The Research, Design and Fabrication of
a Friction Based Precision Optical
Positioner
By Burton B. Bruce P.E.
1
1 Table of Contents
Contents
1
Table of Contents .................................................................................................................................. 2
2
Table of Illustrations ............................................................................................................................. 4
3
Introduction .......................................................................................................................................... 5
4
5
3.1
Scope ............................................................................................................................................. 5
3.2
Historical Perspective.................................................................................................................... 5
3.3
General Theory ............................................................................................................................. 7
3.3.1
Friction .................................................................................................................................. 7
3.3.2
Travel..................................................................................................................................... 7
3.3.3
Speed and Heat ..................................................................................................................... 7
3.3.4
Vibration................................................................................................................................ 7
3.3.5
Lubrication ............................................................................................................................ 7
3.3.6
Magnitude of Friction ........................................................................................................... 8
Theory and Methodology; .................................................................................................................... 8
4.1
Specific Statement of the Problem ............................................................................................... 8
4.2
Current Art .................................................................................................................................... 9
4.2.1
Piezo Electric Systems; .......................................................................................................... 9
4.2.2
Flexure based systems; ....................................................................................................... 10
4.2.3
The Friction Based system; ................................................................................................. 10
Methods and Discussion ..................................................................................................................... 11
5.1
Basic Requirements..................................................................................................................... 11
5.1.1
Stability; .............................................................................................................................. 11
5.1.2
Repeatability; ...................................................................................................................... 11
5.1.3
Orientation Independence; ................................................................................................. 11
5.1.4
Small size; ............................................................................................................................ 11
5.2
Initial Discussion.......................................................................................................................... 11
5.2.1
5.3
Design Flow ................................................................................................................................. 13
5.3.1
2
Proprietary Information ...................................................................................................... 11
Movement and adjustment ................................................................................................ 13
5.3.2
Normal Force Calculations .................................................................................................. 13
5.3.3
Low Verses High Coefficient of Friction Resolution ............................................................ 13
5.3.4
Coefficient of Friction Determination ................................................................................. 14
5.3.5
Coefficient of Friction Experimentation.............................................................................. 15
5.3.6
Holding Force Calculations .................................................................................................. 16
5.3.7
Overall Vibration Susceptibility ........................................................................................... 16
5.4
Design Summary ......................................................................................................................... 17
6
Conclusion ........................................................................................................................................... 17
7
Bibliography ........................................................................................................................................ 18
3
7.1
Current Art .................................................................................................................................. 18
7.2
Desirability .................................................................................................................................. 18
7.3
References .................................................................................................................................. 18
7.4
Quotations .................................................................................................................................. 19
2 Table of Illustrations
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
4
Figure 1 (replica of the Gutenberg Printing press)
Figure 2 (early machine tool examples)
Figure 3 Typical micro-optic prism with standard paperclip
Figure 4 Piezo electric X-Y Stage
Figure 5 Flexure based X-Y stage
Figure 6 Compact Dovetail Linear Stage, 6.3mm XY Travel, 25 x 25 x 26mm, Metric
Figure 7 Precision Optical Positioner; Optical Carrier Cut-away
Figure 8 Precision Optical Positioner (POP)
Figure 9 Table of some common Coefficients of Friction
Figure 10 316 Stainless steel interfacing with 6061 aluminum friction test
Figure 11 1st harmonic vibration profile
Figure 12 The Precision Optical Platform
3 Introduction
To illustrate the problem and its scope I will use the analogy below:
More than likely you are reading this on a computer with a mouse attached to it. Over the last few
decades the computer mouse has become as ubiquitous as a pencil. One of the features that makes the
mouse useful is that if your” mousing” surface is flat then the mouse stays exactly where you put it until
the user places their hand on it to move it again.
The mouse phenomenon that makes it so useful is due to several factors; the flat mousing surface, the
fact that you are in a gravity field that holds the mouse onto the surface, sufficient friction for the
mouse not to be moved by small disturbances, and the user knowing where the mouse is at all times
even when not touching it.
3.1 Scope
Simply put the goal of this project is to repeat on a much smaller and more precise scale the general
function of a computer mouse. The precision optical platform is usually asked to carry a simple micro
optical device such as a lens or mirror that is usually smaller than 1 mm square and masses <1 gram.
Modern optical structures are made of a series of devices that need to be held stably but in a manner
that will allow the devices to be aligned by small displacements in the x-y directions. To further
complicate the issue there is no assurance that the optical device carrier system will always be oriented
so that a normal for will be in the same direction as the gravity field. Many times optical systems have
devices hanging from their sides or upside down. The needs for adjustment and stability are still there.
3.2 Historical Perspective
One of the earliest ways to keep something in place was simply to put it there. We rely upon the normal
force (gravity) and the fictive force to keep it in place essentially on a flat surface. From there to move
an objet the ramp was invented and the act of pushing an item up a ramp got it to a higher elevation
with much less effort than lifting it. Then someone came up with the idea of putting the ramp around a
shaft and the simple screw was invented. All of these items relied upon friction to secure the item being
moved in place so that when the force was released the item did not slid back down the path it came
up.
The screw thread has been used for translating circular motion into linier motion for hundreds of years.
The screw provided the press for the wine press and the printing press. In the case of a screw thread
unless the reaction force was quite large or the pitch of the thread was quite coarse the screw stayed in
one place until a torsional force was applied to the driven device. This was due to the inherent friction
between the male surfaces of the thread and the female surfaces of the thread. The best analogy is a
very long plank sitting on a very long incline. Since one of the general issues with frication is that it is
rather independent of contact area the screw is still functional even though there is a great deal of
seeming contact area. When in simple motion or in an unloaded screw state where the internal threads
are free to turn with respect to external threads there is minimal surface contact. The load is carried by
the asperities in a dry system and by the lubrication in a lubricated system. Upon reaching the fully
tightened condition the normal forces go up considerably and the system is locked.
5
Figure 1 (replica of the Gutenberg Printing press) [12]
In figure 1 it can be clearly seen that the “press” is provided by a screw thread. As time progressed it
was realized that the screw thread could be used for moving loads very small distances and keeping
them in place. Another example would be a carpenter’s vise.
The traditional way of achieving small movement has been the use of a drive screw that has an
extremely fine pitch. The French Screw shown below in figure 2 is an example of an early precision
mechanism. It relied upon the fine screw for adjustment of the cutting edge and the natural friction of a
fine screw for stability.
Figure 2 (early machine tool examples) [11]
Hence the friction developed between two surfaces has been relied upon for centuries to do work and
to stably place an object in a required position.
6
3.3 General Theory
3.3.1 Friction
In general, friction is used to keep an object in a particular location that you may want to move again.
The simplest equation that involves friction is Coulomb friction F (the force needed to move and object
on a flat surface) = μ (the coefficient of friction) * f (the normal force to the surface). The two basic type
of Coulombic friction are static and dynamic friction. As their names imply one type of friction is
associated with getting an object moving and the other is the effort that is required to keep it moving.
3.3.2 Travel
In this project the movement will be small, on the order of 1 μm with a full travel range of 100 to 200
μm. While the motive forces to accomplish these movements will be discussed, the way to motivate
movement of the optical device is secondary to the method of keeping it in place in a manner to allow
adjustment numerous times.
3.3.3 Speed and Heat
When friction is commonly thought of it is associated with speed and the heat that is generated. In this
inquiry since the movement is small and there is no need for speed heat will not be a factor. Since this is
the case there will not need to be any mitigation for heat dissipation.
3.3.4 Vibration
In addition since the speeds will be low and the displacements are small there will no need for
dampening of the potential vibrations created by the relative movement of the two surfaces.
3.3.5 Lubrication
When dealing with friction the issue of lubrication arises quite often. It has been know for millennia that
lubrication of some form will considerably lessen friction between two bodies. Lubrication can be
embedded in one or both of the touching surfaces such as graphite, Teflon or some other low friction
surface treatment. In the case of a modern car engine the and many other high speed applications
there is an active lubrication system present that is vital to the smooth operation of the system.
Another way to mitigate friction is to apply a coating of a high viscosity lubricant (grease) to the surface
interfaces to facilitate sliding.
According to O.M. Braun and A.G. Naumovets, “Almost always there is a lubricant between the solids
(called \the third bodies" by tribologists), either a specially chosen lubricant film, or a grease (oil), or
dust, or wear debris produced by sliding, or water or/and a thin layer of hydrocarbons, etc. adsorbed
from air. Thus, the frictional force is almost entirely determined by the force required to shear the
lubricant film itself.” [a]
In addition to other third body lubricants that may be present there also may be the oxide of the base
material itself. For example using aluminum in a normal air environment the surface layer is aluminum
oxide unless heroic measures (inert gas, vacuum etc.) have been enacted to prevent the oxidation of the
primary aluminum.
7
All the friction mitigation systems mentioned above will be considered but some such as active
lubrication seems to add complication and infrastructure that may be unnecessary. Part of the goal of
this exercise is to keep the design simple and to design in the needed features at the material level. To
the end of simplicity since neither heat not speed is a factor the lubricating elements will be the
naturally occurring oxides that appear on the surface of the material interface.
In dealing with optics the use of free or secondary lubricants is contraindicated. Historically there have
been many cases of the degradation of optical systems due to a lubricant migrating or outgassing and
depositing on optical surfaces. Keeping this in mind the desirable lubrication regime is an embedded
lubrication (dry lubrication). The easiest of dry lubrication method to achieve is the use of the inherent
oxides that are naturally occurring on one or both of the materials when existing in air.
3.3.6 Magnitude of Friction
One of the questions that will need to be answered early in the design is whether a high friction or low
friction system is more desirable. A low friction system would be easier to adjust and use less energy to
make the appropriate adjustments. The high friction system would at first glance seem to be more
desirable due to the motion resistance that would seem to be inherent in the system. Of course there
is another factor; the normal force. If there is a high normal force then the forces needed to move the
device would be greater but so would be the holding force.
In the next section all of the issues will be explored at greater depth
4 Theory and Methodology;
4.1 Specific Statement of the Problem
The goal of this project is to repeat on a much smaller and more precise scale the general function of a
computer mouse. The precision optical platform is usually asked to carry a simple micro optical device
such as a lens, prism or mirror that is usually smaller than 2 mm square and masses <<1 gram. Simply
put, the range of motion is on a planar surface with a scale of 200μm in either X or Y direction with a
resolution of <1μm independent of the orientation of the system to the gravitation field in a very small
package is the desired outcome.
8
Figure 3 Typical micro-optic prism with standard paperclip
4.2 Current Art
As will be shown below the current state of art is to use relatively large structures to achieve the sub μm
movement desired. The devices shown are some of the smallest devices. There are many larger ones
that are used in manufacturing and machining. These devices rely on a brute force and massive stability
approach to achieve small movement
There are many different ways to achieve the movement in a 200μm X 200μm X-Y plane. A few of the
more common ones are:
4.2.1 Piezo Electric Systems;
By using a piezoelectric effect to achieve the desired goal accuracy and travel can be achieved. The
down fall of this in the past has been that if there is a lapse in power the device goes to home and
optical calibration has to start all over. The device in figure 4 is a single stage so to achieve a viable X-Y
device 2 stages would have to be stacked one upon the other, this would achieve a device that would
occupy about .5 inch cubed. This is a step in the right direction but is still quite large for the purposes
stated.
Figure 4 Piezo electric X-Y Stage
9
4.2.2 Flexure based systems;
By using various flexure devices to position the precision optical platform in the appropriate position the
system can be quite accurate. The system shown in figure 5 is repeatable to 0.1 μm but is still many
orders of magnitude larger than its range. The flexure based system meets most of the needs stated
above except in an environment that is subject to vibration. Many times secondary damping systems
need to be introduced to stabilize the system. These types of devices are quite good in laboratory
environments but due to size, expense, and “touchiness” they are not a practical solution for the real
world.
Figure 5 Flexure based X-Y stage
4.2.3 The Friction Based system;
Using the fricative properties of two materials to hold the device in place against forces that would seek
to dislodge it is the most common and least expensive method to achieve a precision optical platform.
By the use of locking and sliding high precision machined dovetail designs a 1 inch cube device has been
achieved. It can be manually driven or mortised though the addition of motors increases size. This is the
system that will be explored at length in this project
Figure 6 Compact Dovetail Linear Stage, 6.3mm XY Travel, 25 x 25 x 26mm, Metric
10
5 Methods and Discussion
5.1 Basic Requirements
In the field of micro optics there are the same requirements for a precision optical platform. These
requirements in general are:
5.1.1
Stability;
The precision optical platform needs to stay exactly where it is put until an effort is made to
move it.
5.1.2
Repeatability;
The precision optical platform needs to be able to be moved and then moved back to the same
location within the range of motion throughout the life time of the system.
5.1.3
Orientation Independence;
Many times it is unknown what orientation relative to the gravity field will be the final
orientation of the precision optical platform and the supporting structure and mechanism.
5.1.4
Small size;
Just as there has been a revolution in microelectronics over the last quarter century there has
been a lesser revolution of micro optics. It is inadequate to have a 200 gram 2.5cm X 2.5cm X
2.5 cm cube supporting such small optics. It would be like vacuum tubes in your cell phone.
The friction based system is the system most closely analogous to the computer mouse example. There
are many examples of devices that are quite large when compared to the desired movement range. The
scope of this project is to research a possible solution as well as various system concepts to achieve the
desired outcome. By a friction based system the meaning is a system in which the precision optical
platform is held in place by friction and the normal force to that friction.
5.2 Initial Discussion
5.2.1 Proprietary Information
The device that is being proposed is a proprietary device with the inventor being Burton B. Bruce and
the patent will be held by Northrop Grumman Corporation. All the rights and usage of this device
known as the Precision Optical Positioner (POP) are the property of Northup Grumman Corporation and
are being shared for the sole purpose of an educational demonstration. The patent for the Precision
Optical Positioner is pending.
11
Figure 7 Precision Optical Positioner; Optical Carrier Cut-away
Figure 8 Precision Optical Positioner (POP)
12
5.3 Design Flow
The design of this system is that the small optical device (prism, lens mirror etc.) is attached to the
optical device holder using an adhesive common for that purpose. The stationary shim is embedded in
the overall device. The socket head cap screw (SHCS) is threaded into the surface opposite the optical
device on the optical device holder. The force to apply the normal force to the fiction interface is
obtained through the selection of an appropriate spring and preloading it to a set value. (See figures 7
and 8)
5.3.1 Movement and adjustment
With regard to the way of moving the device, in the figure above there is a set of 4 adjusting screws
shown. These screws are at 90° from one another circumferentially located around the tip of the
precision optical positioner. They can easily thrust several Newtons which is more that sufficient to
move the optical carrier. The adjusters shown are 0-80 screws but any high pitch screw can be used for
the desired movement. For example; in the 0-80 there are 80 threads per inch therefore 1/80 = .0125”
per thread. Subsequently the device will translate .0125” (317.5μm) per full revolution of the screw. By
careful bump tightening and then backing off of the screw a better than 1μm resolution can be
obtained. If a higher resolution is desired then down to a 0000-160 screw can be used.
It also should be noted that screws are used to position the precision optical positioner but are then
backed off so that there is no remaining contact. If the screws were left in contact an over-constrained
condition would arise that would jeopardize the stability of the system. By using the screws in a bump
and recede manner the stability is totally dependent on the friction force developed by the retaining
spring and the material interaction at the sliding interface.
5.3.2 Normal Force Calculations
The maximum force that would cause instability in the system is when the device is placed
perpendicular to the gravity field. Through calculation of the masses of the different materials that
make up the device the mass of the moving device is ~.5g. By turning the simplest friction equation on
its side it can be see that the F displacement =μ * F normal evolves into F normal = F displacement/μ static. Since the
displacing force is m*g the displacing force = .5g* 9.8 m/sec2 = .0049N. Hence the minimum holding
force is .0049N/μ static. The smaller the COF, the greater the normal force needs to be to hold the system
stable.
5.3.3 Low Verses High Coefficient of Friction Resolution
At this point the concept of whether a low coefficient of friction or a high coefficient of friction paring
needs to be resolved. Since the force to hold the optic carrier assembly in place is rather low using a
relatively high coefficient of friction paring is not undesirable. If the device was of greater mass then the
forces to hold it in place would be greater and more difficult to achieve. In addition greater interfacial
forces would produce higher stresses that would potentially cause greater wear which would result in a
shift of the forces needed to keep the device stationary. Therefore it would seem that a consistent
moderate COF static (~.5) is in order.
13
5.3.4
Coefficient of Friction Determination
Figure 9 Table of some common Coefficients of Friction
The above table will at least give some guidance and will help in eliminating unsuitable candidates. Part
of the selection process needs to take into account the other material properties of the candidate fiction
pair. These properties would include structural stability, thermal stability, machinability, durability, one
of the materials having an oxide that is stable (as mention previously) and in general a fairly common
material. For example very low fiction materials like Teflon are also unstable. Over a long period of
time they tend to creep and they also tend to have a much high CTE than a more stable metallic
material. It has been discussed earlier that there are two factors at work with fiction one is the static
COF and the other is the dynamic COF. Since the motion will be relatively slow the concept of the device
“skating” off beyond where it is placed is not a factor.
In looking at the chart attached as well as other factors cited below it seems that a combination of
aluminum and steel is the most desirable. Both are common with good stability. To further the long
term stability of the system the use of a stainless steel is indicated. From the chart above the static COF
14
of this combination should be ~.6 and the dynamic COF should be ~.4. The experimentation
documented below will validate these numbers.
5.3.5 Coefficient of Friction Experimentation
“Empirical evidence accumulated over centuries has produced the following so-called, rules of sliding
friction:
For a block resting on a plane under load Fn, motion takes place only when the tangential force
Ft exceeds a critical value. The specific critical value is a function of the materials involved.
Once the block is in motion the friction force Ff acts in the direction opposite to the relative
velocity
The friction force Ff is proportional to the load Fn and the constant of proportionality is the
coefficient of friction f (i.e. Ff = f*Fn)
For a block on an inclined plane the angle of repose θ is directly related to f by tan θ = f
The friction force is independent of the apparent area of contact Aa.
The friction force is independent of the sliding velocity v.” [b]
I will be machining a prototype so it is desirable to use common materials, 316 stainless steel and 6061
aluminum are common and easily machined. Since I could not find the exact COF of 316 stainless steel
interacting with 6061 aluminum data, a simple experiment was in order.
Figure 10 316 Stainless steel interfacing with 6061 aluminum friction test
A pair of polished 316 stainless steel posts was screwed into a rotation stage and the device was fixed to
a stand to orient it vertically. A 5 gram piece of 6061 aluminum plate was placed upon the posts and the
device was tilted from horizontal. The angle was recorded at which the plate started to slide this was
repeated 10 times with the average being 19°. The tan of 19° is .34. According to the quote above the
COF should be ~.34, though it is not a block on plane the quote about the friction force being
independent of the area of contact is apt as well as the quote about the COF being mostly a material
15
property. For the sake of curiosity I repeated the experiment by fixing a 316 SS plate between the two
poles and repeating the experiment. The results were the same.
From the experiment as well as the table it seems that I need to anticipate a COF of between .3 and .6.
While this seems like a broad range a sufficient safety margin will be designed in to the precision optical
carrier to mitigate the range.
5.3.6 Holding Force Calculations
Using the values for the COF gained above the normal forces or need to be the minimum holding force is
.0049N/μ. The lowest value of μ is .3 therefore the minimum holding force is .016N. As stated before
this needs to be sufficiently robust for lab applications so a potential shock of 25Gs is a bogie that is
often aimed for. This being the case the normal force on the device needs to be .41N. This can be
obtained by preloading the spring in the system. For example take a .25mm diameter stainless steel
wire spring that would has an OD of 3mm and a rate of .2N/mm and a free length of 8mm if it is
compressed to 5.9mm it will provide the required .41N.
5.3.7 Overall Vibration Susceptibility
Most optical systems are susceptible to external vibrations. It seems appropriate to explore what the
natural frequency of this system is.
Figure 11 1st harmonic vibration profile
The above COSMOS frequency FEA shows the 1st harmonic to be ~390 Hz; the second harmonic is also in
that range just at 90° to the representation above. Since this is a laboratory device it is extremely
unlikely that it will experience a long term 390 Hz exposure.
16
5.4 Design Summary
Figure 12 Precision Optical Positioner
The goal was to design as precision optical platform that would have:





Several hundred μm range in the X-Y plane,
Stability when subjected to normal laboratory conditions,
Around μm resolution,
Have a small package size compared to what is commercially available.
Be independent of orientation with respect to the gravitational field.
In addition several other factors arose in the design process. These factors became prominent when I
determined to make a prototype for demonstration in class and at work. These factors were:




Simplicity of design
Machinability
o Since I needed to make a prototype I needed to keep the materials common and easy to
machine with the facilities that were available.
Low parts count
The ability to modify the design easily for different experimental requirements.
6 Conclusion
The conclusion is that a successful Precision Optical Positioner has been designed and a prototype has
been fabricated using the Tribological principles laid out in the body of this project.
Of a personal note: the enthusiasm generated by the optical scientists at AOA Northrop Grumman is
such that we are proceeding with finishing released drawings and a production run of these devices.
17
7 Bibliography
7.1 Current Art
Newport Optics have a large variety of mechano-optical devices some of which are shown above
as examples http://www.newport.com/Linear-Translation-StageGuide/1006111/1033/content.aspx
7.2 Desirability
From the National ignition Facility: https://lasers.llnl.gov/about/nif/seven_wonders.php In this
situation the size of the overall system was somewhat driven by the size of the current art
mechano-optical holders and devices.
There are numerous small optical systems in this device
http://www.bizjournals.com/cincinnati/blog/2011/08/testing-out-krogers-new-tunnelscanner.html In this case the size was driven more by function. One needs to be able to get a
large watermelon or package of paper towels through the tunnel.
Small optics were used in the shaping and metrology of the Hinode x-ray mirror.
http://solarb.msfc.nasa.gov/ There was a need to get high accuracy metrology equipment into
the ID of the mirror to measure the profile and surface characteristics.
7.3 References
1. Dewan Muhammad Nuruzzaman , Mohammad Asaduzzaman Chowdhury , "Effect of Load and
Sliding Velocity on Friction Coefficient of Aluminum Sliding Against Different Pin Materials",
American Journal of Materials Science, Vol. 2 No. 1, 2012, pp. 26-31. doi:
10.5923/j.materials.20120201.05.
2. Ashby, Michael F. Jones, David R. H. (2012). Engineering Materials 1 - An Introduction to
Properties, Applications, and Design (4th Edition). Elsevier Chapter 28; Friction Abrasion and
Wear
3. Raman, Aravamudhan (2007). Materials Selection and Applications in Mechanical Engineering.
Industrial Press. Chapter 9; Mechanical Friction and Wear
4. Oberg, Erik Jones, Franklin D. Horton, Holbrook L. Ryffel, Henry H. (2004). Machinery's
Handbook (27th Edition) & Guide to Machinery's Handbook. Industrial Press. Pages 157-161
5. Davis, J.R. (2001). Surface Engineering for Corrosion and Wear Resistance. Maney Publishing.
Chapter 3; Principles of Friction and Wear
6. Marinescu, Joan D. Rowe, W. Brian Dimitrov, Boris Inasaki, Ichiro (2004). Tribology of Abrasive
Machining Processes. William Andrew Publishing. Chapter 5; Forces Friction and Energy
7. Hashiguchi, K., & Ozaki, S. (2008). Constitutive equation for friction with transition from static to
kinetic friction and recovery of static friction. International Journal of Plasticity, 24(11), 21022124. doi:http://dx.doi.org/10.1016/j.ijplas.2008.03.004
18
8. Feyzullahoglu, E., & Sakiroglu, N. (2011). The tribological behaviours of aluminium-based
materials under dry sliding. Industrial Lubrication and Tribology, 63(5), 350-358.
doi:http://dx.doi.org/10.1108/00368791111154968
9. http://www.applied.com/site.cfm/CoefficientsofFriction.cfm
10. M. Kathiresan, T. Sornakumar, (2010) "Friction and wear studies of die cast cast aluminum alloyaluminum oxide-reinforced composites", Industrial Lubrication and Tribology, Vol. 62 Iss: 6,
pp.361 – 371
11. English and American Tool Builders; by Joeseph Wickham Roe; Yale University Press 1914)
12. Made by Urszula Sęczyk Region: kujawsko-pomorskie, Poland
7.4 Quotations
a) Nanotribology: Microscopic Mechanisms of Friction O.M. Braun and A.G. Naumovets Institute
of Physics, National Academy of Sciences of Ukraine, 03028 Kiev, Ukraine
b) http://www.ewp.rpi.edu/hartford/~ernesto/F2013/FWLM/Notes/7-Friction.pdf
19