The Narrow Groove Analysis Revisited

The narrow groove analysis (NGA) as pioneered by Whipple [1] is a two-scale formulation with an infinitesimal micro-scale. Its shortcomings include: ambiguity in minimum required number of grooves, implied assumption of local incompressibility, violation of end conditions and omission of local squeeze effect. Alternative numerical computation methods of the finite-element or finite-volume type [2][3] to treat the problem with a finite number of grooves are at best very expensive because good designs tends to require a large number of grooves. In view that interest in inclined groove gas lubricated devices has intensified [3], a new two-scale formulation is presented here to consider a small but finite micro-scale. Cross-pattern profiles of pressure and induced transverse flux are presented for the entrance condition of a typical thrust bearing with eighteen spiral-grooves.