The dynamical model of the rolling friction of spherical bodies on a plane without slipping
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 4, pp. 599-609.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the model of rolling of spherical bodies on a plane without slipping is presented taking into account viscous rolling friction. Results of experiments aimed at investigating the influence of friction on the dynamics of rolling motion are presented. The proposed dynamical friction model for spherical bodies is verified and the limits of its applicability are estimated. A method for determining friction coefficients from experimental data is formulated.
Keywords: rolling friction, dynamical model, spherical body, nonholonomic model, experimental investigation.
@article{ND_2017_13_4_a11,
     author = {Yu. L. Karavaev and A. V. Klekovkin and A. A. Kilin},
     title = {The dynamical model of the rolling friction of spherical bodies on a plane without slipping},
     journal = {Russian journal of nonlinear dynamics},
     pages = {599--609},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2017_13_4_a11/}
}
TY  - JOUR
AU  - Yu. L. Karavaev
AU  - A. V. Klekovkin
AU  - A. A. Kilin
TI  - The dynamical model of the rolling friction of spherical bodies on a plane without slipping
JO  - Russian journal of nonlinear dynamics
PY  - 2017
SP  - 599
EP  - 609
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2017_13_4_a11/
LA  - ru
ID  - ND_2017_13_4_a11
ER  - 
%0 Journal Article
%A Yu. L. Karavaev
%A A. V. Klekovkin
%A A. A. Kilin
%T The dynamical model of the rolling friction of spherical bodies on a plane without slipping
%J Russian journal of nonlinear dynamics
%D 2017
%P 599-609
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2017_13_4_a11/
%G ru
%F ND_2017_13_4_a11
Yu. L. Karavaev; A. V. Klekovkin; A. A. Kilin. The dynamical model of the rolling friction of spherical bodies on a plane without slipping. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 4, pp. 599-609. http://geodesic.mathdoc.fr/item/ND_2017_13_4_a11/

[1] Borisov A. V., Karavaev Yu. L., Mamaev I. S., Erdakova N. N., Ivanova T. B., Tarasov V. V., “Experimental investigation of the motion of a body with an axisymmetric base sliding on a rough plane”, Regul. Chaotic Dyn., 20:5 (2015), 518–541

[2] Karavaev Yu. L., Kilin A. A., “Nonholonomic dynamics and control of a spherical robot with an internal omniwheel platform: Theory and experiments”, Proc. Steklov Inst. Math., 295 (2016), 158–167

[3] Kilin A. A., Karavaev Yu. L., “Experimental research of dynamic of spherical robot of combined type”, Nelin. Dinam., 11:4 (2015), 721–734 (Russian)

[4] Firlej Sz., “Design, construction and control of a spherical rolling robot with internal two-wheel cart”, Automatyka/Automatics, 19:2 (2015), 63–77

[5] Kilin A. A., Pivovarova E. N., Ivanova T. B., “Spherical robot of combined type: Dynamics and control”, Regul. Chaotic Dyn., 20:6 (2015), 716–728

[6] Terekhov G., Pavlovsky V., “Controlling spherical mobile robot in a two-parametric friction model”, MATEC Web Conf., 113 (2017), 02007, 5 pp.

[7] Kayacan E., Bayraktaroglu Z., Saeys W., “Modeling and control of a spherical rolling robot: A decoupled dynamics approach”, Robotica, 30:4 (2012), 671–680

[8] Ishkhanyan M. V., Karapetyan A. V., “Dynamics of a homogeneous ball on a horizontal plane with sliding, spinning, and rolling friction taken into account”, Mech. Solids, 45:2 (2010), 155–165

[9] Zhuravlev V. F., “On a model of dry friction in the problem of the rolling of rigid bodies”, J. Appl. Math. Mech., 62:5 (1998), 705–710

[10] Kudra G., Awrejcewicz J., “Application and experimental validation of new computational models of friction forces and rolling resistance”, Acta Mech., 226:9 (2015), 2831–2848

[11] Contensou P., “Couplage entre frottement de pivotement et frottement de pivotement dans la théorie de latoupie”, Kreiselprobleme Gyrodynamics: IUTAM Symp. Celerina, Springer, Berlin, 1963, 201–216

[12] Moshchuk N. K., “On the motion of Chaplygin's sphere on a horizontal plane”, J. Appl. Math. Mech., 47:6 (1983), 733–737

[13] Munitsyna M. A., “The motions of a spheroid on a horizontal plane with viscous friction”, J. Appl. Math. Mech., 76:2 (2012), 154–161

[14] Borisov A. V., Kilin A. A., Karavaev Yu. L., “On the retrograde motion of a rolling disk”, Physics–Uspekhi, 60:9 (2017), 931–934

[15] Domenech A., Domenech T., Cebrian J., “Introduction to the study of rolling friction”, Am. J. Phys., 55:3 (1987), 231–235

[16] Cross R., “Coulomb's law for rolling friction”, Am. J. Phys., 84:3 (2016), 221–230

[17] Borisov A. V., Mamaev I. S., Bizyaev I. A., “The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere”, Regul. Chaotic Dyn., 8:3 (2013), 277–328

[18] Kilin A. A., Pivovarova E. N., “The rolling motion of a truncated ball without slipping and spinning on a plane”, Regul. Chaotic Dyn., 22:3 (2017), 298–317

[19] Borisov A. V., Kazakov A. O., Pivovarova E. N., “Regular and chaotic dynamics in the rubber model of a Chaplygin top”, Nelin. Dinam., 13:2 (2017), 277–297 (Russian)

[20] Ma D., Liu C., Zhao Zh., Zhang H., “Rolling friction and energy dissipation in a spinning disc”, Proc. R. Soc. Lond. Ser. A Math. Phys. Sci., 470:2169 (2014), 20140191, 22 pp.

[21] Ma D., Liu C., “Dynamics of a spinning disk”, Trans. ASME J. Appl. Mech., 83:6 (2016), 061003, 7 pp.

[22] Leine R. L., “Experimental and theoretical investigation of the energy dissipation of a rolling disk during its final stage of motion”, Arch. Appl. Mech., 79:11 (2009), 1063–1082