationship; the density-pressure-temperature relationship is as follows:

[0063] in, is the initial density of the lubricant at ambient temperature; is the density-temperature coefficient, .

[0064] (5) Film thickness equation Considering the elastic deformation, the oil film thickness equation is established, that is, the film thickness equation is obtained; among them, the film thickness equation is as follows:

[0065] in, is the rigid body displacement; is the tooth contact ellipse The equivalent radius of curvature in the axial direction; is the tooth contact ellipse The equivalent radius of curvature in the axial direction; is the equivalent elastic modulus; is the integration area; and The integral area Any point inside The horizontal and vertical coordinates of .

[0066] (6) Force balance equation The force balance equation is used to describe the equilibrium relationship between the pressure distribution of the lubricant and the external load; the force balance equation is as follows:

[0067] in, For external load.

[0068] (7) Energy equation During the lubrication process, the oil film generates heat due to viscous shear and compression, causing the temperature to rise. At the same time, the heat generated is dissipated through convection and conduction. As a result of heating and heat dissipation, a steady-state temperature field is formed after the face gear pair reaches thermal equilibrium. Among them, the temperature field is determined by the energy equation and its boundary conditions. The energy equation includes the energy equation of viscous fluid and the energy equation of solid.

[0069] When the effects of body force and thermal radiation are not considered, the energy equation of viscous fluid is as follows:

[0070] in, is the specific heat capacity of the lubricant, which is a constant; is the thermal conductivity of the lubricant, which is a constant; is the temperature field.

[0071] For solids, the main consideration is the heat conduction equation, so the energy equation for solids is as follows:

[0072]

[0073] in, is the specific heat capacity of the pinion; is the density of the pinion; is the heat transfer coefficient of the pinion; For small gear The coordinate system in the axis direction, The axis directions are in the same direction; is the specific heat capacity of the face gear; is the density of the face gear; is the heat transfer coefficient of the face gear; For face gear The coordinate system in the axis direction, The axes are in the same direction.

[0074] The boundary conditions of the energy equation are as follows:

[0075] in, For small gear Directional temperature field calculation depth; For face gear Directional temperature field calculation depth.

[0076] Step 2: Establish an artificial neural network model. The process of establishing an artificial neural network model includes: Step 21: Design the structure of the artificial neural network model.

[0077] The structure of the artificial neural network model includes: the design of the number of network layers and the determination of the number of neurons in each layer; the artificial neural network model includes an input layer, a hidden layer and an output layer to extract the nonlinear mapping relationship between the input parameters and the corresponding output parameters; the structure of the hidden layer determines the training speed and generalization ability of the model to a large extent, and the design of the number of network layers mainly determines the number of hidden layers; the hidden layer described in this embodiment 1 adopts a double hidden layer to make the artificial neural network model have a more powerful nonlinear mapping ability.

[0078] After completing the design of the number of network layers, determine the number of neurons in each layer; the number of neurons in the input layer and the output layer is determined by the established prediction target of the artificial neural network model; specifically, the number of neurons in the input layer is the same as the number of input variables of the artificial neural network model, and the number of neurons in the output layer is the same as the number of output variables of the artificial neural network model.

[0079] If the number of neurons in the hidden layer is too small, the learning may not converge, and the recognition ability and generalization ability of the model will be reduced; if the number of neurons in the hidden layer is too large, the model training will not converge for a long time and the fault tolerance performance will be reduced; the number of neurons in the hidden layer in this embodiment 1 is calculated according to the following formula:

[0080] in, is the number of neurons in the hidden layer; is the number of neurons in the output layer; is the number of neurons in the input layer.

[0081] Step 22: Select learning rate.

[0082] In the artificial neural network model, the learning rate The choice of directly affects the change of weights; among them, the learning rate When the value of is large, the greater the change in weight, the faster the learning convergence speed of the artificial neural network model, but the learning rate If the value is too large, it is easy to cause oscillation, that is, the network is unstable; When the value of is small, the oscillation of the network can be avoided, but the convergence speed is slow; in this embodiment 1, the learning rate The value range is set to 0.01-0.8.

[0083] Step 23: Selection of initial weights and thresholds.

[0084] Since the artificial neural network model needs to select many parameters, its error surface is a relatively complex hypersurface, on which there may be multiple local minimum points; in addition, the initialization of the weights and thresholds of the artificial neural network model determines at which point on the error surface the network training starts; if the initial weights and thresholds are randomly generated, the search will start from a random point; therefore, the selection of initial weights and thresholds is crucial to shortening the network training time and whether it can converge to the global minimum point.

[0085] In the artificial neural network model, the activation function of the neuron is symmetric about the zero point; if the input of each neuron is near the zero point, its output is at the center point of the activation function; the center point of the activation function is not only far away from the two saturation regions of the activation function, but also the region most sensitive to changes, which will inevitably accelerate the learning speed of the network; in order to make the initial input of each neuron near the zero point, the following two methods can be used; the first method is to make the initial weights and thresholds small enough; the second method is to make the initial weights and thresholds between -1 and 1; in this embodiment 1, the first method is used for the initial weights and thresholds of the hidden layer, and the second method is used for the initial weights and thresholds of the output layer.

[0086] Step 24: Selection of activation function In the artificial neural network model, each neuron converts input into output through an activation function, which acts as a strong nonlinear mapping. In this embodiment 1, the S-type function (Sigmoid function) is selected as the activation function in the artificial neural network model; wherein the S-type function is specifically: .

[0087] Step 3: Determine the input variables and output variables of the artificial neural network model.

[0088] The output variables are used as the prediction target of the artificial neural network model, namely, the lubrication characteristics of the face gear pair to be predicted; the output variables include the minimum oil film thickness, the center oil film thickness and the friction coefficient; Input variables are variables that have a strong nonlinear relationship with the prediction targets of the artificial neural network model; in order for the artificial neural network model to accurately and efficiently predict these targets, the selection of input parameters must be related to the prediction targets of the artificial neural network model, and the value range of the input variables must be able to cover the reasonable value range in actual problems.

[0089] In this embodiment 1, the input variables include the geometric parameters of the face gear pair, the material properties of the face gear pair, the lubricant properties and the operating characteristic parameters of the face gear pair to simulate the contact problem in the transmission process of the face gear pair; specifically, the geometric parameters of the face gear pair include the equivalent radius of curvature and the ellipticity; the material properties of the face gear pair include the equivalent elastic modulus; the lubricant properties include atmospheric viscosity, room temperature viscosity-pressure coefficient, room temperature viscosity-temperature coefficient, specific heat capacity, thermal conductivity and Eyring characteristic shear stress; the operating characteristic parameters of the face gear pair include the pinion speed in the direction of the minor axis of the tooth surface contact ellipse, the pinion speed in the direction of the major axis of the tooth surface contact ellipse, the face gear speed in the direction of the minor axis of the tooth surface contact ellipse, the face gear speed in the direction of the major axis of the tooth surface contact ellipse and the normal load, that is, Axial pinion speed, Axial pinion speed, Axial face gear speed, Axial face gear speed and normal load capacity; the types and value ranges of input variables are shown in Table 1 below.

[0090] Table 1 Input variables of artificial neural network model

[0091] Step 4: Sample the input variables to obtain the training sample input parameters. Specifically, the Latin Hypercube Sampling (LHS) method is used to sample the input variables to obtain the training sample input parameters.

[0092] It should be noted that after determining the input variables of the artificial neural network model, the Latin hypercube sampling method is used to perform sampling in the input parameter space of the input variables, so as to provide more representative samples of the artificial neural network model in the input parameter space of the input variables, so as to evenly cover the entire parameter space, reduce sampling errors and improve the representativeness of samples; compared with simple random sampling, the LHS method can achieve better coverage with fewer sample points, and can provide more representative samples for the artificial neural network model.

[0093] It should also be noted that the input parameters of the training samples should make the face gear transmission belong to full-film lubrication thermoelastic hydrodynamic contact and do not violate the physical meaning; therefore, the following restrictions are imposed on the input parameters of the training samples: (1) The minimum oil film thickness shall not be less than 10 nm; (2) Sample points with a maximum hertz pressure (derived from the Hertz contact theory, which refers to the pressure distribution generated on the contact surface of the elastic body) less than 0.05 GPa often experience hydrodynamic lubrication rather than elastic hydrodynamic lubrication; (3) Sample points with a maximum hertz pressure greater than 0.6 GPa and an equivalent elastic modulus less than 100 GPa will experience plastic deformation.

[0094] Step 5: Input the training sample input parameters into the non-Newtonian thermal elastic hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters.

[0095] Step 6: randomly divide the training sample input parameters and the training sample output parameters into a training set and a validation set, and use the training set and the validation set to train and validate the artificial neural network model to obtain a face gear pair lubrication characteristic prediction model.

[0096] Specifically, the training set is used to train the artificial neural network model, and the validation set is used to verify the trained artificial neural network model to improve the generalization ability of the model; by training and verifying the artificial neural network model, a nonlinear mapping relationship between the input and the corresponding output is obtained, and then a prediction model for the lubrication characteristics of the face gear pair is obtained.

[0097] Among them, in order to ensure the stable operation of the artificial neural network model and improve the learning speed and network accuracy of the network, before training and verification, it also includes the step of preprocessing the data in the training set and the verification set; among them, the preprocessing adopts normalization processing, that is, through a simple linear transformation, the data in the training set and the verification set are transformed into numbers within a certain interval to ensure the accuracy of the model and the training of the model.

[0098] Step 7: Obtain the characteristic parameters of the gear pair to be predicted.

[0099] Among them, the characteristic parameters of the face gear pair to be predicted include the geometric parameters of the face gear pair to be predicted, the material properties of the face gear pair to be predicted, the lubricant properties in the gear pair to be predicted and the operating characteristic parameters of the face gear pair to be predicted; specifically, the geometric parameters of the face gear pair to be predicted include the equivalent radius of curvature and the ellipticity; the material properties of the face gear pair to be predicted include the equivalent elastic modulus; the lubricant properties of the face gear pair to be predicted include atmospheric viscosity, room temperature viscosity-pressure coefficient, room temperature viscosity-temperature coefficient, specific heat capacity, thermal conductivity and Eyring characteristic shear stress; the operating characteristic parameters of the face gear pair to be predicted include the pinion speed in the direction of the minor axis of the tooth contact ellipse, the pinion speed in the direction of the major axis of the tooth contact ellipse, the face gear speed in the direction of the minor axis of the tooth contact ellipse, the face gear speed in the direction of the major axis of the tooth contact ellipse and the normal load capacity.

[0100] Step 8: Input the characteristic parameters of the face gear pair to be predicted into the face gear pair lubrication characteristic prediction model, and output the face gear pair lubrication characteristic prediction result.

[0101] Test results explanation: Based on the characteristic parameters of the face gear pair to be predicted, the lubrication characteristics prediction model of the face gear pair and the non-Newtonian thermal elastic hydrodynamic lubrication model are used to predict and analyze the lubrication characteristics of the face gear pair to be predicted. The prediction and analysis results are shown in the attached figure. Figure 3-5 As shown; among them, Figure 3 The schematic diagram of the predicted results of the center film thickness of the gear pair to be tested is given in the attached figure. Figure 4 The schematic diagram of the minimum film thickness prediction result of the gear pair to be tested is given in the attached figure. Figure 5 A schematic diagram of the predicted results of the friction coefficient of the gear pair to be tested is given in FIG.

[0102] From the attached Figure 3-5 It can be seen that the predicted results of the center film thickness, minimum film thickness and friction coefficient of the face gear pair to be tested are all concentrated on the diagonal line of the figure, that is, the prediction results of the lubrication characteristics prediction model of the face gear pair and the non-Newtonian thermal elastic hydrodynamic lubrication model are very close.

[0103] It should be noted that in the attached Figure 3-5 The middle dot represents the predicted results of the center film thickness, minimum film thickness or friction coefficient of the face gear pair to be tested, the actual value of the horizontal axis is the predicted result output by the non-Newtonian thermal elastic hydrodynamic lubrication model, and the vertical axis represents the predicted result output by the face gear pair lubrication characteristics prediction model.

[0104] Secondly, in order to intuitively describe the performance of the face gear pair lubrication characteristics prediction model, the determination coefficient Describes the closeness of the above prediction results; among them, the coefficient of determination , specifically:

[0105] in, is the coefficient of determination, The values ​​are distributed in ; is the actual value, is the predicted value, is the sample size.

[0106] Through calculation, it is found that the determination coefficient corresponding to the prediction results of the center film thickness, minimum film thickness and friction coefficient of the face gear pair to be tested output by the face gear pair lubrication characteristics prediction model is The values ​​are 0.997, 0.996 and 0.997 respectively; due to the coefficient of determination The closer the value is to 1, the better the performance of the model is. Therefore, it can be seen that the face gear pair lubrication characteristics prediction model can show excellent performance in the prediction process of the face gear pair lubrication characteristics.

[0107] The method for predicting the lubrication characteristics of face gear pairs based on a neural network model in this embodiment 1 utilizes a non-Newtonian thermal elastic-hydrodynamic lubrication model through a numerical simulation method to efficiently and accurately obtain the lubrication characteristics of the face gear transmission process, so as to obtain the data set required for artificial neural network model training and verification, and then establish a face gear pair lubrication characteristics prediction model; once the face gear pair lubrication characteristics prediction model is constructed, for a new face gear pair to be predicted, it is only necessary to input the characteristic parameters of the face gear pair to be predicted to quickly obtain the lubrication characteristics prediction results, which greatly improves the prediction efficiency and accuracy.

[0108] In this embodiment 1, by obtaining the characteristic parameters of the face gear pair to be predicted and inputting the characteristic parameters into the face gear pair lubrication characteristics prediction model, since the face gear pair lubrication characteristics prediction model is constructed based on the artificial neural network model and is trained and verified by the training sample input parameters and the training sample output parameters, it can more accurately reflect the lubrication characteristics of the face gear pair; wherein, when constructing the face gear pair lubrication characteristics prediction model, the output variables are solved by the non-Newtonian thermal elastic-hydrodynamic lubrication model, which can more accurately simulate the lubrication state of the face gear pair under actual working conditions, and further improve the accuracy of the prediction; secondly, the artificial neural network model is trained and verified by randomly dividing the training set and the verification set, which helps to reduce the risk of model overfitting, enhance the generalization ability of the model, and enable the model to better adapt to different face gear pairs and lubrication conditions; the method described in this embodiment 1 improves the accuracy and efficiency of the prediction, enhances the generalization ability of the model, and facilitates practical application by combining the artificial neural network and the non-Newtonian thermal elastic-hydrodynamic lubrication model.

[0109] Example 2 As attached Figure 6As shown, this embodiment 2 provides a face gear pair lubrication characteristic prediction system based on a neural network model, including: a lubrication model establishment module, a network model establishment module, a variable determination module, an input sample sampling module, an output sample solution module, a model training module, a characteristic parameter acquisition module and a performance prediction module.

[0110] A lubrication model establishment module is used to construct a non-Newtonian thermal elastic-hydrodynamic lubrication model; wherein the non-Newtonian thermal elastic-hydrodynamic lubrication model is used to obtain the lubrication characteristics of the face gear pair during the transmission process; a network model establishment module is used to establish an artificial neural network model; a variable determination module is used to determine the input variables and output variables of the artificial neural network model; an input sample sampling module is used to sample the input variables to obtain the training sample input parameters; an output sample solution module is used to input the training sample input parameters into the non-Newtonian thermal elastic-hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters; a model training module is used to randomly divide the training sample input parameters and the training sample output parameters into a training set and a validation set, and use the training set and the validation set to train and verify the artificial neural network model to obtain a face gear pair lubrication characteristics prediction model; a characteristic parameter acquisition module is used to obtain the characteristic parameters of the face gear pair to be predicted; a performance prediction module is used to input the characteristic parameters of the face gear pair to be predicted into the face gear pair lubrication characteristics prediction model, and output the face gear pair lubrication characteristics prediction result.

[0111] Example 3 As attached Figure 7 As shown, this embodiment 3 provides a device for predicting the lubrication characteristics of a face gear pair based on a neural network model, including: a memory for storing a computer program; and a processor for implementing the steps of a method for predicting the lubrication characteristics of a face gear pair based on a neural network model when executing the computer program.

[0112] When the processor executes the computer program, the steps of implementing the above-mentioned method for predicting lubrication characteristics of face gear pairs based on a neural network model are, for example: A non-Newtonian thermal elastohydrodynamic lubrication model is constructed; the non-Newtonian thermal elastohydrodynamic lubrication model is used to obtain the lubrication characteristics of the face gear pair during the transmission process; an artificial neural network model is established; the input variables and output variables of the artificial neural network model are determined; the input variables are sampled to obtain the training sample input parameters; the training sample input parameters are input into the non-Newtonian thermal elastohydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters; the training sample input parameters and the training sample output parameters are randomly divided into a training set and a validation set, and the artificial neural network model is trained and validated using the training set and the validation set to obtain a face gear pair lubrication characteristics prediction model; the characteristic parameters of the face gear pair to be predicted are obtained; the characteristic parameters of the face gear pair to be predicted are input into the face gear pair lubrication characteristics prediction model, and the face gear pair lubrication characteristics prediction result is output.

[0113] Alternatively, when the processor executes the computer program, the functions of each module in the above-mentioned face gear pair lubrication characteristic prediction system based on the neural network model are realized, for example: A lubrication model establishment module is used to construct a non-Newtonian thermal elastic-hydrodynamic lubrication model; wherein the non-Newtonian thermal elastic-hydrodynamic lubrication model is used to obtain the lubrication characteristics of the face gear pair during the transmission process; a network model establishment module is used to establish an artificial neural network model; a variable determination module is used to determine the input variables and output variables of the artificial neural network model; an input sample sampling module is used to sample the input variables to obtain the training sample input parameters; an output sample solution module is used to input the training sample input parameters into the non-Newtonian thermal elastic-hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters; a model training module is used to randomly divide the training sample input parameters and the training sample output parameters into a training set and a validation set, and use the training set and the validation set to train and verify the artificial neural network model to obtain a face gear pair lubrication characteristics prediction model; a characteristic parameter acquisition module is used to obtain the characteristic parameters of the face gear pair to be predicted; a performance prediction module is used to input the characteristic parameters of the face gear pair to be predicted into the face gear pair lubrication characteristics prediction model, and output the face gear pair lubrication characteristics prediction result.

[0114] Exemplarily, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of completing preset functions, and the instruction segments are used to describe the execution process of the computer program in the device for predicting lubrication characteristics of face gear pairs based on a neural network model.

[0115] For example, the computer program can be divided into a lubrication model building module, a network model building module, a variable determination module, an input sample sampling module, an output sample solving module, a model training module, a characteristic parameter acquisition module and a performance prediction module, and the specific functions of each module are as follows: a lubrication model building module, used to construct a non-Newtonian thermal elastic-hydrodynamic lubrication model; wherein the non-Newtonian thermal elastic-hydrodynamic lubrication model is used to obtain the lubrication characteristics of the face gear pair during the transmission process; a network model building module, used to establish an artificial neural network model; a variable determination module, used to determine the input variables and output variables of the artificial neural network model; an input sample sampling module, used to sample the input variables to obtain training samples; The input parameters; the output sample solving module is used to input the training sample input parameters into the non-Newtonian thermal elastic-hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters; the model training module is used to randomly divide the training sample input parameters and the training sample output parameters into a training set and a validation set, and use the training set and the validation set to train and verify the artificial neural network model to obtain the face gear pair lubrication characteristics prediction model; the characteristic parameter acquisition module is used to obtain the characteristic parameters of the face gear pair to be predicted; the performance prediction module is used to input the characteristic parameters of the face gear pair to be predicted into the face gear pair lubrication characteristics prediction model, and output the face gear pair lubrication characteristics prediction result.

[0116] The lubrication characteristics prediction device for face gear pairs based on the neural network model can be a computing device such as a desktop computer, a notebook, a PDA, and a cloud server. The lubrication characteristics prediction device for face gear pairs based on the neural network model can include, but is not limited to, a processor and a memory. Those skilled in the art can understand that the above is an example of a lubrication characteristics prediction device for face gear pairs based on a neural network model, and does not constitute a limitation on the lubrication characteristics prediction device for face gear pairs based on a neural network model. It can include more components than the above, or a combination of certain components, or different components. For example, the lubrication characteristics prediction device for face gear pairs based on the neural network model can also include input and output devices, network access devices, buses, etc.

[0117] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc. The processor is the control center of the face gear pair lubrication characteristic prediction device based on the neural network model, and uses various interfaces and lines to connect the various parts of the face gear pair lubrication characteristic prediction device based on the neural network model.

[0118] The memory can be used to store the computer program and / or module, and the processor implements various functions of the face gear pair lubrication characteristics prediction device based on the neural network model by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0119] The memory may mainly include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function (such as a sound playback function, an image playback function, etc.), etc.; the data storage area may store data created according to the use of the mobile phone (such as audio data, a phone book, etc.), etc. In addition, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (SmartMediaCard, SMC), a secure digital (SecureDigital, SD) card, a flash card (FlashCard), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0120] Example 4 This embodiment 4 also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method for predicting lubrication characteristics of a face gear pair based on a neural network model are implemented, for example: A non-Newtonian thermal elastohydrodynamic lubrication model is constructed; the non-Newtonian thermal elastohydrodynamic lubrication model is used to obtain the lubrication characteristics of the face gear pair during the transmission process; an artificial neural network model is established; the input variables and output variables of the artificial neural network model are determined; the input variables are sampled to obtain the training sample input parameters; the training sample input parameters are input into the non-Newtonian thermal elastohydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters; the training sample input parameters and the training sample output parameters are randomly divided into a training set and a validation set, and the artificial neural network model is trained and validated using the training set and the validation set to obtain a face gear pair lubrication characteristics prediction model; the characteristic parameters of the face gear pair to be predicted are obtained; the characteristic parameters of the face gear pair to be predicted are input into the face gear pair lubrication characteristics prediction model, and the face gear pair lubrication characteristics prediction result is output.

[0121] The module / unit integrated in the neural network model-based face gear pair lubrication characteristic prediction system can be stored in a computer-readable storage medium if it is implemented in the form of a software functional unit and sold or used as an independent product.

[0122] Based on such understanding, the present invention implements all or part of the processes in the above-mentioned method for predicting lubrication characteristics of face gear pairs based on a neural network model, and can also be completed by instructing related hardware through a computer program, and the computer program can be stored in a computer-readable storage medium, and when the computer program is executed by a processor, the steps of the above-mentioned method for predicting lubrication characteristics of face gear pairs based on a neural network model can be implemented. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or preset intermediate form, etc.

[0123] The computer-readable storage medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal and software distribution medium, etc.

[0124] It should be noted that the content contained in the computer-readable storage medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable storage media do not include electrical carrier signals and telecommunication signals.

[0125] Example 5 This embodiment 5 provides a computer product, which includes a computer program, and the computer program is stored in a computer-readable storage medium; the processor of the face gear pair lubrication characteristics prediction device based on the neural network model reads the computer program from the computer-readable storage medium, and the processor executes the computer program, so that the face gear pair lubrication characteristics prediction device based on the neural network model can execute the face gear pair lubrication characteristics prediction method based on the neural network model described in Embodiment 1, which will not be repeated here.

[0126] It should be noted that a person skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing related hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods.

[0127] The method for predicting the lubrication characteristics of a face gear pair based on a neural network model described in the present invention integrates an artificial neural network model with a non-Newtonian thermal elastohydrodynamic lubrication model, utilizes the non-Newtonian thermal elastohydrodynamic lubrication model to accurately describe the rheological characteristics of the lubricating oil and the elastohydrodynamic lubrication state of the gear pair, and utilizes the characteristics of the artificial neural network model that is good at handling complex nonlinear relationships. It can efficiently learn and predict the lubrication characteristics of the face gear pair, achieve fast and efficient prediction of lubrication characteristics, greatly reduce prediction costs and time costs, and provide strong support for the design and optimization of face gear pairs.

[0128] The above embodiment is only one of the implementation methods that can realize the technical solution of the present invention. The scope of protection claimed by the present invention is not limited only to this embodiment, but also includes changes, replacements and other implementation methods that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention.

Claims

1. A method for predicting lubrication characteristics of face gear pairs based on a neural network model, characterized in that: include: Obtain characteristic parameters of the gear pair to be predicted; Inputting characteristic parameters of the face gear pair to be predicted into the face gear pair lubrication characteristic prediction model, and outputting the face gear pair lubrication characteristic prediction result; The construction process of the face gear pair lubrication characteristics prediction model includes: Establish an artificial neural network model; determine the input variables and output variables of the artificial neural network model; wherein the input variables include the geometric parameters of the face gear pair, the material properties of the face gear pair, the lubricant properties and the operating characteristic parameters of the face gear pair; the output variables are the minimum oil film thickness, the center oil film thickness and the friction coefficient; sample the input variables to obtain the training sample input parameters; input the training sample input parameters into the non-Newtonian thermal elastic hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters; randomly divide the training sample input parameters and the training sample output parameters into a training set and a validation set, and use the training set and the validation set to train and validate the artificial neural network model to obtain a face gear pair lubrication characteristics prediction model.

2. The method for predicting lubrication characteristics of a face gear pair based on a neural network model according to claim 1, characterized in that: The geometric parameters of the face gear pair include the equivalent radius of curvature and the ellipticity; the material properties of the face gear pair include the equivalent elastic modulus; the lubricant properties include atmospheric viscosity, room temperature viscosity-pressure coefficient, room temperature viscosity-temperature coefficient, specific heat capacity, thermal conductivity and Eyring characteristic shear stress; the operating characteristic parameters of the face gear pair include the pinion speed in the direction of the minor axis of the tooth contact ellipse, the pinion speed in the direction of the major axis of the tooth contact ellipse, the face gear speed in the direction of the minor axis of the tooth contact ellipse, the face gear speed in the direction of the major axis of the tooth contact ellipse and the normal load capacity.

3. The method for predicting lubrication characteristics of a face gear pair based on a neural network model according to claim 1, characterized in that: Sampling the input variables to obtain training sample input parameters includes: sampling the input variables using a Latin hypercube sampling method to obtain training sample input parameters.

4. The method for predicting lubrication characteristics of a face gear pair based on a neural network model according to claim 1, characterized in that: The control equations of the non-Newtonian thermoelastic-hydrodynamic lubrication model include the non-Newtonian fluid constitutive model, the non-Newtonian thermoelastic-hydrodynamic Reynolds equation, the viscosity-pressure-temperature relationship, the density-pressure-temperature relationship, the film thickness equation, the force balance equation and the energy equation. The constitutive model of non-Newtonian fluid is as follows: in, For lubricant Flow velocity in the axial direction; For lubricant along Flow velocity in the axial direction; For along Shear stress in the axial direction; For along Shear stress in the axial direction; is the equivalent viscosity defined by the Eyring rheological model; is the apparent viscosity; is the hyperbolic sine function; is the Eyring characteristic shear stress, which is a constant; is an intermediate variable; for Axis direction; The non-Newtonian thermoelastic hydrodynamic Reynolds equation is as follows: in, is the density of the lubricant; is the oil film thickness; is the oil film pressure; , , , as well as They are all intermediate variables that characterize the density of lubricants; For along The entrainment velocity in the axial direction; For along The entrainment velocity in the axial direction; for Pinion speed in axial direction; for Face gear speed in axial direction; for Pinion speed in axial direction; for Face gear speed in axial direction; , It is an intermediate variable that characterizes the viscosity of the lubricant; For the inner integral Axis direction integration variable.

5. The method for predicting lubrication characteristics of a face gear pair based on a neural network model according to claim 4, characterized in that: The viscosity-pressure-temperature relationship is as follows: in, is the initial viscosity of the lubricant at ambient temperature; is a constant; is the temperature field; is the ambient temperature; is the viscosity-pressure coefficient; is the viscosity-temperature coefficient; is the viscosity-pressure coefficient at room temperature; is the temperature viscosity coefficient at room temperature; The density-pressure-temperature relationship is as follows: in, is the initial density of the lubricant at ambient temperature; is the density-temperature coefficient.

6. The method for predicting lubrication characteristics of a face gear pair based on a neural network model according to claim 5, characterized in that: The film thickness equation is as follows: in, is the rigid body displacement; is the tooth contact ellipse The equivalent radius of curvature in the axial direction; is the tooth contact ellipse The equivalent radius of curvature in the axial direction; is the equivalent elastic modulus; is the integration area; and The integral area Any point within The horizontal and vertical coordinates of The force balance equation is as follows: in, is the external load; The energy equation includes the energy equation of viscous fluid and the energy equation of solid; The energy equation for viscous fluid is as follows: in, is the specific heat capacity of the lubricant, which is a constant; is the thermal conductivity of the lubricant, which is a constant; is the temperature field; The energy equation for a solid is as follows: in, is the specific heat capacity of the pinion; is the density of the pinion; is the heat transfer coefficient of the pinion; For small gear The coordinate system in the axis direction, The axis directions are in the same direction; is the specific heat capacity of the face gear; is the density of the face gear; is the heat transfer coefficient of the face gear; For face gear The coordinate system in the axis direction, The axes are in the same direction.

7. A face gear pair lubrication characteristics prediction system based on a neural network model, characterized in that: include: A characteristic parameter acquisition module is used to acquire characteristic parameters of the face gear pair to be predicted; A performance prediction module, used for inputting characteristic parameters of the face gear pair to be predicted into the face gear pair lubrication characteristic prediction model, and outputting the prediction result of the face gear pair lubrication characteristic; The construction process of the face gear pair lubrication characteristics prediction model includes: Establish an artificial neural network model; determine the input variables and output variables of the artificial neural network model; wherein the input variables include the geometric parameters of the face gear pair, the material properties of the face gear pair, the lubricant properties and the operating characteristic parameters of the face gear pair; the output variables are the minimum oil film thickness, the center oil film thickness and the friction coefficient; sample the input variables to obtain the training sample input parameters; input the training sample input parameters into the non-Newtonian thermal elastic hydrodynamic lubrication model to solve the output variables and obtain the training sample output parameters; randomly divide the training sample input parameters and the training sample output parameters into a training set and a validation set, and use the training set and the validation set to train and validate the artificial neural network model to obtain a face gear pair lubrication characteristics prediction model.

8. A device for predicting lubrication characteristics of face gear pairs based on a neural network model, characterized in that: include: a processor suitable for executing a computer program; A computer-readable storage medium having a computer program stored therein, wherein when the computer program is executed by the processor, the method for predicting the lubrication characteristics of a face gear pair based on a neural network model as described in any one of claims 1 to 6 is executed.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for predicting the lubrication characteristics of a face gear pair based on a neural network model as described in any one of claims 1 to 6 is implemented.

10. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor, the method for predicting lubrication characteristics of a face gear pair based on a neural network model as described in any one of claims 1 to 6 is implemented.

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