Directional Stability of Truck-Dolly-Trailer System

SUMMARY

The present state of knowledge on the handling behaviour of truck-dolly-trailer system is based on parametric studies made through simulation or eigen value analysis. Any convincing study using the equations to the stability boundaries have not been reported so far due to algebraic complexities. This paper fills the gap. Effects of system parameters are assessed using equations to the stability boundaries obtained from Routh-Hurwitz criterion. The system equations of motion are derived from a bondgraph model of a linearised system.     

Eigensystem of Tangential Contact in Tyre Models

Summary In this paper, a simplified model of tangential contact between tyre and rigid surface is investigated. By linearization the eigensystem of the contact equations is obtained and parameter variations are carried out. It is shown, that some vehicle model parameters have great influence on the eigensystem of tangential contact and can determine the highest eigenfrequency of the system vehicle and tyre. Root loci are used to investigate the influence of parameters like vehicle velocity and gridwidth of the discretization. Based on the eigensystem, stability areas of numerical methods in solving the partial differential equations of tangential contact are calculated. Numerical solutions using stiff and nonstiff integrators are compared with respect to the stability areas, computational effort and accuracy. The results are discussed with a view to further development.     

Eigensystem of Tangential Contact in Tyre Models

Summary In this paper, a simplified model of tangential contact between tyre and rigid surface is investigated. By linearization the eigensystem of the contact equations is obtained and parameter variations are carried out. It is shown, that some vehicle model parameters have great influence on the eigensystem of tangential contact and can determine the highest eigenfrequency of the system vehicle and tyre. Root loci are used to investigate the influence of parameters like vehicle velocity and gridwidth of the discretization. Based on the eigensystem, stability areas of numerical methods in solving the partial differential equations of tangential contact are calculated. Numerical solutions using stiff and nonstiff integrators are compared with respect to the stability areas, computational effort and accuracy. The results are discussed with a view to further development.     

Closed-Loop Directional Stability of Car-Trailer Combinations in Straight-Line Motion

This work focuses on the interaction between a driver and a car-trailer combination. A model characterizing human operator behavior in regulation task is employed to study directional stability of the overall system. The vehicle-trailer model retains nonlinear cornering force and other kinematic nonlinearities. Linear stability of the straight line motion is analyzed by the application of Routh-Hurwitz criteria and stability boundaries in parameter space are constructed by setting appropriate Hurwitz determinant to zero. It is shown that two types of transition in stability are possible in the driver/car-trailer system. They correspond to one pair or two pairs of complex conjugate eigenvalues crossing the imaginary axis simultaneously. The implications in terms of resulting motions for the nonlinear system are also discussed. It is shown that stabilization of the combination can be achieved by adding a passive controller at the articulation point. Articulation damper turns out to be a more useful device for controlling trailer oscillations instability although a combination of damper and torsional spring would be a more ideal solution.     

Closed-Loop Directional Stability of Car-Trailer Combinations in Straight-Line Motion

SUMMARY

This work focuses on the interaction between a driver and a car-trailer combination. A model characterizing human operator behavior in regulation task is employed to study directional stability of the overall system. The vehicle-trailer model retains nonlinear cornering force and other kinematic nonlinearities. Linear stability of the straight line motion is analyzed by the application of Routh-Hurwitz criteria and stability boundaries in parameter space are constructed by setting appropriate Hurwitz determinant to zero. It is shown that two types of transition in stability are possible in the driver/car-trailer system. They correspond to one pair or two pairs of complex conjugate eigenvalues crossing the imaginary axis simultaneously. The implications in terms of resulting motions for the nonlinear system are also discussed. It is shown that stabilization of the combination can be achieved by adding a passive controller at the articulation point. Articulation damper turns out to be a more useful device for controlling trailer oscillations instability although a combination of damper and torsional spring would be a more ideal solution.     

基于滑模控制的时滞自动车辆跟随系统数学模型

基于非线性车辆动力学方程和固定车辆间距跟随策略,对具有时间滞后的自动化公路系统车辆纵向跟随控制问题进行了研究。在假定车队中的每个被控制车辆能够接收到车队领头车辆以及该车前面一个车辆的位移、速度和加速度信息的情况下,应用滑模变结构控制方法,通过对滑模运动方程的分析,得到了关于车辆间距误差的车辆纵向跟随系统的数学模型。该模型属于一类具有时间滞后的无限维非线性关联大系统。在具有时间滞后的车辆纵向跟随控制器设计中,利用该类非线性关联大系统的稳定性判定条件来设计控制参数,可确保车辆纵向跟随控制系统的稳定性。     

Hierarchical Direct Yaw-Moment Control System Design for In-Wheel Motor Driven Electric Vehicle

In this study, a hierarchical structured direct yaw-moment control (DYC) system, which consists of a main-loop controller and a servo-loop controller, is designed to enhance the handling and stability of an in-wheel motor driven driven electric vehicle (IEV). In the main loop, a Fractional Order PID (FO-PID) controller is proposed to generate desired external yaw moment. A modified Differential Evolution (M-DE) algorithm is adopted to optimize the controller parameters. In the servo-loop controller, the desired external yaw moment is optimally distributed to individual wheel torques by using sequential quadratic programming (SQP) approach, with the tire force boundaries estimated by Unscented Kalman Filter (UKF) based on a fitted empirical tire model. The IEV prototype is virtually modelled by using Adams/Car collaborating with SolidWorks, validated by track tests, and serves as the control plant for simulation. The feasibility and effectiveness of the designed control system are examined by simulations in typical handling maneuver scenarios.     

Spatial Dynamics of Multibody Tracked Vehicles Part I: Spatial Equations of Motion

In this paper, the nonlinear dynamic equations of motion of the three dimensional multibody tracked vehicle systems are developed, taking into consideration the degrees of freedom of the track chains. To avoid the solution of a system of differential and algebraic equations, the recursive kinematic equations of the vehicle are expressed in terms of the independent joint coordinates. In order to take advantage of sparse matrix algorithms, the independent differential equations of the three dimensional tracked vehicles are obtained using the velocity transformation method. The Newton-Euler equations of the vehicle components are defined and used to obtain a sparse matrix structure for the system dynamic equations which are represented in terms of a set of redundant coordinates and the joint forces. The acceleration solution obtained by solving this system of equations is used to define the independent joint accelerations. The use of the recursive equations eliminates the need of using the iterative Newton-Raphson algorithm currently used in the augmented multibody formulations. The numerical difficulties that result from the use of such augmented formulations in the dynamic simulations of complex tracked vehicles are demonstrated. In this investigation, the tracked vehicle system is assumed to consist of three kinematically decoupled subsystems. The first subsystem consists of the chassis, the rollers, the sprockets, and the idlers, while the second and third subsystems consist of the tracks which are modeled as closed kinematic chains that consist of rigid links connected by revolute joints. The singular configurations of the closed kinematic chains of the tracks are also avoided by using a penalty function approach that defines the constraint forces at selected secondary joints of the tracks. The kinematic relationships of the rollers, idlers, and sprockets are expressed in terms of the coordinates of the chassis and the independent joint degrees of freedom, while the kinematic equations of the track links of a track chain are expressed in terms of the coordinates of a selected base link on the chain as well as the independent joint degrees of freedom. Singularities of the transformations of the base bodies are avoided by using Euler parameters. The nonlinear three dimensional contact forces that describe the interaction between the vehicle components as well as the results of the numerical simulations are presented in the second part of this paper.     

植物根系固坡的稳定性计算方法探讨

在公路边坡上种植植物,不仅能改善公路的景观,利于环境保护,而且植物的根系还具有固坡的效果。采用极限平衡方法,从局部和整体2方面建立起根系固坡的稳定性计算式。采用这些计算式,可对根系固坡的稳定性进行分析。     

基于MATLAB/Simulink的车辆转向稳定性的仿真研究

汽车的操纵稳定性是衡量汽车安全性最基本的指标之一,影响汽车行驶稳定性的基本因素主要有横摆角速度与质心侧偏角,将汽车简化为二自由度模型,建立关于横摆角速度与质心侧偏角的转向微分方程.基于MATLAB/Simulink软件建立仿真模型,对前轮转向与四轮转向典型的二自由度汽车模型进行仿真分析.对比两轮转向和四轮转向的稳定性....     

Stability Criteria for Automobile-Trailer Combinations

The characteristic equation for a simple automobile-trailer combination is analyzed, revealing the parameter groups which are important in determining the stability characteristics. Application of Routh's method results in separate criteria for oscillatory and non-oscillatory criteria which can be evaluated algebraically, and which can also be displayed graphically showing a region of stability on a two-dimensional plot. The stability region is bounded by limits of oscillatory and non-oscillatory stability, and the evaluation of a specific case corresponds to the location of a point relative to the boundaries.     

Stability Bounds of a Tractor-Semitrailer

The dynamic stability of a tractor-semitrailer is presented here on a qualitative basis. In a four-dimensional space, equilibrium states of the system are discovered which lead to suitable initial conditions for numerical integration of the system equations. The intergal solutions define the stable and the unstable regions in the state-space, and thereby reveal the system behavior. A simple example concerning the effect of a front tire blowout illustrates how the theory can expose the vehicle motion under external perturbations.     

Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> preview control of an active suspension system with norm-bounded uncertainties

A robust H _∞ preview control is investigated for an active suspension system with look-ahead sensors. The uncertain system is described by a state-space model with linear nominal parts and additional nonlinear time-varying norm-bounded uncertainties. Proof of robust stability and a feedback-type robust H _∞ preview controller are derived by augmenting the dynamics of the original system and previewed road input. As, however, the augmented previewed road input gives the system a much larger dimension than the original system, much more computation time is required for solving of Riccati equations. To resolve this problem, a decomposed robust H _∞ preview controller is proposed. Robust stability and performance variations for system uncertainties are shown using a numerical example of a quarter-car model.     

智能车小车转向系统的建模与仿真分析

文章依据典型的线性二自由度汽车模型结合freescale智能小车的实际转向系统建立数学模型，推导出微分方程，采用比例微分控制（PD）策略，并结合系统模型运用MATLAB进行仿真。采用比例微分控制（PD）策略对小车的转向系统的信号延时进行改进，对稳定性等方面也进行改善，达到预期的优化目的。     

Stability Criteria for Automobile-Trailer Combinations

ABSTRACT

The characteristic equation for a simple automobile-trailer combination is analyzed, revealing the parameter groups which are important in determining the stability characteristics. Application of Routh's method results in separate criteria for oscillatory and non-oscillatory criteria which can be evaluated algebraically, and which can also be displayed graphically showing a region of stability on a two-dimensional plot. The stability region is bounded by limits of oscillatory and non-oscillatory stability, and the evaluation of a specific case corresponds to the location of a point relative to the boundaries.     

The Wheel Shimmy Problem: Its Relationship to Wheel and Road Irregularities

The equations of motion are derived for a single wheel steerable pneumatic tire system. Included in this system are a built-in wheel wobble and wheel-tire irregularities which produce oscillation of the normal load. Special emphasis is placed on the dynamic characterization of the tire cornering force and aligning torque. The results show that the built-in wheel wobble causes a steady shimmy which is large when the wheel rotation frequency is close to the natural shimmy frequency. The results also show that a normal load oscillation which has a frequency approximately twice the natural shimmy frequency causes a decrease in shimmy stability.     

Dynamic and Vibration Analysis of a Vehicle Rear Axle System

A detailed finite element model for the rear axle system of a sport utility vehicle is developed in this investigation. The axle system is treated as a multibody system that consists of nine bodies that include the input shaft, two output shafts, the carrier and tube system, four control arms and a track bar. The rotating input and output shafts are mounted on the carrier and tube system using six bearings. The four control arms and the track bar are connected to the carrier system and the frame of the vehicle using rubber bushings. In the model developed in this investigation, three dimensional beam elements are used to develop the finite element model for the input and output axle shafts, the control arms, and the track bar. A non-conventional finite element formulation is used to develop the equations of motion of the rotating input and output shafts in order to account for the effect of their angular velocities. These equations are expressed in terms of inertia shape integrals that depend on the assumed displacement field. The inertia shape integrals are first evaluated for each finite element. The inertia shape integrals of the rotating shafts are obtained by assembling the inertia shape integrals of its finite elements using a standard finite element assembly procedure. A conventional finite element formulation is used for the control arms and the track bar. The model developed in this investigation includes the effect of the bearing stiffness, the effect of the stiffness of the helical springs of the suspension system, and the effect of the stiffness of the tires. Using the Lagrangian dynamics and the finite element method, the equations of motion of the axle system are developed and expressed in terms of the nodal coordinates of the shafts, the control arms and the track bar as well as the degrees of freedom of the carrier. This finite dimensional model is used to determine the mode shapes and the natural frequencies of the axle system. The discrepancies between several of the natural frequencies predicted using the dynamic model developed in this investigation and natural frequencies determined experimentally are found to be less than 2%. A parametric study is performed in order to investigate the effect of the axle system parameters on the natural frequencies and mode shapes. Using the modal transformation, a set of differential equations of motion of the axle system is developed and used to examine the system dynamics under given loading conditions. The solutions of the resulting equations of motion are obtained using numerical methods.     

Dynamic and Vibration Analysis of a Vehicle Rear Axle System

A detailed finite element model for the rear axle system of a sport utility vehicle is developed in this investigation. The axle system is treated as a multibody system that consists of nine bodies that include the input shaft, two output shafts, the carrier and tube system, four control arms and a track bar. The rotating input and output shafts are mounted on the carrier and tube system using six bearings. The four control arms and the track bar are connected to the carrier system and the frame of the vehicle using rubber bushings. In the model developed in this investigation, three dimensional beam elements are used to develop the finite element model for the input and output axle shafts, the control arms, and the track bar. A non-conventional finite element formulation is used to develop the equations of motion of the rotating input and output shafts in order to account for the effect of their angular velocities. These equations are expressed in terms of inertia shape integrals that depend on the assumed displacement field. The inertia shape integrals are first evaluated for each finite element. The inertia shape integrals of the rotating shafts are obtained by assembling the inertia shape integrals of its finite elements using a standard finite element assembly procedure. A conventional finite element formulation is used for the control arms and the track bar. The model developed in this investigation includes the effect of the bearing stiffness, the effect of the stiffness of the helical springs of the suspension system, and the effect of the stiffness of the tires. Using the Lagrangian dynamics and the finite element method, the equations of motion of the axle system are developed and expressed in terms of the nodal coordinates of the shafts, the control arms and the track bar as well as the degrees of freedom of the carrier. This finite dimensional model is used to determine the mode shapes and the natural frequencies of the axle system. The discrepancies between several of the natural frequencies predicted using the dynamic model developed in this investigation and natural frequencies determined experimentally are found to be less than 2%. A parametric study is performed in order to investigate the effect of the axle system parameters on the natural frequencies and mode shapes. Using the modal transformation, a set of differential equations of motion of the axle system is developed and used to examine the system dynamics under given loading conditions. The solutions of the resulting equations of motion are obtained using numerical methods.     

青藏铁路昆仑山隧道回冻预测分析

针对青藏铁路昆仑山隧道围岩多年冻土融化较多的问题，考虑水分迁移和冰水相变耦合影响，根据瞬态温度场问题的热量平衡控制微分方程和质量迁移方程，应用伽辽金法推导出了有限元计算公式并编制了计算软件。运用该计算软件对昆仑山隧道施工期间的融化进行了回冻预测分析。分析结果表明：保温材料对昆仑山隧道的回冻起着阻碍作用。在现场观测寒区隧道围岩的温度和应力时，必须考虑施工期间融化圈的影响，而且观测时间要长一些。否则，测量的温度和应力与隧道稳定后的温度和应力有较大的差异。     

Automatic generation of the non-holonomic equations of motion for vehicle stability analysis

The mathematical analysis of vehicle stability has been utilised as an important tool in the design, development, and evaluation of vehicle architectures and stability controls. This paper presents a novel method for automatic generation of the linearised equations of motion for mechanical systems that is well suited to vehicle stability analysis. Unlike conventional methods for generating linearised equations of motion in standard linear second order form, the proposed method allows for the analysis of systems with non-holonomic constraints. In the proposed method, the algebraic constraint equations are eliminated after linearisation and reduction to first order. The described method has been successfully applied to an assortment of classic dynamic problems of varying complexity including the classic rolling coin, the planar truck–trailer, and the bicycle, as well as in more recent problems such as a rotor–stator and a benchmark road vehicle with suspension. This method has also been applied in the design and analysis of a novel three-wheeled narrow tilting vehicle with zero roll-stiffness. An application for determining passively stable configurations using the proposed method together with a genetic search algorithm is detailed. The proposed method and software implementation has been shown to be robust and provides invaluable conceptual insight into the stability of vehicles and mechanical systems.