I

E_

I

E_

=

=

=-

NASA/TP_2001-209978

Dynamic Response Assessment for the

MEMS Accelerometer Under Severe

Shock Loads

Mark S. Fan and Harry C. Shaw

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

October 2001
The NASA STI Program Office ... in Profile

Since its founding, NASA has been dedicated to

the advancement of aeronautics and space

science. The NASA Scientific and Technical

Information (STI) Program Office plays a key

part in helping NASA maintain this important

role.

The NASA STI Program Office is operated by

Langley Research Center, the lead center for

NASA's scientific and technical information. The

NASA STI Program Office provides access to

the NASA STI Database, the largest collection of

aeronautical and space science STI in the world.

The Program Office is also NASA's institutional

mechanism for disseminating the results of its

research and development activities. These

results are published by NASA in the NASA STI

Report Series, which includes the following

report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant

phase of research that present the results of

NASA programs and include extensive data or

theoretical analysis. Includes compilations of

significant scientific and technical data and

information deemed to be of continuing

reference value. NASA's counterpart of

peer-reviewed formal professional papers but

has less stringent limitations on manuscript

length and extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies

that contain minimal annotation. Does not

contain extensive analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by NASA.

SPECIAL PUBLICATION. Scientific, technical, or historical information from NASA

programs, projects, and mission, often concerned with subjects having substantial public

interest.

TECHNICAL TRANSLATION.

English-language translations of foreign scientific and technical material pertinent to NASA's

mission.

Specialized services that complement the STI

Program Office's diverse offerings include creating custom thesauri, building customized databases, organizing and publishing research results...

even providing videos.

For more information about the NASA STI Program Office, see the following:

• Access the NASA STI Program Home Page at

http://www.sti.nasa.gov/S TI-homepage.html

• E-mail your question via the Internet to

help @ sti.nasa.gov

• Fax your question to the NASA Access Help

Desk at (301) 621-0134

• Telephone the NASA Access Help Desk at

(301) 621-0390

Write to:

NASA Access Help Desk

NASA Center for AeroSpace Information

7121 Standard Drive

Hanover, MD 21076-1320
NASA/TPm2001-209978

Dynamic Response Assessment for the

MEMS Accelerometer Under Severe

Shock Loads

Mark S. Fan and Harry C. Shaw

NASA Goddard Space Flight Centez Greenbelt, Maryland

National Aeronautics and

Space Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

October 2001
Acknowlegements

The authors would like to thank several colleagues at NASA Goddard Space Flight Center for their interest and

assistance in the study of dynamic microelectromechanical systems (DMEMS) and related technologies. In particular, we thank Jeanette Plante for her constant support and encouragement during the course of this work. We also

thank Ashok Sharma for interesting discussions on the accelerometer evaluation methodologies. Further, we thank

Alex Teverovsky for kindly providing the SEM images for the accelerometer.

The authors are grateful to H. Weinberg (Analog Device, Inc.) for numerous conversations helping us understand

the structure and function of the accelerometer, and to K. d'Souza and A. Laszloffy (Hibbitt, Karlsson & Sorensen,

Inc.) for insightful discussions on the complicated numerical convergence issues relating to highly nonlinear

intermittent dynamic impact simulation.

Available from:

NASA Center for AeroSpace Information

7121 Standard Drive

Hanover, MD 21076-1320

Price Code: A17

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

Price Code: A10
TABLE OF CONTENTS

1. Introduction ...................................................................................... 1

2. Description of the Accelerometer ............................................................. 2

3. Finite Element Analysis (FEA) Model ....................................................... 3

4. Material Properties ............................................................................. 5

5. Input Shock for the Simulation ............................................................... 7

6. Issues Relating to the Numerical Simulation ............................................... 7

7. Numerical Results and Discussions ........................................................ 17

7.1 Modal Results for the System .................................................... 17

7.2 Modal Results for the Sensor ..................................................... 19

7.3 Results of Dynamic Analysis in +Z Axis ........................................ 21

7.4 Results of Dynamic Analysis in +X Axis ....................................... 26

8. Conclusions .................................................................................... 28

Reference ........................................................................................... 31

List of Illustrations ............................................................................... 33
LIST OF ILLUSTRATIONS

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

Fig. 17

Fig. 18

Fig. 19

Fig. 20

Fig. 21

Fig. 22

Fig. 23

Fig. 24

Fig. 25

Fig. 26

Fig. 27

ADXL250 accelerometer device with the lid removed

Overall layout of the sensor elements

Enlarged view of one of the sensors

Overall 3-D FEA model

Enlarged device model with the lid removed

Enlarged FEA model for the sensor area

Details of the FEA model for the sensor

Input shock

Motion stopper structure

Maximum principal stress at the center of the center plate (-Z shock)

Maximum principal stress in the center column tether area (-Z shock)

Nodal acceleration at the center of the center plate (-Z shock)

Nodal acceleration in the center column tether area (-Z shock)

Nodal velocity at the center of the center plate (-Z shock)

Nodal velocity in the center column tether area (-Z shock)

Nodal displacement at the center of the center plate (-Z shock)

Nodal displacement in the center column tether area (-Z shock)

Maximum principal stress at the center of the center plate (+Z shock)

Maximum principal stress in the center column tether area (+Z shock)

Nodal acceleration at the center of the center plate (+Z shock)

Nodal acceleration in the center column tether area (+Z shock)

Nodal velocity at the center of the center plate (+Z shock)

Nodal velocity in the center column tether area (+Z shock)

Nodal displacement at the center of the center plate (+Z shock)

Nodal displacement in the center column tether area (+Z shock)

Maximum principal stress at the edge of the sensor (X shock)

Maximum principal stress in the center column tether area (X shock)

vi
Fig.28

Fig.29

Fig.30

Maximumprincipalstressatthetip of thesensorfingerin thecenter

column(X shock)

Nodalaccelerationattheedgeof thesensor(X shock)

Nodaldisplacementattheedgeof thesensor(X shock)

vii
NOMENCLATURE

Dxyz

E

F

F

G

H

I

J

L

M

N

P

S

To

V

f(i), i = 1,2,..

f

g

n

t

t

u

v

spatial constraints

Young's modulus

unit area force across contact interface

external force

shear modulus

Lagrange multiplier

internal force matrix

Jacobian transformation

Lagrange multiplier force summation

mass matrix

interpolation function

external force matrix

surface

impact occurring moment

volume

ith natural frequency

body force, also d'Alembert force

gravitational constant

surface normal vector

surface traction vector

time

displacement

velocity

Greek Letters

A

Z

differential operator

conventional summation

viii
O_

8

V

P

(Y

"C

numerical damping factor

position dependent matrix

variation operator

strain matrix

Poisson's ratio

density

Cauchy stress matrix

stress measure based on Jacobian transformation

Superscript

+ andM

N

T

infinitesimal time step after and before an impact

nodal variable

nodal variable

transposition

Subscript

A

B

material part coming into impact

material part coming into impact

ix
DYNAMIC RESPONSE ASSESSMENT FOR THE MEMS

ACCELEROMETER UNDER SEVERE SHOCK LOADS

1. _TRODUCTION

NASA Goddard Space Flight Center (GSFC) has evaluated the dynamic response

of a commercial-off-the-shelf (COTS) MEMS device made by Analog Device, Inc. The

device is designated as ADXL250 and is designed mainly for sensing dynamic

acceleration. It is also used to measure the tilting angle of any system or component from

its original level position. The device has been in commercial use (e.g., in automobile

airbag deployment system as a dual-axial accelerometer and in the electronic game playstation as a tilting sensor) with success, but NASA needs an in-depth assessment of its

performance under severe dynamic shock environments. It was realized while planning

this evaluation task that two assessments would be beneficial to NASA's missions: 1.

severe dynamic shock response under nominal thermal environments and 2. general

dynamic performance under cryogenic environments. The first evaluation aims at

obtaining a good understanding of its micromachined structure within a framework of

brittle fracture dynamics, while the second evaluation focuses on the structure integrity

under cryogenic temperature conditions. The information we gathered from the

manufacturer indicated that the environmental stresses under NASA's evaluation

program have been far beyond what the device has experienced with commercial

applications, for which the device was designed [1]. For instance, this device has never

been exposed in a thermal environment below-40 °C in the manufacturer's quality

control testing. Thus NASA needs the outcome of this evaluation in order to make the

selection for possible use for its missions.

This paper provides details of the first evaluation--the dynamic response under

severe multi-axial single-pulse shock load. It was performed using finite element tools

with nonlinear dynamics procedures.
2. DESCRIPTION OF THE ACCELEROMETER

The device is commercially available in a hermetic 14-pin surface mount cerpac

package specified over the -40 °C to +85 °C temperature range. Fig. 1 shows the device

with the lid removed. The silver-loaded adhesive is used to mount the chip onto the

ceramic substrate.

The monolithic MEMS device was fabricated using a proprietary surface

micromachining process, which combines all the signal processing circuitry on a single

chip. The surface micromachined sensor elements are made by depositing polysilicon on

a sacrificial oxide layer that is then etched away leaving the suspended sensor elements.

Fig. 2 shows the overall layout of the surface of the chip, where two identical sensors

orthogonally oriented are present to measure motions in X and Y planar directions. Fig.

3 gives a local view of one of these sensors. As can be seen, each sensor contains

multiple fingers along each side of the center proof mass plate (beam). The fingers are

either directly attached to the center proof mass, or to the silicon substrate (the surface of

the chip) by silicon tethers which provide rigid support. The differential capacitor sensor

is thus formed by fixed fingers (tether supported) and moving fingers attached to the

proof mass that moves in response to acceleration along its longitudinal axis. Any

movement of the proof mass causes the differential capacitance, which is then measured

by the circuitry and converted into acceleration as the output. The device has the

absolute maximum acceleration ratings of 500g if powered and 2000g if unpowered.

Any level beyond 2000g (unpowered) is considered as loads of permanent damage.

Two major factors affect the accuracy of the acceleration measurements. As

discussed above, the proper directions for sensing acceleration are along the planar

orthogonal coordinates X and Y. Thus, measured accelerations off these directions (i.e.,

along Z-axis) are inaccurate because the Z motions do not induce differential capacitance

in the fingers in the way the accelerometer is designed. In practice, the accelerometer

devices are surface mounted on a PCB. Therefore, the PCB must be mounted in such a
waythatthesensitiveaxisis alongtheplanardirections.Thesecondfactorrelatesto the

systemresonance.Whentheaccelerometerdeviceis solderedontoaPCB,it becomesa

partof alargervibrationsystemincludingthePCB,thefixture,theaccelerometer, and

theothercomponentsontheboard.In reality,thePCBandthemountingfixturewill

deflectanddeform,whichcouldbesensedbytheaccelerometerandproducespurious

output.If theresonantfrequencyof thewholestructureiswithinthesignalband,

motionscausedbythestructureitselfwill beshownin thesensoroutputresultingin

signalslargerthantheyreallyare,renderingthemeasurement useless.Thekeyto

alleviatethisproblemisto haveastiff PCBmounting.SinceaPCBis muchstifferin its

planethaninthedirectionperpendicularto its plane,it isimperativeto ensurethe

sensitiveaxisisalongtheplanardirections.Otherpossiblesolutionsto dampthe

resonanceincludemountingtheaccelerometerdevicenearamountingpostif thePCBis

relativelylargerin size,andsecuringthePCBwith addedmountingfixturesto increase

its stiffness.

3. FINITE ELEMENT ANALYSIS (FEA) MODEL

To simulate dual-axis dynamic response to severe shock, a FEA model was

created for the whole accelerometer device surface mounted through 6.0 mil thick solder

joints to a PCB board. To maintain high stiffness, the PCB dimensions are chosen to be

3.0 in x 3.0 in x 0.062 in, and four comers and center points between the comers along

the four edges of the PCB are fixed with nuts and bolts, thereby restraining all the degreeof-freedom in the comers as well as at those four center points. Fig. 4 gives the general

view of the FEA model. The model consists of 22878 8-node solid elements representing

8 different materials including bulk silicon for the chip, thin-film silicon for the

micromachined sensor, ceramic material (A1203 96%) for the cerpac package, die

attachment adhesive, glass seal for the ceramic lid, Kovar for the gull-wing leads,

polyimide glass for the PCB, and the 63:37 eutectic solder. The whole model has the

characteristic lengths ranging from about 1.0 btm to 3.0 in.
SincethisFEAmodelwasbuilt for highlynonlineartransientdynamicanalyses,

thehighnumberof degreesof freedomwill inevitablytakelongCPUtimeto solve.

Becauseof thetiny characteristiclengths(slightlyabove1.0gm)in theacceleration

sensor,finemeshes(in micrometerscales)mustbeutilizedin orderto achievereasonable

accuracy.In fact,thesefinemeshesarealsonumericallynecessarybecauseof the

intermittentcontact(discussedbelow)of thefingersto theirneighbors(X andY

motions),aswell asto thesiliconbase(Z motions).Withoutsufficientlyfinemesh

density,numericalconvergenceis extremelyhardto achievewhenintermittentcontacts

occurinthedynamicmotionsrespondingtothepulsedshockexternallyapplied.

Obviously,for amodelwithcharacteristiclengthsfrom micrometersto inches,finite

elementconnectivityrequireshighdensitymeshesevenintheareaswheretherespective

dynamicresponsesarenotof maininterest.Toreducethedegreesof freedomin those

lessinterestedareasandto makethesolvingprocessmoreefficientwithout

compromisingaccuracy,bilinearmulti-pointconstraintschemeswereincorporatedinto

themodelin severalareasincludingtheinterfacebetweenthesiliconbaseandthedie

attachment,aswell astheinterfacebetweenthecenterleadoneachsideandtheceramic

package.

Tohaveabetterviewforthedevice,Fig. 5showstheinsideof it withits ceramic

lid removed.Thedetailsof thesurfacemicromachinedsensorareshowninFig. 6and

Fig.7.

Twosimplificationsweremadewhenbuildingthismodel. Thefirst oneis that

thechipcontainsonlyonesensingarea,whichistheX sensorshownin Fig.2. Sincethe

twoorthogonallyorientedsensorsareindependentto eachotherin theiroperations,and

thesuspendedthin-filmpartof eachsensoris extremelylight inweight,webelievethat

analyzingonlytheX sensorfor itsresponseto theshockwill sufficein obtaining

informationaboutits structuralintegrityasthesameresultsshalldirectlybeapplicableto

theY sensor.It wasestimatedthatremovingtheY sensorfromthismodelreducedthe

totaldegree-of-freedomby 38%. Thesecondsimplificationis forthetethersusedto hold

thefixedfingersdowntothesurfaceof thechip. Tofurtherreducethedegree-of-
freedomof themodel,thecircular-coneshapedtethersarerepresentedbytherectangularshapedsolidelementswiththeidenticalthickness.Thismodificationin theshapeof the

tethermayincreasethelocalstressconcentrationatthetether-fingerinterface,whichis

consideredmoreconservativeforthelocalstress.Beforeusingthismodelforthefinal

analysis,adual-axistest-runwasconductedunderthesameshockconditionsto examine

whetherthelocalinterfacialstressesarebeyondthethin-film silicon'sfracturestrength.

Theresultsfromthetest-runindicatedthatthelocalstressconcentrationwasstill in the

saferegion. Otherthanthelocalinterfacialareas,thissimplificationshouldhaveno

impactonthedynamicresponseto theshockapplied.Wealsolearnedfromthe

manufacturerthatthetethersweredesignedfor providingrelativelyrigid supporto the

fingerswithout much flexibility. Therefore, this simplification should be justifiable.

4. MATERIAL PROPERTIES

Because the analysis is to be conducted under the normal room temperature,

linear properties are used in the simulation. Thus, in this simulation the nonlinearities are

from two sources, i.e., geometric nonlinearities and intermittent contact nonlinearities.

Table 1 summarizes those property values for the FEA.

The fracture strength of the thin-film silicon needs to be explained, as it is one of

the most critical data to be used for structural integrity assessment for this MEMS device.

Thin-film silicon includes varying thickness of silicon "sheets", but the terminology is

usually for microsized silicon features micromachined on single-crystalline silicon wafers

that have thickness typically under 20 gm. Studies for the elastic fracture of thin-film

silicon under deforming loads have been popular recently because of rapid development

in the MEMS technologies [2, 3, 4, 5 & 6]. Unlike the bulk silicon which is generally

treated as isotropic material, the thin-film silicon in the micrometer scales displays high

directional preferences in its structural properties. Thus, obtaining accurate properties for

the thin-film material is the key to accurate results.
Table 1

Young's MassDensity FractureStrength

Materials Modulus(GPa) Poisson'sRatio (kg/m3) (GPa)

Si(bulk) 161 0.28 2330

Si(film)

Eu0=161

E100=130

Gu0=80

G100=50

vu0=0.279

v100=0.064

2330

A120396% 303 0.21 3720

Adhesive 3.5 0.33 1200

GlassSeal 56.6 0.27 2750

Kovar 138 0.31 8360

Polyimide 21 0.33 2214

Solder 14.9 0.29 8470

Low:0.6

Avg:1.0-3.0

Mostmeasurementsforthefracturestrengthwereconductedby applyingastatic

loadto amicrosizedcantileverbeammicromachinedfromthethinwafer. These

experimentswerewellcontrolledandmonitoredin situ inside a scanning electron

microscope. Studies have found that the fracture strength is sensitive to the surface

roughness and natural flaws, thus the data obtained were within a scattered band.

Attempts were made to polish the Si surfaces by applying diamond paste (typically 1-3

_tm) to increase the fracture strength, but the fracture strength actually decreased by a

fairly large percentage. Later, it was found that a diamond polishing followed by thermal

oxidization could not only restore the original strength, but also slightly increase it. The

data listed in Table 1 are mainly from measurements that are not polished and oxidized

because the expensive treatment for the Si surface resulted only a 15-20% increase in

fracture strength compared to untreated Si. The lowest strength reported is 0.6 GPa,

while the high end goes slightly above 3.0 GPa. As a conservative assessment, we will

use 0.6 GPa as our fracture criterion.
5. INPUT SHOCK FOR THE SIMULATION

The numerical analyses simulate a severe pulsed shock applied to the MEMS

device with a magnitude being equal to the maximum unpowered acceleration rating

(2000g). The duration of the shock is only 0.01 seconds. This input shock profile is

plotted in Fig. 8, and is applied in the analyses to both X (planar) and Z (vertical)

directions. As has been mentioned, this dual-axis accelerometer is designed to withstand

and sense the accelerations in the X and Y (planar) directions, and the Z acceleration

measurement will generate spurious readings. For the most popular applications such as

automobile air bag release systems, ensuring the acceleration in only the planar directions

is not hard to arrange, but this is perhaps impossible for a spacecraft being launched or in

its orbit. Thus vertical shock in Z is also carefully analyzed and examined to ensure

structural integrity when the shock occurs along non-planar directions.

6. ISSUES RELATING TO THE NUMERICAL SIMULATION

ABAQUS/Standard is the FEA code used for this simulation. For highly

nonlinear dynamic analysis of a system under severe shock, a common FEA procedure is

to perform direct time domain integration for all of the degrees of freedom in the model.

Two numerical methods are available to conduct the numerical analysis, namely, explicit

and implicit integration. In our case, the explicit scheme shall provide a more efficient

solution if the upper bound time increment At is well controlled to avoid instability

problem. Unfortunately, we do not have ABAQUS/Explicit code available at this time.

ABAQUS/Standard uses the implicit scheme with the Hilber-Hughes-Taylor operator and

the iteration is performed through Newton's method [7]. For linear systems, the HilberHughes-Taylor operator provides guaranteed numerical stability because the upper bound

of the time increment is theoretically unlimited. In extreme cases where the system is

highly nonlinear, obtaining a stable solution may be difficult with the implicit scheme.

However, nonlinearities are generally more accounted for in dynamic systems than in
static systems since the inertia terms in the nonlinear governing equations provide

theoretical stability to the system. Therefore, the implicit operator is generally very

effective in dealing with most nonlinear dynamic solutions except very few extreme

cases. Implicit integration scheme shall give accurate results in most structural problems

if the set time increments are no more than one order of magnitude of the stability limit of

the explicit scheme, but the accuracy deteriorates in the dynamic response prediction as

the time increment increases to a point where it is comparable to the period of typical

modes of response. To achieve good results utilizing the implicit scheme, time

increments must be closely monitored and controlled using the "half-step residual"

criterion [8]. While there is no technical difficulty in doing so, it is very much CPU

intensive and therefore the analysis could be very expensive compared to the explicit

integration. Nevertheless, explicit scheme in certain cases could also be very expensive

because a conditionally stable integration operator can result in extremely small time

steps in order to achieve stability, therefore, taking much longer to obtain a converged

solution.

An inexpensive alternative to direct integration scheme (especially to the implicit

scheme) is to invoke the transient modal dynamic procedure for many dynamic problems.

This procedure gives the response of the model as a function of time based on a given

time-dependent loading. Since the dynamic response of the structure is based on a subset

of the eigenmodes of the system, sufficient number of eigenmodes must be extracted

before commencing the transient modal dynamic analysis. In this analysis, the modal

amplitudes are integrated through time, and the system response is synthesized from the

modal responses. Transient modal dynamic analysis is a linear perturbation procedure,

and will not give accurate results for problems with nonlinear load inputs. However, the

procedure is very accurate if the load amplitude curve is discretized in such a way that the

magnitude of the excitation varies linearly within each discretized segment. The proper

discretization of the load input is critical to achieve good results. Nevertheless, we were

not able to take the advantage of the modal dynamic analysis, as the model contains

multiple contact surfaces that render the linear perturbation procedure completely useless.

The contact issue will be discussed below.
Another alternative, which can handle nonlinear problems and is less expensive

than the nonlinear direct integration, is the so called subspace dynamic analysis using

"subspace proj ection" method. It performs direct explicit integration of the dynamic

equations expressed in terms of a vector space spanned by a number of eigenvectors. In

this method, eigenmodes must be extracted first before performing dynamic analysis.

This alternative to the direct integration scheme is highly effective and efficient for

solving problems with mild nonlinearities that do not substantially change the

eigenmodes. Unfortunately, just like the transient modal dynamic analysis, the subspace

projection is not useful when contacts present in the model because of the highly

nonlinear nature of contacts. Given the fact that ABAQUS/Standard is the only tool

available, the problem being dealt with in this paper must be solved using the most

expensive approach, i.e., direct integration of all the nonlinear equations with the HilberHughes-Taylor integration operator.

To derive the equations for the nonlinear dynamics, we begin with the classic

form of the virtual work equation:

Ic_'_dV:I_v" tdS+I_v "fdV

V S V

(6.1)

where o is the Cauchy stress matrix, 3 e = 1 (--_-x 33v + [ ]r) is the virtual variation of

the strain matrix, t = n- o is the surface traction vector, and f is the body force.

According to the concept of work conjugacy, we have:

z J cr (6.2)
wherev is the stress measure equivalent to work conjugate to the strain measure, and J is

the Jacobian of the elastic deformation defined as J dV/dVo. Substituting Eq. (6.2) into

Eq. (6.1) yields:

Iv'fed_=Ifv-tdS+Ifv-fdV

vo s v

(6.3)

The finite element interpolator can be written as:

u = NNuN (6.4)

Hence

02U _ N N 02U N

Ot2 Ot2 (6.5)

where N N is the interpolation function that is not displacement dependent [9], and uN is

the nodal variable. Here the summation convention is adopted for the superscripts.

The virtual field in the Eq. 6.2, 6v, needs to be compatible with all kinematic

constraints, thus:

6v=NV6W (6.6)

In Eq. 6.3, & is the virtual rate of strain associated with fly, and because it is a

rate form, it must be linear in fly. Thus, the interpolation assumption leads to:

66 = flN6W (6.7)

where j3 N is a matrix generally depending on the current position x of the material.

Hence Eq. (6.3) becomes:

10
I_C'fl x dVo:INN, tdS+INN .fdV (6.8)

vo s v

Now we write out the d'Alembert force in the equilibrium state:

_2 u

f= F-p 0t 2 (6.9)

where F is an externally prescribed force. The virtual work equation in terms of the body

force is:

1" 02u

If-6vdV= IV-6vdV-Jp-_-i--6vdV

v v v

(6.10)

Based on the d'Alembert principle, the last term in Eq. 6.10 can be written as:

1" 02u

-jOo- F- 6v

vo

where p0 is the reference density. Using the interpolation relations, we can rewrite this

term as:

M o2uM

-(IpoNS-N d_) _-_

Vo

Hence Eq. (6.8) can be expressed as:

M NMO2uM FI N-PN =0

Ot2

(6.11)

11
where

MNM = I poNN "NM dVo

Vo

is the mass matrix;

is the internal force vector, and

PN = I NN . t dS + I NN . F dV

S V

is the external force vector.

Eq. (6.11) is the finite element form of the equilibrium equation. The nonlinear

integration operator defined by Hilber, Hughes and Taylor is based on Eq. (6.11) and has

a more complex form:

MNM 02uM It+At-t-(1-t-a)(I N It+At_pN It+At)- a( IN It _pN It) + LN It+At= 0

Ot2

(6.12)

where LN is the sum of all Lagrange multiplier forces associated with degree of freedom

N. This operator is completed by the following two formulae for displacement and

velocity:

.lt+At=ult+At-_ It+At={[_1_1(1_a_2102u_ Jot=It+1(1_ a)z-gr 02u It+At} (6.13)

and

12
3u 3u 1.32u 1 32u

o3--7It+At= o3--71t +At[(a + _)-3-_ It +(_- a)-3-_ t+At] (6.14)

where 0 >_a >_-1/3.

Eq. 6.12, 6.13, and 6.14 are directly integrated for this nonlinear dynamic analysis

presented here. A salient feature of this set of equations is the built-in controllable

numerical damping. This pure numerical damping is valuable in removing nonlinear

iterative noise inevitably induced by time step changes. As suggested, a = -0.05 is

considered as a good choice for providing proper amounts of damping to control the

nonlinear numerical noise.

Because there are no inelastic materials in the MEMS device, Rayleigh damping

is utilized to simulate the dynamic response more realistically. Essentially, Rayleigh

damping contains two damping factors, one for mass proportional damping and another

for stiffness (strain-rate) proportional damping. The first damping is due to the material

movements through a viscous "ether", thus such an energy dissipation mechanism does

not practically exist in the accelerometer despite the presence of air. The strain rate

proportional damping always exists even though the materials themselves do not have

plastic behavior in this device.

The most challenging issue in this simulation is the intermittent contact and

impact. When the shock is applied to the device and the sensor is responding to the

excitement, the fingers will have large oscillating displacements around their neutral

(undeformed) positions. The amplitudes of the displacements decrease fairly rapidly due

to both damping and the intermittent contacts. When the shock is along the Z axis, the

intermittent contacts are one-sided, i.e., the fingers have intermittent contacts to the

silicon base when moving downward and no contacts when moving upward. In the FEA

model, the surface of the silicon base is categorized as rigid, and the bottom surfaces of

the fingers as deformable. If the shock is applied along the X direction, the fingers will

13
experience two-sided intermittent contacts to their left and right neighbors. Under this

scenario, the fingers' contacting surfaces are all deformable surfaces in the model. For a

successful simulation of intermittent contacts, it is imperative that meshes on master

surfaces and slave surfaces are sufficiently fine and are matching. This criterion was

followed in building the model.

Two methods are commonly adopted to simulate contact impact phenomenon.

The first method, which treats the impact as totally elastic and keeps the total kinetic

energy unchanged, is mathematically simpler. The procedure is using the standard

implicit integration. This method is suitable for dynamic analysis where the contact

impact is less critical and the detailed stress behavior in the contact region is of little

importance. However, for truly high velocity impact cases, this method may lead to

excessive contact chattering and cause convergence problem. Thus the second method

must be utilized in cases where the process of impact and the behavior of local stresses

are critical. When using this method to simulate hard surface intermittent contact, a

"local fully plastic impact" theory is adopted. This theory assumes that the total

momentum of the contacting bodies remains unchanged while the nodes that are

contacting will acquire the same velocity instantaneously in the direction of impact. The

sudden changes in velocity and acceleration due to high-speed impact are incorporated

into the simulation by developing a set of impulse equations that are solved together with

the dynamics equations.

To satisfy the "local fully plastic impact" requirements, velocity and acceleration

in the impact interface region at the time of impact shall be governed by these relations:

n. O"A=n- O"B (6.15)

02UA - 02uB (6.16)

n at 2 n. at----5

14
whereA and B denote part A and part B coming into impact, and n is the local normal to

the contact interface.

Due to contact impact, the interfacial velocity jumps suddenly, which can be

expressed as:

A@)=(au)+a, _(an)_a, (6.17)

where the superscripts + and - denote infinitesimal time steps after and before an impact

respectively. Thus, Eq. 6.15 becomes:

(6.18)

Let F be the force per unit area across the interface along n, and let To be the

moment when the impact occurred, then the following relations hold:

FA -F_ (t >_To) (6.19a)

FA F_ 0 (t<To) (6.19b)

where F includes all forces in the contact interface along n except for d'Alembert forces.

Thus the virtual work equation during the impact is:

A_B(r a2u + I(FAn FBn 5 uB

JP57 an dr) -auA+ )ds=0 (6.20)

Integrating Eq. (6.20) from To- to To+ (time duration of velocity jump) yields:

15
2qf p-_. flu dVdT)+ II (FAn-flu A + FBn.fiuB)dSdT=O

A,B V T S T

(6.21)

In view of Eq. (6.15) and (6.19a), the second term in Eq. (6.21) is zero. However,

the constraint (Eq. 6.18) needs to be satisfied for simulating the process of contact

impact. Eq. (6.21) is then augmented with a Lagrange multiplier term, with H being the

multiplier. After taking the variation calculations, we obtain:

'_[Ip A(-_)-flu dV]+IHn.(fiuA-fiuB)dS

A,B V S

+ S[A(_--_-)-A(_-_-t )]n_HdS

S

,[au__ au__]

+ j (--_-) -(--_-) .n 6HdS=O (6.22)

S

Eq. (6.22) is the impulse equation, which must be solved for velocity jump at the

time of contact impact.

In fact, the Lagrange multiplier H represents the pressure across the contact

interface, so monitoring the H value provides a good indication for separation of the two

contacting surfaces. For this sensor configuration, separation occurs immediately after

impact. In the numerical simulation, impact and separation are assumed to occur at an

intermediate point in a time step. The numerical scheme first solves the time step by

ignoring impact, then calculates the average time of impact or separation of all the points

changed inside the increment, and again solves the increment to that time interval.

16
7. NUMERICAL RESULTS AND DISCUSSIONS

7.1 Modal Results for the System

Modal analysis was first conducted to obtain the resonant frequencies of the

system. As discussed earlier, the modal studies are important in guiding the mounting

scheme of the device so that no spurious signals will be generated due to system

resonance to ensure accuracy of measurements.

No particular difficulty arises in mounting the device as long as the resonant

frequencies are assured to be above the frequency band of interest. For this

accelerometer device, the typically rated bandwidth is 1.0 kHz [1]. The vendor has

suggested a number of mounting ways in their literature to achieve higher system

resonance [10]. Based on vendor's testing results, soldering the device onto a PCB with

conformal coating yields a fundamental resonance of 12 kHz [1]. Thus it is well above

the frequency band of interest. It seems that mounting the device with standard surface

mount onto any PCB would satisfy the requirements for good measurement. However,

care must be taken in interpreting and using the testing data when preparing for the

acceleration measurement. The testing result of 12 kHz is the fundamental resonance of

the device itself, i.e., the whole MEMS device with its ceramic package is the only

vibrational mass supported by the 14 metal leads. In practice, the device is only a part

(perhaps a very small part) of a large vibrational mass when it is attached to a PCB that is

also mounted inside an electronic box containing several PCBs and numerous active and

passive devices. The contribution to the spurious output could be from sources other than

the device itself even if the fundamental resonance of the device satisfies the above

requirement for the frequency band. Thus, we must look into the whole system (or a

subsystem, if deemed proper) when determining whether there are possible interferences

with the actual readings of the sensor. A simple example can well explain this point.

Performing a procedure of linear perturbation eigenmode extraction using our FEA

model, we obtained the following results summarized in Table 2:

17
Table2

PCBlocationsofRestraint Fundamental PCB

Cases D×= Dy = Dz = 0 Resonance (Hz)

1 4 comers 312

4 comer plus 4 center points

2 between corners on the edges 398

3 2 opposite edges 488

4 4 edges 541

5 4 edges plus PCB center point 1325

The above results illustrate how sensitive the resonance could be when a dynamic

system changes its boundary conditions. Attaching a subsystem to a larger dynamic

system is essentially equivalent to changing the boundary conditions of the subsystem,

although it is not always straightforward to modify the subsystem's boundary conditions

to represent an equivalent larger system. If modifying the boundary conditions cannot

obtain an equivalent larger system, then simulation must include all the elements

contained in the larger system in order to get reasonable results. For each of the 5 cases

listed in Table 2, the eigenmode procedure extracted first 6 resonant frequencies ranging

from several hundred Hz to several thousand Hz. Examining these modal shapes

revealed that none of the modes has pure planar motions, indicating that modes with pure

planar motions shall have even higher frequencies (well above 1.0 kHz, which is the

bandwidth for this device). Thus, when the direction of acceleration is known, and the

PCB is mounted so that the sensing direction is in its planar orientations, this device shall

give minimum spurious output. However, when the larger system is complicated,

determining the correct orientation of the mounting is not always easy. A great deal of

effort must be devoted to the study of this issue before the actual measurements start.

18
7.2 Modal Results for the Sensor

An interesting issue relating to modal analysis is the natural frequency for the

sensor itself. Essentially, the sensor includes the proof mass plate, the sensor fingers

attached to the center plate, the force fingers attached to the silicon base, and the tethers

attaching force fingers. The manufacturer has tested its fundamental resonance, which is

24 kHz [1]. The method used to obtain this frequency is to statically displace the center

proof mass along its longitudinal coordinate (X coordinate in the FEA model) by a

microprobe, and release it to induce free vibration. The amplitudes of this vibration

decrease largely due to the strain-rate proportional damping, which is represented by the

second component of Rayleigh damping mechanism. By monitoring the vibration spectra

in a frequency domain, a small peak at 24 kHz was observed.

An independent eigenmode extraction procedure was performed to obtain the

resonant frequencies for the sensor alone. In this analysis, the bottom of each tether is

modeled as rigid attachment to the silicon base, which is essentially the same as the

function of tethers in the microprobe-induced free vibration testing. The results are as

follows:

f(1) = 18.7 kHz

f(2) = 32.5 kHz

f(3) = 43.1 kUz

f(4) = 46.8 kUz

f(5) = 78.1 kUz

f(6) = 9O.2 kUz

Among these resonant frequencies, only f(3) is a pure planar mode moving

strictly along the X-axis. Other frequencies have significant Z components in their

modes and are not comparable to the microprobe measurement. Obviously, f(3) is much

higher than 24 kHz from measurement. To further investigate this discrepancy and to

verify the results from the first eigenmode analysis, another eigenmode extraction

19
procedurewasconductedforthepurposeof searchingfor anyexistingeigenmodeswithin

thefrequencybandbetween20kHzand30kHzusingtheLanczosalgorithm.Nonewere

foundwithinthatfrequencyband.An expandedLanczosprocedureproducedthe

identicalresultslistedabove.Soweconcludedthatf(3) shouldbethemodethatwas

inducedby themicroprobeexperiment.

Now weneedto explainthelargediscrepancybetweentheexperimentandthe

simulation.Fortheinducedfreevibrationwithviscouseffectof airbeingnegligible,our

experiencepointedoutthatthefundamentalresonancefrombothexperimentandanalysis

shouldbeveryclose.A 15%discrepancywouldindicateaproblem.Afteracareful

examinationof thefreevibrationalmotionsalongtheX-axis,wegainedagood

understandingof theissue.In eigenmodextractionanalysis,theprocedureis alinear

perturbationandall thecontactsurfacesareignoredin carryingoutthesimulation.Thus

thecenterplateis allowedto movefreelyalongtheX-axis. However,thesensorwas

designedto havetwo"motionstoppers",oneoneachsideof thecenterplatealongtheXaxis(Fig.9). Thesestoppersarerigidly tethereddownto thesiliconbaseandconfinethe

centerplatemovementsalongtheX-axiswithin about1.2gm fromits undeformed

position(1.2gmbeingthegapbetweentheendof thecenterplateandtheheadof the

stopper).Whenthecenterplateis displacedalongtheX-axisby themicroprobeduring

thefrequencyexperiment,themaximumdistanceit couldstaticallytravelisnomorethan

1.2gm. Twothingscouldbediscussedhere:firstly,becausetheinitial amplitudesand

thesystempotentialenergyareextremelysmall,themeasurement apparatusmaynot

havesufficientresolutionto pickupthehigherfrequencymodeswhichgenerallyrequire

higherkineticenergyto getexcited.Secondly,evenif theinitial potentialenergyis

sufficientto excitehighermodesafterthecenterplateisreleasedbythemicroprobe,the

impactsbetweentheplateandthestoppersquicklyconsumethekineticenergyof the

plate.Thustheunderlyingphysicsof theoscillatingmotionunderthesecondscenariois

quitedifferentfromthatof linearperturbationmotion.

Basedonourobservationandthewaythesensoresonancewasmeasured,we

believethatthetheoreticalresonantfrequencyforthepureplanarmodeshouldbehigher

2O
than 24 kHz. Because of the presence of multiple contact surfaces, the theoretical

resonance should not be compared directly with the experimental result (24 kHz). The

measured resonance is perhaps due to complicated secondary effect of the dynamic

system, and is likely measurement-technique dependent.

7.3 Results of Dynamic Analysis in +_ZAxis

As has been discussed earlier, the Z-axis is not a sensing orientation by design

and the mounting scheme should make the X-axis (or Y-axis because of the dual-axis

capabilities) be the direction of measurement. However, it is inevitable for the device to

experience shocks along the Z-axis during space flight, though this is practically not a

concern for most commercial applications. For space flight applications, study of shock

impact in the Z-axis is as important as in other axes to ensure that the sensor can

withstand severe dynamic conditions.

The impact mechanism in the Z-axis shock is different from that in the X- or Yaxis shocks. In the Z-axis, the major potential damaging mechanism is the contact impact

between the fingers and the silicon base. Intuitively this impact is severer than that in the

X-axis shock for the fingers, as in the X-axis both the sensor fingers and the force fingers

move in the same direction [11] in response to the shock applied, making all the contact

surfaces deformable. In the case of Z shock however, the surface of the silicon chip does

not deform (rigid surface) during the impact, and the dynamic stresses in the center plate

and in the fingers are expected to be higher. This is the stress on which the analysis is

focused.

Several areas in the sensor are of key interest for local stress evaluation. For the

Z impact, the geometric center of the center plate and the tether area of the force fingers

in the center column are expected to have high stress concentrations. In the case of X

impact, the interest of the stress in the center column fingers remains the same, but the

center of the center plate is no longer a critical area because no contact will occur in that

21
area. Instead, the critical area to be examined is at the edge of the center plate where it

will have intermittent contact with the stopper. To obtain better stress results, these areas

of interest are analyzed with locally refined meshes.

Unlike motions along the X-axis where +X or -X shock produces nearly identical

dynamic results due to nearly symmetric geometry of the sensor, shocks applied to +Z

and -Z directions will produce highly different results. When the shock is applied along

the -Z-axis (pointing downward), the initial motion of the center plate is upward with no

contact to the silicon base. The plate then moves downward after the end of the shock

duration, having the first contact to the base, then moves up again with the contact

surfaces separated. This cycle of oscillating motion repeats many times with a decreasing

amplitude due to the intrinsic damping. If the shock is along +Z however, the initial

center plate movement goes downward, making instant contact to the base. Then the

contact surfaces separate and the plate moves upward. This pattern of motion also

repeats many times till all the kinetic energy is completely consumed. Obviously, the +Z

shock should result in higher dynamic stresses in the sensor because the initial impact of

the contact surfaces is severer.

Let us first examine the -Z shock in greater detail. Fig. 10 depicts the time

history of the maximum principal stress at the center point of the center plate. As

expected, the response starts at 0.01 sec at which the shock (Fig. 8) is applied. Since the

shock is in the direction of-Z, the initial movement of the center plate and the fingers is

upward (+Z). The highest maximum principal stress induced is about 4.8 MPa, which

occurs at the moment the shock is applied (at 0.01 sec). As seen in Fig. 8, the shock has a

duration of 0.01 sec with a constant value of 2000g. Within the duration of the shock, the

maximum principal stress is kept in a positive level with a maximum range from 2.0 MPa

to 4.8 MPa. This maximum stress range decreases fairly rapidly to a smaller range from

roughly 2.5 MPa to 3.6 MPa within 0.01 sec of time due to the damping effect. That

positive level of stress within the 0.01 sec duration of the input shock indicates that no

contacts occurred between the sensor and the silicon base before 0.02 sec of total time

elapsed. This is because, for the contact to occur, the sensor must move down (after the

22
initial upward peaks) towards the silicon base passing through its neutral position (i.e.,

undeformed position), and the maximum principal stress at the sensor's neutral position

must be zero.

If there were no silicon base underneath the sensor, the downward amplitude of

the center plate would be quite comparable to the upward amplitude starting from 0.02

sec when the input shock ends. However, the presence of the silicon base prevents the

sensor plate from moving downward for more than 2 gm (the thickness of the tether).

Thus, despite the dynamic impact from the contacts, the compressive maximum principal

stress is very low due to the physical restraint of the sensor structure. This is well

reflected in Fig. 10 after 0.02 sec of total time elapsed. It is also seen that, due to the

intrinsic damping, the stress decreases to virtually zero at somewhere between 0.15 and

0.2 sec of the total time. This indicates that the thin-film sensor structure is indeed very

stiff, taking only a fraction of a second to return to the neutral position.

Another area of interest from the stress standpoint is the tether area of the force

finger in the center column. This area is found to have the highest dynamic stresses in

the whole sensor structure being subject to the -Z shock. The time history of the

maximum principal stress is shown in Fig. 11 where the highest stress at the time of

shock application is found to be 68 MPa. The stress behavior within the duration of the

shock is very similar to the case plotted in Fig. 10. Interestingly, the oscillating stress

after 0.02 sec time elapse is only in the positive side, indicating non-existence of

compressive stress. This must be true as the area reflected in Fig. 11 is in close proximity

to the tether of the force finger in the center column, and the tether structure prevents any

downward movement that results in the compressive stress. Thus, there is no intermittent

contact in this case.

Time history of nodal acceleration is also computed corresponding to the above

cases. Figs. 12 and 13 show the nodal acceleration at the geometric center of the sensor

and near the tether of the center column respectively. The behavior of these acceleration

curves is well expected under the -Z shock. The peak acceleration at 0.01 sec is higher

23
near the tether compared to that at the geometric center. For the area near the tether, the

peak acceleration is as high as 26670 m/s 2. For extremely tiny and light structure being

subject to a shock of this magnitude, this huge acceleration is no surprise.

Nodal velocity plots for the geometric center as well as the tether area with the

highest stress are presented in Figs. 14 and 15 where both velocity plots display very

similar behavior. As expected from their acceleration comparison, the peak velocity near

the tether (1549 m/s) is higher that that at the center of the sensor.

The last variable of interest in these two locations is the nodal displacement. Figs.

16 and 17 plot the displacements at the plate center and near the tether respectively. In

Fig. 16, one can see that the maximum upward displacement at the center of the plate

within the duration of the shock is about 2.6 mil (66 gm). During the time period of

intermittent contacts between the sensor and the silicon base (a small fraction of a second

starting from 0.02 sec), the maximum downward displacement is about 0.09 mil. In

reality, the sensor's center point can move no more than 2 gm (0.08 mil) downward.

Similarly, Fig. 17 reveals a maximum upward displacement of 0.8 mil and a downward

displacement of 0.05 mil. This is obviously due to the motion restriction from the rigid

tether structure.

The results from the analysis with a +Z shock input are, as expected, quite

different. We shall examine the +Z results in the same order as in the -Z case. Fig. 18

depicts the maximum principal stress at the sensor's center. As can clearly be seen, the

peak stress (about 80 MPa) occurs right at the moment when the shock is applied (at 0.01

sec). After a fast damping pattern, a second peak is observed at 0.02 sec and the value of

which is about 65 MPa. Severe impacts due to intermittent contact between the sensor

plate and the base surface is seen from 0.01 sec till about 0.042 sec, which is indicated by

the compressive stresses. After the period of the intermittent contacts, the plate is

actually oscillating around a level which is slightly higher (towards +Z) from its neutral

level. This behavior is also observed in Fig. 10 where the shock is in the -Z direction. It

is revealed in Fig. 10 that this upward-moving oscillation is gradually going down and at

24
about 0.15 sec the oscillation is almost back around the neutral level with the stress

amplitude close to zero. However, this pattern is not completely shown in Fig. 18, as the

data get cut off at 0.125 sec due to excessive CPU time to solve the +Z case. It took a

total CPU time of 288 hours of a SUN Ultra Sparc-10 workstation to get to 0.125 sec

because of the highly nonlinear nature of the solutions [12]. Based on the -Z charts, we

believe that after 0.125 sec all the results (stress, acceleration, velocity, etc) are of no

importance as they are all practically approaching to zero. Thus, after 288 hours of CPU

time, we decided to terminate the ABAQUS procedure. All the plots in the case of +Z,

therefore, only show data till 0.125 sec.

Fig. 19 is the stress results near the tether in the center column, with the highest

value being 200 MPa at the moment of initial impact. The behavior is again well

expected, i.e., the highest peak at 0.01 sec and the second peak at 0.02 sec with no

compressive stress due to downward motion restriction from the tether.

The nodal acceleration behavior is very different compared with the -Z case.

Figs. 20 and 21 show the acceleration in the plate center and near the tether respectively.

Unlike the acceleration behavior under the -Z shock, the acceleration under the +Z shock

is around the neutral level of the sensor because the silicon base prevents further

penetration. It is also seen that the acceleration near the tether is higher than that at the

center of the sensor, which is also the case under -Z shock.

Figs. 22 and 23 present nodal velocity in these two locations of interest. There

are no large spikes at 0.01 sec and 0.02 sec (as can be seen in the -Z case) mainly due to

the intermittent contacts at the beginning of the shock. It is easy to see that the +Z shock

produced nodal velocity that is well over an order of magnitude higher than that in the

case of-Z shock.

The behavior of nodal displacement (Fig. 24 and 25) in these locations can be

well conjectured. The lowest level the center point can move is -0.08 mil and instant

contacts occurred at the time of shock application. After the shock duration, the

25
oscillation of the plate is around its neutral level and will eventually be damped to zero.

The displacement near the tether exhibits an extremely similar pattern except the

amplitudes are much smaller due to motion restriction from the tether.

7.4 Results of Dynamic Analysis in +_XAxis

Because of nearly symmetric geometry, dynamic analysis was performed only

along the +X direction. As has been mentioned above, the locations of examination are

no longer the same as that in Z-shock analysis since the center of the sensor is no longer a

point of concern. Instead, we have identified the worst-case location being the edge of

the sensor plate where it will have intermittent contact with the stopper under the shock

along either +X or -X. In this section, we will examine three locations of interest,

namely, the edge having contacts with the stopper, the point in close proximity to the

tether in the center column (this is also the location examined in the +Z analyses), and the

tip of the sensor finger (attached to the sensor plate) in the center column. For each

variable to be discussed below, these three locations will be shown in that order for

simplicity. To save CPU time without losing critical information, the analysis was

conducted for the length of 0.1 sec.

The worst-case stress among all the cases analyzed in this study, as intuitively

conjectured, is at the edge having contact with the stopper. The time history of the

maximum principal stress is depicted in Fig. 26. As can be seen, the highest impact

stress is as high as 450 MPa, which is induced by the initial contacts. Within the duration

of the shock, the stress magnitude decreases fairly rapidly due to the damping effect. It is

interesting to note that the time duration of higher stress (above 150 MPa in Fig. 26) lasts

longer than the duration of the shock (0.01 sec total time). Recalling the -Z shock

analysis where there are intermittent contacts, the typical duration of higher stress is

almost identical to the duration of the shock, which is from 0.01 sec to 0.02 sec (see Fig.

10). In the case of +Z analysis, however, the higher stress duration is also lasting longer

than the duration of the shock (see Fig. 18). It is obvious that motions shown in Fig. 18

26
and Fig. 26 have much severer intermittent contacts than that shown in Fig. 10. There is

no doubt that the higher stress duration in Fig. 26 must be at most equal to or even less

than the duration of intermittent contact because, if without contact, a mere 1.2 btm

maximum displacement (1.2 btm being the gap between the stopper and the edge of the

center plate) cannot possibly induce such high stresses. Similar arguments can also be

made directly to the stress behavior in Fig. 18 where the gap underneath the center plate

is only 2 btm. Nevertheless, even the stress behavior in Fig. 18 is somewhat similar to

that in Fig. 26, the dynamic impact due to intermittent contacts is far severer in Fig. 26 as

the relative stress level (compared to the respective peak stress) within the higher stress

duration is much higher. This is because the intermittent contacts are double-sided in Xshock scenario since both edges of the sensor are restricted in movement by the stoppers.

Thus, the frequency of impact is much higher and the higher stress duration is relatively

longer.

A slightly different stress pattern is found at the point in close proximity to the

tether in the center column (Fig. 27). It is quite clear that the duration of higher stress is

practically no longer than the duration of the input shock simply because there are no

contacts in this area of the sensor. The highest stress at this point is just above 300 MPa.

In Z analysis, the stress in this location is the highest in the whole sensor, but in the X

shock scenario, the highest stress is actually at the center of the edge contacting with the

stopper. This conclusion is physically reasonable because, in +_Z shock, the contact area

between the sensor plate and the silicon base is as large as the whole area of the center

plate. In the X shock, the area of intermittent contact is equal only to the area of the

vertical surface (facing the center of the sensor) of the stopper head (see Fig. 9). It is this

small and rigid area (roughly 40 btm 2) that takes the dynamic impact load directly from

the center plate of the sensor.

The last area of interest in this +X analysis is the tip of the sensor finger in the

center column, and its stress behavior is plotted in Fig. 28. Again, because of the doublesided intermittent contact, the duration of higher stress is longer than the duration of

shock input. The highest stress is less than 80 MPa. The mild stress is likely to be

27
causedby thedeform-deformintermittentcontactbecausedeformationof thecontact

surfacesof themovingfingersallowsmoretravelingdistancesbetweenthecontactsand

therefore,reducestheintensityof structuralimpact.

Sincethecenterpointof theedgeof thesensorhasbeendeterminedto bethe

worst-caselocationin termsof highstresses,wewill onlypresentresultsof interestin

thisparticularlocation.Fig.29isthenodalaccelerationatthisedgepointwherethe

dominantaccelerationis inducedby theinitial intermittentcontacts.Themagnitudeof

accelerationdecreasesquickly,indicatingfastconsumptionof kineticenergydueto highfrequencyintermittentcontacts.Thedisplacementhistoryatthecenterof theedgeis

shownin Fig.30,whereit clearlyindicatesthespacingrestrictionof nodaltraveling

imposedbythestoppersateachendof thesensorplate.It canalsobededucedfromFig.

30thatthetimedurationof intermittentcontactsstartsat0.01secandendsatabout0.028

sec,lasting0.018secof time. Thisalsoprovidesfurtherexplanationto thelonger

"durationof higherstress"observedin Fig.26andFig.28.

Examiningall theresultsof themaximumprincipalstresshasleadusto conclude

thatthemicrosensorstructureof thisaccelerometershallnotfail dueto brittlefractureof

thin-film siliconunderpulsed2000gshockin all thethreeaxes.Thispredictionwill hold

evenif weutilizethemostconservativecriterion,namely,0.6GPafracturestrength.

Thisconclusionsupportsthemanufacturer'smaximumratingforthedevice,andis also

verifiedbytheNASA experimentin whichtheaccelerometerwassubjecto 2000g

shocksin its threeaxes[13].

8. CONCLUSIONS

Using the nonlinear direct dynamic integration techniques together with

sophisticated mathematical treatment of high-frequency impact resulting from

intermittent contact, we have obtained a good insight of the dynamic performance of this

MEMS accelerometer under 2000g pulsed shock conditions. Based on a series of modal

28
analysis,thisassessment alsoprovidedmorepracticalinformationasguidelinesforthe

propermountingof thedevicewhenpreparingfortheactualmeasurements. A properly

mounteddevicemusthavethecorrectsensingorientationandtherequireddynamic

stiffnessto avoidspurioussignaloutput.Whenthesystemconfigurationis complex,an

in-depthdynamicstudywill berequiredfor apropermounting.

Thedynamicresponseresultsobtainedunder2000gshockconditionsindicatethat

themaximumaccelerationratingof thisdevice(2000g)is acceptable.A 2000gpulsed

shockappliedinthenormalsensingorientationresultedin a0.45GPapeakstress,which

is concentratedattheedgeof theproofmassplateastheconsequenceof high-frequency

intermittentcontactswiththeheadof thestopper.Thestressesaresignificantlylowerif

theshockis appliedin thedirectionperpendicularto thesensingdirectiondespitethefact

thatsevereintermittentcontactsalsooccur. Shocksin theperpendiculardirectioncan

usuallybeavoidedbythepropermountingof thedeviceinmostcommercial

applications,butin spaceflight applicationsit isbynomeanseasilyavoidable.The

resultsof theanalysisprovidethatif thedevicecanwithstandagivenshockin its sensing

orientation,it shouldhavenoproblemsurvivingthesameshockin thedirection

perpendicularto thesensingaxis.Thisanalyticalresulthaspracticallyremovedtheneed

for multi-axisdynamictesting,if it isplannedbasedongenericrequirements.

Although0.45GPadoesprovideasenseof safetyat2000g,it is bynomeans

adequateto deploythedevicein suchaharshdynamicenvironmentfromthematerial

perspective.Sincebrittlefracturestrengthof thin-film siliconis highlysurfaceroughnessdependent,afilm witharougher-than-usual backsideusedin thedevice

fabricationcouldhavealowerfracturestrengthandcouldfractureunder2000g.For

almostall thefracturestrengthtestingreported,thefilms werecarefullyselectedand

preparedto weedouttherougher-than-usual specimens.Thus,the0.60GPafracture

strength,althoughconsideredveryconservative,wasderivedfromsampleswithout

abnormalroughness.Takingintoconsiderationthepossibilityof thin-film material

variationduringthedevicefabricationprocess,werecommendtheuseof thisdevicefor

29
NASA missions under the nominal temperature range with a maximum acceleration limit

of 1500g.

The second phase of this assessment will deal with the dynamic characteristics of

the device under the cryogenic conditions.

30
REFERENCES

[1] "+5g to +50g, low noise, low power, single/dual axis iMEMS accelerometers",

Analog Device, Inc. document, Rev. 0, 1998.

[2] Ericson, F. and Schweitz, J-A., "Micromechanical fracture strength of silicon", J.

Appl. Phys., Vol. 68, No. 11, pp. 5840-5844, 1990.

[3 ] Johansson, S. and Schweitz, J-A., "Fracture testing of silicon microelements in situ in

a scanning electron microscope", J. Appl. Phys., Vol. 63, No. 10, pp. 4799-4803, 1988.

[4] Wilson, C. J., Ormeggi, A., and Narbutovskih, M., "Fractrure testing of silicon

microcantilever beams", J. Appl. Phys., Vol. 79, No. 5, 1996.

[5] Saif, M. T. A. and MacDonald, N. C., "Measurement of forces and spring constants

of microinstruments", Rev. Sci. Instrum., Vol. 69, No. 3, 1998.

[6] Zhoga, L. V., Kozachuk, A. I., Stepanov, V. A., Tutovets, Y. F., and Shpeizman, V.

V., "Brittle strength of Si single crystals and its relationship to the lifetime under static

and cyclic loads", Sov. Phys. Solid State, Vol. 21, No. 11, 1979.

[7] Hilber, H. M., Hughes, T. J. R., and Taylor, R. L., "Collocation, dissipation and

'overshoot' for time integration schemes in structural dynamics", Earthquake Eng.

Struct. Dynamics, Vol. 6, pp. 99-117, 1978.

[8] Hibbitt, H. D. and Karlsson, B. I., "Analysis of pipe whip", EPRI, ReportNP-1208,

1979.

31
[9] Thisistruefor mostof theelementsin ABAQUS,butseveralbeamelementsdonot

follow thisrule. TheFEAmodelestablishedforthecurrentworkdoesnotusethose

beamelements.

[10] Shuster,M, Briano,B, andKitchin,C.,"Increasingthefrequencyresponseof the

ADXL seriesaccelerometers", Analog Device, Inc. AppBcation Note AN-377.

[11] This is true in the initial oscillating motions when the effect of impact is the

severest. The motion of the force fingers and the sensor fingers could go out of phase

after perhaps several initial impacts. However, the stresses induced by impact decrease

fairly rapidly due to the intrinsic damping. Thus the focus of analysis is on the moment

of initial impact when the stress is the highest.

[12] During the intermittent contact time period from 0.01 sec to nearly 0.05 sec,

ABAQUS' averaged iterative time increment was as small as 2×10 -6. In fact, several

increments at the initial contact time (at 0.01 sec) were as tiny as 1×10 -9.

[13] Teverovsky, A. and Sharma, A., "Evaluation of thermal-mechanical stability of

COTS dual-axis MEMS accelerometers for Space Applications," NASA NEPP Report,

April 2000.

32
LIST OF ILLUSTRATIONS

33
34
Fig. 1 ADXL250 accelerometer device with the lid removed

35
Fig. 2 Overall layout of the sensor elements

36
Fig. 3 Enlarged view of one of the sensors

37
Fig. 4 Overall 3-D FEA model

38
Fig.5 Enlargeddevicemodelwiththelid removed

39
Fig.6 EnlargedFEAmodelfor thesensorarea

40
Fig. 7 Details of the FEA model for the sensor (top view)

41
2500

2OOO

<

1500

E

.£ 1000

500

0

o

0

-500 ................................................ '............

0 0.05

I

0.1

f

0.15 0.2

Time (sec)

Fig. 8 Input shock

42
Fig. 9 Motion stopper structure

43
n,.

e-

.--

L.

E

E

3

-1 i i L i

0 0.05 0.1 0,15 0.2 0.25 0.3

Time (see)

Fig. 10 Maximum principal stress at the center of the center plate (-Z shock)

44
e_

e_

e"

,m

a.

E

E

8O

70

60

50

40

30

20

10

0

-10

d_,.llL ._.., ......... h ......... d ..................

I t I 1 • J

0 0.05 0.1 0.15 0.2 0.25 0.3

Time (see)

Fig. 11 Maximum principal stress in the center column tether area (-Z shock)

45
2.00E+08

0.00E+00

O

O

-2.00E+08

.m

E

e,-

o

'_ -4.00E+08

_.e

O

.

"_ -6.00E+08

m

O

Z

-8.00E+08

-1.00E+09 ..... '

0 0.05 0.1 0.15 0.2 0.25

Time (sec)

0.3

Fig. 12 Nodal acceleration at the center of the center plate (-Z shock)

46
2.00E+08

O.OOE+O0

-2.00E+08

= -4.00E+08

O

-6.00E+08

O

-8.00E+08

O

z

-1.00E+09

-1.20E+09 --,- ' _ ............. _.........

0 0.05 0.1 0.15 0.2 0.25

Time (see)

0.3

Fig. 13 Nodal acceleration in the center column tether area (-Z shock)

47
40000

30000

"5" 20000

EE 10000

o

o

m

o

z -10000

-20000,

-30000 _ .............

0 0.05 0.1 0.15 0.2 0.25 0.3

Time (see)

Fig. 14 Nodal velocity at the center of the center plate (-Z shock)

48
80000

60000

40000

E

"" 20000

o

0

0

o -20000

Z

-40000

-60000

0 0.05 0.1 0.15 0,2 0.25 0.3

Time (sec)

Fig. 15 Nodal velocity in the center column tether area (-Z shock)

49
m

=m

E

V

eE

O

.m

3

2.5

2

1.5

1

0.5

0

-0.5 I I

0 0.1 0.2 0.3

Time (sec)

Fig. 16 Nodal displacement at the center of the center plate (-Z shock)

50
0.8

0.6

e15 0.4

_- 0.2

-0.2

0 0.1 0.2 0.3

Time (see)

Fig. 17 Nodal displacement in the center column tether area (-Z shock)

51
.£.

0

e,-

Q.

E

E

"3

9O

8O

7O

6O

5O

4O

3O

2O

10

0

-10

0 0.1 0.15 0.2

Time (sec)

Fig. 18 Maximum principal stress at the center of the center plate (+Z shock)

52
250

A

_. 200

._ 150

._ 100

o

c

E 50

E=m

X

0

-50

0 0.05 0.1 0.15 0.2

Time (see)

Fig. 19 Maximum principal stress in the center column tether area (+Z shock)

53
F=

tO

m

z

2.00E+10

1.50E+10

1.00E+IO

5.00E+09

O.OOE+O0

-5.00E+09

-1.00E+IO

-1.50E+ 10

-2.00E+10

-2.50E+10

0 0:05 0.1 0.15 0.2

Time (see)

Fig. 20 Nodal acceleration at the center of the center plate (+Z shock)

54
8.00E+10

6.00E+10

N"

<

4.00E+10

E

,- 2.00E+10

0

O.OOE+O0

0

<,,)

-- -2.00E+10

"0

0

Z

-4.00E+10

-6.00E+10 _ ' '

0 0.05 0.1 0.15 0.2

Time (sec)

Fig. 21 Nodal acceleration in the center column tether area (+Z shock)

55
o

O

Z

500000

400000

300000

200000

100000

0

-100000

-2OOOO0

-300000

-400000

-500000

0 0.05 0.1 0.15 0.2

Time (sec)

Fig. 22 Nodal velocity at the center of the center plate (+Z shock)

56
E

O

O

Z

800000

600000

400000

200000

0

-2O0000

-400000

-600000

-800000

0 0.05 0.1 0.15 0.2

Time (see)

Fig. 23 Nodal velocity in the center column tether area (+Z shock)

57
0.15

0.1

.m

I:: 0.05

E o

•_ -0.05

a

-0.1

-0.15

0 0.05 0.1 0.15 0.2

Time (sec)

Fig. 24 Nodal displacement at the center of the center plate (+Z shock)

58
0.07

0.035

ii

E

E

E 0

0

.m

-0.035

-0.07

0 0.05 O.1 O.15 0.2

Time (sec)

Fig. 25 Nodal displacement in the center column tether area (+Z shock)

59
A

0.

(1}

(l)

carl

=m

,m

el

E

E.m

x

500

45O

4O0

35O

3OO

25O

2OO

150

IO0

50

0

-50 I P I

0 0.05 0.1 0.15 0.2

Time (sec)

Fig. 26 Maximum principal stress at the edge of the sensor (X shock)

60
350

"-'_ 300

_' 250

200

.0 150

0

,m

,', 100

E

1= 50

0

-5O

0 0.05 0.1 0.15 0.2

Time (see)

Fig. 27 Maximum principal stress in the center column tether area (X shock)

61
m

III

ca

ca.

E

.E_

X

90

8O

70

60

5O

40

30

20

10

0

-10 _ I _ L £_ :

0 0.05 0.1 0.15 0.2

Time (sec)

Fig. 28 Maximum principal stress at the tip of the sensor finger

in the center column (X shock)

62
2.00E+10

1.50E+10

N"

<

O

1.00E+10

E 5.00E+09

0

O.OOE+O0

_.e

oe -5.00E+09

0

"_ -1.00E+10

0

z

-1.50E+10

'2.00E+10

0 0.05 0.1 0.15 0.2

Time (sec)

Fig. 29 Nodal acceleration at the edge of the sensor (X shock)

63
0.08

0.04

E

E 0

Ill

¢O

,M

121

-0.04

-0.08

0 0.05 0.1 0.15 0.2

Time (sec)

Fig. 30 Nodal displacement at the edge of the sensor (X shock)

64
I Form Approved

REPORT DOCUMENTATION PAGE OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway, Suite 1204,Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

October 2001 Technical Paper

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Dynamic Response Assessment for the MEMS Accelerometer Under

Severe Shock Loads 562

6. AUTHOR(S)

Mark S. Fan and Harry C. Shaw

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS (ES)

Goddard Space Flight Center

Greenbelt, Maryland 20771

9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS (ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

8. PEFORMING ORGANIZATION

REPORT NUMBER

2002-01008-0

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

TP--2001-209978

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION / AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Category: 39

Report available from the NASA Center for AeroSpace Information,

7121 Standard Drive, Hanover, MD 21076-1320. (301) 621-0390.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

NASA Goddard Space Flight Center (GSFC) has evaluated the dynamic response of a commercial-off-the-shelf

(COTS) MEMS device made by Analog Device, Inc. The device is designated as ADXL250 and is designed mainly

for sensing dynamic acceleration. It is also used to measure the tilting angle of any system or component from its

original level position. The device has been in commercial use (e.g., in automobile airbag deployment system as a

dual-axial accelerometer and in the electronic game play-station as a tilting sensor) with success, but NASA needs an

in-depth assessment of its performance under severe dynamic shock environments. It was realized while planning this

evaluation task that two assessments would be beneficial to NASA's missions: 1. severe dynamic shock response

under nominal thermal environments and 2. general dynamic performance under cryogenic environments. The first

evaluation aims at obtaining a good understanding of its micromachined structure within a framework of brittle

fracture dynamics, while the second evaluation focuses on the structure integrity under cryogenic temperature conditions. The information we gathered from the manufacturer indicated that the environmental stresses under NASA's

evaluation program have been far beyond what the device has experienced with commercial applications, for which

the device was designed [1]. Thus NASA needs the outcome of this evaluation in order to make the selection for

possible use for its missions. This paper provides details of the first evaluation the dynamic response under severe

multi-axial single-pulse shock load. It was performed using finite element tools with nonlinear dynamics procedures.

14. SUBJECT TERMS

MEMS accelerometer, dynamic acceleration, tilting angle sensor.

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

NSN 7540-01-280-5500

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

15. NUMBER OF PAGES

64

16. PRICE CODE

20. LIMITATION OF ABSTRACT

UL

Standard Form 298 (Rev. 2-89)

Prescribed byANSI Std. Z39.18

298-102