Mechanical properties of rectangular flexure hinges

In the 1960s, due to the development of aerospace technology, to achieve a small range of deflection of the supporting structure, not only presents a high-resolution, further miniaturization required to have the characteristics of the structure. People go through all kinds of elastic supports After the experiment exploration, and gradually develop a variety of types of flexible hinge.
        Flexible hinge is a kind of precision transmission mechanism specific shape, from generation to date, much favored by researchers. 1965, Paros, who first published its circular flexible hinge design and development, and gives rigidity formulas. Smith et al. and Lobont iu, who used similar means to draw the oval flexible hinge (ellipt icalhinge) and having a fillet flexible hinge (corner-filleted hinge) mechanical expression.
        On this basis, a number of researchers to carry out research to optimize the design of a flexible hinge, flexible hinge work performance and behavior that may occur and design were predicted, including Furukawa et al., The two-dimensional flexible hinge bridge (bridge-type hinge) were analyzed, it was reduced to a spring structure;
        Xu, who used finite element simulation, the performance of the flexible hinge design were predictive analysis; Ryu in his doctoral thesis using the method of two-dimensional matrix bridge flexible hinges were modeled and analyzed the results with theoretical analysis The test results comparing the analytical error of less than 10%. Jae, who analyzed the effect of machining errors on the accuracy of the flexible hinge.
        The researchers further studied the performance overhead flexible hinge, wherein the flexible hinge mechanism part of the bridge right angle flexible hinge. In recent years, researchers have used the card's Law (Cast iglianops theorem) and other mechanical methods hinges round, oval hinge P flexibility and stiffness and other key performance parameters fillet has a flexible hinge in-depth study. Compared with other mechanical transmission mechanism such as gears, hinge mechanism, flexible hinge with a compact, smooth motion, without lubrication, zero delay, no gap resolution advantages, often with a piezoelectric element used in conjunction with other power conversion components, precision positioning stage, gyroscope printheads applications and are widely used.
        A commonly used form flexible hinge and Performance Comparison
        Currently typical flexible hinge is often used in piezo drive technology include right-angle (right angle) flexible hinge with fillet (corner-fi-lleted) of the hinge, oval (ellipse) flexible hinge and perfect circle (rightcircle) flexible hinge etc. These various types of flexible hinge has better features, there are some minor differences.
        Therefore it requires in-depth analysis of the performance of various types of flexible hinges, preferably for inchworm-type piezoelectric actuator working characteristics of flexible hinge structure for the same material parameters (65Mn), using the same boundary, load conditions, application MSC. PatranPNastran finite element software of the flexible hinge structure has been static simulation, deformation and stress distribution results.
        The simulation conditions are material 65Mn, hinge minimum thickness t = 1 mm, hinge length L = 10 mm, hinge width b = 7 mm; boundary conditions for the right of fixation; load conditions for the free end of the left middle 100 N. on the above results, Finishing the corresponding flexible hinge maximum deformation and maximum stress values ​​are shown in Table 1. In the same minimum cross section and load boundary conditions, rectangular flexible hinge deformation of the largest, in other words, two deformation and stress distribution unit typical flexible hinge of the structure of foreign diagram The most sensitive response to minor incentives.
        Deformation of several other flexible hinge according to the order of: a flexible hinge, elliptical flexure hinges and round flexible hinge having a fillet in the several typical flexible hinge structure, rectangular flexure hinge both for translational precision motion bending precision movement, but also in the reverse case work; moreover, easier to design and processing, and therefore more widely used in recent years in the field of ultra-precision positioning technology.
        Rectangular flexible hinge 2 space coordinate system
        According to research, based on the mechanical properties of rectangular flexible hinge analysis and study of flexible hinge structure model shown in Figure 3, the constraint is left bound for ease of analysis, make the following assumptions:
        (1) The material is homogeneous isotropic material;
        (2) material deformation, the internal strain - stress relationship is linear elastic and elastic deformation is relatively small;
        (3) hinge L is larger than the size of the parameters t and b, it can be thought of as a cantilever.
        3 Analysis of the mechanical properties of flexible hinge according to formula
        (4) at right angles to the flexible hinge structure for different size and other parameters on the mechanical properties of flexible hinges were analyzed.
        Analysis of the figures listed in the curve can be found: in the case of a flexible hinge sectional dimensions determine when to increase the effective length of the flexible hinge when its stiffness in all directions has a different degree of reduction, in other words, when the sensitivity of the flexible hinge deformation improved; in addition, by appropriately modifying other sizes flexible hinge may also increase the deformation sensitivity, but must meet the work requirements when using a flexible hinge spring-back action to achieve precise positioning, in addition to the requirements of a flexible hinge with good deformation sensitivity outside. but also have good stiffness.
        4 Conclusion
        The finite element simulation compares several common structure of the basic form of a flexible hinge deformation behavior, found that rectangular flexible hinge on the most sensitive to external stimuli, and therefore more suitable for micro and nano-level ultra-precision positioning.
        System derived rectangular flexible hinge space stiffness matrix, from the flexible hinge basic structure size, etc. The factors that influence rectangular flexible hinge stiffness properties, these work for in-depth analysis of the mechanical properties of flexible hinge in order to optimize the design of the piezoelectric drive mechanical structure, improve its overall performance has more important theoretical significance, the class structure in the form of a flexible hinge has some practical value in the micro-nano-precision positioning technology.