Chaotic Motion of Wheels

Abstract

Trolleys have wheels which can choose the direction of their rolling. Studying the motion of a wheel like this, we can often find periodic motions (“shimmy”) or even chaotic ones. It has also been experienced that the chaotic motions sometimes disappear quite unexpectedly. A strongly simplified model of these systems is analysed in the paper by means of the methods of bifurcation theory. Analytical and numerical results are shown to characterize the system, including simulation results. Similar behaviour can be found in more complicated systems as well, like the trailers or the nose-gears of aeroplanes. The development of the so-called transient chaotic motion is explained in these systems.     

Longitudinal Oscillations of Vehicle/Trailer Combinations Induced by Overrun Braking

A mathematical model for the representation of longitudinal oscillations which can occur in car/trailer systems in braking, when the trailer brakes are applied through compression of the towing hitch, is described. The model is used to show how the trailer braking system parameters affect the steady deceleration performance of the vehicle combination, and the stability, in the linear system sense, of the steady motions. The sensitivity of the stability to other system design parameters is also examined.

Digital simulation of the motions occurring in response to a step input of car braking torque is reported, with the results confirming the predictions of the linear stability analysis, and also showing the influence of backlash in the trailer brake actuating mechanism.

The system is shown to be capable of self-excitation in a “shunting” mode, in which the car and trailer motions are in antiphase, with the stability/damping property critically dependent on drawbar damping, and only weakly dependent on other system parameters. The characteristic frequency of the “shunting” mode oscillations is shown to be controllable via the stiffness of the trailer brake linkage, but this frequency is closely related to the steady drawbar deflection which occurs in uniform deceleration.

The model behaviour described provides a basis for the design of relevant systems whose longitudinal dynamic characteristics will be satisfactory.     

黏滞性阻尼器对千米级斜拉桥纵向减震效果的振动台试验研究

为了研究千米级斜拉桥纵向采用黏滞性阻尼器的减震效果,以一座主跨1 088 m的斜拉桥为工程背景,按相似理论设计制作了一座几何缩尺比为1：35的全桥振动台试验模型,通过改变塔梁间的连接方式,建立了塔梁间纵向无约束的非减震体系和塔梁间纵向采用黏滞性阻尼器的减震体系,选用4条具有代表性的地震动进行了4个振动台纵向一致激励的全桥振动台试验,然后将不同地震动输入下2种体系的试验结果进行对比分析。试验结果表明：千米级斜拉桥纵向无约束体系的地震响应受输入地震动的特性影响较大,对于长周期成分丰富,特别是对应于结构一阶周期的加速度谱和位移谱谱值较大的地震动,结构的地震响应较大;千米级斜拉桥非减震体系的地震响应同样也受输入地震动特性的影响较大;纵向采用黏滞性阻尼器的减震体系可以减小结构的梁端位移、塔顶位移以及塔底钢筋应变,但输入地震动的特性会影响黏滞性阻尼器的减震效果,对于特征周期较长、长周期成分丰富的地震动,黏滞性阻尼器的减震效果较好,而对于有明显速度脉冲的地震动,黏滞性阻尼器的减震效果相对较差,当地震动峰值加速度PGA为0.4g时,在场地人工地震动、Loma Prieta地震动作用下,梁端最大位移分别减小了62.41%、37.75%;对于有明显速度脉冲的地震动,需要选择阻尼系数更大的黏滞性阻尼器。     

On model-based longitudinal feed-forward motion control for low velocities on known road profiles

ABSTRACT

So far, longitudinal motion control has focused on situations like highway driving, where disturbances of the road profile can be neglected. In this paper, we show how the Two Point Tire Model can be used to derive a novel feed-forward control law for a vehicle's longitudinal motion that considers the effects of the road profile and can complement existing control approaches. For this purpose, we recapitulate the basic model assumptions and equations and briefly discuss how it can be used on arbitrary road profiles. Two approaches for implementation in a real vehicle are presented. Comparisons of these approaches in simulation and to a human driver of an experimental vehicle show that the controller can deal with stepped obstacles of up to 14?cm in height. However, the control performance is essentially limited by the actuator delay and human drivers outperform the controller due to their ability of sensing subtle vehicle motions. The results indicate that the control performance can be further improved by using a preview on the necessary drive torque, which can be provided by the solution that we propose.     

路面连续减速带下汽车悬架的混沌振动分析

针对汽车通过连续减速带时所产生振动,采用二自由度非线性悬架系统为研究对象,分析其混沌动力学行为,从而实现对系统混沌进行抑制.通过分析高速公路上特殊路段连续减速带的参数和设置方式,建立其静态激励模型和得出动态激励相关函数,以数值仿真研究了非线性汽车模型在此激励下的混沌振动,获得导致系统发生混沌振动的频率条件,及车速、减速...     

Dynamics of a railway vehicle on a laterally disturbed track

In this article a theoretical investigation of the dynamics of a railway bogie running on a tangent track with a periodic disturbance of the lateral track geometry is presented. The dynamics is computed for two values of the speed of the vehicle in combination with different values of the wavelength and amplitude of the disturbance. Depending on the combinations of the speed, the wavelength and the amplitude, straight line forward motion, different modes of symmetric or asymmetric periodic oscillations or aperiodic motions, which are presumably chaotic, are found. Statistical methods are applied for the investigation. In the case of sinusoidal oscillations they provide information about the phase shift between the different variables and the amplitudes of the oscillations. In the case of an aperiodic motion the statistical measures indicate some non-smooth transitions.     

Energy Flow in Active Attitude Control Suspensions: A Bond Graph Analysis

Fully active ground vehicle suspensions which completely replace the passive spring and damper elements with a force generating actuator have required a significant amount of power. Alternative systems which retain compliant elements to handle high frequency isolation but include active elements to control the vehicle body attitude have been developed to reduce the power requirements. These suspensions are called “low bandwidth” or “fast load leveler” systems and they often incorporate semi-active dampers which produce high frequency controllable forces with low power requirements. Here, two contrasting attitude control systems are studied to show that actuator power can be significantly reduced if the actuator is used to vary a lever ratio instead of being used to compress the suspension spring directly. Both types of systems have been successfully implemented in prototype form. Bond graphs for idealized versions of the suspensions show clearly the significant differences in actuator power and energy requirements even though the abstract mathematical structures of the two systems are remarkably similar. Computer simulations confirm the analytical results.     

Two-Dimensional Motion of Vehicles Damaged due to Collision

This paper deals with two-dimensional motion analysis of vehicles damaged due to collision. Various parts of vehicles are damaged due to collision in general. The effects of the damage in vehicle body and wheels on the vehicle motions are investigated. The center of gravity of the vehicle and the polar moment of inertia are changed by the deformation of vehicle body. Furthermore, the geometrical relations of wheels like wheelbase, treads and steering angles may be changed by damage of the wheels. Thus the vehicle loses symmetry with respect to the vehicle axis. The four-wheel vehicle model is extended to take into account the vehicle damage due to collision. The motions of damaged vehicles are compared with those of undamaged vehicles. It is found that vehicle damages have a significant influence on vehicle motion after impact.     

Two-Dimensional Motion of Vehicles Damaged due to Collision

This paper deals with two-dimensional motion analysis of vehicles damaged due to collision. Various parts of vehicles are damaged due to collision in general. The effects of the damage in vehicle body and wheels on the vehicle motions are investigated. The center of gravity of the vehicle and the polar moment of inertia are changed by the deformation of vehicle body. Furthermore, the geometrical relations of wheels like wheelbase, treads and steering angles may be changed by damage of the wheels. Thus the vehicle loses symmetry with respect to the vehicle axis. The four-wheel vehicle model is extended to take into account the vehicle damage due to collision. The motions of damaged vehicles are compared with those of undamaged vehicles. It is found that vehicle damages have a significant influence on vehicle motion after impact.     

Flexible Bodies in Multibody System Codes

SUMMARY

Multibody codes are'efficient tools to simulate nonlinear dynamic behaviour of rigid and flexible multibody systems undergoing large overall motions overlaid by small elastic deformation. This paper gives an overview of common approaches for the equations of motion of flexible body models and presents a general way to prepare the required data including geometric stiffening terms. In particularly, for the nodal approach the data are derived using standard results of a finite element analysis of the body. The computation of coefficient matrices describing the equations of motion is done outside the finite element code by matrix manipulations only. The data are stored in a standardised object-oriented structure. Consequently, the data set is independent of the formulation of the multibody system code.     

Flexible Bodies in Multibody System Codes

Multibody codes are'efficient tools to simulate nonlinear dynamic behaviour of rigid and flexible multibody systems undergoing large overall motions overlaid by small elastic deformation. This paper gives an overview of common approaches for the equations of motion of flexible body models and presents a general way to prepare the required data including geometric stiffening terms. In particularly, for the nodal approach the data are derived using standard results of a finite element analysis of the body. The computation of coefficient matrices describing the equations of motion is done outside the finite element code by matrix manipulations only. The data are stored in a standardised object-oriented structure. Consequently, the data set is independent of the formulation of the multibody system code.     

Dynamic Simulation of Taipei EMU Train

Simplified train dynamics for the trains of the Taipei Metro are presently being studied, with the aid of numerical methods, to avoid possible dangerous conditions of coupler failure and to understand the deformation of the “mechanical fuse” in a train collision. A multiple degree-of-freedom system is utilized to simulate the EMU train. Equations of motion are set up in a matrix and solved to calculate the transient responses of the couplers. Analytical solutions are checked by comparison with the results of the Runge-Kutta method. Energy absorption devices such as the coupler and the “mechanical fuse” as well as the vehicle body structure are taken into consideration to complete an integrated study of the structural crashworthiness. It is found that sudden failure of couplers would not happen for a train at coupling speeds up to 5 km/h. Coupler force for a train running at a normal acceleration from the start or at an emergency stop are also investigated. In addition, it is found that damage is confined to the fuse structures and the fuse deformation is less than the maximum allowable deformation designed in the trains, under an impact speed of 25 km/h.     

Inverse Analysis of Pre- and Post-Impact Dynamics for Vehicle Accident Reconstruction

In the dynamic analysis of the vehicular accident reconstruction, the vehicle motion is typically analyzed in three phases. These are pre-impact motion, impact motion, and post-impact motion, which are usually analyzed in reverse order of occurrence. Tire-ground forces are important during the pre- and post-impact motions, and less important during the impact. We present a vehicular dynamic model for pre- and post-impact as a rigid body which moves under the influence of tire-ground forces. Using a forward simulation analysis, we show how the initial sliding conditions can be computed with several final data points for vehicle's position and orientation, referred to as the inverse analysis algorithm for the accident reconstruction.     

On-track test of tilt control strategies for less motion sickness on tilting trains

Carbody tilting is today a mature and inexpensive technology that permits higher train speeds in horizontal curves, thus shortening travel time. However, tilting trains run a greater risk of causing motion sickness than non-tilting ones. It is likely that the difference in motions between the two train types contributes to the observed difference in risk of motion sickness. Decreasing the risk of motion sickness has until now been equal to increasing the discomfort related to quasi-static lateral acceleration. But, there is a difference in time perception between discomfort caused by quasi-static quantities and motion sickness, which opens up for new solutions. One proposed strategy is to let the local track conditions influence the tilt and give each curve its own optimised tilt angle. This is made possible by new tilt algorithms, storing track data and using a positioning system to select the appropriate data. The present paper reports from on-track tests involving more than 100 test subjects onboard a tilting train. A technical approach is taken evaluating the effectiveness of the new tilt algorithms and the different requirements on quasi-static lateral acceleration and lateral jerk in relative terms. The evaluation verifies that the rms values important for motion sickness can be influenced without changing the requirements on quasi-static lateral acceleration and lateral jerk. The evaluation shows that reduced quantities of motions assumed to have a relation to motion sickness also lead to a reduction in experienced motion sickness. However, a limitation of applicability is found as the lowest risk of motion sickness was not recorded for the test case with motions closest to those of a non-tilting train. An optimal level of tilt, different from no tilt at all, is obtained. This non-linear relation has been observed by other researchers in laboratory tests.     

Fault Diagnostics for GPS-based Lateral Vehicle Control

Summary This paper develops a fault diagnostic system to monitor the health of the lateral motion sensors on an instrumented highway vehicle. The fault diagnostic system utilizes observer design with the observer gains chosen so as to ensure that each sensor failure causes estimation errors to grow in an unique direction. The performance of the fault diagnostic system is verified through extensive experimental results obtained from an instrumented truck called the “Safetruck”. The fault diagnostic system is able to monitor the health of a GPS system, a gyroscope and an accelerometer on the Safetruck. It can correctly detect a failure in any one of the three sensors and accurately identify the source of the failure. A GPS-based geographic database containing information on road coordinates, curvature and bank angles plays a key role in ensuring accurate experimental performance of the observers.     

近场脉冲地震作用下穿越断层带隧道地震响应

在地震动峰值、速度脉冲及结构的地震响应等方面,近场地震动常表现出和远场地震动不同的特性。依据地震动破坏势从NGA-West2地震动库中选出2条近场脉冲型地震动,并与2条远场地震动进行对比分析,从而得到其频谱特性,即近场脉冲型地震波具有较明显的速度幅值,PGV与PGA比值及PGD与PGA比值较大,速度敏感区位于长周期段等特点。结合都汶高速公路龙洞子隧道工程,建立穿越断层带的隧道结构三维有限元模型,并以横断面方向分别输入近、远场地震波进行计算,研究近场脉冲型地震作用下穿越断层带隧道结构地震响应特性。结果表明：在近场脉冲型地震动作用下隧道的等效应变峰值较远场地震动大,并且在速度脉冲特性更显著的集集地震波作用下的应变峰值更大;与远离断层处相比,在断层面附近隧道横断面的等效应变峰值分布规律发生了变化,其横截面等效应变峰值最大处由拱脚变为拱顶,且在4种地震波作用下拱顶处结构的等效应变均超过了混凝土的峰值应变,进入破坏阶段;断层带内的隧道地震响应明显强于围岩条件较好的地层中的隧道,而断层带与较好围岩交界面附近的隧道地震响应更为剧烈,应变峰值随距断层距离的增大而迅速衰减。所得数值模拟结果与实际震害现象一致,可以为近场脉冲型地震动作用下穿越断层隧道的抗震设防提供参考。     

The Static Stability of Articulated Commercial Vehicles

This review of the state of the art emphasizes recent results that have been obtained in extending conventionalanalysis techniques to the treatment of “Highway Trains”, that is, to heavy trucks that have multiple articulation points and employ suspensions with multiple axles. Equations of motion applicable to the equilibrium turning performances of articulated vehicles are examined with respect to using analysis techniques involving steering gains, understeer gradients, effective wheel-bases, handling diagrams, and critical speeds. These examinations provide the basis for in sights into simplified approaches for understanding the steady turning mechanics of articulated, multi-axle vehicles riding on pneumatic tires.     

双层钢桁梁斜拉桥振型模态及地震响应特征研究

为研究典型双层钢桁梁斜拉桥的振型模态及地震动响应特征,建立了三维精细化有限元模型,并选取1条人工波和4条天然波分别作为输入地震荷载以模拟双层钢桁梁的地震响应过程.结果表明,桥梁整体为长周期结构体系,一阶自振周期为8.11 s,基本振型特征为主梁横弯、主梁纵飘和横飘、反对称横弯.不同地震波作用下桥梁主要结构的位移峰值、内...     

Optimal Performance of Variable Component Suspensions

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.