Lateral forces on tapered pistons – An overview

Abstract

The purpose of this article is to contribute to a more comprehensive overview of the lateral force on tapered pistons. Numerical analyses are carried out to evaluate the lateral force on a piston; the flow rate through the clearance is also calculated. The range of parameters, namely, length-to-diameter ratio, the taper and the eccentricity, covers almost all the applications that appear in fluid power engineering. The pressure distribution obtained by difference equations is verified using an iteration convergence test. The lateral force is obtained applying Simpson’s integral to the obtained pressure. Using the dimensionless lateral forces obtained using finite mesh sizes, an evaluation of the dimensionless lateral force for an infinitely fine mesh size is made. The numerical results coincide well with experiments reported in the literature. An approximate function is shown by expressing the dimensionless force with an accuracy of about 3% for a region of the taper and the length/diameter ratio appearing frequently in practice. Four types of difference equations that are derived from the laminar flow equation are compared with respect to necessary iteration numbers and accuracy of the results.