The phase-plane analysis of sliding motion

Abstract

This paper is a report on an investigation of the stick-slip motion which can arise when a body slides along a machined surface, with or without lubrication, at low speeds. This type of motion is encountered in machine-tool practice and can cause serious deficiency in the accuracy and finish of machined surfaces. In any positioning system such a motion is unavoidable. The effect can be reduced by increasing the natural frequency of the driving spring-mass system. Working from the coefficient of friction-velocity relationship the phaseplane trajectory method indicates that as relative speed increases motion passes through the stick-slip region into a region of smooth movement and then at higher speeds into a region of oscillatory motion. The work was carried out on a modified lathe-bed 8 ft. long using loads of up to 500 lb. at speeds from 1/10 in./min up to 100 in./min using a variety of lubricants. Actual results are quoted and analysed for one typical set of conditions. From the experimental results a series of non-dimensional curves can be obtained from which optimum relationships between mass, stiffness and speed can be derived for smoothest motion.