Біфуркаційний підхід до аналізу дивергентної втрати стійкості нелінійної моделі колісного екіпажа за наявності постійного силового збурення

Volodymyr  VERBITSKIІ; Valeriy  KHREBET; Yevgen  MISKO

doi:10.36910/automash.v1i14.345

Volodymyr VERBITSKIІ Doctor of Physical and Mathematical Sciences, Professor, head of Department of Software Automated Systems, Zaporizhzhya National University https://orcid.org/0000-0002-1039-8548
Valeriy KHREBET Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Applied Mathematics, National Aviation University https://orcid.org/0000-0002-0191-1768
Yevgen MISKO senior lecturer of Department of Mechanical engineering, Odessa State Academy of Civil Engineering and Architecture http://orcid.org/0000-0002-9020-5266

DOI: https://doi.org/10.36910/automash.v1i14.345

Abstract

A bifurcation approach to the analysis of the divergent loss of stability of a nonlinear model of a biaxial vehicle in case of constant force disturbance is presented. With proper correction of the steering angle of the steered wheel module, the vehicle returns to a stable rectilinear movement. The dependence of the steering angle on the lateral perturbation is presented in the paper (the control function significantly depends on the nonlinear characteristics of the forces slip of the vehicle model). In linear lateral forces slip the proposed control function coincides with the known ratio obtained by a number of authors. Based on the bifurcation approach, which does not require prior determination of the set of stationary states of the vehicle model, an appropriate method of constructing a critical set of control parameters was implemented (longitudinal speed and the steered wheels angle). When intersecting the critical set of parameters, there is a divergent loss of stability of the stationary mode, which is guaranteed to be stable until the moment of reaching the critical values of the control parameters. The critical set of parameters has a point of sharpening, within a small vicinity of which this critical set can be represented analytically by a semicubic parabola. When changing significant design parameters, the critical set of parameters is transformed, this is associated with a change in the nature of the safety of rectilinear motion stability loss. It is shown that the condition of safe-dangerous loss of stability of straight-line motion is determined by the ratio between dimensionless coefficients of slip on the vehicle axes and the coefficients of clutch on the axes of the vehicle in the transverse direction. Therewith, coefficients of clutch are not included in the linearized system of perturbed motion equations, but refer to a substantially nonlinear characteristic of the forces slip.

Keywords: dynamic system, wheeled vehicle, steady-state conditions, stability, divergent bifurcations

A bifurcation approach to analysis of divergent loss of stability of a nonlinear wheeled vehicle model with constant force disturbance

Abstract