In this work, the authors have developed a mathematical model that simulates the run in of external gear pumps, as an useful tool in the optimization of this time-consuming process. The model calculates the wear profile of the case by enveloping the tip circle of the gears concerning all the run in steps. For each step, the positions of the gear centers are obtained by the equilibrium between pressure forces and torques due to the pressure distribution, meshing forces and hydrodynamic journal bearing reactions. The pressure distribution depends on the clearance between case and gears, so for each run in step, since the positions of the gear centers change, the pressure distribution is recalculated considering the wear profile obtained in the previous step. Besides, the model also estimates the quantity of material taken away in each step and it shows the effects of modifications in the run in parameters (time, pressure and speed). In particular, the simulation results indicate that a meaningful reduction of run in global time, can be obtained by increasing the duration of the steps that remove the greater part of material and by decreasing the duration of the other steps. This model is used by TRW Automotive Italia S.p.A. (section Automotive Pumps, Ostellato, Italy) to improve the run in process with good reduction in manufacturing-time.

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