Structural Analysis of a Semi-Trailer Tractor Truck

Structural Analysis of a Semi-Trailer Tractor Truck | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Structural Analysis of a Semi-Trailer Tractor Truck Changnian Lu, Fanling Zeng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8736320/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper focuses on the finite element analysis of a complete vehicle structure. Compared to component models such as the frame and axles, the full-vehicle model is characterized by its large computational scale and the difficulty in simulating the connections and assemblies between components. By appropriately simplifying the geometric model and strictly controlling the finite element mesh size, this study seeks an optimal balance between computational scale and accuracy. During the component connection and assembly process, the finite element models of the components are imported, translated, and rotated, and then connected using rigid links and couplings. This results in the final full-vehicle finite element model. A preliminary analysis of the finite element model is conducted, followed by electrical testing on the actual vehicle. This provides a practical basis for the finite element analysis and verifies the correctness of the model. Subsequently, using the validated finite element model, the stress distribution and deformation of the tractor under single-wheel lift and braking conditions are analyzed. Finally, a modal analysis of the tractor's complete structure is performed to determine its natural frequencies and mode shapes, assessing whether they effectively avoid external excitation frequencies. Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Mathematics and computing Semi-trailer tractor Finite Element Analysis Modal Analysis Full-vehicle Structure Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1. Introduction The semi-trailer tractor serves as a core piece of equipment in modern road logistics transportation. Its function is to tow semi-trailers via its saddle, undertaking the majority of medium to long-distance heavy-duty freight transport tasks. The rationality, reliability, and lightweight level of the entire vehicle structure directly affect transport efficiency, driving safety, fuel economy, and regulatory compliance. Therefore, conducting a systematic analysis of the full-vehicle structure of a semi-trailer tractor is of critical importance for design improvement, performance optimization, maintenance, and technical evaluation. Finite element modeling and analysis of a complete semi-trailer tractor is a complex and challenging engineering task. The difficulties are mainly reflected in model complexity, balance of computational resources, and reliability of analysis results, among other aspects:( 1 ) Geometric and structural complexity. The tractor consists of a large number of components with diverse shapes and intricate connection relationships. The structure is extensive and comprises numerous parts from the cab, frame, suspension system, and powertrain to the saddle involving thousands of individual components. ( 2 ) Treatment of material and contact nonlinearities. Linear analysis is often insufficient to reflect real-world conditions. Nonlinearities are a primary cause of increased analysis complexity and computational cost. The full vehicle contains numerous contact pairs, such as bolted joint surfaces, gear meshing, and contact between leaf spring laminations. Changes in contact states can lead to computational instability and a sharp increase in calculation time. ( 3 ) Authenticity of loads and boundary conditions. Accurately applying real-world physical loads to the finite element model is key to ensuring the credibility of the results. ( 4 ) Balance between model scale and computational efficiency. Under the premise of not significantly affecting overall accuracy, reasonable simplifications such as omitting minor features or replacing complex components with beam or rod elements are employed to reduce model scale. 2. Establishment of Finite Element Model 2.1 Element Selection and Meshing The full vehicle model includes components such as the cab, frame, leaf springs, and axles. Shell elements are used to simulate the cab, frame, and leaf springs, while solid elements are employed for the axles. Shell elements possess both bending and membrane capabilities, enabling them to withstand in-plane and normal loads. Solid elements have the ability to account for plasticity, creep, expansion, stress stiffening, large deformation, and large strain. For components modeled with shell elements, 2D meshing can be directly applied. For parts modeled with solid elements, 2D meshing is first performed on their surfaces, after which the 2D mesh is mapped into a 3D mesh. 2.2 Material Properties Material properties are typically defined by several physical parameters: density, elastic modulus, Poisson's ratio, tensile strength, and yield limit, among others. The cab of this tractor model is made of SPCC, the frame uses B550L, the leaf springs are made of 50CrVA, and the axle housing is constructed from 16Mn. The properties of each material are shown in Table 1 . Table 1 Material properties Material Name Tensile strength Yield limit Elastic modulus Density Poisson's ratio σ b (MPa) σ s (MPa) (MPa) (t/mm 3 ) B550L 550 ≥ 400 2.1×10 5 7.85×10 − 9 0.3 SPCC 319 222 2.1×10 5 7.85×10 − 9 0.28 50CrVA 1274 1127 2.06×10 5 7.85×10 − 9 0.29 16Mn 510 345 2.0×10 5 7.85×10 − 9 0.3 2.3 Load Processing When the tractor is fully loaded, the loads acting on the frame include the engine, transmission, fuel tank, cab, spare tire, and radiator, among others, as detailed in Table 2 below. Additionally, the cargo weight is not directly applied to the tractor. Instead, it is transferred to the tractor's saddle through the trailer and must be calculated according to the following steps. The force analysis of the saddle is illustrated in Fig. 1 . Table 2 Vehicle loads No. Loads Mass(Kg) 1 engine 875 2 transmission 270 3 fuel tank 128 4 cab 300 5 spare tire 139 6 radiator 23.8 7 cargo 19740 Total 21475.8 When the vehicle is stationary or moving forward at a constant speed, the trailer is taken as the subject of study. Based on the known parameters of the vehicle, the fully loaded trailer load is G=197400N. It is assumed that the vertical component of the force exerted by the saddle on the trailer is N 1 , and the horizontal component is N 2 . From the vehicle parameters, it is derived that L 1 ≈2L 2 . Due to the force equilibrium on the trailer, the following can be concluded: 2.3 Step-by-Step Assembly of the Model After importing the finite element models of the cabin, frame, axle, and leaf springs together, each sub-assembly model is moved to its assembly position through translation and rotation. Following the connection of these parts, the finite element model of the complete vehicle can be obtained. The key considerations during the model assembly process are as follows: the vehicle comprises numerous components, each with many sub-components. Therefore, a bottom-up, step-by-step assembly approach is adopted. This involves first assembling the chassis model, followed by the assembly of the complete vehicle model. This method facilitates model verification and helps avoid connection or assembly errors. 3. Static Condition Analysis Using Finite Element Method This analysis focuses on the structural static strength and stiffness of the tractor under full-load conditions with all four wheels on the ground. It primarily calculates the stress distribution and deformation of the tractor in a stationary state or during uniform linear motion. The loads borne by the vehicle include the powertrain, spare tire, battery, fuel tank, cargo weight, and others. Additionally, to eliminate rigid body displacement, constraints are applied at the wheel positions. The boundary conditions are as follows: all degrees of freedom at the nodes of the front and rear wheel assembly positions are constrained. Based on the finite element calculation, the maximum stress in the vehicle is 102 MPa, located at the intersection of the right longitudinal beam and the second crossbeam, as shown in Fig. 4 . Furthermore, the stress in the rear section of the right longitudinal beam is also relatively high, reaching a maximum of 86 MPa, as illustrated in Fig. 5. In contrast, the stress in the cab and the middle section of the frame is relatively low, all within 10 MPa. The front end of the vehicle experiences sinking, with a maximum deformation of 1.23 mm, located at the front right end of the cab floor. 4. Experimental Verification 4.1 Test Equipment The main equipment and instruments used in the test include: a test prototype vehicle, resistance strain gauges, a strain indicator, a computer, and a data acquisition system. 4.2 Test Plan Based on the results of the finite element analysis, locations with higher stress and greater deformation are selected. Drawing upon relevant experience, the strain gauge placement plan is determined to conduct static and dynamic electrical testing on the entire vehicle. The layout scheme for the measurement points is as follows. 4.3 Test Results The strain signals from 28 measuring points were recorded. The stress value at each measuring point was then calculated using the generalized Hooke's law, F=Eε (where F is stress, E is the material's elastic modulus, and ε is the material strain). Tensile stress was taken as positive, and compressive stress as negative. The finite element calculation results under static conditions were compared with the experimental data. A comparison of data from some measuring points is shown in Table 3 . As can be seen from the table, the errors for most measuring points are within 10%, while a very small number of measuring points have errors exceeding 15%. The deviations between calculated values and experimental values are mainly due to the following reasons:( 1 ) Simplification of the geometric model: During the finite element modeling process, minor features of the components were neglected, such as fillets, grooves, etc. These features may cause stress concentration, thereby significantly affecting local stress results.( 2 ) The material was simplified as a linear elastic model, whereas the actual material may exhibit nonlinear behaviors such as plasticity, creep, anisotropy, and damage.( 3 ) Input parameters such as elastic modulus, Poisson’s ratio, and density were obtained from material manuals and standard tests, which may deviate from the actual parameters of the specific specimens used in the experiment.( 4 ) Ideal fixed constraints were applied in the model, whereas the actual structural supports may involve certain elasticity or friction.( 5 ) Insufficient mesh density: In areas of stress concentration, the mesh may not be fine enough to capture the true peaks of stress and strain.( 6 ) Experimental errors: For example, insufficient sensor accuracy, inadequate sampling frequency, or environmental temperature effects. Taking the above factors into consideration, it can be concluded that the test results are in good agreement with the calculation results, indicating that the established finite element model is fundamentally correct. Using the experimentally validated finite element model, we proceeded with dynamic condition analysis and finite element modal analysis of the entire vehicle structure. Dynamic Condition Analysis Simulation and Analysis of Single Wheel Suspension Condition When a vehicle travels on uneven road surfaces, situations may occur where a single wheel is off the ground. This simulation analyzes the condition of the left front wheel being off the ground. The boundary conditions are as follows: all degrees of freedom at the nodes of the left front wheel assembly position are released; at the right front wheel assembly position, the three translational degrees of freedom (UX, UY, UZ) are constrained, while the three rotational degrees of freedom (ROTX, ROTY, ROTZ) are released; at the rear wheel assembly positions, the vertical degree of freedom is constrained, and all other degrees of freedom are released. After calculation, under torsional conditions, the maximum stress of the entire vehicle is 212 MPa, located at the intersection of the right longitudinal beam and the second crossbeam, as shown in Fig. 9 . Additionally, the stress near the saddle at the rear section of the longitudinal beam remains relatively high, reaching a maximum of 129 MPa. The left front section of the vehicle sinks, with a maximum deformation of 6.14 mm at the left front of the cab roof, as shown in Fig. 10. Table 3 Comparison of calculated values and experimental values No. Measuring point location calculated value experimental value error value 4 The outer side of the rear end of the left longitudinal beam -19.6 -19.3 1.53% 8 The outer side of the rear end of the right longitudinal beam 12.8 14.6 14.06% 11 The upper side of the upper right reinforcement plate at the saddle location 14.2 12.9 9.15% 12 The upper side of the fourth crossbeam of the frame -21.3 -23.2 8.92% 20 The lower left end of the first crossbeam of the frame 50.4 51.2 1.59% 22 The lower side of the front end of the left front leaf spring -25.5 -28.2 10.59% 23 The lower side of the rear end of the right front leaf spring -22.3 -26.2 17.49% 27 The upper side of the right end of the front axle 30.7 29.6 3.58% 28 The upper side of the front push-pull rod at the saddle location 66.2 67.3 1.66% Braking Condition Simulation and Analysis During normal driving, vehicles often encounter sudden situations that require emergency braking. At this time, the vehicle body is subjected to a significant inertial force, the magnitude of which is related to the braking acceleration and the overall mass of the vehicle. To simulate the stress conditions during braking, an acceleration of 0.8g is applied in the -X direction of the vehicle body, while a gravitational acceleration of 1g is applied in the -Z direction. At the connection points between the front suspension and the vehicle body, translational degrees of freedom in the X, Y, and Z directions are constrained. At the connection points between the rear suspension and the vehicle body, translational degrees of freedom in the Y and Z directions are constrained. After calculation, under emergency braking conditions, the maximum stress of the entire vehicle is 118 MPa, located at the right front section of the cab floor, as shown in Fig. 11 . Additionally, significant stress is also observed at the intersection of the second crossbeam and the longitudinal beam, as well as near the saddle in the rear section of the longitudinal beam. The vehicle exhibits a forward tilt, with a maximum deformation of 1.26 mm at the front section of the cab roof, as shown in Fig. 12. Finite Element Modal Analysis Theoretical Basis of Modal Analysis For a linearly elastic structure, its dynamic equation can be expressed as: Finite Element Modal Analysis Results Free modal analysis is used to examine the dynamic characteristics of the vehicle structure under unconstrained conditions. After determining the modal solution method and boundary conditions for the full-vehicle modal analysis, the calculation can be performed by setting the corresponding modal extraction parameters. In free modal analysis, the first six modes are referred to as rigid body modes and involve no elastic deformation. The natural frequencies obtained from the computation approach or equal zero, primarily manifesting as translational or rotational motions of the object in space. Therefore, rigid body modes can be disregarded. For ease of discussion, the first mode mentioned hereafter refers to the first elastic mode. The frequency of the first torsional mode is an extremely critical indicator. If it is too low, it may coincide with the excitation frequency from road surfaces during daily driving, leading to resonance. Based on finite element calculations, the frequency of the first torsional deformation is 8.06 Hz, and its mode shape is illustrated in Fig. 13 . The frequency of the first-order bending mode is another important indicator. If it is too low and couples with road excitation, it may lead to strong vehicle shaking, affecting ride comfort. Therefore, we typically aim for a higher first-order bending mode frequency. According to calculations, the first-order bending mode frequency of this vehicle model is 15.67 Hz, and the corresponding mode shape is illustrated in Fig. 14. Elastic modes beyond the third order primarily involve complex vibrations or local modes. The specific modal frequencies and mode shapes are detailed in Table 4 . Table 4 Finite element modal analysis results Modal order Modal frequency(Hz) Mode shape description 1 8.06 First-order torsion 2 15.67 First-order bending 3 17.35 Compound vibration 4 18.94 Local vibration 5 19.33 Compound vibration 6 24.39 Compound vibration 7 25.56 Local vibration 8 26.35 Compound vibration 9 28.32 Local vibration During vehicle operation, the primary sources of excitation are the road surface, wheel imbalance, engine, and driveshaft imbalance. Among these, road-induced excitation is largely determined by road conditions. On modern highways and well-maintained urban roads, the frequency of this excitation force is typically below 3 Hz (assuming a road wavelength of 10 m and a vehicle speed of 120 km/h), with a relatively significant excitation component. The excitation frequency caused by wheel imbalance is generally below 11 Hz (based on a maximum vehicle speed of 120 km/h and a tire rolling radius of 950 mm). Thanks to improvements in modern rim manufacturing quality and testing techniques, the contribution from this source is relatively minor. When the truck operates at typical speeds of 50 km/h to 80 km/h, the engine firing frequency ranges from 48 Hz to 52 Hz, contributing a significant excitation component. Vibrations caused by driveshaft imbalance occur at frequencies above 33 Hz, with a relatively small excitation contribution. Therefore, from the perspectives of vibration control and structural integrity, and considering the minimal impact of wheel imbalance, the dominant low-order vibration modes of the vehicle body should be controlled within the frequency range of 3 Hz to 33 Hz. The calculated results indicate that the low-order natural frequencies of this truck fall precisely within this required range, effectively avoiding resonance phenomena. 5. Conclusion In this paper, a finite element model of a semi-trailer tractor is established using finite element software, and electrical testing experiments are employed to verify and refine the model. Subsequently, the validated finite element model is utilized to analyze the stress distribution characteristics under dynamic operating conditions and the modal properties of the vehicle structure. However, the finite element model of a semi-trailer tractor is highly complex, making it extremely challenging to create a highly accurate model. All finite element models are simplified to find a balance between model scale and accuracy. Additionally, the analysis process of the finite element model involves a great deal of specialized knowledge in fields such as material science, structural mechanics, and finite element theory, leading to several areas in this paper that require further refinement and supplementation: ( 1 ) During the finite element modeling process, certain detailed features of the vehicle structure were simplified to reduce the model scale, which has a certain impact on the model's accuracy. ( 2 ) In the modeling of the leaf spring, the contact between each steel plate was primarily simulated using a coupling method, the accuracy of which warrants further exploration and experimental validation. ( 3 ) Due to the substantial computational scale of the vehicle's finite element model and limitations such as computer hardware constraints, sensitivity analysis and optimization design of the tractor's full-vehicle model have not been conducted for now. Declarations Funding This study was financially supported by the Major Scientific Research Project of Universities in Anhui Province (Grant No. 2025AHGXZK20079 and 2025AHGXZK20089), the Key Scientific Research Project of Universities in Anhui Province (Grant No. 2025AHGXZK30383). Author Contribution The contributions of the authors to this paper are as follows: C.L. was responsible for the modeling of the finite element model, the organization of theoretical analysis data, and the writing of the final manuscript. F.Z. was responsible for the design of the experimental protocol and the comparison between theoretical analysis and experimental data. All authors have read and agreed to the final published version of the manuscript. Acknowledgments We sincerely acknowledge the colleagues from the Anhui University of Applied Technology for their valuable contributions to the collection and management of data. Data Availability The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. References Guo Ningning. Research on Lightweight Design of Automotive Body Structure Based on Finite Element Analysis and Optimization [J]. Intern. Combust. Engine Parts , (14):111–113. DOI: 10.3969/j.issn.1674-957X.2025.14.036 . (2025). Li Hui. Finite Element Analysis of Key Components of Automotive Door Welding Manipulator [J]. Mech. Manage. Dev. , 40 (7):78–80. DOI: 10.16525/j.cnki.cn14-1134/th.2025.07.028 . (2025). Lei, H. Chen Junbao. Finite Element Analysis and Optimization Design of Heavy Truck Frame Considering Transportation Conditions [J]. China Equip. Eng. , (10):111–115. DOI: 10.3969/j.issn.1671-0711.2025.10.049 . (2025). Wang Shichuan, T. et al. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8736320","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":597451247,"identity":"8489b748-1b25-4495-b0d1-c1ba5232117a","order_by":0,"name":"Changnian Lu","email":"","orcid":"","institution":"Anhui University of Applied Technology","correspondingAuthor":false,"prefix":"","firstName":"Changnian","middleName":"","lastName":"Lu","suffix":""},{"id":597451251,"identity":"2ca58217-e354-46d2-ac0e-3e937ab8c550","order_by":1,"name":"Fanling 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9","display":"","copyAsset":false,"role":"figure","size":521510,"visible":true,"origin":"","legend":"\u003cp\u003eLocation of Maximum Stress\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8736320/v1/6cbf647043aa3afc8291e918.png"},{"id":104401904,"identity":"f801d9da-e3a6-4744-9cce-5ed29e52dab0","added_by":"auto","created_at":"2026-03-11 12:13:52","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":259020,"visible":true,"origin":"","legend":"\u003cp\u003eLocation of Maximum Deformation\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-8736320/v1/312ed3b838536322eee7445d.png"},{"id":104401800,"identity":"79b1ae1c-ff24-4468-852f-b84faa844616","added_by":"auto","created_at":"2026-03-11 12:13:35","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":391608,"visible":true,"origin":"","legend":"\u003cp\u003eLocation of Maximum Stress\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-8736320/v1/701d2ec20bcf30cff484ede0.png"},{"id":103942486,"identity":"c60af2f7-9359-40fc-97ae-419f47afa6b0","added_by":"auto","created_at":"2026-03-04 19:40:47","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":262993,"visible":true,"origin":"","legend":"\u003cp\u003eLocation of Maximum Deformation\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-8736320/v1/4afb2de92f20fd348b1eea7f.png"},{"id":104401516,"identity":"acc9e616-195e-4684-ab95-ec21176984be","added_by":"auto","created_at":"2026-03-11 12:12:54","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":64369,"visible":true,"origin":"","legend":"\u003cp\u003eFirst-Order Torsional Mode Shape\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-8736320/v1/4c2a34d84f926044cd1bc600.png"},{"id":103942488,"identity":"2db23a5b-0845-4a0e-a589-f344a601ffb9","added_by":"auto","created_at":"2026-03-04 19:40:48","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":58684,"visible":true,"origin":"","legend":"\u003cp\u003eFirst-Order Bending Mode Shape\u003c/p\u003e","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-8736320/v1/1f7630c56c37ec642a54cae0.png"},{"id":104806221,"identity":"33bb2432-a998-4dba-baf9-d712d3921a47","added_by":"auto","created_at":"2026-03-17 11:42:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":9525432,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8736320/v1/a4417532-9b7d-4242-9299-fcdd80d109f7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Structural Analysis of a Semi-Trailer Tractor Truck","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe semi-trailer tractor serves as a core piece of equipment in modern road logistics transportation. Its function is to tow semi-trailers via its saddle, undertaking the majority of medium to long-distance heavy-duty freight transport tasks. The rationality, reliability, and lightweight level of the entire vehicle structure directly affect transport efficiency, driving safety, fuel economy, and regulatory compliance. Therefore, conducting a systematic analysis of the full-vehicle structure of a semi-trailer tractor is of critical importance for design improvement, performance optimization, maintenance, and technical evaluation.\u003c/p\u003e\u003cp\u003eFinite element modeling and analysis of a complete semi-trailer tractor is a complex and challenging engineering task. The difficulties are mainly reflected in model complexity, balance of computational resources, and reliability of analysis results, among other aspects:(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) Geometric and structural complexity. The tractor consists of a large number of components with diverse shapes and intricate connection relationships. The structure is extensive and comprises numerous parts from the cab, frame, suspension system, and powertrain to the saddle involving thousands of individual components. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) Treatment of material and contact nonlinearities. Linear analysis is often insufficient to reflect real-world conditions. Nonlinearities are a primary cause of increased analysis complexity and computational cost. The full vehicle contains numerous contact pairs, such as bolted joint surfaces, gear meshing, and contact between leaf spring laminations. Changes in contact states can lead to computational instability and a sharp increase in calculation time. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) Authenticity of loads and boundary conditions. Accurately applying real-world physical loads to the finite element model is key to ensuring the credibility of the results. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) Balance between model scale and computational efficiency. Under the premise of not significantly affecting overall accuracy, reasonable simplifications such as omitting minor features or replacing complex components with beam or rod elements are employed to reduce model scale.\u003c/p\u003e "},{"header":"2. Establishment of Finite Element Model","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1 Element Selection and Meshing\u003c/h2\u003e\n \u003cp\u003eThe full vehicle model includes components such as the cab, frame, leaf springs, and axles. Shell elements are used to simulate the cab, frame, and leaf springs, while solid elements are employed for the axles. Shell elements possess both bending and membrane capabilities, enabling them to withstand in-plane and normal loads. Solid elements have the ability to account for plasticity, creep, expansion, stress stiffening, large deformation, and large strain. For components modeled with shell elements, 2D meshing can be directly applied. For parts modeled with solid elements, 2D meshing is first performed on their surfaces, after which the 2D mesh is mapped into a 3D mesh.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2 Material Properties\u003c/h2\u003e\n \u003cp\u003eMaterial properties are typically defined by several physical parameters: density, elastic modulus, Poisson\u0026apos;s ratio, tensile strength, and yield limit, among others. The cab of this tractor model is made of SPCC, the frame uses B550L, the leaf springs are made of 50CrVA, and the axle housing is constructed from 16Mn. The properties of each material are shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eMaterial properties\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eMaterial Name\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTensile strength\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eYield limit\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eElastic modulus\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDensity\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003ePoisson\u0026apos;s ratio\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026sigma;\u003csub\u003eb\u003c/sub\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u0026sigma;\u003csub\u003es\u003c/sub\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e(MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e(t/mm\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eB550L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e550\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026ge;\u0026thinsp;400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.1\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.85\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSPCC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e319\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e222\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.1\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.85\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.28\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e50CrVA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1274\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1127\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.06\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.85\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.29\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16Mn\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e510\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e345\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.0\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7.85\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;9\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3 Load Processing\u003c/h2\u003e\n \u003cp\u003eWhen the tractor is fully loaded, the loads acting on the frame include the engine, transmission, fuel tank, cab, spare tire, and radiator, among others, as detailed in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e below.\u003c/p\u003e\n \u003cp\u003eAdditionally, the cargo weight is not directly applied to the tractor. Instead, it is transferred to the tractor\u0026apos;s saddle through the trailer and must be calculated according to the following steps. The force analysis of the saddle is illustrated in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eVehicle loads\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"3\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNo.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLoads\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMass(Kg)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eengine\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e875\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003etransmission\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e270\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003efuel tank\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e128\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ecab\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003espare tire\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e139\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eradiator\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ecargo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19740\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eTotal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21475.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\u003cbr\u003e\n \u003cp\u003eWhen the vehicle is stationary or moving forward at a constant speed, the trailer is taken as the subject of study. Based on the known parameters of the vehicle, the fully loaded trailer load is G=197400N. It is assumed that the vertical component of the force exerted by the saddle on the trailer is N\u003csub\u003e1\u003c/sub\u003e, and the horizontal component is N\u003csub\u003e2\u003c/sub\u003e. From the vehicle parameters, it is derived that L\u003csub\u003e1\u003c/sub\u003e\u0026asymp;2L\u003csub\u003e2\u003c/sub\u003e. Due to the force equilibrium on the trailer, the following can be concluded:\u003c/p\u003e\n \u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/127393_c7e80a1c9bb65875/127393_custom_files/img1772651386.png\" style=\"width: 615px;\"\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3 Step-by-Step Assembly of the Model\u003c/h2\u003e\n \u003cp\u003eAfter importing the finite element models of the cabin, frame, axle, and leaf springs together, each sub-assembly model is moved to its assembly position through translation and rotation. Following the connection of these parts, the finite element model of the complete vehicle can be obtained. The key considerations during the model assembly process are as follows: the vehicle comprises numerous components, each with many sub-components. Therefore, a bottom-up, step-by-step assembly approach is adopted. This involves first assembling the chassis model, followed by the assembly of the complete vehicle model. This method facilitates model verification and helps avoid connection or assembly errors.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Static Condition Analysis Using Finite Element Method","content":"\u003cp\u003eThis analysis focuses on the structural static strength and stiffness of the tractor under full-load conditions with all four wheels on the ground. It primarily calculates the stress distribution and deformation of the tractor in a stationary state or during uniform linear motion. The loads borne by the vehicle include the powertrain, spare tire, battery, fuel tank, cargo weight, and others. Additionally, to eliminate rigid body displacement, constraints are applied at the wheel positions. The boundary conditions are as follows: all degrees of freedom at the nodes of the front and rear wheel assembly positions are constrained.\u003c/p\u003e \u003cp\u003eBased on the finite element calculation, the maximum stress in the vehicle is 102 MPa, located at the intersection of the right longitudinal beam and the second crossbeam, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. Furthermore, the stress in the rear section of the right longitudinal beam is also relatively high, reaching a maximum of 86 MPa, as illustrated in Fig.\u0026nbsp;5. In contrast, the stress in the cab and the middle section of the frame is relatively low, all within 10 MPa. The front end of the vehicle experiences sinking, with a maximum deformation of 1.23 mm, located at the front right end of the cab floor.\u003c/p\u003e"},{"header":"4. Experimental Verification","content":"\u003ch2\u003e4.1 Test Equipment\u003c/h2\u003e\n\u003cp\u003eThe main equipment and instruments used in the test include: a test prototype vehicle, resistance strain gauges, a strain indicator, a computer, and a data acquisition system.\u003c/p\u003e\n\u003ch2\u003e4.2 Test Plan\u003c/h2\u003e\n\u003cp\u003eBased on the results of the finite element analysis, locations with higher stress and greater deformation are selected. Drawing upon relevant experience, the strain gauge placement plan is determined to conduct static and dynamic electrical testing on the entire vehicle. The layout scheme for the measurement points is as follows.\u003c/p\u003e\n\u003ch2\u003e4.3 Test Results\u003c/h2\u003e\n\u003cp\u003eThe strain signals from 28 measuring points were recorded. The stress value at each measuring point was then calculated using the generalized Hooke\u0026apos;s law, F=Eε (where F is stress, E is the material\u0026apos;s elastic modulus, and ε is the material strain). Tensile stress was taken as positive, and compressive stress as negative. The finite element calculation results under static conditions were compared with the experimental data. A comparison of data from some measuring points is shown in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eAs can be seen from the table, the errors for most measuring points are within 10%, while a very small number of measuring points have errors exceeding 15%. The deviations between calculated values and experimental values are mainly due to the following reasons:(\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e) Simplification of the geometric model: During the finite element modeling process, minor features of the components were neglected, such as fillets, grooves, etc. These features may cause stress concentration, thereby significantly affecting local stress results.(\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e) The material was simplified as a linear elastic model, whereas the actual material may exhibit nonlinear behaviors such as plasticity, creep, anisotropy, and damage.(\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e) Input parameters such as elastic modulus, Poisson\u0026rsquo;s ratio, and density were obtained from material manuals and standard tests, which may deviate from the actual parameters of the specific specimens used in the experiment.(\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e) Ideal fixed constraints were applied in the model, whereas the actual structural supports may involve certain elasticity or friction.(\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e) Insufficient mesh density: In areas of stress concentration, the mesh may not be fine enough to capture the true peaks of stress and strain.(\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e) Experimental errors: For example, insufficient sensor accuracy, inadequate sampling frequency, or environmental temperature effects.\u003c/p\u003e\n\u003cp\u003eTaking the above factors into consideration, it can be concluded that the test results are in good agreement with the calculation results, indicating that the established finite element model is fundamentally correct. Using the experimentally validated finite element model, we proceeded with dynamic condition analysis and finite element modal analysis of the entire vehicle structure.\u003c/p\u003e\n\u003cp\u003eDynamic Condition Analysis\u003c/p\u003e\n\u003cp\u003eSimulation and Analysis of Single Wheel Suspension Condition\u003c/p\u003e\n\u003cp\u003eWhen a vehicle travels on uneven road surfaces, situations may occur where a single wheel is off the ground. This simulation analyzes the condition of the left front wheel being off the ground. The boundary conditions are as follows: all degrees of freedom at the nodes of the left front wheel assembly position are released; at the right front wheel assembly position, the three translational degrees of freedom (UX, UY, UZ) are constrained, while the three rotational degrees of freedom (ROTX, ROTY, ROTZ) are released; at the rear wheel assembly positions, the vertical degree of freedom is constrained, and all other degrees of freedom are released.\u003c/p\u003e\n\u003cp\u003eAfter calculation, under torsional conditions, the maximum stress of the entire vehicle is 212 MPa, located at the intersection of the right longitudinal beam and the second crossbeam, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e. Additionally, the stress near the saddle at the rear section of the longitudinal beam remains relatively high, reaching a maximum of 129 MPa. The left front section of the vehicle sinks, with a maximum deformation of 6.14 mm at the left front of the cab roof, as shown in Fig.\u0026nbsp;10.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eComparison of calculated values and experimental values\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNo.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMeasuring point location\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ecalculated value\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eexperimental value\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eerror value\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe outer side of the rear end of the left longitudinal beam\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-19.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-19.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.53%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe outer side of the rear end of the right longitudinal beam\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.06%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe upper side of the upper right reinforcement plate at the saddle location\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.15%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe upper side of the fourth crossbeam of the frame\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-21.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-23.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.92%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe lower left end of the first crossbeam of the frame\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e50.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e51.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.59%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe lower side of the front end of the left front leaf spring\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-25.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-28.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.59%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe lower side of the rear end of the right front leaf spring\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-22.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-26.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.49%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe upper side of the right end of the front axle\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e29.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.58%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eThe upper side of the front push-pull rod at the saddle location\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e66.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e67.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.66%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eBraking Condition Simulation and Analysis\u003c/p\u003e\n\u003cp\u003eDuring normal driving, vehicles often encounter sudden situations that require emergency braking. At this time, the vehicle body is subjected to a significant inertial force, the magnitude of which is related to the braking acceleration and the overall mass of the vehicle. To simulate the stress conditions during braking, an acceleration of 0.8g is applied in the -X direction of the vehicle body, while a gravitational acceleration of 1g is applied in the -Z direction. At the connection points between the front suspension and the vehicle body, translational degrees of freedom in the X, Y, and Z directions are constrained. At the connection points between the rear suspension and the vehicle body, translational degrees of freedom in the Y and Z directions are constrained.\u003c/p\u003e\n\u003cp\u003eAfter calculation, under emergency braking conditions, the maximum stress of the entire vehicle is 118 MPa, located at the right front section of the cab floor, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e. Additionally, significant stress is also observed at the intersection of the second crossbeam and the longitudinal beam, as well as near the saddle in the rear section of the longitudinal beam. The vehicle exhibits a forward tilt, with a maximum deformation of 1.26 mm at the front section of the cab roof, as shown in Fig.\u0026nbsp;12.\u003c/p\u003e\n\u003cp\u003eFinite Element Modal Analysis\u003c/p\u003e\n\u003cp\u003eTheoretical Basis of Modal Analysis\u003c/p\u003e\n\u003cp\u003eFor a linearly elastic structure, its dynamic equation can be expressed as:\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/127393_c7e80a1c9bb65875/127393_custom_files/img1772651887.png\" style=\"width: 638px;\"\u003e\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/127393_c7e80a1c9bb65875/127393_custom_files/img1772651948.png\" style=\"width: 616px;\"\u003e\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/127393_c7e80a1c9bb65875/127393_custom_files/img1772652020.png\" style=\"width: 634px;\"\u003e\u003c/p\u003e\n\u003cp\u003eFinite Element Modal Analysis Results\u003c/p\u003e\n\u003cp\u003eFree modal analysis is used to examine the dynamic characteristics of the vehicle structure under unconstrained conditions. After determining the modal solution method and boundary conditions for the full-vehicle modal analysis, the calculation can be performed by setting the corresponding modal extraction parameters. In free modal analysis, the first six modes are referred to as rigid body modes and involve no elastic deformation. The natural frequencies obtained from the computation approach or equal zero, primarily manifesting as translational or rotational motions of the object in space. Therefore, rigid body modes can be disregarded. For ease of discussion, the first mode mentioned hereafter refers to the first elastic mode.\u003c/p\u003e\n\u003cp\u003eThe frequency of the first torsional mode is an extremely critical indicator. If it is too low, it may coincide with the excitation frequency from road surfaces during daily driving, leading to resonance. Based on finite element calculations, the frequency of the first torsional deformation is 8.06 Hz, and its mode shape is illustrated in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eThe frequency of the first-order bending mode is another important indicator. If it is too low and couples with road excitation, it may lead to strong vehicle shaking, affecting ride comfort. Therefore, we typically aim for a higher first-order bending mode frequency. According to calculations, the first-order bending mode frequency of this vehicle model is 15.67 Hz, and the corresponding mode shape is illustrated in Fig.\u0026nbsp;14.\u003c/p\u003e\n\u003cp\u003eElastic modes beyond the third order primarily involve complex vibrations or local modes. The specific modal frequencies and mode shapes are detailed in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eFinite element modal analysis results\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModal order\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModal frequency(Hz)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMode shape description\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFirst-order torsion\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFirst-order bending\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCompound vibration\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLocal vibration\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCompound vibration\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e24.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCompound vibration\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e25.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLocal vibration\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e26.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCompound vibration\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eLocal vibration\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\u003cbr\u003e\n\u003cp\u003eDuring vehicle operation, the primary sources of excitation are the road surface, wheel imbalance, engine, and driveshaft imbalance. Among these, road-induced excitation is largely determined by road conditions. On modern highways and well-maintained urban roads, the frequency of this excitation force is typically below 3 Hz (assuming a road wavelength of 10 m and a vehicle speed of 120 km/h), with a relatively significant excitation component. The excitation frequency caused by wheel imbalance is generally below 11 Hz (based on a maximum vehicle speed of 120 km/h and a tire rolling radius of 950 mm). Thanks to improvements in modern rim manufacturing quality and testing techniques, the contribution from this source is relatively minor. When the truck operates at typical speeds of 50 km/h to 80 km/h, the engine firing frequency ranges from 48 Hz to 52 Hz, contributing a significant excitation component. Vibrations caused by driveshaft imbalance occur at frequencies above 33 Hz, with a relatively small excitation contribution.\u003c/p\u003e\n\u003cp\u003eTherefore, from the perspectives of vibration control and structural integrity, and considering the minimal impact of wheel imbalance, the dominant low-order vibration modes of the vehicle body should be controlled within the frequency range of 3 Hz to 33 Hz. The calculated results indicate that the low-order natural frequencies of this truck fall precisely within this required range, effectively avoiding resonance phenomena.\u003c/p\u003e"},{"header":"5. Conclusion","content":" \u003cp\u003eIn this paper, a finite element model of a semi-trailer tractor is established using finite element software, and electrical testing experiments are employed to verify and refine the model. Subsequently, the validated finite element model is utilized to analyze the stress distribution characteristics under dynamic operating conditions and the modal properties of the vehicle structure. However, the finite element model of a semi-trailer tractor is highly complex, making it extremely challenging to create a highly accurate model. All finite element models are simplified to find a balance between model scale and accuracy. Additionally, the analysis process of the finite element model involves a great deal of specialized knowledge in fields such as material science, structural mechanics, and finite element theory, leading to several areas in this paper that require further refinement and supplementation: (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) During the finite element modeling process, certain detailed features of the vehicle structure were simplified to reduce the model scale, which has a certain impact on the model's accuracy. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) In the modeling of the leaf spring, the contact between each steel plate was primarily simulated using a coupling method, the accuracy of which warrants further exploration and experimental validation. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) Due to the substantial computational scale of the vehicle's finite element model and limitations such as computer hardware constraints, sensitivity analysis and optimization design of the tractor's full-vehicle model have not been conducted for now.\u003c/p\u003e "},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis study was financially supported by the Major Scientific Research Project of Universities in Anhui Province (Grant No. 2025AHGXZK20079 and 2025AHGXZK20089), the Key Scientific Research Project of Universities in Anhui Province (Grant No. 2025AHGXZK30383).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eThe contributions of the authors to this paper are as follows: C.L. was responsible for the modeling of the finite element model, the organization of theoretical analysis data, and the writing of the final manuscript. F.Z. was responsible for the design of the experimental protocol and the comparison between theoretical analysis and experimental data. All authors have read and agreed to the final published version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eWe sincerely acknowledge the colleagues from the Anhui University of Applied Technology for their valuable contributions to the collection and management of data.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eGuo Ningning. Research on Lightweight Design of Automotive Body Structure Based on Finite Element Analysis and Optimization [J]. \u003cem\u003eIntern. Combust. Engine Parts\u003c/em\u003e, (14):111\u0026ndash;113. 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Research Progress on Reliability Analysis and Optimization Design of Automotive Structures [J].\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Semi-trailer tractor, Finite Element Analysis, Modal Analysis, Full-vehicle Structure","lastPublishedDoi":"10.21203/rs.3.rs-8736320/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8736320/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper focuses on the finite element analysis of a complete vehicle structure. Compared to component models such as the frame and axles, the full-vehicle model is characterized by its large computational scale and the difficulty in simulating the connections and assemblies between components. By appropriately simplifying the geometric model and strictly controlling the finite element mesh size, this study seeks an optimal balance between computational scale and accuracy. During the component connection and assembly process, the finite element models of the components are imported, translated, and rotated, and then connected using rigid links and couplings. This results in the final full-vehicle finite element model. A preliminary analysis of the finite element model is conducted, followed by electrical testing on the actual vehicle. This provides a practical basis for the finite element analysis and verifies the correctness of the model. Subsequently, using the validated finite element model, the stress distribution and deformation of the tractor under single-wheel lift and braking conditions are analyzed. Finally, a modal analysis of the tractor's complete structure is performed to determine its natural frequencies and mode shapes, assessing whether they effectively avoid external excitation frequencies.\u003c/p\u003e","manuscriptTitle":"Structural Analysis of a Semi-Trailer Tractor Truck","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-04 19:40:42","doi":"10.21203/rs.3.rs-8736320/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"586f4a1d-d1e1-469e-b09f-e7771b7cc793","owner":[],"postedDate":"March 4th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":63574343,"name":"Physical sciences/Engineering"},{"id":63574344,"name":"Physical sciences/Materials science"},{"id":63574345,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-03-17T11:41:19+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-04 19:40:42","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8736320","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8736320","identity":"rs-8736320","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}