InternationalJournalofMechanicalSciences44(2002)1999–2023ModiÿedslabanalysisofasymmetricalplaterollingM.Salimia,F.Sassanib;∗aDepartmentofMechanicalEngineering,IsfahanUniversityofTechnology,IslamicRepublicofIranbDepartmentofMechanicalEngineering,UniversityofBritishColumbia,Vancouver,BC,CanadaV6T1Z4Received1August2000;receivedinrevisedform13May2002AbstractInthispaperthegeneralcaseofasymmetricalplanestrainrollingduetounequalrolldiameter,unequalsurfacespeedoftherollsanddi*erentcontactfrictionisconsidered.Ananalyticalmodelbasedontheslabmethodofanalysiswasusedandfurtherdevelopedtoobtainthecharacteristicsofasymmetricalsheetrollingandtopredictstripcurvature.Thismethoddescribesanenhancementtotherollingtheorywherefrictionbecomesanintegralpartofdeformationmechanicsintherollgap.Toverifythevalidityoftheproposedanalyticalmodel,theanalyticalrollingforce,torqueandcurvaturewerecomparedwithexperimentalandanalyticalresultsofotherinvestigators.Verygoodagreementsarefound.Capabilityaswellasthesimplicityoftheproposedmodelinpredictingmoreaccuratetheoreticalresultsfortherollingforce,torqueandcurvaturemakesitsuitablefortheonlinecontrolapplication.?2002ElsevierScienceLtd.Allrightsreserved.Keywords:Asymmetricalrolling;Curvature;Frictionfactor;Slabmethod1.IntroductionAsymmetricalplanestrainrollinginwhichtheradius,velocity,torqueorsurfaceroughnessofrollsmaybedi*erenthasbeenasubjectofinteresttoengineers.Whilethisformofrollingcano*erbeneÿtssuchaslowerrollingpressure,sometimesitcanalsobetroublesomeduetodevelopmentofstripcurvature,whichwouldleadtodimensionalinaccuraciesandmisalignment.Thedevelopmentofcurvaturemaycausedamagetothemillrollsandstandsinmultistagerolling.Apartfromsuchproblemsevenslightdevelopedcurvaturecancauseproductiondelaysduetothedi5cultyofslabre-entry.Inearlysingledrivemills,di*erentrolldiameterandsurfaceÿnishwereusedtoonlycontroltheproblemofcurlingupanddown.∗Correspondingauthor.0020-7403/02/$-seefrontmatter?2002ElsevierScienceLtd.Allrightsreser