On the Occurrence Conditions of Stick-Slip Phenomena in a Hydraulic Driving System: 1st Report, In Case of Maximum Static Friction Equal to Kinetic Friction without Slipping

When the critical value of static friction is equal to the value of kinetic friction without slipping, oscillations caused by solid friction in a hydraulic driving system are treated theoretically. The system consists of a table lying on a rectilinear sliding surface, an actuater cylinder, a 4-way servovalve, a releaf valve, an oil pump and so on. The solid friction force considered is assummed to vary with the relative sliding velocities between the table and sliding surface. Namely, the frictionvelocity characteristic function is given by a polygon having two straight line segments. 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 which they occur are shown in figures according to the parameters mentiond above.