Rμ−REFLECTIVE TECHNOLOGY GROUP

High-speed, Adjustable, and Cost-effective

Compliant Mechanism Design1 DOF Tip Micro-Mirror Design

Agraj Sobti, Alexie Pogue, Hari Krishnan, Sepehr GhassemiVincent Partusch, Yu-Hsiu Lee

UCLA

Client Specifications

• Channel switching between

30 and 15 µs

• Low cost

• Simple control

• Small form factor

• Low power consumption

1X2, optical switch for the fiber

optic telecom or other networking

equipment sector

http://www.mdpi.com/sensors/sensors-07-02174/article_deploy/html/images/sensors-07-02174f1.png

• Optical phase modulation:Micro-mirrors fabricated using microelectromechanical systems

(MEMS) technology are well suited to steer a potentially large

number of laser beams.

Applications

Stable Optical Phase Modulation with Micromirrors- Caleb Knoernschild, Taehyun Kim, Peter Maunz,

Stephen Crain, Jungsang Kim

• MOEMS Target DetectorA two-dimensional (2D) scanning micro-mirror for target detection

and measurement has been developed. This new micro-mirror is

used in a MOEMS target detector to replace the conventional

scanning detector.

Applications…

Study on a Two-Dimensional Scanning Micro-Mirror and Its Application in a MOEMS Target Detector

Chi Zhang *, Zheng You, Hu Huang and Guanhua Li

• Raster Scanning MechanismsRaster scanning is used to project images by sequentially directing

a single light beam to different locations on a rectangular target

screen. To avoid visual flickering of the projected image the

entire screen should be scanned usually above 50 Hz.

Applications…

A novel tilting micromirror with a triangular waveform resonance response and an adjustable

resonance frequency for raster scanning applications- D. Elata1, V Leus1, A. Hirshberg1, O.

Salomon1, and M. Naftali.

• Electrostatic Comb DrivesHigher initial comb-offsets produce higher scan angles with a

lowering of the resonance frequency. An increase in the initial

maximum comb-offset from 5 µm to 10 µm results in a 50% increase

of the angular response for an offset square-wave actuation with 80

Vp-p.

Approaches to tune the Resonant Frequency

Modeling and Simulation of a Parametrically Resonant Micromirror With Duty-Cycled Excitation

Wajiha Shahid, Zhen Qiu, Xiyu Duan, Haijun Li, Thomas D. Wang, and Kenn R. Oldham

• Application of an axial force on the flexure

elements.

Approaches to tune the Resonant Frequency…

Linear tuning of the resonant frequency in tilting oscillators by an axially loaded suspension flexure-

T. Shmilovich and S. Krylov

• Using angle limitersEffectively, the stiffness of the torsion bar increases discontinuously

when contact is made between the bar and angle limiters.

Approaches to tune the Resonant Frequency…

A novel tilting micromirror with a triangular waveform resonance response and an adjustable resonance

frequency for raster scanning applications- D. elata1, V Leus1, A. Hirshberg1, O. Salomon1, and M. Naftali2

• Using Multistate Latching mechanism to change

flexure orientation.

Approaches to tune the Resonant Frequency…

Multistate Latching MEMS Variable Optical Attenuator-

R. R. A. Syms, H. Zou, J. Stagg, and D. F. Moore

Topology Synthesis by FACT

Freedom Space & Constraint Space:

Topology Synthesis by FACT

Possible Variations:

Topology Synthesis by FACT

Possible Variations:

G G

S

Topology Synthesis by FACT

Frequency Tuning:

S

2. Changing Flexure Topology:1. Changing Inertia:

S

G G

S

SS

𝐿0

𝐿1

𝑀0

𝑀1

S3

Sn

…

Topology Synthesis by FACT

S1

S2G G

S

2. Changing Flexure Topology:1. Changing Inertia:

Topology Synthesis by FACT

S3

Sn

…

S1

S2G G

S

2. Changing Flexure Topology:1. Changing Inertia:

Topology Synthesis by FACT

S3

Sn

…

S1

S2G G

S

2. Changing Flexure Topology:1. Changing Inertia:

S2

Topology Synthesis by FACT

S3

Sn

…

S1

G G

S

2. Changing Flexure Topology:1. Changing Inertia:

Topology Synthesis by FACT

S2

S3

Sn

…

S1

G G

S

2. Changing Flexure Topology:1. Changing Inertia:

Topology Synthesis by FACT

S2

S3

Sn

…

S1

G G

S

2. Changing Flexure Topology:1. Changing Inertia:

Topology Synthesis by FACT

Evaluation:

Change of Stiffness Change of Inertia

• Dynamic stiffness variation

• Continuous frequency switching

• Large deformation

• Static mass addition

• Discrete frequency switching

• Additional energy

• Latching mechanism

• Gravity

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

Topology Synthesis by FACT

Synthesis Based on FACT:

A

A

Section A-A:

0o Deflection / 36477 Hz 4o Deflection / 41765 Hz

8o Deflection / 55848 Hz 12o Deflection / 73731 Hz

Frequency Analysis

1st Natural Frequencies:

30

40

50

60

70

80

90

0 2 4 6 8 10 12 14

Na

tura

l F

req

ue

ncy (

kH

z )

Angular Deflection ( Degrees )

Tuned Resonant Frequencies

First Mode Second Mode

Frequency Analysis

1st & 2nd Natural Frequencies v.s. Deformed Angle:

Structural Analysis

at 5 degrees 512.7 MPa 2.3 FOS

at 10 degrees 845 MPa 1.42 FOS

at 12 degrees 1009.2 MPa 1.18 FOS

Frequency Analysis

2. Deformed Configuration:1. Initial Configuration:

MATLAB Verification:

𝑓𝑛1 = 41,531; 𝑇1 =

𝜔𝑥

𝜔𝑦

𝜔𝑧

𝑣𝑥𝑣𝑦𝑣𝑧

=

2.35𝐸 − 56.20𝐸 − 6

1−1.26𝐸 − 5−7.55𝐸 − 62.64𝐸 − 9

𝑓𝑛1 = 60,282; 𝑇1 =

2.12𝐸 − 61.38𝐸 − 6

1−2.80𝐸 − 52.09𝐸 − 42.11𝐸 − 10

X

Y

Z X

Y

Z

SOLIDWORKS: 36,477 Hz SOLIDWORKS: 73,731 Hz

Mirror Actuation

• Need periodic actuation of the stage to keep

the mirror in resonance

• Electromagnetic actuation– Pulse of voltage to electromagnetic coil below the stage

– The stage has a small layer of permanent magnetic material

Figure 1 on p. 79 in Cho, H. J., and C. H. Ahn. "A Bidirectional Magnetic Microactuator Using Electroplated Permanent Magnet Arrays." Journal of

Microelectromechanical Systems 11, no. 1 (February 2002): 78-84. © 2002 IEEE.

Mirror Actuation

Electromagnet

Metallic Layer

Fabrication Process

Fabrication Process

Fabrication Process

Fabrication Process

Fabrication Process

Final Fabricated Component

High Performance

Compact

Simple

Actuation

http://www.pi-usa.us/products/Piezo_Motors_Stages/Linear-Motor-Precision-Positioning.php?onl_YTB_nexmew#NEX

Future Work

Compact

Packaging

(Compared to a Quarter)Design for Optimal

use and economic feasibility

Ques

QUESTIONS ?

APPENDIX

Simulated Designs

Initial Flexure Design Concepts

Pinching Mechanism Design Concepts

Transmission Systems Tested

Sources1. Bagdahn, Jörg, William N. Sharpe Jr, and Osama Jadaan. "Fracture strength of polysilicon at stress concentrations." Microelectromechanical Systems, Journal of 12.3 (2003): 302-312.

2. Bauer, Ralf, et al. "A novel continuously variable angular vertical comb-drive with application in scanning micromirror." Micro Electro Mechanical Systems (MEMS), 2013 IEEE 26th International Conference on. IEEE, 2013.

3. Bayat, Dara. "Large Hybrid High Precision MEMS Mirrors." (2011).

4. Bifano, Thomas G., et al. "Microelectromechanical deformable mirrors." Selected Topics in Quantum Electronics, IEEE Journal of 5.1 (1999): 83-89.

5. Elata, D., et al. "A novel tilting micromirror with a triangular waveform resonance response and an adjustable resonance frequency for raster scanning applications." Solid-State Sensors, Actuators and Microsystems Conference, 2007. TRANSDUCERS 2007. International. IEEE, 2007.

6. Fedder, Gary K. "MEMS fabrication." null. IEEE, 2003.

7. Hopkins, J. B., R. M. Panas, and Y. Song. Categorization and Review of Existing Micro-mirror Array Technologies. No. LLNL-CONF-676358. Lawrence Livermore National Laboratory (LLNL), Livermore, CA, 2015.

8. Hopkins, Jonathan B., and R. M. Panas. "Flexure Design for a High-Speed Large-Range Tip-Tilt-Piston Micro-mirror Array." Proc ASPE 29th mtg, Boston, MA: Nov (2014): 9-14.

9. Kang, Byoung Hun, and Kyoung Rae Cho. "Micro Planar Parallel Mechanism Design using Configuration Change Effect of Flexure Mechanism." Computational Intelligence in Robotics and Automation, 2007. CIRA 2007. International Symposium on. IEEE, 2007.

10. Kapels, Hergen, Robert Aigner, and Josef Binder. "Fracture strength and fatigue of polysilicon determined by a novel thermal actuator [MEMS]."Electron Devices, IEEE Transactions on 47.7 (2000): 1522-1528.

11. Michalicek, M. Adrian, Darren E. Sene, and Victor M. Bright. "Advanced modeling of micromirror devices." (1995).

12. Panas, R. M., et al. Hybrid Additive and Microfabrication of an Advanced Micromirror Array. No. LLNL-CONF-676306. Lawrence Livermore National Laboratory (LLNL), Livermore, CA, 2015.

13. Seo, Kyoung-Sun, Young-Ho Cho, and Sung-Kie Youn. "A bulk-micromachined silicon micromirror for tunable optical switch applications."Emerging Technologies and Factory Automation, 1996. EFTA'96. Proceedings., 1996 IEEE Conference on. Vol. 2. IEEE, 1996.

14. Sharpe Jr, William N., et al. "Measurements of Young's modulus, Poisson's ratio, and tensile strength of polysilicon." Micro Electro Mechanical Systems, 1997. MEMS'97, Proceedings, IEEE., Tenth Annual International Workshop on. IEEE, 1997.

15. Shmilovich, T., and S. Krylov. "Linear tuning of the resonant frequency in tilting oscillators by an axially loaded suspension flexure." Micro Electro Mechanical Systems, 2008. MEMS 2008. IEEE 21st International Conference on. IEEE, 2008.

16. Syms, R. R. A., et al. "Multistate latching MEMS variable optical attenuator." Photonics Technology Letters, IEEE 16.1 (2004): 191-193.

17. Syms, R. R. A., H. Zou, and J. Stagg. "Robust latching MEMS translation stages for micro-optical systems." Journal of Micromechanics and Microengineering 14.5 (2004): 667.

18. Vaezi, Mohammad, Hermann Seitz, and Shoufeng Yang. "A review on 3D micro-additive manufacturing technologies." The International Journal of Advanced Manufacturing Technology 67.5-8 (2013): 1721-1754.

19. Williams, Kirt R., Kishan Gupta, and Matthew Wasilik. "Etch rates for micromachining processing-Part II." Microelectromechanical Systems, Journal of 12.6 (2003): 761-778.

20. Wu, Xiaoming, et al. "A frequency adjustable vibration energy harvester." Proceedings of PowerMEMS (2008): 245-248.

21. Xu, Yingshun, et al. "Two-axis gimbal-less electrothermal micromirror for large-angle circumferential scanning." Selected Topics in Quantum Electronics, IEEE Journal of 15.5 (2009): 1432-1438.

22. Yang, Hsueh-An, et al. "A novel coilless scanning mirror using eddy current Lorentz force and magnetostatic force." Microelectromechanical Systems, Journal of 16.3 (2007): 511-520.

Roles

Agraj Sobti: Mechanical Design, Design Optimization, CAD Modelling

Alexie Pogue: Conceptual Design, Mechanical Design, Design Analysis

Hari Krishnan: Frequency Optimization, FEA, Material Properties

Sepehr Ghassemi: PowerPoint, Manufacturing, Design for feasibility, Actuation

Vincent Partusch: Mechanical Design, Design Simplification and Optimization

Yu-Hsui Lee: PowerPoint, Matlab, Conceptual Design, Transmission

1

Table of Contents....................................................................................................................................... 1build stiffness matrix .......................................................................................................... 1build mass matrix ............................................................................................................... 2solve the eigenvalue problem of matrix Mtw^(-1)*Ktw ............................................................. 2

clc; clear all; close all;

build stiffness matrixE=169E9; nu=0.22; G=E/(2*(1+nu)); rho=2200;

px1=0; py1=-.125e-3; pz1=-.5e-3;n13=[0 0 1]; n12=[1 0 0];l1=1e-3; w1=0.25e-3; t1=0.03e-3;

px2=-.5e-3; py2=-.015e-3; pz2=-.425e-3;n23=[1 0 0]; n22=[0 1 0];l2=1.25e-3; w2=0.15e-3; t2=0.03e-3;

px3=-.5e-3; py3=-.0125e-3; pz3=0;n33=[1 0 0]; n32=[0 1 0];l3=1.25e-3; w3=0.4e-3; t3=0.025e-3;

px4=-.5e-3; py4=-.015e-3; pz4=.425e-3;n43=[1 0 0]; n42=[0 1 0];l4=1.25e-3; w4=0.15e-3; t4=0.03e-3;

px5=0; py5=-.125e-3; pz5=.5e-3;n53=[0 0 -1]; n52=[1 0 0];l5=1e-3; w5=0.25e-3; t5=0.03e-3;

px6=.5e-3; py6=-.015e-3; pz6=.425e-3;n63=[-1 0 0]; n62=[0 1 0];l6=1.25e-3; w6=0.15e-3; t6=0.03e-3;

px7=.5e-3; py7=-.0125e-3; pz7=0;n73=[-1 0 0]; n72=[0 1 0];l7=1.25e-3; w7=0.4e-3; t7=0.025e-3;

px8=.5e-3; py8=-.015e-3; pz8=-.425e-3;n83=[-1 0 0]; n82=[0 1 0];l8=1.25e-3; w8=0.15e-3; t8=0.03e-3;

row1=[px1 py1 pz1 n13 n12 l1 w1 t1 E G 1 0];row2=[px2 py2 pz2 n23 n22 l2 w2 t2 E G 1 0];row3=[px3 py3 pz3 n33 n32 l3 w3 t3 E G 1 0];row4=[px4 py4 pz4 n43 n42 l4 w4 t4 E G 1 0];row5=[px5 py5 pz5 n53 n52 l5 w5 t5 E G 1 0];

2

row6=[px6 py6 pz6 n63 n62 l6 w6 t6 E G 1 0];row7=[px7 py7 pz7 n73 n72 l7 w7 t7 E G 1 0];row8=[px8 py8 pz8 n83 n82 l8 w8 t8 E G 1 0];rowN=zeros(1,16);rowN(1:3)=[1 0 8];Constraint=[ row1; row2; row3; row4; row5; row6; row7; row8; rowN];

Ktw=EulerStiffnessMatrix(Constraint);

build mass matrixlm1=1e-3; bm1=.25e-3; hm1=1e-3; Vm1=lm1*bm1*hm1;

% mass matrix about center of massInx1=rho*Vm1*(bm1^2+hm1^2)/12;Iny1=rho*Vm1*(lm1^2+hm1^2)/12;Inz1=rho*Vm1*(bm1^2+lm1^2)/12;In1=diag([Inx1,Iny1,Inz1,rho*Vm1,rho*Vm1,rho*Vm1]);

% transformationPx1=0; Py1=-.125e-3; Pz1=0;L1=[Px1 Py1 Pz1].';n1=[1 0 0].';n2=[0 1 0].';n3=[0 0 1].';N1=[n1 n2 n3 zeros(3,1) zeros(3,1) zeros(3,1); cross(L1,n1) cross(L1,n2) cross(L1,n3) n1 n2 n3];

% swapping matrixDelta=[zeros(3) eye(3); eye(3) zeros(3)];

% mass matrixM1 = N1*Delta*In1*N1^-1;Mtw = M1;% Mtw = blkdiag(M1,M2);

solve the eigenvalue problem of matrixMtw^(-1)*Ktw

[EigenVec Lambda]=eig(inv(Mtw) * Ktw);Omega = sqrt(diag(Lambda));

3

% sorting[Omega, I] = sort(Omega);temp = zeros(6);for k=1:6 temp(:,k)=EigenVec(:,I(k));end

% print the resultsEigenVec=temp;format short gdisp('Natural frequencies in ascending order in Hertz:')disp(Omega/(2*pi))disp('Associated mode shapes:')disp(EigenVec)

Natural frequencies in ascending order in Hertz: 41573 86088 3.0162e+05 3.6311e+05 4.9241e+05 5.1967e+05

Associated mode shapes: 0 0 -1 -1 -5.7001e-18 0 0 0 0 0 1 0 -1 0 0 0 0 1 1.2915e-05 0 0 0 0 -0.00091495 0 1 0 0 0 0 0 0 -8.4838e-05 -0.0023296 -5.2033e-21 0

Published with MATLAB® R2013a

1

Table of Contents....................................................................................................................................... 1build stiffness matrix .......................................................................................................... 1build mass matrix ............................................................................................................... 2solve the eigenvalue problem of matrix Mtw^(-1)*Ktw ............................................................. 2

clc; clear all; close all;

build stiffness matrixE=169E9; nu=0.22; G=E/(2*(1+nu)); rho=2200;

px1=0; py1=-.125e-3; pz1=-.5e-3;n13=[0 0 1]; n12=[1 0 0];l1=1e-3; w1=0.25e-3; t1=0.03e-3;

px2=-.5e-3; py2=-.015e-3; pz2=-.425e-3;n23=[1 0 0]; n22=[0 1 0];l2=1.25e-3; w2=0.15e-3; t2=0.03e-3;

px3=-.5e-3; py3=-.0125e-3; pz3=0;n33=[0.978 -0.208 0]; n32=[0.208 0.978 0];l3=1.25e-3; w3=0.4e-3; t3=0.025e-3;

px4=-.5e-3; py4=-.015e-3; pz4=.425e-3;n43=[1 0 0]; n42=[0 1 0];l4=1.25e-3; w4=0.15e-3; t4=0.03e-3;

px5=0; py5=-.125e-3; pz5=.5e-3;n53=[0 0 -1]; n52=[1 0 0];l5=1e-3; w5=0.25e-3; t5=0.03e-3;

px6=.5e-3; py6=-.015e-3; pz6=.425e-3;n63=[-1 0 0]; n62=[0 1 0];l6=1.25e-3; w6=0.15e-3; t6=0.03e-3;

px7=.5e-3; py7=-.0125e-3; pz7=0;n73=[-0.978 -0.208 0]; n72=[0.208 -0.978 0];l7=1.25e-3; w7=0.4e-3; t7=0.025e-3;

px8=.5e-3; py8=-.015e-3; pz8=-.425e-3;n83=[-1 0 0]; n82=[0 1 0];l8=1.25e-3; w8=0.15e-3; t8=0.03e-3;

row1=[px1 py1 pz1 n13 n12 l1 w1 t1 E G 1 0];row2=[px2 py2 pz2 n23 n22 l2 w2 t2 E G 1 0];row3=[px3 py3 pz3 n33 n32 l3 w3 t3 E G 1 0];row4=[px4 py4 pz4 n43 n42 l4 w4 t4 E G 1 0];row5=[px5 py5 pz5 n53 n52 l5 w5 t5 E G 1 0];

2

row6=[px6 py6 pz6 n63 n62 l6 w6 t6 E G 1 0];row7=[px7 py7 pz7 n73 n72 l7 w7 t7 E G 1 0];row8=[px8 py8 pz8 n83 n82 l8 w8 t8 E G 1 0];rowN=zeros(1,16);rowN(1:3)=[1 0 8];Constraint=[ row1; row2; row3; row4; row5; row6; row7; row8; rowN];

Ktw=EulerStiffnessMatrix(Constraint);

build mass matrixlm1=1e-3; bm1=.25e-3; hm1=1e-3; Vm1=lm1*bm1*hm1;

% mass matrix about center of massInx1=rho*Vm1*(bm1^2+hm1^2)/12;Iny1=rho*Vm1*(lm1^2+hm1^2)/12;Inz1=rho*Vm1*(bm1^2+lm1^2)/12;In1=diag([Inx1,Iny1,Inz1,rho*Vm1,rho*Vm1,rho*Vm1]);

% transformationPx1=0; Py1=-.125e-3; Pz1=0;L1=[Px1 Py1 Pz1].';n1=[1 0 0].';n2=[0 1 0].';n3=[0 0 1].';N1=[n1 n2 n3 zeros(3,1) zeros(3,1) zeros(3,1); cross(L1,n1) cross(L1,n2) cross(L1,n3) n1 n2 n3];

% swapping matrixDelta=[zeros(3) eye(3); eye(3) zeros(3)];

% mass matrixM1 = N1*Delta*In1*N1^-1;Mtw = M1;% Mtw = blkdiag(M1,M2);

solve the eigenvalue problem of matrixMtw^(-1)*Ktw

[EigenVec Lambda]=eig(inv(Mtw) * Ktw);Omega = sqrt(diag(Lambda));

3

% sorting[Omega, I] = sort(Omega);temp = zeros(6);for k=1:6 temp(:,k)=EigenVec(:,I(k));end

% print the resultsEigenVec=temp;format short gdisp('Natural frequencies in ascending order in Hertz:')disp(Omega/(2*pi))disp('Associated mode shapes:')disp(EigenVec)

Natural frequencies in ascending order in Hertz: 93090 1.1313e+05 3.0943e+05 3.6678e+05 4.8959e+05 4.899e+05

Associated mode shapes: 0 0 -1 1 -3.028e-19 0 0 0 0 0 1 0 -1 0 0 0 0 -1 6.6282e-05 0 0 0 0 0.0016329 1.856e-20 1 0 0 0 -3.3757e-22 0 0 -3.2546e-05 0.0010827 -4.5676e-21 0

Published with MATLAB® R2013a