scholarly journals Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations

2009 ◽  
Vol 465 (2107) ◽  
pp. 2267-2292 ◽  
Author(s):  
Zhen Zhao ◽  
Caishan Liu ◽  
Bernard Brogliato
Keyword(s):  
Qualitative Analysis ◽  
Rigid Body ◽  
Numerical Simulations ◽  
Contact Point ◽  
Impulsive Differential Equations ◽  
Companion Paper ◽  
Rigid Body Dynamics ◽  
Drift Motion ◽  
Contact Points ◽  
Static Coefficient Of Friction

The objective of this paper is to implement and test the theory presented in a companion paper for the non-smooth dynamics exhibited in a bouncing dimer. Our approach revolves around the use of rigid body dynamics theory combined with constraint equations from the Coulomb's frictional law and the complementarity condition to identify the contact status of each contacting point. A set of impulsive differential equations based on Darboux–Keller shock dynamics is established that can deal with the complex behaviours involved in multiple collisions, such as the frictional effects, the local dissipation of energy at each contact point, and the dispersion of energy among various contact points. The paper will revisit the experimental phenomena found in Dorbolo et al . ( Dorbolo et al . 2005 Phys. Rev. Lett. 95 , 044101), and then present a qualitative analysis based on the theory proposed in part I. The value of the static coefficient of friction between the plate and the dimer is successfully estimated, and found to be responsible for the formation of the drift motion of the bouncing dimer. Plenty of numerical simulations are carried out, and precise agreements are obtained by the comparisons with the experimental results.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

A Contact Force Solution for Non-Colliding Contact Dynamics Simulation

2006 ◽  
Author(s):  
Inna Sharf ◽  
Yuning Zhang
Keyword(s):  
Rigid Body ◽  
Contact Force ◽  
Contact Point ◽  
Closed Form Solution ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Contact Dynamics ◽  
Dynamics Simulation ◽  
Friction Forces ◽  
Contact Points

Rigid-body impact modeling remains an intensive area of research spurred on by new applications in robotics, biomechanics, and more generally multibody systems. By contrast, the modeling of non-colliding contact dynamics has attracted significantly less attention. The existing approaches to solve non-colliding contact problems include compliant approaches in which the contact force between objects is defined explicitly as a function of local deformation, and complementarity formulations in which unilateral constraints are employed to compute contact interactions (impulses or forces) to enforce the impenetrability of the contacting objects. In this article, the authors develop a novel approach to solve the non-colliding contact problem for objects of arbitrary geometry in contact at multiple points. Similarly to the complementarity formulation, the solution is based on rigid-body dynamics and enforces contact kinematics constraints at the acceleration level. Differently, it leads to an explicit closed-form solution for the normal forces at the contact points. Integral to the proposed formulation is the treatment of tangential contact forces, in particular the static friction. These friction forces must be calculated as a function of microslip velocity or displacement at the contact point. Numerical results are presented for three test cases: 1) a thin rod sliding down a stationary wedge; 2) a cube rotating off the stationary wedge under application of an external moment and 3) the cube and the wedge both moving under application of a moment. To ascertain validity and correctness, the solutions to frictionless and frictional scenarios obtained with the proposed formulation are compared to those generated by using a commercial simulation tool MSC ADAMS.

scholarly journals A kinematics-based model for the settling of gravity-driven arbitrary-shaped particles on a surface

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0243716
Author(s):  
Mohsen Daghooghi ◽  
Iman Borazjani
Keyword(s):  
Equilibrium State ◽  
Contact Point ◽  
Center Of Mass ◽  
Stable State ◽  
Rigid Body Dynamics ◽  
Contact Points ◽  
Shaped Particle ◽  
Instantaneous Center ◽  
Point Line ◽  
Discrete Element Methods

A discrete model is proposed for settling of an arbitrary-shaped particle onto a flat surface under the gravitational field. In this method, the particle dynamics is calculated such that (a) the particle does not create an overlap with the wall and (b) reaches a realistic equilibrium state, which are not guaranteed in the conventional discrete element methods that add a repulsive force (torque) based on the amount of overlap between the particle and the wall. Instead, upon the detection of collision, the particle’s kinematics is modified depending on the type of contact, i.e., point, line, and surface types, by assuming the contact point/line as the instantaneous center/line of rotation for calculating the rigid body dynamics. Two different stability conditions are implemented by comparing the location of the projection of the center of mass on the wall along gravity direction against the contact points to identify the equilibrium (stable) state on the wall for particles with multiple contact points. A variety of simulations are presented, including smooth surface particles (ellipsoids), regular particles with sharp edges (cylinders and pyramids) and irregular-shaped particles, to show that the method can provide the analytically-known equilibrium state.

scholarly journals On a paradox in the impact dynamics of smooth rigid bodies

2018 ◽  
Vol 24 (3) ◽  
pp. 573-597 ◽  
Author(s):  
Peter Palffy-Muhoray ◽  
Epifanio G Virga ◽  
Mark Wilkinson ◽  
Xiaoyu Zheng
Keyword(s):  
Conservation Laws ◽  
Contact Point ◽  
Classical Mechanics ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Impact Dynamics ◽  
Contact Points ◽  
Impact Impulse ◽  
2D And 3D ◽  
The Impact

Paradoxes in the impact dynamics of rigid bodies are known to arise in the presence of friction. We show here that, on specific occasions, in the absence of friction, the conservation laws of classical mechanics are also incompatible with the collisions of smooth, strictly convex rigid bodies. Under the assumption that the impact impulse is along the normal direction to the surface at the contact point, two convex rigid bodies that are well separated can come into contact, and then interpenetrate each other. This paradox can be demonstrated in both 2D and 3D when the collisions are tangential, in which case no momentum or energy transfer between the two bodies is possible. The postcollisional interpenetration can be realized through the contact points or through neighboring points only. The penetration distance is shown to be [Formula: see text]. The conclusion is that rigid-body dynamics is not compatible with the conservation laws of classical mechanics.

Non-Jamming Conditions in Multi-Contact Constrained Rigid-Body Dynamics

2005 ◽  
Author(s):  
Tong Liu ◽  
Michael Yu Wang
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Applied Force ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Contact Points ◽  
Multiple Contacts ◽  
Unilateral Contacts ◽  
Body Dynamics ◽  
Free Body

In this paper, we study a rigid body system of one free body (e.g., workpiece) in contact with multiple fixed bodies (e.g., locators). The contacts are unilateral. The investigation is motivated for planning the task of insertion of a workpiece in a fixture. The key issue of the problem is to determine an applied force that can move the workpiece while maintaining all existing contacts with the locators. We first analyze the kinematics of the rigid body constrained by multiple unilateral contacts. The contact constraints are classified into two categories, the configuration constraints and kinematic constraints. We then find a sufficient condition for non-jamming among the multiple contacts in the constrained rigid-body dynamics. This condition is also a necessary condition when the number of contacts is no less than four. Moreover, a method to find the applied force on the workpiece that results in sliding on all contact points is presented, based on the sufficient condition for non-jamming. Numerical examples are presented and the results of the method are compared with the results of a quasistatic method.

Context Dependent Contact Preserving Off-Line Model Simplification for Interactive Rigid Body Dynamics Simulations

2009 ◽  
Author(s):  
Atul D. Thakur ◽  
Satyandra K. Gupta
Keyword(s):  
Rigid Body ◽  
Collision Detection ◽  
A Priori ◽  
Rigid Body Dynamics ◽  
Model Simplification ◽  
Detection Algorithms ◽  
Contact Points ◽  
Body Dynamics ◽  
Speed Up ◽  
Dynamics Simulations

Rigid body dynamics simulations require use of accurate computation of contacts among bodies. Often collision detection algorithms are used for determining the contact between moving bodies. Many mechanical parts have a large number of features and hence collision detection with the detailed part models often slows down the rigid body dynamics simulations. Model simplification techniques developed for efficient graphical rendering may change the part geometry in such a manner that the contact points between parts may change as a result of the simplification. Hence, such simplifications may alter the resulting simulated behavior. In many simulation scenarios, all the parts participating in the simulation are known in advance. In such cases, the simulation context (i.e., a priori knowledge of parts) can be exploited to simplify the part geometries such that the contact points among parts do not change. For example, parts with significant concavities may have regions on their boundaries that will be inaccessible to other parts in the simulation and hence contact points cannot lie on such inaccessible regions. Removing such regions from the parts can simplify the model and hence speed up the simulation for interactive applications.

Wedge Damper Modeling and Forced Response Prediction of Frictionally Constrained Blades

2007 ◽  
Author(s):  
Ender Cigeroglu ◽  
Ning An ◽  
Chia-Hsiang Menq
Keyword(s):  
Rigid Body ◽  
Relative Motion ◽  
Harmonic Balance ◽  
Contact Stiffness ◽  
Contact Point ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Points ◽  
Contact Surfaces

In this paper, an improved wedge damper model is presented, based on which the effects of wedge dampers on the forced response of frictionally constrained blades are investigated. In the analysis, while the blade is modeled as a constrained structure, the damper is considered as an unconstrained structure. The model of the damper includes six rigid body modes and several elastic modes, the number of which depends on the excitation frequency. In other words, the motion of the damper is not artificially constrained. When modeling the contact surfaces of the wedge damper, discrete contact points along with contact stiffness are evenly distributed on the two contact surfaces. At each contact point, contact stiffness is determined and employed in order to take into account the effects of higher frequency modes that are omitted in the dynamic analysis. Depending on the engine rpm, quasi-static contact analysis is initially employed to determine the contact area as well as the initial preload or gap at each contact point due to the centrifugal force. A friction model is employed to determine the three-dimensional nonlinear contact forces and the relationship between the contact forces and the relative motion is utilized by the Harmonic Balance method. As the relative motion is expressed as a modal superposition, the unknown variables, and thus the resulting nonlinear algebraic equations, in the Harmonic Balance method is in proportion to the number of modes employed, and therefore the number of contact points used is irrelevant. The developed method is applied to tuned bladed disk system and the effects of normal load on the rigid body motion of the damper are investigated. It is shown that, the effect of rotational motion is significant, particularly for the in-phase vibration modes.

Influence of rail flexibility in a wheel/rail wear prediction model

2016 ◽  
Vol 231 (1) ◽  
pp. 57-74 ◽  
Author(s):  
Javier F Aceituno ◽  
Pu Wang ◽  
Liang Wang ◽  
Ahmed A Shabana
Keyword(s):  
Prediction Model ◽  
Rigid Body ◽  
Contact Point ◽  
Three Dimensional ◽  
Contact Forces ◽  
Wear Model ◽  
Material Loss ◽  
Wear Prediction ◽  
Contact Points ◽  
Rail Wear

The aim of this paper is to study the influence of rail flexibility when a wheel/rail wear prediction model that computes the material loss based on an energy approach is used. The wheel/rail wear model used in this investigation is a simplified combined wear hypothesis that is based on the frictional energy loss in the contact patch. In order to account for wear and its distribution in a profiled wheel surface, the contact forces, creepages and location of the wheel/rail contact points are first calculated using a fully nonlinear multibody system (MBS) and three-dimensional contact formulations that account for the rail flexibility. The contact forces, creepages and contact point locations are defined as nonlinear functions of the rail deformations. These nonlinear expressions are used in the wear calculations. The wear distribution is considered to be proportional to the normal force in the contact area. Numerical simulations are first performed in order to compare between the results obtained using the simplified wheel/rail wear model and the results obtained using Archard’s wear model with a focus on sliding when the track is modeled as a rigid body. This simplified wear model is then used in the simulation of the MBS vehicle model in the case of a flexible body track, in which the rails are modeled using the finite element floating frame of reference approach and modal reduction techniques. The effect of the rail deformation on the wear results are examined by comparing these results with those obtained using the rigid-body track model.

scholarly journals Cavitation between cylinder-liner and piston-ring in a new designed optical IC engine

2021 ◽  
pp. 146808742110080
Author(s):  
Jamshid Malekmohammadi Nouri ◽  
Ioannis Vasilakos ◽  
Youyou Yan
Keyword(s):  
High Speed ◽  
Contact Point ◽  
Cylinder Liner ◽  
Optical Methods ◽  
Engine Management System ◽  
Great Success ◽  
Ic Engine ◽  
Contact Points ◽  
Lubricant Flow ◽  
Cavitation Intensity

A new engine block with optical access has been designed and manufactured capable of running up to 3000 r/min with the same specification as the unmodified engine. The optical window allowed access to the full length of the liner over a width of 25 mm to investigate the lubricant flow and cavitation at contact point between the rings and cylinder-liner. In addition, it allowed good access into the combustion chamber to allow charged flow, spray and combustion visualisation and measurements using different optical methods. New custom engine management system with build in LabView allowed for the precise full control of the engine. The design of the new optical engine was a great success in producing high quality images of lubricant flow, cavitation formation and development at contact point at different engine speeds ranging from 208 to 3000 r/min and lubricant temperatures (30°C–70°C) using a high-speed camera. The results under motorised operation confirmed that there was no cavitation at contact points during the intake/exhaust strokes due to low in-cylinder presure, while during compression/expansion strokes, with high in-cylinder pressure, considerable cavities were observed, in particular, during the compression stroke. Lubricant temperatures had the effect of promoting cavities both in their intensity and covered ring area up to 50°C as expected. Beyond that, although the cavitation intensity increases further with temperature, its area reduces due to possible collapse of the cavitating bubbles at higher temperature. The change of engine speed from 208 to 800 r/min increased cavitating area considerably by 52% of the ring area and was further increased by 19% at 1000 r/min. After that, the results showed very small increase in cavitation area (1.3% at 2000 r/min) with similar intensity and distribution across the ring.

New solutions of classical problems in rigid body dynamics

2015 ◽  
Vol 69 ◽  
pp. 40-44
Author(s):  
H.M. Yehia ◽  
E. Saleh ◽  
S.F. Megahid
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Body Dynamics
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