Vibration analysis of stylus instrument for random surface measurement

This paper presents dynamic modeling and vibration analysis methodologies for investigating surface profile fidelity in stylus instruments, using a novel dynamic model that takes account of Hertzian contact stiffness between the stylus tip and surface. It briefly describes generation methods for modelling random surfaces and finite tips, which provide input for this nonlinear dynamic system. The influence of the damping ratio on the dynamic performance of the stylus instrument is examined and tends to confirm other recent work. The best combinations of signal fidelity and measurement speed occur with damping ratios considerably higher than conventionally used, mainly because the damping can suppress or delay tip flight. Residual vibrations associated with start-up transients are shown to have potentially serious effects on the signal fidelity. Hence, the responses of the stylus system to three typical velocity control signals are investigated. The normally used step control signal can generate relatively large residual vibration, while slope control and, even better, cycloidal control signal can suppress the residual vibration and guarantee the signal fidelity.