Stability Analysis of Spools with Imperfect Sealing Gap Geometries

Abstract

Spools in hydraulic valves are prone to sticking caused by unbalanced lateral forces due to geometric imperfections of their sealing lands. This sticking problem can be related to the stability of the coaxial spool position. Numerical methods are commonly used to study this behaviour. However, since several parameters can influence the spool stability, parametric studies become significantly computationally expensive and graphical analysis of the numerical results in multidimensional parameter space becomes difficult. 
 To overcome this difficulty, in this work, an analytical approach for studying the stability characteristics of the spool valve is presented. A Rayleigh-Ritz method is used for solving the Reynolds equation in an approximate way in order to determine an analytical expression for the lateral force on the sealing lands. This analytical expression allows stability analysis of the spool via analytical means which finally results in the expression of critical axial velocity which demarcates the regions of stable behaviour. Simplicity of the expression allows an immediate insight into the role of design parameters in the stability of the spool. To verify the analytical model, a numerical model for spool dynamics is developed in this work and the numerical results are found to match the analytical model in terms of the stability behaviour of the spool.