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From geotechnical applications to space exploration, auger drilling is often used as a standard tool for soil sample collection, instrument installation, and others. Focusing on granular flow associated with the rotary drilling process, we investigate the performance of auger drilling in terms of sampling efficiency, defined as the mass ratio of the soil sample collected in the coring tube to its total volume at a given penetration depth, by means of experiments, numerical simulations, as well as theoretical analysis. The ratio of rotation to penetration speed is found to play a crucial role in the sampling process. A continuum model for the coupled granular flow in both coring and discharging channels is proposed to elucidate the physical mechanism behind the sampling process. Supported by a comparison to experimental results, the continuum model provides a practical way to predict the performance of auger drilling. Further analysis reveals that the drilling process approaches a steady state with constant granular flow speeds in both channels. In the steady state, sampling efficiency decreases linearly with the growth of the rotation to penetration speed ratio, which can be well captured by the analytical solution of the model. The analytical solution also suggests that the sampling efficiency is independent of gravity in the steady state, which has profound implications for extraterrestrial sample collection in future space missions., Comment: 23 pages, 10 figures

In this paper, we propose the reduced model for the full dynamics of a bicycle and analyze its nonlinear behavior under a proportional control law for steering. Based on the Gibbs-Appell equations for the Whipple bicycle, we obtain a second-order nonlinear ordinary differential equation (ODE) that governs the bicycle's controlled motion. Two types of equilibrium points for the governing equation are found, which correspond to the bicycle's uniform straight forward and circular motions, respectively. By applying the Hurwitz criterion to the linearized equation, we find that the steer coefficient must be negative, consistent with the human's intuition of turning toward a fall. Under this condition, a critical angular velocity of the rear wheel exists, above which the uniform straight forward motion is stable, and slightly below which a pair of symmetrical stable uniform circular motions will occur. These theoretical findings are verified by both numerical simulations and experiments performed on a powered autonomous bicycle.