# Optomechanics* – Jade Brittle Fracture Analysis Tool

*A note from Teale Hatheway: As I pored over Dad’s emails to organize and archive AEH’s Optomechanics Newsletter, I came across this gem which, dated 7-18-18, was never shared. I also discovered an abundance of conversations sparked by these communications. It’s no wonder Dad enjoyed his work well past “retirement age”: your camaraderie combined with his intellectual pursuits gave him great joy. He would’ve called it “sport.” With well over 100 Optomechanics Newsletters published since 2006, the experience of compiling these brought me renewed clarity on Al’s life work. From AEH product announcements, to carefully worded client stories, to occasionally revealing his trade secrets, I hope you will continue to enjoy his wit and his wisdom here… So here we go! The last Optomechanics. I sure hope he finished editing it. Enjoy!

———–

Colleagues:

Put fracture mechanics to work for you!

Fracture mechanics says that glass is sensitive to static stress corrosion fatigue effects.  Glass parts have finite fatigue lives when operated in a normal moist environment.  If the fatigue life, T, is defined as the time to fracture under the conditions of service, that life may be calculated from

noting that KIi is the initial stress intensity, KI is the instantaneous stress intensity, KIc is the fracture toughness, v is the instantaneous crack growth rate and the local stress, s, is time-variable and it is inside the integral.

AEH recruits our Jade Brittle Fracture Analysis Tool, to perform the numerical integration and determine T, the fatigue life.  For Jade it’s a piece of cake!

For instance, take this thermal-structural stress transient for an aircraft’s window requiring 10,000 flight hours of service life:

FULL STRESS CYCLES AT FRACTURE= 3563
TIME TO FRACTURE= 44896587.75
SECONDS= 12471.274375 HOURS
CRITICAL INITIAL TENSILE STRESS= 55002270.5466022
INITIAL CRACK DEPTH= .000149

If the engineer applies a reasonable factor of safety, say 1.5, to the critical initial tensile stress (the ultimate load) it will provide a proof test load (82.5 MPa in this case) that will assure the safety of the window throughout its service life.

There’s no way to get there with closed-form solutions and it’s way too big for an Excel spreadsheet.  Jade goes through the complete calculation in just seconds, allowing the engineer to try various combinations of design variables to optimize a safe concept.

Now available from AEH.

Al H.
7-18-18

# Optomechanics – Tensile Strength of Glass

Colleagues:

OK, AEH hit you in May you with analyzing the tensile stresses in cemented glass doublets.  Then AEH hit you in June with analyzing the tensile stresses in ring-mounted glass lenses.  And you responded with numerous queries about AEH’s analytical methods… but they were surrounded by a massive silence.

No one asked, “What’s the tensile strength of the glass?”

It’s a characteristic attitude in the optical industry, that the strength of glass is not its problem, “Leave that to the structural engineers.”

Well, surprise!   The structural engineers don’t care either.   Glass, being brittle, is in no-way a structural material.  Structural engineers design with ductile materials like steel and aluminum.  The only brittle material they routinely design with is concrete and they insist that it never see tensile stresses.  That’s why they invented pre-stressed concrete: to eliminate the tensile stresses!

The tensile strength of a glass is determined by its “fracture toughness,” a material property of the glass that can be measured in a test lab and is repeatable.  However, among the silica glasses the values for fracture toughness appears to vary, based on the very limited data available, by factors between 3 and 5, depending upon the specific glass composition.  It makes a big difference which glass is used in high-stress situations.

Ah, just one of the challenges
(and one of the joys!)
of optomechanical engineering.

Al H.
7-2-18

# Optomechanics – SOLVED: Elastic Theory’s Differential Equations for the Tensile Stresses in Glass Lenses Mounted in Threaded Metal Rings

Colleagues:

AEH has solved elastic theory’s differential equations for the tensile stresses in glass lenses mounted in threaded metal rings, and it’s good news.

Paul Yoder had originally proposed Delgado and Hallinan’s 1975 solution (Opt. Eng. 14) but their solution gave very high tensile stresses in the lenses, high enough that virtually all such lenses should have fractured.  None of my ring mounted glass lenses had ever suffered that fate.  I surveyed a number of my colleagues and none of them recalled a ring mounted glass lens fracture.

Delgado and Hallinan’s work was flawed.  To correct their flaw would require a new solution to the equations of elasticity that honored the appropriate contact geometry.  AEH finally made it happen and the result is surprisingly simple,

s = p(1-2u)/b,

where s is the peak tensile stress, p is the linear ring load, b is the radius of the contact ring and u is the Poisson’s ratio of the glass.  This stress is three-to-four orders of magnitude lower than that predicted by Delgado and Hallinan.

Using Nastran AEH was also able to verify the general shape of the stress distribution in spite of Nastran’s notorious difficulty at the point of load application.

Closed-form solution       >>>         Nastran solution

To learn more you have choices:  Either download AEH’s peer reviewed paper from SPIE [Optical Engineering 57(5), 055105] or go through the gory details with me in my tutorial,

“Optomechanical Analysis,”
SPIE’s Optics and Photonics Symposium in San Diego
8:30 AM to 5:00 PM on the 21st of August.Cheers!

Al H.
6-6-18

# Optomechanics – Fabricate Glass to Meet Proof Test Requirements

Colleagues:

Well, AEH has had another full year with no broken glass!

We do this by defining, for the glass fabricator, a proof test that his product must pass to meet the project’s service life requirements.

The strength of glass is knowable to the engineer if the glass suppliers will provide some simple fracture properties for their glasses:  the critical stress intensity factor and two or three points on the stress corrosion curve.  The glass suppliers tend to not publish these data.  So most of AEH’s successes are steering designs into using optical glasses for which the data have been published (or using that client’s proprietary data).  The balance of AEH’s successes have used larger factors of safety with conservative estimates of the glass’s fracture properties.

In either case, AEH feeds the service conditions (the thermal-structural dynamic stress profile and the initial surface crack size) into Jade with the appropriate fracture properties to analyze the service life of the glass product.  The independent variable is the initial surface crack size.  With the acceptable initial crack size determined AEH then designs a static proof test for the glass fabricator to demonstrate that the glass product will meet the required service conditions.  The glass fabricator may then design the fabrication process (grinding and polishing) to meet the proof test requirements.

There are some disappointed glass suppliers but it’s their choice whether (or not) to publish the fracture properties of their glasses.

Spring arrived right on time.

When the safety of glass is at risk AEH has these tools too!

Al H.
3-28-18

# Optomechanics – Secret Sauce

Colleagues:

Optomechanical engineers are a lot like professional chefs.  Each has a “secret sauce.”  Just like chefs we sample and adjust our sauces all the time to be sure they’ll come out consistently good.

AEH’s secret sauce is selections from W. J. Smith and R. J. Roark blended into K-J. Bathe.  Below I use the optical prescription to determine the optomechanical constraint equations (OCE) between each of its ten optical elements and the image on the detector (pink).  I then estimate the required stiffness properties of the structure between the elements, I define a lumped mass for each of the optical elements and connect them together with the nine beams (yellow) with the (estimated) proper stiffnesses.  I run it for the LOS error:

This initial run is usually off-target but it provides a starting point.  I replace the lumped masses with the actual lenses (from step files) and adjust the stiffness of the beams until I’m in the ballpark of the required LOS error.  Then I guide the design of the CAD structure to have the proper proportions to meet the required LOS error…

Voi-la!

1.3 ur rms . . . LOS . . .  1.4 ur rms
from Proposal    ——————————————————>    to Product.

AEH’s sauce provides the project a continuous and traceable record of the adequacy of the structural stiffness supporting the optical system from the earliest concepts to the final tested product.  AEH’s sauce is a little different every time, just like its culinary counterpart.

Bon appetite!

Al H.
2-7-18

# Optomechanics – Zoom Lenses

Colleagues:

Zoom lenses are getting hot again.  They seem to come in cycles for AEH.

There was the 20:1 MWIR zoom with a 300 mm entrance pupil.  It was a lot of fun!  Good for a mechanical engineer to cut his teeth on too.  As tough as it was, it actually inspired much of AEH’s optomechanical engineering practice.

The 8:1 visible microscope zoom for medical diagnostics was an application that brought its own challenges.  Using commercial optical assemblies where only the focal lengths were known required some lab work to find their principal points.  Those of you who’ve taken my short course in optomechanical analysis or used my Ivory Optomechanical Modeling Tools will appreciate that need.

Then there was the 10:1 NIR zoom with 36 individual images, five moving lens groups and two working distances.  And it had to be packaged into a convenient instrument case.  AEH used a customized version of the Ivory Optomechanical Modeling Tools to make that one happen too.  One of the advantages of having the source code is that I can make it do whatever is needed at the time.  And the current version’s users receive the upgrades as I develop them.

It’s a New Year with new opportunities and new challenges.  As I said last time,

Here we go-o-o-o-o-o…….

Al H.
1-9-18

# Optomechanics – So Many Tiger Teams

Colleagues:

Hold that Tiger…

I told you a while ago about attending a Massachusetts “TigerTeam” review of an external store for the F-16.  It took three days of talking about everything else to finally get to the crux:  High thermal gradients in the slab made the cavity unstable!  Surprise, surprise!  After the final session I got a tour of the brassboard’s laboratory.  The mechanical engineer confided to me that the brassboard would not work when it was up-side-down (talk about a tender cavity structure for a tactical aircraft application).

I’ve also told you about the two day “Tiger Team” in Texas for a laser, the brassboard of which worked just fine but the flight system lost power when a laboratory door was opened or closed.  In the final session the mechanical engineers described how the system’s flexure mounts for the cavity had been replaced (since they were not space-rated) with hex-head bolts!

Then there was the four-day “Tiger Team” in Illinois that reviewed the flight tests for a two-color recce system.  When I asked to see the imagery they declined and when I pressed for some quantitative data on the image quality they said they were unable to measure it.  And that was their “improved” design.

And the Culver City “Tiger Team” that couldn’t get their encrypted light back into their fibers.  The optical designer and I both stumbled onto the fix for that one at the same time.

Well, the Massachusetts folks managed to pull it out and Culver City folks went into production in Texas.  As “Tiger Teaming” goes two out of four ain’t bad.

…and, here comes 2018.  Hold onto your hats too!!!

Al H.
1-5-18

# Optomechanics – Unified Approach to Thermal Structural Optical Analysis

Colleagues:

Optics is a crazy industry.  We’re so dedicated to the digital computer that we often overlook underlying realities.  That’s especially true in the mechanical engineering art of heat transfer.  Management structures have insisted on each discipline using its own software which has Balkanized the disciplines of structures and heat transfer: i.e., the temperatures must be analyzed in a finite difference (FD) code and the results imported to a finite element (FE) code.  The importation involves extensive extrapolation and interpolation of the FD data to the much larger (often by two or three orders of magnitude) of the FE data-set and it can lead to some peculiar results.

AEH has long preferred a more Unified approach:  Select a code that can do them both, usually an FE code, and use engineering judgement to adapt the other discipline (usually a few boundary temperatures).  It usually requires several runs of the problem to assure that the underlying assumptions of the adaptation were appropriate but they go much faster than the Balkanized approach (and, often, more accurately for the optics behavior).

It’s the thermal-structural-optical method I used on the LACE Ultra-Violet Plume Instrument, which made Aviation Week’s75th Anniversary Issue.  Check out the UV plume image from AW’s cover, above!

More recently, a colleague was directed to thermally analyze an optical system in CFD and I was to apply his temperatures and gradients to calculate the boresight errors among the optical instruments.  Well, what he was handing me made no sense at all.  So, I added heat transfer terms to my opto-structural FE model and ran the operational transient of concern to the project.  The thermo-structural-optical results were spot-on.

There are a lot of ways that an engineer needs to keep his tools sharp.  And they require maintaining confidence in the analytical methods as well.

More later.  Happy Holloween!!!!!

Al H.
10-23-17

# Optomechanics – The Industry Needs to Know the Strength of Optical Glasses

Colleagues:

Fall is coming in two weeks and the Great Pumpkin is right down the road.  It’s time to kick-back and just look around a bit at this Glorious Summertime…

I’ve had about four weeks on the road lately, touching base with all of you (or most of you, I hope).  Then I cruised around SoCal in my spare time chinning and jawboning with the local industries’ participants.  So, what are the “hot items” for optomechanical engineers today?  Well, how ’bout…

precision dimensioning and tolerancing of optical structures
repeatability and stability of instrument performance
broken optical glass

I’d have trouble identifying the most important of these, it all depends upon what’s happening NOW.  All three of these have kept me pretty busy since Valentine’s Day.  The greatest uncertainty for the engineer, however, is in the strength of optical glasses.  Its not just mirrors and windows.

I’ve participated in two projects in which the optical design had to be revised (compromising performance) to replace glasses that could not pass the environmental tests.  Perhaps, someday, the glass houses will start to provide strength information on their data sheets near the Young’s modulus and Poison’s ratio.  Today the engineer can’t be sure until the tests are passed.

And we, all of us, managed to squeeze-in a terrific conference with SPIE in San Diego last month (32 papers published).  How we were able to pull that together, I just don’t know.  But, it would never have happened without you and the terrific staff at SPIE who keep us on the right track.

Here comes Guy Fawkes Day. Get your bonfires, and marshmallows, ready! All our prayers this day are with those who may be in harm’s way.

Al H.
9-7-17

# Optomechanics – MatLab Models and Ivory

Colleagues:

Hey, Control Systems Engineers, this one’s for you!  I’m sure you remember my dear friend who likes to declare, “You have to know the answer before you do the analysis!”  And his wicked “eye-twinkle” was part of that message too.  I used him then as a vehicle to highlight the importance of engineers making estimates and developing a “sense of smell” about the quality of their decisions.

So, my question for you is:  How do you incorporate the line-of-sight into the MatLab model of your “stabilized” optical system?

Well, AEH knows of three ways:  1) You can calculate it yourself, from the optical prescription, and insert it in your MatLab file, with some luck, or 2) you can copy the Optomechanical Constraint Equations (OCE) from Ivory and patch them into your Matlab file, with a little better luck, or 3) you can speak nicely enough to the structural engineer for him or her to import the OCE (from Ivory) into his FE model and the resulting eigenvectors, BINGO and…

If you want to learn more here’s an opportunity:  On August 7th, all day, I’ll be teaching my course, Optomechanical Analysis, for SPIE’s Symposium Optics+Photonics 2017 at San Diego’s Convention Center and Marriott Marina Hotel.  The first half of the course is all about the OCE, how you generate them and how they’re used.  Then you might stick around for our Conference, Optomechanics 2017, on the 8th and 9th to find out what everyone else is doing.  On Tuesday evening, the 8th, I’ll be hosting a meeting of the Optomechanical Technical Group between 8 and 10.  Dan Vukobratovich will be our principal speaker followed by an open discussion.

Yeah, you guessed it.  My dear friend is a control systems engineer.  One of the things I did for him was to assure that the structural engineer incorporated Ivory’s OCE into the FE model that produced the eigenvectors he used in MatLab to design the control system.  Later system tests on the shaker-table confirmed the quality “smell” of this decision.  Ivory nailed it, dead-on!

I’ll see all of you in San Diego!

Al H.
7-10-17