Influence of the asymmetry of cornering forces on the static stability of a two-axle vehicle

Abstract

The influence of design characteristics (elastic characteristics of tires and asymmetry of cornering forces) on the stability and handling of a vehicle is studied. The parameter continuation method is used to validate the results of constructing bifurcation sets in the space of two control parameters.Instable rectilinear motion of a vehicle model is the simplest partial case in the instability analysis of stable circular motions. In symmetric models of automobile and articulated truck [9], the critical velocity of circular motion tends to the critical velocity of rectilinear motion ν cr + as the drive wheel angle tends to zero. Moreover, as follows from singularity theory [1], the critical set in the neighborhood of ν cr + is described by a semicubical parabola.For local and global analyses of the bifurcation set (critical parameter set) of a symmetric vehicle model, the authors of [5,6] proposed methods that do not require preliminary determination of the equilibrium values of the phase variables. The present paper sets forth possible approaches to determine the critical set of an asymmetric vehicle model (in the presence of small perturbations disturbing the symmetry of the dynamic system with two control parameters, the critical set shifts, losing symmetry; finite perturbations may give rise to new dynamic properties of the model, which is manifested as a more complex bifurcation set).

Mechanical phenomena in ground run of an aircraft with near-critical slip angles

“…Thus, we may conclude that conditions (16) and (17) cause the aileron to intensively vibrate along the axis of its hinges. Such vibrations were observed in full-scale experiments, which were conducted to ascertain the cause of the fatigue failure and damage of aileron wing-mounting brackets.…”

“…To improve flight safety and create a high-efficiency air transport system, it is necessary to study the dynamics of aircraft over the entire range of motion variables. In studying off-nominal modes of operation, it is necessary to do mathematical simulation.Analysis of the ground dynamics of aircraft as well as any pneumatic-tired vehicle [12][13][14]17] is difficult because of the absence of a well-developed and convenient model of tire. Engineering theories of rolling tire consider that the frictional force acting along the wheel axel in the road plane (so-called side force) depends on the angle U between the wheel direction and the contact patch direction (slip angle).…”

An analytic model of a rolling pneumatic tire

“…The present paper addresses a pneumatic-tired wheel freely rolling with steady-state slip and analyzes the contact pressure, side force, and self-aligning torque. The objective of the paper is to study the nature of the mechanical interaction between the tire and the roadbed.Technical theories of steady-state slip study the dependences of the cornering force and self-aligning torque on the slip angle, which are used to describe the dynamics of pneumatic-tired vehicles [14]. The Gim-Nikravesh analytic model [4-6] was validated against experimental data [11,12].…”

“…Technical theories of steady-state slip study the dependences of the cornering force and self-aligning torque on the slip angle, which are used to describe the dynamics of pneumatic-tired vehicles [14]. The Gim-Nikravesh analytic model [4-6] was validated against experimental data [11,12].…”

“…we arrive at an equation relating the unknown coefficients: Table 1): -specify values of x ad ∈ [0, 1]; -find u ∈ [0, 1] by formula (19); -determine the side force and self-aligning torque by formulas (12), (13), and (16); -if u > 1, use formulas (14) and (15). The graphs of F U ( )thus plotted are similar to those in [6,12].…”