Illustrazione opzionale qui in mezzo? (meglio se su fondo bianco) ESEMPIO DI PRESENTAZIONE POWERPOINT PER TESI DI LAUREA – SCRIVERE TITOLO QUI Candidato Luigi Serbelloni Mazzanti Relatore Prof. Luigi Tizio Correlatori Prof. Pino Tizio Ing. Gino Tizio Illustrazione opzionale qui in mezzo? (meglio se su fondo bianco)
Introduzione Nota: allego una dozzina di slide come esempio di PPT con foto/etc. Multiple clearances: a numerical challenge… Dry friction model Rigid body assumption Formulation as vector-measure differential inclusions Solution by means of Second-Order Cone Complementarity Problem
Introduzione Clearances with dry friction sometimes are unavoidable: Cheap devices: Printers Home appliances … Sturdy, rough mechanisms: firearms, earth-moving machines harvesting machines
Known approaches Smooth ODE with deformable kinematic pairs (ex. Hertz theory, FEM, regularization, etc.) Problems: - computationally expensive - knowledge of material/geometry Non-smooth dynamics with piece-wise integration (stop-and-restart schemes) Problems: multiple contacts?
Our approach Assumptions: - multi-rigid-body model - N point-like contacts in clearances - Coulomb dry friction model Kinematic pairs with clearances: set of unilateral contacts with friction
Signorini’s complementarity condition Revolute joints In three dimensional case: Signorini’s complementarity condition
Prismatic joint For the three dimensional case, at most 16 unilateral contacts For all the edge-pairs, (l1, e4) (l1, e1) (l2, e1) (l2, e2) (l3, e2) (l3, e3) (l4, e3) (l4, e4) (l1, e8) (l1, e5) (l2, e5), (l2, e6) (l3, e6) (l3, e7) (l4, e7) (l4, e8) :
Contact model For each contact pair: Vectors w and u from Gram-Schmidt Friction force: Coulomb friction as maximum-dissipation principle (from Kuhn-Tucker form):
Eccetera eccetera… Modificare / inserire slide a piacimento Usare liste con punti tipo questa quando possibile Preferire immagini a descrizioni testuali Meglio tante slide semplici piuttosto che poche complesse Eccetera eccetera Bla bla Etc.
Conclusioni Pochi punti qui.. (sintetizzare principali conclusioni) Bla bla… Bla bla.