Development of A New Type of 2-DOF Piezo-Actuated Pseudo-Decoupled Compliant Mechanism for Elliptical Vibration Machining

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.

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

“…Unfortunately, this type of 2-DOF PDCM with nonbisymmetrical structures will inevitably cause adverse cross-coupling motions that must be removed to the best extent possible, further improving the precision of 2-DOF PDCMs in tracking elliptical trajectories. Motivated by the above reasons, we previously developed a sort of pseudo-decoupling 2-DOF PDCM that adopted a non-orthogonally decoupling configuration to improve the tracking precision of elliptical trajectories [20], as shown in Figure 1b. The innovation of the above 2-DOF PDCM lies in two decoupling LSFMs that are non-perpendicularly configured with an optimal decoupling angle (Θ ≥ 90 • ) instead of the perpendicular configuration (Θ = 90 • ) in conventional 2-DOF PDCMs.…”

“…It is very important to note that the coupling coefficient ω is a small negative value, which means that an input actuated motion along the positive X-direction will slightly cause an output cross-coupling motion along the negative Y-direction, and As shown in Figure 6, both the arithmetic average deviation ξ av and root mean squared deviation ξ rm exhibited a non-monotonic correlation with motion amplification coefficient κ and coupling coefficient ω, but the amplification coefficient κ presented a stronger influence on error deviation ξ av and ξ rm than the coupling coefficient ω, which distinctly indicates that this actually adopted 2-DOF PDCM had the optimum amplification coefficient and coupling coefficient (κ = 1.0328 and ω = −0.0732); corresponding error deviations were ξ av = 2.20 × 10 −4 µm and ξ rm = 2.60 × 10 −4 µm. However, the amplification coefficient κ and coupling coefficient ω both had relatively low values, which was because the structural dimensions of this adopted 2-DOF PDCM were strictly optimized in previous research [20]. It is very important to note that the coupling coefficient ω is a small negative value, which means that an input actuated motion along the positive X-direction will slightly cause an output cross-coupling motion along the negative Y-direction, and vice versa.…”

“…As shown in Figure 6, both the arithmetic average deviation ξav and root mean squared deviation ξrm exhibited a non-monotonic correlation with motion amplification coefficient κ and coupling coefficient ω, but the amplification coefficient κ presented a stronger influence on error deviation ξav and ξrm than the coupling coefficient ω, which distinctly indicates that this actually adopted 2-DOF PDCM had the optimum amplification coefficient and coupling coefficient (κ = 1.0328 and ω = −0.0732); corresponding error deviations were ξav = 2.20 × 10 −4 μm and ξrm = 2.60 × 10 −4 μm. However, the amplification coefficient κ and coupling coefficient ω both had relatively low values, which was because the structural dimensions of this adopted 2-DOF PDCM were strictly optimized in previous research [20]. It is very important to note that the coupling coefficient ω is a small negative value, which means that an input actuated motion along the positive X-direction will slightly cause an output cross-coupling motion along the negative Y-direction, and As shown in Figure 6, both the arithmetic average deviation ξ av and root mean squared deviation ξ rm exhibited a non-monotonic correlation with motion amplification coefficient κ and coupling coefficient ω, but the amplification coefficient κ presented a stronger influence on error deviation ξ av and ξ rm than the coupling coefficient ω, which distinctly indicates that this actually adopted 2-DOF PDCM had the optimum amplification coefficient and coupling coefficient (κ = 1.0328 and ω = −0.0732); corresponding error deviations were ξ av = 2.20 × 10 −4 µm and ξ rm = 2.60 × 10 −4 µm.…”

“…In particular, these two PDC-based and EPC-based methods can guarantee that the EVM devices comprised of 2-DOF PDCMs strictly track our desirable elliptical trajectories with arbitrary motion parameters, but this does not mean that the intrinsic cross-coupling motions of PDCMs can be completely eliminated, thus can only be called a "pseudo-decoupling" method. Compared with our previous study on pseudo-decoupling compliant mechanisms with non-orthogonal substructures [20], these two new types of pseudo-decoupling methods can be directly applied to almost all conventional 2-DOF PDCMs without designing any extra decoupling substructures. In consideration of the involved issues in these two new pseudo-decoupling methods, the remainder of this research will be divided into several main sections as follows.…”

Design and Modeling of a Curved Beam Compliant Mechanism with Six Degrees of Freedom

“…Due to advantages such as no requirement for lubrication, no backlash, and less assembly [1][2][3][4][5], compliant mechanisms are widely used in the fields of precision processing, biological cell manipulation, microelectronics and micro-/nano-manipulation [6][7][8][9][10]. The demand of multi degrees of freedom leads to the structure of compliant mechanism becoming increasingly complex.…”