Static friction, differential algebraic systems and numerical stability

Chen, Jian; Schinner, Alexander; Matuttis, Hans‐Georg

doi:10.1016/j.phpro.2010.09.030

Cited by 7 publications

(3 citation statements)

References 8 publications

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“…[3,22,24], numerical stiffness and stability e.g. [1,6,9,43], etc. These problems are visible end discussed even in quite simple 1D, single-mass discrete systems.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Simulation of the Automated Lane Change Process, Taking Into Account Freeplay and Friction in the Vehicle Steering System

Żardecki

Gidlewski

Jáskiéwicz

et al. 2022

Preprint

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The paper reports rather unique research on the influence of freeplay and friction in the car steering mechanism on automatically controlled process of lane change. The developed controller algorithm was based on very simplified (and thus effective in on-line calculations) reference models of the car dynamics, obviously without taking into account the nonlinearities of its steering system. Extensive simulation investigations of the developed controller algorithm carried out in a very wide range of changes in road and operational conditions, with regard to two-axle medium-duty truck, confirmed its advantages. The research presented in this article concerns the unpublished area of analyzes concerning the sensitivity of the lane change controller to freeplay and friction occurring in the steering mechanism of a controlled car. Some results of the simulation tests turned out to be surprising The piecewise-linear luz(...) and tar (...) projections used in these studies to describe the freeplay and friction effects facilitated modeling and simulation calculations.

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“…[3,22,24], numerical stiffness and stability e.g. [1,6,9,43], etc. These problems are visible end discussed even in quite simple 1D, single-mass discrete systems.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Simulation of the Automated Lane Change Process, Taking Into Account Freeplay and Friction in the Vehicle Steering System

Żardecki

Gidlewski

Jáskiéwicz

et al. 2022

Preprint

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“…where V is the overlap volume of the particles and Y is the Young modulus [2,3]. We use particles with Y = 6.5 · 10 7 N/m 2 , and density = 1000kg/m 3 , which gives a theoretical sound velocity of the continuum material of c c = 254.951m/s.…”

Section: Introductionmentioning

confidence: 99%

“…The direction of the force is given by the weighted average of the intersection between the contacting polyhedra, see Ref. [2] for details. The definition with the characteristic length in eq.…”

Section: Introductionmentioning

confidence: 99%

Granular acoustics of polyhedral particles

Cheng

Chen

Matuttis

2013

AIP Conference Proceedings

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Abstract. Our previous time-of-flight studies with two-dimensional polygonal simulations and one-and three-dimensional experiments showed that the sound-velocity in granular materials in one and two dimensions is of the order of 10% of that of the bulk material, while in three dimensions with spherical beads, it is only of the order of one percent. The conclusion was that the force network in three dimensions leads to a reduction of the sound velocity compared to two dimensions. With our newly completed fully three dimensional discrete element method with polyhedral particles, we investigate the relation between particle shape, size dispersion and sound velocity. The force-law is able to reproduce the sound velocity of the bulk material for space-filling particle packings. We find that the sound velocities in polyhedral assemblies are about 3% to 5% of the bulk sound velocities. This means that the influence of the particle geometry on the contact is significant. Aggregates with particles with many surfaces show higher sound velocities than those with sharp edges. Additionally, solitonic waves were observed which propagated in front of the sound-waves, but only in a relatively short range.

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Numerical Integration of Ordinary Differential Equations

Matuttis

Chen

2014

Understanding the Discrete Element Method

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Static friction, differential algebraic systems and numerical stability

Cited by 7 publications

References 8 publications

Modeling and Simulation of the Automated Lane Change Process, Taking Into Account Freeplay and Friction in the Vehicle Steering System

Modeling and Simulation of the Automated Lane Change Process, Taking Into Account Freeplay and Friction in the Vehicle Steering System

Granular acoustics of polyhedral particles

Numerical Integration of Ordinary Differential Equations

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