Method for constructing mathematical model of oil churning loss of covered gear in vehicle transmission system

Abstract

The present invention discloses a method for constructing a mathematical model of oil stirring loss of a covered gear in a vehicle transmission system, and relates to the technical field of gear transmission. The method comprises: building an oil stirring test bench, configuring a plurality of shield structures with different design parameters; collecting the oil stirring resistance torque of the covered gear at different speeds under different shield structures; constructing a basic model of oil stirring loss of the covered gear, using a plurality of undetermined parameters to describe the mathematical relationship between the oil stirring loss influencing factor and the structural parameters of the covered gear; using a plurality of undetermined coefficients to construct a mathematical relationship between each undetermined parameter and the gear speed; substituting the optimal solution of each undetermined coefficient into the mathematical relationship, and then substituting the relationship between each undetermined parameter and the gear speed into the basic model to obtain a mathematical model of oil stirring loss of the covered gear. Through the present invention, the construction of a model of oil stirring loss of the covered gear can be realized, providing an effective tool for evaluating and optimizing the oil stirring loss of the covered gear.

Description

Technical Field

[0001] The present invention relates to the technical field of gear transmission, and in particular to a method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system. Background Art

[0002] With the growing global demand for environmental protection and sustainable development, new energy products (particularly electric drive technologies) have achieved significant progress in both performance and sales across the passenger car, commercial vehicle, and construction machinery industries. The widespread adoption of these new energy vehicles not only marks a milestone in technological advancement but also has a profound impact on the transformation of the energy structure of our economy and society. Their widespread adoption has significantly reduced our economy and society's dependence on non-renewable resources like oil and natural gas, providing crucial support for promoting the sustainable and healthy development of a green economy and society.

[0003] In electric drive transmissions, gear systems are essential components due to their superior performance, including high transmission efficiency, long life, and wide speed ratio range. To further optimize transmission system efficiency, especially in high-power transmissions, oil baffles are often installed around the gears. These baffles are designed to reduce energy losses caused by the oil churning effect during gear rotation, thereby improving the overall operating efficiency of the system. The actual effectiveness of the oil baffle during gear operation and its ability to suppress churning losses are important factors affecting transmission system efficiency. Accurately predicting the energy losses during lubrication of covered gears and their surrounding components has become a key technical challenge in the design of efficient electric drive transmissions. Currently, research on mathematical models for the churning loss behavior of covered gears is still in its early stages, lacking a theoretical framework that can comprehensively and accurately describe this complex phenomenon. Therefore, evaluating churning losses in covered gears through more economical and reliable strategies has become a core task in the lubrication design of electric drive systems, and is of great significance to the future development of efficient electric drive technologies. Summary of the Invention

[0004] The object of the present invention is to provide a method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system, so as to realize the construction of a model of oil churning loss of a covered gear.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] According to one aspect of the present invention, a method for constructing a mathematical model of oil stirring loss of a covered gear of a vehicle transmission system is provided, comprising: constructing an oil stirring test bench including a gear and a shield, and configuring a plurality of shield structures with different design parameters; based on the constructed oil stirring test bench, collecting the oil stirring resistance torque of the covered gear at different speeds under different shield structures, and calculating the oil stirring loss influencing factors of different shield structures; constructing a basic model of oil stirring loss of the covered gear, wherein the independent variables of the model are the structural parameters of the covered gear, and the dependent variables are the oil stirring loss influencing factors, and a plurality of undetermined parameters are used to describe the mathematical relationship between the oil stirring loss influencing factors and the structural parameters of the covered gear; and the obtained different shields are used to determine the oil stirring loss influencing factors. The oil stirring loss influencing factor of the structure and the corresponding structural parameters of the covered gear are substituted into the basic model for solution to obtain the values of each undetermined parameter at different speeds; a mathematical relationship between each undetermined parameter and the gear speed is constructed using multiple undetermined coefficients, and the mathematical relationship is fitted according to the obtained values of each undetermined parameter at different speeds and the corresponding gear speeds to obtain the optimal solution of each undetermined coefficient; the optimal solution of each undetermined coefficient is substituted into the mathematical relationship to obtain the relationship between each undetermined parameter and the gear speed, and then the relationship between each undetermined parameter and the gear speed is substituted into the basic model to obtain the mathematical model of oil stirring loss of the covered gear.

[0007] Optionally, the design parameters of the guard structure in the oil stirring test bench include tooth top clearance, axial clearance, and radial clearance; the structural parameters of the covered gear in the oil stirring loss basic model of the covered gear include tooth top clearance, axial clearance, radial clearance, gear pitch circle radius, gear module, and tooth width.

[0008] Optionally, the collecting of the oil stirring resistance torque of the covered gears under different shield structures at different speeds and the calculation of the oil stirring loss influence factors of the different shield structures include: for each speed, collecting the first oil stirring resistance torque of the gear without a shield, and collecting the second oil stirring resistance torque of the covered gear under each shield structure; for each shield structure and each speed, the ratio of the second oil stirring resistance torque to the first oil stirring resistance torque is the oil stirring loss influence factor of the corresponding shield structure at the speed.

[0009] Optionally, the basic model includes four undetermined parameters, which are the first undetermined parameter , the second undetermined parameter , the third undetermined parameter 、The fourth undetermined parameter , the mathematical relationship expression of the basic model is as follows:

[0010] ;

[0011] Where, represents the influencing factor of churning loss; is the tooth tip clearance; is the axial clearance; is the radial clearance; is the gear pitch radius; is the gear module; is the tooth width.

[0012] Optionally, using multiple undetermined coefficients to construct a mathematical relationship between each undetermined parameter and the gear speed includes: using the first undetermined coefficient and the second undetermined coefficient Establish the first pending parameter Speed of gear with cover n The power function relationship between ; Using the third undetermined coefficient Establish the second pending parameter Speed of gear with cover n The constant function relationship between ; Using the fourth undetermined coefficient and the fifth undetermined coefficient Establish the third pending parameter Speed of gear with cover n The logarithmic function relationship between ; Using the sixth undetermined coefficient and the seventh undetermined coefficient Establish the fourth pending parameter Speed of gear with cover n The logarithmic function relationship between .

[0013] Optionally, fitting the mathematical relationship according to the obtained values of each undetermined parameter at different speeds and the corresponding gear speeds, and solving the optimal solution for each undetermined coefficient includes: using a curve fitting strategy driven by the least squares method to fit the mathematical relationship between each undetermined parameter and the gear speed, when the sum of the squares of the vertical distances between the actual data points and the fitted curve is minimized, determining it as the best fitting curve, and obtaining the values of each undetermined coefficient according to the equation of the fitted best fitting curve.

[0014] Optionally, after obtaining the mathematical model of the oil stirring loss of the covered gear, the method further includes: using the BP neural network and the particle swarm optimization algorithm to construct an intelligent prediction model, and introducing the NSGA-III algorithm to construct a multi-objective optimization framework to optimize the intelligent prediction model, wherein the intelligent prediction model is used to solve the influencing factor of the oil stirring loss of the covered gear, the particle swarm optimization is used to improve the versatility of the prediction model, and the NSGA-III algorithm is used to simultaneously seek the comprehensive minimum oil stirring loss influencing factor under different cover configurations.

[0015] The present invention systematically constructs a mathematical model of the oil churning loss of the covered gear of a vehicle transmission system through the steps of building a test bench, collecting data, constructing a basic model, establishing mathematical relationships, and solving model parameters, providing an effective tool for evaluating and optimizing the oil churning loss of the covered gear.

[0016] The present invention constructs a mathematical model of the oil stirring loss of covered gears taking into account the near-wall turbulence effect, collects and fits data through cover structures with various design parameters, establishes a general calculation formula for the oil stirring loss factor of the covered gear model, and converts the engineering problem of high-speed gear oil stirring loss into a mathematical problem through simple mathematical configuration, thereby obtaining a mathematical model of oil stirring loss suitable for different cover structures. The model can accurately reflect the oil stirring loss of covered gears under different cover structures and speeds, and realizes high-precision prediction of the oil stirring loss of covered gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0018] Figure 1 4 is a flow chart of a method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] In order to enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only embodiments of a part of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work should fall within the scope of protection of this application. It should be noted that, in the absence of conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0020] It should be noted that the terms "first", "second", etc. in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequential order. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0021] In this embodiment, a method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system is provided.

[0022] Reference Figure 1 , Figure 1 FIG. 1 is a flow chart of a method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system according to an embodiment of the present invention. Figure 1 As shown, the method includes the following steps:

[0023] Step 1: Build an oil stirring test bench including gears and shields, and configure shield structures with various design parameters;

[0024] In order to evaluate the oil stirring loss of covered gears, this embodiment builds an oil stirring test bench including gears and shields, and establishes four shield configurations with different tooth top clearance, radial clearance, and axial clearance to carry out oil stirring tests. The four shield configurations are used to study the influence of different shield clearances on the oil stirring loss, and provide data for mathematical modeling to obtain a more universal mathematical modeling model for the oil stirring loss of covered gears.

[0025] Tip clearance refers to the gap between the gear tooth tip and the inner wall of the shield; radial clearance refers to the gap between the gear shaft and the shield side plate in the direction perpendicular to the gear axis. Axial clearance refers to the gap between the gear end face and the shield side plate in the direction along the gear axis.

[0026] The shield configuration 1 with specific tooth top clearance, axial clearance and radial clearance is taken as the basic configuration. On the basis of configuration 1, the tooth top clearance is changed to obtain shield configuration 2, the axial clearance is changed to obtain shield configuration 3, and the radial clearance is changed to obtain shield configuration 4. The specific configuration data can be selected according to experimental requirements or actual conditions.

[0027] Step 2: Based on the constructed oil stirring test bench, the oil stirring resistance torque of the covered gear under different shroud structures at different speeds is collected to calculate the oil stirring loss influencing factors of the different shroud structures;

[0028] The oil churning loss influencing factor refers to the ratio of the oil churning loss of the gear with a shield to the oil churning loss of the gear without a shield, which reflects the degree to which the shield structure reduces the gear oil churning resistance, that is, the relative size of the oil churning loss.

[0029] The oil stirring test bench built in step 1 is used to conduct splash lubrication behavior tests on covered gears. The oil stirring resistance torques under four shield configurations are collected at different speeds, as well as the oil stirring resistance torques when no shield is configured at the corresponding speeds. The oil stirring loss influencing factors of different shield structures are calculated based on the ratio of the oil stirring resistance torque when the shield is configured to the oil stirring resistance torque when the shield is not configured, so as to study the relationship between the oil stirring loss and the shield design parameters, thereby better optimizing the efficiency of the gear system.

[0030] Specifically, for each speed, the first oil stirring resistance torque of the gear without a shroud is collected, as is the second oil stirring resistance torque of the gear with a shroud for each shroud configuration. For each shroud configuration and each speed, the ratio of the second oil stirring resistance torque to the first oil stirring resistance torque is the oil stirring loss influence factor for the corresponding shroud configuration at that speed. This formula is expressed as: Where, represents the influencing factor of churning loss; T ch is the oil stirring resistance torque of the model with shroud, unit is N·m; T ref is the oil stirring resistance torque of the gear model without a shield at the same speed, in N·m.

[0031] In one example, the speed range is set from 100 rpm to 5000 rpm, and data is recorded every 100 rpm, with 50 sets of data (50 speed points) recorded. A torque sensor is used to measure the oil stirring resistance torque at each speed, and data is collected for each of the four shroud configurations, obtaining a total of 200 sets of data (4 configurations × 50 sets of data). Data is also collected for gears without shrouds, obtaining 50 sets of data. The collected oil stirring resistance torque data are sorted and analyzed, and the changing trends of the oil stirring resistance torque with speed and design parameters (tooth top clearance, axial clearance, and radial clearance) are observed. The oil stirring losses under different shroud configurations are compared, and the oil stirring loss influencing factors of different shroud structures are obtained.

[0032] Step 3: Construct a basic model of oil churning loss for a covered gear. The independent variables of the model are the structural parameters of the covered gear, and the dependent variables are the oil churning loss influencing factors. Multiple undetermined parameters are used to describe the mathematical relationship between the oil churning loss influencing factors and the structural parameters of the covered gear.

[0033] The commonly used expression for gear churning loss is:

[0034] ;

[0035] Where, Indicates gear churning loss, unit is w, Indicates the circumferential friction resistance of the gear, in N. Indicates the friction resistance of the gear tooth surface, unit is N, Indicates the rotation speed, unit is rad / s, The value is the gear pitch circle radius, that is, Dp / 2 (Dp is the gear pitch circle diameter), Indicates oil density in kg / m 3 , Indicates the gear oil immersion depth, unit is m, is the dimensionless torque;

[0036] The basic model of oil churning loss for shrouded gears in the embodiments of the present invention is based on the mathematical model of oil churning loss for gears with flanges or baffles developed by Changenet et al., as follows:

[0037] ;

[0038] Where, is the gear churning loss, unit is W; It represents the oil churning loss of the shroud model, in W; 、 are the gear pitch circle radius and diameter respectively, in m; is the outer arc diameter of the shield, in m; is the axial clearance between the side plate and the tooth end, in m; Indicates the gear speed, unit is rad / s; Indicates the kinematic viscosity of lubricating oil, unit: m 3 / s; is the gear module (which can be calculated by gear pitch diameter / number of teeth, or tooth pitch / pi); is the tooth width, unit is m.

[0039] Since the above mathematical model cannot characterize the churning loss of the shrouded gear, in order to describe the churning loss of the shrouded gear, the embodiment of the present invention fully considers the influence of the shroud in all directions on the oil flow around the gear, and establishes a general basic model of the churning loss factor of the shrouded gear model based on the Vaschy-Buckingham theory. The model calculation formula is as follows:

[0040] ;

[0041] Where, represents the influencing factor of churning loss; is the tooth tip clearance; is the axial clearance; is the radial clearance; is the gear pitch radius; is the gear module; is the tooth width.

[0042] In this formula, the structural parameters of the gear and the shield ( 、 、 、 、 、 ) is the independent variable, and the influencing factor of churning loss ( ) is the dependent variable, ~ These are the undetermined parameters, which are the constant terms of the formula and are determined through subsequent data fitting, optimization algorithms, etc.

[0043] This formula introduces the shield configuration parameters and can be applied to different shield configurations. In the embodiment of the present invention, the oil stirring test bench is equipped with four shield configurations S1 to S4. Substituting them into the above basic model, the following equations can be obtained:

[0044] ;

[0045] Where, ~ represents the oil churning loss influence factors corresponding to the four shroud configurations; ~ Indicates the tooth tip clearance corresponding to the four guard configurations; ~ Indicates the axial clearance corresponding to the four shield configurations; ~ Indicates the radial clearance corresponding to the four shroud configurations.

[0046] Step 4: Substitute the obtained oil churning loss influencing factors of different shroud structures and the corresponding shrouded gear structural parameters into the basic model to obtain the values of each unknown parameter at different speeds;

[0047] Substitute the oil stirring loss influencing factors of the four different shroud structures determined based on the test data in step 1 and the corresponding configuration of the shrouded gear structure parameters into the equation group in step 3 above, and use the built-in solver of MATLAB to solve the corresponding unknown parameters at each speed. ~ value.

[0048] Step 5: Using multiple undetermined coefficients to construct a mathematical relationship between each undetermined parameter and the gear speed, fitting the mathematical relationship based on the obtained values of each undetermined parameter at different speeds and the corresponding gear speeds, and solving to obtain the optimal solution for each undetermined coefficient;

[0049] According to the evolution trend of the four undetermined parameters with the gear speed, after multiple experiments, the embodiment of the present invention uses power function, constant function and logarithmic function to track the evolution of parameters with the speed, and proposes ~ The seven undetermined coefficients are fitted to obtain the mathematical expression between each undetermined parameter and the speed of the covered gear, as follows:

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] Using the first undetermined coefficient and the second undetermined coefficient Establish the first pending parameter Speed of gear with cover n The power function relationship between them; using the third unknown coefficient Establish the second pending parameter Speed of gear with cover n The constant function relationship between them; using the fourth unknown coefficient and the fifth undetermined coefficient Establish the third pending parameter Speed of gear with cover n The logarithmic function relationship between the six unknown coefficients and the seventh undetermined coefficient Establish the fourth pending parameter Speed of gear with cover n The logarithmic function relationship between them. n is the gear speed, unit is r / min.

[0055] The corresponding undetermined parameters at each speed obtained in step 4 are ~ The value of and the corresponding speed are fitted into the above four mathematical relationships to obtain the various unknown coefficients. ~ The optimal solution of .

[0056] Among them, solving the optimal solution of each undetermined coefficient includes: using the least squares method to drive the curve fitting strategy to fit the mathematical relationship between each undetermined parameter and the gear speed, assuming that The relevant data sets have random errors and satisfy the independent and identically distributed normal distribution. When the sum of the squares of the vertical distances between the actual data points and the fitting curve is minimized, it is determined to be the best fitting curve. The values of each unknown coefficient are obtained according to the equation of the fitted best fitting curve.

[0057] The goal of the least squares method is to minimize the error function:

[0058] ;

[0059] Where, N is the number of sample points in the data set, i is the index of the dataset sample; l It is known by a Parameterized speed n The function of , consisting of the minimum number of coefficients. The parameter seta Contains several undetermined coefficients ( ~ ), once the parameter set a Knowing that, we can uniquely determine the function l . for l The measured value of l ( , a ) to determine its value ( is the speed n measured value).

[0060] Fitting the function by using the least squares method l To the data set, by minimizing the error function s(a) , we can get the parameter set a The optimal solution is to find the parameter set that minimizes the sum of the squares of the vertical distances between the actual data points and the fitted curve. a .

[0061] The accuracy of curve fitting can be measured using R 2 To evaluate, as shown in the following formula. The coefficient of determination R 2 It represents the ratio of the regression sum of squares to the total sample sum of squares;

[0062] ;

[0063] in, P and Q are the fitted data and actual data, respectively, R 2 The closer the value is to 1, the better the fitting effect is.

[0064] Step 6: Substitute the optimal solution of each undetermined coefficient into the mathematical relationship to obtain the relationship between each undetermined parameter and the gear speed, and then substitute the relationship between each undetermined parameter and the gear speed into the basic model to obtain the mathematical model of oil stirring loss of the covered gear.

[0065] The mathematical model of oil stirring loss of the covered gear is used to reflect the oil stirring loss of the covered gear under different cover structures and speeds. The optimal solution of each undetermined coefficient obtained in step 5 is substituted into step 5. ~ In the mathematical relationship of ~ and gear speed n Then, substitute these relationships into the basic model constructed in step 3 The complete mathematical model of oil churning loss of covered gears is obtained in the formula. This model can be used to predict the influencing factors of oil churning loss under different cover structures and speeds, providing a theoretical basis for the design and optimization of gear systems.

[0066] In addition, the present invention also uses a BP neural network and a particle swarm optimization (PSO) algorithm to build an intelligent prediction model, and introduces the NSGA-III algorithm to build a multi-objective optimization framework. The PSO-BP and NSGA-III algorithms are run in MATLAB 2021.

[0067] By using the seven characteristic variables in the mathematical model and combining the error back propagation algorithm, an intelligent prediction model for the churning loss coefficient based on BP neural network was established. In order to improve the generalization ability of the proposed mathematical model, the NSGA-III algorithm was introduced to reduce the error of the mathematical model.

[0068] Among them, the stirring loss influence coefficient prediction model based on the BP neural network consists of an input layer, a hidden layer, and an output layer. The input layer receives the sample matrix obtained by the experimental design (including parameters such as gear speed, tooth top clearance, axial clearance, radial clearance, gear pitch radius, gear module, and tooth width), passes it to the internal information processing layer, and then passes it to the output layer (the stirring loss influence coefficient error corresponding to each shield), and finally completes the forward propagation process. The input layer transmits the data to the internal information processing layer, and then to the output layer (the stirring loss influence coefficient error corresponding to different shields). Finally, the forward propagation process is completed. If the stirring loss influence coefficient is different from the expected value, the deviation will move in the opposite direction of the previous positive learning, and the gradient descent method will be used to correct the weight to minimize the deviation. The output of the neural network is shown in the following formula:

[0069] ;

[0070] Where, is the output value of the jth neuron in the output layer; is the input of the jth neuron; For input signal The connection weight between the output layer; is the threshold of the kth neuron, where k represents the layer number in the neural network.

[0071] Update the weights according to the strategy shown below:

[0072] ;

[0073] ;

[0074] Where, is the learning rate; is the weight between the i-th input and the j-th neuron; x ( i ) is the input value of BP neural network; is the number of nodes in the output layer; is the error term;

[0075] The thresholds are updated as follows:

[0076] ;

[0077] is the threshold of the jth neuron.

[0078] Particle swarm optimization (PSO) is an optimization strategy inspired by the hunting behavior of birds. By sharing information among individuals, the entire swarm achieves a transition from a disordered state to an ordered state in the solution space. The PSO algorithm (PSO) uses this principle to obtain the optimal solution, boasting fast search speed and high accuracy. In the PSO algorithm, the particle swarm is first initialized with a random solution, and then iterates until the optimal solution is found.

[0079] NSGA (Non-dominated Sorting Genetic Algorithms) is a genetic algorithm based on the concept of Pareto optimality. NSGA-III is an improved version of NSGA-II, primarily optimizing the survival selection mechanism. NSGA-III utilizes widely distributed and adaptively updated reference points to maintain diversity among population members. The optimization objective of NSGA-III is to simultaneously find the minimum combined churn loss coefficient under four shroud configurations. NSGA-III generates a set of equally important solutions, known as Pareto (non-dominated) solutions, which represent the optimization objective under the four shroud configurations, ensuring a comprehensive solution for space exploration.

[0080] The steps in the above-described embodiments of the present invention may be adjusted in order, combined, or deleted as needed. The various technical features may be combined in any manner. To simplify the description, not all possible combinations of the various technical features in the embodiments are described. However, as long as there are no contradictions in the combination of these technical features, they should be considered to be within the scope of the present invention.

[0081] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system, characterized in that: include: Build an oil stirring test bench including gears and shields, and configure shield structures with various design parameters; Based on the constructed oil stirring test bench, the oil stirring resistance torque of the covered gears with different shroud structures at different speeds was collected, and the oil stirring loss influencing factors of different shroud structures were calculated. A basic model of oil churning loss of covered gear is constructed. The independent variables of the model are the structural parameters of the covered gear, and the dependent variables are the oil churning loss influencing factors. Multiple undetermined parameters are used to describe the mathematical relationship between the oil churning loss influencing factors and the structural parameters of the covered gear. The multiple undetermined parameters are the first undetermined parameters , the second undetermined parameter , the third undetermined parameter 、The fourth undetermined parameter The mathematical expression of the basic model of oil churning loss of covered gear is as follows: ； Where, represents the influencing factor of churning loss; is the tooth tip clearance; is the axial clearance; is the radial clearance; is the gear pitch radius; is the gear module; is the tooth width; Substituting the obtained oil stirring loss influencing factors of different shroud structures and the corresponding shrouded gear structural parameters into the basic model to solve and obtain the values of each unknown parameter at different speeds; A mathematical relationship between each undetermined parameter and the gear speed is constructed using multiple undetermined coefficients. The mathematical relationship is fitted based on the values of each undetermined parameter at different speeds and the corresponding gear speeds to obtain the optimal solution for each undetermined coefficient. Substituting the optimal solution of each undetermined coefficient into the mathematical relationship to obtain the relationship between each undetermined parameter and the gear speed, and then substituting the relationship between each undetermined parameter and the gear speed into the basic model to obtain the mathematical model of oil stirring loss of the covered gear; The mathematical relationship between each undetermined parameter and the gear speed is constructed using multiple undetermined coefficients, including: Using the first undetermined coefficient and the second undetermined coefficient Establish the first pending parameter Speed of gear with cover n The power function relationship between ; Using the third undetermined coefficient Establish the second pending parameter Speed of gear with cover n The constant function relationship between ; Using the fourth undetermined coefficient and the fifth undetermined coefficient Establish the third pending parameter Speed of gear with cover n The logarithmic function relationship between ; Using the sixth undetermined coefficient and the seventh undetermined coefficient Establish the fourth pending parameter Speed of gear with cover n The logarithmic function relationship between .

2. The method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system according to claim 1, characterized in that: The design parameters of the shield structure in the oil stirring test bench include tooth top clearance, axial clearance, and radial clearance; The structural parameters of the covered gear in the basic model of oil churning loss of the covered gear include tooth top clearance, axial clearance, radial clearance, gear pitch circle radius, gear module, and tooth width.

3. The method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system according to claim 1, wherein: The oil stirring resistance torque of the covered gear at different speeds under different cover structures is collected, and the oil stirring loss influencing factors of different cover structures are calculated, including: For each speed, the first oil stirring resistance torque of the gear without a shield is collected, and the second oil stirring resistance torque of the gear with a shield under each shield structure is collected; For each shroud structure and each rotational speed, the ratio of the second oil stirring resistance torque to the first oil stirring resistance torque is the oil stirring loss influence factor of the corresponding shroud structure at the rotational speed.

4. The method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system according to claim 1, wherein: According to the obtained values of the unknown parameters at different speeds and the corresponding gear speeds, the mathematical relationship is fitted to obtain the optimal solutions of the unknown coefficients, including: A curve fitting strategy driven by the least squares method is used to fit the mathematical relationship between each undetermined parameter and the gear speed. When the sum of the squares of the vertical distances between the actual data points and the fitted curve is minimized, the best fitting curve is determined. The values of each undetermined coefficient are obtained according to the equation of the fitted best fitting curve.

5. The method for constructing a mathematical model of oil churning loss of a covered gear in a vehicle transmission system according to claim 4, characterized in that: After obtaining the mathematical model of oil churning loss of the covered gear, the method further includes: An intelligent prediction model is constructed using BP neural network and particle swarm optimization algorithm, and the NSGA-III algorithm is introduced to construct a multi-objective optimization framework to optimize the intelligent prediction model. The intelligent prediction model is used to solve the influencing factor of oil churning loss of covered gears, the particle swarm optimization is used to improve the versatility of the prediction model, and the NSGA-III algorithm is used to simultaneously seek the comprehensive minimum oil churning loss influencing factor under different cover configurations.

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