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.     

Static and Dynamic Instabilities of Bogie Railway Vehicles with Linkage Steered Wheelsets

The root loci of a type of bogie railway vehicle with linkage steered wheelsets are discussed and contrasted with those of conventional configurations. Approximate solutions of the equations of motion are used to derive stability criteria associated with the various modes of static and dynamic instability that are identified. The physical origin of each form of instability is discussed. It is shown that, in addition to the more common forms of dynamic instability arising from the joint action of creep, conicity and inertia, other forms of static and oscillatory instability are the result of structural asymmetry and wheelset articulation.     

隧道稳定性分析与设计方法讲座之二：隧道围岩稳定性分析及其判据

作为一个讲座对以往研究成果作一综述。分析隧道围岩稳定性的3种判据,提出有严格力学依据的稳定安全系数作为围岩稳定分析的定量判据。指出围岩有剪切安全系数与拉裂安全系数,并建议采用强度储备安全系数作为围岩稳定安全系数。建立土体隧道稳定分析的新理念和新方法,计算中考虑了围岩的荷载释放,初期支护作为弹塑性材料加固围岩,并应具有一定安全系数,以确保施工安全。二次衬砌作为弹性结构,围岩、初期支护与二次衬砌共同作用确保运行安全。对岩石围岩分级提出初步建议,并以无衬砌围岩安全系数作为各级围岩自稳能力的定量判据,由此反推出各级围岩的力学强度参数,改善了参数的合理性。     

Theoretical Analysis of the Steering Behaviour of Articulated Frame Steer Vehicles

A theoretical analysis of the steering behaviour of articulated frame steer vehicles is presented. It includes details of the hydraulic steering system as well as the equations governing motion of the front and rear body units. Both oscillatory and exponential instabilities can occur with this type of vehicle. The most sensitive design feature is the steering system, which governs the effective torsional stiffness around the pivot. Other important features which influence stability are speed and centre of gravity positions of the bodies.     

Finite Disturbance Directional Stability of Vehicles with Human Pilot Considering Nonlinear Cornering Behavior

The driver of a vehicle has a significant influence on handling and stability of the vehicle. Due to the complex behavior of a human pilot, a driver model is usually neglected when dealing with the problem of vehicle stability. This work focuses on the interaction between the vehicle and the human pilot. A model characterizing human operator behavior in a regulation task is employed to study directional stability. Linear stability is analyzed by the application of the Routh-Hurwitz criterion and stability boundaries separating the stable domain of operation of the driver from the unstable one are constructed.

The linear analysis predicts that the only possible instability in a driver/vehicle system is an oscillatory instability with increasing amplitude. It is shown that the addition of kinematic as well as slip angle nonlinearities in the vehicle model can have a stabilizing effect on these oscillations of the combined driver/vehicle system. They may also be responsible for the opposite, namely a linearly stable motion may become unstable to finite size disturbances. These nonlinear motions are predicted by a bifurcation analysis and are verified by direct numerical simulation.     

基于等效面积Drucker-Prager模型探讨边坡破坏机制

强度折减有限元法在边坡稳定性分析中得到了广泛应用。基于等效面积的D-P屈服准则如DP1,DP2,DP3,DP4等模型来模拟二维和三维边坡稳定状况,进行了边坡稳定性分析计算。得出不同折减系数下边坡中广义塑性应变的变化情况,结果表明用该模型能较好地模拟土坡的渐近破坏过程,有助于对边坡的破坏机制的更深层次的理解;并把计算结果和传统极限平衡方法进行了对比,表明三维稳定有限元分析可较二维有限元更加真实地反映边坡的稳定状况;基于等效面积的D-P屈服准则的DP3模型的计算比较真实,更好地模拟了边坡的破坏机制。     

海屯高速公路熔岩空洞地基稳定性二级模糊综合评判方法应用研究

以海屯高速公路为工程背景,结合该地区熔岩空洞地基的主要特点,提取该类型地基的稳定性影响因素,得到了符合海屯高速熔岩空洞地基特点的影响因素关系集及各级权重影响因素权重集,并以K9＋680~K9＋800填方路基处一通道型空洞为例,系统介绍了运用二级模糊综合评判方法对该区域空洞地基进行稳定性评价的一般步骤,可将本方法进一步推广,以期为海屯高速公路熔岩地区高速公路建设提供指导。     

Effects of multiple axles on the lateral dynamics of multi-articulated vehicles

This paper describes an analytical study of the lateral dynamics of multi-articulated vehicles with multiple axles. A linear planar model of vehicle dynamics is adopted for multiple-axle vehicle combinations with an optional number of trailers. Two tractor and double-trailer combinations are examined for their directional stability and response. Non-oscillatory stability and steering sensitivity in steady-state turning and lane changing are analysed using a stability factor of multiple-axle vehicle combinations. Off-tracking in the steady-state turning of multiple-axle vehicle combinations is also analysed. Numerical calculations for oscillatory stability, steering sensitivity, and off-tracking are presented for multiple-axle vehicle combinations.     

液压互联悬架抗侧倾控制研究（双语出版）

针对车辆减少能量消耗与提高抗侧倾能力需求,提出了一种主/被动可切换的液压互联悬架抗侧倾控制方法。基于9自由度车辆动力学模型,考虑蓄能器、液压缸、液压泵三者之间耦合的体积-流量-压力特性,建立液压互联悬架主动控制时域模型;结合"车身侧倾角-车身侧倾角速度"相平面法及车辆侧向加速度,得到车辆侧倾稳定域,并提出液压互联悬架系统侧倾稳定性控制介入与退出判据;在此基础上,采用Backstepping非线性控制算法设计主动液压互联抗侧倾控制器。最后,分析并改进侧倾稳定性评价指标,通过在MATLAB/Simulink环境下进行高速双移线、鱼钩试验等极端工况数值仿真,验证所提出的液压互联悬架主/被动切换控制系统能在减少能量消耗的情况下能否提高车辆抗侧翻的能力。研究结果表明：所提出的控制系统能有效提高车辆抗侧翻能力;当车辆侧倾状态超出设定的侧倾稳定区域介入线时,液压互联悬架系统由被动模式切换为主动抗侧倾模式,控制车辆侧倾状态回到稳定区域,以提高车辆侧倾稳定性;当判定车辆侧倾状态满足主动控制退出条件时,液压互联悬架系统回到被动模式,以减小能量消耗。     

Evaluation of idle stability through in-situ torque measurement in automatic transmission vehicles

Idle stability directly affects a vehicle’s NVH (Noise, Vibration and Harshness) and is closely related to driver satisfaction. The present study proposes a method of measuring an engine’s idle roughness, which is useful in quantifying the idle stability. Engine brake torque was measured directly using a torque sensor, which can be installed without modification of the engine’s mounting structure. In addition, angular acceleration was measured at the same position as the torque measurement, to compare dynamic characteristics of the angular acceleration with the torque variation. Both torque and angular acceleration oscillate between positive and negative values. In this study, torque data were divided into several regions, and each region starts from the point where the torque data changes its sign from negative to positive. The root mean square values of both torque and angular acceleration were calculated for each region. This calculation showed a very good correlation between the torques and the angular accelerations. The idle stability was evaluated with the standard deviation of the measured torque, and the cycle-to-cycle variation is a more dominant factor in the idle stability than is the cylinder-to-cylinder variation. Because it is easier to measure the angular acceleration than to measure the torque, the variations of angular accelerations are usually compared between engines. However, the present study showed that the moment of inertia of an engine and the angular acceleration should be considered together when comparing the idle stability between engines.     

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.     

地震区隧道稳定性分析方法

结合大量文献及工程实例，指出地震区隧道稳定性可以从定性和定量两方面分析评价。结合定性和定量的具体方法，提出了实用的地震区隧道稳定性分忻流程，并指出隧道设计、施工应注意采取的抗震措施，可为在地震区隧道的设计、施工、加固等方面提供参考依据。     

采用振荡压实技术的SMA沥青路面施工及质量控制

结合振荡压路机及其压实技术的特点,分析了振荡压实技术应用于公路SMA路面的施工工艺及施工技术要求,同时对振荡压实技术在SMA路面施工的效果进行了分析。结果表明:振荡压实技术用于沥青路面的压实是可行的,只要严格按照施工技术要求并合理组织施工,应用振荡压实技术就能有效提高路面使用性能和延长路面使用寿命,是一种值得大力推广的施工技术。     

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.     

Static and Dynamic Stability of a Class of Three-Axle Railway Vehicles Possessing Perfect Steering

For railway vehicles having coned wheels mounted on solid axles there is, in general, a conflict between stability of lateral deviations from the motion along the track and ability to steer round curves. However, the three-axle vehicle with zero bending stiffness and with shear elasticity between all wheelsets can satisfy the requirement of perfect steering and for a range of values of equivalent conicity possesses both static and dynamic stability. The static and dynamic stability of the most general form of symmetric three-axle vehicle is investigated, and stability criteria derived.     

振荡压实技术在SMA沥青面层压实中的应用

针对SMA面层采用振动压实易破坏表层粗集料的完好性，使路面产生波纹，影响路面的平整度，导致表层材料振松，降低表层密实度的问题，运用振荡压实技术压揉结合的特点对SMA沥青面层进行了压实。结果表明：振荡压实能够保证SMA骨料不被破坏，提高了路面的平整度、压实度和光滑度，减少了离析现象的发生，延长了路面的使用寿命。     

剪胀角对路基边坡稳定性的影响分析

将强度折减法基本理论与弹塑性有限元相结合,以有限元计算收敛条件作为边坡失稳评判指标,分析某高速公路的边坡土体剪胀角对边坡稳定性的影响。计算结果表明：随着剪胀角的增长,边坡稳定安全系数逐渐增长,当土体剪胀角从0°增长到15°时,边坡的稳定安全系数增长了11%;边坡最终破坏的塑性区域随着土体剪胀角的增长而逐渐较小,这表明土体剪胀角对边坡稳定性有着显著的影响。     

Region of attraction analysis for nonlinear vehicle lateral dynamics using sum-of-squares programming

In this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates.