Lateral stability analysis of on-road vehicles using the concept of Lyapunov exponents

Abstract The lateral stability of railroad vehicles travelling on tangent tracks is one of the important problems that has been the subject of extensive research since the nineteenth century. Early detailed studies of this problem in the twentieth century are the work of Carter and Rocard on the stability of locomotives. The linear theory for the lateral stability analysis has been extensively used in the past and can give good results under certain operating conditions. In this paper, the results obtained using a linear stability analysis are compared with the results obtained using a general nonlinear multibody methodology. In the linear stability analysis, the sources of the instability are investigated using Liapunov’s linear theory and the eigenvalue analysis for a simple wheelset model on a tangent track. The effects of the stiffness of the primary and secondary suspensions on the stability results are investigated. The results obtained for the simple model using the linear approach are compared with the results obtained using a new nonlinear multibody based constrained wheel/rail contact formulation. This comparative numerical study can be used to validate the use of the constrained wheel/rail contact formulation in the study of lateral stability. Similar studies can be used in the future to define the limitations of the linear theory under general operating conditions.

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The stability analysis using Lyapunov exponents for high-DOF nonlinear vehicle plane motion

Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering ◽

10.1177/09544070211043358 ◽

2021 ◽

pp. 095440702110433

Author(s):

Shuming Shi ◽

Fanyu Meng ◽

Minghui Bai ◽

Nan Lin

Keyword(s):

Stability Analysis ◽

Quantitative Analysis ◽

Lyapunov Exponents ◽

Plane Motion ◽

Vehicle Model ◽

Motion Stability ◽

Motion System ◽

Nonlinear Vehicle Model ◽

The Stability ◽

Different Characteristics

The Lyapunov exponents method is an excellent approach for analyzing the vehicle plane motion stability, and the researchers demonstrated the effectiveness under 2-DOF vehicle model. However, whether the Lyapunov exponents approach can effectively reveal the characteristics of high-DOF nonlinear vehicle model is the key problem at present. In this paper, the Lyapunov exponents is applied to quantitatively analyze the stability of the nonlinear three and five degree of freedom vehicle plane motion system. The different characteristics between 2-DOF and high-DOF model are revealed and explained by using Lyapunov exponents. It illustrates the feasibility of using Lyapunov exponents to analyze the stability of high-DOF vehicle models, which supplements and perfects the existing quantitative analysis conclusion.

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Lateral Stability Analysis for Car-Trailer Combinations

Volume 12: Transportation Systems ◽

10.1115/imece2016-65648 ◽

2016 ◽

Cited By ~ 2

Author(s):

Eungkil Lee ◽

Tao Sun ◽

Yuping He

Keyword(s):

Stability Analysis ◽

Linear Stability ◽

Linear Stability Analysis ◽

Parametric Study ◽

Degrees Of Freedom ◽

Linear Quadratic Regulator ◽

Lateral Stability ◽

Linear Quadratic ◽

Lqr Control ◽

Ct System

This paper presents a parametric study of linear lateral stability of a car-trailer (CT) combination in order to examine the fidelity, complexity, and applicability for control algorithm development for CT systems. Using MATLAB software, a linear yaw-roll model with 5 degrees of freedom (DOF) is developed to represent the CT combination. In the case of linear stability analysis, a parametric study was carried out using eigenvalue analysis based on a linear yaw-roll CT model with varying parameters. Built upon the linear stability analysis, an active trailer differential braking (ATDB) controller was designed for the CT system using the linear quadratic regulator (LQR) technique. The simulation study presented in this paper shows the effectiveness of the proposed LQR control design and the influence of different trailer parameters.

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Stability Modelling of Boom Mover by the Maple Program

Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis ◽

10.11118/actaun201765041113 ◽

2017 ◽

Vol 65 (4) ◽

pp. 1113-1119 ◽

Cited By ~ 1

Author(s):

Stanislav Bartoň ◽

Jan Červinka ◽

Jiří Pospíšil

Keyword(s):

Stability Analysis ◽

Graphical Form ◽

Lateral Stability

This paper shows the usage of the Maplesoft 13 program to study the lateral stability of the tractor mulcher mounted on a hydraulic arm connected to the tractor using a 3 point hitch. The results of the tractor stability analysis are in a graphical form with respect to the torque forces caused by the mulcher support arms weight and other present forces during its work operation.

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