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However, highly detailed nonlinear electromagnetic and mechanical modeling must be performed to
                                 design high-performance MEMS. Therefore, the research is concentrated on high-fidelity mathematical
                                 modeling, data intensive analysis, and nonlinear simulations, as well as control (design of control algo-
                                 rithms to attain the desired performance). The reported synthesis, modeling, analysis, simulation, opti-
                                 mization, and control concepts, tools, and paradigms ensure a cost-effective solution and can be used to
                                 guarantee rapid prototyping of high-performance state-of-the-art MEMS. It is often very difficult, and
                                 sometimes impossible, to solve a large array of nonlinear analysis and design problems for motion
                                 microdevices using conventional methods. Innovative concepts, methods, and tools that fully support
                                 the analysis, modeling, simulation, control, design, and optimization are needed. The fabrication tech-
                                 nologies used in MEMS were developed [2,3], and micromachining technologies are discussed in this
                                 chapter. This chapter solves a number of long-standing problems for electromagnetic-based MEMS.
                                 14.2 MEMS Motion Microdevice Classifier
                                         and Structural Synthesis


                                 It was emphasized that the designer must design MEMS by devising novel high-performance motion
                                 microdevices, radiating energy microdevices, microscale driving/sensing circuitry, and controlling/pro-
                                 cessing ICs. A step-by-step procedure in the design of motion microdevices is:

                                     • define application and environmental requirements,
                                     • specify performance specifications,
                                     • devise motion microstructures and microdevices, radiating energy microdevices, microscale driv-
                                       ing/sensing circuitry, and controlling/processing ICs,
                                     • develop the fabrication process using micromachining and CMOS technologies,
                                     • perform electromagnetic, energy conversion, mechanical, and sizing/dimension estimates,
                                     • perform  electromagnetic, mechanical, vibroacoustic, and thermodynamic design with performance
                                       analysis and outcome prediction,
                                     • verify, modify, and refine design with ultimate goals and objectives to optimize the performance.
                                 In this section, the design and optimization of motion microdevices is reported.
                                   To illustrate the procedure, consider two-phase permanent-magnet synchronous slotless microma-
                                 chines as documented in Fig. 14.1.
                                   It is evident that the electromagnetic system is endless, and different geometries can be utilized as
                                 shown in  Fig. 14.1.  In  contrast,  in translational (linear) synchronous micromachines,  the open-ended
                                 electromagnetic system results. The attempts to classify microelectromechanical motion devices were
                                 made in [1,4,5]; however, the qualitative and quantitative comprehensive analysis must be researched.
                                   Motion microstructure geometry and electromagnetic systems must be integrated into the synthesis,
                                 analysis, design, and optimization. Motion microstructures can have the plate, spherical, torroidal, conical,
                                 cylindrical, and asymmetrical geometry. Using these distinct geometry and electromagnetic systems,
                                 we propose to classify MEMS. This idea is extremely useful in the study of existing MEMS as well as in
                                 the synthesis of an infinite number of innovative motion microdevices. In particular, using the possible
                                 geometry and electromagnetic systems (endless,  open-ended, and  integrated), novel high-performance
                                 MEMS can be synthesized.
                                   The basic electromagnetic micromachines (microdevices) under consideration are direct- and alternating-
                                 current, induction and synchronous, rotational and translational (linear). That is, microdevices are classified
                                 using a type classifier
                                                                  Y =  { y : y ∈  Y}

                                   Motion microdevices are categorized using a geometric classifier (plate  P, spherical  S, torroidal  T,
                                 conical N, cylindrical C, or asymmetrical A geometry) and an electromagnetic system classifier (endless
                                 E, open-ended O, or integrated I). The microdevice classifier, documented in Table 14.1, is partitioned

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