A continuous contact force model for impact analysis

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

Journal of Mechanical Design ◽

10.1115/1.2912617 ◽

1990 ◽

Vol 112 (3) ◽

pp. 369-376 ◽

Cited By ~ 537

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.

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Dynamics of Multibody Systems With Spherical Clearance Joints

Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2005-84392 ◽

2005 ◽

Cited By ~ 1

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.

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

18th Design Automation Conference: Volume 2 — Geometric Modeling, Mechanisms, and Mechanical Systems Analysis ◽

10.1115/detc1992-0189 ◽

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.

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

Multibody System Dynamics ◽

10.1007/s11044-018-09638-0 ◽

2018 ◽

Vol 44 (4) ◽

pp. 397-419 ◽

Cited By ~ 13

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

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

Advances in Mechanical Engineering ◽

10.1177/1687814017690477 ◽

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.

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

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406215607903 ◽

2016 ◽

Vol 230 (18) ◽

pp. 3161-3174 ◽

Cited By ~ 12

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.

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