Hydraulic locking-in spool-type valves: tapered clearances analysis

The paper deals with the analysis on the influence of geometrical characteristics on the locking force acting on spools in tapered clearances exposed to decentralizing pressure drops. An estimation is presented of the different results in locking force prediction deriving from the comparison of the 'classical' one-dimensional approach of flow and a more complex description represented by the Reynolds equation. A sensitivity analysis on the influence of clearance geometrical parameters is performed, showing the limits of application of the one-dimensional approach. Two non-dimensional geometric variables are identified, which can be adopted to define some polynomial corrective functions correlating one-dimensional results with more reliable two-dimensional solutions. The determination of the locking force can therefore be performed by an analytical process, involving the 'classical' one-dimensional solution and a polynomial correction which is a simple two-variable function of the clearance geometry. In comparison with results coming from the direct solution of the Reynolds equation, the process leads to errors confined within the range of a few per cent, considering clearances in a wide dimensional range representing a large amount of couplings actually encountered in hydraulic spool valves.