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In order to solve the problem of stylus vibration of the spherical capacitive probe with ultra-large aspect ratio, modal analysis of the stylus is done and optimal design of stylus structure is carried out. The Euler–Bernoulli Beam model is introduced to build the dynamic equation of lateral vibration of the stylus. Based on results of modal analysis and simulation, the first order natural frequency of the stylus is optimized to near 100 Hz, and the resolution of the probing sensor is improved from 20 nm to 4 nm with adoption of damping material.

Optimal design of spherical capacitive probe with ultra-large aspect ratio based on modal analysis