Characterization of the Optimal Damping Coefficient in the Continuous Contact Model

2020 ◽  
Vol 15 (9) ◽  
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 paper presents an analytical formula to characterize the damping coefficient as a function of system's parameters in a continuous force model of 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, only 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 equivalent damping coefficient. The analytical and numerical investigations show that the resulting damping coefficient can be expressed as a function of system's parameters such as the effective mass, penetration speed at the start of the impact, Hertz spring constant, and the coefficient of restitution.

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.

scholarly journals Optimal damping coefficient for a class of continuous contact models

2020 ◽  
Vol 50 (2) ◽  
pp. 169-188
Author(s):  
Mohammad Poursina ◽  
Parviz E. Nikravesh
Keyword(s):  
Contact Force ◽  
Analytical Formula ◽  
Coefficient Of Restitution ◽  
Damping Coefficient ◽  
Optimization Strategy ◽  
Continuous Contact ◽  
Optimal Damping ◽  
Wide Range ◽  
Contact Models ◽  
The Impact

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.

scholarly journals Dynamics of Multibody Systems With Spherical Clearance Joints

2005 ◽  
Author(s):  
P. Flores ◽  
J. Ambro´sio ◽  
J. C. P. Claro ◽  
H. M. Lankarani
Keyword(s):  
Contact Force ◽  
Multibody Systems ◽  
Contact Forces ◽  
Force Model ◽  
Clearance Joints ◽  
Continuous Contact ◽  
Clearance Joint ◽  
Contact Force Model ◽  
Dynamics Of Multibody Systems ◽  
The Impact

This work deals with a methodology to assess the influence of the spherical clearance joints in spatial multibody systems. The methodology is based on the Cartesian coordinates, being the dynamics of the joint elements modeled as impacting bodies and controlled by contact forces. The impacts and contacts are described by a continuous contact force model that accounts for geometric and mechanical characteristics of the contacting surfaces. The contact force is evaluated as function of the elastic pseudo-penetration between the impacting bodies, coupled with a nonlinear viscous-elastic factor representing the energy dissipation during the impact process. A spatial four bar mechanism is used as an illustrative example and some numerical results are presented, being the efficiency of the developed methodology discussed in the process of their presentation. The results obtained show that the inclusion of clearance joints in the modelization of spatial multibody systems significantly influences the prediction of components’ position and drastically increases the peaks in acceleration and reaction moments at the joints. Moreover, the system’s response clearly tends to be nonperiodic when a clearance joint is included in the simulation.

scholarly journals A continuous contact force model of planar revolute joint based on fitting method

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769047
Author(s):  
Yuntao Li ◽  
Qiquan Quan ◽  
Dewei Tang ◽  
Zhonghong Li ◽  
Zongquan Deng
Keyword(s):  
Contact Force ◽  
Contact Stiffness ◽  
Elastic Force ◽  
Contact Model ◽  
Force Model ◽  
Damping Force ◽  
Revolute Joint ◽  
Continuous Contact ◽  
Contact Force Model ◽  
Fitting Method

Both the process of eliminating the clearance in joints and the contact–impact process involve movement of a clearance mechanism, which may reduce transmission accuracy and lengthen the response time. An appropriate continuous contact force model is able to describe the contact phenomena of a joint with clearance in a facile manner. However, two main problems still should be solved in building the continuous contact force model. First, the elastic force parts in previous continuous contact force models for a revolute joint were established by amending the force exponent of the Hertz spherical contact model or by the modified Winkler contact model. Nevertheless, the force exponent is usually given by experience, and the thickness of the elastic layer in the Winkler theory is difficult to determine. Second, for the previous damping force parts of a revolute joint, the hysteretic damping coefficients were obtained by substituting the stiffness coefficient with the contact stiffness of revolute joint directly instead of using the energy conservation method for the complicated form of elastic force model. A feasible continuous contact force model based on a fitting method was proposed to avoid these problems. According to the experimental results, the continuous contact force model can be used to predict the contact characteristics of a planar revolute joint in a facile manner.

Dynamic characteristics of planar linear array deployable structure based on scissor-like element with joint clearance using a new mixed contact force model

2016 ◽  
Vol 230 (18) ◽  
pp. 3161-3174 ◽  
Author(s):  
Bo Li ◽  
San-Min Wang ◽  
Ru Yuan ◽  
Xiang-Zhen Xue ◽  
Chang-Jian Zhi
Keyword(s):  
Contact Force ◽  
Dynamic Characteristics ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Contact Model ◽  
Joint Clearance ◽  
Force Model ◽  
Continuous Contact ◽  
Deployable Structure ◽  
Contact Force Model

This paper aims at investigating precisely the dynamic performance of deployable structure constituted by scissor unit mechanisms with clearance joint. Based on the motion law in real joints, the contact model is established using an improved Gonthier nonlinear continuous contact force model, and the friction effect is considered using LuGre model. Moreover, the resulting contact force is suitable to be included into the generalized force of the equations of motion of a multibody system and contributes to replace motion constraints. In the sequel of this process, the effect of joint clearance is successfully introduced into the dynamical model of scissor deployable structure and the dynamic characteristics of deployable structure with joint clearance are obtained using a direct default correction method, which can directly modify the coordinates and speed of the system to avoid the numerical results divergence. Also, the new hybrid contact force model of revolute joint clearance is verified through comparing with the original model. The numerical simulation results show that the improved contact model proposed here has the great merit that predicts the dynamic behavior of scissor deployable structure with joint clearance.

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.

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

1990 ◽  
Vol 112 (3) ◽  
pp. 369-376 ◽  
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

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 incorporated 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.

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.

scholarly journals Dynamics of Multibody Systems With Spherical Clearance Joints

2006 ◽  
Vol 1 (3) ◽  
pp. 240-247 ◽  
Author(s):  
P. Flores ◽  
J. Ambrósio ◽  
J. C. P. Claro ◽  
H. M. Lankarani
Keyword(s):  
Contact Force ◽  
Multibody Systems ◽  
Contact Forces ◽  
Force Model ◽  
Clearance Joints ◽  
Continuous Contact ◽  
Clearance Joint ◽  
Contact Force Model ◽  
Dynamics Of Multibody Systems ◽  
The Impact

This work deals with a methodology to assess the influence of the spherical clearance joints in spatial multibody systems. The methodology is based on the Cartesian coordinates, with the dynamics of the joint elements modeled as impacting bodies and controlled by contact forces. The impacts and contacts are described by a continuous contact force model that accounts for geometric and mechanical characteristics of the contacting surfaces. The contact force is evaluated as function of the elastic pseudo-penetration between the impacting bodies, coupled with a nonlinear viscous-elastic factor representing the energy dissipation during the impact process. A spatial four-bar mechanism is used as an illustrative example and some numerical results are presented, with the efficiency of the developed methodology discussed in the process of their presentation. The results obtained show that the inclusion of clearance joints in the modelization of spatial multibody systems significantly influences the prediction of components’ position and drastically increases the peaks in acceleration and reaction moments at the joints. Moreover, the system’s response clearly tends to be nonperiodic when a clearance joint is included in the simulation.

Experimental Validation of a Volumetric Planetary Rover Wheel/Soil Interaction Model

2013 ◽  
Author(s):  
Willem Petersen ◽  
John McPhee
Keyword(s):  
Contact Force ◽  
Interaction Model ◽  
Contact Model ◽  
Soil Parameters ◽  
Model Parameters ◽  
Force Model ◽  
Normal Contact ◽  
Planetary Rover ◽  
Normal Contact Force ◽  
Contact Force Model

For the multibody simulation of planetary rover operations, a wheel-soil contact model is necessary to represent the forces and moments between the tire and the soft soil. A novel nonlinear contact modelling approach based on the properties of the hypervolume of interpenetration is validated in this paper. This normal contact force model is based on the Winkler foundation model with nonlinear spring properties. To fully define the proposed normal contact force model for this application, seven parameters are required. Besides the geometry parameters that can be easily measured, three soil parameters representing the hyperelastic and plastic properties of the soil have to be identified. Since it is very difficult to directly measure the latter set of soil parameters, they are identified by comparing computer simulations with experimental results of drawbar pull tests performed under different slip conditions on the Juno rover of the Canadian Space Agency (CSA). A multibody dynamics model of the Juno rover including the new wheel/soil interaction model was developed and simulated in MapleSim. To identify the wheel/soil contact model parameters, the cost function of the model residuals of the kinematic data is minimized. The volumetric contact model is then tested by using the identified contact model parameters in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain and compared against experiments.

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