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Research Papers

Dynamics of a Spinning Disk

[+] Author and Article Information
Daolin Ma

State Key Laboratory for Turbulence
and Complex Systems,
College of Engineering,
Peking University,
Beijing 100871, China;
MOE Key Laboratory of High-Speed
Railway Engineering,
Southwest Jiaotong University,
Chdengdu, 610031, China

Caishan Liu

State Key Laboratory for Turbulence and
Complex Systems,
College of Engineering,
Peking University,
Beijing 100871, China
e-mail: liucs@pku.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 21, 2015; final manuscript received March 9, 2016; published online March 28, 2016. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 83(6), 061003 (Mar 28, 2016) (7 pages) Paper No: JAM-15-1441; doi: 10.1115/1.4032993 History: Received August 21, 2015; Revised March 09, 2016

A spinning disk on a rough horizontal surface is a familiar example presented in the textbooks of classical mechanics. Recent studies have revealed that this simple system would exhibit an intriguing phenomenon that cannot be well examined by existing theories. Reason for that is due to the lack of reasonable understanding for the influence of combined sliding and rolling friction on the disk dynamics. To unveil how the two types of friction affect the disk motion, this paper presents a combined investigation of experiments and simulations on the dynamics of a spinning disk. We employed a pair of high-speed cameras to perform omnidirectional measurements for the six degrees-of-freedom in describing the disk motion. Numerical calculations are implemented under an integrated model including both the Coulomb friction law and a viscous rolling friction model. Exposure for the details of the disk motion in experiments and simulations sheds light on a novel mechanism underlying the rolling friction: the rolling friction exhibits viscosity relating to the square of rolling velocity.

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Figures

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Fig. 1

A disk with a sharp edge moving on a rough surface

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Fig. 2

Picture of a disk–ball system captured from experiment apparatus

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Fig. 3

Time histories of the nutation angle θ for case 1 in Table2

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Fig. 4

Time histories of precession rate ψ˙ for case 1

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Fig. 5

Velocity of the disk's center of mass in the x and y directions

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Fig. 6

Trajectories of the disk's center of mass obtained from simulation and experiment data

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Fig. 7

Amplitude of the velocity of the contact point between disk and rough surface from simulation and experiment data

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Fig. 8

Normal contact force at contact point A versus time

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Fig. 9

Temporal behaviors of the energy dissipated by the sliding and rolling friction during the entire disk motion process. The curves of Eds(t), Edr(t), and Ed(t) correspond to the blue, black, and red lines, respectively. Solid and dotted lines are, respectively, denoted as the simulated and experimental values. The inset details the energy dissipation in the initial stage of disk motion.

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Fig. 10

The duration of spinning time versus the coefficient of rolling friction for the test disk under initial condition case 1

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