Electric vehicles can alleviate the energy crisis. This paper analyzes the electric vehicle handling stability model. At the same time, we analyze the dynamic interaction between the electric vehicle and the driver's human body. Furthermore, we established a nonlinear dynamic mathematical model of human-vehicle 6-DOF steering driving, including the car's lateral, yaw, and roll motions and the driver's body [1]. In this paper, we analyze the influence of human-vehicle dynamics coupling on the steering stability of electric vehicles through numerical calculation.

The wheelbase and wheelbase of the electric vehicles studied in this paper are relatively small, so the driver/occupant is distributed front and rear. Because of the nonlinear dynamic interaction between the driver's human body and the electric vehicle, we established the coordinate system shown in Fig. 1 and the electric vehicle's handling stability [2]. The dynamic effect between the car and the driver's body is mainly realized through the elastic connection between the human body and the seat, seat belt, steering wheel, and underbody. When building the model, we treat the sitting human body as a rigid body. The connection between the human and the vehicle is simplified as the spring-damping force connection between the driver's body and the seat at point _{1} of the lower body mass center and _{2} point of the upper body mass center. We set the intersection of the vertical line of the center of gravity and the roll axis when the car is stationary as

Based on the mechanical model in Fig. 1, we establish the differential equation of the steering stability motion of the human-vehicle system for the relative motion of the driver's human body and the electric vehicle [3]. We set _{1} as the total mass of the electric vehicle. _{s}

The force balance equation of the electric vehicle along the

In the formula, _{Y}

In the formula, _{Z}

In the formula, _{X}

_{f}, k_{r}_{f}, α_{r}_{f}, F_{r}

We denote the reference base fixed to the body as _{1} _{1} _{1}, _{2}, _{3}). The driver's body has three degrees of freedom, lateral, yaw, and roll, and the general spatial motion in the inertial reference base

The first derivative of a vector _{BC}

Among them: the coordinate of the driver's body in the base _{BC}_{x}_{y} h_{z}_{x}_{z}_{2} is the inertial moment of the driver's body. _{2} is the angular acceleration matrix.
_{2} is the inertia tensor in the non-inertial basis _{2} = _{2X} _{2Y} _{2Z}].

Assuming that the electric vehicle roll angle is small, consider cos _{1} = 1. Then the balance equation of lateral force, roll, and yaw motion moment balance equation of the driver body is as follows: _{2}_{2y} = _{Y}_{2X}ϕ_{2} = _{2}_{2} − _{X}_{2}_{2y}_{z}_{2Z}_{2} = − _{Z}

The relative displacement Δ_{q}_{1y}, Δ_{q}_{2y}, of the driver's body and the electric vehicle along the Δ_{q}_{1y}, = Δ_{y}_{q}_{1} (_{2} − _{1}) + _{q}_{1} (_{2} − _{1}); _{1}, _{2} is Δ_{q}_{2y}, = Δ_{y}_{q}_{2} (_{2} − _{1}) + _{q}_{2} (_{2} − _{1}), respectively, _{q}_{1}, _{q}_{2} is the relative vertical position of the point _{1}, _{2} and the roll center, and _{q}_{1}, _{q}_{2} is the relative horizontal position. _{1}, _{2} are the yaw angles of the electric vehicle and the human body, respectively [5]. The spring-damping forces along the _{q1y} = _{q1y}Δ_{q1y} + _{q1y}Δ_{q1y}; _{q2y} = _{q2y}Δ_{q2y} + _{q2y}Δ_{q2y} respectively.

_{q}_{1y}, _{q}_{2y}, are the translational stiffness coefficients along the _{1}, _{2} between the driver's body and the electric vehicle, respectively. _{q}_{1y}, _{q}_{2y} are the damping coefficients, respectively [6]. The lateral force of the driver's body on the electric vehicle along the _{Y}_{q}_{1y} + _{q}_{1y}) cos _{1} = _{q}_{1y} + _{q}_{1y}.

The acting moment about the _{q}_{1x}, _{q}_{2x} are the torsional stiffness coefficients around the _{q}_{1x}, _{q}_{2x} are the torsional damping coefficients around the

The acting moment about the Z axis is
_{q}_{1z}, _{q}_{2z} is the torsional stiffness _{q}_{1y}, _{q}_{1} − _{q}_{2y}, _{q}_{2} coefficient around the axis, respectively. _{q}_{1z}, _{q}_{2z} is the torsional damping coefficient around the

Parameters such as inertia and structural dimensions of electric vehicles and drivers are easy to measure. The stiffness damping element connected between people and vehicles needs to combine vibration test and modeling for parameter identification. The interaction between the human body and the car is complex [7]. The detection method is mainly realized through the human body and the seat system. We analyzed the stiffness damping coefficient between the human body and the seat and built a vibration test bench. We performed low-frequency multidirectional vibration experiments as well as data acquisition and processing.

The test bench consists of a servo motor, a vibration exciter, a seat, a base plate, and sensors. Each excitation can realize a single direction of motion of the sitting human body. However, the test bench can be disassembled and reassembled to realize the translational vibration test in the y-direction and the rotational vibration test around the x and z axes, respectively.

The inertial sensor we use in the test is a miniature attitude reference system. The system can measure the angular velocity and acceleration signals in the local coordinate system of the sensor [8]. According to the output data, we obtain the direction cosine matrix describing its attitude transformation relative to the inertial coordinate system. Before the test, according to the national standard GB/T17245-2004, we calculated the position of the center of mass of the lower body and the upper body, respectively. Experimentally measure the initial displacements _{1} _{2} of the lower body mass center to sensor II and the upper body mass center to sensor III. In the test, I collect the acceleration time-domain signal along the y-axis on the seat pan. Sensors II and III measure the y-axis acceleration time-domain signal in their local coordinate system [9]. Based on the response signal, we obtain the time domain signal of acceleration along the y-axis at the position of the lower and upper body centroid. Then we perform the following coordinate transformation:

Among them: _{0}, _{1}, _{2} is the direction cosine matrix describing the posture transformation of seat, lower body and upper body, respectively. _{1}, _{2} are the original measured response accelerations of the lower and upper body, respectively. ^{′}_{1}, ^{′}_{2}, are the accelerations in the local coordinate system of the sensor

In the rotational vibration test around the

where _{1}, _{2} is the original measured response angular velocity of the lower body and the upper body, respectively. ^{′}_{1}, ^{′}_{2} are the angular velocity in the local coordinate system of the sensor

The human body is composed of elastic tissues such as tendons, muscles, ligaments, and bones. The seat surface is also a layer of viscoelastic foam. Therefore the person-chair system has translational motion in the y-axis and rotation around the x- and z-axes. We can use a lumped parameter model including stiffness and damping elements to describe it (Figure 3). The point _{1} is the centroid of the lower body [10]. The point _{2} is the centroid of the upper body. Figure 3(a) describes the y-axis translation of the sitting human body, and Figure 3(b) can be used to describe the rotation of the sitting human body around the x-axis or the z-axis. The upper and lower bodies are elastically connected at point p.

The differential equations of these three motions have the following unified form:

Among them: _{1}, _{2} is the mass (moment of inertia) of the lower and upper body. _{1}, _{2} is displacement (angular displacement). _{q}_{1}, _{q}_{2} and _{q}_{1}, _{q}_{2} are stiffness and damping, respectively [11]. The expression in the frequency domain after Fourier transform is performed on both sides of the equation at the same time is:

We fit the above mathematical model to the experimental data. In this way, the stiffness and damping parameters of the person-chair interface can be identified. The objective function used for parameter identification is as follows:

_{1e}, _{2e} is the amplitude-frequency response function of the lower and upper body measured experimentally. _{1m}, _{1} / _{0}, _{2m}, _{2} / _{0}. We first established a 3D model of a sitting human body in SolidWorks and imported it into ADAMS. A three-dimensional human model enables the calculation of the lower and upper body centers of mass and the moment of inertia relative to their respective centers of mass [12]. The results are shown in Figure 4 and Table 1.

Person-chair model identification parameters

Parameter | Mean | Standard deviation |
---|---|---|

kq1rx/N·m·rad^{−1}) |
186.3 | 37.2 |

kq1ty/kN·m^{−1}) |
14.1 | 1.1 |

kq1rz/(N·m·rad^{−1}) |
1383.3 | 61.3 |

kq2rx/N·m·rad^{−1}) |
156.3 | 9 |

kq2ty/kN·m^{−1}) |
12.5 | 1 |

kq2rz/N·m·rad^{−1}) |
542 | 52.9 |

cq1rx/(N·m·s·rad^{−1}) |
3.7 | 1.1 |

cq1ty/(N·s·m^{−1}) |
198.1 | 32.6 |

cq1rz/(N·m·s·rad^{−1}) |
26.5 | 2.8 |

cq2rx/(N·m·s·rad^{−1}) |
5 | 2.8 |

cq2ty/(N·s·m^{−1}) |
423.3 | 181.1 |

cq2rz/(N·m·s·rad^{−1}) |
20.4 | 7.6 |

In equations (1)–(3), we let _{Y}_{Z}_{X}

We take the model car's roll angle of 2.5° under 0.4g lateral acceleration as the standard. We choose the relative damping coefficient of the suspension to be 0.3. The moment of inertia is estimated by the ADAMS virtual prototype model and empirical formula [14]. The parameters required for the calculation are shown in Table 2. We combined the mathematical model and Matlab/Simulink to calculate and analyze the dynamic coupling between the driver's human body and the electric vehicle when the front wheel rotation angle is 5°. We analyze the effect of this model on the handling stability of electric vehicles with different curb weights. The calculation results are shown in Figure 5 and Table 3.

Calculated main parameters

Model | A | B | C | Model | A | B | C |
---|---|---|---|---|---|---|---|

m^{1}/kg |
450 | 200 | 100 | m^{1}/kg |
270 | 100 | 50 |

a/m | 0.8 | 0.8 | 0.6 | b/m | 0.8 | 0.8 | 0.6 |

K/(N·rad^{−1}) |
13000 | 7200 | 5700 | Cp/(N·m·s·rad^{−1}) |
1143 | 663 | 486 |

kf/(N·rad^{−1}) |
−28600 | −22600 | −25600 | kr/(N·rad^{−1}) |
−31800 | −27800 | −18800 |

h^{1}/m |
0.35 | 0.35 | 0.35 | h^{2}/m |
0.55 | 0.55 | 0.55 |

lx/m | 0.05 | 0.05 | 0.05 | u/(m·s^{−1}) |
10 | 10 | 6 |

Iz1/(kg·m^{2}) |
380 | 174 | 48 | Iz2/(kg·m^{2}) |
5.4 | 5.4 | 5.4 |

Ix1/(kg·m^{2}) |
120 | 52 | 18 | Ix2/(kg·m^{2}) |
26 | 26 | 26 |

la/m | 0.152 | 0.152 | 0.152 | lb/m | −0.153 | −0.153 | −0.153 |

ha/m | 0.577 | 0.577 | 0.577 | hb/m | 0.767 | 0.767 | 0.767 |

Roll Response Steady-State Values and Overshoot

Model car | Steady-state value/(°) | Overshoot/% | ||
---|---|---|---|---|

no coupling | Consider coupling | no coupling | Consider coupling | |

A | 3.58 | 3.81 | 11.5 | 14 |

B | 3.1 | 3.37 | 14.2 | 17.8 |

C | 11.2 | 1.26 | 23.1 | 34.8 |

The human-vehicle dynamic coupling effect prolongs the roll response time and increases the roll angle's steady-state value and transient peak value. The larger the overshoot is, the more unstable the electric vehicle is. The differences between the steady-state values of roll angles of models A, B, and C are 0.23°, 0.27°, and 0.14°, respectively [15]. The corresponding relative increments were 6.4%, 8.7%, and 13.3%, respectively. The difference of overshoot is 2.5%, 3.6%, and 11.7%, respectively. The structural scale and quality of Model A are relatively close to Model B and Model C of the human body. Human-vehicle dynamic coupling reduces the steady-state value of its response. Under the action, the curve fluctuation becomes larger, and the peak response time is prolonged.

1) The human-vehicle dynamic coupling significantly impacts the roll angle response of electric vehicles. 2) Human-vehicle dynamics coupling increases the tendency of electric vehicles to understeer. Under the influence of this effect, the system response time is prolonged, and the steady-state value and transient peak value of the roll angle are increased. At this time, the steady-state value of the yaw angular velocity is reduced, and the curve fluctuation becomes larger.

#### Calculated main parameters

Model | A | B | C | Model | A | B | C |
---|---|---|---|---|---|---|---|

m^{1}/kg |
450 | 200 | 100 | m^{1}/kg |
270 | 100 | 50 |

a/m | 0.8 | 0.8 | 0.6 | b/m | 0.8 | 0.8 | 0.6 |

K/(N·rad^{−1}) |
13000 | 7200 | 5700 | Cp/(N·m·s·rad^{−1}) |
1143 | 663 | 486 |

kf/(N·rad^{−1}) |
−28600 | −22600 | −25600 | kr/(N·rad^{−1}) |
−31800 | −27800 | −18800 |

h^{1}/m |
0.35 | 0.35 | 0.35 | h^{2}/m |
0.55 | 0.55 | 0.55 |

lx/m | 0.05 | 0.05 | 0.05 | u/(m·s^{−1}) |
10 | 10 | 6 |

Iz1/(kg·m^{2}) |
380 | 174 | 48 | Iz2/(kg·m^{2}) |
5.4 | 5.4 | 5.4 |

Ix1/(kg·m^{2}) |
120 | 52 | 18 | Ix2/(kg·m^{2}) |
26 | 26 | 26 |

la/m | 0.152 | 0.152 | 0.152 | lb/m | −0.153 | −0.153 | −0.153 |

ha/m | 0.577 | 0.577 | 0.577 | hb/m | 0.767 | 0.767 | 0.767 |

#### Roll Response Steady-State Values and Overshoot

Model car | Steady-state value/(°) | Overshoot/% | ||
---|---|---|---|---|

no coupling | Consider coupling | no coupling | Consider coupling | |

A | 3.58 | 3.81 | 11.5 | 14 |

B | 3.1 | 3.37 | 14.2 | 17.8 |

C | 11.2 | 1.26 | 23.1 | 34.8 |

#### Person-chair model identification parameters

Parameter | Mean | Standard deviation |
---|---|---|

kq1rx/N·m·rad^{−1}) |
186.3 | 37.2 |

kq1ty/kN·m^{−1}) |
14.1 | 1.1 |

kq1rz/(N·m·rad^{−1}) |
1383.3 | 61.3 |

kq2rx/N·m·rad^{−1}) |
156.3 | 9 |

kq2ty/kN·m^{−1}) |
12.5 | 1 |

kq2rz/N·m·rad^{−1}) |
542 | 52.9 |

cq1rx/(N·m·s·rad^{−1}) |
3.7 | 1.1 |

cq1ty/(N·s·m^{−1}) |
198.1 | 32.6 |

cq1rz/(N·m·s·rad^{−1}) |
26.5 | 2.8 |

cq2rx/(N·m·s·rad^{−1}) |
5 | 2.8 |

cq2ty/(N·s·m^{−1}) |
423.3 | 181.1 |

cq2rz/(N·m·s·rad^{−1}) |
20.4 | 7.6 |

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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