Compliant Force Modelling for Impact Analysis

2004 ◽  
Author(s):  
Yuning Zhang ◽  
Inna Sharf
Keyword(s):  
Contact Force ◽  
Impact Analysis ◽  
Nonlinear Damping ◽  
Simple Expression ◽  
Contact Dynamics ◽  
Damping Coefficient ◽  
Force Model ◽  
Dynamics Modeling ◽  
Contact Phase ◽  
New Research

Contact dynamics modeling remains an intensive area of research with new applications emerging in robotics, biomechanics and multibody dynamics areas. Many formulations for contact dynamics problem have been proposed. The two most prominent categories include the discrete approach, which employs the impulse-momentum relations, and the continuous approach, which requires integration of dynamics equations through the contact phase. A number of methods in the latter category are based on an explicit compliant model for the contact force. One such model was developed by Hunt and Crossley three decades ago who introduced a nonlinear damping term of the form λxnx˙ into the contact force model. In addition to proposing the general form of this damping component of the contact force, Hunt and Crossley derived a simple expression for relating the damping coefficient λ to the coefficient of restitution e. This model gained considerable popularity due to its simplicity and realistic physics. It also spurred new research in the area, specifically on how to evaluate the damping coefficient λ. Subsequently, several authors put forward different approximations for λ, however, without clearly revealing the range of validity of their simplifying assumptions or the accuracy limitations of the resulting contact force models. The authors of this paper analyze the various approaches employed to derive the damping coefficient. We also evaluate and compare performance of the corresponding models by using a meaningful measure for their accuracy. A new derivation is proposed to calculate more precisely the damping coefficient for the nonlinear complaint contact model. Numerical results comparing all models are presented for a sphere dropping on a stationary surface.

Validation of Nonlinear Viscoelastic Contact Force Models for Low Speed Impact

2009 ◽  
Vol 76 (5) ◽  
Author(s):  
Yuning Zhang ◽  
Inna Sharf
Keyword(s):  
Contact Force ◽  
Nonlinear Damping ◽  
Coefficient Of Restitution ◽  
Contact Dynamics ◽  
Dynamics Simulation ◽  
Damping Coefficient ◽  
Force Model ◽  
Nonlinear Viscoelastic ◽  
The Impact ◽  
Viscoelastic Contact

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.

Experimental Validation of Nonlinear Compliant Contact Force Models

2007 ◽  
Author(s):  
Yuning Zhang ◽  
Inna Sharf
Keyword(s):  
Contact Force ◽  
Research Area ◽  
Local Deformation ◽  
Contact Dynamics ◽  
Dynamics Simulation ◽  
Damping Coefficient ◽  
Engineering Practice ◽  
Dynamics Modeling ◽  
Normal Contact ◽  
The Impact

Contact dynamics modeling continues to be an intensive research area with new applications of contact dynamics simulation arising in engineering practice. One approach to normal contact force modeling that has gained significant popularity is the compliant model in which the contact force between two objects is defined explicitly as a function of local deformation and its rate. Probably the most well-known model in this category is the Hunt and Crossley model, which employs a nonlinear damping term to model the energy dissipation during contact, with the damping coefficient related to the coefficient of restitution. This 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 nonlinear contact force models and furthermore, to compare the experimental results to the model predictions obtained with different values of the damping coefficient. The paper reports our findings from the sphere to plate impact experiments, conducted for a range of initial impacting velocities, with measurements of impact forces and accelerations. The experimental forces are compared to 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.

Hertz Contact Force Model With Permanent Indentation in Impact Analysis of Solids

1992 ◽  
Author(s):  
Hamid M. Lankarani ◽  
Parviz E. Nikravesh
Keyword(s):  
Contact Force ◽  
Impact Analysis ◽  
Equations Of Motion ◽  
Solid Particles ◽  
Hertzian Contact ◽  
Contact Period ◽  
Force Model ◽  
Unknown Parameters ◽  
Contact Force Model ◽  
Energy And Momentum

Abstract A continuous analysis method for the direct-central impact of two solid particles is presented. Based on the assumption that local plasticity effects are the sole factor accounting for the dissipation of energy in impact, a Hertzian contact force model with permanent indentation is constructed. Utilizing energy and momentum considerations, the unknown parameters in the model are analytically evaluated in terms of a given coefficient of restitution and velocities before impact. The equations of motion of the two solids may then be integrated forward in time knowing the variation of the contact force during the contact period. For Illustration, an impact of two soft metallic particles is studied.

A continuous contact force model for impact analysis

2022 ◽  
Vol 168 ◽  
pp. 108739
Author(s):  
Jie Zhang ◽  
Xu Liang ◽  
Zhonghai Zhang ◽  
Guanhua Feng ◽  
Quanliang Zhao ◽  
...  
Keyword(s):  
Contact Force ◽  
Impact Analysis ◽  
Force Model ◽  
Continuous Contact ◽  
Contact Force Model

Characterization of the Damping Coefficient in the Continuous Contact Model

2019 ◽  
Author(s):  
Mohammad Poursina ◽  
Parviz E. Nikravesh
Keyword(s):  
Contact Force ◽  
Analytical Formula ◽  
Deformation Characteristic ◽  
Contact Model ◽  
Damping Coefficient ◽  
Force Model ◽  
Separation Condition ◽  
Continuous Contact ◽  
Continuous Contact Model ◽  
The Impact

Abstract This article presents an analytical formula to characterize the damping coefficient in a continuous force model of the direct central impact. The contact force element consists of a linear damper which is in a parallel connection to a spring with Hertz force-deformation characteristic. Unlike the existing models in which the separation condition is assumed to be at the time at which both zero penetration (deformation) and zero force occur, in this study, zero contact force is considered as the separation condition. To ensure that the continuous contact model obtains the desired restitution, an optimization process is performed to find the damping coefficient. The numerical investigations show that the damping coefficient can be analytically expressed as a function of system’s parameters such as the effective mass, penetration speed just before the impact, Hertz spring constant, and the coefficient of restitution.

A contact force model considering constant external forces for impact analysis in multibody dynamics

2018 ◽  
Vol 44 (4) ◽  
pp. 397-419 ◽  
Author(s):  
Yinhua Shen ◽  
Dong Xiang ◽  
Xiang Wang ◽  
Li Jiang ◽  
Yaozhong Wei
Keyword(s):  
Multibody Dynamics ◽  
Contact Force ◽  
Impact Analysis ◽  
Force Model ◽  
Contact Force Model ◽  
External Forces

Model order reduction for impact-contact dynamics simulations of flexible manipulators

Robotica ◽  
2007 ◽  
Vol 25 (4) ◽  
pp. 397-407 ◽  
Author(s):  
Ou Ma ◽  
Jiegao Wang
Keyword(s):  
Contact Force ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Contact Dynamics ◽  
Force Model ◽  
Flexible Manipulators ◽  
Model Order ◽  
Reduction Techniques ◽  
Contact Force Model ◽  
Stiffness And Damping

SUMMARYDynamic simulation of a flexible manipulator performing physical contact (including low-speed impact) tasks with stiff environment is very time consuming because very small integration step sizes have to be used for numerical stability. Existing model order reduction techniques cannot be readily applied due to the nonlinear nature of the contact dynamics. In this paper, a method is introduced to deal with this problem. The method first linearizes the contact force model on the right-hand side of the dynamics equations periodically. It then identifies the linear “stiffness” and “damping” terms from the linearized contact force model and combines them with the existing structural stiffness and damping matrices of the associated multibody system on the left-hand side of the equations. After such a process, the traditional modal analysis and reduction techniques for linear dynamic systems can be applied to reduce the order of the resulting dynamic system. Two numerical examples of flexible manipulators performing a contact task are presented to demonstrate the significant gain in computational efficiency and the improved output results.

A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems

1989 ◽  
Author(s):  
H. M. Lankarani ◽  
P. E. Nikravesh
Keyword(s):  
Contact Force ◽  
Impact Analysis ◽  
Multibody System ◽  
Particle Collision ◽  
Dissipated Energy ◽  
Particle Model ◽  
Force Model ◽  
Continuous Contact ◽  
Contact Force Model ◽  
The Impact

Abstract A continuous contact force model for the impact analysis of a two-particle collision is presented. The model uses the general trend of the Hertz contact law. A hysteresis damping function is encorporated in the model which represents the dissipated energy in impact. The parameters in the model are determined, and the validity of the model is established. The model is then generalized to the impact analysis between two bodies of a multibody system. A continuous analysis is performed using the equations of motion of either the multibody system or an equivalent two-particle model of the colliding bodies. For the latter, the concept of effective mass is presented in order to compensate for the effects of joint forces in the system. For illustration, the impact situation between a slider-crank mechanism and another sliding block is considered.

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