Periodic Motions and Chaos With Impacting Chatter and Stick in a Gear Transmission System

Luo, Albert C. J.; O’Connor, Dennis M.

doi:10.1142/s0218127409023858

Cited by 30 publications

(9 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Systems of oscillators with piecewise smooth springs and the related grazing bifurcations find applications in many other engineering systems, e.g. gear pairs , Parker-Vijayakar-Imajo [289], Luo-O'Connor [246]) vibrating screens and crushers (Krukov [214], Wen [376]), vibro-impact absorbers and impact dampers (Ibrahim [178]), ships interacting with icebergs (see Ibrahim [151,178]), offshore structures (see ), suspension bridges , de Freitas-Viana-Grebogi [129]), and pressure relief valves (see the paper by Hos-Champneys [171] in this special issue 5 ). Similar differential equations with nonsmooth continuous right-hand sides describe the so-called Chua circuit, for which border-collision and grazing bifurcations are discussed in Yu.…”

Section: Applicationsmentioning

confidence: 99%

Dynamics and bifurcations of nonsmooth systems: A survey

Makarenkov

Lamb

2012

Physica D: Nonlinear Phenomena

274

159

View full text Add to dashboard Cite

In this survey we discuss current directions of research in the dynamics of nonsmooth systems, with emphasis on bifurcation theory. An introduction to the state-of-the-art (also for non-specialists) is complemented by a presentation of main open problems. We illustrate the theory by means of elementary examples. The main focus is on piecewise smooth systems, that have recently attracted a lot of attention, but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities. This extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context. A dedicated section is devoted to concrete applications that stimulate the development of the field. This survey is concluded by an extensive bibliography.

show abstract

Section: Applicationsmentioning

confidence: 99%

Dynamics and bifurcations of nonsmooth systems: A survey

Makarenkov

Lamb

2012

Physica D: Nonlinear Phenomena

274

159

View full text Add to dashboard Cite

show abstract

“…Gear transmission system is commonly used in automobile, robotics, machinery, aerospace and other areas. Scholars have done a lot of research on the nonlinear dynamic of gear transmission system [1][2][3][4]. Kahranman [5][6][7] et al studied the dynamic response of gear transmission system under different forms of excitation.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Nonlinear Dynamics and Chaos Control in Gear Transmission System with Stochastic Perturbation

Wang¹,

Wang²

2017

mech

View full text Add to dashboard Cite

“…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%

“…The occurrence mechanism of periodic motions with impacting chatter and stick in the vibro-impact systems generally involves grazing dynamics and attendant bifurcations. 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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

View full text Add to dashboard Cite

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.

show abstract

Periodic Motions and Chaos With Impacting Chatter and Stick in a Gear Transmission System

Cited by 30 publications

References 23 publications

Dynamics and bifurcations of nonsmooth systems: A survey

Dynamics and bifurcations of nonsmooth systems: A survey

Analysis of Nonlinear Dynamics and Chaos Control in Gear Transmission System with Stochastic Perturbation

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

Contact Info

Product

Resources

About