The work analyzes the properties of handling and bicycle vehicle model motion stationary states manifold stability taking into account drift force nonlinear characteristics. Determining single two-axle vehicle nonlinear model stationary states and analyzing their stability were based on a graphical method (Y. M. Pevzner, H. Pacejka). It has its disadvantages: the absence of evident analytical stability criteria for the entire wheeled vehicle circular stationary states manifold. And also the absence of global stability threshold characteristics in the controlled parameter space. The task part suggests developing methods for building bifurcation manifold or critical parameters manifold (longitudinal velocity and wheel turning angle) with which the divergent loss of stability occurs. Known H. Troger, K. Zeman and Fabio Della Rossaa, GiampieroMastinub, Carlo Piccardia results are based on parameter continuation numerical methods which makes the quality analysis of drift force nonlinear characteristics impact on the entire stationary states manifold stability conditions more difficult. A compelling grapho-analytic approach towards bifurcation manifold building and getting circular stationary states analytical stability conditions based on moving from nonlinear drift forces on axles dependencies to their inverse dependence is developed in the suggested work. This methodology allows defining dangerous/safe stability threshold conditions in the control parameters space.
| Published in | Mathematics and Computer Science (Volume 3, Issue 1) |
| DOI | 10.11648/j.mcs.20180301.13 |
| Page(s) | 13-22 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2018. Published by Science Publishing Group |
Non-linear Bicycle Model, Stationary States Manifold, Vehicle Handling, Divergent Stability Loss, Parameters Bifurcation Set
| [1] | Gillespie, Thomas D. Fundamentals of Vehicle Dynamics. Society of Automotive Engineers, Inc., 1992, p. 470. |
| [2] | Kravchenko, A. P., Verbitskii V. G., Zagorodnov M. I., Bannikov V. O., Sakno O. P., Efimenko A. N., TurchinaN. A. On the problem of the steerability analysis of the automobile non-linear model. NaukovivistiDalivskogouniversitetu. Electronenaukovefakhovevidanua, 2010, №1 (in Russian). |
| [3] | Yu, N., SaravananMuthiah S., Kulakowski, B. T. Analysis of steady-state handling behavior of a transit bus. 9th International Symposium on Heavy Vehicle Weights and Dimensions, June 18-22, 2006, Pennsylvania State University, State College, Pennsylvania, 01388838. |
| [4] | Liu Lil, Shi Shuming, ShenShuiwen, Chu Jiangwei. Vehicle Planar Motion Stability Study for Tyres Working in Extremely Nonlinear Region. Chinese journal of mechanical engineering, Vol. 23, No. 2, 2010. |
| [5] | Vladimir, Sakhno, Alexander, Kravchenko, Andrey, Kostenko, Vladimir, Verbitskii Influence of hauling force on firmnessof plural stationary motions of passenger car model ТЕКА Кom. Mot. iEnerg. Roln. OL PAN, 2011, 11B, pp. 147-155. |
| [6] | Pevsner, J. M. Theory of stability of automobile. Moscow: Mashisdat, 1947, p. 156. |
| [7] | Verbitskii, V., Danilenko, E., Nowak, A., Sitarz, M. Introduction in the Stability Theory of the Wheel Vehicles and Railway. Donetsk department: Veber, 2007, p. 255. |
| [8] | Pacejka, H. B. Tyre factors and vehicle handling. Delf Univ. Technol, 1978,№ 108, p. 31. |
| [9] | Fabio, Della Rossaa, GiampieroMastinub, Carlo Piccardia. Bifurcation analysis of an automobile model negotiating a curve. Vehicle System Dynamics, Vol. 50, No. 10, 2012, pp. 1539-1562. |
| [10] | Arnold, V. I. Catastrophe Theory. Moscow: Nauka, 1990, p. 128. |
| [11] | Poston, T., Stewart, I. Catastrophe Theory AndIts Applications. Moscow: Mir, 1980, p. 607. |
| [12] | Verbitskii, V. G. Bifurcation sets and catastrophes in manifold of the steady states of pneumowheel vehicles. Kiev: Pricl. Mech, Vol. 31, ¹3, 1995, pp. 89-95. |
| [13] | Shinohara, Y. A geometric method for the numerical solution of non-linear equations and its application to non-linear oscillations. Publ. Res. Inst. Math. Sci., Kyoto Univ. 8, 1, 1972, pp. 13-42. |
| [14] | Holodniok, M., Klic, A., Kubicek, M., Marek, M. Methods of Analysing Non-linear Dynamic Systems. Moscow: Mir, 1991, p. 368. |
| [15] | Rokar, I. Instability in Mechanics Automobiles. Airplanes. Suspension Bridges. Moscow: IL, 1959, p. 288 (Russian translation). |
| [16] | [16]Ellis, J. R. Vehicle Dynamics. Moscow: Mashinostroenie, 1975, p. 216. (Russian translation). |
| [17] | Lobas, L. G., Verbitskii, V. G. Qualitative and Analytical Methods in the Dynamics of Wheel Machines. Kiev: NaukovaDumka, 1990 (in Russian). |
| [18] | Troger, H., Zeman, K. A nonlinear analysis of the generic types of loss of stability of the steady state motion of the tractor – semitrailer, Vehicle System Dynamics, Vol. 13, № 4, 1984, pp. 161-172. |
| [19] | Verbitskii, V. G., Lobas, L. G. Method of determination of the special points and their character. Applied mathematics and mechanics, 1981, № 45 (5), pp. 944-948. |
| [20] | Bruce, J., Giblin, P. Curves and Singularities. Moscow: Mir, 1988, p. 262. |
APA Style
Verbitskii Vladimir Grigorievich, Bezverhyi Anatoliy Igorevich, Tatievskyi Dmitry Nikolayevich. (2018). Handling and Stability Analysis of Vehicle Plane Motion. Mathematics and Computer Science, 3(1), 13-22. https://doi.org/10.11648/j.mcs.20180301.13
ACS Style
Verbitskii Vladimir Grigorievich; Bezverhyi Anatoliy Igorevich; Tatievskyi Dmitry Nikolayevich. Handling and Stability Analysis of Vehicle Plane Motion. Math. Comput. Sci. 2018, 3(1), 13-22. doi: 10.11648/j.mcs.20180301.13
AMA Style
Verbitskii Vladimir Grigorievich, Bezverhyi Anatoliy Igorevich, Tatievskyi Dmitry Nikolayevich. Handling and Stability Analysis of Vehicle Plane Motion. Math Comput Sci. 2018;3(1):13-22. doi: 10.11648/j.mcs.20180301.13
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Download@article{10.11648/j.mcs.20180301.13,
author = {Verbitskii Vladimir Grigorievich and Bezverhyi Anatoliy Igorevich and Tatievskyi Dmitry Nikolayevich},
title = {Handling and Stability Analysis of Vehicle Plane Motion},
journal = {Mathematics and Computer Science},
volume = {3},
number = {1},
pages = {13-22},
doi = {10.11648/j.mcs.20180301.13},
url = {https://doi.org/10.11648/j.mcs.20180301.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20180301.13},
abstract = {The work analyzes the properties of handling and bicycle vehicle model motion stationary states manifold stability taking into account drift force nonlinear characteristics. Determining single two-axle vehicle nonlinear model stationary states and analyzing their stability were based on a graphical method (Y. M. Pevzner, H. Pacejka). It has its disadvantages: the absence of evident analytical stability criteria for the entire wheeled vehicle circular stationary states manifold. And also the absence of global stability threshold characteristics in the controlled parameter space. The task part suggests developing methods for building bifurcation manifold or critical parameters manifold (longitudinal velocity and wheel turning angle) with which the divergent loss of stability occurs. Known H. Troger, K. Zeman and Fabio Della Rossaa, GiampieroMastinub, Carlo Piccardia results are based on parameter continuation numerical methods which makes the quality analysis of drift force nonlinear characteristics impact on the entire stationary states manifold stability conditions more difficult. A compelling grapho-analytic approach towards bifurcation manifold building and getting circular stationary states analytical stability conditions based on moving from nonlinear drift forces on axles dependencies to their inverse dependence is developed in the suggested work. This methodology allows defining dangerous/safe stability threshold conditions in the control parameters space.},
year = {2018}
}
TY - JOUR T1 - Handling and Stability Analysis of Vehicle Plane Motion AU - Verbitskii Vladimir Grigorievich AU - Bezverhyi Anatoliy Igorevich AU - Tatievskyi Dmitry Nikolayevich Y1 - 2018/02/23 PY - 2018 N1 - https://doi.org/10.11648/j.mcs.20180301.13 DO - 10.11648/j.mcs.20180301.13 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 13 EP - 22 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20180301.13 AB - The work analyzes the properties of handling and bicycle vehicle model motion stationary states manifold stability taking into account drift force nonlinear characteristics. Determining single two-axle vehicle nonlinear model stationary states and analyzing their stability were based on a graphical method (Y. M. Pevzner, H. Pacejka). It has its disadvantages: the absence of evident analytical stability criteria for the entire wheeled vehicle circular stationary states manifold. And also the absence of global stability threshold characteristics in the controlled parameter space. The task part suggests developing methods for building bifurcation manifold or critical parameters manifold (longitudinal velocity and wheel turning angle) with which the divergent loss of stability occurs. Known H. Troger, K. Zeman and Fabio Della Rossaa, GiampieroMastinub, Carlo Piccardia results are based on parameter continuation numerical methods which makes the quality analysis of drift force nonlinear characteristics impact on the entire stationary states manifold stability conditions more difficult. A compelling grapho-analytic approach towards bifurcation manifold building and getting circular stationary states analytical stability conditions based on moving from nonlinear drift forces on axles dependencies to their inverse dependence is developed in the suggested work. This methodology allows defining dangerous/safe stability threshold conditions in the control parameters space. VL - 3 IS - 1 ER -
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