{"paper":{"title":"Two-dimensional FrBD friction models for rolling contact","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A two-dimensional FrBD model for rolling contact eliminates sliding velocity via the Implicit Function Theorem and preserves passivity in its linear formulations for nearly all practical parameters.","cross_cats":[],"primary_cat":"physics.app-ph","authors_text":"Luigi Romano","submitted_at":"2026-01-11T08:50:45Z","abstract_excerpt":"This paper develops a comprehensive two-dimensional generalisation of the recently introduced Friction with Bristle Dynamics (FrBD) framework for rolling contact problems. The proposed formulation extends the one-dimensional FrBD model to accommodate simultaneous longitudinal and lateral slips, spin, and arbitrary transport kinematics over a finite contact region. The derivation combines a rheological representation of the bristle element with an analytical local sliding-friction law. By relying on an application of the Implicit Function Theorem, the notion of sliding velocity is then eliminat"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For the linear formulations, the analysis reveals that the model preserves passivity under almost any parametrisation of practical interest.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The derivation relies on the Implicit Function Theorem being applicable to eliminate sliding velocity, which requires the local sliding-friction law to satisfy suitable invertibility conditions that are not verified in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A two-dimensional dynamic friction model for rolling contact is obtained by generalizing the FrBD framework, combining a rheological bristle representation with an analytical sliding law, and using the Implicit Function Theorem to eliminate sliding velocity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A two-dimensional FrBD model for rolling contact eliminates sliding velocity via the Implicit Function Theorem and preserves passivity in its linear formulations for nearly all practical parameters.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6eb3c5febbcdbd3b3158723aad10e15e8dc65b71e4ab5bd3cba6818228c7885d"},"source":{"id":"2601.06811","kind":"arxiv","version":10},"verdict":{"id":"1cb21a47-dfce-4c9d-a40f-2d88214240ee","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T15:38:24.436674Z","strongest_claim":"For the linear formulations, the analysis reveals that the model preserves passivity under almost any parametrisation of practical interest.","one_line_summary":"A two-dimensional dynamic friction model for rolling contact is obtained by generalizing the FrBD framework, combining a rheological bristle representation with an analytical sliding law, and using the Implicit Function Theorem to eliminate sliding velocity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The derivation relies on the Implicit Function Theorem being applicable to eliminate sliding velocity, which requires the local sliding-friction law to satisfy suitable invertibility conditions that are not verified in the abstract.","pith_extraction_headline":"A two-dimensional FrBD model for rolling contact eliminates sliding velocity via the Implicit Function Theorem and preserves passivity in its linear formulations for nearly all practical parameters."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.06811/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"8ea66abbe43e3077a04ce9ed7c1c41f4df36d25f8cf1863b774eae8d8b79ed10"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}