Mathematical formulation of the film thickness in a multi-pad externally adjustable hydrodynamic bearing using the transformation technique

Instability problem of a hydrodynamic plain journal bearing at higher speeds is conventionally resolved by using the non-circular bearings. High speed precision rotating shafts demands accurate positioning of the journal centres. A multi-pad adjustable bearing is a non-circular bearing, provides a fine-tuning option of the journal centre by continuously changing the bearing profile. In the present study, the bearing has a configuration of four bearing pads that are adjustable both in the radial and tilt directions. The fluid film thickness profile is conventionally obtained using the trigonometric relations, which has computational limitations, especially in multi-pad adjustable bearings. In this investigation, the film thickness profile of a multi-pad adjustable bearing is mathematically formulated using the transformation technique. The results obtained are compared with those available in the literature for a similar bearing. The observation shows that transformation technique eliminates the projection approximation error present in the conventional technique.