Rolling resistance modelling in the Celtic stone dynamics

Abstract

In the work there is presented a mathematical model of a rattleback lying on a horizontal plane, with special attention paid to modelling of the contact forces. Friction force modelling concerns a certain class of problems, where it is possible to assume fully developed sliding on the contact zone. The models are based on the integral expressions assuming the classical Coulomb friction law valid at each point of the contact. In order to obtain a higher simulation speed, a special class of approximations if integral functions is used, being some kind of generalization of Padé expansion. The rolling resistance is modelled as a result of special distortion of contact pressure distribution and takes into account the rolling direction and the elliptic shape of the contact. The work uses previous results of the authors, but more attention is paid to the rolling resistance model, which is extended and analysed in more detail. The models are validated experimentally and their various elements are tested.

The normal parameterization and its application to collision detection

“…[64]; any dissipation due to drilling or rolling motions is neglected. This simplification is appropriate for the present case study since more physical interaction laws for this type of non-holonomic rolling contact as for example proposed in [42,46] are much more complicated and distract from the actual focus of this manuscript: the introduction of the normal parameterization and its application for collision detection.…”

“…This yields the behavior of a non-linear spring which, depending on the principal curvatures of the two surfaces at the points of maximum penetration 2 , generates a restoring force which opposes the penetration of the undeformed object geometries. There are numerous extensions of this model where both dissipative effects due to local material deformation [40,41,42,43,44,45,46] 3 and forces due to friction [49,50,51,52,53] are added. All these approaches require the common normal and the maximum penetration depth to determine the interaction forces.…”

Dynamics of a four‐wheeled mobile robot with Mecanum wheels

“…There are more complex models of rolling bodies on the surface, taking into account the contact spot, the distribution of normal pressure F I G U R E 1 Four wheeled mobile robot with Mecanum wheels F I G U R E 2 Model of a Mecanum wheel forces on the contact spot and rolling resistance. Such studies are contained in [18][19][20], and others. Taking these phenomena into account is useful in solving a number of practical problems related to the dynamics of Mecanum wheels.…”