The Random Vibration of a Nonuniform Cantilever Beam with Concentrated Mass

The random vibration of a nonuniform cantilever beam with a concentrated mass at its end, is studied as a simple model of the suspension spring of a motor vehicle. The spectral response of the displacement of the concentrated mass is obtained when the beam is subjected to the random motion of the support. The conditions for the validity of the single degree approximation is also discussed.     

Natural Frequencies of Bernoulli–Euler Beams Resting on Two Elastic Supports: Application to Railway Vehicles

SUMMARY

The purpose of the present study is to investigate the effect of the different parameters of the elastic supports upon which a deformable beam lies, upon the natural frequencies of the system.

The influence of support parameters is obtained by exploiting characteristic transcendental equations. The natural flexural vibrations of the beam are only affected by the stiffness of the supports over a very restricted range; outside this range the frequencies are those of a completely free beam or of a beam supported by two simple rigid supports (infinite stiffness).     

Linearization Function of a Complex Nonlinear Two-Force-Element

Abstract

Output force of a nonlinear two-force-element (TFE) excited by a stationary random process is stationary random as well and is described by its autocorrelation function.

Dependence of this autocorrelation function on the autocorrelation functions of the excitation process and of its velocity and on their crosscovanance function is indicated by the linearization (describing) function.

This paper describes the determination of the linearization function for a complex TFE composed of a parallel spring and damper, both having characteristics described by polynosmial functions. Knowledge of the linearization function is necessary for carrying out the second order linearization procedure of nonlinear dynamic systems excited by stationary random processes described in ‘1’, ‘2’, ‘3’.     

Random Vehicle Vibrations as Effected by Dry Friction in Wheel Suspensions

SUMMARY

The changes of vibration comfort and stability of vehicles as effected by the value of frictional force generated in laminated springs are discussed and the probability of departure of the tyres from the ground is described.

A partly automated analogue computer simulation being equivalent to a great number of highway experiments was applied in the study.

The computer model was excited by several stochastic roadprofile - analogue signals generated by filters from the wide-band random signal of a digital noise generator.     

Dynamic Response of a Six-axle Locomotive to Random Track Inputs

SUMMARY

Spectral analysis techniques are employed to analyze the dynamic response of a six-axle locomotive on tangent track to vertical and lateral random track irregularities. The locomotive is represented by a thirty-nine (39) degrees of freedom model. A linear model is employed by considering small displacements, linear suspension elements and a linear theory for the wheel-rail interaction. Power spectral densities of displacements, velocities and accelerations and the statistical average frequencies of the system are obtained for each degree of freedom. Comparison of the calculated dominating frequencies with existing experimental values shows good agreement. The technique of spectral analysis is an effective tool for model validation, and for the determination of rail vehicle response to track irregularities. The probability functions for the response can be used as a measure for the ride quality of rail vehicles and for the study of fatigue damage of components.

     

Frequency Spectral Analysis of Bridge-Vehicle System due to Road Surface Roughness

SUMMARY

The paper presents a new method to study the dynamic properties of the bridge-vehicle system. The transfer function of the system is obtained by iteration in the frequency domain instead of the time domain. The relationship between vehicle speed and the lowest natural frequency of the system is investigated and a parametric study of the system stability is made. The varying parameters concerned are the vehicle speed, the ratio of vehicle mass to bridge mass, the ratio of vehicle eigenfrequency to bridge eigenfrequence, and the relative damping of the vehicle and bridge.     

Transient Response Test Procedures for Measuring Vehicle Directional Control

SUMMARY

A comparative study of four different test procedures for quantifying the transient lateral response of automobiles is presented in this paper. Both full-scale testing and analysis have been used in this study. The random steering technique appears to offer several advantages over other procedures in terms of space-requirement and the amount of transient dynamics information generated, whereas the step-steering procedure is more suited to the measurement of steady-state behavior of the automobile.     

Direct Covariance Analysis for the Calculation of Creepages and Creep-Forces for Various Bogies on Straight Track with Random Irregularities

SUMMARY

In this paper creep-forces and creepages for an ICE express train coach and an electric locomotive BR 120 of the DB on straight track with random irregularities are investigated. The calculations are made with the multibody program MEDYNA using direct covariance analysis. One of the aims of this article is to emphasize the advantages of the direct covariance method (time domain) compared with the power spectral density method (frequency domain).     

Dynamic Interaction between Wheel and Track - A Parametric Search towards an Optimal Design of Rail Structures

SUMMARY

The dynamic vertical interaction between a moving rigid wheel and a flexible railway track is investigated. A round and smooth wheel tread and an initially straight and noncorrugated rail surface are assumed in the present optimization study. A symmetric linear three-dimensional beam structure model of a finite portion of the track is suggested including rail, pads, sleepers and ballast with spatially nonproportional damping. The full interaction problem is numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the track. Transient bending stresses in sleepers and rail are calculated. The influence of seven selected track parameters on the dynamic behaviour of the track is investigated. A two-level fractional factorial design method is used in the search for a combination of numerical levels of these parameters making the maximum bending stresses a minimum.     

Roadway Elevation Profile Generation for Vehicle Simulation

SUMMARY

With a simplified approach for creating road surface elevation information for simulation of vehicle vertical response to roadway unevenness, roadways for single and parallel track simulations and averaged roads for variable velocity simulation are developed. Sets of correctly chosen random roadway slopes are averaged appropriately for the variable velocity simulation. The procedure generates approximately “white” slope spectral density roadways in the frequency ranges of interest, and the elevation profiles are representative of average road profiles. The method is simple in practice yet suffices for many parameter studies of suspensions and vehicle dynamics.     

Road roughness estimation based on discrete Kalman filter with unknown input

ABSTRACT

The road roughness acts as a disturbance input to the vehicle dynamics, and causes undesirable vibrations associated with the ride and handing characteristics. Furthermore, the accurate measurement of road roughness plays a key role in better understanding a vehicle dynamic behaviour and active suspension control systems. However, the direct measurement by laser profilometer or other distance sensors are not trivial due to technical and economic issues. This study proposes a new road roughness estimation method by using the discrete Kalman filter with unknown input (DKF-UI). This algorithm is built on a quarter-car model and uses the measurements of the wheel stroke (suspension deflection), and the acceleration of the sprung mass and unsprung mass. The estimation results are compared to the measurements by laser profilometer in-vehicle test.     

An Active Suspension with Optimal Linear State Feedback

SUMMARY

In this paper modern optimal control theory is applied to the design of an active suspension system for a motor vehicle. The road profile is assumed to be continuous and random with a power spectral density (P.S.D.) which varies inversely with the square of the frequency. The quadratic integral type performance index employed is a weighted sum of the integral squares of body acceleration, dynamic tyre deflection and relative body-to-axle displacement. A solution is obtained for the infinite time case which is both computationally and physically realizable as an active suspension in which the only continuous measurements required are the body absolute velocity and the body displacement relative to the road. The performance is compared with that of a conventional type passive suspension and found to be significantly better in practically all respects.     

Comparison of the properties of active and semiactive suspension

In this article, the properties of active and semi-active suspension for heavy goods vehicles are compared. The criteria for the comparison are the RMS sprung mass vertical acceleration, RMS dynamic tyre force, and suspension power consumption. The active system is based on an air-spring with controlled in-flow and out-flow of the air. In the semi-active system, a controlled hydraulic damper is employed. The results concerning the semi-active suspension system were taken from the article by Besinger et al. [Besinger, F.H., Cebon, D. and Cole, D.J., 1995, Force control of a semi-active damper. Vehicle System Dynamics, 24(9), 695–723.].     

Semi-Active Suspension with Preview Using a Frequency-Shaped Performance Index

SUMMARY

The objective of this study is to develop a control law for a semi-active suspension for the purpose of ride quality improvement. The semi-active control law is determined by reproducing the control force of an optimally controlled active suspension while suppressing its damping coefficient variation. The performance index of the optimal control for the active suspension is modified to include frequency-shaping by use of Parseval's theorem, which allows us to de-emphasize the effects of particular variables over specific frequency bands.

Through the numerical simulations, it was found that the semi-active suspension may reduce the vertical acceleration of the driver's seat and the sprung mass motions significantly. The road-holding and tire deflections were not affected much.     

Validation of an Articulated Vehicle Simulation

SUMMARY

Tests were performed on a typical UK articulated vehicle to measure dynamic tyre forces and sprung mass accelerations. The measured road profile data and vehicle response data are used to determine some of the important characteristics of articulated vehicle vibration behaviour. In particular, roll motions and their effect on dynamic tyre forces are examined. The measured data are used to validate two and three-dimensional computer models of the vehicle. Attention is given to modelling the tandem leaf-spring trailer suspension. The conditions under which a two-dimensional model can accurately simulate vehicle behaviour are examined.     

Hybrid Laboratory Test Method for Anti-Lock Systems

SUMMARY

Railway vehicles with steered axles possess some unique dynamic characteristics. This paper reviews the reasons for the differences between these and more conventional vehicles and examines the results of analysis demonstrating the sensitivity of the phenomena to various mass, stiffness and geometric parameters. The implications which these results carry are discussed in terms of their design importance and their effect upon the performance boundaries of steel-wheeled rail vehicles. This review shows that a profound understanding of steered axle railway vehicles is developing and that this leads to the conclusion that a wide range of applications can benefit from their use.     

Random Response of Tractor-Semitrailer System

SUMMARY

This work describes an analytical study of the dynamic behaviour of a tractor-semitrailer vehicle. A digital computer simulation was used to describe the longitudinal, vertical, and pitching motions of the vehicle travelling over a stationary random road surface. A man-seat model was also incorporated into the simulation. Vehicle response to road irregularities has been studied by assuming two different roads for loaded and unloaded cases.

Numerical results are presented for vehicle, showing system eigenvalues, power spectral densities and root mean square values of the linear and angular accelerations and displacements. Vehicle acceleration response is compared with the ISO riding comfort standard. All results for the loaded and unloaded cases and for smooth and rough roads indicated that an uncomfortable ride would result from vehicle response.