This paper introduces a dynamic method for the stiffness identification of an impacted object via analysis of its corresponding impact duration. To accurately detect the impact durations from experimental signals, nonlinear time series methods are applied. Two low-dimensional dynamical systems, including a piecewise-linear impact oscillator and a rock impacting system, are studied experimentally and numerically to demonstrate the proposed method. Meanwhile, the analytical prediction of the impact duration for the period-one one-impact motion is developed. The results of both systems indicate that, for a certain stiffness, the impact duration of the period-one one-impact motion is nearly constant. The higher the stiffness, the lower the impact duration. This monotone correlation provides a mechanism to estimate the stiffness of the impacted object once the impact duration has been accurately detected. The developed method can be used to optimise percussive drilling parameters.

This paper focuses on the experimental verification of a dynamical model describing percussive drilling.The design of the experimental apparatus is introduced firstly, and then the dynamic interactions between rock and indenter are studied experimentally by varying three control parameters, including frequency and amplitude of excitation, and pneumatic pressure applied on the indenter. Additionally, the influence of rock stiffness is analyzed by testing different rock-indenter combinations. Meanwhile, the corresponding numerical simulations were conducted showing good agreements with the experimental results. According to the detailed bifurcation analyses, the dynamic responses of indenter mainly display period-one motions which can further develop into period-two motions via period-doubling bifurcation scenarios, or even chaotic motions by period-doubling cascade. The chaotic vibration of indenter can also return to periodic motions via inverse period-doubling bifurcation or fold bifurcation. Although the period-one motion is the main dynamic response in the considered parameter ranges, its impact number per excitation period varies with parameters, which directly affects the maximal impact acceleration of indenter. This results in more energy being dissipated during repeated weak impacts. Therefore, strong impacts are obtained if the indenter is exhibiting the period-one with one-impact motion. For such a purpose, high excitation frequency and amplitude are suggested, however, the high pneumatic pressure should be avoided since it can trigger chattering of the indenter.

This paper presents a simple and novel approach, based on nonlinear time series analysis of an experimental system, to infer from subtle alteration of the system dynamics the changes caused in the system parameters. Using the acceleration time-series as a measurement of simulated and experimental impact oscillators (serving as a model for the drilling conditions with intermittent contact between the drill bit and the formation), the systems attractor is reconstructed and characterised. It is shown that the stiffness correlates with the topology of the reconstructed attractor. Non-impacting trajectories form an approximate plane within the three dimensional reconstructed phase-space, and contact with the constraint causes a systematic deviation from the linear subspace, the inclination of which, measured by the statistics of the tangent vector, can be used to infer the stiffness. This relationship between the topology of attractor and the stiffness was also verified experimentally. Based on the developed framework, it is now possible to classify the stiffness of the impacted material from a single variable in a simple way and in real time.

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