Multi-body elastic simulation of a go-kart: Correlation between frame stiffness and dynamic performance

The elastic response of a vehicle to an applied force determines the dynamic performance, comfort, and support of the vehicle, where the elastic response depends primarily on the stiffness of the frame/chassis. Significant variations in the dynamic response of a vehicle are typically achieved with suitable shock absorbing systems, which contribute significantly to whole body flexibility. The defining feature of a go-kart is the lack of devices capable of absorbing shock and dampening vibration. The tires and body of a go-kart, which consist of a frame of welded beams, must also function as a shock absorption system. The objective of this study was to reproduce the elastic behavior of a commercially available Italian go-kart by modeling the frame in a multibody ADAMS environment and to determine the effect of elastic features on the dynamic performance of the vehicle. Frame stiffness was assessed by applying a static torsion moment, while the circular trajectory of the go-kart was evaluated at different speeds and steering wheel angles. The proposed multibody, flexible model was validated by comparing the static and dynamic response of the go-kart in simulated and experimental analyses. The results of numerical simulations demonstrated that this method may be extended to the design of customized go-kart frames and to the tuning of go-karts for specific racing conditions.     

Heave-Pitch-Roll Dynamics of Flexible Vehicle in Variable Velocity Run

Analysis for response statistics evaluation of a flexible vehicle travelling with variable velocity over nonhomogeneously profiled flexible track is presented with a heave-pitch-roll model. The vehicle body is idealised as a flexible member with variable cross-section, inertia, damping and stiffness distributions. The vehicle may also have variable section slender elastic attachments. Coupled dynamics with rigid body heave-pitch-roll modes and elastic bending-torsion modes of the vehicle body along with coupled bending-torsion modes of the attachments are considered. Equivalent linear suspension system characteristics are employed for developing the analysis. Numerical results are presented for an aircraft with tricycle landing gear arrangements and comparison is made with other models.     

Heave-Pitch-Roll Dynamics of Flexible Vehicle in Variable Velocity Run

Analysis for response statistics evaluation of a flexible vehicle travelling with variable velocity over nonhomogeneously profiled flexible track is presented with a heave-pitch-roll model. The vehicle body is idealised as a flexible member with variable cross-section, inertia, damping and stiffness distributions. The vehicle may also have variable section slender elastic attachments. Coupled dynamics with rigid body heave-pitch-roll modes and elastic bending-torsion modes of the vehicle body along with coupled bending-torsion modes of the attachments are considered. Equivalent linear suspension system characteristics are employed for developing the analysis. Numerical results are presented for an aircraft with tricycle landing gear arrangements and comparison is made with other models.     

基于柔性模型的多轴汽车平顺性的仿真研究

基于弹性梁弯曲振动理论和模态分析法建立了多轴汽车平顺性分析的柔性模型。按照汽车行驶平顺性评价方法，运用建立的柔性模型，分析了车速、路面等级、悬挂质量的分布、车架刚度以及悬架系统的刚度和阻尼对多轴汽车平顺性的影响。分析结果表明：悬挂质量的弯曲振动是影响多轴汽车行驶平顺性的一个不可忽略的重要因素；常用的刚体模型不能准确地描述多轴汽车的平顺性，不适合用于多轴汽车平顺性的分析。     

Vertical random vibration analysis of vehicle–track coupled system using Green's function method

A vertical vehicle–track coupled dynamic model, consisting of a high-speed train on a continuously supported rail, is established in the frequency-domain. The solution is obtained efficiently by use of the Green's function method, which can determine the vibration response over a wide range of frequency without any limitations due to modal truncation. Moreover, real track irregularity spectra can be used conveniently as input. The effect of the flexibility of both track and car body on the entire vehicle–track coupled dynamic response is investigated. A multi-body model of a vehicle with either rigid or flexible car body is defined running on three kinds of track: a rigid rail, a track stiffness model and a Timoshenko beam model. The results show that neglecting the track flexibility leads to an overestimation of both the contact force and the whole vehicle vibration response. The car body flexibility affects the ride quality of the vehicle and the coupling through the track and can be significant in certain frequency ranges. Finally, the effect of railpad and ballast stiffness on the vehicle–track coupled vibration is analysed, indicating that the stiffness of the railpad has an influence on the system in a higher frequency range than the ballast.     

基于虚拟迭代技术的中型货车驾驶室载荷谱的求取

某货车驾驶室疲劳载荷激励输入位置位于驾驶室与悬置连接处,在进行整车强化道路耐久试验时无法安装设备直接采集。为获取较为准确的驾驶室疲劳寿命分析载荷谱,对强化耐久路面下整车加速度响应信号进行虚拟迭代。虚拟迭代时需调用整车多体动力学模型,为提高整车模型精度,基于Craig-Bampton综合模态理论生成柔性体车架,建立刚柔耦合的整车多体动力学模型。将Femfat-lab与ADAMS/Car进行联合仿真计算,以白噪声为初始输入,求解刚柔耦合整车多体动力学模型的非线性传递函数,基于循环迭代原理,进行各种典型强化路况下驾驶室悬置附近加速度响应信号的虚拟迭代。利用时域信号对比法及损伤阈值法作为迭代收敛判据,获得满足精度需求的位移驱动信号。将位移驱动信号导入到ADAMS/Car中,对整车多体动力学模型进行驱动仿真,提取驾驶室疲劳分析所需激励载荷谱,将虚拟迭代求得的载荷谱用于疲劳寿命分析所得结果与驾驶室疲劳强化台架试验结果进行对比。研究结果表明：出现疲劳破坏的部位相同度达75%,疲劳寿命误差在20%左右,表明虚拟迭代过程中基于柔性体车架建立的刚柔耦合多体动力学模型的仿真计算,可获得较高精度的迭代结果;以位移谱驱动整车多体动力学模型进行仿真能够有效避免六分力直接驱动时模型翻转等不稳定现象,并且整车模型仿真加速度响应结果与实测相应位置加速度响应吻合度较高;相比于传统的疲劳分析载荷获取方法,虚拟迭代技术可以在较低试验成本的情况下获取较高精度的载荷谱,并能够提取由于连接位置导致的无法直接进行载荷测量部位的疲劳分析载荷。     

Effects of rail thermal stress on the dynamic response of vehicle and track

A new method is proposed to obtain the dynamic responses of the vehicle–track coupling system under the conditions of rail thermal stress changes in high-speed railways. Exact models are established with different rail longitudinal forces, in which multibody dynamic models are used for vehicles and the direct stiffness method for structures. In order to provide a general, simple and flexible formulation to express longitudinal stress distribution, the accurate model of long slab track consists of many small units with parameters which can be initialised separately. The exact analytical equation of track frequency and modal function was obtained by the transition matrix method, which can be used in calculating the dynamic response of wheel–rail coupling model. The proposed model is verified through comparisons with other classical solutions. Under the influence of train velocities and track irregularities, the specific vibration performances that frequency shifted and amplitude peak enhanced with thermal force are demonstrated through examples. The results show that the response analyses of vehicle and track have great application potentiality for fast estimation of the rail longitudinal stress.     

Track Induced Heave-Pitch Dynamics of Vehicles with Variable Section Flexible Attachments

Multi-wheeled vehicles travelling on a rough track are subjected to unequal inputs at different wheel locations and are set to oscillate in various combinations of possible modes. Elastic bending and torsional deformations may be critical in design for vehicles with slender flexible body and components. In the present study, an analytical approach has been developed to study the track induced heave-pitch dynamics of a linear vehicle model composed of lumped masses and slender, non uniform section elastic attachments in coupled bending-torsion modes. Exact modal solutions for the variable section beam member with general end conditions have been derived and utilised to develop the second order response statistics for the system. Results are presented for an aircraft model with tapered flexible wings during ground runs on a non homogeneously profiled track supported by elastic foundation.     

某重型卡车白车身模态分析

在汽车结构设计中,为了避免弹性体产生共振问题,需要适当提高低阶固有频率,做好频率分布规划。白车身系统可以看成是一个多自由度的振动系统,模态分析可以帮助我们了解结构自身的基本振动特性。本文以某重型卡车白车身为研究对象,利用有限元软件Radioss进行模态计算,然后与基于LMS Test.Lab的模态试验结果进行对比,验证有限元仿真计算的精确性,对白车身的设计具有重要的指导意义。     

工程车辆非线性橡胶悬架动力学建模与优化

以AD250铰接式自卸车的非线性变刚度橡胶悬架为研究对象,应用模态综合法和多柔体系统动力学理论,并通过整车试验建立了整车刚柔耦合动力学模型。以行驶平顺性和操纵稳定性为优化目标,采用序列二次规划法,对不同载荷、不同等级路面和不同车速下的悬架特性参数进行优化,得到了不同工况下的最优悬架特性参数。通过最小二乘法拟合得到了橡胶悬架刚度参数的理想非线性特性曲线。仿真结果表明,优化后的橡胶悬架系统能使车辆保持良好的行驶平顺性。     

Material characteristics of a vehicle door seal and its effect on vehicle vibrations

The vibration characteristics of the door panels are affected by the weatherstrip seals used in between the doors and vehicle body along the perimeter of the doors. The weatherstrip seals exhibit nonlinear and viscoelastic material properties that vary with frequency, temperature, strain rate and amplitude, and previous load history. The material properties of the seal must be investigated carefully in order to predict the vibration characteristics of the automobiles under different loading conditions.

In this study, we developed hyperelastic and viscoelastic models of the weatherstrip seal to predict dynamic performance of a vehicle door and its effect on the overall vehicle dynamics. For this purpose, first, static compression and stress relaxation experiments were performed on the seal using a robotic indenter equipped with force and displacement sensors and then a finite element model utilising the results of these experiments was developed in ANSYS. Finally, a representative model of the seal was integrated into the finite element model of the vehicle door to investigate its effect on the vehicle vibrations. The model predictions were validated using experimental modal analysis performed on the vehicle door with and without the seal. It was observed that the seal has a significant effect on the vehicle dynamics.     

牵引车车架的模态分析

在汽车结构设计中,为了避免弹性体产生共振问题,需要适当提高低阶固有频率,做好频率分布规划。车架系统可以看成是一个多自由度的振动系统,模态分析可以帮助我们了解结构自身的基本振动特性。本文以某牵引车车架为研究对象,利用有限元软件Radioss进行模态计算,然后与基于LMS Test．Lab的模态试验结果进行对比,验证有限元仿真计算的精确性,同时也对车架的合理性进行评价,对车架的设计具有重要的指导意义。     

某多功能商用车白车身静动态特性试验与分析

对某多功能商用车白车身进行了静态、动态特性试验测试.通过分析静态特性试验结果可知,车身弯曲刚度曲线基本光滑,车身各部位变形不大,其参数可作为新车设计参考;车身扭转刚度值中等,新车开发时需要进一步提高.通过分析动态特性试验结果可知,该车整体模态值较高,分布基本合理,表明其低阶动态特性良好,但需注意与动力总成的匹配,防止出现过大振动.     

Vehicle modeling with the exhaust system and experimental validation to investigate the exhaust vertical vibration characteristics excited by road surface inputs

An 8 degree-of-freedom (DOF) vehicle model is established to investigate the vertical vibration characteristics of an exhaust system excited by road surface inputs. The simplification of an exhaust system relevant to the vehicle model is discussed in detail, including the steps of exhaust modal analysis, definition of mass element, exhaust partitioning, parameter acquisition, and simplified exhaust validation. The vehicle model is developed based on a half-vehicle model, simulated using MATLAB/SIMULINK, and validated by comparing the simulation and experiment on various road profiles. Results show that the vehicle model effectively represents the dynamics of the vehicle characteristic in vertical vibration.     

Aeroelastic Effects in Multibody Dynamics

To enable a realistic assessment of the aeroelastic phenomena of aircraft, a simultaneous application of computational fluid dynamics (CFD), computational structural mechanics and flight mechanics has to be performed. Each discipline has developed powerful specialized tools which have to be adapted for multidisciplinary applications. The combination of CFD and elastic multibody systems is well suited for the simulation of a range of aircraft applications, especially for aircraft ground dynamics. Approaches to a coupling of elastic multibody systems and computational fluid dynamics have been performed using close coupling, that is a modal approach, and loose coupling, that is by co-simulation. In the article the applied programs and the coupling methods are presented. Advantages and limits of using multibody simulation as compared to the direct use of FEA methods for the representation of structural dynamics are discussed. Results of coupled steady and unsteady simulations are presented. Finally, an approach to the aeroelastic trim problem is shown.     

基于控制瞬态冲击电机振动的悬置系统优化方法

文章建立了包含电机和悬置在内的整车动力学模型,仿真得到了整车在加速和过减速带两个典型工况下电机的动力学响应。建立综合评价指标,在考虑电机悬置系统模态、解耦等设计边界的基础上,建立了考虑悬置刚度和间隙的控制电机振动优化模型,对悬置的关键设计参数进行优化,为开发前期悬置系统的正向设计提供有效的依据。     

Influence of polygonal wear of railway wheels on the wheel set axle stress

The coupled vehicle/track dynamic model with the flexible wheel set was developed to investigate the effects of polygonal wear on the dynamic stresses of the wheel set axle. In the model, the railway vehicle was modelled by the rigid multibody dynamics. The wheel set was established by the finite element method to analyse the high-frequency oscillation and dynamic stress of wheel set axle induced by the polygonal wear based on the modal stress recovery method. The slab track model was taken into account in which the rail was described by the Timoshenko beam and the three-dimensional solid finite element was employed to establish the concrete slab. Furthermore, the modal superposition method was adopted to calculate the dynamic response of the track. The wheel/rail normal forces and the tangent forces were, respectively, determined by the Hertz nonlinear contact theory and the Shen–Hedrick–Elkins model. Using the coupled vehicle/track dynamic model, the dynamic stresses of wheel set axle with consideration of the ideal polygonal wear and measured polygonal wear were investigated. The results show that the amplitude of wheel/rail normal forces and the dynamic stress of wheel set axle increase as the vehicle speeds rise. Moreover, the impact loads induced by the polygonal wear could excite the resonance of wheel set axle. In the resonance region, the amplitude of the dynamic stress for the wheel set axle would increase considerably comparing with the normal conditions.     

Integration of car-body flexibility into train–track coupling system dynamics analysis

The resonance vibration of flexible car-bodies greatly affects the dynamics performances of high-speed trains. In this paper, we report a three-dimensional train–track model to capture the flexible vibration features of high-speed train carriages based on the flexible multi-body dynamics approach. The flexible car-body is modelled using both the finite element method (FEM) and the multi-body dynamics (MBD) approach, in which the rigid motions are obtained by using the MBD theory and the structure deformation is calculated by the FEM and the modal superposition method. The proposed model is applied to investigate the influence of the flexible vibration of car-bodies on the dynamics performances of train–track systems. The dynamics performances of a high-speed train running on a slab track, including the car-body vibration behaviour, the ride comfort, and the running safety, calculated by the numerical models with rigid and flexible car-bodies are compared in detail. The results show that the car-body flexibility not only significantly affects the vibration behaviour and ride comfort of rail carriages, but also can has an important influence on the running safety of trains. The rigid car-body model underestimates the vibration level and ride comfort of rail vehicles, and ignoring carriage torsional flexibility in the curving safety evaluation of trains is conservative.     

Aeroelastic Effects in Multibody Dynamics

To enable a realistic assessment of the aeroelastic phenomena of aircraft, a simultaneous application of computational fluid dynamics (CFD), computational structural mechanics and flight mechanics has to be performed. Each discipline has developed powerful specialized tools which have to be adapted for multidisciplinary applications. The combination of CFD and elastic multibody systems is well suited for the simulation of a range of aircraft applications, especially for aircraft ground dynamics. Approaches to a coupling of elastic multibody systems and computational fluid dynamics have been performed using close coupling, that is a modal approach, and loose coupling, that is by co-simulation. In the article the applied programs and the coupling methods are presented. Advantages and limits of using multibody simulation as compared to the direct use of FEA methods for the representation of structural dynamics are discussed. Results of coupled steady and unsteady simulations are presented. Finally, an approach to the aeroelastic trim problem is shown.