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.     

Recent Research and Development on Advanced Technologies of High-Speed Railways in Japan

Summary This report outlines the rolling stock of “Shinkansen” and conventional “narrow-gauge” railways, and reviews the research and development to put railway vehicles into revenue service from the viewpoint of rolling stock dynamics in Japan.     

A 3D Brush-type Dynamic Tire Friction Model

The use of advanced dynamic friction models can improve the brush-type tire friction models. This paper presents a 3D dynamic brush model based on the LuGre friction model. The model describes the dynamics of longitudinal and lateral tire friction forces, as well as the self aligning torque dynamics. It has been originally derived in a distributed-parameter form, and then transformed to a simpler lumped-parameter form with only three internal states. Both uniform and non-uniform normal pressure distributions are considered. The model has analytical solution for steady-state conditions. The steady-state behavior is validated with respect to “magic” formula static model, which served as an “ideal” benchmark. The lumped model dynamic behavior is validated by comparing its time-responses with original distributed model responses. The model parameterization with respect to normal force and other tire/road parameters is considered as well.     

A Radial-Spring Terrain-Enveloping Tire Model

A radial-spring tire model was developed to envelop irregular features of a rigid terrain and redefine the terrain as an “equivalent ground plane” reflecting both the elevation and slope characteristic of the original terrain contacting the tire. Three different methods were proposed for defining the maximum deflection of the tire, thereby locating the “equivalent ground plane” and defining the radial tire force. Errors in the maximum tire deflections resulting from approximations in the solution procedure could be maintained below 3 per cent of the actual tire deflections when the tire model was tested on a rigid planar surface.     

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.     

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.     

Achievable Dynamic Response for Automotive Active Suspensions *

A complete set of constraints is derived for the road disturbance transfer functions in a quarter car model of an automotive active suspension, for typical choices of measured outputs. It is shown that any road disturbance responses which are achievable using “full state feedback” can be achieved, to within an arbitrary small tolerance, using a dynamic compensator measuring suspension deflection only. Also considered are the disturbance responses to loads acting on the sprung mass, and a complete set of constraints is derived for these. It is shown that road disturbance and load disturbance responses can be determined independently if suspension deflection and sprung mass velocity are measured. Indeed, any responses achievable separately with “full measurements” can be approximated together to an arbitrary small tolerance. Certain integral relationships are shown to follow from the derived transfer function constraints. These relationships imply fundamental limitations for certain responses (e.g. tyre deflection) no matter what measurements are available for feedback.     

The Available Methods to Calculate the Wheel/Rail Forces in Non Hertzian Contact Patches and Rail Damaging

In the present paper, the methods used in railway dynamics to take into account the non Hertzian multi contact patches occurring on a wheel, are summarised. Some application cases are presented as well as an explanation of the so called “squat” rail deterioration.     

Performance of Low-bandwidth, Semi-active Damping Concepts for Suspension Control

Active damping has been shown to offer increased suspension performance in terms of vehicle isolation, suspension packaging, and road-tire contact force. It can even approximate the performance of full state feedback control without requiring the difficult measurement of tire deflection. Many semi-active damping strategies have been introduced to approximate the response of active damping with the modulation of passive damping parameters. These strategies have typically required a relatively high bandwidth for actuator response. This paper investigates the simulation performance and “frequency response” of two concepts in low-bandwidth semi-active suspension control, one that sets a damping force directly and another that sets the damping resistance. The electronically controlled bandwidth of these actuators is approximately an order of magnitude less than other semi-active devices; high frequency control is handled mechanically. A quarter-car model is studied with the controlled damping replacing both passive and active damping of typical control schemes. Both low-bandwidth damping strategies perform remarkably well compared to both active and high-bandwidth, semi-active damping. In certain dynamic performances, the new semi-active strategies outperform active damping and what the author calls “nominal” semi-active damping.     

A Comparison of Tyre Representations in a Simple Wheel Shimmy Problem

A simple system capable of wheel shimmy is analysed in three different ways and the results are compared. The tyre in each case is taken to be representable by a “taut string”, and the three ways involve (a) developing a digital tyre simulation which operates sequentially with a digital simulation of the mechanical system, (b) representing the tyre responses by linear constant coefficient differential equations derived empirically to match the string responses, and (c) as in (b) but employing fundamentally derived equations which approximate the exact string responses. The approximations are shown to give good results at reduced frequencies typical of the wheel shimmy phenomenon.     

Determining the Characteristics of Helical Springs for Application in Suspensions of Railway Vehicles

This study concerns the theoretical calculation of the characteristics of helical springs used, particularly, for the primary and secondary suspensions of railway vehicles: the static characteristics will be determined by an exact method where as the dynamic characteristics will be determined with the help of an approximate method whose precision is, however, sufficient to make a valid evaluation of the dynamic behavior of the vehicles themselves.

The first part of the study is presented here, while a second part will appear in the next issue of “Vehicle System Dynamics”.     

Application of Nonlinear Control Theory to Electronically Controlled Suspensions

This paper illustrates the use of nonlinear control theory for designing electro-hydraulic active suspensions. A nonlinear, “sliding” control law is developed and compared with the linear control of a quarter-car active suspension system acting under the effects of coulomb friction. A comparison will also be made with a passive quarter-car suspension system. Simulation and experimental results show that nonlinear control performs better than PID control and improves the ride quality compared to a passive suspension.     

A Simplified Framework for String Stability Analysis of Automated Vehicles*

Automated vehicles traveling in platoons must exhibit stability both individually and as a group, a property referred to as “string stability”. We propose a new framework for evaluating the longitudinal string stability properties of platoons of automated vehicles. In this framework, the platoon is considered to be a mass-spring-damper system with linear characteristics. The resulting closed-loop representation yields transfer functions and impulse responses that can be analyzed to determine the string stability properties of the platoon. This framework facilitates qualitative comparisons of the effects of various controller characteristics, such as time headway and intervehicle communication, on string stability.     

Optimales Abbremsen eines Fahrzeuges bei Kurvenfahrt

The problem of minimizing the stopping distance of a vehicle along a given trajectory is considered. A simple “one-wheel-model” for the vehicle and a suitable performance index for the optimization problem are derived. A simplified problem is considered first from which an analytical solution for the optimal trajectory is obtained. The suboptimal open loop control inputs are then approximately computed via a search algorithm. The results show that the performance nearly matches the predicted value.     

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.     

Chaotic Motion of Wheels

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.     

Design of an Active Unilateral Brake Control System for Five-Axle Tractor-Semitrailer Based on Sensitivity Analysis

This paper presents the results of a parametric sensitivity analysis of a five-axle tractor-semitrailer vehicle combination using 3-DOF linear yaw/plane model. The first order logarithmic sensitivity functions are derived with respect to several vehicle design parameters. For stabilization of the vehicle's directional behaviour a fairly new control concept called “Active Unilateral Braking Control (AUBC)” acting on the tractor rear wheel's in order to produce a stabilizing yaw torque is investigated. The AUBC system improves not only the directional stability, but also affects the roll dynamics of the vehicle. The sensitivity of the controlled vehicle system with linear quadratic controller (LQR) is also examined, a robust controller design procedure is proposed as a result of the sensitivity analysis. The robustness of this controller in the presence of both internal (including parametric uncertainties, non-linear dynamics) and external disturbances (such as road irregularities and side wind) allows its implementation with confidence with a non-linear vehicle model. The applicability of this control system to a non-linear vehicle model is tested using a 34 DOF, non-linear vehicle model of the tractor-semitrailer combination.     

The Kalker book of tables for non-Hertzian contact of wheel and rail

A new regularisation of non-elliptical contact patches has been introduced, which enables building the look-up table called by us the Kalker book of tables for non-Hertzian contact (KBTNH), which is a fast creep force generator that can be used by multibody dynamics system simulation programs. The non-elliptical contact patch is regularised by a simple double-elliptical contact region (SDEC). The SDEC region is especially suitable for regularisation of contact patches obtained with approximate non-Hertzian methods for solving the normal contact problem of wheel and rail. The new regularisation is suitable for wheels and rails with any profiles, including worn profiles.

The paper describes the new procedure of regularisation of the non-elliptical contact patch, the structure of the Kalker book of tables, and parameterisation of the independent variables of the tables and creep forces.

A moderate volume Kalker book of tables for SDEC region suitable for simulation of modern running gears has been computed in co-simulation of Matlab and program CONTACT.

To access the creep forces of the Kalker book of tables, the linear interpolation has been applied.

The creep forces obtained from KBTNH have been compared to those obtained by program CONTACT and FASTSIM algorithm. FASTSIM has been applied on both the contact ellipse and the SDEC contact patch. The comparison shows that KBTNH is in good agreement with CONTACT for a wide range of creepage condition and shapes of the contact patch, whereas the use of FASTSIM on the elliptical patch and SDEC may lead to significant deviations from the reference CONTACT solutions.

The computational cost of calling creep forces from KBTNH has been estimated by comparing CPU time of FASTSIM and KBTNH. The KBTNH is 7.8–51 times faster than FASTSIM working on 36–256 discretisation elements, respectively.

In the example of application, the KBTNH has been applied for curving simulations and results compared with those obtained with the creep force generator employing the elliptical regularisation. The results significantly differ, especially in predicted creepages, because the elliptical regularisation neglects generation of the longitudinal creep force by spin creepage.     

Interaction Dynamics Between an Electric Vehicle's 'Pantograph' and the Road

In this paper, we briefly describe the patented E-TRAN electric roadway & vehicle concept and then proceed to study the dynamic effects of an associated road pantograph in contact with a road mounted power strip. During usage, the road pantograph (supported underneath the vehicle) allows power to be drawn from the strip for powering the motor driven vehicle. From a mechanical point of view, friction, wear and dynamic bounce effects impact the reliability arid maintainability of the pantograph/strip concept. To study bounce effects, a dynamic model of a one degree of freedom road pantograph was developed for both contact and noncontact situations. These dynamic “bounce” effects were simulated using a MATRIXx™ based model of the road pantograph and associated road surface (and strip). In order to do so, several simulation issues had to be addressed (some of which may be of interest to those studying wheel/rail contact effects). To corroborate the dynamic model, an instrumented experimental pantograph/road simulator was fabricated. Reasonable correspondence was achieved between the experimentally measured and simulated support forces and pantograph angle. Parametric variations in the design were also studied through simulation. The work presented serves as a paradigm for designing, building, and testing road pantographs for specific applications.     

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.