lecture 1b analysis
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Lecture 1b Analysis . …of MEMS and of structures and compliant mechanisms undergoing small and large deformations. Contents. Analysis and simulation of MEMS Deformation and stress analysis of deformable structures - PowerPoint PPT PresentationTRANSCRIPT
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.1
Lecture 1bAnalysis …of MEMS and of structures and compliant mechanisms undergoing small and large deformations.
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.2
Contents
• Analysis and simulation of MEMS• Deformation and stress analysis of
deformable structures• Pseudo rigid-body model-based analysis
of elastic structures undergoing large deformations
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.3
Hierarchical view of MEMS
System
Device 1
Device 2
Device 3
…Device nD
Device 1
Component 2
Component 1
…Component nC
Component 1
Mask 1
Process
…Mask nMMask 2
Flow channel Masks
ProcessValve
Specimen collector
Plumbing system
Reaction chamber Signal transduction
Signal amplifier and processor
Digital readoutLab on a chip
Pump
Ref: Microsystems Design—S. D. Senturia
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.4
Modeling challengesIntegration of sensor, actuator, mechanism, processor, power, and communication makes system level tasks challenging
-- common representation for multiple energy domains is needed.
Device level too has multiple energy domains-- “macromodels” are necessary.
Component (physical) level-- coupled energy domain equations need
to be solved.
Mask level-- geometric modeling has its own
difficulties.
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.5
Modeling at four levels
System
Device
Component(physical)
Artwork of masksand process
Each level involves designThere is “analysis” (forward) problem and “synthesis” (inverse) problem.
Representing as block diagrams of multi-domain subsystems
Redcuced order “macro models” of the components
Multiple, coupled energy behavioral simulations
Defining mask geometry for the process steps
Ref: Microsystems Design—S. D. Senturia
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.6
Structural analysis of MEMS
• Roark’s formulas• Energy methods• Finite element and boundary element
analyses– Commercial packaged software are now
available exclusively for MEMS– Intellisuite– CoventorWare– Memscap– Etc.
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.7
Roark’s formulas
• These are widely used by MEMS designers• They are very accessible to people with any
engineering/science background• Reasonably accurate• Well suited for back-of-the-envelope
calculations, which most situations demand in the initial stages
• Disadvantage: Large deformations and residual stresses require special attention
Roark’s formulas for stress and strain, Raymond J. Roark, Richard G. Budynas, Warren C. Young, McGraw-Hill, 2001.
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.8
Example: compliant ortho-planar platform
For details, see: Compliant Mechanisms, Howell, L. L., Wiley, 2003.
Doing FEA for this is an overkill.Instead, think of simple beam analysis.
The platform moves up and down without rotation.
FEncastered-guided beam
EI
Fl12
3
Stiffness = 3
18lEIk
Maximum stress:3
3
3
leEhClEh
Txy
x
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.9
Approximate solutions using energy methodsMostly Rayleigh-Ritz and Castiglianos methods.
Assume a polynomial deflection profile for the beam and obtain coefficients by minimizing the potential energy.Axial stretching is also accounted for.Residual stress effect is also considered.
The membrane of a pressure sensorEven the spherical approximation is used for large deflection analysis because it is simple and suits capacitance calculation.
r
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.10
Support boundary conditions can be tricky
• Most processes do not give perfect supports as in encastered beams
• Especially true of surface micromachined structures
A A
A
B
B
B
It is an artifact of the fabrication process.
The compliance of the support is to be modeled properly.
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.11
Finite/boundary element analysis of MEMS structures
• Several energy domains are coupled and self-consistent solutions need to be obtained.
• Aspect ratios (thickness to lateral dimensions) poses problems in meshing.
• What commercial MEMS-CAD software do:– Enable model construction from mask layouts and process
description to get realistic geometry– Hide FEA related details from the user (e.g., type of
elements, imposing boundary conditions, etc.)– Include “wrappers” that communicate between different
solvers and the user’s model– Finally, they show cool animations
• Lately, some also provide “macromodeling” capability and circuit simulation– Automatic extraction of reduced order models– Simulation of dynamic behavior with equivalent circuit models
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.12
Equivalent circuit modeling of electrostatic MEMS structures
Layout schematic
Behavioral schematic
Circuit schematic
3-D model(of a portion)
Nodas, CMU.SUGAR, Berkeley
E.g., electrostatic linear actuator Components: Combs, suspension, shuttle mass, anchor, electrodes
(Gary Fedder and Tamal Mukherjee, CMU)
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.13
Electro-thermally actuated MEMSElectrical analysis
Thermal analysis Elastic analysis
Jx Jy
TJ = current densityT = Temperature
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.14
How to handle more complicated geometries?
Heavy computational load if FEA is used.
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.15
One-dimensional approximation of electro-thermal micro structures
R1
R4 R3
R2
Electrical Model Thermal Model
Narrow arm, seg. 1
End connection,
seg. 2
Wide arm, seg. 3Flexure, seg. 4
Tin
Tout
Elastic ModelBeam1
Beam2
Beam4 Beam3
NA
Encastre supports
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.16
Maizel’s theorem: energy method for thermo-elastic deformationsDeformation at a point of interest in a desired direction due to temperature loading
Maizel’s theorem is similar to the unit dummy load method used for computing deflection at a point (in a given direction) due to mechanical loads:
V
kk dVTT )( 0ofinterestpointaat σ Maizel’s theorem
V
ijij dVεσofinterestpointaat
σ = stress tensor due to unit load applied at point of interest in the desired direction
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.17
Advantages of equivalent circuit models
• Can be embedded into system-level simulators (SPICE-like)
• Parameterize the model for design refinement or optimization
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.18
Pseudo rigid-body (PRB) modeling
• Approximating an elastic structure using rigid bodies connected with joints and springs.
• Reasonable accuracy over large deformations.
• Can use the simpler analysis and synthesis techniques of rigid bodies.
• Good reduced order models can be obtained.
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.19
PRB for a prismatic cantilever beam with a vertical tip load
L
L
F
Burns and Crossley, 1968:
Howell and Midha, 1995:
65
LEIK 25.285.0
Accurate up to…Kinematics:Kinetostatics:
3.64 5.58
Burns, R.H. and Crossley, F.R.E., 1968, “Kinetostatic Synthesis of Flexible Link Mechanisms,” ASME Paper No. 66-Mech-5.
Howell, L.L., and Midha, A., 1995, "Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms," ASME Journal of Mechanical Design, Vol. 117, No. 1, pp. 156-165.
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.20
Example: Fully compliant bistable switch (thermally-actuated)
Shuttle Compression beam
Switch Thermal actuator
N. Masters and L. L. Howell, JMEMS, Vol. 12, No. 3, 2003, pp. 273-280
d
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.21
Principle of bistability and design issues
dPE
d
F
PE = potential energyF = actuating forceDesign objective:Achieve suitable PE curve with the available actuating force.Stable 1
Stable 2
Unstable
Adjusting geometry with FEA is very time-consuming.
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.22
Modeling using PRB approach
Determining suitable spring constants and lengths (and hence the geometry) using kinematic analysis is much easier!
Stiff Structures, Compliant Mechanisms, and MEMS: A short course offered at IISc, Bangalore, India. Aug.-Sep., 2003. G. K. Ananthasuresh Slide 1b.23
Main points
• Hierarchical view of analyzing MEMS– System level– Circuit simulation at device level– Detailed domain level simulation
• Methods of analysis– Roark’s formulas– Energy methods– Finite element analysis– Pseudo rigid-body analysis