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    Patrick Weidman

    Boulder, CO 80309-0427, USA
    Department of Mechanical Engineering, University of Colorado


    Weidman P. D., Malhotra C. P.
    We review previous investigations concerning the terminal motion of disks sliding and spinning with uniform dry friction across a horizontal plane. Previous analyses show that a thin circular ring or uniform circular disk of radius $R$ always stops sliding and spinning at the same instant. Moreover, under arbitrary nonzero initial values of translational speed $v$ and angular rotation rate $ω$, the terminal value of the speed ratio $ε_0 = v/Rω$ is always 1.0 for the ring and 0.653 for the uniform disk. In the current study we show that an annular disk of radius ratio $η = R_2/R_1$ stops sliding and spinning at the same time, but with a terminal speed ratio dependent on $η$. For a twotier disk with lower tier of thickness $H_1$ and radius $R_1$ and upper tier of thickness $H_2$ and radius $R_2$, the motion depends on both $η$ and the thickness ratio $λ = H_1/H_2$. While translation and rotation stop simultaneously, their terminal ratio $ε_0$ either vanishes when $k > \sqrt{2/3}$, is a nonzero constant when $1/2 < k < \sqtr{2/3}$, or diverges when $k < 1/2$, where $k$ is the normalized radius of gyration. These three regimes are in agreement with those found by Goyal et al. [S.Goyal, A.Ruina, J.Papadopoulos, Wear 143 (1991) 331] for generic axisymmetric bodies with varying radii of gyration using geometric methods. New experiments with PVC disks sliding on a nylon fabric stretched over a plexiglass plate only partially corroborate the three different types of terminal motions, suggesting more complexity in the description of friction.
    Keywords: rigid body dynamics, terminal motion, nonlinear behavior
    Citation: Weidman P. D., Malhotra C. P.,  On the terminal motion of sliding spinning disks with uniform Coulomb friction, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 2, pp.  339-365

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