Nonlinear viscoelastic modelling of stylus probing for surface metrology

This paper presents a nonlinear viscoelastic methodology for modelling probe–surface interactions and so explores the signal fidelity in stylus based surface metrology. A novel model is introduced to simulate the nonlinear contact behaviour between the stylus tip and the measured surface. After briefly describing existing models of contact between solid bodies, a modified nonlinear viscoelastic contact model is introduced into the dynamic modelling of the stylus instrument. Based on this model, two scanning modes, i.e., raster scanning and spiral scanning, have been examined for high-speed measurement of a circular sinusoidal XY grid. The tip flight and residual vibrations associated with start-up transients are shown to have potentially serious effects on the signal fidelity during fast surface scanning. The effects of the scanning speed and direction have been investigated to show the influences of the scanning methodologies on the measurement. It is demonstrated that the spiral scanning methodology has inherent advantages for fast scanning with acceptable measurement accuracy.