Stiffness of Machine Tool Joints: A Random-Process Approach

Abstract

A random-process surface model of elastically yielding asperities with a gaussian height distribution is proposed to represent the deflection of a machine tool joint. A passband of surface wavelengths taking part in the interaction is derived in terms of workpiece dimensions, material properties, and a plasticity criterion. The necessary moments of the surface power spectrum are computed from profile measurements on a lathe bed, and hence the stiffness of the joint between it and the saddle is calculated. Finally, theoretical predictions of the variation of stiffness with load are compared with published measurements on bolted joints. Good agreement is found for a rectangular planform; for other planforms agreement is reasonable at low preloads.