Convex optimization framework with drift control strategies for simulating joints with clearance and friction.
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| Title: | Convex optimization framework with drift control strategies for simulating joints with clearance and friction. |
|---|---|
| Authors: | Chaturvedi, Ekansh1 (AUTHOR) ekanshchat96@vt.edu, Sandu, Corina1 (AUTHOR), Sandu, Adrian2 (AUTHOR) |
| Source: | Mechanics Based Design of Structures & Machines. 2025, Vol. 53 Issue 5, p3842-3886. 45p. |
| Subjects: | Many-body problem, Granular flow, Quadratic programming, Flow simulations, Nonlinear programming, Multibody systems |
| Abstract: | The convex formulations of non-smooth dynamics (NSD) approach have been implemented successfully into many-body problems, such as granular material flow simulations. NSD for multibody-dynamics formulation results in a nonlinear programming problem because of additional constraint on quaternions. This study modifies the convex formulation into a framework for multibody systems applications dealing with joints with friction and clearances as well as ideal joints. This is achieved by: (1) Converting the existing formalism into canonical forms, which gives the advantage of utilizing advanced general-purpose convex optimization solvers. (2) Modifying the non-smooth integration scheme to preserve rotations, thus mitigating the drift. A detailed convexity analysis on the nonlinear formulation showed that variable step-size scheme makes the problem non-convex. Further, it was found that certain windows appear where step-size variation can be achieved without sacrificing the convexity. Based on the analysis, the NSD problem is reformulated as a canonical form quadratic programming (QP) problem. Then, a canonical second-order con-programming (SOCP) problem is presented for including friction in the joints with clearances. Furthermore, an analysis on state-of-the-art non-smooth integrator is presented which shows that the perceived drift is because of violation of normalization constraint on quaternions. Two strategies are derived for preserving the normalization constraint: Projection and Lie-integration on quaternions. The proposed methods are evaluated against state-of-the-art scheme using numerical experiments on a rigid pendulum with clearance. Further, the framework has been tested on a pendulum with ideal revolute joint, to establish the applicability of the framework on smooth, as well as, on non-smooth problems. [ABSTRACT FROM AUTHOR] |
| Copyright of Mechanics Based Design of Structures & Machines is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 184650839 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Convex optimization framework with drift control strategies for simulating joints with clearance and friction. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Chaturvedi%2C+Ekansh%22">Chaturvedi, Ekansh</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ekanshchat96@vt.edu</i><br /><searchLink fieldCode="AR" term="%22Sandu%2C+Corina%22">Sandu, Corina</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sandu%2C+Adrian%22">Sandu, Adrian</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mechanics+Based+Design+of+Structures+%26+Machines%22">Mechanics Based Design of Structures & Machines</searchLink>. 2025, Vol. 53 Issue 5, p3842-3886. 45p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Many-body+problem%22">Many-body problem</searchLink><br /><searchLink fieldCode="DE" term="%22Granular+flow%22">Granular flow</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+programming%22">Quadratic programming</searchLink><br /><searchLink fieldCode="DE" term="%22Flow+simulations%22">Flow simulations</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+programming%22">Nonlinear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Multibody+systems%22">Multibody systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The convex formulations of non-smooth dynamics (NSD) approach have been implemented successfully into many-body problems, such as granular material flow simulations. NSD for multibody-dynamics formulation results in a nonlinear programming problem because of additional constraint on quaternions. This study modifies the convex formulation into a framework for multibody systems applications dealing with joints with friction and clearances as well as ideal joints. This is achieved by: (1) Converting the existing formalism into canonical forms, which gives the advantage of utilizing advanced general-purpose convex optimization solvers. (2) Modifying the non-smooth integration scheme to preserve rotations, thus mitigating the drift. A detailed convexity analysis on the nonlinear formulation showed that variable step-size scheme makes the problem non-convex. Further, it was found that certain windows appear where step-size variation can be achieved without sacrificing the convexity. Based on the analysis, the NSD problem is reformulated as a canonical form quadratic programming (QP) problem. Then, a canonical second-order con-programming (SOCP) problem is presented for including friction in the joints with clearances. Furthermore, an analysis on state-of-the-art non-smooth integrator is presented which shows that the perceived drift is because of violation of normalization constraint on quaternions. Two strategies are derived for preserving the normalization constraint: Projection and Lie-integration on quaternions. The proposed methods are evaluated against state-of-the-art scheme using numerical experiments on a rigid pendulum with clearance. Further, the framework has been tested on a pendulum with ideal revolute joint, to establish the applicability of the framework on smooth, as well as, on non-smooth problems. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mechanics Based Design of Structures & Machines is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1080/15397734.2024.2438797 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 45 StartPage: 3842 Subjects: – SubjectFull: Many-body problem Type: general – SubjectFull: Granular flow Type: general – SubjectFull: Quadratic programming Type: general – SubjectFull: Flow simulations Type: general – SubjectFull: Nonlinear programming Type: general – SubjectFull: Multibody systems Type: general Titles: – TitleFull: Convex optimization framework with drift control strategies for simulating joints with clearance and friction. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chaturvedi, Ekansh – PersonEntity: Name: NameFull: Sandu, Corina – PersonEntity: Name: NameFull: Sandu, Adrian IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 15397734 Numbering: – Type: volume Value: 53 – Type: issue Value: 5 Titles: – TitleFull: Mechanics Based Design of Structures & Machines Type: main |
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