Application and experimental validation of new computational models of friction forces and rolling resistance

Abstract

In the process of modelling of the Celtic stone rotating and rolling on a plane surface, different versions of simplified models of contact forces between two contacting bodies are used. The considered contact models take into account coupled dry friction force and torque, as well as rolling resistance. They were developed using Padé approximations, their modifications, and polynomial functions. Before the use of these models, some kinds of regularisations have been made, allowing to avoid singularities in the differential equations. The models were tested both numerically and experimentally, giving some practical guesses of the most essential elements of contact modelling in the Celtic stone numerical simulations. Since the tested contact models do not require the space discretisation, they can find application in relatively fast numerical simulations of rigid bodies with friction contacts.

Rolling resistance modelling in the Celtic stone dynamics

“…(11)u stands for the local derivative of the variable u. Based on the previous work of the authors [10,34], the following model of the resultant contact forces is proposed:…”

“…Models (12)- (13) represent special case of approximations developed in [10] and tested in modelling of the Celtic stone in [34]. They are a minimal but sufficient form of more general models, allowing one to simulate the rattleback dynamics quickly and realistically.…”

“…The first scientific work on rattleback was published at the end of the 19th century [17] and it has been an object of interest till today [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34], both from the point of view of dynamics and of modelling. During modelling and analysis of the Celtic stone, rolling without sliding is often assumed, leading to non-holonomic constraints [17, 21, 22, 24-26, 29, 31].…”

“…Detailed modelling of contact between the Celtic stone and horizontal base, including rolling resistance and using results of the work [10], is presented in Ref. [34], where also experimental validation of particular parts of the model is performed. The same approach is used in modelling and numerical simulations of a billiard ball rolling and sliding on a table [35,36].…”

“…[34], but deeper insight into the rolling resistance model is achieved-an extended expression for the rolling resistance additional elements and aspects are investigated.…”