Abstract

The theory of multi-component dry friction accounting for the coupled kinematics of relative motion in finite contact spots is applied to the modelling of pneumatic tires. The analytical models of the combined dry friction accounting for the anisotropy of the dry friction factors as well as the distribution of the contact pressure close to the real one are introduced. The exact integral relationships between the dry friction force and torque and the generalized velocities, i. e. the speed of sliding and angular velocity of spinning, appears as a result of integration over the contact spot and are too complex to be implemented analytically into the engineering practice. The proposed approximate models are based on the fractional approximations and could be interpreted as rheological models with low number of constitutive constants. These constants could be identified after the solution of some specific inverse problems with input data given by the diagrams of the dry friction forces and torque obtained as a result of simple physical tests. Here these inverse problem are formulated and solved using the perturbed benchmark solutions of the corresponding direct problems with the factors obtained after the numerical solution of the contact problem for the heterogeneous pressurized tire. The possibility of stable solution for the inverse problems on the basis of the proposed approach is shown. The presented models as well as the method if constitutive constants identification could be applied for more detailed investigation of unsteady rolling regimes of pneumatics which are characterized by the non-vanishing sliding and spin.

Abstract

It is proposed applications of the theory of combined dry friction [1-14] in the problem of the ball rolling on boundaries of two identical frames. Father development of this model can be used in investigation of the dynamic of the a so-called 'Butterfly' robot, consisting of two identical shaped plates rigidly placed parallel to each other on a small distance aimed at manipulating a ball that can freely roll on the plates' boundaries as on rails [15]. The difficult control system, considered in [16-18] are another engineering application of the combined dry theory. Following developed in previous investigation approach, the friction force and torque are computed by the integration over the contact area so that the exact dynamically coupled integral model accounting the relationship of all the components of friction is obtained. This exact model is replaced by approximated analytical model [6] which is completely satisfy to all analytical properties of integral model as function kinematics parameters without increasing the number of coefficients.

Abstract

The extended and improve version of the investigation described in [1-2] and the firstly presented in [3] is proposed in this work. Distinguish features of these investigations are applications of the theory of multi-component dry friction [4-16] in the problem of the ball rolling on boundaries of two identical frames. Father development of this model can be used in investigation of the dynamic of the a so-called 'Butterfly' robot, consisting of two identical shaped plates rigidly placed parallel to each other on a small distance aimed at manipulating a ball that can freely roll on the plates' boundaries as on rails [17]. The difficult control systems considered in [18-20] are another engineering application of the combined dry theory. Following developed in previous investigation approach, the friction force and torque are computed by the integration over the contact area so that the exact dynamically coupled integral model accounting the relationship of all the components of friction is obtained. This exact model is replaced by approximated analytical model [1-2] which is completely satisfy to all analytical properties of integral model as function kinematics parameters without increasing the number of coefficients.