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Engineering Optimization Applications

Engineering Optimization Applications. 柯春旭 義守大學電機系 2010/5/21. Optimization Problem. Design and Fabrication of an Efficient Magnetic Microactuator. I Introduction II Efficient Magnetic Microactuator III Optimal Design of Efficient Magnetic Microactuator

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Engineering Optimization Applications

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  1. Engineering Optimization Applications 柯春旭 義守大學電機系 2010/5/21

  2. Optimization Problem

  3. Design and Fabrication of an Efficient Magnetic Microactuator I Introduction II Efficient Magnetic Microactuator III Optimal Design of Efficient Magnetic Microactuator IV Simulation of Magnetic Microactuator Using the Macromodel V Fabrication of Efficient Magnetic Microactuator

  4. Introduction • Magnetic microactuators have the advantages of - large force and large deflection - low driving voltage • Micromachined microactuators achieve the needs of - miniaturization, - mass production and low cost • Research activities of magnetic microactuator - design and fabrication - simulation and optimization • MEMS applications micromotors, microrelays, optics, printer.

  5. Permalloy plate Magnetic core Planar coils attractive force Study of Magnetic Microactuator • Magnetic microactuator • a micromachined electromagnet • as flux generator • a movable microstructure • with the magnetic material • magnetic field interacts with magnetic material to product a force, the microstructure displaced attractive and repulsive force

  6. force vs. coil number n Magnetic flux Study of Magnetic Microactuator • Planar coils • Basic design of electromagnet is only using planar • coils • The advantage • - easily fabricated • The drawbacks • - leakage flux results in low efficiency • - truns n increases, force approaches to a • constant

  7. Study of Magnetic Microactuator • External Flux • Using a non-micromachined external • magnetic field generator [6,10,23,24] • The advantage • - force effectively increases • The drawbacks • - filed generator is larger over all device • dimensions • - requiring additional assembling steps • - EM interference in array • Design of magnetic circuit Chang Liu, et al. Ranan A. Miller, et al.

  8. Magnetic Circuits • Three types: • 1. Spiral Type • The advantages • - coils are easily fabricated • - accurate line pitch and width • The drawbacks • - the resistance nonlinearly increases • - internal leakage flux, reduced by using • LIGA or high mr 7 layers Micropump, Ahn Microrelay, E. Fullin

  9. Magnetic Circuits • 2. Solenoid Type • The advantages • - the magnetic circuit is easily constructed • - easily achieving the desired shape of • microactuator • The drawbacks • - not suitable for the fine coil • - non-flat coil contacts raise the resistance, • increasing local high temperature 5 layers Microactuator, H. Ren, E. Gerhard Micropump, SADLER et al.

  10. Magnetic Circuits • 3. Meander Type • The advantages • - the magnetic circuit is easily constructed • - the coils are flat • The drawbacks • - not suitable for the fine coil • - non-flat core contacts increases magnetic reluctance, reducing the efficiency 5 layers Microrelay, Marc et al.

  11. Simulation of Magnetic Microactuator • Detailed knowledge of all of the magneto-structural effects is a prerequisite for effective and efficient design • Trying the simulation experiments only in hours instead of months, thus shorten the development cycle • Utilizing the optimization algorithm to achieve the optimal performances of the devices • Magneto-structural coupled problem

  12. Objectives (1)To design an efficient magnetic microactuator with the magnetic circuit. (2) To optimize the magnetic microactuator for applications. (3) To develop an efficient macromodeling techniques for dynamic coupled simulation of magnetic microactuator. (4) To realize the efficient magnetic microactuator with micromachining processes.

  13. Efficient Magnetic Microactuator with An Enclosed Core Improved Design pole area can optimally enlarge 1. Increasing the efficiency in producing magnetic force 2. Increasing the frequency of the microactuator 3. Increasing the rotation range. 4. Increasing the utilization area.

  14. Efficient Magnetic Microactuator with An Enclosed Core • Improved Design • 7 layers • - 2 coil layers • - 2 permalloy layers • - 3 insulators • Dimensions of coils • and plate are dependent • EM isolation

  15. L g p1 p2 c tp tc ti 800 20 0 - 400 0 – 400 0-400 5-50 5-30 40-60 Table 3.1 The ranges of the geometrical parameters (mm) Design Problem • Magnetic microactuators with magnetic circuits • - magnetic force varies with given designed dimensions • This proposed microactuator allows • - a large variation in lengths of poles • The optimal design is to find the optimal values of the geometrical parameters to generate a maximum force

  16. Design Procedure • First, the effects of geometrical parameters on magnetic force generation are analyzed by conducting a series of finite element simulations. • Then, those geometrical parameters which have critical effect in optimization are found as design variables. • Finally, the GA is applied to find the optimal values of the design variables and the maximum magnetic force.

  17. Model for Magnetic Force Computation • Maxwell equations in the magnetostatic case • The flux density expressed in terms of vector potential • The magnetic co-energycan be calculated as • Using the virtual work principle, magnetic force is • With the equations above, the finite element method is used to solve the problem.

  18. L g p1 p2 c tp tc ti 800 20 200 100 100 10 10 50 Model for Magnetic Force Computation • FEM Model • 2D axial symmetry element • 2D infinite boundary element • unsaturated, mr is a constant • ANSYS software • Initial Design • magnetic force is 512.2 mN with the current of 0.08 A

  19. Geometrical Parameter Analysis • six geometrical parameters need to be determined • - pole length p1 • - pole length p2 • - radius c • - plate thickness tp • - core thickness tc • - insulator thickness h • with all of six parameters as design variables in optimization, difficult • analyze the effects of the geometrical parameters • - take out those not so critical • - use the remaining critical ones as the design variables

  20. Geometrical Parameter Analysis • Pole Length p1, p2 • peak force occurs when pole length p1 is about 250 mm • Similar results for pole length p2 • Fig. 3.3 Magnetic fluxes at different pole lengths p1: • a) p1=150mm, (b) p1=200mm, • (c) p1=250mm, and (d) p1=300mm. Fig. 3.2 Relation between pole length p1 and the generated magnetic force.

  21. Geometrical Parameter Analysis • Magnetic core radius c • peak force obtained when radius c is about 115 mm, the reasons are in twofold. • - c increases, core reluctance decreases that helps to increase the magnetic force. • - c increases, the positions of all coils move outward which leads to magnetic force reduction Fig. 3.4 Relation between core radius c and the generated magnetic force.

  22. Geometrical Parameter Analysis • Magnetic core radius c • force generation on different positions of the single coil • Fig. 3.6 Magnetic fluxes for different coil position • a) inner of the microactuator, • b) under the plate, • c) center of the microactuator, • d) outer of the microactuator. Fig. 3.5 The influence of the position of a single coil on magnetic force generation.

  23. Geometrical Parameter Analysis • Thickness parameters • larger tp, smaller plate reluctance • magnetic core thickness tc has the • same phenomenon • larger the insulator thickness ti, • less the internal leakage flux • The parameters affect magnetic force monotonically • The maximum force is obtained with the maximum thickness parameters Pole lengths p1, p2, and radius c are taken as the major design variables design, to be found by using GA

  24. Genetic Algorithm • Developed by Holland, the concept of biological evolution • multiple search points, not a single point, the probability of reaching for the global optimum is raised • do not use any derivative or mathematical information • nonlinear or unknown systems with a large search space • Three operators: reproduction, crossover, and mutation • drawbacks including premature convergence, low search efficiency, and difficulty for parameter setting

  25. Modified Genetic Algorithm A. Fitness scaling to maintain diversity in the population B. Population-elitist with rank selection reproduction use the relatively good individuals from the previous generation C. Adaptation of operator probabilities to avoid premature convergence and excessive diversity

  26. Modified Genetic Algorithm Step 1: Initialize the GA parameters, and generate initial population. Step 2: Decode each chromosome for design variables and compute each fitness value. Step 3: Execute the fitness scaling. Step 4: Evaluateeach chromosome by performing the population-elitist with rank selection reproduction scheme. Step 5: Perform the adaptation of the crossover and mutation probabilities. Step 6: Create the new chromosomes by applying the operations of crossover and mutation. Step 7: If not convergent, go to step 2 for the next generation; otherwise, stop and output the optimal values.

  27. Modified Genetic Algorithm • GA based optimizer that contains a simulator driver to interface with the FEM is developed • the modified GA includes the three proposed operators, • while the SGA (simple GA) does not • the modified GA can converge much • more quickly than the SGA Fig. 3.9 Comparison of the evolution processes between the SGA and the modified GA.

  28. Modified Genetic Algorithm Effects of GA parameters on the evolution crossover rate is better selected as 60% number of individuals is better selected as 20 mutation rate is better selected as 10%

  29. p1 p2 c Initial design 200 100 100 Optimal design 290.8 61.1 152.4 Results • The optimal variables are found to be • Magnetic flux flows much more through • the permalloy plate after optimization • force is 589.2 mN for the optimized model, • larger than 512.2 mN for theinitialdesign • the improvement can be achieved by only designing the layout of mask Fig. 3.11 Magnetic flux distribution for the initial and optimized geometry: (a) initial geometry and (b) optimal geometry.

  30. Results • Thickness Design • The maximum force increases as these thickness parameters increase, coincides the previous assumption • The maximum force approaches the largest value when the plate thickness increases • core thickness has the most evident effect on maximum force generation • the relation between the maximum force and insulator thickness is approximately linear • set the thicknesses to be their maximum value simultaneously at 50, 30, and 60 mm, maximum magnetic force is 1160.9 mN, the largest among all of the models

  31. Macromodel Approach Generate a Macromodel Directly from 3-D Geometry and Physics Low order state-space model which captures input (u)/output(y) behavior Complicated Geometry, Coupled Elastics, Magnetics

  32. Macromodel Approach Fig. 4.1 Block diagram of the macromodel approach.

  33. Theoretical Approach Lagrange’s equations, L is defined by T is the kinetic energy and U is the potential energy. Selecting the meshed nodal displacements u as the generalized coordinate, and assuming u be the small displacements M is mass matrix, and Fm is the nodally defined electromagnetic force with

  34. Theoretical Approach Selecting the n-dimensional generalized coordinates, By introducing the above Eq. into dynamic Eqs. and premultiplying the result by by FT The basis functions can be determined by using the natural modes, The dynamic equations become Fm is proportional to the square of the input current

  35. Theoretical Approach • The equations can be expressed as • is the generalized force, referred to as the force macromodel • On the other hand, the equations derived with the magnetic co-energy [42], • is the magnetic co-energy with unit input current, referred to as the • energy macromodel • The force and energy macromodels are with different computation procedures

  36. Macromodel Generation • Building the approximate closed-form macromodels by • identification technique. • Sampling a set of the FEM solutions as the fitting data (experimental design) • Selecting a model (FLM) • Fitting the selected model to data (cluster estimation, backpropagation)

  37. Sampling data • Design of experiments • n input variables • The levels are used to adequately span the predetermined input, m levels. • nm runs or Taguchi’s method input output Magnetic Analysis orthogonal array force, energy • Training data L25(56) Testing data L16(45)

  38. c - s c c + s Fig. 4.2 Gaussian type membership function. Fuzzy Logic Model • In Sugeno-type FLM, the ith rule is described as • the representation is an integration of the rules rather than a single crisp correlation • the Gaussian-type membership function

  39. Fuzzy Logic Model • The weight for each rule’s output becomes • For the FLM with r rules, the output • can be expressed as • The differentiation of FLM output • can be analytically derived for • energy macromodel • The parameters to be determined are

  40. Gradient-decent and Backpropagation methods • Minimize the square of instantaneous error with respect to the unknown parameters • Gradient-descent method • by applying the chain rule, • Backpropagation method

  41. Simulation Results • Magnetic microactuator with complex structure for • demonstrating the efficiency of proposed approach • Geometry: • an asymmetric 625 x 625 x 5mm plate • four beams 50mm wide by 5mm thick, • - the shortest 150mm, the longest 300-mm, • - the others 200mm, and 250mm • a 500 x 500 x 5mm permalloy • 32-turn coil, 8 –mm thickness for each layer • 16-mm gap • FEM: • Structure, 411 elements, 799 nodes • Magnetics, 17408 elements, 19602 nodes • the resulting deformation is depicted

  42. Mode # Mode # Contribution (mm) Frequency (kHz) Period (ms) 1 -5.2941 1 16.3 61.46 3 0.1789 3 53.5 18.70 Mode 1 Mode 3 2 0.0569 2 34.4 29.09 6 0.0142 6 192.5 5.20 Mode 2 Mode 6 8 0.0044 8 266.3 3.76 10 0.0031 Mode 8 Mode 10 10 363.1 2.75 7 0.0021 12 0.0021 5 0.0014 9 -0.0013 Simulation Results • Modal analysis • QR factorization • Selecting 6 modes (> 99.5%)

  43. Computation Times (sec) Force macromodel Energy macromodel Quasi-static analysis 4320 4320 Modal analysis 10 10 Modes selection 30 30 Data sampling 10660 10824 FLM identification 148 16 Total time (hours) 4.21 4.22 Simulation Results • Macromodeling Computation Times • (Pentium III 850MHz) • The total time would have been longer without experimental design • FLM identification took only a few minutes, demonstrating its efficiency

  44. Simulation Results • Static Simulation • Force macromodel yielded an error of less than 1.5% • Energy macromodel shows a much greater error • due to the differentiation of the fitted energy macromodel

  45. time (ms) time (ms) Simulation Results • Dynamic Simulation • Each mode response containing the ripple has the same timing as the applied square waves • Mode 1 dominated the main response while the other modes reflected the general shape of the applied sawtooth wave • Each simulation took • about 2 minutes

  46. 1. Deposite SiO2 4. Electroplate Cu or NiFe 5.release resist 2. deposite seed layer 3. resist layer is spun, exposed, and developed 6. release seed layer Fabrication of Electromagnet Fig 5.1 A schematic processing sequence for electroplating Cu or NiFe

  47. 1. electroplate NiFe 5. electroplate 2nd coil 2. coate 1st insulation layer 6. coate 3rdinsulation layer 3. electroplate 1st coil 7. electroplate NiFe 4. coate 2ndinsulation layer Fabrication of Electromagnet Fig 5.2 A schematic processing sequence for the fabrication of the coil with enclosed core

  48. 1. deposite SiO2 on the double side 5. pattern the SiO2 etching window on the backside wafer 6. etch in KOH with the Teflon chuck 2. coate polyimide membrane 3. deposite Au as the mask for the polyimide beams 7. etch SiO2 8. release the polyimide beam with polyimide etch 4. electroplate NiFe Fabrication of Permalloy Plate Fig 5.3 A schematic processing sequence for the fabrication of the permalloy plate with a 4-suspended-beam structure

  49. Results and Discussion • NiFe permalloy is 10mm thichness • Insulator is 10mm thichness 6st layer 7st layer, enclosed Fig 5.4 Photograph of the electromagnet with the enclosed core: (a) perspective view and (b) top view

  50. Results and Discussion • NiFe plate is 800mm long and 10mm thick. • The length and width of beam are 1000mm and 200mm Fig 5.5 Photograph of the NiFe plate supported by 4-suspended-beam structure: (a) perspective view and (b) enlarged view

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