Mathematics – Classical Analysis and ODEs
Scientific paper
2006-06-19
Mathematics
Classical Analysis and ODEs
From a paper accepted for talk at AITC-AIT 2006, 5th International Congress on Tribology, Sept. 20-22, 2006, Parma University,
Scientific paper
In this paper we present a mathematical model for estimate the collapse time of a gas bubble in a vane of a oil gerotor pump. This amount of time cannot be greater of the total time spent by the pump for filling and then emptying out a vane in a single revolution, otherwise there is a loss of lubrication between internal and external gears. We assume that oil is incompressible and viscous, the bubble has a spherical shape and it is not translating into the external fluid. The analytical treatment of the model shows that the Navier-Stokes equations for the velocity field of the oil can be reduced to a single non linear ordinary differential equation for the variation in time of the bubble radius. The collapse time estimated by a numerical resolution of this equation and the collapse time calculated from an analytical resolution of the linearized equation are substantially equal.
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