Analysis of Lens Mount Interfaces - University of Arizona

Analysis of Lens Mount Interfaces

K. A. Chase, J. H. Burge

College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USA

ABSTRACT

Lenses are typically mounted into precision machined barrels and constrained with spacers and retaining rings. The details of the interfaces between the metal and the glass are chosen to balance the accuracy of centration and axial position, stress in the glass, and the cost for production. This paper presents a systematic study of sharp edge, toroidal, and conical interfaces and shows how to control accuracy, estimate stress, and limit production costs. Results are presented from computer models, finite element simulations, and experimental testing.

Keywords: lens mounts, lens seats, lens survivability, lens stresses geometric dimensioning & tolerancing

1. INTRODUCTION Lenses are typically mounted into metal barrels that use well defined, accurately manufactured surfaces that contact the polished glass surfaces. Additional spacers and retainers also contact the lenses to hold the lens in place. This paper summarizes both the art and the science that are used for the design of the glass to metal interfaces. We focus on three common configurations of lens interfaces – the sharp edge, a radiused toroid, and a conical or tangent interface. The intent of this analysis is to develop a greater understanding of what factors affect the accuracy of a lenses location within an optical mount as well as how different lens interfaces can influence the survivability of a lens.

The most accurate method of mounting a lens uses the polished optical surface itself as an interface datum. This method of mounting a lens provides the greatest potential for accuracy, but it can create highly localized contact stresses on the optical surface. These stress concentrations may or may not create issues with survivability that must be accounted for.

The details of the glass to metal interface, or the lens seat, provide the accuracy for positioning the lens. A toroidal lens seat refers to the standard rounded edge that a lens seats against. As the radius of the rounded edge reaches the minimum limit, the seat may be considered to represent the “sharp edge” lens seat that is most common in optical mounting. The conical lens seat refers to a lens seat that is designed and manufactured to be tangent to the curved surface of the lens at a specific axial radius. This cone shaped lens seat is also referred to as a “tangent lens seat” for the tangent nature of the interface. This seat is usually chosen because of an increased area for the distribution of contact forces, but there can be a trade-off for accuracy in manufacturing and inspection.

This paper will start by looking at mounting basics and achieving tight mechanical tolerances. In this section, the geometry and dimensioning of the toroidal and conical lens seats will be explored in detail. In the next section the focus of this analysis will shift to estimating the survivability of a lens and the reasons why one lens seat might be preferred to another.

2. ACHIEVING TIGHT MECHANICAL TOLERANCES

There are a few general considerations that need to be taken into account when it comes to achieving tight mechanical tolerances. In most opto-mechanical systems, cost is a factor that must be considered and can have an effect and be affected by the design. Focusing on the necessary tolerances of a design is not always obvious, but is important for not only the cost but also the manufacturability of a design. The capabilities and the standard practices of machine shops will vary but being aware of how they operate and what you can expect can also affect a design. Another feature of a design that can have larger than expected impacts on the survivability and accuracy of lens interfaces is the notes section of a drawing.

The cost of a design is driven by many factors. For the cases that are being analyzed here, the cost considerations will be limited to the number of features present and the level of the drawing’s tolerances. When looking at a specific part, it is

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important to note that the more features a part has and the more tightly it is dimensioned will be driving factors in the difficulty of manufacturing a part and therefore the cost. It is therefore, more efficient and effective to develop designs that meet the system requirements with the fewer features designed and dimensioned. This method can improve accuracy as well.

In order to keep tight the necessary tolerances of a design and relax the tolerances of unimportant features, it is important to know what degrees of uncertainty are present in our chosen mounting interface. In Figure 1 there are three examples of lens mounting interfaces. On the left, there is the sharp edge lens seat which has the fewest degrees of uncertainty. In the middle is the toroidal lens seat which increases in features that need to be tolerance and detailed. On the Right is the conical lens seat which can be dimensioned in a few different ways, it also has more degrees of uncertainty than the sharp edge seat.

Figure 1. Design examples for sharp, toroid and conical lens interfaces. Each interface can be called out in the engineering drawings with specific notes for manufacturing. More details are required for a complete design, but these are good examples to start with for the necessary dimensions.

In the following sections of this paper more detailed examples of these interfaces will be explored in order to illustrate the most important features of the designs. Particular attention will be paid to what these features and tolerances can mean for the positional accuracy of the lens. For various considerations it is also important that one pay particular attention to the engineering drawing notes and make sure that the tolerances for “unless otherwise specified” section of the drawing are not overly constrained. If the important features are dimensioned correctly, then the unspecified sections should be of little concern. Specifically, it is good to note whether or not all edges should be broken or left harp, what angular tolerances are present, and if there is a max radius for sharp corners. Machines shops that have experience with optics and opto-mechanical elements have many variations when it comes to their methods, standards, and limitations for manufacturing accuracy and inspection accuracy. It is good practice to have a clear understanding of what their capabilities and standard procedures are when it comes to a design. By picking a machine shop that sees the design’s requirements as standard, should provide a better end result along with a better cost level. Now a few specific cases of how various manufacturing and inspection uncertainties may affect a final manufactured lens system will be examined. The specific changes that can be expected to show up for a toroidal lens seat and for a conical lens seat will be detailed.



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ometry of the toters. This is als

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2.2 The Con

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o hold the conece for our lens

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Figu

In Figure 8 ibarrel for reathe specific dour lens’ raddimensions o

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2.3 Using a

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ure 8. The geom

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he cone angle ch the cone anthe position of

Gauge For M

gauge to verifthe measurem

of the one to be

harp corner at was to be avoid

metry of the co

hat the corner oe outlined prevn the notes secure we can deure 8.

for our lens inngle extends frof the lens vertex

Manufacturing

fy manufacturement and inspee used in the fi

the edge of thded by mountin

onical lens seat

of the one whiviously. It is imction of your enetermine our ax

nterface, rb is thom, rt is the rax, and R is the

g and Inspectio

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t

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he radius of ouadius for the pradius of curva

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prove accuracyns seat. A gaa specially des

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oned by the anll out your angwings. From thin z from the

ur barrels datuoint of contactature for the sp

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n this case, is a e a sacrificial nufactured par

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specialty part lens that matc

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A gauge radius can be specified on a sharp edge lens seat, a toroidal lens seat, or a conical lens seat. In figure 9 a) is an example of how a gauge radius can be dimensioned. In the dimension a reference is made to a part number corresponding to the gauge to be supplied or manufactured.

Figure 9. Using a gauge for manufacturing and inspection. a) an example of how to dimension a gauge properly b) the procedure for manufacturing and inspecting a feature defined by a gauge

For a machinist using a gauge, the procedure is rather straight forward. For an example using a sacrificial lens, the machinist will first make their initial cut, making sure to leave an excess of material for future adjustments. Next, they will insert the gauge provided along with some type of centering plug. By measuring the axial position of the sacrificial lens with a depth micrometer or coordinate measuring machine (CMM), the machinist can calculate how to make the final cut. After making the final cut, the machinist can then verify the cut in the same way as the initial measurement was made.

This is useful for working with all types of lens seat interfaces, given that the ability to obtain possibly sacrificial lenses or manufacturing specialized gauges is not limited.

3. ESTIMATING SURVIVABILITY When it comes to survivability of lenses in our various mounting interfaces there are many factors that we can focus on in order to ensure lens safety. These factors that may lead to reduced glass strength can include micro-flaws in the surface of your part, simple humidity, as well as unexpected point stresses that may result from a burr or a buildup of material on your lens interface.

Micro-flaws, also known as subsurface damage, can be, for the most part, polished out of an optical surface. One issue that arises with subsurface damage is that it cannot be accurately measured or identified by non-destructive means after the polishing process is completed. These flaws, if present in conjunction with atmospheric humidity and global stress fields, can degrade the survivability of an optic.

Humidity and global stress fields can cause a flaw to propagate over time if the stress is of a significant magnitude[2]. Water is a catalyst for lens crack propagation and as such, it is important to avoid high contact localized stress fields when there are global stress fields present in a part. An example of this case would be for an optic that is exposed to high pressure differentials such as a vacuum window.

Manufacturing using a gauge

1. Initial CutLeave Material

2. Insert GaugeMeasure Position withDepth Mic or CMM

3. Final CutBy The Numbers 4. Verify Cut

Teflon Centering Plug

a) b)



Burrs or the lens seats dushould be nosuch as “Dimwith anodizinenough for an

Mounting intto understand

3.1 Stress in

The Toroidalstresses can bare acceptababout 1000 lthese estimat

It was mentiostays shallow

Figure 1Region I

If no flaws restress intensi

is roughly eqsquare root ofailure of the

It has alreadyBurge have dinterface. Wbarrel.

point stresses ue to their geomoted that parts mensions after ng a part. Thisny opto-mecha

terfaces on thed how these dif

n the Toroidal

l case for estimbe very high, tle. Under typilbs/in2 [3]. Thtes may be too

oned earlier thw, any micro fla

10. The stressI is experiencin

each the criticaity factor,

quivalent to twoof the flaw depte optic may occ

y been mentiodemonstrated t

With typical pre

that result frometry. A methocan develop banodizing” an

s information wanical designer

eir own producfferent mountin

l Interface

mating survivabthese stresses acal conditions,

he tensile stresconservative f

at cracks will paws or subsurf

s field produceng tensile stres

al depth in the p

o times the nomth, a. The fraccur.

oned that the hthat there is noload torques ar

om them shoulod for avoidinbuildups that wnd an indicationwith a caveat tor to prevent poi

es compressiveng interfaces w

bility is well dare highly loca, glass can sursses are the limfor polished op

propagate overface damage th

ed by a sharp s. The darker

presence of a h

minal tensile stcture toughness

ighest localizeo loss in strenground 10in-lbs

ld not be commg burrs on a sh

would cause pon of the surfaco indicate that int stresses from

e and tensile stwill produce dif

defined in somealized and for rvive compressmiting factor inptical glass.

r time with strehat may be pres

edge lens seathe stress field

high intensity d

tress perpendics, KIC is the cri

ed stresses willgth for axial ps, a preload for

mon problems harp edge lensoint stresses dce quality shoupoint stresses

m being an issu

tresses as a resfferent stresses

e cases. For thmost environmsive stress of 5n most cases. C

ess and humidisent on the surf

at. Region II d, the greater th

deep stress field

cular to the craitical value of t

l be produced preload stressesrce of only 16 l

for the specifs seat was prevduring an anoduld prevent anyshould be largue to the safety

sult of preload s in the optic.

he sharp edge ments and appl50,000 lbs/in2 Cai and Burge

ity. As long asface of on optic

is under comp

he tensile stress

d, then the lens

ck plane, σ0, mthe stress inten

by the sharp es under 100 lblbs/in is applie

fied toroidal orviously discussdizing process. y issues that mgely avoided shy of their lense

forces. It is im

lens seat, axiallications, theseand tensile str

e have determi

s the tensile strc will not prop

pressive stresss. [2]

ses will surviv

multiplied by thnsity factor at w

edge lens seat. bs/in for a shared for a 1 inch

r conical ed but it A note

may arise hould be es.

mportant

l contact e stresses resses of ined that

ress field pagate.

s,

e. The

(5)

he which a

Cai and rp corner diameter



If larger lensassociated wwith a larger

The toroidal tangential or the radius of

Figucont

Yoder [3] anmount with alens seat. Th

Axial compre

Where F is ththe lens, vm retainer or se

3.2 Stress in

The axial cosharp edge lgreater surfacmargin.

ses are being with high stress

value for ρ or

lens seat can conical interfa

f our toroidal in

ure 11. The shtact with each

nd Vukobratovia toroidal lens he equation for

essive stress, σ

he retainer preis poisons rati

eat, y is the heig

n the Conical

ntact stresses rens seats. Thce area over w

mounted, or ths fields. For tha conical lens

be consideredace at the uppenterface increas

harp edge andother. Adapted

ich [4] have adseat. This is a

r calculating the

σA, is defined a

load, d1 is twicio for the retaight of the line

Interface

resulting from his is the case which to disturb

here are globahis reason, a dseat.

d to live betweer limit. Becauses, the stress e

d the toroidal ld from Yoder [

dapted a methoalso the same me stress is repro

as

ce the lens radiner, Eg is thecontact on the

the conical lefor interfaces

bed the contact

al stress fields designer should

een the radii liuse of this basicexperienced by

lens interfaces[3]

d from Roark fmethod for deaoduced below.

ius, d2 is twicee elastic modulens. [3]

ens interface arwith the same

t stresses. For

present, than d consider wor

imits of the shc understandin

y our lens will d

s stresses are e

for computing aling with the s

e the toroid or culus for the len

re lower than te preload sincethis reason the

it is importanrking with eith

harp edge on thng of the interfadecrease.

equated to two

the axial compstresses that re

corner radius, ns, Em is the e

those resultinge the tangentiae survivability

nt to mitigate ther a toroidal l

he lower limitace we can not

o cylinders in

pressive stress esult from a sha

vg is poisons relastic modulus

g from the toroal interface prois increased by

the risks lens seat

t and the te that as

in a lens arp edge

(6)

ation for s for the

oidal and ovides a y a large



FiguAda

Yoder develothat of the le[3] this gives

The axial com

Where D1 is the toroidal i

We have expinterfaces. Wand axial comissues that mhow to calcu

[1] C. L. HoContact

[2] W. Cai, (2011).

[3] P.R. Yod

[4] Vukobra

ure 12. Conicaapted from Yod

oped a rule of ens radius beins a good limit a

mpressive stres

twice the radiunterface examp

plored the factoWe have seen tmpressive stres

may affect surviulate the ways i

opkins, J. H. BLens Seats,” P

B. Cuerden,

der, Opto-Mec

atovich, D. Intr

l tangent lens ider [3]

f thumb that shg seated will bat which point

ss for the tange

us of curvatureple above.

ors that are mothat for both csses experienceivability in conin which the er

Burge, “ApplicaProc. SPIE 813

R.E. Parks, J.

hanical System

roduction to Op

interface stress

hows the contabe the same as we can conside

ential surface c

e of the optical

4. COost pertinent toases we have ed by our lensenjunction with rrors in our man

REFation of Geom1, (2011).

. Burge, “Stren

ms Design, 2nd

ptomechanical

ses are equated

act stress resultthe stress pres

er changing ou

can be calculate

l surface and a

ONCLUSIOo the survivabia trade-off betes at their intercontact stressenufacturing ma

FERENCESetric Dimensio

ngth of Glass

d Ed., pp. 174-1

l Design, SPIE

d to cylinders co

ting from a torsent in a conicaur design for a

ed as

ll other values

ON ility and locatitween the easerfaces and retaies as well as thay affect the ac

oning & Tolera

From Hertzia

185, Marcel De

E Short Course

ontacting a tan

roidal surface al lens seat witdifferent lens i

are the same a

ional accuracy e of optical suriners. We disce geometry of ccuracy of our

ancing for Shar

an Line Conta

ekker, (1993).

014 (2008).

ngent plane.

with a radius th all else beininterface.

as in equation

of 2 basic lenrface location acussed briefly tour lens interflenses location

rp Corner and

act,” Proc. SPI

10 times ng equal.

(7)

(6) from

ns mount accuracy the other faces and n.

Tangent

IE 8125,



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Analysis of Lens Mount Interfaces - University of Arizona