The stability analysis of two-wheeled vehicle model

Juraj Gerlici,Vladimir Verbitskii,Vladimir Sakhno,Alexandr Kravchenko,Kateryna Kravchenko,Alla Yefymenko,M Vasko,L Jakubovičová,M Sága,P Kopas,M Handrik,M Blatnická,V Baniari,O Štalmach,A Sapietová

doi:10.1051/matecconf/201815701007

Juraj Gerlici, Vladimir Verbitskii + Show 13 more

Open Access

https://doi.org/10.1051/matecconf/201815701007

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Abstract

This research investigates the stability of a two-wheeled vehicle model on the basis of numerical determination of full range of eigenvalues of a linear approximation matrix in the vicinity of the rectilinear driving mode. The received result was checked by numerical integration of the initial equations system of the disturbed motion of the model. The discrepancy of two research techniques is explained by the specialty of the considered mathematical model in which two pairs of complex conjugate eigenvalues close to each other are realized, that explains the emergence of standard derivations at calculating their numerical determination. The model is asymptotically stable in the range much wider than an operational interval (up to 100 m/s). In order to provide more intensive dampening of initial disturbances, it is possible to introduce additional resilient and damping elements between the trucks and the body in the design of the wheeled vehicle that will counteract the yaw mode of trucks.

Highlights

Monorail vehicles are used in many countries
The equations of the dynamics of the plane-parallel motion of a wheeled vehicle assuming that the system maintains a constant value of the longitudinal component of the body mass center velocity and there are no longitudinal forces Xii (LA, LB is the distance from the car mass center to the hinges "A" and "B" ) are written in the form: m v U Y1 cos 1+Y11 cos 1+sin 1 X11+Y2 cos 2 + Y 22 cos 2
The results of numerical integration of the initial equations of the disturbed motion indicated the damping of the initial perturbations in the velocity range, which is much broader than the boundary of the oscillatory instability found. The analysis of this discrepancy is based on the numerical integration of the wheeled vehicle system at the speed of 12.3 m/s and 22.3 m/s with a fixed initial disturbance at the heading angle ψ2 = 0.001 rad

Summary

Introduction

Monorail vehicles are used in many countries. That provides safety work of transport systems in big cities. The determination of lateral and longitudinal projections of the mass center velocity of the guiding wheeled module “A” was calculated using the following equations: u1 v sin 1 u LA cos 1;. The determination of lateral and longitudinal projections of the mass center acceleration of the guiding wheeled modules: U1 = –V sin 1 – v cos 1 1 + (U + LA ) cos 1 + (u + LA ) sin 1 1; (6). The equations of the dynamics of the plane-parallel motion of a wheeled vehicle assuming that the system maintains a constant value of the longitudinal component of the body mass center velocity (parameter v) and there are no longitudinal forces Xii (LA, LB is the distance from the car mass center to the hinges "A" and "B" ) are written in the form:. The elastic forces Yi (15) and the elastic moment Mi (16) linearly depend on the transverse displacement of the truck mass center relative to the program trajectory and the difference of the truck heading angles and the program curve respectively

Research results

Conclusions