The rapid development of the new energy industry reflects the importance of green and low-carbon transportation. However, short battery life and limited range limit its development. For new-energy vehicles, weight loss means more mileage. Research shows that when the total vehicle weight of a pure electric vehicle decreases by 10KG, the range can increase by 5%–6%. The lightweight of the automobile becomes the direction that more automobile manufacturers pay attention to. The technology of plastic instead of steel is one of the important means of vehicle lightweight. The weight of the automobile can be greatly reduced by replacing the original steel parts with plastics under the condition that the service performance of the product is invariable. The proportion of plastic parts in the whole car parts is increasing, including the whole car interior and exterior trim parts and even functional parts and structural parts.

An important role in improving the quality of plastic parts. However, many times of traditional model tests, not only will reduce the production efficiency, but also lack of scientific basis. With the emergence of injection molding CAE technology and CAE simulation of the molding process, the influence of processing conditions, molding conditions, mold design, and runner design was analyzed and predicted, thus, the possible defects in the molding process can be simulated. It is of great significance to obtain high-quality plastic products.

In this paper, the new energy automobile front-end frame of a factory is studied, and the traditional sheet metal is replaced by polypropylene plastic. Then the mechanical performance is proved by hyper mesh, and the injection molding process is simulated by Moldflow. In this paper, through the design of the orthogonal test, selection of test factors and evaluation indicators, the simulation results of variance analysis, and range analysis to find out the impact of test factors on the experimental objectives, to reduce the defects of the optimal parameter combination.

According to the requirements of manufacturers, the automobile front-end frame is modeled by UG software. The original sheet metal quality is 10.5 kg, if plastic instead of steel for polypropylene PPLGF30, the quality is 6.8 kg, weight loss of 3.7 kg. Its structure must meet certain mechanical performance before production, and mechanical analysis is done in the hyper mesh. Therefore, we need to carry out a finite element analysis. The original data model is imported into Hyper Mesh to preprocess the 3D model, and the Mesh is divided. Then we apply a load to add a rigid connection element Reb 2 near the force point frame engine lock grid. As shown in Figure 1, using the mid-level technique, the mid-level is automatically extracted and manually repaired. It uses 5mm as the edge length of the global grid to divide the product grid and automatically sets the thickness as shown in Figure 2.

The Opti struct solver in the hyper mesh is used to analyze the six main stress points of the front-end frame. They are, respectively, the limit tension of the latch, the cushioning impact, the pedestrian impact, the condenser support strength, the radiator support strength, and the oil cooler support strength. The results of the static analysis are shown in Table 1.

Information table of statics analysis

Load | Size/(N) | Mounting point displacement/mm | Maximum stress / (Mpa) | Design requirements/(mm) | Whether it meets the design requirements |
---|---|---|---|---|---|

Lock limit pull | 5200 | 15 | 139 | 15 | Yes |

Cushion impact | 1000 | 0.8 | 20 | 4 | No |

Pedestrian impact | 4900 | 15 | 208 | 20 | Yes |

Condenser support strength | 390 | 0.6 | 6.8 | 3 | No |

Radiator support strength | 360 | 0.6 | 5.6 | 3 | Yes |

Oil cooler installation strength | 180 | 0.3 | 3.6 | 2 | Yes |

The speed of a car on the road is not always the same. As a result, the force on the engine lock changes alternately. To prevent fatigue failure under alternating stress, we also need to carry on the fatigue analysis to the plastic part. According to the data provided by the manufacturer, the stress sub-value is 1000N, using N-code solver in hyper mesh, the total time of load spectrum is set to 200s, the sampling frequency is 1000, and the material is PP-LGF30. Then get front-end frame damage cloud figure 3 and Life Cloud Figure 4. Both figures show that the longitudinal beam mounting hole and the engine latch mounting hole are the most vulnerable parts. Moreover, the life in 6122s, which is much longer than the required 1200s. Therefore, the front-end frame material itself meets the design requirements and meets the requirements. No modification of the material is required.

To reduce the mesh quantity and improve the mesh quality, we first triangulate the mesh in Hyper mesh, whose size is 15mm. And then import it into Moldflow. To guarantee the quality of the grid and the accuracy of die flow analysis, the aspect ratio should be modified. The maximum aspect ratio was 6.79, and the average aspect ratio was 1.78. It meets the analysis requirements, the matching percentage value of the mesh partition is 90%, the partition result is as shown in Figure 5.

To reduce pressure and heat loss and control costs, we choose to use a hot runner in the main channel. In this paper, the gating system combined with customer requirements, the use of balanced runner. We choose to use “Point gate” at the gate. There are eight of them, and they each have three gates on the top beam. We set them symmetrically at the engine lock and set one gate on each side of the beam. The lower beam is provided with three gates, and the positions of gates and runner are arranged as shown in Figure 6.

The front-end frame is made of SABIC Innovative Plastics US, LLC. As requested by the manufacturer. PP-LGF30, aka polypropylene. Its advantages are low density, lightweight, high crystallinity, regular structure, and excellent mechanical properties. It is suitable for making mechanical parts and corrosion-resistant parts. In combination with Moldflow software, the recommended processing parameters for this material are mold temperature 70 °C ∼ 90 °C, melt temperature 200 °C ∼ 360 °C, holding pressure 40 ∼ 44Mpa, injection time 2s ∼ 4s, holding time 40S ∼ 60s respectively. The forming window analysis determined that the initial forming process parameters were mold temperature 70 °C, melt temperature 200 °C, holding pressure 40 Mpa, injection time 2 s, holding time 40 s, as shown in Table 2.

Preliminary molding process parameters

Mold temperature (°C) | Melt temperature (°C) | Holding pressure (Mpa) | Injection time (s) | compress time (s) |
---|---|---|---|---|

70 | 200 | 40 | 2 | 40 |

After cooling, filling, compression, and warpage analysis, it is found that the main defect is warpage. From Fig. 7, it can be concluded that the maximum warpage is 1.023 mm, and the warpage is controlled to 0.5–0.8 mm according to the requirement of the enterprise.

The standardized orthogonal test table can not only reduce the number of blind tests but also make the factors be more comprehensive tests in fewer test times. Through the data processing, we can also find out the influence degree of each test factor on the test index.

According to the above analysis, this paper takes y 2 warpage as the optimization target, and marks it as a, B, C, D, E with mold temperature, melt temperature, holding pressure, injection time, and holding time as the experimental factors. For each process parameter, a test range is selected based on previous experience as shown in table 3. Based on the number of test factors and levels, 25 sets of orthogonal tables with 5 Factor 5 levels are used as shown in table 4. Based on the number of test factors and levels, using 25 sets of orthogonal tables with 5 factors and 5 levels, the different process parameters and their corresponding plastic warpage values are as shown in table 4: RA = 0.080, RB = 0.208, RC = 0.096, RD = 0.198, Re = 0.163, it can be seen that the factors that influence the amount of warpage are the melt temperature B > the injection time d > The holding time e > the holding pressure c > the die temperature a, that is, the melt temperature has the greatest influence on the amount of warpage, die temperature has the least effect on warpage.

Factor range table

Horizontal range | A Mold temperature (°C) | B Melt temperature (°C) | C Holding pressure (Mpa) | D Injection time (s) | E compress time (s) |
---|---|---|---|---|---|

1 | 70 | 200 | 40 | 2.0 | 40 |

2 | 75 | 240 | 41 | 2.5 | 45 |

3 | 80 | 280 | 42 | 3.0 | 50 |

4 | 85 | 320 | 43 | 3.5 | 55 |

5 | 90 | 360 | 44 | 4.0 | 60 |

Orthogonal test table and test results

N0. | A | B | C | D | E | Y2/mm |
---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 1 | 1 | 0.812 |

2 | 1 | 2 | 2 | 2 | 2 | 1.201 |

3 | 1 | 3 | 3 | 3 | 3 | 0.794 |

4 | 1 | 4 | 4 | 4 | 4 | 1.221 |

5 | 1 | 5 | 5 | 5 | 5 | 0.964 |

6 | 2 | 1 | 2 | 3 | 4 | 1.102 |

7 | 2 | 2 | 3 | 4 | 5 | 0.881 |

8 | 2 | 3 | 4 | 5 | 1 | 1.093 |

9 | 2 | 4 | 5 | 1 | 2 | 0.812 |

10 | 2 | 5 | 1 | 2 | 3 | 1.048 |

11 | 3 | 1 | 3 | 5 | 2 | 0.870 |

12 | 3 | 2 | 4 | 1 | 3 | 0.939 |

13 | 3 | 3 | 5 | 2 | 4 | 0.989 |

14 | 3 | 4 | 1 | 3 | 5 | 1.102 |

15 | 3 | 5 | 2 | 4 | 1 | 0.712 |

16 | 4 | 1 | 4 | 2 | 5 | 0.904 |

17 | 4 | 2 | 5 | 3 | 1 | 0.971 |

18 | 4 | 3 | 1 | 4 | 2 | 0.632 |

19 | 4 | 4 | 2 | 5 | 3 | 1.102 |

20 | 4 | 5 | 3 | 1 | 4 | 0.924 |

21 | 5 | 1 | 5 | 4 | 3 | 0.791 |

22 | 5 | 2 | 1 | 5 | 4 | 0.888 |

23 | 5 | 3 | 2 | 1 | 5 | 0.901 |

24 | 5 | 4 | 3 | 2 | 1 | 1.211 |

25 | 5 | 5 | 4 | 3 | 2 | 0.801 |

k1 | 0.962 | 0.896 | 0.897 | 0.960 | 0.917 | |

k2 | 0.987 | 0.940 | 0.968 | 0.827 | 1.002 | |

k3 | 0.922 | 0.882 | 0.936 | 0.935 | 0.839 | |

k4 | 0.907 | 1.090 | 0.992 | 1.025 | 1.002 | |

k5 | 0.918 | 0.890 | 0.905 | 0.950 | 0.970 | |

R | 0.080 | 0.208 | 0.096 | 0.198 | 0.163 |

The effect of each factor level on the warpage is shown in Figure 8. The value of the ordinate represents the warpage under different factors. With the increase of the horizontal value of the die temperature, the warpage of the product decreases at first and then increases and reaches the lowest value at A4. The melt temperature and holding pressure increase with the horizontal value, the amount of warpage first increased, then decreased, then increased, then decreased, and reached the lowest value at B3 and C1. With the increase of injection time, the amount of warpage first increased and then decreased, then the trend increased and reached the minimum value at d4, and the warpage deformation decreased first, then increased and finally decreased as the holding time increased with the level value and reached the minimum value at E2. The optimum parameters are A4B3C1D2E4, the die temperature a level 4(85 °C), melt temperature B level 3(280 °C), holding pressure C Level 1(40 MPA), injection time D Level 4(3.5 s), and holding pressure time E level 2(45 s), as the combination is in group 18 of the orthogonal test table, Moldflow carries out die flow analysis and the result is shown in Fig. 9. The warp deformation is 0.632 mm.

The analysis of variance can correctly reflect the degree of influence of each test factor on the target and distinguish whether the difference in test results corresponding to each level of a certain factor is caused by a change in a certain level. As shown in Table 5, the melt temperature F value is 6.565, the melt temperature is a significant factor affecting the warpage deformation of the product, and the mold temperature has the least influence. The degree of influence of each test factor on the warpage deformation from high to low is melt Temperature B>Injection time D>Holding time E>Holding pressure C>Mold temperature A, that is, the melt temperature has the greatest influence on the warpage deformation, and the mold temperature has the least influence on the warpage deformation. This conclusion is consistent with the results of the range analysis.

Analysis of variance of warpage deformation

factor | Deviation sum of squares | Degree of freedom | Mean square error | variance | F Compare | F (a=0.05) Critical value |
---|---|---|---|---|---|---|

A | 0.023 | 4 | 0.03656 | 0.009141 | 1.000 | 6.390 |

B | 0.151 | 4 | 0.15660 | 0.039149 | 6.565 | 6.390 |

C | 0.033 | 4 | 0.04802 | 0.012005 | 1.435 | 6.390 |

D | 0.117 | 4 | 0.15693 | 0.039233 | 5.087 | 6.390 |

E | 0.102 | 4 | 0.06699 | 0.016748 | 4.435 | 6.390 |

error | 0.02 | 4 | 0.12869 | 0.032171 | ||

total | 0.59379 | 24 |

We install the mold on the injection machine and set the best injection process parameters combination of A4B3C1D4E2 corresponding value, after confirmation, injection molding production. Fig. 10 is a sample from the trial mold. The sample has no obvious appearance defect, and the warpage deformation is within the tolerance. It meets production requirements.

In this paper, the automobile front-end frame is taken as the research object, the whole plastic front-end frame is designed with Hyper mesh software, and the mechanical performance is verified.

The results of Moldflow were analyzed by the method of orthogonal test, the optimal configuration of injection molding process parameters, and the influence of each factor on the warp deformation of evaluation index under the test conditions are as follows: melt temperature B > injection time D > holding time E > holding pressure C > Die temperature A.

CAE analysis of optimized configuration process parameter combination A4B3C1D4E2. We compared the optimized analysis results with the analysis results of the system's recommended process parameters, and the simulation results showed that the warpage was 0.632 mm. It is 38% less than the initial warpage (1.023 mm). It achieves the optimization goal.

Put into actual production. In the premise of satisfying mechanical properties, plastic instead of steel, to achieve a lightweight design. It provides correct theoretical guidance for setting the actual injection molding process parameters. The weight of the automobile can be greatly reduced by replacing the original steel parts with plastics under the condition that the service performance of the product is invariable.

#### Factor range table

Horizontal range | A Mold temperature (°C) | B Melt temperature (°C) | C Holding pressure (Mpa) | D Injection time (s) | E compress time (s) |
---|---|---|---|---|---|

1 | 70 | 200 | 40 | 2.0 | 40 |

2 | 75 | 240 | 41 | 2.5 | 45 |

3 | 80 | 280 | 42 | 3.0 | 50 |

4 | 85 | 320 | 43 | 3.5 | 55 |

5 | 90 | 360 | 44 | 4.0 | 60 |

#### Analysis of variance of warpage deformation

factor | Deviation sum of squares | Degree of freedom | Mean square error | variance | F Compare | F (a=0.05) Critical value |
---|---|---|---|---|---|---|

A | 0.023 | 4 | 0.03656 | 0.009141 | 1.000 | 6.390 |

B | 0.151 | 4 | 0.15660 | 0.039149 | 6.565 | 6.390 |

C | 0.033 | 4 | 0.04802 | 0.012005 | 1.435 | 6.390 |

D | 0.117 | 4 | 0.15693 | 0.039233 | 5.087 | 6.390 |

E | 0.102 | 4 | 0.06699 | 0.016748 | 4.435 | 6.390 |

error | 0.02 | 4 | 0.12869 | 0.032171 | ||

total | 0.59379 | 24 |

#### Preliminary molding process parameters

Mold temperature (°C) | Melt temperature (°C) | Holding pressure (Mpa) | Injection time (s) | compress time (s) |
---|---|---|---|---|

70 | 200 | 40 | 2 | 40 |

#### Information table of statics analysis

Load | Size/(N) | Mounting point displacement/mm | Maximum stress / (Mpa) | Design requirements/(mm) | Whether it meets the design requirements |
---|---|---|---|---|---|

Lock limit pull | 5200 | 15 | 139 | 15 | Yes |

Cushion impact | 1000 | 0.8 | 20 | 4 | No |

Pedestrian impact | 4900 | 15 | 208 | 20 | Yes |

Condenser support strength | 390 | 0.6 | 6.8 | 3 | No |

Radiator support strength | 360 | 0.6 | 5.6 | 3 | Yes |

Oil cooler installation strength | 180 | 0.3 | 3.6 | 2 | Yes |

#### Orthogonal test table and test results

N0. | A | B | C | D | E | Y2/mm |
---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 1 | 1 | 0.812 |

2 | 1 | 2 | 2 | 2 | 2 | 1.201 |

3 | 1 | 3 | 3 | 3 | 3 | 0.794 |

4 | 1 | 4 | 4 | 4 | 4 | 1.221 |

5 | 1 | 5 | 5 | 5 | 5 | 0.964 |

6 | 2 | 1 | 2 | 3 | 4 | 1.102 |

7 | 2 | 2 | 3 | 4 | 5 | 0.881 |

8 | 2 | 3 | 4 | 5 | 1 | 1.093 |

9 | 2 | 4 | 5 | 1 | 2 | 0.812 |

10 | 2 | 5 | 1 | 2 | 3 | 1.048 |

11 | 3 | 1 | 3 | 5 | 2 | 0.870 |

12 | 3 | 2 | 4 | 1 | 3 | 0.939 |

13 | 3 | 3 | 5 | 2 | 4 | 0.989 |

14 | 3 | 4 | 1 | 3 | 5 | 1.102 |

15 | 3 | 5 | 2 | 4 | 1 | 0.712 |

16 | 4 | 1 | 4 | 2 | 5 | 0.904 |

17 | 4 | 2 | 5 | 3 | 1 | 0.971 |

18 | 4 | 3 | 1 | 4 | 2 | 0.632 |

19 | 4 | 4 | 2 | 5 | 3 | 1.102 |

20 | 4 | 5 | 3 | 1 | 4 | 0.924 |

21 | 5 | 1 | 5 | 4 | 3 | 0.791 |

22 | 5 | 2 | 1 | 5 | 4 | 0.888 |

23 | 5 | 3 | 2 | 1 | 5 | 0.901 |

24 | 5 | 4 | 3 | 2 | 1 | 1.211 |

25 | 5 | 5 | 4 | 3 | 2 | 0.801 |

k1 | 0.962 | 0.896 | 0.897 | 0.960 | 0.917 | |

k2 | 0.987 | 0.940 | 0.968 | 0.827 | 1.002 | |

k3 | 0.922 | 0.882 | 0.936 | 0.935 | 0.839 | |

k4 | 0.907 | 1.090 | 0.992 | 1.025 | 1.002 | |

k5 | 0.918 | 0.890 | 0.905 | 0.950 | 0.970 | |

R | 0.080 | 0.208 | 0.096 | 0.198 | 0.163 |

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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 Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation 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 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 Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets 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 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 MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations 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 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 Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model 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 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 -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research 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 Research on threat assessment problems of island air defence system based on the leader-follower model 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 Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay 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 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 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 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 Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model