Using an Anti-Relaxation Step to Improve the Accuracy of the Frictional Contact Solution in a DVI Framework for Rigid Body Dynamics

2016 ◽  
Author(s):  
Daniel Melanz ◽  
Hammad Mazhar ◽  
Dan Negrut
Keyword(s):  
Frictional Contact ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Science And Engineering ◽  
Complementarity Condition ◽  
Body Dynamics ◽  
Engineering Problems ◽  
The Impact

Systems composed of rigid bodies interacting through frictional contact are manifest in several science and engineering problems. The number of contacts can be small, such as in robotics and geared machinery, or large, such as in terrame-chanics applications, additive manufacturing, farming, food industry, and pharmaceutical industry. Currently, there are two popular approaches for handling the frictional contact problem in dynamic systems. The penalty method calculates the frictional contact force based on the kinematics of the interaction, some representative parameters, and an empirical force law. Alternatively, the complementarity method, based on a differential variational inequality (DVI), enforces non-penetration of rigid bodies via a complementarity condition. This contribution concentrates on the latter approach and investigates the impact of an anti-relaxation step that improves the accuracy of the frictional contact solution. We show that the proposed anti-relaxation step incurs a relatively modest cost to improve the quality of a numerical solution strategy which poses the calculation of the frictional contact forces as a cone-complementarity problem.

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.

scholarly journals Econometric Evaluation of Impact of Education Quality on Economic Growth in Azerbaijan

2021 ◽  
Vol 12 (6) ◽  
pp. 1397-1404
Author(s):  
Nazim Hajiyev, Sardar Shabanov, Yadulla Hasanli
Keyword(s):  
Higher Education ◽  
Economic Growth ◽  
Quality Index ◽  
Education Quality ◽  
Average Score ◽  
Regression Equations ◽  
Science And Engineering ◽  
Linear Type ◽  
The Impact

The article is dedicated to study of the impact of the quality of education on the economic growth in Azerbaijan. The quality index of education has been selected for two levels: a) up to higher education; b) higher school and post higher school. The indicator of average score (if available) that an applicant obtained in the current year on the country in student admission to the higher schools as a quality index of education in the country at the pre-higher education is offered as an alternative to the number of upper grades (10-12) in the secondary education. In the higher and post-higher education level, the number of articles printed on basic science and engineering per million people in Azerbaijan, and indexed on the Web of Science is taken as a quality index of education. Semi-linear type regression equations were made to assess the dependence of the indicators characterizing economic development.

Study on the Commercial Vehicle's Ride Comfort at Idle Speed by Simulation

2014 ◽  
Vol 955-959 ◽  
pp. 890-893
Author(s):  
Li Hu ◽  
Chi Jie Yang ◽  
Qi Liang Yang ◽  
Zhe Tang
Keyword(s):  
Ride Comfort ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Test Results ◽  
Dynamics Model ◽  
Power Train ◽  
Idle Speed ◽  
Simulating Calculation ◽  
Body Dynamics ◽  
Improvement Measures

A commercial vehicle was taken as the study object to establish vehicle rigid-body dynamics model which included seventeen-degree-of-freedom. This model consisted of three rigid bodies which were power-train, frame and body and there were flex connections among the rigid bodies. The model was used to carry out simulating calculation and analysis of vehicle ride comfort. By comparing simulation results with test results, some improvement measures for vehicle ride comfort at idle speed were presented in this paper.

scholarly journals Zeolites application in terrestrial and space industry – a review

2020 ◽  
Vol 32 ◽  
pp. 209-223
Author(s):  
Adelina Miteva ◽  
Valeria Stoyanova
Keyword(s):  
Chemical Properties ◽  
Waste Materials ◽  
Ion Exchangers ◽  
Science And Engineering ◽  
Space Industry ◽  
Synthetic Zeolites ◽  
The Impact ◽  
And Chemical Properties

This brief overview presents an attempt to systematize some of the available historical and recent data on the impact of zeolite science and engineering on the progress of various areas of Earth and Space development. The basic structural and chemical properties of natural and synthetic zeolites are presented. Valuable applications of the zeolites, such as catalysts, gas adsorbers and ion exchangers are also included. The most commonly used methods for the synthesis of zeolites from different materials are presented, as well as some Bulgarian developments for the reuse of waste materials to zeolites. The important role of zeolites as an indispensable material for improving the quality of soil, fuels, water, air, etc., required for the needs of orbiting space stations and spacecrafts has been confirmed by typical examples.

Analysis of rigid-body dynamics for closed-loop mechanisms—its application to a novel satellite tracking device

2003 ◽  
Vol 217 (4) ◽  
pp. 285-298
Author(s):  
T P Jones ◽  
G R Dunlop
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Satellite Tracking ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Parallel Mechanisms ◽  
Body Dynamics ◽  
Tracking Device ◽  
General Method

A general method for analysing the velocity and acceleration kinematics of parallel mechanisms is introduced. A method for analysing the forces experienced by rigid bodies in parallel mechanisms is then introduced, which builds on the kinematics that result in a solution to the dynamics of rigid bodies in parallel mechanisms.

On Analytical Evaluation of Gear Dynamic Factors Based on Rigid Body Dynamics

1985 ◽  
Vol 107 (2) ◽  
pp. 301-311 ◽  
Author(s):  
C. C. Wang
Keyword(s):  
System Dynamics ◽  
Rigid Body ◽  
Time Derivative ◽  
Transmission Error ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Dynamic Factor ◽  
Lumped Mass ◽  
Body Dynamics ◽  
Cubic Spline Curve

This paper proposes an initial step to rationalize the dynamic factor calculation and bring it under the control of the laws of mechanics. The theory is straight forward. The concept of mathematical scaling is utilized to simplify the system dynamics’ formulation. The rigid body dynamics accounts for the gear dynamic tooth loads resulting from the prescribed transmission error of each gear step—including the artificial ones. The latter converts a lumped-mass-elastic system into a rigid-bodies-transmission-error system subjected to the solution of the rigid body system dynamics according to Newton’s law. The entire concept of the solution has been implemented into a FORTRAN program approximately 600 statements in length. The results obtained through computer simulation of various test cases demonstrate the potential and effectiveness of the proposed concept. Contrary to the current practice of grossly ignoring the inertial and system effects, this paper has taken all these important factors into account. The transmission-error-induced acceleration is approximated by the second-order time derivative of one of the cubic spline curve-fitting methods. The approach is cost effective and numerically satisfactory. The model can be further improved to reduce the extent of basic assumptions, or to increase the number of conditional constraints without losing economical attractiveness.

Wheel–Rail Impact at Crossings: Relating Dynamic Frictional Contact to Degradation

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Zilong Wei ◽  
Chen Shen ◽  
Zili Li ◽  
Rolf Dollevoet
Keyword(s):  
Plastic Deformation ◽  
Contact Force ◽  
Frictional Contact ◽  
Point Contact ◽  
Strain Analysis ◽  
Dynamic Contact ◽  
Contact Forces ◽  
Fe Method ◽  
Normal Contact ◽  
The Impact

Irregularities in the geometry and flexibility of railway crossings cause large impact forces, leading to rapid degradation of crossings. Precise stress and strain analysis is essential for understanding the behavior of dynamic frictional contact and the related failures at crossings. In this research, the wear and plastic deformation because of wheel–rail impact at railway crossings was investigated using the finite-element (FE) method. The simulated dynamic response was verified through comparisons with in situ axle box acceleration (ABA) measurements. Our focus was on the contact solution, taking account not only of the dynamic contact force but also the adhesion–slip regions, shear traction, and microslip. The contact solution was then used to calculate the plastic deformation and frictional work. The results suggest that the normal and tangential contact forces on the wing rail and crossing nose are out-of-sync during the impact, and that the maximum values of both the plastic deformation and frictional work at the crossing nose occur during two-point contact stage rather than, as widely believed, at the moment of maximum normal contact force. These findings could contribute to the analysis of nonproportional loading in the materials and lead to a deeper understanding of the damage mechanisms. The model provides a tool for both damage analysis and structure optimization of crossings.

Rigid Body Dynamics, Constraints, and Inverses

2005 ◽  
Vol 74 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Hooshang Hemami ◽  
Bostwick F. Wyman
Keyword(s):  
Rigid Body ◽  
State Space ◽  
Tracking Error ◽  
Feedback System ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Contact Forces ◽  
Constraint Forces ◽  
Inverse Systems ◽  
Body Dynamics

Rigid body dynamics are traditionally formulated by Lagrangian or Newton-Euler methods. A particular state space form using Euler angles and angular velocities expressed in the body coordinate system is employed here to address constrained rigid body dynamics. We study gliding and rolling, and we develop inverse systems for estimation of internal and contact forces of constraint. A primitive approximation of biped locomotion serves as a motivation for this work. A class of constraints is formulated in this state space. Rolling and gliding are common in contact sports, in interaction of humans and robots with their environment where one surface makes contact with another surface, and at skeletal joints in living systems. This formulation of constraints is important for control purposes. The estimation of applied and constraint forces and torques at the joints of natural and robotic systems is a challenge. Direct and indirect measurement methods involving a combination of kinematic data and computation are discussed. The basic methodology is developed for one single rigid body for simplicity, brevity, and precision. Computer simulations are presented to demonstrate the feasibility and effectiveness of the approaches presented. The methodology can be applied to a multilink model of bipedal systems where natural and/or artificial connectors and actuators are modeled. Estimation of the forces is accomplished by the inverse of the nonlinear plant designed by using a robust high gain feedback system. The inverse is shown to be stable, and bounds on the tracking error are developed. Lyapunov stability methods are used to establish global stability of the inverse system.

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.

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