Fluid film pressure description in finite turbulent lubricated journal bearings by using the Warner’s theory

The purpose of this paper is to propose a method for the analytical description of the non-steady fluid film for the liquid-lubricated finite journal bearings operating in a fully developed turbulent regime. The analytical description takes in account a symmetrical rigid rotor supported on two lubricated journal bearings under the classical assumptions of the Reynolds theory. The proposed methodology represents an extension of the Warner’s approach and allows to solve analytically in approximate way the equation governing the distribution of pressure in the bearing oil gap and then to obtain the analytical expressions for the unsteady fluid film forces giving particular attention to their continuity in the entire definition domain, introducing original analytical functions called “jump function”. The proposed model allows not only to minimize the computation time without any significant loss of accuracy in the nonlinear dynamic analysis of rotors on turbulent journal bearings but also permits a better readability of the parameter effects on the system unsteady behavior.