Chaotic behaviour in an impact vibration system (2nd report, Influence of damping coefficient and coefficient of restitution)

1986 ◽  
Vol 52 (479) ◽  
pp. 1883-1886 ◽  
Author(s):  
Tadashi KOTERA ◽  
Hideyuki YAMANISHI
2020 ◽  
Vol 50 (2) ◽  
pp. 169-188
Author(s):  
Mohammad Poursina ◽  
Parviz E. Nikravesh

Abstract In this study, we develop an analytical formula to approximate the damping coefficient as a function of the coefficient of restitution for a class of continuous contact models. The contact force is generated by a logical point-to-point force element consisting of a linear damper connected in parallel to a spring with Hertz force–penetration characteristic, while the exponent of deformation of the Hertz spring can vary between one and two. In this nonlinear model, it is assumed that the bodies start to separate when the contact force becomes zero. After separation, either the restitution continues or a permanent penetration is achieved. Therefore, this model is capable of addressing a wide range of impact problems. Herein, we apply an optimization strategy on the solution of the equations governing the dynamics of the penetration, ensuring that the desired restitution is reproduced at the time of separation. Furthermore, based on the results of the optimization process along with analytical investigations, the resulting optimal damping coefficient is analytically expressed at the time of impact in terms of system properties such as the effective mass, penetration velocity just before the impact, coefficient of restitution, and the characteristics of the Hertz spring model.


Author(s):  
Yuan-bo Ye ◽  
Hao Zheng ◽  
Wei Wang ◽  
Gui-zhong Wang ◽  
Hong-bo Li ◽  
...  

2009 ◽  
Vol 76 (5) ◽  
Author(s):  
Yuning Zhang ◽  
Inna Sharf

Compliant contact force modeling has become a popular approach for contact and impact dynamics simulation of multibody systems. In this area, the nonlinear viscoelastic contact force model developed by Hunt and Crossley (1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Appl. Mech., 42, pp. 440–445) over 2 decades ago has become a trademark with applications of the model ranging from intermittent dynamics of mechanisms to engagement dynamics of helicopter rotors and implementations in commercial multibody dynamics simulators. The distinguishing feature of this model is that it employs a nonlinear damping term to model the energy dissipation during contact, where the damping coefficient is related to the coefficient of restitution. Since its conception, the model prompted several investigations on how to evaluate the damping coefficient, in turn resulting in several variations on the original Hunt–Crossley model. In this paper, the authors aim to experimentally validate the Hunt–Crossley type of contact force models and furthermore to compare the experimental results to the model predictions obtained with different values of the damping coefficient. This paper reports our findings from the sphere to flat impact experiments, conducted for a range of initial impacting velocities using a pendulum test rig. The unique features of this investigation are that the impact forces are deduced from the acceleration measurements of the impacting body, and the experiments are conducted with specimens of different yield strengths. The experimental forces are compared with those predicted from the contact dynamics simulation of the experimental scenario. The experiments, in addition to generating novel impact measurements, provide a number of insights into both the study of impact and the impact response.


1977 ◽  
Vol 99 (3) ◽  
pp. 513-518 ◽  
Author(s):  
R. G. Herbert ◽  
D. C. McWhannell

With the need to improve the reliability and noise emissions from real mechanisms, an impact in the classical impact pair configuration is investigated considering the impact pulse level and its frequency composition as possible sources of high-frequency energy in articulated systems. The analog representation of the impact pair uses a nonlinear surface stiffness together with a nonlinear surface damping. Developments of the Dubowsky model carried out by Crossley are further extended to allow the surface damping coefficient, as a function of the coefficient of restitution, to be calculated assuming energy is dissipated throughout the impact for any series power law representation of the surface stiffness. The practical system used by Veluswami is simulated, and the results for Dubowsky, Crossley, and the direct solution are compared to Veluswami’s practical data.


Author(s):  
Hany A. Sherif ◽  
Fahad. A. Almufadi

Common parameters between metallic and polymeric materials are the coefficient of restitution, the damping coefficient, and loss factor. Although the relationship between the coefficient of restitution and the loss factor is quite direct, their dependence on the damping coefficient is not so simple and mainly affected by the adopted model used to describe the material response under impact. In the present study, Kelvin–Voigt linear model and Hunt–Crossley complex model are analyzed to describe how the coefficient of restitution depends on the viscous damping coefficient of impact. The correlation between the theoretical models and the experimental data is also shown. A simple method to predict the impact damping factor of both polymeric and metallic materials from the measured temporal signal of the impact force is demonstrated.


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