White Light Interferometry of Elastohydrodynamic Lubrication of Foil Bearings

This paper describes an experiment performed to verify the one-dimensional model of elastic foil behavior developed by Stahl, White, and Deckert [ 11. In the experiment, a loop of tape one-inch wide passes over a stationary recording head, and the air-film thickness between the head and the foil is determined using white light interferometry. Measured data for various experimental conditions are compared with the predictions of the model and also with prior foil-bearing analyses. The influence of parameters such as tape thickness, head radius, tape tension, etc. on the nature of the spacing field is demonstrated. Introduction The desire to gain a better understanding of the phenomena associated with tape transport in magnetic recording is frequently cited as one of the main motivating factors in foil-bearing studies of the last two decades. The impact of this important application on the development of foil bearings continues because the technological requirements for recording on flexible media demand that these phenomena be even better understood and controlled. The trend toward higher recording bit densities and higher data transfer rates requires maller separation between head and tape and larger relative velocity between the two. Moreover, significant and rapid damage to the medium and undue wear of the head must be avoided, hence the importance of maintaining and controlling a suitable air film at the head-to-tape interface. The interaction between an elastic foil and a fluid film has been extensively studied in recent years. This effort has provided considerable insight into the behavior of foil bearings, but it has not been effectively applied to investigating the performance of noncircular heads and to wave propagation phenomena in tape. In an attempt to analyze such problems, Stahl, White, and Deckert [ I ] developed a model of the interaction between tape and fluid film that differs in a number of respects from conventional foil bearing studies. In [ I ] the undeflected straight-line configuration of the tape is used as a reference configuration, whereas in conventional approaches the coordinate system is attached to the surface of the cylindrical head. Conventional foil-bearing analyses employ asymptotic foil boundary conditions: the Stahl, White, and Deckert model, on the other hand, allows one to consider a finite piece of tape and to write appropriate conditions at each end. Finally, the time-dependent terms are an integral part of the formulation in [ I ] , whereas these terms are not usually present in conventional theory because it is mainly concerned with steadystate solutions. The intent of this paper is to present an experimental study that complements and verifies some aspects of the theory presented in [ I ] . In particular, we have focused our attention on comparing theory and experiment for the case of the steady-state separation between tape and head. Licht [ 2 ] and Ma [3] have provided such a comparison between conventional theory and experimental data. However, because conventional theory is concerned only with asymptotic boundary conditions, those authors did not provide some of the geometrical details which would be required if Stahl et al. were to simulate their experiments. Moreover, most of their tests would constitute a case of large penetration of the head into the tape; a situation for which the linearized theory of [ 1 3 is not particularly appropriate. As a consequence, it was decided to design an experiment that closely duplicates the conditions underlying the theoretical considerations in [ I ] .Another feature of the experimental investigations reported in the literature is that the conditions of the experiment lead to rather large separations between the foil and the head, usually greater than three pm. In 52 NOVEMBER 1974 WHITE LIGHT INTERFEROMETRk Power supplies Capstan motor -48V