Engineering Optimization Applications 2010521 Optimization Problem Design and

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 IV Simulation of Magnetic Microactuator Using the Macromodel V Fabrication of Efficient Magnetic Microactuator

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.

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

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 Magnetic flux force vs. coil number n

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 Chang Liu, et al. Ø Design of magnetic circuit Ranan A. Miller, et al.

Magnetic Circuits Three types: 1. Spiral Type 7 layers Micropump, Ahn • 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 Microrelay, E. Fullin

Magnetic Circuits 2. Solenoid Type 5 layers • 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 Microactuator, H. Ren, E. Gerhard Micropump, SADLER et al.

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

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 Ø Magneto-structural coupled problem

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.

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.

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

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 Table 3. 1 The ranges of the geometrical parameters (mm) L g p 1 p 2 c tp tc ti 800 20 0 - 400 0 – 400 0 -400 5 -50 5 -30 40 -60 Ø The optimal design is to find the optimal values of the geometrical parameters to generate a maximum force

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.

Model for Magnetic Force Computation Maxwell equations in the magnetostatic case The flux density expressed in terms of vector potential The magnetic co-energy can 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.

Model for Magnetic Force Computation FEM Model • 2 D axial symmetry element • 2 D infinite boundary element • unsaturated, mr is a constant • ANSYS software Initial Design L g p 1 p 2 c tp tc ti 800 20 200 100 10 10 50 Ø magnetic force is 512. 2 m. N with the current of 0. 08 A

Geometrical Parameter Analysis • six geometrical parameters need to be determined - pole length p 1 - pole length p 2 - 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

Geometrical Parameter Analysis Pole Length p 1, p 2 • peak force occurs when pole length p 1 is about 250 mm • Similar results for pole length p 2 Fig. 3. 2 Relation between pole length p 1 and the generated magnetic force. Fig. 3. 3 Magnetic fluxes at different pole lengths p 1: (a) p 1=150 mm, (b) p 1=200 mm, (c) p 1=250 mm, and (d) p 1=300 mm.

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.

Geometrical Parameter Analysis Magnetic core radius c • force generation on different positions of the single coil Fig. 3. 5 The influence of the position of a single coil on magnetic force generation. 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.

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 Ø The maximum force is obtained with the maximum thickness parameters Pole lengths p 1, p 2, and radius c are taken as the major design variables design, to be found by using GA

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

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

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: Evaluate each 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.

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.

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%

Results • The optimal variables are found to be p 1 p 2 c Initial design 200 100 Optimal design 290. 8 61. 1 152. 4 • Magnetic flux flows much more through the permalloy plate after optimization • force is 589. 2 m. N for the optimized model, larger than 512. 2 m. N for the initial design Fig. 3. 11 Magnetic flux distribution for the initial and optimized geometry: (a) initial geometry and (b) optimal geometry. Ø the improvement can be achieved by only designing the layout of mask

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 Ø set the thicknesses to be their maximum value simultaneously at 50, 30, and 60 mm, maximum magnetic force is 1160. 9 m. N, the largest among all of the models

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

Macromodel Approach Fig. 4. 1 Block diagram of the macromodel approach.

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

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

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 Ø The force and energy macromodels are with different computation procedures

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)

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 orthogonal array Training data L 25(56) Magnetic Analysis output force, energy Testing data L 16(45)

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 c-s c c+s Fig. 4. 2 Gaussian type membership function.

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

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

Simulation Results Magnetic microactuator with complex structure for demonstrating the efficiency of proposed approach Geometry: • an asymmetric 625 x 5 mm plate • four beams 50 mm wide by 5 mm thick, - the shortest 150 mm, the longest 300 -mm, - the others 200 mm, and 250 mm • a 500 x 5 mm 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

Simulation Results • Modal analysis • QR factorization • Selecting 6 modes (> 99. 5%) Mode # Contribution (mm) 1 -5. 2941 3 0. 1789 2 0. 0569 6 0. 0142 8 0. 0044 10 0. 0031 7 0. 0021 12 0. 0021 5 0. 0014 9 -0. 0013 Mode # 1 Frequency (k. Hz) 16. 3 Period (ms) 61. 46 3 53. 5 18. 70 2 34. 4 29. 09 6 192. 5 5. 20 8 266. 3 3. 76 10 363. 1 2. 75 Mode 1 Mode 3 Mode 2 Mode 6 Mode 8 Mode 10

Simulation Results Macromodeling Computation Times (Pentium III 850 MHz) • The total time would have been longer without experimental design • FLM identification took only a few minutes, demonstrating its efficiency Computation Times (sec) Quasi-static analysis Force macromodel Energy macromodel 4320 Modal analysis 10 10 Modes selection 30 30 10660 10824 FLM identification 148 16 Total time (hours) 4. 21 4. 22 Data sampling

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

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 time (ms)

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

Fabrication of Electromagnet 1. electroplate Ni. Fe 5. electroplate 2 nd coil 2. coate 1 st insulation layer 6. coate 3 rd insulation layer 3. electroplate 1 st coil 7. electroplate Ni. Fe 4. coate 2 nd insulation layer Fig 5. 2 A schematic processing sequence for the fabrication of the coil with enclosed core

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

Results and Discussion • Ni. Fe permalloy is 10 mm thichness • Insulator is 10 mm thichness 6 st layer 7 st layer, enclosed Fig 5. 4 Photograph of the electromagnet with the enclosed core: (a) perspective view and (b) top view

Results and Discussion • Ni. Fe plate is 800 mm long and 10 mm thick. • The length and width of beam are 1000 mm and 200 mm Fig 5. 5 Photograph of the Ni. Fe plate supported by 4 -suspended-beam structure: (a) perspective view and (b) enlarged view

Results and Discussion • Each coil layer includes - 17 turns - line width and spacing are 25 mm - thickness about 12 mm. • The total electrical resistance is approximately 14 Ohm Fig 5. 6 Photograph of the Cu coils: (a) the resister pattern and (b) the electroplated coils

Results and Discussion • A nanoindentor is used to measure the stiffness of the four-beam structure, the stiffness k is about 45 m. N/mm • B-H curve as magnetic properties of electroplated Ni. Fe permalloy Fig 5. 7 The load-deflection curve of the 4 -beam structure Fig 5. 8 B-H curve of the Ni. Fe permalloy

Results and Discussion • The current-deflection curve is obtained using a laser displacement system • The test results are well with numerical solution • 27. 6 mm displacement at 292 m. A and 4. 5 V • The estimated force is bout 1240(m. N) Fig 5. 9 The comparison between the experimental and theoretical results of the current-deflection curves

Conclusions Ø The proposed magnetic microactuator is ready for practical applications

Crane Vibration Suppression • • Tower cranes are widely used in construction and transportation industries. The payload acts as a pendulum, operating the crane inappropriately may result in dangerous situations. One way to suppress the oscillation is to move the payload slowly, which leads to inefficiency. A control scheme to reduce the oscillation and increase the efficiency of the operation is important.