This work presents an approach for evaluating the cavitating conditions encountered in the lateral lubricating interfaces which exist between floating lateral bushings and gears in external gear machines (EGMs). Previous work in the authors’ research team had resulted in the development of a full fluid-structure-interaction (FSI)-EHD lubricating model for the lateral lubricating gaps, which was also validated against experiments. However, such a model uses a very simplified and approximate approach to consider aeration or cavitating conditions in the lubricating gap, where the pressures are simply saturated to a constant minimum value during their solution whenever they cross a minimum threshold. This subsequently results in numerically unstable predictions of pressure when substantial cavitating regions are encountered while also violating mass conservation laws.
To overcome these issues, this paper presents a stable mass conserving cavitation algorithm by implementing the universal Reynolds equation in the existing FSI-EHD model which is applicable for both full film and cavitating conditions and has been found to be applicable in several other tribological interfaces. Such a method offers to predict the onset and shape of the cavitating regions without the need for considering complex bubble dynamics. After outlining the formulation and implementation of the new cavitation algorithm, this paper also presents simulations of a commercially available EGM, where using this cavitation algorithm was found to predict realistic pressure distributions in the lubricating interface while also maintaining the stability of such a complex lubricating gap model for EGMs.
Algebraic dichotomies with an application to the stability of Riemann solutions of conservation laws
