Simulation and stability analysis of impacting systems with complete chattering

Nordmark, Arne; Piiroinen, Petri T.

doi:10.1007/s11071-008-9463-y

Cited by 85 publications

(66 citation statements)

References 32 publications

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“…Other types of motion can include an accumulation of an infinite number of impacts (with the impact velocity decreasing in a geometric progression), in a finite time [20,42,43]. This behaviour, which arises when the rotor is being forced towards the TDB at the same time as it rebounds from it, is often called chattering [44][45][46] in the context of impact dynamics. Chattering can lead to sticking [46] and sliding motion [10] and hence can be used to predict the onset of continuous contact motion without actually computing continuous contact trajectories.…”

Section: (D) Other Dynamicsmentioning

confidence: 99%

Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery

et al. 2014

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We analyse the novel dynamics arising in a nonlinear rotor dynamic system by investigating the discontinuity-induced bifurcations corresponding to collisions with the rotor housing (touchdown bearing surface interactions). The simplified Föppl/ Jeffcott rotor with clearance and mass unbalance is modelled by a two degree of freedom impact-friction oscillator, as appropriate for a rigid rotor levitated by magnetic bearings. Two types of motion observed in experiments are of interest in this paper: no contact and repeated instantaneous contact. We study how these are affected by damping and stiffness present in the system using analytical and numerical piecewisesmooth dynamical systems methods. By studying the impact map, we show that these types of motion arise at a novel non-smooth Hopf-type bifurcation from a boundary equilibrium bifurcation point for certain parameter values. A local analysis of this bifurcation point allows us a complete understanding of this behaviour in a general setting. The analysis identifies criteria for the existence of such smooth and non-smooth bifurcations, which is an essential step towards achieving reliable and robust controllers that can take compensating action.

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Section: (D) Other Dynamicsmentioning

confidence: 99%

Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery

et al. 2014

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“…[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], with the pioneering work due to Nordmark [16]. Besides grazing bifurcation, richness and complexity in non-linear dynamical behavior induced by the non-smoothness, such as sticking [32], sliding [33,34], border-collision [35] and chattering [36][37][38][39][40][41][42][43][44][45] etc., have also been reported.…”

Section: Introductionmentioning

confidence: 99%

Periodically forced system with symmetric motion limiting constraints: Dynamic characteristics and equivalent electronic circuit realization

Luo

Wang

2016

International Journal of Non-Linear Mechanics

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“…Detailed studies of chattering-impact characteristics were carried out for the vibro-impact systems in Refs. [39][40][41][42][43][44][45][46][47][48]. Wagg [42,43] studied rising phenomena and multiple non-smooth events of impacting chatter with stick in multi-degree-of-freedom vibro-impact systems.…”

Section: Introductionmentioning

confidence: 99%

“…Luo [45,46] presented an idealized, piecewise linear system to model non-smooth vibration of gear transmission arising from impacts between the gear teeth and studied mechanism of impacting chatter with stick in the gear transmission system. Nordmark and Piiroinen [47] emphasized that the continuous transformation of a trajectory like complete chattering into one like incomplete chattering clearly involves the loss of an infinite number of impacts, and at a point where the number of impacts decreases, the trajectory must have a grazing impact. Hősa and Champneysb [48] considered a mechanical model of a pressure relief valve and analyzed the geometry of the chattering region via the computation of several pre-images of the grazing set.…”

Section: Introductionmentioning

confidence: 99%

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

et al. 2014

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A two-degree-of-freedom periodically forced system with a clearance is considered. The correlative relationship and matching law between dynamics and system parameters are analyzed by the co-simulation analysis of multi-parameter and multiperformance. Key parameters of the system, such as the exciting frequency, clearance value and constraint stiffness, are emphasized to analyze the influence of the main factors on its soft impact characteristics and reveal diversity, evolution and distribution regions of periodic-impact motions. The quantity of the fundamental group of p/1 impact motions, which have the excitation period and differ by the number p of impacts, is basically determined by the constraint stiffness. A series of grazing bifurcations occur with decreasing the exciting frequency so that the number p of impacts of the fundamental group of motions correspondingly increases one by one. As the constraint stiffness is very large, the impact number p of the fundamental group of motions becomes also big enough in low exciting frequency range. Consequently, the system possibly exhibits chattering-impact characteristics and the relative impact velocities successively attenuate in an excitation period. There exist a series of singular points between any two adjacent ones of the fundamental group of motions as the damping ratio or the damping constant of the viscous dashpot connecting two masses is very small, i.e., real-grazing and baregrazing bifurcation boundaries of one of them, saddlenode and period-doubling bifurcation boundaries of the other mutually cross themselves at the point of intersection and create two types of transition regions: hysteresis and tongue-shaped regions. A series of zones of regular and complex subharmonic impact motions are found to dominate in the tongue-shaped regions. The dimensionless parameters have been designed technically, under which large mass ratio or small supporting stiffness ratio leads to diversity and complexity of periodic-impact motions of the system. Based on the sampling ranges of parameters, the influence of system parameters on relative impact velocities, existence regions and correlative distribution of different types of periodic-impact motions of the system is emphatically studied.

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Simulation and stability analysis of impacting systems with complete chattering

Cited by 85 publications

References 32 publications

Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery

Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery

Periodically forced system with symmetric motion limiting constraints: Dynamic characteristics and equivalent electronic circuit realization

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

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