Optimal Design and Control of a z-Tilt Piezoelectric Based Nano-Scale Compensation Stage with Circular Flexure Hinges

The Taguchi method is widely used for the optimization of mechanical design and this study is used it in the design of a 2D circular flexure hinge for a z-tilt piezoelectric based nano-scale compensation stage. Maximum displacement of the stage is 16 μm at z-axis and ±30 arcsec at θx and θy. The most important design parameters for such a flexure hinge are minimal diameter, body height, and notch radius. The important requirements for the optimal design of a flexure hinge is that the z-tilt stage should have the highest possible natural frequency and the smallest coupling displacement. Simulation results show the nano-stage to have a higher natural frequency (626 Hz) and lower coupling displacement (0.032%). A kinematic model for the z-tilt stage has also been proposed in this study and the experimental results show the actual natural frequency of 510 Hz to be slightly lower than in the simulation. By keeping the angular displacement less than ±30 arcsec for z-tilt motion of the stage, the results of tracking experiments show a coupling displacement of 300 nm for the z-axis and 1 arcsec for θx while the θy tracked a sine wave of 1 Hz and an amplitude of 5 arcsec.