A Novel Type of Pseudo-Decoupling Method for Two Degree-of-Freedom Piezoelectrically Driven Compliant Mechanisms Based on Elliptical Parameter Compensation

Abstract

At present, a large number of two-degree-of-freedom piezoelectrically driven compliant mechanisms (2-DOF PDCMs) have been widely adopted to construct various elliptical vibration machining (EVM) devices employed in precisely fabricating functional micro-structured surfaces on difficult-to-cut materials, which have broad applications in many significant fields like optical engineering and precision manufacturing. For a higher precision of conventional 2-DOF PDCMs on tracking elliptical trajectories, a novel type of pseudo-decoupling method is proposed based on phase difference compensation (PDC). With finite element analysis (FEA), the dependences of elliptical trajectory tracking precision on PDC angles will then be investigated for optimizing PDC angles under different elliptical parameters. As the modification of the PDC-based method, another type of pseudo-decoupling method will be improved based on elliptical parameter compensation (EPC) for much higher tracking precision, an amplification coefficient and a coupling coefficient will be introduced to mathematically construct the EPC-based model. A series of FEA simulations will also be conducted on a conventional 2-DOF PDCM to calculate the amplification and coupling coefficients as well as optimize the EPC parameters under four series of elliptical parameters. The tracking precision and operational feasibility of these two new pseudo-decoupling methods on four series of elliptical trajectories will be further analyzed and discussed in detail. Meanwhile, a conventional 2-DOF PDCM will be practically adopted to build an experimental system for investigating the pseudo-decoupling performances of an EPC-based method, the input and output displacements will be measured and collected to actually calculate the amplification coefficients and coupling coefficients, further inversely solving the actual input elliptical parameters with EPC. The error distances between the expected and experimental elliptical trajectories will also be calculated and discussed. Finally, several critical conclusions on this study will be briefly summarized.