tailieunhanh - Mechanics of Microelectromechanical Systems - N.Lobontiu and E.Garcia Part 7

Tham khảo tài liệu 'mechanics of microelectromechanical systems - and part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 168 Chapter 3 The terms in the right-hand side of Eq. are the axial stiffnesses of the two compliant members taken with respect to their local frames their x-axes are parallel to their length dimensions . The spring stiffness about the out-of-the-plane motion the z-direction of the mass can be found by also using Fig. . A force F Z is applied at point 1 about the z-direction and the corresponding Ulz out-of-the-plane displacement can be determined by considering bending and torsion of the two compliant members. The z-direction stiffness of the half-model is which is valid when the two compliant segments are of constant crosssections. The whole folded-beam microspring is formed of two parallelconnection identical parts as the one sketched in Fig. and therefore the stiffness of the full microspring is KZ 2KZ Example In a folded-beam microsuspension the long legs cannot exceed a maximum length of 11 max 200 gm. What is the length of the short legs which would produce a specified stiffness Kx 60 N m of the microsuspension about the motion direction for a given rectangular crosssection and material properties w t 5 gm E 130 GPa Solution If the short leg length is connected to the length of the long leg as Figure Stiffness for a folded-beam suspension 3. Microsuspensions 169 2 cZ1 and for the given moment of inertia and Young s modulus the stiffness Kx depends on 11 and c as shown in Fig. . The stiffness Kx decreases with 11 and c increasing. For the values of lirnax and Kx the solution is c and therefore the length of the short leg is 12 188 gm. Example A sagittal suspension and a folded-beam spring can be inscribed within the same a x b rectangular area a 300 gm b 200 gm . What are their stiffnesses about the motion direction in the case both designs have the same cross-section of their compliant members Consider that Oi 15 and 11 213 for the sagittal spring and that 1 3 1 4 for the folded-beam suspension. Solution