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Hydraulic gear pumps are used in a wide variety of machines, for example agricultural and construction vehicles, and airplanes, to provide flexible power from the engine to lifting gear or ancillary equipment. The pump under investigation here forms part of the power steering mechanism of an agricultural tractor. As shown in Fig. 1, it consists of a drive gear and a driven gear which sit in two bearing blocks, floating within a housing, with a flange plate on one side and a cover on the other to press the blocks onto the gears.
To improve the engineering design, the manufacturer wished to investigate how the many geometrical aspects of the components and their relative positions influence leakage of the hydraulic fluid around the internal components. The physical phenomenon underlying the leakage process is very complicated, primarily because of the flexing of components under high pressure, and the dynamical motion of the gears in oil. Thus no mathematical model is available to predict leakage accurately, and consequently experiments on a software model (for example, Aslett et al., 1998) are not an option for this type of study. Real prototypes must be used which incur costs of manufacture, measurement and testing, and lead to restrictions on experiment size. The final part of the manufacturing process involves running the pump so that the gears cut into the bearing blocks, creating a seal against oil leakage. This bedding-in process creates an additional restriction as it changes features of the components of a completed pump so that its components cannot be re-used in another prototype.
As a first attempt to experiment on the pump, a small pilot study was planned to establish laboratory testing procedures, and to gain some insights into how the leakage might arise. In this study only features related to the drive gear, the driven gear and the two bearing blocks (known collectively as the gear pack) were varied, and all other features were held constant. A sample of components, sufficient to make twelve pumps, was available. The relevant dimensions of these components were carefully measured, and a design was then needed to specify which components should be selected and assembled to make each of the twelve pumps. Although the specific reasons for leakage occurring are not known, the engineers identified three possible leakage paths through the pump. For each path a derived factor (side gap, clearance and gear form) was defined giving the size of the path as an explicit formula in terms of the geometrical dimensions of the components. The clearance is based on the difference between the diameter of the drive shaft and that of the journal bearing into which it fits, the gear form is a function of the profile of the gears, and the side gap corresponds to the size of the gaps between the gears and bearing blocks. An aim of the pilot study was to obtain information on which of these derived factors might be important for leakage so that more detailed follow-up experiments could be focussed on the appropriate leakage paths.
This paper was referenced here.