scholarly journals Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement

2022 ◽  
Vol 43 (1) ◽  
pp. 93-112
Author(s):  
Kaiming Zhang ◽  
Xudong Zheng ◽  
Zhang Chen ◽  
Bin Liang ◽  
Tianshu Wang ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Friction Force ◽  
Contact Force ◽  
Contact Point ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Force Model ◽  
Lagrange Equations ◽  
Stick Slip ◽  
Normal Contact

AbstractThe non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground. According to the Carvallo-Whipple configuration, the unmanned bicycle is reduced to four rigid bodies, namely, rear wheel, rear frame, front fork, and front wheel, which are connected by perfect revolute joints. The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point, and these forces are described by the Hunt-Crossley contact force model and the LuGre friction force model, respectively. According to the characteristics of flat and curved pavements, calculation methods for contact forces and their generalized forces are presented. The dynamics of the system is modeled by the Lagrange equations of the first kind, a numerical solution algorithm of the dynamic equations is presented, and the Baumgarte stabilization method is used to restrict the drift of the constraints. The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies. The feasibility of the proposed model is demonstrated by simulations under different motion states.

Dynamic Modeling and Response Analysis of a Planar Rigid-Body Mechanism With Clearance

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Chen Xiulong ◽  
Jiang Shuai ◽  
Deng Yu ◽  
Wang Qing
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Dynamic Modeling ◽  
Contact Force ◽  
Kinematic Model ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Prototype Model ◽  
Force Model ◽  
Normal Contact

In order to understand dynamic responses of planar rigid-body mechanism with clearance, the dynamic model of the mechanism with revolute clearance is proposed and the dynamic analysis is realized. First, the kinematic model of the revolute clearance is built; the amount of penetration depth and relative velocity between the elements of the revolute clearance joint is obtained. Second, Lankarani-Nikravesh (L-N) and the novel nonlinear contact force model are both used to describe the normal contact force of the revolute clearance, and the tangential contact force of the revolute clearance is built by modified Coulomb friction model. Third, the dynamic model of a two degrees-of-freedom (2DOFs) nine bars rigid-body mechanism with a revolute clearance is built by the Lagrange equation. The fourth-order Runge–Kutta method has been utilized to solve the dynamic model. And the effects of different driving speeds of cranks, different clearance values, and different friction coefficients on dynamic response are analyzed. Finally, in order to prove the validity of numerical calculation result, the virtual prototype model of 2DOFs nine bars mechanism with clearance is modeled and its dynamic responses are analyzed by adams software. This research could supply theoretical basis for dynamic modeling, dynamic behaviors analysis, and clearance compensation control of planar rigid-body mechanism with clearance.

scholarly journals A Study on the Dynamics of Spatial Mechanisms With Frictional Spherical Clearance Joints

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Filipe Marques ◽  
Fernando Isaac ◽  
Nuno Dourado ◽  
António Pedro Souto ◽  
Paulo Flores ◽  
...  
Keyword(s):  
Friction Force ◽  
Contact Process ◽  
Contact Forces ◽  
Force Model ◽  
Spherical Joint ◽  
Normal Contact ◽  
Clearance Joints ◽  
Dissipative Term ◽  
Contact Points ◽  
Spatial Mechanisms

An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket, which compose a spherical joint, are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian-based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudopenetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb's law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems' dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four-bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.

A Study on the Dynamics of Spatial Mechanisms With Frictional Spherical Clearance Joints

2016 ◽  
Author(s):  
Filipe Marques ◽  
Fernando Isaac ◽  
Nuno Dourado ◽  
António Pedro Souto ◽  
Paulo Flores ◽  
...  
Keyword(s):  
Friction Force ◽  
Contact Process ◽  
Contact Forces ◽  
Force Model ◽  
Spherical Joint ◽  
Normal Contact ◽  
Clearance Joints ◽  
Dissipative Term ◽  
Contact Points ◽  
Spatial Mechanisms

An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket which compose a spherical joint are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudo-penetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb’s law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems’ dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.

scholarly journals Influence of the contact model on the dynamic response of the human knee joint

2011 ◽  
Vol 225 (4) ◽  
pp. 344-358 ◽  
Author(s):  
M Machado ◽  
P Flores ◽  
J Ambrosio ◽  
A Completo
Keyword(s):  
Knee Joint ◽  
Dynamic Response ◽  
Contact Force ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Force Model ◽  
Elastic Model ◽  
Human Knee ◽  
Human Knee Joint ◽  
Sphere Contact

The goal of this work is to study the influence of the contact force model, contact geometry, and contact material properties on the dynamic response of a human knee joint model. For this purpose, a multibody knee model composed by two rigid bodies, the femur and the tibia, and four non-linear spring elements that represent the main knee ligaments, is considered. The contact force models used were the Hertz, the Hunt–Crossley, and the Lankarani–Nikravesh approaches. Results obtained from computational simulations show that Hertz law is less suitable to describe the dynamic response of the cartilage contact, because this pure elastic model does not account for the viscoelastic nature of the human articulations. Since knee can exhibit conformal and non-conformal contact scenarios, three different geometrical configurations for femur–tibia contact are considered, that is convex–convex sphere contact, convex–concave sphere contact, and convex sphere–plane contact. The highest level of contact forces is obtained for the case of convex–convex sphere contact. As far as the influence of the material contact properties is concerned, the dynamic response of a healthy and natural knee is analysed and compared with three pathological and two artificial knee models. The obtained results demonstrate that the presence of the cartilage reduces significantly the knee contact forces.

Computational and Experimental Analysis of Mechanical Systems With Revolute Clearance Joints

2013 ◽  
Author(s):  
Sony Cheriyan ◽  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Contact Force ◽  
Computational Models ◽  
Mechanical Systems ◽  
Contact Forces ◽  
Force Model ◽  
Connecting Rod ◽  
Normal Contact ◽  
Clearance Joints ◽  
Coulomb’S Friction ◽  
Experimental Apparatus

The main objective of this work is to present a computational and experimental study on the contact forces developed in revolute clearance joints. For this purpose, a well-known slider-crank mechanism with a revolute clearance joint between the connecting rod and slider is utilized. The intra-joint contact forces that generated at this clearance joints are computed by considered several different elastic and dissipative approaches, namely those based on the Hertz contact theory and the ESDU tribology-based for cylindrical contacts, along with a hysteresis-type dissipative damping. The normal contact force is augmented with the dry Coulomb’s friction force. An experimental apparatus is use to obtained some experimental data in order to verify and validate the computational models. From the outcomes reported in this paper, it is concluded that the selection of the appropriate contact force model with proper dissipative damping plays a significant role in the dynamic response of mechanical systems involving contact events at low or moderate impact velocities.

scholarly journals Dynamic Response of Multibody Systems with Multiple Clearance Joints

2012 ◽  
Vol 7 (3) ◽  
Author(s):  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Contact Force ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Physical And Mechanical Properties ◽  
Contact Forces ◽  
Force Model ◽  
Normal Contact ◽  
Clearance Joints ◽  
Continuous Contact ◽  
Dissipative Term

A general methodology for the dynamic modeling and analysis of planar multibody systems with multiple clearance joints is presented. The inter-connecting bodies that constitute a real physical mechanical joint are modeled as colliding components, whose dynamic behavior is influenced by the geometric, physical and mechanical properties of the contacting surfaces. A continuous contact force model, based on the elastic Hertz theory, together with a dissipative term associated with the internal damping, is utilized to evaluate the intra-joint normal contact forces. The incorporation of the friction phenomenon, based on the classical Coulomb’s friction law, is also included in this study. The suitable contact force models are embedded into the dynamic equations of motion for the multibody systems. In the sequel of this process, the fundamental methods to deal with contact-impact events in mechanical systems are presented. Finally, two planar mechanisms with multiple revolute clearance joints are used to demonstrate the accuracy and efficiency of the presented approach and to discuss the main assumptions and procedures adopted. The effects of single versus multiple clearance revolute joints are discussed.

On the Contact Modeling and Analysis of the Human Knee Joint

2011 ◽  
Author(s):  
Margarida Machado ◽  
Paulo Flores
Keyword(s):  
Knee Joint ◽  
Dynamic Response ◽  
Contact Force ◽  
Rigid Bodies ◽  
Contact Forces ◽  
Applied Force ◽  
Force Model ◽  
Elastic Model ◽  
Human Knee ◽  
Human Knee Joint

The goal of this work is to study the influence of the contact force model and contact material properties on the dynamic response of a human knee joint. For this purpose, a multibody knee model composed by two rigid bodies, the femur and the tibia, and four nonlinear spring elements that represent the main knee ligaments, is considered. The contact geometrical profiles are extracted from medical images and fitted using spline functions. The tibia motions are modeled, not using a conventional kinematic joint, but rather in terms of the action of the ligaments and potential contact between the bones. Besides, an external force is applied on the center of mass of the tibia in order to simulate the force of the quadriceps muscle group. When a contact is detected, a continuous contact force law is applied. The contact force laws studied are the Hertz, the Hunt-Crossley and the Lankarani-Nikravesh models. Results obtained from computational simulations show that Hertz law is less suitable to describe the dynamic response of the cartilage contact, because this pure elastic model does not account for the viscoelastic nature of the human articulations. Moreover, the effect of the amplitude of the external applied force on the dynamic response of the knee joint model is also evaluated. The obtained results show that the increase of the amplitude of the external applied force increases the contact indentations and lead to an earlier first impact. As far as to the influence of the material contact properties is concerned, the dynamic response of a healthy and natural knee is analyzed and compared with three pathological and two artificial knee models. Results demonstrate that the presence of the cartilage reduces significantly the knee contact forces.

Three-Dimensional Wear Prediction of Four-Degrees-of-Freedom Parallel Mechanism With Clearance Spherical Joint and Flexible Moving Platform

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Gengxiang Wang ◽  
Hongzhao Liu
Keyword(s):  
Contact Force ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Contact Forces ◽  
Force Model ◽  
Spherical Joint ◽  
Normal Contact ◽  
Tangential Contact ◽  
Moving Platform

Three-dimensional (3D) wear of the clearance spherical joint in four-degrees-of-freedom (DOF) parallel mechanism is predicted based on Archard's wear model. The flexible moving platform is treated as thin plate element based on absolute nodal coordinate formulation (ANCF). The tangent frame is introduced to formulate the constraint equation of universal joint. One of the spherical joints is treated as clearance joint. The normal and tangential contact forces are calculated based on Flores contact force model and modified Coulomb friction model. In order to predict 3D wear, the normal contact force, tangential contact velocity, and eccentricity vector are decomposed in the global coordinate system. Simulation results show that 3D wear occurred in three directions are not uniform each other.

Analysis of Postbuckling Drillstring Vibrations in Rotary Drilling of Extended-Reach Wells

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Vadim S. Tikhonov ◽  
Alexander I. Safronov
Keyword(s):  
Angular Velocity ◽  
Friction Factor ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Friction Force ◽  
Contact Force ◽  
Normal Component ◽  
Method Of Lines ◽  
Force Model ◽  
Nonlinear Dynamic Model

One of the most serious concerns of extended-reach drilling is the dynamic behavior of the drillstring and the cleaning of well. Good cleaning requires an increased angular velocity. This paper presents a 3D nonlinear dynamic model of drillstring in a wellbore of 3D profile. The model suggests possible contact/lift-off of drill pipes with/from the wellbore wall. The interaction of lateral, torsional, and axial vibrations is taken into account. The relation between the normal component of contact force and the deformation of the wellbore wall is taken as quadratic-elastic. The friction force is described based on a hysteretic dynamic model. The friction force model also takes into account, the transition from a sliding to whirling. The equations of drillstring dynamics are solved numerically using the method of lines. The DYNTUB software is developed to analyze the drillstring time-varying processes under different loads. The program is used to study the effects of angular velocity, compression load, torque, friction factor, well profile, and availability of connectors on the drillstring dynamic behavior. From the study follows the key conclusions: (1) The friction factor has a considerable effect on the drillstring rotational behavior in the wellbore; (2) no whirling of drillstring at real value of rolling friction factor in a horizontal well in the discussed examples could be seen at all; (3) when whirling takes place, the contact force shows a dramatic times increase; and (4) snaking can be seen in any wells at moderate compressive load and angular velocity.

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.

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