Analytical Compliance Equations of Generalized Elliptical-Arc-Beam Spherical Flexure Hinges for 3D Elliptical Vibration-Assisted Cutting Mechanisms

Abstract

Elliptical vibration-assisted cutting technology has been widely applied in complicated functional micro-structured surface texturing. Elliptical-arc-beam spherical flexure hinges have promising applications in the design of 3D elliptical vibration-assisted cutting mechanisms due to their high motion accuracy and large motion ranges. Analytical compliance matrix formulation of flexure hinges is the basis for achieving high-precision positioning performance of these mechanisms, but few studies focus on this topic. In this paper, analytical compliance equations of spatial elliptic-arc-beam spherical flexure hinges are derived, offering a convenient tool for analysis at early stages of mechanism design. The mechanical model of a generalized flexure hinge is firstly established based on Castigliano's Second Theorem. By introducing the eccentric angle as the integral variable, the compliance matrix of the elliptical-arc-beam spherical flexure hinge is formulated. Finite element analysis is carried out to verify the accuracy of the derived analytical compliance matrix. The compliance factors calculated by the analytical equations agree well with those solved in the finite element analysis for the maximum error; average relative error and relative standard deviation are 8.25%, 1.83% and 1.78%, respectively. This work lays the foundations for the design and modeling of 3D elliptical vibration-assisted cutting mechanisms based on elliptical-arc-beam spherical flexure hinges.

Dynamic modeling and optimization of mechanical drift for compliant parallel micromanipulation driven by V-shape linear ultrasonic motors

“…Figure 5 shows a simplified force diagram of a flexure hinge. The compliance matrix of a flexure hinge can be obtained by the method in the literature [4], and its general form is…”

Modelling and performance analysis of a curvature-adjustable multiple-axis flexure hinge based on Bézier curve

“…Then, Wang et al have presented the compliance equations for the generalised elliptic-arc beam spherical flexure hinge. 34 Wei et al have derived the closed-form compliance equation for elliptic-revolute notch type multiple-axis flexure hinges. 35 Additionally, Wei et al have analysed the compliance and experimental principles of hybrid multiple-axis flexure hinges.…”

Ultra-Precision Manufacturing Technology for Difficult-to-Machine Materials

“…Additionally, Laiyun Song et al [ 7 ] analyzed the nonlinear dynamic characteristics of the hybrid air bearing-rotor system at ultra-high speeds and theoretically investigated the rotor trajectory and non-linear behavior. Han Wang et al [ 8 ] developed compliance equations for spatial elliptic-arc-beam spherical flexure hinges, providing a foundation for designing and modeling 3D elliptical vibration-assisted cutting mechanisms based on these hinges.…”