ixandstiffnessmatrix AsanexampleinthefiniteelementmodelinFig.1,theblackdotsrepresentnodes,andeach nodehasthreeCartesiantranslationaldisplacementsandtworotations.Thepulleyismodeledasa rigiddisk,thebearingspacerasabarelement,andthenutandsleeveasalumpedmass.The spindleinthiscasehastwofrontbearingsintandemandthreebearingsintandemattherear.The fivebearingsareinoverallback-to-backconfiguration.Thetoolisassumedtoberigidly connectedtothetoolholderwhichisfixedtothespindleshaftrigidlyorthroughspringswith stiffnessinbothdirectionstranslationandrotation.Theflexibilityofthespindlemountinghasto bereflectedinthemodelofthespindle-machinesystem.Springsarealsousedbetweenthespindle housingandspindlehead,whosestiffnessisobtainedfromexperience. Fig.1.Thefiniteelementmodelofthespindle-bearing-machine-toolsystem
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