?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%2F270%2F&rft.title=Homogenization+of+the+Equations+Governing+the+Flow+Between+a+Slider+and+a+Rough+Spinning+Disk&rft.creator=Cargill%2C+D.&rft.creator=Fehribach%2C+J.&rft.creator=Lin%2C+T-S&rft.creator=Please%2C+Colin&rft.creator=Raymond%2C+C.&rft.creator=Schwendeman%2C+D.&rft.creator=Skorczewski%2C+T.&rft.creator=Tilley%2C+B.&rft.creator=Witelski%2C+T.&rft.creator=Wrobel%2C+J.&rft.creator=Wang%2C+J.&rft.creator=Zhang%2C+S.&rft.subject=Materials&rft.subject=Information+and+communication+technology&rft.description=We+have+analyzed+the+behavior+of+the+flow+between+a+slider+bearing+and+a+hard-drive+magnetic+disk+under+two+types+of+surface+roughness.+For+both+cases+the+length+scale+of+the+roughness+along+the+surface+is+small+as+compared+to+the+scale+of+the+slider%2C+so+that+a+homogenization+of+the+governing+equations+was+performed.%0D%0A%0D%0AFor+the+case+of+longitudinal+roughness%2C+we+derived+a+one-dimensional+lubrication-type+equation+for+the+leading+behavior+of+the+pressure+in+the+direction+parallel+to+the+velocity+of+the+disk.+The+coefficients+of+the+equation+are+determined+by+solving+linear+elliptic+equations+on+a+domain+bounded+by+the+gap+height+in+the+vertical+direction+and+the+period+of+the+roughness+in+the+span-wise+direction.%0D%0A%0D%0AFor+the+case+of+transverse+roughness+the+unsteady+lubrication+equations+were+reduced%2C+following+a+multiple+scale+homogenization+analysis%2C+to+a+steady+equation+for+the+leading+behavior+of+the+pressure+in+the+gap.+The+reduced+equation+involves+certain+averages+of+the+gap+height%2C+but+retains+the+same+form+of+the+usual+steady%2C+compressible+lubrication+equations.%0D%0A%0D%0ANumerical+calculations+were+performed+for+both+cases%2C+and+the+solution+for+the+case+of+transverse+roughness+was+shown+be+in+excellent+agreement+with+a+corresponding+numerical+calculation+of+the+original+unsteady+equations.&rft.date=2009&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%2F270%2F1%2FhitachiReport.pdf&rft.identifier=++Cargill%2C+D.+and+Fehribach%2C+J.+and+Lin%2C+T-S+and+Please%2C+Colin+and+Raymond%2C+C.+and+Schwendeman%2C+D.+and+Skorczewski%2C+T.+and+Tilley%2C+B.+and+Witelski%2C+T.+and+Wrobel%2C+J.+and+Wang%2C+J.+and+Zhang%2C+S.++(2009)+Homogenization+of+the+Equations+Governing+the+Flow+Between+a+Slider+and+a+Rough+Spinning+Disk.++%5BStudy+Group+Report%5D+++++