Numerical Analysis of the Shaft Motion in the Journal Bearing of a Gear Pump

This paper describes a numerical analysis of the dynamics of the shaft in the journal bearing of a gear pump. The modulus and direction of the load is a function of the relative position of the gears, causing a precession motion around an equilibrium position. The mean load is the function of the working pressure of the gear pump. The numerical analysis presented in this paper combines the equation of motion of the journal-gear set, based on the linearization of the fluid film load, with calculation of the load due to the pressure distribution on the gears. The damping and stiffness coefficients for the motion equation are calculated with the distributions around the shaft of the pressure and its derivatives. These distributions are calculated from the Reynolds equations using an in-house 2D finite element code with quadrangular elements; the equation of motion is solved with a fifth-order Runge–Kutta scheme. The results provide the stabilized position of the shaft for certain conditions, and allow limitation of the working pressure and the angular velocity of the pump in order to minimize, or to avoid, metal-metal contact and consequent wear of material. The results are compared with experiments and previously reported numerical results.