# Mathematical Modeling and Multivariable Optimization Design of SUV Chassis Structure Based on SFE CONCEPT

Authors: Jingyi Liu; Suifeng Wang; Guodong Wang
Journal: Security and Communication Networks
 (2022)

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## Abstract

The car chassis design concept is an important part of the car design process. Analyzing the car chassis structure in the conceptual design process is of great significance for improving the efficiency and accuracy of car chassis design. This paper takes SUV models as the research object and uses SFE CONCEPT software to realize the mathematical modeling and multivariate optimization of the SUV chassis structure. The concept of “implicit” parameterization and the concept of “CAE analysis-driven design” are adopted to quickly realize large-scale geometric transformation and consistency of interconnection, while achieving automated production and grid parameters. Through this research, it can be found that in the concept development stage of the vehicle chassis structure, the CAE performance analysis is introduced into the early development stage as soon as possible; combined with the implicit parametric design method, it can quickly and effectively realize the exploration and optimization of a larger range of structures. In addition, the SFE CONCEPT software used in this article can create parametric structural models, and combined with automatic meshing technology, it can realize continuous changes of topology variables, shape variables, size variables, and material variables, and compare the design results with the detailed design results to confirm the feasibility of the design. In addition, the experimental test shows that the success rate of SFE CONCEPT and other CAD software docking reaches 100%.


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## Body

## 1. Introduction

The chassis of a car is usually composed of components for rotation, driving, and transmission and braking systems. Most transmission systems transfer appropriate kinetic energy to the steering wheel, so they can be driven in any situation, are cost-effective, and are maneuverable. The turning system not only can withstand the force of the wheels in all directions, but also has strong steering force. At the same time, scientific installation of related components through the frame can improve the coordination of the machine. The suspension transmits torque and pressure between the frame and the wheels, reducing steering shock and making driving more stable.Chassis system platform is the demand and trend of the development of the automotive industry. The platform design of the chassis structure is an important feature that supports its actual implementation. The structure of the chassis usually refers to the bearing and transmission and current structural elements related to the chassis, such as suspension arms, subframes, and steering knuckles. The structural elements of the chassis play a role in performance. The design of chassis structural parts must consider the self-realization, actual performance, and specifications of the model, as well as the development cycle and risks. The component development process includes multiple steps such as conceptual stage design, conceptual prototype production testing, detailed stage design, engineering testing, production testing, optimization design, tool manufacturing, and mass production testing. The chassis development cycle is long and complex. The development cycle of parts and components may exceed 2 years. In today’s diversified consumer demand, original equipment manufacturers can shorten the development cycle, develop a variety of models at low cost, and bring them to the market to meet the needs of different consumers. The design of the SUV chassis system has played a leading role in the development of the automotive industry.There are already many references at home and abroad for the research on SFE CONCEPT, SUV chassis structure, and mathematical modeling and multivariable optimization. Ferreira conducted a critical review of multivariate techniques used to optimize food analysis methods. Comparisons between response surface methods have been carried out, proving the advantages and disadvantages of these methods. The application of the main chemometric tools (central composite, Box–Behnken design, and Doehlert matrix) is shown, which are commonly used to optimize sample preparation procedures, as well as the instrument conditions of analytical techniques for the determination of organic and inorganic species in food samples. In addition, the use of multiple responses and robustness testing in food analysis is briefly discussed [1]. Shao proposed a simplified model that can simultaneously consider the effects of Rayleigh scattering and Fraunhofer diffraction to describe the nonlinear relationship between particle volume and single-particle angular luminous flux. This model can be used for signal processing of commercial low-cost particle sensors based on laser scattering. Based on the Trust-Region and Levenberg–Marquardt methods, combined with robust methods, the optimal parameters of the model are obtained [2]. Hamedi introduced the theoretical and experimental concepts of using the surface free energy (SFE) concept and laboratory dynamic testing to predict moisture loss in asphalt concrete mixtures. The SFE characteristics of aggregate and asphalt binder have been evaluated using Universal Adsorption Unit (USD) and Wilhelmy Plate (WP) methods. The results of this study show that the polyvinyl chloride (PVC) coating significantly reduces the total SFE and polar SFE and leads to an increase in the nonpolar SFE of the aggregates, thereby making the aggregates hydrophobic. The comparison of the dynamic modulus test results under dry and wet conditions confirmed the results obtained from the SFE method [3]. Ji proposed optimization process based on the finite element model and genetic algorithm, which can successfully reduce the noise of the middle channel. They also explained some background theories of genetic algorithm and acoustic radiation efficiency under the framework of vibro-acoustics to understand the optimization process. Vehicle performance evaluation and experimental research verified this research. Finally, this proven process was applied to the sport utility vehicle (SUV) under development, and its road noise reduction proved to be successful [4]. Teter used four different methods to estimate univariate distributions, namely, Beta and Gaussian distributions, standard Gaussian kernel estimation, and extra-exponential splines. Teter generated scenarios and implemented a capital budget optimization model based on superquantile risk. Numerical experiments compare the differences between the estimators and their influence on the optimal solution. The flexibility of the extra-exponential spline estimator to fuse soft information with observational data generates reasonable density functions for univariate and multivariate random variables. Including the risk aversion of decision makers through risk-based optimization can provide conservative results while combining the uncertainties of unknown parameters [5]. Albert J proposed a fast and accurate method to obtain the balanced single-mode joint probability distribution of a multimer system. This method requires only two assumptions: the copy number of all molecular species can be regarded as continuous, and the probability density function (pdf) can be well approximated by the multivariate skew normal distribution (MSND). Starting from the main equation, Albert J transformed the problem into a set of statistical moment equations and then expressed them with the inherent parameters of MSND. Using the optimization package on Mathematica, Albert J minimized a Euclidean distance function that contains the sum of the squared differences on the left and right sides of these equations. The comparison between the results obtained by Albert J’s method and the results presented by Gillespie’s algorithm shows that Albert’s method is highly accurate and efficient [6]. Ley proposed a new general version of the Stein method for univariate distribution. In particular, Ley proposed the canonical definition of the Stein operator of the probability distribution, which is based on linear difference or differential type operators. The resulting Stein identities highlight the unified theme behind the Stein method (continuous and discrete) literature. Regarding Stein operators as operators acting on pairwise functions, Ley provided an extensive toolkit for distribution comparison. Several abstract approximation theorems were provided [7]. The data of these studies are not comprehensive, and the experimental results are not suitable for general and important fields, so they are not recognized and adopted by the public.In this paper, the SFE CONCEPT software is used to model and analyze the SUV chassis structure, and the concept of “implicit” parameterization and the concept of “CAE analysis-driven design” are adopted. It can quickly achieve large-scale geometric transformation and interconnect consistency while also enabling automated production. Combined with the rich processing capabilities and optimized software interfaces of the software itself, the automation of design, analysis, and optimization becomes possible. In the early stage of product development and the realization of multiple design concepts, the design time and cost are significantly reduced. At the same time, the designed chassis structure model can achieve performance improvement in many aspects through multivariable optimization, and the model can be seamlessly connected to multiple platforms.


## 2. SFE CONCEPT Modeling and Four Optimization Designs

### 2.1. Introduction to SFE CONCEPT Software

Everyone has realized long ago that if CAE can guide engineers’ design decisions in the early design stage, it will play a greater role. Because in the early design stage, many parameters such as geometry and materials have not been fixed, engineers can have a lot of space to seek multiple solutions. In order to use numerical simulation technology to predict performance, a good finite element model is based on an accurate CAD model. In other words, only when the design phase freezes and the CAD model is built, it is possible to perform numerical simulation analysis.SFE CONCEPT software adopts a simulation-driven design concept and uses an implicit full explanation method [8]. It can make complex geometric figures by modifying parameters such as the position of the control point, the curvature of the line, and the shape of the intersection, without CAD modeling, rapid transformation, geometric modeling. In addition, SFE CONCEPT also provides finite element (mesh) automated modeling technology, which can be improved in real time due to changes in parameterized geometric models and can quickly provide CAE analysis models [9]. Automobile CAE mainly refers to analysis calculation and analysis simulation in engineering design, and its core is finite element analysis technology based on modern computational mechanics. It can be used for product performance analysis, prediction, and optimization.The most important question is how to model numerical analysis in the early stages of design when CAD data is not yet available. In fact, most new product designs are based on existing models, and the geometric design and numerical analysis results of these models can be obtained. New design variables are created by additional or advanced methods based on existing models [10]. The importance and benefit of digital simulation is to establish a link between design changes and implementation so that our decision-making is clearer. However, due to the lack of suitable tools to quickly analyze the model, quantitative analysis was not performed in the early stages of the design [11]. Even with high-quality automatic mesh tools, they can only work after the CAD design is completed.The SFE CONCEPT provides a brand-new solution that helps to modify the CAD model and finite element design in the early stages of design [12]. SFE CONCEPT uses the completely hidden parameter definition of the product topology to modify the complex structure of the product in the form of cross-sections, beams, nodes, and free-form surfaces, which greatly shortens the design time and makes it available to design engineers. This concept is transformed into design variables for optimization analysis and finally into a CAD model based on assembly or subsequent production. Using default design parameter interpretation, SFE CONCEPT can easily handle geometric design variables by default. Design variables are based on the design level, such as key points and curves. Each new design change can be quickly and easily submitted to numerical simulation analysis to determine the impact of the editing project on key performance [13, 14].


### 2.2. Features of SFE CONCEPT Software System

#### 2.2.1. Comprehensive Understanding of CAE Engineering Software System

After importing the CAD model into the CAE software, the CAE analysis of the structure can be started, and many geometric shapes need to be cleaned. The SFE CONCEPT includes analysis-based design concepts [15]. Through SFE CONCEPT modeling, CAD modeling, multi-geometric modeling, and rapid analytical modeling can be used to interpret the design as a whole, fully integrate and optimize the environment, and create an automated optimization environment. CAE is not only a verification tool in the product development process; it can guide engineers from the early stages of design to the use of large design space to find better design solutions [16].


#### 2.2.2. Implicit Full-Parameter Interpretation Method

In other software environments, whether it is an efficient geometric CAD modeling solution or a finite element direct solution, even the simplest modeling variables are more cumbersome. The SFE CONCEPT uses an implicit way to interpret all parameters. Just by adjusting the position of the influence point, the shape of the line, the shape of the part, and other parameters, it can automatically change and adjust the complex geometric model arbitrarily [17].


#### 2.2.3. The Finite Element Mesh Technology Automatically Converts the Geometric Model

The traditional deformation technology achieves the purpose of changing the shape of the geometric model by changing the finite element mesh. The requirements of grid computing will affect the accuracy of new network calculations and even make them unpredictable [18]. It is also necessary to update the relevant tables once to redefine the connections such as rivets, welded joints, and bolts. SFE CONCEPT uses a new, higher-resolution deformation technology. When the design model is modified, its limited component model will be automatically updated, and the network will also be automatically updated [19, 20]. When it is detected that the quality of the grid does not meet the criterion requirements, a high-quality grid with various connection relationships can be generated in real time according to the new geometric model. The schematic diagram of the traditional mode and the new SFE solution is shown in Figure 1.Figure 1
Traditional model and new SFE solution.


#### 2.2.4. Rear System-Level Structure Optimization and Automatic Cycle Processing

In other software systems, usually only part of the structure is optimized. In terms of system-level structure, due to the excessive parameter changes and the need to redefine the connection relationship between components after design changes, the optimization process is difficult to implement [21]. SFE CONCEPT works by identifying multivariate, is compatible with most transaction constraint component solutions and interactive optimization solutions, and truly realizes automatic background optimization and recognition [22]. The closed optimized integrated environment is shown in Figure 2.Figure 2
Closed optimized integration environment.


#### 2.2.5. Smartly Connected Modular Database

The SFE CONCEPT database function provides a classification method for storing reusable design data for future projects. All product components and subcomponents in the database are “smart”; that is, they fully adapt to the new geometric environment to support the development of future platforms [23].Advantages of SFE CONCEPT:(1)
It quickly creates the best conceptual design plan, saving time and development costs.(2)
The model is fully parametrically driven, which can quickly meet customer needs.(3)
It reduces the number of subsequent project updates and saves the cost of product design changes.(4)
It establishes a corporate knowledge base to ensure the reuse of resources.(5)
The adoption of the concept of “design-driven analysis” makes it possible to make the design successful the first time.(6)
Real-time feedback of parameter optimization results promotes product design innovation.(7)
Rich experience in product development and engineering consulting provides comprehensive technical support for enterprises.


### 2.3. SUV Model Chassis Structure Design Requirements

When designing a vehicle chassis, we must first analyze the customer’s needs and then determine what type of product the customer wants; finally, each product is defined separately according to the principle of analytic hierarchy process. The analyzed sequence structure is usually divided into upper, middle, and lower layers, which can be obtained by hierarchically dividing the corresponding structural patterns of the lower layers. With the rapid economic development, cars have gradually entered the homes of ordinary people, consumer groups have been studied, and satisfied customers are identified at the highest level (target level) based on real-world chassis product models. To this end, four principles are embodied: safety, comfort, price, and environmental protection. It also reflects the following criteria: service life of parts, engine performance, service braking performance, parking brake efficiency, shift uniformity, steering performance, frame length, low vibration, low noise, etc. All these factors, including cost and energy saving, constitute the final production line [24, 25].


#### 2.3.1. Chassis Structural Design

The chassis is mainly responsible for the body pressure and power of the steering system and transmits the engine power of the engine to the chassis. Parts and chassis allow you to drive a car anytime and anywhere, most of which consist of thousands of parts. This is the basis of the vehicle. Accessories such as engines, power tools, and body functions are directly or indirectly installed on the chassis under the car. It is divided into four main systems [26]. The main functional structure diagram of the car chassis is shown in Figure 3.(1)
Transmission system: Most of the energy produced by the engine is transferred to the steering wheel. The steering wheel usually includes half shafts and transmissions, clutches, drive shafts, and differentials. The engine is the power source of most cars, including five main systems and four main mechanisms. In addition, there is an installation relationship between the air filter and the cooler [27].(2)
Driving system: It mainly ensures that the car can drive normally under different conditions. The quality of the driving system determines the driver’s driving experience and the passenger’s car experience. It is composed of the frame, axle, wheels, and suspension of the car. The driving system of the SUV receives the power of the drive train and generates gravity through the action of the driving wheels and the road surface, so that the car can drive normally. It withstands the total weight of the car and the reaction force of the ground, alleviates the impact of uneven roads on the body, attenuates the vibration of the car in driving, maintains the smoothness of driving, and cooperates with the steering system to ensure the steering stability of the car.(3)
Steering system: Its main function is to drive in the direction selected by the driver. Usually the steering system plays a key role in driving.(4)
Braking system: The main task is to stop or slow down the moving car. It is mainly used in driving or parking, including brakes, control devices, transmission devices, and application devices.(5)
Frame: The weight of the entire body is borne by it, which directly affects the service life of the car [28].Figure 3
The main function structure of automobile chassis.The parameter table of the vehicle chassis of the Volkswagen Tiguan in the SUV is shown in Table1.Table 1
Parameters of vehicle chassis.
ProjectsSymbolsValuesWheelbaseWB (mm)6100Front axle loadWf (kg)6000Rear axle loadWr (kg)11700High-quality coreCG (mm)955Spring stiffness (front/rear)K (N/mm)204/191Shock absorber damping (front/rear)δ (Nsec/mm)14.2/13.2The platformization of the chassis structure can realize the structured design of a variety of car model types, mainly with the following parameters.(1)
Electric power assist and hydraulic power assist, (the schematic diagram is shown in Figure4): The electric power assist and hydraulic power assist of the same model have different configurations, and the original steering knuckles are the same, but the positions of the openings on the original electric mechanical steering knuckle and hydraulic power steering knuckle are different, and the positions of the holes on the corresponding lower swing arms are also different.(2)
Two-wheel drive models and four-wheel drive models, as shown in Figure5: The two-wheel drive and four-wheel drive models of the same car are just the shape of the subframe. The formula is different, the rest of the structural parts are the same, and they can all be used.(3)
Size parameters or quality parameters: Within a certain range, even the models of the same platform may have different quantitative parameters of size and mass. For example, the height of the center of mass is different, wheelbase is also different, and the front and rear axle loads are different. These differences are often caused by structural elements.Figure 4
Electric power steering and hydraulic power steering parts diagram.Figure 5
Diagram of 2WD and 4WD models.


### 2.4. Modeling and Multivariable Optimization of Chassis Structure

#### 2.4.1. Chassis Structure Design and Modeling

The traditional automobile development process includes modeling, conceptual design, detailed design of CAD information, and CAE analysis. In the design stage of the traditional concept, the structural design is based on the work experience of the chassis designer, first of all to ensure the possibility and optimization of the modeling, chassis design, and process constraints. After completing the detailed 3D data, it can simply calculate the weight of the vehicle chassis, identify related performance issues through CAE analysis, and optimize the structure [29]. The problem with implementation is the duplication of related work, such as vehicle CAD chassis data generation, vehicle design, and vehicle chassis modeling, which will slow down the entire project process and increase the development cycle. Based on the concept of efficient steering structure design analysis, the development process of the chassis is simplified [30]. The overall block diagram of the modeling is shown in Figure 6.Figure 6
General framework diagram of modeling.Geometric model design is a prerequisite for analyzing end elements. The precise geometric model will greatly improve the design accuracy. In the detailed design process, the design should only adapt to the structural characteristics of the vehicle chassis and strive to be simple and easy to modify. The analytical model used in this paper is an implicit full-parameter model based on the SFE CONCEPT full-parameter modeling concept, which is mainly based on the point-line-surface-beam-connection sequence. It can form designs in structures such as cover plates, beam units, and accessories to create a vehicle chassis. At the same time, the topological relationship between the models is established through mapping, and the model assembly parameters are identified [31]. Therefore, the geometry of the model is controlled by points, lines, and sections. When adjusting the geometry of the model, the model associated with it will also change according to the parameters of the assembly relationship. Unlike other CAD software, adjacent parts need to be repaired one by one. By creating a full-parameter model, structural design engineers can easily create and configure vehicle chassis and topology interactions. This is very helpful in the early stages of vehicle chassis development, as many solutions require major restructuring and flexible handling. The data sheet of the three SUV models currently on the market is shown in Table 2.Table 2
Three types of car classification data sheet.
Vehicle classCompactMedium-sized carsLarge vehiclesLength (mm)3600–39004300–46004800–5200Width (mm)1550–16701670–17701800–1900Height (mm)1350–14801360–14301400–1500Wheelbase (mm)2350–25002500–28001700–3200Ground clearance (mm)100–150100–150110–150Approach angle (°)15–2012–2012–20Departure angle (°)15–2012–2012–20


#### 2.4.2. Multivariable Optimization of Chassis Structure

The implicit parameterized modeling method provided by SFE CONCEPT can parameterize the variables involved in the above four optimization methods, which can quickly change the structure model and create a CAE model simultaneously. This enables shape optimization and size optimization, which are more constrained and difficult to achieve in the optimization process, to be realized. At the same time, the model parameterized in the SFE CONCEPT can also keep the topological connection between the components unchanged. In the structural optimization research of this paper, the characteristics of the parametric structural design method are also used to synergistically apply the optimization methods of shape, size, and material to the structural design [32, 33].(1)Topology Optimization Design. The scope of topology optimization, that is, “bionic optimization,” covers the entire chassis structure. Regardless of the field, the finite element method is needed. The use of this method is extremely effective in structural design that considers the force transmission path and load distribution of the chassis structure, and can make the chassis structure have good load-bearing performance. The parameterized model can be used to realize rapid geometric model changes when designing different force transmission paths. The main content of this paper is the structural optimization of the submodules in the conceptual design stage, thus retaining the overall structure and connection relationship of the reference model. For a brand-new chassis structure design, topology optimization is required first when the overall structure design is performed. The topology change of the frame is shown in Figure 7.Figure 7
Topology change of the frame.(2)Shape Optimization Design. Shape optimization needs to change variables other than the overall number of beams, connection methods, and overall structure in a determined structure, including the curvature of the control line of the joint, the position of the control point, and its relative position in the chassis structure. In the traditional chassis structure optimization process, since all the chassis structures have been basically finalized during the analysis phase, the constraints between the various structural components have greatly reduced the freedom of shape optimization, resulting in lightweight and other performance optimization. The possibilities have not been exploited. If the shape variable of the structure is changed during the analysis phase, a lot of reconstruction work is required to support this change. However, based on the expression of implicit parametric modeling, the curvature and cross-sectional shape of the beam structure can be quickly changed, and the shape of the structure can be optimized. The shape change of the frame is shown in Figure 8.Figure 8
Frame shape change.(3)Size Optimization. It is relatively mature to be used in the field of optimization of the current chassis structure. Among them, the variable mesh technology enables the modification of the finite element model to reflect the change of the geometric model when the geometric model of the chassis structure has been determined, so as to optimize the size. Although this method has its practicability, the technology is limited to small geometric size changes due to the limitations of the existing grid topology. The automatic update of the finite element model in the implicit parametric design method used in this paper is to redivide the grid, rather than modify the original grid. This method can avoid the distortion of the grid due to the large deformation in the morphing technology; at the same time, the quality control of the finite element model grid can be achieved by setting or writing the corresponding batch file statement, which greatly guarantees the quality of the finite element model. At present, the most common size optimization in traditional chassis structures is the optimization of sheet thickness, and the SFE CONCEPT can parameterize the thickness of structural parts to achieve continuous changes in material thickness.(4)Material Optimization Design. In recent years, emerging materials gradually used in automobiles have gradually increased. When using aluminum alloy materials to optimize the design of auto parts, under the same mechanical performance conditions, aluminum, a lightweight material, can absorb 50% more energy than steel, and it can also reduce the mass by 69%. High-strength steel is used in the thin-walled longitudinal beam structure, which has better energy absorption characteristics than low-carbon steel and improves the crashworthiness of the longitudinal beam. Especially in recent years, high-strength steel plates have been widely used and have greatly improved the collision safety performance of the chassis structure and the lightweight of the vehicle chassis. Table 3 provides a list of the main parameter values of commonly used steel for chassis structures.Table 3
List of main parameters of steel commonly used in chassis structure of models.
DesignationYield strength (MPa)Ultimate tensile strength (MPa)Total elongation (%)HSLA 350/45035045023–27DP 300/50030050030–34DP 350/60035060024–30TRIP 450/80045080026–32DP 500/80050080014–20CP 700/100070080010–15DP 700/1000700100012–17Mart 1250/1250125015204–6SFE CONCEPT’s variable logging feature is used to collect these design parameters into a design variable that changes the shape of the model by changing geometric values. When the geometric parameter is 0, the model will maintain the shape of the original model; when the geometric parameter is 1, the model will change to the shape of the model with the largest variable value. The final optimization result can be any value in the continuous interval of [0, 1].


## 2.1. Introduction to SFE CONCEPT Software

Everyone has realized long ago that if CAE can guide engineers’ design decisions in the early design stage, it will play a greater role. Because in the early design stage, many parameters such as geometry and materials have not been fixed, engineers can have a lot of space to seek multiple solutions. In order to use numerical simulation technology to predict performance, a good finite element model is based on an accurate CAD model. In other words, only when the design phase freezes and the CAD model is built, it is possible to perform numerical simulation analysis.SFE CONCEPT software adopts a simulation-driven design concept and uses an implicit full explanation method [8]. It can make complex geometric figures by modifying parameters such as the position of the control point, the curvature of the line, and the shape of the intersection, without CAD modeling, rapid transformation, geometric modeling. In addition, SFE CONCEPT also provides finite element (mesh) automated modeling technology, which can be improved in real time due to changes in parameterized geometric models and can quickly provide CAE analysis models [9]. Automobile CAE mainly refers to analysis calculation and analysis simulation in engineering design, and its core is finite element analysis technology based on modern computational mechanics. It can be used for product performance analysis, prediction, and optimization.The most important question is how to model numerical analysis in the early stages of design when CAD data is not yet available. In fact, most new product designs are based on existing models, and the geometric design and numerical analysis results of these models can be obtained. New design variables are created by additional or advanced methods based on existing models [10]. The importance and benefit of digital simulation is to establish a link between design changes and implementation so that our decision-making is clearer. However, due to the lack of suitable tools to quickly analyze the model, quantitative analysis was not performed in the early stages of the design [11]. Even with high-quality automatic mesh tools, they can only work after the CAD design is completed.The SFE CONCEPT provides a brand-new solution that helps to modify the CAD model and finite element design in the early stages of design [12]. SFE CONCEPT uses the completely hidden parameter definition of the product topology to modify the complex structure of the product in the form of cross-sections, beams, nodes, and free-form surfaces, which greatly shortens the design time and makes it available to design engineers. This concept is transformed into design variables for optimization analysis and finally into a CAD model based on assembly or subsequent production. Using default design parameter interpretation, SFE CONCEPT can easily handle geometric design variables by default. Design variables are based on the design level, such as key points and curves. Each new design change can be quickly and easily submitted to numerical simulation analysis to determine the impact of the editing project on key performance [13, 14].


## 2.2. Features of SFE CONCEPT Software System

### 2.2.1. Comprehensive Understanding of CAE Engineering Software System

After importing the CAD model into the CAE software, the CAE analysis of the structure can be started, and many geometric shapes need to be cleaned. The SFE CONCEPT includes analysis-based design concepts [15]. Through SFE CONCEPT modeling, CAD modeling, multi-geometric modeling, and rapid analytical modeling can be used to interpret the design as a whole, fully integrate and optimize the environment, and create an automated optimization environment. CAE is not only a verification tool in the product development process; it can guide engineers from the early stages of design to the use of large design space to find better design solutions [16].


### 2.2.2. Implicit Full-Parameter Interpretation Method

In other software environments, whether it is an efficient geometric CAD modeling solution or a finite element direct solution, even the simplest modeling variables are more cumbersome. The SFE CONCEPT uses an implicit way to interpret all parameters. Just by adjusting the position of the influence point, the shape of the line, the shape of the part, and other parameters, it can automatically change and adjust the complex geometric model arbitrarily [17].


### 2.2.3. The Finite Element Mesh Technology Automatically Converts the Geometric Model

The traditional deformation technology achieves the purpose of changing the shape of the geometric model by changing the finite element mesh. The requirements of grid computing will affect the accuracy of new network calculations and even make them unpredictable [18]. It is also necessary to update the relevant tables once to redefine the connections such as rivets, welded joints, and bolts. SFE CONCEPT uses a new, higher-resolution deformation technology. When the design model is modified, its limited component model will be automatically updated, and the network will also be automatically updated [19, 20]. When it is detected that the quality of the grid does not meet the criterion requirements, a high-quality grid with various connection relationships can be generated in real time according to the new geometric model. The schematic diagram of the traditional mode and the new SFE solution is shown in Figure 1.Figure 1
Traditional model and new SFE solution.


### 2.2.4. Rear System-Level Structure Optimization and Automatic Cycle Processing

In other software systems, usually only part of the structure is optimized. In terms of system-level structure, due to the excessive parameter changes and the need to redefine the connection relationship between components after design changes, the optimization process is difficult to implement [21]. SFE CONCEPT works by identifying multivariate, is compatible with most transaction constraint component solutions and interactive optimization solutions, and truly realizes automatic background optimization and recognition [22]. The closed optimized integrated environment is shown in Figure 2.Figure 2
Closed optimized integration environment.


### 2.2.5. Smartly Connected Modular Database

The SFE CONCEPT database function provides a classification method for storing reusable design data for future projects. All product components and subcomponents in the database are “smart”; that is, they fully adapt to the new geometric environment to support the development of future platforms [23].Advantages of SFE CONCEPT:(1)
It quickly creates the best conceptual design plan, saving time and development costs.(2)
The model is fully parametrically driven, which can quickly meet customer needs.(3)
It reduces the number of subsequent project updates and saves the cost of product design changes.(4)
It establishes a corporate knowledge base to ensure the reuse of resources.(5)
The adoption of the concept of “design-driven analysis” makes it possible to make the design successful the first time.(6)
Real-time feedback of parameter optimization results promotes product design innovation.(7)
Rich experience in product development and engineering consulting provides comprehensive technical support for enterprises.


## 2.2.1. Comprehensive Understanding of CAE Engineering Software System

After importing the CAD model into the CAE software, the CAE analysis of the structure can be started, and many geometric shapes need to be cleaned. The SFE CONCEPT includes analysis-based design concepts [15]. Through SFE CONCEPT modeling, CAD modeling, multi-geometric modeling, and rapid analytical modeling can be used to interpret the design as a whole, fully integrate and optimize the environment, and create an automated optimization environment. CAE is not only a verification tool in the product development process; it can guide engineers from the early stages of design to the use of large design space to find better design solutions [16].


## 2.2.2. Implicit Full-Parameter Interpretation Method

In other software environments, whether it is an efficient geometric CAD modeling solution or a finite element direct solution, even the simplest modeling variables are more cumbersome. The SFE CONCEPT uses an implicit way to interpret all parameters. Just by adjusting the position of the influence point, the shape of the line, the shape of the part, and other parameters, it can automatically change and adjust the complex geometric model arbitrarily [17].


## 2.2.3. The Finite Element Mesh Technology Automatically Converts the Geometric Model

The traditional deformation technology achieves the purpose of changing the shape of the geometric model by changing the finite element mesh. The requirements of grid computing will affect the accuracy of new network calculations and even make them unpredictable [18]. It is also necessary to update the relevant tables once to redefine the connections such as rivets, welded joints, and bolts. SFE CONCEPT uses a new, higher-resolution deformation technology. When the design model is modified, its limited component model will be automatically updated, and the network will also be automatically updated [19, 20]. When it is detected that the quality of the grid does not meet the criterion requirements, a high-quality grid with various connection relationships can be generated in real time according to the new geometric model. The schematic diagram of the traditional mode and the new SFE solution is shown in Figure 1.Figure 1
Traditional model and new SFE solution.


## 2.2.4. Rear System-Level Structure Optimization and Automatic Cycle Processing

In other software systems, usually only part of the structure is optimized. In terms of system-level structure, due to the excessive parameter changes and the need to redefine the connection relationship between components after design changes, the optimization process is difficult to implement [21]. SFE CONCEPT works by identifying multivariate, is compatible with most transaction constraint component solutions and interactive optimization solutions, and truly realizes automatic background optimization and recognition [22]. The closed optimized integrated environment is shown in Figure 2.Figure 2
Closed optimized integration environment.


## 2.2.5. Smartly Connected Modular Database

The SFE CONCEPT database function provides a classification method for storing reusable design data for future projects. All product components and subcomponents in the database are “smart”; that is, they fully adapt to the new geometric environment to support the development of future platforms [23].Advantages of SFE CONCEPT:(1)
It quickly creates the best conceptual design plan, saving time and development costs.(2)
The model is fully parametrically driven, which can quickly meet customer needs.(3)
It reduces the number of subsequent project updates and saves the cost of product design changes.(4)
It establishes a corporate knowledge base to ensure the reuse of resources.(5)
The adoption of the concept of “design-driven analysis” makes it possible to make the design successful the first time.(6)
Real-time feedback of parameter optimization results promotes product design innovation.(7)
Rich experience in product development and engineering consulting provides comprehensive technical support for enterprises.


## 2.3. SUV Model Chassis Structure Design Requirements

When designing a vehicle chassis, we must first analyze the customer’s needs and then determine what type of product the customer wants; finally, each product is defined separately according to the principle of analytic hierarchy process. The analyzed sequence structure is usually divided into upper, middle, and lower layers, which can be obtained by hierarchically dividing the corresponding structural patterns of the lower layers. With the rapid economic development, cars have gradually entered the homes of ordinary people, consumer groups have been studied, and satisfied customers are identified at the highest level (target level) based on real-world chassis product models. To this end, four principles are embodied: safety, comfort, price, and environmental protection. It also reflects the following criteria: service life of parts, engine performance, service braking performance, parking brake efficiency, shift uniformity, steering performance, frame length, low vibration, low noise, etc. All these factors, including cost and energy saving, constitute the final production line [24, 25].


### 2.3.1. Chassis Structural Design

The chassis is mainly responsible for the body pressure and power of the steering system and transmits the engine power of the engine to the chassis. Parts and chassis allow you to drive a car anytime and anywhere, most of which consist of thousands of parts. This is the basis of the vehicle. Accessories such as engines, power tools, and body functions are directly or indirectly installed on the chassis under the car. It is divided into four main systems [26]. The main functional structure diagram of the car chassis is shown in Figure 3.(1)
Transmission system: Most of the energy produced by the engine is transferred to the steering wheel. The steering wheel usually includes half shafts and transmissions, clutches, drive shafts, and differentials. The engine is the power source of most cars, including five main systems and four main mechanisms. In addition, there is an installation relationship between the air filter and the cooler [27].(2)
Driving system: It mainly ensures that the car can drive normally under different conditions. The quality of the driving system determines the driver’s driving experience and the passenger’s car experience. It is composed of the frame, axle, wheels, and suspension of the car. The driving system of the SUV receives the power of the drive train and generates gravity through the action of the driving wheels and the road surface, so that the car can drive normally. It withstands the total weight of the car and the reaction force of the ground, alleviates the impact of uneven roads on the body, attenuates the vibration of the car in driving, maintains the smoothness of driving, and cooperates with the steering system to ensure the steering stability of the car.(3)
Steering system: Its main function is to drive in the direction selected by the driver. Usually the steering system plays a key role in driving.(4)
Braking system: The main task is to stop or slow down the moving car. It is mainly used in driving or parking, including brakes, control devices, transmission devices, and application devices.(5)
Frame: The weight of the entire body is borne by it, which directly affects the service life of the car [28].Figure 3
The main function structure of automobile chassis.The parameter table of the vehicle chassis of the Volkswagen Tiguan in the SUV is shown in Table1.Table 1
Parameters of vehicle chassis.
ProjectsSymbolsValuesWheelbaseWB (mm)6100Front axle loadWf (kg)6000Rear axle loadWr (kg)11700High-quality coreCG (mm)955Spring stiffness (front/rear)K (N/mm)204/191Shock absorber damping (front/rear)δ (Nsec/mm)14.2/13.2The platformization of the chassis structure can realize the structured design of a variety of car model types, mainly with the following parameters.(1)
Electric power assist and hydraulic power assist, (the schematic diagram is shown in Figure4): The electric power assist and hydraulic power assist of the same model have different configurations, and the original steering knuckles are the same, but the positions of the openings on the original electric mechanical steering knuckle and hydraulic power steering knuckle are different, and the positions of the holes on the corresponding lower swing arms are also different.(2)
Two-wheel drive models and four-wheel drive models, as shown in Figure5: The two-wheel drive and four-wheel drive models of the same car are just the shape of the subframe. The formula is different, the rest of the structural parts are the same, and they can all be used.(3)
Size parameters or quality parameters: Within a certain range, even the models of the same platform may have different quantitative parameters of size and mass. For example, the height of the center of mass is different, wheelbase is also different, and the front and rear axle loads are different. These differences are often caused by structural elements.Figure 4
Electric power steering and hydraulic power steering parts diagram.Figure 5
Diagram of 2WD and 4WD models.


## 2.3.1. Chassis Structural Design

The chassis is mainly responsible for the body pressure and power of the steering system and transmits the engine power of the engine to the chassis. Parts and chassis allow you to drive a car anytime and anywhere, most of which consist of thousands of parts. This is the basis of the vehicle. Accessories such as engines, power tools, and body functions are directly or indirectly installed on the chassis under the car. It is divided into four main systems [26]. The main functional structure diagram of the car chassis is shown in Figure 3.(1)
Transmission system: Most of the energy produced by the engine is transferred to the steering wheel. The steering wheel usually includes half shafts and transmissions, clutches, drive shafts, and differentials. The engine is the power source of most cars, including five main systems and four main mechanisms. In addition, there is an installation relationship between the air filter and the cooler [27].(2)
Driving system: It mainly ensures that the car can drive normally under different conditions. The quality of the driving system determines the driver’s driving experience and the passenger’s car experience. It is composed of the frame, axle, wheels, and suspension of the car. The driving system of the SUV receives the power of the drive train and generates gravity through the action of the driving wheels and the road surface, so that the car can drive normally. It withstands the total weight of the car and the reaction force of the ground, alleviates the impact of uneven roads on the body, attenuates the vibration of the car in driving, maintains the smoothness of driving, and cooperates with the steering system to ensure the steering stability of the car.(3)
Steering system: Its main function is to drive in the direction selected by the driver. Usually the steering system plays a key role in driving.(4)
Braking system: The main task is to stop or slow down the moving car. It is mainly used in driving or parking, including brakes, control devices, transmission devices, and application devices.(5)
Frame: The weight of the entire body is borne by it, which directly affects the service life of the car [28].Figure 3
The main function structure of automobile chassis.The parameter table of the vehicle chassis of the Volkswagen Tiguan in the SUV is shown in Table1.Table 1
Parameters of vehicle chassis.
ProjectsSymbolsValuesWheelbaseWB (mm)6100Front axle loadWf (kg)6000Rear axle loadWr (kg)11700High-quality coreCG (mm)955Spring stiffness (front/rear)K (N/mm)204/191Shock absorber damping (front/rear)δ (Nsec/mm)14.2/13.2The platformization of the chassis structure can realize the structured design of a variety of car model types, mainly with the following parameters.(1)
Electric power assist and hydraulic power assist, (the schematic diagram is shown in Figure4): The electric power assist and hydraulic power assist of the same model have different configurations, and the original steering knuckles are the same, but the positions of the openings on the original electric mechanical steering knuckle and hydraulic power steering knuckle are different, and the positions of the holes on the corresponding lower swing arms are also different.(2)
Two-wheel drive models and four-wheel drive models, as shown in Figure5: The two-wheel drive and four-wheel drive models of the same car are just the shape of the subframe. The formula is different, the rest of the structural parts are the same, and they can all be used.(3)
Size parameters or quality parameters: Within a certain range, even the models of the same platform may have different quantitative parameters of size and mass. For example, the height of the center of mass is different, wheelbase is also different, and the front and rear axle loads are different. These differences are often caused by structural elements.Figure 4
Electric power steering and hydraulic power steering parts diagram.Figure 5
Diagram of 2WD and 4WD models.


## 2.4. Modeling and Multivariable Optimization of Chassis Structure

### 2.4.1. Chassis Structure Design and Modeling

The traditional automobile development process includes modeling, conceptual design, detailed design of CAD information, and CAE analysis. In the design stage of the traditional concept, the structural design is based on the work experience of the chassis designer, first of all to ensure the possibility and optimization of the modeling, chassis design, and process constraints. After completing the detailed 3D data, it can simply calculate the weight of the vehicle chassis, identify related performance issues through CAE analysis, and optimize the structure [29]. The problem with implementation is the duplication of related work, such as vehicle CAD chassis data generation, vehicle design, and vehicle chassis modeling, which will slow down the entire project process and increase the development cycle. Based on the concept of efficient steering structure design analysis, the development process of the chassis is simplified [30]. The overall block diagram of the modeling is shown in Figure 6.Figure 6
General framework diagram of modeling.Geometric model design is a prerequisite for analyzing end elements. The precise geometric model will greatly improve the design accuracy. In the detailed design process, the design should only adapt to the structural characteristics of the vehicle chassis and strive to be simple and easy to modify. The analytical model used in this paper is an implicit full-parameter model based on the SFE CONCEPT full-parameter modeling concept, which is mainly based on the point-line-surface-beam-connection sequence. It can form designs in structures such as cover plates, beam units, and accessories to create a vehicle chassis. At the same time, the topological relationship between the models is established through mapping, and the model assembly parameters are identified [31]. Therefore, the geometry of the model is controlled by points, lines, and sections. When adjusting the geometry of the model, the model associated with it will also change according to the parameters of the assembly relationship. Unlike other CAD software, adjacent parts need to be repaired one by one. By creating a full-parameter model, structural design engineers can easily create and configure vehicle chassis and topology interactions. This is very helpful in the early stages of vehicle chassis development, as many solutions require major restructuring and flexible handling. The data sheet of the three SUV models currently on the market is shown in Table 2.Table 2
Three types of car classification data sheet.
Vehicle classCompactMedium-sized carsLarge vehiclesLength (mm)3600–39004300–46004800–5200Width (mm)1550–16701670–17701800–1900Height (mm)1350–14801360–14301400–1500Wheelbase (mm)2350–25002500–28001700–3200Ground clearance (mm)100–150100–150110–150Approach angle (°)15–2012–2012–20Departure angle (°)15–2012–2012–20


### 2.4.2. Multivariable Optimization of Chassis Structure

The implicit parameterized modeling method provided by SFE CONCEPT can parameterize the variables involved in the above four optimization methods, which can quickly change the structure model and create a CAE model simultaneously. This enables shape optimization and size optimization, which are more constrained and difficult to achieve in the optimization process, to be realized. At the same time, the model parameterized in the SFE CONCEPT can also keep the topological connection between the components unchanged. In the structural optimization research of this paper, the characteristics of the parametric structural design method are also used to synergistically apply the optimization methods of shape, size, and material to the structural design [32, 33].(1)Topology Optimization Design. The scope of topology optimization, that is, “bionic optimization,” covers the entire chassis structure. Regardless of the field, the finite element method is needed. The use of this method is extremely effective in structural design that considers the force transmission path and load distribution of the chassis structure, and can make the chassis structure have good load-bearing performance. The parameterized model can be used to realize rapid geometric model changes when designing different force transmission paths. The main content of this paper is the structural optimization of the submodules in the conceptual design stage, thus retaining the overall structure and connection relationship of the reference model. For a brand-new chassis structure design, topology optimization is required first when the overall structure design is performed. The topology change of the frame is shown in Figure 7.Figure 7
Topology change of the frame.(2)Shape Optimization Design. Shape optimization needs to change variables other than the overall number of beams, connection methods, and overall structure in a determined structure, including the curvature of the control line of the joint, the position of the control point, and its relative position in the chassis structure. In the traditional chassis structure optimization process, since all the chassis structures have been basically finalized during the analysis phase, the constraints between the various structural components have greatly reduced the freedom of shape optimization, resulting in lightweight and other performance optimization. The possibilities have not been exploited. If the shape variable of the structure is changed during the analysis phase, a lot of reconstruction work is required to support this change. However, based on the expression of implicit parametric modeling, the curvature and cross-sectional shape of the beam structure can be quickly changed, and the shape of the structure can be optimized. The shape change of the frame is shown in Figure 8.Figure 8
Frame shape change.(3)Size Optimization. It is relatively mature to be used in the field of optimization of the current chassis structure. Among them, the variable mesh technology enables the modification of the finite element model to reflect the change of the geometric model when the geometric model of the chassis structure has been determined, so as to optimize the size. Although this method has its practicability, the technology is limited to small geometric size changes due to the limitations of the existing grid topology. The automatic update of the finite element model in the implicit parametric design method used in this paper is to redivide the grid, rather than modify the original grid. This method can avoid the distortion of the grid due to the large deformation in the morphing technology; at the same time, the quality control of the finite element model grid can be achieved by setting or writing the corresponding batch file statement, which greatly guarantees the quality of the finite element model. At present, the most common size optimization in traditional chassis structures is the optimization of sheet thickness, and the SFE CONCEPT can parameterize the thickness of structural parts to achieve continuous changes in material thickness.(4)Material Optimization Design. In recent years, emerging materials gradually used in automobiles have gradually increased. When using aluminum alloy materials to optimize the design of auto parts, under the same mechanical performance conditions, aluminum, a lightweight material, can absorb 50% more energy than steel, and it can also reduce the mass by 69%. High-strength steel is used in the thin-walled longitudinal beam structure, which has better energy absorption characteristics than low-carbon steel and improves the crashworthiness of the longitudinal beam. Especially in recent years, high-strength steel plates have been widely used and have greatly improved the collision safety performance of the chassis structure and the lightweight of the vehicle chassis. Table 3 provides a list of the main parameter values of commonly used steel for chassis structures.Table 3
List of main parameters of steel commonly used in chassis structure of models.
DesignationYield strength (MPa)Ultimate tensile strength (MPa)Total elongation (%)HSLA 350/45035045023–27DP 300/50030050030–34DP 350/60035060024–30TRIP 450/80045080026–32DP 500/80050080014–20CP 700/100070080010–15DP 700/1000700100012–17Mart 1250/1250125015204–6SFE CONCEPT’s variable logging feature is used to collect these design parameters into a design variable that changes the shape of the model by changing geometric values. When the geometric parameter is 0, the model will maintain the shape of the original model; when the geometric parameter is 1, the model will change to the shape of the model with the largest variable value. The final optimization result can be any value in the continuous interval of [0, 1].


## 2.4.1. Chassis Structure Design and Modeling

The traditional automobile development process includes modeling, conceptual design, detailed design of CAD information, and CAE analysis. In the design stage of the traditional concept, the structural design is based on the work experience of the chassis designer, first of all to ensure the possibility and optimization of the modeling, chassis design, and process constraints. After completing the detailed 3D data, it can simply calculate the weight of the vehicle chassis, identify related performance issues through CAE analysis, and optimize the structure [29]. The problem with implementation is the duplication of related work, such as vehicle CAD chassis data generation, vehicle design, and vehicle chassis modeling, which will slow down the entire project process and increase the development cycle. Based on the concept of efficient steering structure design analysis, the development process of the chassis is simplified [30]. The overall block diagram of the modeling is shown in Figure 6.Figure 6
General framework diagram of modeling.Geometric model design is a prerequisite for analyzing end elements. The precise geometric model will greatly improve the design accuracy. In the detailed design process, the design should only adapt to the structural characteristics of the vehicle chassis and strive to be simple and easy to modify. The analytical model used in this paper is an implicit full-parameter model based on the SFE CONCEPT full-parameter modeling concept, which is mainly based on the point-line-surface-beam-connection sequence. It can form designs in structures such as cover plates, beam units, and accessories to create a vehicle chassis. At the same time, the topological relationship between the models is established through mapping, and the model assembly parameters are identified [31]. Therefore, the geometry of the model is controlled by points, lines, and sections. When adjusting the geometry of the model, the model associated with it will also change according to the parameters of the assembly relationship. Unlike other CAD software, adjacent parts need to be repaired one by one. By creating a full-parameter model, structural design engineers can easily create and configure vehicle chassis and topology interactions. This is very helpful in the early stages of vehicle chassis development, as many solutions require major restructuring and flexible handling. The data sheet of the three SUV models currently on the market is shown in Table 2.Table 2
Three types of car classification data sheet.
Vehicle classCompactMedium-sized carsLarge vehiclesLength (mm)3600–39004300–46004800–5200Width (mm)1550–16701670–17701800–1900Height (mm)1350–14801360–14301400–1500Wheelbase (mm)2350–25002500–28001700–3200Ground clearance (mm)100–150100–150110–150Approach angle (°)15–2012–2012–20Departure angle (°)15–2012–2012–20


## 2.4.2. Multivariable Optimization of Chassis Structure

The implicit parameterized modeling method provided by SFE CONCEPT can parameterize the variables involved in the above four optimization methods, which can quickly change the structure model and create a CAE model simultaneously. This enables shape optimization and size optimization, which are more constrained and difficult to achieve in the optimization process, to be realized. At the same time, the model parameterized in the SFE CONCEPT can also keep the topological connection between the components unchanged. In the structural optimization research of this paper, the characteristics of the parametric structural design method are also used to synergistically apply the optimization methods of shape, size, and material to the structural design [32, 33].(1)Topology Optimization Design. The scope of topology optimization, that is, “bionic optimization,” covers the entire chassis structure. Regardless of the field, the finite element method is needed. The use of this method is extremely effective in structural design that considers the force transmission path and load distribution of the chassis structure, and can make the chassis structure have good load-bearing performance. The parameterized model can be used to realize rapid geometric model changes when designing different force transmission paths. The main content of this paper is the structural optimization of the submodules in the conceptual design stage, thus retaining the overall structure and connection relationship of the reference model. For a brand-new chassis structure design, topology optimization is required first when the overall structure design is performed. The topology change of the frame is shown in Figure 7.Figure 7
Topology change of the frame.(2)Shape Optimization Design. Shape optimization needs to change variables other than the overall number of beams, connection methods, and overall structure in a determined structure, including the curvature of the control line of the joint, the position of the control point, and its relative position in the chassis structure. In the traditional chassis structure optimization process, since all the chassis structures have been basically finalized during the analysis phase, the constraints between the various structural components have greatly reduced the freedom of shape optimization, resulting in lightweight and other performance optimization. The possibilities have not been exploited. If the shape variable of the structure is changed during the analysis phase, a lot of reconstruction work is required to support this change. However, based on the expression of implicit parametric modeling, the curvature and cross-sectional shape of the beam structure can be quickly changed, and the shape of the structure can be optimized. The shape change of the frame is shown in Figure 8.Figure 8
Frame shape change.(3)Size Optimization. It is relatively mature to be used in the field of optimization of the current chassis structure. Among them, the variable mesh technology enables the modification of the finite element model to reflect the change of the geometric model when the geometric model of the chassis structure has been determined, so as to optimize the size. Although this method has its practicability, the technology is limited to small geometric size changes due to the limitations of the existing grid topology. The automatic update of the finite element model in the implicit parametric design method used in this paper is to redivide the grid, rather than modify the original grid. This method can avoid the distortion of the grid due to the large deformation in the morphing technology; at the same time, the quality control of the finite element model grid can be achieved by setting or writing the corresponding batch file statement, which greatly guarantees the quality of the finite element model. At present, the most common size optimization in traditional chassis structures is the optimization of sheet thickness, and the SFE CONCEPT can parameterize the thickness of structural parts to achieve continuous changes in material thickness.(4)Material Optimization Design. In recent years, emerging materials gradually used in automobiles have gradually increased. When using aluminum alloy materials to optimize the design of auto parts, under the same mechanical performance conditions, aluminum, a lightweight material, can absorb 50% more energy than steel, and it can also reduce the mass by 69%. High-strength steel is used in the thin-walled longitudinal beam structure, which has better energy absorption characteristics than low-carbon steel and improves the crashworthiness of the longitudinal beam. Especially in recent years, high-strength steel plates have been widely used and have greatly improved the collision safety performance of the chassis structure and the lightweight of the vehicle chassis. Table 3 provides a list of the main parameter values of commonly used steel for chassis structures.Table 3
List of main parameters of steel commonly used in chassis structure of models.
DesignationYield strength (MPa)Ultimate tensile strength (MPa)Total elongation (%)HSLA 350/45035045023–27DP 300/50030050030–34DP 350/60035060024–30TRIP 450/80045080026–32DP 500/80050080014–20CP 700/100070080010–15DP 700/1000700100012–17Mart 1250/1250125015204–6SFE CONCEPT’s variable logging feature is used to collect these design parameters into a design variable that changes the shape of the model by changing geometric values. When the geometric parameter is 0, the model will maintain the shape of the original model; when the geometric parameter is 1, the model will change to the shape of the model with the largest variable value. The final optimization result can be any value in the continuous interval of [0, 1].


## 3. Material Analysis and Data Description

### 3.1. Material Properties

The automobile power chassis is mainly composed of thin-walled parts and entities, and the materials mainly include steel, aluminum alloy, and rubber. In the case of a frontal collision of the chassis, it mainly relies on the plastic deformation of the components to absorb energy. Therefore, in this simulation, the properties of the steel and aluminum alloy thin-walled parts are all of the SectShll type, given the corresponding thickness, and the material is of the Mat24 elastoplastic type.The stress-strain curve of Q800 and aluminum alloy in the main load-bearing members of automobile chassis is shown in Figure9.Figure 9
Stress-strain curve of Q800 and aluminum alloy.
(a)(b)The deformation process of the component in the finite element model can be regarded as the sum of the movement and deformation of the nodes in the model, and the relationship between the node positions and time t can be expressed as follows:(1)s1=s1s0,t.At T0, the initial position of the node is as follows:(2)s1s0,0=s0,s1•s0,0=v1s0.The vehicle model at the moment of collision is as follows:(3)ρDv1Dt=F+∂∂siσji.During the entire process of vehicle collision deformation,(4)ρDeDt=12σji⋅vj,i+vi,j.During the collision process of the particle,(5)ρs1=ρ0S0∂S0∂s1,where v represents the speed, ρ0 represents the density of the structure at the beginning of the vehicle collision, ρ represents the density of the structure during deformation, F is the force, σji is the stress field, and e represents the internal energy of the structural unit mass.During the flow of power battery fluid,(6)∂ρ∂t+∂ρu∂x+∂ρv∂y+∂ρw∂z=0.The fluid follows the N-S equation when flowing:(7)∂ρu∂t+divρUu=divμgradu−∂p∂x+Su,∂ρv∂t+divρUv=divμgradv−∂p∂y+Sv,∂ρw∂t+divρUw=divμgradw−∂p∂z+Sw.In the coupled field where heat exchange occurs in the system,(8)∂ρT∂t+∂ρuT∂x+∂ρvT∂y+∂ρwT∂z=∂∂xkcp∂T∂x+∂∂ykcp∂T∂y+∂∂zkcp∂T∂z+ST.The system of equations has a unique solution:(9)p=ρRT,where R is the gas constant.Turbulence pulsation equation is as follows:(10)ρ∂k∂t+ρuj∂k∂xj=∂∂xjη+ηt∂xj∂k∂xj+ηt∂ui∂xj∂ui∂xj+∂uj∂xi−ρ.Dissipation rate governing equation is as follows:(11)ρ∂ε∂t+ρuk∂ε∂xk=∂∂xkη+ηt∂ε∂ε∂xk+c1εkηt∂ui∂xj∂ui∂xj+∂uj∂xi−c2ρε2k.In(12)ηt=cμρk2ε,the total heat generated when the battery is working is as follows:(13)Q=Qcr+Qr1+Qr2+Qscr.In(14)Qcr=Q03600FI,Qr2=I2Rr1,the total heat generated by the battery during charging and discharging is as follows:(15)Q=Qr1+Qr2=I2RR1+RR2=I2R.Thermal model of the battery in the right-hand coordinate system is as follows:(16)ρCp∂T∂t=λx∂2T∂x2+λy∂2T∂y2+λz∂2T∂z2+Q1.When the surface of the battery is convectively exchanged with the fluid, the surface energy satisfies the following:(17)Q2=hAT1−T0.From the frontal collision finite element model of the vehicle chassis, it is known that the longitudinal dimension from the front end of the chassis to the rear end of the front side member (recorded as the front longitudinal dimension) changes as shown in Figure10. The longitudinal dimension change of the module stringer behind the power chassis is shown in Figure 11.Figure 10
Front-end longitudinal dimension change curve.Figure 11
Longitudinal dimension change curve of longitudinal beam.Figure10 shows that the compression of the frame before the collision gradually increases, and then the chassis tilts forward and the longitudinal compression decreases. By organizing and analyzing the chart data, the maximum longitudinal dimension of the front end is compressed by 3.98 cm, and the final compression is 2.48 cm.It can be seen from Figure11 that the longitudinal beam is first compressed, and then the longitudinal compression size becomes smaller due to the forward tilt phenomenon; the maximum compression amount is 7.5 mm. In general, the model is suitable for collision environments.The longitudinal intrusion amount of the front cross beam and the longitudinal dimension change of the longitudinal beam of the middle module of the power chassis are shown in Figure12.Figure 12
Intermediate module collision results: (a) longitudinal intrusion of front cross member; (b) longitudinal compression variation curve of longitudinal beam.
(a)(b)It can be seen from Figure12 that the forward tilt phenomenon occurred during the collision, the maximum intrusion of the front cross member was 6.20 mm, and the maximum compression of the longitudinal beam was 4.40 mm.SFE CONCEPT software offers a greater advantage in design than other CAD software, which is specifically reflected in time efficiency. The result of the time spent designing the same model is shown in Figure13(a). In addition, the result of comparing SFE CONCEPT software docking with other CAD software is shown in Figure 13(b).Figure 13
Comparison of SFE CONCEPT with other CAD.
(a)(b)It can be seen from Figure13 that SFE CONCEPT has the shortest modeling time and can be seamlessly connected with other CAD software.


## 3.1. Material Properties

The automobile power chassis is mainly composed of thin-walled parts and entities, and the materials mainly include steel, aluminum alloy, and rubber. In the case of a frontal collision of the chassis, it mainly relies on the plastic deformation of the components to absorb energy. Therefore, in this simulation, the properties of the steel and aluminum alloy thin-walled parts are all of the SectShll type, given the corresponding thickness, and the material is of the Mat24 elastoplastic type.The stress-strain curve of Q800 and aluminum alloy in the main load-bearing members of automobile chassis is shown in Figure9.Figure 9
Stress-strain curve of Q800 and aluminum alloy.
(a)(b)The deformation process of the component in the finite element model can be regarded as the sum of the movement and deformation of the nodes in the model, and the relationship between the node positions and time t can be expressed as follows:(1)s1=s1s0,t.At T0, the initial position of the node is as follows:(2)s1s0,0=s0,s1•s0,0=v1s0.The vehicle model at the moment of collision is as follows:(3)ρDv1Dt=F+∂∂siσji.During the entire process of vehicle collision deformation,(4)ρDeDt=12σji⋅vj,i+vi,j.During the collision process of the particle,(5)ρs1=ρ0S0∂S0∂s1,where v represents the speed, ρ0 represents the density of the structure at the beginning of the vehicle collision, ρ represents the density of the structure during deformation, F is the force, σji is the stress field, and e represents the internal energy of the structural unit mass.During the flow of power battery fluid,(6)∂ρ∂t+∂ρu∂x+∂ρv∂y+∂ρw∂z=0.The fluid follows the N-S equation when flowing:(7)∂ρu∂t+divρUu=divμgradu−∂p∂x+Su,∂ρv∂t+divρUv=divμgradv−∂p∂y+Sv,∂ρw∂t+divρUw=divμgradw−∂p∂z+Sw.In the coupled field where heat exchange occurs in the system,(8)∂ρT∂t+∂ρuT∂x+∂ρvT∂y+∂ρwT∂z=∂∂xkcp∂T∂x+∂∂ykcp∂T∂y+∂∂zkcp∂T∂z+ST.The system of equations has a unique solution:(9)p=ρRT,where R is the gas constant.Turbulence pulsation equation is as follows:(10)ρ∂k∂t+ρuj∂k∂xj=∂∂xjη+ηt∂xj∂k∂xj+ηt∂ui∂xj∂ui∂xj+∂uj∂xi−ρ.Dissipation rate governing equation is as follows:(11)ρ∂ε∂t+ρuk∂ε∂xk=∂∂xkη+ηt∂ε∂ε∂xk+c1εkηt∂ui∂xj∂ui∂xj+∂uj∂xi−c2ρε2k.In(12)ηt=cμρk2ε,the total heat generated when the battery is working is as follows:(13)Q=Qcr+Qr1+Qr2+Qscr.In(14)Qcr=Q03600FI,Qr2=I2Rr1,the total heat generated by the battery during charging and discharging is as follows:(15)Q=Qr1+Qr2=I2RR1+RR2=I2R.Thermal model of the battery in the right-hand coordinate system is as follows:(16)ρCp∂T∂t=λx∂2T∂x2+λy∂2T∂y2+λz∂2T∂z2+Q1.When the surface of the battery is convectively exchanged with the fluid, the surface energy satisfies the following:(17)Q2=hAT1−T0.From the frontal collision finite element model of the vehicle chassis, it is known that the longitudinal dimension from the front end of the chassis to the rear end of the front side member (recorded as the front longitudinal dimension) changes as shown in Figure10. The longitudinal dimension change of the module stringer behind the power chassis is shown in Figure 11.Figure 10
Front-end longitudinal dimension change curve.Figure 11
Longitudinal dimension change curve of longitudinal beam.Figure10 shows that the compression of the frame before the collision gradually increases, and then the chassis tilts forward and the longitudinal compression decreases. By organizing and analyzing the chart data, the maximum longitudinal dimension of the front end is compressed by 3.98 cm, and the final compression is 2.48 cm.It can be seen from Figure11 that the longitudinal beam is first compressed, and then the longitudinal compression size becomes smaller due to the forward tilt phenomenon; the maximum compression amount is 7.5 mm. In general, the model is suitable for collision environments.The longitudinal intrusion amount of the front cross beam and the longitudinal dimension change of the longitudinal beam of the middle module of the power chassis are shown in Figure12.Figure 12
Intermediate module collision results: (a) longitudinal intrusion of front cross member; (b) longitudinal compression variation curve of longitudinal beam.
(a)(b)It can be seen from Figure12 that the forward tilt phenomenon occurred during the collision, the maximum intrusion of the front cross member was 6.20 mm, and the maximum compression of the longitudinal beam was 4.40 mm.SFE CONCEPT software offers a greater advantage in design than other CAD software, which is specifically reflected in time efficiency. The result of the time spent designing the same model is shown in Figure13(a). In addition, the result of comparing SFE CONCEPT software docking with other CAD software is shown in Figure 13(b).Figure 13
Comparison of SFE CONCEPT with other CAD.
(a)(b)It can be seen from Figure13 that SFE CONCEPT has the shortest modeling time and can be seamlessly connected with other CAD software.


## 4. Discussion

The SFE CONCEPT allows the creation and modification of implicit parametric surface models quickly and efficiently. The unique mode of attribute-based single-layer geometry ensures high performance even when dealing with large structures (such as entire car chassis structures or larger structures). Existing model components can be reconnected to make full use of the existing model, and a large number of variants can be constructed in a short period of time for functional comparison. The finite element mesh that can be used for simulation at any time includes connections and associations with external components and can be exported at any time with the click of a button.The SFE CONCEPT provides strong support for the design of lightweight and safer vehicles. By enhancing the understanding of the mechanical behavior of the product, the design cycle can be shortened and a more complete product can be created. Especially in terms of the car life cycle and the need for the speed of the development process, this tool is extremely valuable. Its rapid geometry creation, topological and geometric modifications to the vehicle chassis structure, plus an integrated finite element mesh creator are among its unique capabilities. With these functions, SFE CONCEPT can meet the requirements for speeding up the design process. A large number of variant studies can be carried out very quickly to strengthen the understanding of product behavior and to observe and ensure performance through multispecialty simulation analysis. All these factors combine to form a flexible pre-CAE development process, making it widely welcomed in the global automotive industry.From the structural point of view, Volkswagen Tiguan adopts the common front MacPherson independent suspension and rear four-link independent suspension. The advantage of this combination is that it can not only take up the smallest space but also ensure good chassis performance. Although the suspension forms are similar, the details are different. Take the most common front MacPherson suspension as example; the S-shaped eccentric spring used by the Tiguan allows the Tiguan to get more accurate support of the spring when cornering and, at the same time, reduces the bending moment of the side force on the shock absorber to improve the working efficiency of the shock absorber and obtain better cornering characteristics.


## 5. Conclusions

The traditional finite element modeling is completed after a complete CAD modeling, and the CAD model requires a lot of preprocessing. The traditional finite element design takes a long construction time and is inefficient. SFE CONCEPT software can directly use the complete parameter template to create the finite element model, without the need for detailed CAD information templates, and adjust it according to the geometric pattern changes. The traditional finite element model needs to rebuild the finite element model based on the new CAD model. Using the SFE full-parameter model, the finite element model can be adjusted in real time as the geometric model changes. It greatly reduces the modeling time of finite components. However, it was discovered in the process of this design that the quality of the model has not been well improved, which will have a certain impact on the performance of the chassis structure.



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*Source: 3699708-2022-04-23.xml*