Large rolling bearings are widely used in engineering and construction machinery, such as tower cranes, excavators and concrete pump trucks. On such occasions, the bearing should have a large bearing capacity and high reliability [1, 2]. In addition, large rolling bearings are also used in heavy equipment such as metallurgy and mining. Such bearings have a poor working environment, large load, high temperature, and large dust, which requires bearings to have a large bearing capacity, good sealing and high-temperature resistance [3–5]. Large rolling bearings are also used in offshore equipment, such as offshore platforms, various port cranes and deck cranes. It requires large rolling bearings to have high safety, good anti-corrosion, sealing and reliability [6]. Large rolling bearings are also used in wind turbine equipment and military equipment such as radar, antenna and airborne vehicles [7, 8]. Therefore, it is very necessary to design the channel structure and study the service life of a large four-point contact ball bearing.

Four-point contact ball bearings are used more and more in the aviation transmission system, automobile transmission systems, precision machinery and other aspects because of their advantages of many balls, large bearing capacity, two-way axial load, small axial space and high limit speed [9, 10]. With the progress of technology, users put forward higher requirements for the accuracy, performance, service life and reliability of bearings. The structural design of the cage directly affects the service performance of the bearing [11, 12]. S. Zupn, Z. pre and others believe that the flexible support of a large four-point contact ball bearing and the deformation of its ferrule have a great impact on the load distribution of the bearing. In this paper, two different models are established. After comparing the results, it is found that the deformation of flexible support and ferrule has a great impact on the load distribution of the bearing [13]. Jose

First, the channel structure parameters of a large four-point contact ball bearing are optimised by optimisation, and its fatigue life is analysed. At present, the fatigue life of rolling bearings is analysed according to the standard load rating life formula [22], but this formula is established based on ordinary bearings made of steel and does not consider the impact of bearing materials and their attribute changes on bearing life. There is a certain error in using this formula to calculate the life of large rolling bearings.

The geometric structure of four-point angular contact ball bearing is shown in Figure 1(a) [23]. The inner diameter of the bearing is _{i}_{M}_{W}_{I}_{0} are the radius of curvature of the inner and outer ring channels of the bearing respectively. The bearing channel is composed of four channel surfaces, of which ci1 is the curvature centre of the upper channel of the inner ring, _{i2} is the curvature centre of the lower channel of the inner ring, _{01} is the curvature centre of the upper channel of the outer ring, and _{02} is the curvature centre of the lower channel of the outer ring, _{i1} of the upper channel of the inner ring and the curvature centre _{02} of the lower channel of the outer ring, and the two ends of the other spring are the curvature centre _{i2} of the lower channel of the inner ring and the curvature centre _{01} of the upper channel of the outer ring. _{i1} is connected with the upper channel of the inner ring through two rigid rods, _{i2} is connected with the lower channel of the inner ring through two rigid rods, _{01} is connected with the upper channel of the outer ring through two rigid rods, and _{02} is connected with the lower channel of the outer ring through two rigid rods. The four-point angular contact ball bearing deforms under the action of external load, and its contact angle

The simplified finite element model of a large four-point angular contact ball bearing mainly uses the nonlinear spring connecting the centre points of curvature of two channels to simulate the compression of rolling elements [25, 26]. Therefore, the nonlinear spring only acts when in tension to simulate the compression of the bearing rolling element, which can well simulate the mechanical characteristics and geometric structure changes of the bearing under the action of load. As shown in Figure 2, under the action of load, the distance between the compression channels of the rolling element close to the curvature centre of the channel becomes larger. At this time, the compression of the rolling element can be simulated as the tension of the nonlinear spring connecting the curvature centre of the channel, The load-deformation curve of the spring in tension is defined according to the load-deformation relationship when the rolling element and the channel contact are compressed [27]. This method can not only analyse the load on the rolling element but also analyse the change of the contact angle between the rolling element and the channel through the displacement of the centre points _{i1}, _{i2}, _{01} and _{02} of the channel curvature.

The simplified finite element model of four-point angular contact ball bearing is shown in Figure 3.

General steps of stress life analysis method: first, calculate the isotropic stress, maximum and minimum stress, average stress and stress amplitude at the fatigue part of parts by theoretical method or finite element method, and then calculate the equivalent stress, equal effect stress amplitude and equal effect average stress by distortion energy theory; second, the reverse bending stress is calculated by selecting different fatigue analysis models in Table 1. Finally, the fatigue life is calculated according to the life calculation formula [28].

Calculation of stress in opposite direction

Fatigue model | Calculation formula |
---|---|

Gerber model | |

Modified Gerber model | |

SAE model | |

Soderberg model |

Midpoint data in S-N diagram

Fatigue model | _{f} | N_{f} | _{e} | N_{e} |
---|---|---|---|---|

Toughness and rigidity ( | ||||

Gerber theory | 0.9_{u} | 10^{3} | K_{u} | 10^{6} |

Modified Gerber theory | 0.9_{u} | 10^{3} | K_{u} | 10^{6} |

SAE theory | _{u} | 1 | K_{u} | 10^{6} |

Soderberg theory | 0.9_{u} | 10^{3} | K_{u} | 10^{6} |

Toughness and rigidity ( | ||||

Gerber theory | 0.9_{u} | 10^{3} | K_{u} | 10^{8} |

Modified Gerber theory | 0.9_{u} | 10^{3} | K_{u} | 10^{8} |

SAE theory | _{u} | 1 | K_{u} | 10^{8} |

Soderberg theory | 0.9_{u} | 10^{3} | K_{u} | 10^{8} |

The average amplitude of stress and strain can be calculated by the following formula:

_{m}_{a}_{m}_{a}

Von-Mises equivalent stress calculation formula is:

Equivalent force amplitude

Among _{n}_{y}

The average equivalent stress is:

The maximum principal strain criterion is to use the maximum strain amplitude of dangerous parts of parts _{a1} calculate the fatigue life by Manson coffin formula [29]:

The maximum shear strain criterion is to calculate the maximum shear strain of the dangerous part

The fatigue life is calculated by Manson’s coffin formula according to the maximum shear strain:

The maximum strain criterion is to calculate the equivalent strain of dangerous parts of parts by using the Von-Mises principle

Then use the Manson-Coffin formula to calculate the fatigue life of parts:

Fatigue damage accumulation theory includes Miner linear cumulative damage theory and cortan Dolan [24] modified damage theory. Miner linear cumulative damage theory is generally used for accumulation in the early stage of component design, because Miner linear cumulative damage theory is relatively simple, practical and convenient, but cortan Dolan modified damage theory considers the interaction between various groups of stresses, Therefore, the accuracy of calculating the service life of parts by the modified damage theory is higher than that by miner’s linear cumulative damage theory [30].

The total damage rate D calculated by Miner linear cumulative damage theory is as follows:

The calculation formula of Cortan-Dolan modified damage theory to calculate the life _{g}

Where _{1} is the component under the maximum constant amplitude load stress σ_{1} fatigue life, α is the ratio of the action times of group I constant amplitude load stress to the action times of total load, and D is the material constant [31].

The structural parameters of double row four-point angular contact ball bearing are shown in Figure 4. The influence of channel spacing x on the distribution of load on the two-channel rolling body is analysed. When the distance between the two channels of the bearing decreases, it is conducive to improve the bearing capacity of the bearing. However, with the decrease of channel spacing, the H-Side decreases, the stiffness of the side begins to decrease, and the deformation will increase under the action of load. The influence is analysed by establishing a simplified finite element model [32].

The calculation results of six groups of finite elements are shown in Table 3. According to the analysis results, when the distance between the two channels of the bearing is 105 mm, the maximum load on the first channel rolling element is 101.097 kn, the maximum load on the second channel rolling element is 137.313 kn, and the ratio of the maximum load of the first channel to the second channel rolling element is 0.7499. When the distance between the two channels of the bearing is 65 mm, the maximum load on the rolling element of the first channel is 107.778, the maximum load on the rolling element of the second channel is 126.754, and the ratio of the maximum load of the first channel to the rolling element of the second channel is 0.8503. When the bearing channel spacing gradually decreases from 105 mm to 65 mm, the maximum contact load on the first channel rolling element gradually increases from 103.097 kn to 107.778 kn, the maximum contact load on the second channel rolling element gradually decreases from 137.383 kn to 126.754 kn, and the ratio of the maximum value of the first channel load to the maximum value of the second channel load gradually increases from 0.7504 to 0.85029, which indicates that when the distance between the two channels of the bearing decreases, The closer the load is distributed between the first channel and the second channel.

Load comparison of two channels with different channel spacing

X/mm | 105 | 97 | 89 | 81 | 73 | 65 |
---|---|---|---|---|---|---|

1-Qmax/kN | 101.097 | 103.847 | 105.77 | 106.65 | 107.809 | 107.778 |

2-Qmax/kN | 137.313 | 137.211 | 133.59 | 131.39 | 129.510 | 126.754 |

Level | 0.7499 | 0.7568 | 0.79175 | 0.81170 | 0.83244 | 0.85029 |

In the process of reducing the channel spacing, the thickness of the retaining edge between the two channels will be reduced accordingly, which will reduce the stiffness of the retaining edge. Under the action of external load, the deformation of the retaining edge between the two channels will increase, which will reduce the mechanical properties and service life of the bearing. The maximum deformation of the retaining edge of each model is shown in Table 4. When the bearing channel spacing is 105 mm, the maximum deformation of the retaining edge is 0.1714 mm, when the bearing channel spacing is 81 mm, the maximum deformation of the retaining edge is 0.1572 mm, and when the bearing channel spacing is 65 mm, the deformation of the retaining edge is 0.1903 mm. It can be seen from the data in the table that when the bearing channel spacing gradually decreases from 105 mm to 81 mm, since the load on the first channel rolling element tends to be consistent with the load on the second channel rolling element, the load on the first channel rolling element increases, the load on the second channel rolling element decreases, and the deformation of the retaining edge between the first channel and the second channel gradually decreases from 0.1714 mm to 0.1572 mm. When the bearing channel spacing gradually decreases from 81 mm to 65 mm, Although the load on the first channel rolling element continues to be consistent with the load on the second channel rolling element, and the maximum load of the second channel decreases, the deformation of the retaining edge between the two channels increases from 0.1572 mm to 0.1903 mm due to the reduction of the stiffness of the retaining edge between the two channels.

Deformation of retaining edge at different channel spacing

Spacing/mm | 65 | 73 | 81 | 89 | 97 | 105 |
---|---|---|---|---|---|---|

Deformation/mm | 0.1903 | 0.1617 | 0.1572 | 0.1601 | 0.1648 | 0.1714 |

The Newton difference method is used to fit the difference between different channel spacing and retaining edge deformation, and the channel spacing at the minimum deformation of retaining edge is obtained. The Newton interpolation fitting curve of different channel spacing and retaining edge deformation is shown in Figure 5. From the fitting curve, it can be seen that the corresponding channel spacing is 78 mm.

The bearing channel spacing x = 80 mm is selected, and the finite element simplified model of large rolling bearing is used for modelling and analysis. The results are that the maximum load of the first channel is 107.777 kn and the maximum load of the second channel is 129.922 kn. The ratio of the maximum load of the first channel to the maximum load of the second channel is 0.8295. The deformation of the retaining edge between channels is shown in Figure 5. At this time, the maximum deformation of the retaining edge is 0.1569 mm. To sum up, it is reasonable to take 80 mm as the spacing between the two channels of the bearing.

Where _{w}

The influence of groove radius of curvature coefficient on bearing performance mainly includes: contact stress, friction torque, lubrication performance (oil film thickness). Since the rotating speed of large rolling bearings is low, generally no more than 10 R/min, and grease lubrication is adopted, the influence on lubrication is not considered here. When the bearing rotates, the steel ball makes a complex three-dimensional motion. That is, the rotation motion, revolution motion and spin sliding of the steel ball, so the friction in the rolling bearing is a complex tribological system. For heavy-duty low-speed rolling bearings with solid lubrication or grease lubrication, due to their low speed, the lubricating oil film cannot be formed, and there is certain friction between the rolling body and the channel. Its manifestation is the friction torque on the rotation axis of the bearing. The factors affecting the bearing friction torque include the micro slip between the rolling body and the channel, the elastic lag of the material at the contact between the rolling body and the channel, and the spin during the revolution of the rolling body, To consider the friction torque formed at the contact between the rolling element and the inner and outer rings of the bearing respectively by these three factors, the following assumptions should be made [33]:

In the process of contact with the inner and outer ring channels, the rolling body pure rolls with one channel and rolls and spins with the other channel.

Micro slip only appears on the channel contact surface where the rolling element and the channel are pure rollings, and the elastic hysteresis of the material at the contact between the rolling element and the channel appears on the inner and outer ring channels in contact with the rolling element at the same time.

The sliding friction coefficient between the rolling element and the channel is a fixed value, which is independent of the contact stress between them.

Because there is a certain speed difference in the contact area during the contact between the rolling body and the channel, there is not only pure rolling but also sliding in the contact area. The following equilibrium equation can be obtained:

Among

Q – contact load of rolling element, N; E ‘– equivalent elastic modulus, MPa; _{w}

The resistance caused by micro sliding is:

Among:

The rolling resistance Fm generated by micro sliding acts on the bearing rolling element. At this time, there are two situations: one is that the micro sliding of the rolling element in contact with the channel appears on the contact surface with the outer channel; Second, the micro slip of the contact between the rolling element and the channel appears on the contact surface with the inner channel. Therefore, there are two forms when the rolling resistance generated by micro sliding is transformed into the friction torque of the bearing [24].

First, micro slip occurs on the contact surface between the rolling element and the outer channel. At this time, there are:

First, micro slip occurs on the contact surface between the rolling element and the inner channel. At this time, there are:

Where _{i}

To sum up, if the groove radius of curvature coefficient is too large, the bearing contact stress is large, and the bearing life is reduced. If it is too small, the total friction resistance moment will increase and the bearing friction will increase proportionally. Normalise the contact stress and friction resistance moment and draw them on the same figure. As shown in Figure 6, the intersection of the two curves is the optimal groove curvature radius coefficient. The best value is 0.524.

The stress life and strain life analysis are used to analyse the fatigue life of the bearing after changing the bearing structure. After changing the bearing structure, the maximum contact load between the rolling element and the channel is 130.5 kN, the maximum contact pressure stress between the rolling element and the inner ring channel is 3148.5 MPa, the maximum contact pressure stress between the rolling element and the outer ring channel is 3100 MPa, and the maximum equivalent stress on the contact subsurface between the rolling element and the outer ring is 1976.7 MPa. The maximum shear strain of the contact subsurface between the rolling element and the outer ring is 12.24×10^{−3} mm. The fatigue life of the bearing after changing the bearing structure is shown in Table 5.

Bearing life

Life calculation method | |||
---|---|---|---|

σ-N | ε-N | ||

N (2Nf) | [·10^{6}cyc] | 12.190 | 7.26 |

L | [·10^{4}cyc] | 21.818 | 12.91 |

The bearing life calculated by the stress life model is 21.818×10^{4}r. The bearing life calculated by the strain life model is 12.91×10^{4}r. The calculation result of the stress life model is 1.699 times that of strain life.

Firstly, the structure and simplified model of four-point contact ball bearing are introduced, and the analysis method of fatigue life is introduced. The channel parameters of four point contact ball bearing are designed and optimised. First, the bearing finite element calculation results are analysed, then the bearing channel spacing is optimised, and finally, the parameters of the channel curvature radius coefficient are optimised. After the design and optimization of the channel parameters of four point contact ball bearing, the fatigue life is analysed, The conclusions are as follows: (1) for double row four-point contact ball bearing, the smaller the channel spacing is, the more uniform the load is in the two channels, which can reduce the maximum load of the bearing, but the deformation of the retaining edge between the two channels will increase after the channel spacing is reduced to a certain extent; (2) For ball bearings, when the load on the rolling element is constant, the maximum contact compressive stress between the rolling element and the channel, the maximum equivalent stress and the maximum shear strain on the secondary surface of the channel decrease with the decrease of the curvature radius coefficient of the channel; (3) For the optimised bearing life, the result of the model calculation is significantly higher than that of the first case of strain calculation.

#### Deformation of retaining edge at different channel spacing

Spacing/mm | 65 | 73 | 81 | 89 | 97 | 105 |
---|---|---|---|---|---|---|

Deformation/mm | 0.1903 | 0.1617 | 0.1572 | 0.1601 | 0.1648 | 0.1714 |

#### Calculation of stress in opposite direction

Fatigue model | Calculation formula |
---|---|

Gerber model | |

Modified Gerber model | |

SAE model | |

Soderberg model |

#### Bearing life

Life calculation method | |||
---|---|---|---|

σ-N | ε-N | ||

N (2Nf) | [·10^{6}cyc] |
12.190 | 7.26 |

L | [·10^{4}cyc] |
21.818 | 12.91 |

#### Midpoint data in S-N diagram

Fatigue model | _{f} |
N_{f} |
_{e} |
N_{e} |
---|---|---|---|---|

Toughness and rigidity ( |
||||

Gerber theory | 0.9_{u} |
10^{3} |
K_{u} |
10^{6} |

Modified Gerber theory | 0.9_{u} |
10^{3} |
K_{u} |
10^{6} |

SAE theory | _{u} |
1 | K_{u} |
10^{6} |

Soderberg theory | 0.9_{u} |
10^{3} |
K_{u} |
10^{6} |

Toughness and rigidity ( |
||||

Gerber theory | 0.9_{u} |
10^{3} |
K_{u} |
10^{8} |

Modified Gerber theory | 0.9_{u} |
10^{3} |
K_{u} |
10^{8} |

SAE theory | _{u} |
1 | K_{u} |
10^{8} |

Soderberg theory | 0.9_{u} |
10^{3} |
K_{u} |
10^{8} |

#### Load comparison of two channels with different channel spacing

X/mm | 105 | 97 | 89 | 81 | 73 | 65 |
---|---|---|---|---|---|---|

1-Qmax/kN | 101.097 | 103.847 | 105.77 | 106.65 | 107.809 | 107.778 |

2-Qmax/kN | 137.313 | 137.211 | 133.59 | 131.39 | 129.510 | 126.754 |

Level | 0.7499 | 0.7568 | 0.79175 | 0.81170 | 0.83244 | 0.85029 |

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Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsResearch on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network