A piezoelectric/elastic spring-coupled surface profiler

A piezoelectric element/elastic spring-coupled system is analyzed to simulate the mechanical and electrical characteristics of the surface profile probe. The coupled system includes a piezoelectric element with an elastic spring attached at the free end, and the spring is fixed at another end. The electro-elasticity theory is derived to formulate and solve the governing equations of the system. Two types of the piezoelectric element/elastic spring-coupled system are analyzed for the displacement, stress, resonant and anti-resonant frequencies, and with emphasis on the electromechanical coupling coefficient. Application of a d31-mode piezoelectric ceramic used as a surface profile probe is simulated for analysis of the frequency response, the resolution of displacement, and the contact force. Finally, a multilayered d33-mode piezoelectric ceramic/elastic spring-coupled specimen is constructed for experimental measurements. The agreement between theoretical and experimental results confirms the validity of the study.