Đang chuẩn bị liên kết để tải về tài liệu:
Mechanics of Microelectromechanical Systems - N.Lobontiu and E.Garcia Part 4

Tham khảo tài liệu 'mechanics of microelectromechanical systems - n.lobontiu and e.garcia part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 78 Chapter 2 where h is the distance measured about the z-direction between the microcantilever and the xy detection plane. Figure 2.9 indicates the in-plane position of the attached mass. The torsion moment produced by the added mass is Fịzlịy Amgljy 2.39 such that the tip torsion angle is Figure 2.8 Experimental system for in-plane mass detection Figure 2.9 In-plane position of added mass 2. Microcantilevers microhinges microbridges 79 By coupling Eqs. 2.36 through 2.40 it is possible to determine the amount of deposited mass Am as well as its in-plane position defined by lix and liy. Example 2.4 Determine the added mass Am as well as its position lix and liy on a variable cross-section microcantilever when the tip slopes 0lx and 0iy and the deflection Ulz are known. Solution When the cross-section of the microcantilever is variable the tip slope ớiy which is given in Eq. 2.35 for a constant cross-section can be found by means of Castigliano s displacement theorem as 0 y AmgCị uz_My 2.41 where il Ci.U2-My ịx EIy x dx 2.42 hl is the compliance of the microcantilever portion which is comprised between the point of application of the deposited mass and the fixed root. In a similar manner the tip deflection can be expressed as U z Amg Cị UZ-1 Z lixCị uz My 2.43 where the new partial compliance is I C M ịx2 EIy x Jdx 2.44 hl The torsion-related tip slope is expressed as ớlx AtngljyCj fa_Mx 2-45 with the partial torsional compliance being ịdx í GIt x J 2.46 hl 80 Chapter 2 Equations 2.41 2.43 and 2.45 can be solved for the unknown amounts Am lix and liy by also employing Eqs. 2.42 2.44 and 2.46 . 2.2.2.2 Three Dimensional Force Detection in Atomic Force Microscopy Applications In atomic force microscopy AFM reading applications a microcantilever such as the one sketched in Fig. 2.10 is designed to determine the amounts of force that are applied on its tip about the x- y- and z-directions and thus describe read a three-dimensional variable geometry. The experimental .