analysis of lens mount interfaces - university of arizona
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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
Optomechanics 2011: Innovations and Solutions, edited by Alson E. Hatheway,Proc. of SPIE Vol. 8125, 81250F · © 2011 SPIE · CCC code: 0277-786X/11/$18
doi: 10.1117/12.893948
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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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2.1 The Tor
As was mentare when it climit, earlier inspect. Theoptical surfac
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Although, thedge. The shdepending onedge radius fcalled out ontoroidal seat
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or this reason ithould be called
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case, e seat nspect.
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Figuspecrequ
Figure 5 shoall other dimsurface whicdatum A. Foconcentric tothat this is alis an importalimit that corfeatures of thposition of th
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ance than e the flat d by the
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own to a mportant the axial ances.
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In Figure 6, aaxial position
2.2 The Con
The conical lform of contlens interfacethe lens accu
There is an standard. In designing anright, is an eand manufacconical seat w
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In the case osurface in recone’s start p
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n our ability tocontact distanc
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o hold the conece for our lens
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ensure that theolerance, then
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(2) ce. This arp edge cation of
than the d way of . On the features
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r tangent us of our
dius of a ction. By motion of
ce of the either be
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seated on its This is the ex
Figu
In Figure 8 ibarrel for reathe specific dour lens’ raddimensions o
Where θ is thpoint at whicsurface, z is t
2.3 Using a
The use of a assisting in dimensions oor shape.
edge, or the sxact case that w
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
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ed parts can impection of a lennal system, or
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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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ngle θ is the samular tolerance,hese points of ifollowing equ
um cylinder wht between the pherical surface
n this case, is a e a sacrificial nufactured par
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specialty part lens that matc
rt with a specif
surface.
us of the done on
ned with ng to the
(3)
(4)
ds to the spherical
used for ches the
fic radius
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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)
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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
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mating survivabthese stresses acal conditions,
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r time with strehat may be pres
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mon problems harp edge lensoint stresses dce quality shoupoint stresses
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deep stress field
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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
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forces. It is im
lens seat, axiallications, theseand tensile str
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ses will surviv
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Cai and rp corner diameter
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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
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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
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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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