Abstract
Currently, the elliptical vibration cutting/coining (EVC2) has been widely employed in fabricating various functional microstructure surfaces applied in many significant engineering fields. Therefore, for this study, a novel type of two-degree-of-freedom (2-DOF) piezoelectrically actuated pseudo-decoupled compliant mechanisms (PDCMs) with non-orthogonal decoupling structures, which can exactly generate the strict ellipse trajectories, was developed for improving the forming accuracies of the EVC2 microstructures. First, the compliance matrices of 2-DOF PDCMs were theoretically modeled using the popular finite beam-based matrix modeling (FBMM) and the matrix-based compliance modeling (MCM) methods, then finite element analysis (FEA) was adopted to verify the effectiveness of the built compliance model for the 2-DOF PDCM with arbitrary structure parameters. Second, the static FEA method was employed to systematically reveal the dependencies of the tracking accuracies of the elliptical trajectories on the decoupling structures of 2-DOF PDCMs. Moreover, their main dynamic performances were also investigated through the FEA-based harmonic response analysis and modal analysis. On these bases, the critical angle of the decoupling structure was optimally set at 102.5° so that the PDCMs had minimum shape distortions of the ellipse trajectories. Thirdly, a series of experiments was conducted on this PDCM system for practically investigating its kinematic and dynamic performances. The actual aspect ratio between the major axis and minor axis of the ellipse trajectory was approximately 1.057, and the first-order and second-order resonant frequencies were 863 Hz and 1893 Hz, respectively. However, the obtained testing results demonstrated well the effectiveness and feasibility of 2-DOF PDCM systems in precisely tracking the ellipse trajectories with different geometric parameters. Several critical conclusions on this study are summarized in detail in the final section of this paper.
Highlights
Elliptical vibration machining (EVM) has been extensively explored and applied in many significant fields, including the precise manufacturing of optical freeform surfaces and functional microstructure surfaces on various difficult-to-cut materials such as ferrous materials and carbide alloy [1,2,3,4,5,6]
In order to but strictly track the ellipse trajectories that have been widely applied in elliptical vibration cutting/coining (EVC2) processes for the manufacturing of various functional microstructure surfaces, a new type of two-degree-of-freedom (2-DOF) piezoelectrically actuated pseudo-decoupled compliant mechanism (PDCM) with non-orthogonal decoupling configurations was innovatively developed
The compliance model of the developed 2-DOF pseudo-decoupled compliant mechanisms (PDCMs) was theoretically built based on the finite beam-based matrix modeling (FBMM) and the matrix-based compliance modeling (MCM) method, the effectiveness of the built compliance model was verified using the finite element analysis (FEA) method
Summary
Elliptical vibration machining (EVM) has been extensively explored and applied in many significant fields, including the precise manufacturing of optical freeform surfaces and functional microstructure surfaces on various difficult-to-cut materials such as ferrous materials and carbide alloy [1,2,3,4,5,6]. The reported micro-/nanopositioning XY stages, micro-/nanomanipulators and grippers cannot be directly applied to the EVC2 processes due to certain apparent limitations, and the FTS mechanisms are too rigorous to be widely applied to the EVC2 processes because of their development difficulties Motivated by these potentials, this study aimed to develop a novel type of two-DOF piezo-driven pseudo-decoupled compliant mechanisms (PDCMs) to construct various elliptical vibration machining (EVM) systems by adopting the novel non-orthogonal decoupling substructures instead of the orthogonal configurations in traditional EVM mechanisms, which will greatly suppress or even eliminate the geometric distortions of elliptical trajectories. Ci denotes the compliance matrix of the i-th single micro-beam in its local coordinate, which has been proposed and widely employed in characterizing the elastic deformation behaviors of leaf-spring flexure hinges [24,25], as mathematically expressed by the equation below: Micromachines 2019, 10, x; doi: www.mdpi.com/journal/micromachines dx.
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