A comparative study of the vibro-impact capsule systems with one-sided and two-sided constraints

Abstract

This paper studies the dynamics of the vibro-impact capsule systems with one-sided and twosided soft constraints under variations of various system and control parameters, including mass ratio, stiffness ratio, gap of contact, and amplitude and frequency of external excitation. The aim of this study is to optimise the progression speed and energy consumption of the capsule and minimise the required cabin length for prototype design used for engineering pipeline inspection. Our studies focus on three systems: the capsule with a right constraint, the capsule with a right and a weak left constraints, and the capsule with a right and a strong left constraints. Bifurcation analyses show that the behaviour of the capsule with onesided constraint is mainly periodic, and the dynamic responses of the other two capsules with two-sided constraints become complex when the stiffness of the left constraint increases. Based on our extensive comparisons, the following optimisation strategies are recommended. When the capsule speed is paramount, one can employ the two-sided capsule with a weak left constraint under large amplitude of excitation. When energy consumption is taken into account, the onesided capsule is preferable. When a miniaturized prototype is needed, the two-sided capsule with a strong left constraint is the best choice.

The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification

“…Once the net force of their interaction is greater than the environmental resistance, rectilinear motion of the entire system can be obtained. To implement this, various driving means for the small body were proposed by researchers, such as vibration-driven [5,6], vibro-impact driven [7][8][9][10], and pendulum-like driven [11][12][13]. The common feature of these methods is that the small body needs to be controlled precisely in order to obtain a desired motion for the entire system.…”

“…The merit of such a capsule is its simplicity in mechanical design and control which does not require any external driving accessories, while allowing independent movements in a complex environment. The study of this method was initiated from mathematical modelling [7,8,26,27], early proof-of-concept investigation [28], multistable dynamics control [15,29], to our recent capsule-intestine contact modelling [30], intestinal friction study [31] and mesoscale demonstration [32,33]. Since the mathematical model of the system belongs to the class of piecewise-smooth dynamical systems, for this type of systems, the state space can be divided into disjoint subregions [34].…”

Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

“…In one-degree-of-freedom (1-DoF) mechanical oscillators, impacts can occur with rigid/soft end-stops, whereas in multi-DoF oscillators, collisions can also occur amongst moving elements. e wide interest in these impacting systems has spurred researchers and engineers to analyze their motions and hence the implications of impacts, as, for example, in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

Modelling and experimental validation of 1-degree-of-freedom impacting oscillator

“…Dynamics of a vibro-impact capsule with one-sided and two-sided compliant stops has been analysed in the work. 20 A special attention has been paid to the problems of optimisation of the progression speed and energy consumption.…”

“…During the literature survey on mechanical systems with impacts, one can encounter hard (instantaneous and usually based on restitution coefficient) 1–10,13,21 and soft models of impacts. However, in the second case, one should distinguish systems with soft obstacles 15–17,19,20,23 and systems with impacts between hard objects modelled as locally compliant, 5,17,18,31–33 usually based on the Hertz theory. The last case is the object of interest in the present work.…”