Directional Stability of Truck-Dolly-Trailer System

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.     

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.     

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

SUMMARY

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.     

Vehicle control synthesis using phase portraits of planar dynamics

ABSTRACT

Phase portraits provide control system designers strong graphical insight into nonlinear system dynamics. These plots readily display vehicle stability properties and map equilibrium point locations and movement to changing parameters and system inputs. This paper extends the usage of phase portraits in vehicle dynamics to control synthesis by illustrating the relationship between the boundaries of stable vehicle operation and the state derivative isoclines in the yaw rate–sideslip phase plane. Closed-loop phase portraits demonstrate the potential for augmenting a vehicle's open-loop dynamics through steering and braking. The paper concludes by applying phase portrait analysis to an envelope control algorithm for yaw stability and a sliding surface controller for stabilising a saddle point equilibrium in drifting.     

Dynamic Parameter Estimation of a MacPherson Strut Suspension

SUMMARY

The dynamic parameters of a MacPherson strut suspension were estimated from the kinematic responses and measured external forces on the system. First, Lagrange equation was used to develop the equations of motion of the system, and then equations of motion were written as linear with respect to the dynamic parameters being estimated. The generalized coordinate partitioning technique was applied to create a reduced set of equations of motion of the constrained dynamic system. In this method only the measurements of positions and kinematic responses of the independent coordinates, and the external forces applied on the system are required as inputs. The rank deficient linear system was solved by QR decomposition. Good correlation was obtained between the actual parameters and the estimated parameters, by comparison between the simulated system response from the actual parameters and from the estimated parameters.     

Effect of Frame Compliance on the Lateral Dynamics of Motorcycles

SUMMARY

The lateral dynamics of an uncontrolled motorcycle, running on a straight, level road surface, is investigated in this paper. The structural compliances in the front and the rear frames of the motorcycle are taken into account by introducing additional degrees of freedom in the analysis. The kinematics of the tires is represented by linear differential equations which are based on the taut-string model of pneumatic tires. The linear differential equations of motion are solved to yield the eigensolutions of the system. Numerical results, obtained for parameters corresponding to a Honda CB750 motorcycle, are presented and discussed.     

Analyses of Vision-based Lateral Control for Automated Highway System

SUMMARY

The stability and performance of a vision-based vehicle lateral control system are analyzed. Effects of look-ahead distance, vision delay, and vehicle speed on the performance of vision feedback control system are examined by using frequency domain and time domain methods. A measurement model of the vision system is derived from the point of view of multiple sensors. The quantization error of the vision system is analyzed and the way of extracting essential information for control is studied. Based on this analysis, some guidelines for the design of vision-based controllers are proposed. A design example is further illustrated for a vision system with a substantial time delay.     

Simulation of Multibody Vehicles Moving over Elastic Guideways1

SUMMARY

This paper describes the present state of a general purpose computer program for calculating the dynamic response of vehicles travelling over guideways which may be elastic.

The linearized state-equations of motion for general multibody vehicles are constructed automatically by the program, these equations are supplemented by the equations for the active subsystems. Finally, the vehicle system equations are combined with the modal equations for elastic guideways and the complete set of coupled equations is solved simultaneously by numerical integration.     

Damping Performance of Power Transmission System with Hydraulic Torque Converter

Abstract

In this work three first-order nonlinear, nonstationary differential equations describing a hydraulic torque converter in a power transmission system are used.

A linear model is obtained on the basis of these equations. This model is verified both theoretically and by an experimental test. On the basis of the calculations the torsional damping was determined. This permitted the damping performance of a power transmission system with a hydraulic torque converter to be defined and established.     

Precision analysis and dynamic stability in the numerical solution of the two-dimensional wheel/rail tangential contact problem

ABSTRACT

In this paper the two-dimensional contact problem is analysed through different mesh topologies and strategies for approaching equations, namely; the collocation method, Galerkin, and the polynomial approach. The two-dimensional asymptotic problem (linear theory) associated with very small creepage (or infinite friction coefficient) is taken as a reference in order to analyse the numerical methods, and its solution is tackled in three different ways, namely steady-state problem, dynamic stability problem, and non-steady state problem in the frequency domain. In addition, two elastic displacements derivatives calculation methods are explored: analytic and finite differences. The results of this work establish the calculation conditions that are necessary to guarantee dynamic stability and the absence of numerical singularities, as well as the parameters for using the method that allows for maximum precision at the minimum computational cost to be reached.     

Stability Criteria for Articulated Railway Vehicles Possessing Perfect Steering

SUMMARY

The general form of the equations o f motion o f multi-body articulated railway vehicles are used to establish the conditions which the elastic stiffness matrix, which describes the nature and configuration o f the suspension elements connecting the various bodies, must satisfy in order to achieve both perfect steering on circular curves and dynamic stability. The resulting criteria are then used to discuss the properties of various multi-axle configurations which are either typical of current practice or possibilities for future designs.     

Stability Analysis of Constant Speed Transit Vehicles On Straight,Horizontal, Fixed Guideways

SUMMARY

Several methods of motion stability analysis are examined and compared in the context of the problem posed by a simple idealization of a transit vehicle moving at constant speed on a straight, horizontal, fixed guideway, supported by idealized rubber tires, air cushion pads, or semiconical steel wheels on steel rails. Stability analysis methods examined include Liapunov analysis with the Hamiltonian and with a modified Hamiltonian proposed by Walker, and analysis of characteristic equations using theorems due to Routh, Hurwitz, Cronin, and Liénard and Chipart It is concluded that for rubber-tired and aircushioned vehicles a Liapunov analysis employing the Hamiltonian is most efficient, and for the tracked vehicle the criteria of Liénard and Chipart are most useful.     

Railway Vehicles With Generic Bogies Capable of Perfect Steering

SUMMARY

The general form of the equations of motion of a symmetric railway vehicle with two unsymmetric two-axle bogies is derived. The equations include a generic elastic stiffness matrix that describes the nature and configuration of the structural connections between the various components of the vehicle. This matrix satisfies the condition for perfect steering (without generating creep forces) on uniform curves and the necessary condition for dynamic stability derived in previous work. The paper shows the application of these basic conditions to a class of generic unsymmetric bogies. The analysis has as its objective the derivation of the simplest rather than the most general configuration that meets the conditions imposed. The results are related to past and current practice. It is shown that perfect steering, with stability at low speeds, can be achieved by means of passive suspension elements not employing linkages, and that it is possible to simplify existing steering arrangements.     

Identification Methods for Vehicle System Dynamics

SUMMARY

The paper presents a survey on parameter identification techniques for complex vehicle models. In order to cope with the complexity of the model, the information on the system available from the equations of motion has to be included in the identification process. Basic methods for the solution of this problem are shown. The application of the approach is demonstrated by identification of the vertical automobile dynamics. It is concluded that the presented techniques will become more important with increasing applications of theoretical modeling in vehicle system dynamics.     

Exact Equations for Tractrix Curves Associated with Vehicle Offtracking

Abstract

Vehicle offtracking behavior at low speeds is closely approximated by a geometric entity called a tractrix. This paper presents differential equations for generalized coordinates of a planar multibody vehicle model based on tractrix behavior. The equations are exact, can be used with any type of input path, are valid for forward and backward movements, and are much simpler than previously published formulations used to compute transient offtracking. The differential equations can be integrated using conventional numerical integration algorithms to obtain plots of the low-speed tracking performance of articulated vehicles. The equations were formulated symbolically by a computer program used to analyze the kinematic and dynamic behavior of multibody systems. Example numerical results are plotted.     

Modeling and Analysis of Nonlinear Multibody Systems

SUMMARY

The method of multibody systems is introduced for the modeling of nonlinear vehicle systems. The equations of motion and the equations of reaction are found. For the dynamical analysis a classification of nonlinear phenomena is presented using objective and subjective criteria. As an illustrative example the dynamical behaviour of a four-body pendulum is investigated.     

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.     

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.     

Investigation on Stability and Possible Chaotic Motions in the Controlled Wheel Suspension System

SUMMARY

The suspension system has to fulfil a large number of partly contradictory requirements which can be improved by the application of controllable elements in the wheel suspension system. A number of studies dealing with the improvement of suspension characteristics have been published. In the present paper the stability of the controlled suspension systems will be examined. In the paper the stability problems of the active suspension system is analysed and the stable parameter regions are determined.