On the reynolds equation and the load problem in lubrication: Literature review and mathematical modelling

In this chapter, we provide a literature review concerning the theory of hydrodynamic lubrication, especially applied to journal bearings. The device consists of an external cylinder surrounding a rotating shaft, both separated by a lubricant to prevent contact. In particular, we derive the fluid film thickness model for journal bearings, considering both the parallel and the misaligned case. The hydrodynamic Reynolds equation with cavitation phenomenon, through both Reynolds and Elrod-Adams models are fully derived in this chapter. Subsequently, we pose two suitable variational formulations for the hydrodynamic problem considering both cavitation models. In addition, we present the admissible range of misalignment angle projections for prescribed values of the shaft eccentricity and angular coordinate. Finally, we properly state the problem of a loaded misaligned journal bearing for stationary regime, considering the balance of force and torque components involved.