?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F253%2F&rft.title=Shape+optimization+of+pressurized+air+bearings&rft.creator=Howell%2C+Peter&rft.creator=Kedzior%2C+M.&rft.creator=Kramer%2C+P.&rft.creator=Please%2C+Colin&rft.creator=Rossi%2C+Louis&rft.creator=Saintval%2C+W.&rft.creator=Salazar%2C+D.&rft.creator=Witelski%2C+T.&rft.subject=Materials&rft.subject=None%2FOther&rft.description=Use+of+externally+pressurized+air+bearings+allows+for+the+design+of+mechanical+systems+requiring+extreme+precision+in+positioning.+One+application+is+the+fine+control+for+the+positioning+of+mirrors+in+large-scale+optical+telescopes.+Other+examples+come+from+applications+in+robotics+and+computer+hard-drive+manufacturing.+Pressurized+bearings+maintain+a+finite+separation+between+mechanical+components+by+virtue+of+the+presence+of+a+pressurized+flow+of+air+through+the+gap+between+the+components.+An+everyday+example+is+an+air+hockey+table%2C+where+a+puck+is+levitated+above+the+table+by+an+array+of+vertical+jets+of+air.+Using+pressurized+bearings+there+is+no+contact+between+%E2%80%9Cmoving+parts%E2%80%9D+and+hence+there+is+no+friction+and+no+wear+of+sensitive+components.%0D%0A%0D%0AThis+workshop+project+is+focused+on+the+problem+of+designing+optimal+static+air+bearings+subject+to+given+engineering+constraints.+Recent+numerical+computations+of+this+problem%2C+done+at+IBM+by+Robert+and+Hendriks%2C+suggest+that+near-optimal+designs+can+have+unexpected+complicated+and+intricate+structures.+We+will+use+analytical+approaches+to+shed+some+light+on+this+situation+and+to+offer+some+guides+for+the+design+process.%0D%0A%0D%0AIn+Section+2+the+design+problem+is+stated+and+formulated+as+an+optimization+problem+for+an+elliptic+boundary+value+problem.%0D%0AIn+Section+3+the+general+problem+is+specialized+to+bearings+with+rectangular+bases.%0D%0ASection+4+addresses+the+solutions+of+this+problem+that+can+be+obtained+using+variational+formulations+of+the+problem.%0D%0AAnalysis+showing+the+sensitive+dependence+to+perturbations+(in+numerical+computations+or+manufacturing+constraints)+of+near-optimal+designs+is+given+in+Section+5.%0D%0AIn+Section+6%2C+a+restricted+class+of+%E2%80%9Cgroove+network%E2%80%9D+designs+motivated+by+the+original+results+of+Robert+and+Hendriks+is+examined.%0D%0AFinally%2C+in+Section+7%2C+we+consider+the+design+problem+for+circular+axisymmetric+air+bearings.&rft.date=2002&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F253%2F1%2Fibm01.pdf&rft.identifier=++Howell%2C+Peter+and+Kedzior%2C+M.+and+Kramer%2C+P.+and+Please%2C+Colin+and+Rossi%2C+Louis+and+Saintval%2C+W.+and+Salazar%2C+D.+and+Witelski%2C+T.++(2002)+Shape+optimization+of+pressurized+air+bearings.++%5BStudy+Group+Report%5D+++++