the design of a precision mechanical assembly for a hard x

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THE DES

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Abstract This paper d

polarizer and ttion. In additioquirements of maximum flexfiner mesh, homodel stiffnestional advancear methods. Fithe polarizer w

A hard x-raAdvanced PhoLaboratory (Apolarization ofa narrow bandfor Mossbauerenergy spectrawhich is norm

The paper wdesign of the attention is painvolved in naof a single notsimulation of experimental r

P

Assembly – ZThe complet

degrees of freeed using indivFigure 1. TheST05A-S1T-RportTM 8301Nin the yaw antwo DOF withhigh precision a KohzuTM STporates a slighpositioning. Fithe base stage designated Z4-KohzuTM XM0tilt stage with specifications

SIGN OF A

anced Photo

discusses the mthe analysis of on, insight waflexure mecha

xure stress wilowever there iss and deflectio

ed FEA analysiinally, it was sh

will be capable

INTRODay polarizer isoton Source

ANL). It has f synchrotron rwidth of 14.4 kr spectroscopya to be collectal in synchrotr

will first detail polarizer devicid to the analyano-radian levetch type flexurthe complete

resolution resul

POLARIZE

Z8-4600 te polarizer assedom (DOF). Tidual actuator e left crystal

R tilt stages mF PicomotorsT

nd roll angles. h the base stapitch flexure s

T07A-S1T yawhtly larger 830inally, the thirdbeing a more

-4602. Atop th05A-C1-R, andPicomotorTM

for the assemb

A PRECI

S. P.

on Source, A

mechanical desthe design usin

as made into thanisms. It wasl increase in a a limit to how

on without incois techniques suhown that the pof a least 80 nr

DUCTION s under develo(APS) at Argbeen previousradiation can bkeV [1]. This y (MS) in thated rather than

ron radiation [2and describe

ce for hard x-rysis of the flexel rotations. FEre are conductflexure mech

lts are shown.

ER DESIGN

sembly consistThree crystals stacks, as can will sit atop

modified to incTM for controlThe middle c

age being a custage (Z4-4601

w tilt stage, wh2 PicomotorTM

d crystal has thcompact versi

his stage is a trd another ST08301NF. The

bly can be seen

SION MEX-RAY P

. Kearney, D

Argonne Nati

sign of an x-rayng FEA simulahe meshing re found that th

accuracy with w well FEA canorporating addiuch as nonlinepitch stages forad resolution.

opment for thgonne Nationasly shown thabe used to filtehas advantage

at it allows fon time spectra2]. the mechanicarays. Particulaure mechanismEA simulationed followed by

hanism. Finally

N

ts of a total of 7are manipulatbe seen in Figtwo KohzuTM

corporate Newled positioning

crystal also haustom-designed1) and atop thahich also incorM for controlledhree DOF withion of Z4-460ranslation stag05A-S1T-R roldetailed design in Table 1.

ECHANICPOLARIZ

D. Shu, T. S.

ional Labora

y a-e-e a n i-e-or

e al at er es or a,

al ar m ns y y,

7 t-g. M

w-g

as d at r-d h 1 e ll n

Figure 1:items are ST05A-SKohzuTM

KohzuTM

portTM NP4602 pitch

Table 1: tions listethe comm

Specific

Volume

Mass

Degrees

KohzuTM

ST05A

ST07A

KohzuTM

ST05A

XM05A

Pitch Fl

Z4-460

Pitch Fl

Z4-460

Pitch RoTwo lam

fine pitchsmaller dishown inNewportT

sine bar laminar w

CAL ASSEZER

Toellner

atory, Argon

: Z8-4600 as1) 3X Picom

1T-R tilt stagST07A-S1T tiXM05A-C1-R

PM140SG mich stage.

Design specified are derived

mercial actuator

cation

(L x W x H) m

of Freedom M Tilt Stages R

A-S1T-R (Open

A-S1T(Open LoM Stages Rang

A-S1T-R & ST0

A-C1-R

lexure Stages R

01 & Z4-4602 (

lexure Stages R

01 & Z4-4602

otation Stageminar weak-lin

h rotation. For iameter (73.34Fig. Figure 2

TM NPM140SGattached to a

weak-link struc

EMBLY F

nne, IL 60439

ssembly modemotorTM 8301Nge, 3) Z8-46ilt stage, 5) PiR translation crometer adapt

fications for Z8from the publ

rs and represen

mm3

Resolution

n Loop)

oop)

ge

07A-S1T

Resolution

(Closed Loop)

Range

e – Z8-4602 nk stages haver this paper, w4 mm vs. 97.782. Pitch rotatioG actuator pus

pair of weakcture is comp

FOR A HA

9, U.S.A.

el view. NumNF, 2) 3X Ko01 pitch stagicomotorTM 83stage, 7) 2X er piezo, and 8

8-4600. The rlished resolutiont the lower lim

Value

(365x214x

4.1 kg

7

0.5 µra

0.4 µra

±3°

±3.25 m

15 nrad

±0.7°

e been designewe will focus o8 mm) flexureon is achievedshing on an 80k-link flexuresrised of 30 bo

ARD

mbered

hzuTM ge, 4) 02, 6) New-

8) Z8-

esolu-ons of

mit.

e

x89)

g

ad

ad

mm

d

ed, for on the e stage d by a 0 mm s. The onded

9th Edit. of the Mech. Eng. Des. of Synchrotron Radiat. Equip. and Instrum. Conf. MEDSI2016, Barcelona, Spain JACoW PublishingISBN: 978-3-95450-188-5 doi:10.18429/JACoW-MEDSI2016-TUBA01

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Precision MechanicsNano-positioning

Fiptl

avi4

F

pt

wlr

ta

sheets of 17-7[3-5].

Figure 2: Z8-4items are 1) 80plate, 3) 2X transparent forlink flexure.

As of publicand is used avalidation and ies have prov4601 and simil

Flexure ModThe princip

pitch stage is this larger flesingle notch ty

Figure 3 showith its coordlytical modelsradius, t flexur

By integratinthe flexure anabout θY is giv

1∆

7 PH stainless

4602 sub-assem0 mm sine barextension spr

r clarity), 5) 2

cation only the as the base pr

experimentativided insight ilar stages based

DESIGN A

delling pal componenta flexure mech

exure mechaniype flexure. ows a single ninates and crit

s. The critical re thickness, anng the beam eqn approximatioven by

23

3 4 2∆

steel 0.1524 m

mbly model vir, 2) 440 harderings, 4) baseX 73.34 mm d

Z8-4602 stagerototype for Fion. The resultnto the develod on this desig

ANALYSIS

t of the Z4-4hanism. To beism, we will

notch type flextical dimensiondimensions ar

nd b flexure dequation with ston of the tors

23

,

6∆ ⁄ tan 1

mm thick each

iew. Numberedened SS contace plate (showndiameter weak

e has been builFEA simulations of these studopment of Z8

gn.

4602 precisionetter understandfirst analyze

xure on the lefns used in anare R the notch

epth. trip elements osional stiffnes

2,

(1

h

d ct n

k-

lt n

d-8-

n d a

ft a-h

of ss

Figure 3: in this stusions desccircular noweak-linked at the c and withYoung’s m[6]. Equatsimplifica

The nomition

However,cross sectof stress sectional tion for thinal stress

The stressically usin

For this p(4), and (approxim For ttorsional 4.752 mmN·mm. Tcan be seimate metthat therequired to mate meth

)

Coordinate fraudy. On the lecribing b depthotch radius. On

k structure withcenter of the pi

t/(2R), modulus, and tion (1) is an aation given by

inal stress can t

, it should be tion and does that comes f

geometry. C. Bhis stress and its using a stress

s concentrationng the chart in

paper we will r(5) as Ling’s m

mate method. the Z4-4602 fstiffness are ca

m, R = 1.524 These calculatieen in Table 2.thod is at mos

e is no substanuse Ling’s mehod there is no

ames for the tweft is a single fh, t flexure thicn the right is thh the coordinaitch pivot axis,

1 , ∆M the applie

approximation,

2 ⁄

9 ⁄

then be determ

6.

noted that thinot account fo

from a suddenB. Ling [7] dert can be determs concentration

.

n factor can be[8] or from [6]

1 ⁄

refer to calculamethod and Eq

flexure designalculated usingmm, E = 20

ions for both The error from

st 2.7 % for thintially greater ethod as compo reason not to

wo FEA modelsflexure with dckness, and R he complete la

ate frame now , θY.

∆ 2 , ed bending mo, and it has a f

⁄

⁄ .

mined from the

is assumes coor the concentn change in rived the exact

mined from then factor Kt

e determined g] using

ations using Eqqs. (2) and (3)

n stress, angleg t = 0.115 mm4 GPa, and Manalytical me

m using the apis case. Considnumerical effoared to the app

o use the more

s used

dimen-semi-

aminar locat-

E the oment further

(2)

equa-

(3)

nstant tration cross-t solu-

e nom-

(4)

graph-

(5)

qs. (1), as the

e, and m, b = M = 1 ethods pprox-dering ort re-proxi-

e com-



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pt

T

F mt

d

imt wuaettnntt

Fiatm

e

plete Ling metthis paper to as

Table 2: Compstress, angle of

Method

Ling’s

Approx.

% Error

FEA FlexureTo ensure

meshed with there can be cosingle notch fdescribed in a[9]. For a singin density usinmesh refiningtheoretical calc

The FEA with the same used in the preadaptive meshelements acrosthe setup is thethe stress resulnear the surfaneeds to be cathe elements nthose within th

Figure 4: Setupis the FEA setarrows on thethe magenta armoment aboutstress results w

The resultespecially for t

thod. Thereforessess FEA mod

paring theoreticf rotation, and

Stress [Mpa]

A

100.9

99.2

-1.65

e Mesh Valide that the laran adequate n

onfidence in thflexure mesh. a previous MEle notch flexurng SolidWorks

loops. The rculations. mesh and setgeometry, mat

evious section. h loops. At this ss the thinneste von Mises strlts a sudden space. This is taptured for thenear the surfacehe volume.

p and results otup of the sing

e bottom reprerrows on the tot the axis θY. Owith an exagger

ts of the setup ithe max stress

e, Ling’s methodel validity.

cal methods fostiffness of the

Angle [°]

Torsio[N

0.25

0.24

-2.68

dation rger flexure Fnumber of ele

he results, we fiWe do this u

EDSI 2014 core, the mesh ws Simulation 2results are then

tup can be seterial, and momThe mesh shomesh size ther

t part of the flress results. In

pike in stress cathe stress cone FEA model te are much mo

of the 5 loops cgle flexure moesent the fixedop represent thOn the right israted deformat

in Figure 4 arecriteria, as can

od is be used in

or calculation oe notch flexure

onal Stiffness N·mm/°]

4.07

4.18

2.70

FEA model iements so tha

first validate thusing a methodnference pape

will be increased2016 h-adaptivn compared to

en in Figure 4ment propertiewn is that for 5re are at least 2lexure. Next tothe close up o

an be seen onlyncentration thato be valid. Soore critical than

case. On the lefodel. The greend condition andhe pure bending the von Mise

tion shown.

low in error, n be seen in the

n

of e.

is at e d

er d e o

4 es 5 2 o

of y at o, n

ft n d g

es

e

plot of Figpared to thincreased.(increasintorsional sstress erroalso see thness and astress erromodel we

Figure 5:mesh looprameters:stress com

FEA Wetion

Now usstress errothe full flfirst validthe derivestiffness, stage.

Figure 6: and 0.5 (Ntop is the represention the intorque. Onabout 0.6°

gure 5. Here, thheory is shown. Interestingly,

ng mesh loops)stiffness becomor continues to hat a mesh usinangle errors as ors will be aroue then used 5 ad

: A plot of thps and the abs

rotation angmpared to theor

eak-Link Mod

sing the 5 h-aor to about 5%exure model w

date the qualityed stiffness vaand then predi

Setup and resN·m) of torqueFEA setup wit

ing the fixed cnside hole din the bottom i° rotation abou

he error of the n as the numbe, as the mesh d the error in ro

mes constant, w decrease. Fromng 4 or 5 loopsfar as they wil

und 5%. For thdaptive mesh l

he relationshipsolute error of gle, torsional retical predicti

del Validatio

adaptive mesh %, as shown in will be implemy of the FEA malues to experict the load cap

sults using 5 ae applied aboutth green arrowcondition and iameter repress the von Mise

ut θY.

FEA results coer of mesh loopdensity increaseotation angle anwhile the maximm the plot we cs will reduce stll go, and the m

he larger flexuroops.

p between adthe FEA modstiffness, andons.

on and Simu

loops to reducthe previous s

mented, Figure model by comprimentally meapacity of the fl

adaptive mesh t the θY axis. O

ws on the outsidthe magenta a

senting the apes stress result

om-ps is es nd mum can tiff-max re

aptive

del pa-d max

la-

ce the ection 6. We paring asured flexure

loops

On the de axis arrows pplied s with


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lmrtrimamt3tad

Ft

Fao±ptu

gditmMdtt

For stiffnstiffness is melinear spring smeasured usinresults of the stwo force gaureliability of thing at the FEAmatch betweenabout ~300 μmmany reasons this range; suc30 laminar shetolerance variaaccounted for.dressed.

Figure 7: Expethe Z4-4602 su

Figure 8: A passembly expeof different pre± 0.001 N andplotted is the sthe max stressuse from 0 to ~

Lastly, thegion to assessdirection. An inside diametethat would be ment. The resMPa and causdirection. Thistion of 31.3 N/the pitch rotati

ess validation easured and thestiffness that i

ng the setup in stiffness validauge lines overhe experimentaA stiffness resun model and em of equivalewhy the FEA m

ch as the real seets of metal, thations in the r. In future stu

erimental setupub-assembly.

plot of the stierimentally meecision, gauge

d gauge 2 with stiffness acquirs. Note the mo~300 μm of equ

e model is use the effect of equivalent loa

er of the flexurapplied due to

sulting maximused 0.63 µm os is equivalent /µm, three ordion direction.

the flexure men converted tois equivalent tFigure 7. Figution. Here we

rlap, which deally measured sults it can be seexperiment onlent actuator tramodel might nstructure is a bhe FEA analysreal flexure thidies these issu

p of stiffness m

iffness of the asured with tw1 being the fina precision of red from the Fdel can only buivalent actuat

ed inside of thloading the fl

ad of 2 kg wasre and an equio a 270 µm actum von Miseof parasitic mto a stiffness

ders of magnitu

model torsionao an equivalento the stiffnesure 8 shows thcan see that th

emonstrates thstiffness. Lookeen that a goodly occurs up toavel. There ar

not be valid pasbonded stack osis is linear, andickness are noues will be ad

measurement fo

Z4-4602 subwo force gaugener precision o± 0.01 N. Also

FEA model andbe validated fotor travel.

he validated relexure in the Ys placed on thivalent momentuator displaces stress is 17

motion in the Yin the Y direc

ude greater than

al nt ss e e e

k-d o e st of d

ot d-

or

b-es of o d

or

e-Y e

nt e-1 Y c-n

Z4-4The

PITM P84NPM140Sloop resoseen in FPolytecTM

~80 nrad about 20 nclosed lonoise flooabout 5 –

Desigx-ray polaexperimenwill increais a limit ttion withtechniqueshown thaof a least

Figure 9: In this setultimate c

4602 EXPERfine positionin40.10 piezo SG actuator. Tlution of 1 nm

Figure 9. DispM OFV 534 vib

steps. The nonrad which is mop control. If

or of the setup 10 nrad.

CONgn and developarizer was assnt. It was founase in accuracyto how well FE

hout incorporaes such as noat pitch stages80 nrad resolu

Experimental tup an alternatcapabilities of t

Figure 10: A

RIMENTALng resolution

due to unaThe P840.10 m. The experimplacement wasbrometer. Figuroise floor of thmostly contribf we disregardwith P840.10

NCLUSIONpment of a mesessed using F

nd that the maxy with a finer mEA can model ating additionaonlinear methos for the polariution.

setup to meastive actuator isthe stage desig

A plot of ~80 nr

L RESULTwas tested us

availability ofhas a stated cmental setup cs measured usre 10 shows a

he setup looks buted by the P8d slow driftingopen loop con

N echanism for aFEA simulatioximum flexure mesh, howeverstiffness and dal advanced mods. Finally, iizer will be ca

sure the pitch used to analy

gn.

rad steps.

S sing a f the closed can be sing a set of to be

840.10 g, the

ntrol is

a hard n and stress

r there deflec-model it was apable

angle.

yze the



TUBA01119

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f0

AWork suppo

fice of Scie06CH11357.

[1] T. Toe

resonaphysic

[2] T. S. Zhao, Argon

[3] D. Shconstrmecha2003

[4] D. Shconstrmecha2006

[5] D. ShPreissndesignray m(2007)

[6] S. T. "ElliptInstru

[7] C.-B. Appl. M1952.

[8] R. PetWilley

[9] M. Hifor tuAustra

ACKNOWLorted by the U.Sence, under

REFER

ellner et al., "Poant scattering ofcs letters, vol. 67

Toellner, A. Al"Next-Generat

nne National Lab

u, T. S. Toellnerained laminaanisms," U.S. P

u, T. S. Toellnerained laminaanisms," U.S. P

hu, S. Narayanner, and J. S

n of an UHV-commonochromator,").

Smith, V. G. Btical flexure hments, vol. 68, n

Ling, "On the sMech. Trans. AS

terson, "Stress coy and Sons

illman, "Design urbo slits," in alia, 2014.

LEDGMENS. Department

Contract N

RENCES

olarizer/analyzer f synchrotron rad7, no. 14, pp. 199

latas, E. E. Alption Mossbauerboratory, 2015-1

er, and E. E. Alar structure Patent granted

er, and E. E. Alar structure Patent granted

nan, A. Sandy, ullivan, "Precismpatible artifici" AIP CP879,

Badami, J. S. Dhinges," Reviewno. 3, pp. 1474-1

stresses in a notSME, vol. 19, no

oncentration fact

of a flexural hProc. MEDSI

T of Energy, Of

o. DE-AC02

filter for nucleadiation," Applied93-1995, 1995.

p, M. Hu, and Jr Spectroscopy,64-N0, 2015.

lp, "Redundantlyas weak-linkNo. 6,607,840

lp, "Redundantlyas weak-linkNo. 6,984,335

M. Sprung, Csion mechanicaal channel-cut x

pp. 1073-107

Dale, and Y. Xuw of Scientifi1483, 1997.

ched strip," J. oo. 2, pp. 141-146

tors, 1974," John

hinge mechanism'14, Melbourne

f-2-

ar d

J. ,"

y k

0,

y k

5,

C. al x-6

u, ic

of 6,

n

m e,


TUBA01120

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the design of a precision mechanical assembly for a hard x

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