A Friction Model for Non-Singular Complementarity Formulations for Multibody Systems With Contacts

2017 ◽  
Author(s):  
Albert Peiret ◽  
József Kövecses ◽  
Josep M. Font-Llagunes
Keyword(s):  
Multibody Systems ◽  
Iterative Algorithms ◽  
Full Rank ◽  
Linear Complementarity ◽  
Friction Model ◽  
Physical Problem ◽  
The Other ◽  
Dynamics Of Multibody Systems ◽  
Friction Models ◽  
Coulomb Model

The dynamics of multibody systems with many contacts are frequently formulated as a Linear Complementarity Problem (LCP), for which several direct or iterative algorithms are available to solve it efficiently. These formulations rely on discretized friction models that approximate the friction cone of the Coulomb model to a pyramid. However, they produce rank-deficient LCPs even though the physical problem does not have constraint redundancy and has a unique solution. Here, a new discretized friction model is presented which results in an LCP formulation with a full-rank lead matrix. This model relies on an inertial term to couple the equations of the model, which behaves as close to the Coulomb model as the other discretized models. Moreover, it is shown through some simulations that some algorithms can be used with this formulation, which could not be used with the other rank-deficient LCP formulations.

A Regularized Contact Model for Multibody System Simulation

2016 ◽  
Author(s):  
Albert Peiret ◽  
Farnood Gholami ◽  
József Kövecses ◽  
Josep M. Font-Llagunes
Keyword(s):  
Multibody Systems ◽  
Large Scale ◽  
Multibody System ◽  
Linear Complementarity Problems ◽  
Friction Model ◽  
Computational Performance ◽  
Unilateral Contacts ◽  
Wheel Model ◽  
Friction Models ◽  
Coulomb Model

Simulation of large-scale multibody systems with unilateral contacts requires formulations with which good computational performance can be achieved. The availability of many solver algorithms for Linear Complementarity Problems (LCP) makes the LCP-based formulations a good candidate for this. However, considering friction in contacts asks for new friction models compatible with this kind of formulations. Here, a new, regularized friction model is presented to approximate the Coulomb model, which allows to formulate the multibody system dynamics as a LCP with bounds. Moreover, a bristle approach is used to approximate the stiction force, so that it improves the numerical behaviour of the system and makes it able to handle redundancy coming from the friction interfaces. Several examples using a 3D wheel model has been carried out, and the proposed friction model shows a better approximation of the Coulomb model compared to other LCP-based formulations.

Ensemble Grey and Black-box Nonlinear System Identification of a Positioning System

2020 ◽  
Author(s):  
Walisson Chaves Ferreira Pinto ◽  
Helon Vicente Hultmann Ayala
Keyword(s):  
Nonlinear System ◽  
Nonlinear System Identification ◽  
Viscous Friction ◽  
Black Box ◽  
Friction Model ◽  
Model Construction ◽  
Ensemble Model ◽  
Positioning System ◽  
Friction Models ◽  
Coulomb Model

In this work, grey and black-box approaches are used in order to model a electromechanical positioning system (EMPS). An ensemble model is then constructed by combining these two approaches, by using the predictions of both models in order to generate an improved estimated output. Four friction models, in their symmetric and asymmetric versions,namely (i) Coulomb model with finite slope at zero velocity and viscous friction, (ii) Coulomb model with viscous friction, (iii) Tustin friction model, (iv) Coulomb model with viscous friction and Stribeck effect were used to describe the dynamic behavior of the EMPS. The results have shown that the combination of grey and black-box models was able to perform better than the grey-box model and that the proposed friction models are also able to improve the relativeerror. This encourages further research on the application of the concept of ensemble model construction from machine learning to the nonlinear system identication context towards more accurate model construction.

A Fast Algorithm for Contact Dynamics of Multibody Systems Using the Box Friction Model

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Farnood Gholami ◽  
Mostafa Nasri ◽  
József Kövecses ◽  
Marek Teichmann
Keyword(s):  
Complementarity Problem ◽  
Multibody Systems ◽  
Friction Model ◽  
Contact Dynamics ◽  
Redundant Constraints ◽  
Solution Algorithms ◽  
Mixed Complementarity Problem ◽  
Dynamics Of Multibody Systems ◽  
Novel Approach ◽  
Mixed Linear Complementarity Problem

One of the major challenges in dynamics of multibody systems is to handle redundant constraints appropriately. The box friction model is one of the existing approaches to formulate the contact and friction phenomenon as a mixed linear complementarity problem (MLCP). In this setting, the contact redundancy can be handled by relaxing the constraints, but such a technique might suffer from certain drawbacks, specially in the case of large number of redundant constraints. Most of the common pivoting algorithms used to solve the resulting mixed complementarity problem might not converge when the relaxation terms are chosen as small as they should be. To overcome the aforementioned shortcoming, we propose a novel approach which takes advantage of the sparse structure of the formulated MLCP. This novel approach reduces the sensitivity of the solution of the problem to the relaxation terms and decreases the number of required pivots to obtain the solution, leading to shorter computational times. Furthermore, as a result of the proposed approach, much smaller relaxation terms can be used while the solution algorithms converge.

scholarly journals A Review on the Application of Friction Models in Wheel-Rail Adhesion Calculation

2021 ◽  
Vol 7 (1) ◽  
pp. 1-11
Author(s):  
Zewang Yuan ◽  
Mengling Wu ◽  
Chun Tian ◽  
Jiajun Zhou ◽  
Chao Chen
Keyword(s):  
Structural Characteristics ◽  
Critical Role ◽  
Exponential Model ◽  
Friction Model ◽  
Rational Model ◽  
Friction Behavior ◽  
Normal Forces ◽  
Interface Modeling ◽  
Friction Models ◽  
Coulomb Model

AbstractFriction is the bond linking the tangential and normal forces at the wheel-rail interface. Modeling friction is the precondition for the wheel-rail adhesion calculation. In this work, the critical role of friction in the calculation of wheel-rail adhesion is discussed. Four types of friction models (Coulomb model, linear model + Coulomb model, rational model and exponential model) which are commonly used for the calculation of wheel-rail adhesion are reviewed, in particular with regard to their structural characteristics and application state. The adhesion coefficients calculated from these four friction models using the Polach model are analyzed by comparison with the measured values. The rational model and the exponential model are more flexible for defining the falling friction, and the adhesion coefficient calculated by these two models is highly consistent with the measured one. Though the rational model and exponential model describe the falling friction well, the existing friction models are not applicable for calculating adhesion after considering more realistic factors, such as thermal effect, contaminants and so on. Developing a novel and practical friction model to accurately describe the wheel-rail friction behavior is still an essential but challenging and significant task. This review provides a reference for the selection of existing friction models and generates fresh insights into developing novel and practical friction models.

scholarly journals Massive Parallelization of Multibody System Simulation

10.14311/1686 ◽  
2012 ◽  
Vol 52 (6) ◽  
Author(s):  
Michael Valášek ◽  
Ladislav Mráz
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
The Other ◽  
Algebraic Equations ◽  
Simultaneous Solution ◽  
Cpu Time ◽  
Dynamics Of Multibody Systems ◽  
Linear Algebraic Equations ◽  
Multiple Processors ◽  
Massive Parallelization

This paper deals with the decrease in CPU time necessary for simulating multibody systems by massive parallelization. The direct dynamics of multibody systems has to be solved by a system of linear algebraic equations. This is a bottleneck for the efficient usage of multiple processors. Simultaneous solution of this task means that the excitation is immediately spread into all components of the multibody system. The bottleneck can be avoided by introducing additional dynamics, and this leads to the possibility of massive parallelization. Two approaches are described. One is a heterogeneousmultiscale method, and the other involves solving a system of linear algebraic equations by artificial dynamics.

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.

Modeling of Piezo-Actuated Stick-Slip Micro-Drives: An Overview

2012 ◽  
Vol 81 ◽  
pp. 39-48 ◽  
Author(s):  
Ha Xuan Nguyen ◽  
Christoph Edeler ◽  
Sergej Fatikow
Keyword(s):  
Mechanical Model ◽  
Integrated Model ◽  
Friction Model ◽  
Fundamental Importance ◽  
Future Research ◽  
Stick Slip ◽  
Research Activities ◽  
Model Combining ◽  
Friction Models

This paper gives an overview about problems of modeling of piezo-actuated stick-slip micro-drives. It has been found that existing prototypes of such devices have been investigated empirically. There is only few research dealing with the theory behind this kind of drives. By analyzing the current research activities in this field, it is believed that the model of the drive depends strongly on the friction models, but in most cases neglecting any influences of the guilding system.These analyses are of fundamental importance for an integrated model combining friction model and mechanical model offering promising possibilities for future research.

On Slip Inception and Static Friction for Smooth Dry Contact

2014 ◽  
Vol 81 (12) ◽  
Author(s):  
Xi Shi
Keyword(s):  
Shear Strength ◽  
Contact Area ◽  
Material Properties ◽  
Static Friction ◽  
Friction Model ◽  
Interfacial Bonding ◽  
The Other ◽  
Material Failure ◽  
Bonding Failure ◽  
Dry Contact

Slip inception mechanism is very important for modeling of static friction and understanding of some experimental observations of friction. In this work, slip inception was treated as a local competence of interfacial bonding failure and weaker material failure. At any contacting point, if bond shear strength is weaker than softer material shear strength, slip inception is governed by interfacial bonding failure. Otherwise, it is governed by softer material failure. Considering the possible co-existence of these two slip inception mechanisms during presliding, a hybrid static friction model for smooth dry contact was proposed, which indicates that the static friction consists of two components: one contributed by contact area where bonding failure is dominant and the other contributed by contact area where material failure is dominant. With the proposed static friction model, the effects of contact pressure, the material properties, and the contact geometry on static friction were discussed.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

Sign in / Sign up

Export Citation Format

Share Document