Oscillations Gaused by Solid Friction in a Hydraulic Driving System : 1st Report, In the Case of Maximum Static Friction Equal to Kinetic Friction without Slipping

Abstract

Oscillations caused by solid friction in hydraulic driving systems are treated theoretically. The system consists of a table lying on a rectilinear sliding surface, an actuater cylinder, a 4-way servo valve, a relief valve, an oil pump and so on. The solid friction force considered is assumed to vary with the relative sliding velocities between the table and sliding surface, namely the friction-velocity characteristic is given by a polygon having two straight line segments and the critical value of static friction is equal to the value of kinetic friction without slipping. The stick-slip motions of the table are analysed considering the 4-way valve pressure-flow characteristic, friction-velocity relation, oil compressibility and the sizes of the hydraulic driving elements. Several types of limit cycles and the regions in which they occur are shown in figures according to the parameters meotioned above. Lastly, the steady-state displacement waves of the table are described and the curves of amplitudes and their periods are given.