Mirror Mount
Logan R. Graves
Optomechanics
University of Arizona
Introduction
A mirror mount was designed to support a small mirror with tight tolerances. The mount was designed to allow for
correct orientation when mounted and to meet the requirements of the project. The performance of the mount and
the mirror’s performance were measured using FEA and SAGUARO, in soldiworks and Matlab respectively.
Below the requirements are shown.
Requirements
Mirror Specifications:
Diameter: 15 cm
Thickness: 1.5 cm (at center)
Material: ULE
Performance Specifications:
< 12 nm surface irregularity for zenith or horizon pointing
 Surface irregularity
 Nominal self-weight deflection
 Mount induced deflections
Lowest Frequency: 200 Hz
RMS Power: 20 nm
Stability Specifications:
50 µrad tip/tilt
25 µm axial position
Environment & Survival:
20 ° C +/- 3 ° C
-20 ° C to 50 ° C
20 G shock
Preliminary Design
Due to the small size of the mirror there were two straightforward designs which were considered. Both a simple
three point support under the mirror, and a three point support at the outer edge face of the mirror. The outer
support provided the simplest and most cost effective design, and thus this was the selected method. To confirm
the design preliminary simple calculations were made, as described below.
Self-weight Deflection
The self-weight deflection of the mirror had to be calculated to assure the design would be meet specifications. The
equation for self-weight deflection is shown below.
Mirror Specifications:
•
•
•
•
•
•

D=15cm
H=1.5 cm
ρ= 2.21 g/cm3
E= 67.6Gpa
ρg= 21656 N/m3
CTE=0.03ppm/o
v: 0.17
With the edge support method the self weight deflection came out to be:
𝛿𝑉𝑚𝑎𝑥 = 6.96 nm
Clearly the self-weight deflection would leave plenty of room to meet the 20 nm RMS specification. Further, it
leaves room for the power RMS error. Therefore, this design is preliminarily valid. At this point due to the use of
flexures in the design the stiffness of the flexures had to be calculated to assure the minimum resonant frequency of
the mirror was larger than 200 Hz.
The frequency of a mirror is determined by the stiffness and mass of the mirror. Because there are three flexures
being used in the system the minimum stiffness per flexure can be calculated as a third the minimum stiffness of the
total minimum stiffness. This calculation is shown below:
Mass of mirror: 651.44 grams
𝑓=
1
𝑘
∗√
2𝜋
𝑚
𝑘 = (2 ∗ 𝜋 ∗ 𝑓)2 ∗ 𝑚=102.8 kN/m
With 3 support flexures that means a stiffness of 34.2 kN/m per flexure
The flexures being used are made of 1060 Al and are mounted to the edge of the mirror using RTV 2216 adhesive.
The flexures deform by 23 nm under a 20° C temperature change. This is well within the decenter tolerance.
Further, the axial change is uniform due to the symmetric nature of the flexures. The stiffness in the lateral
direction of the flexures is 12300 N/m, which well exceeds the required minimum stiffness of the flexures. This
guarantees that the minimum frequency will be met by the mirror.
Flexure Analysis
The flexure will be made out of Al 1060. The material properties and dimensions of the flexure are listed below.
These were used to calculate the stiffness properties of the flexure.
Young’s Modulus
b
t
L
69 GPa
0.016
0.001
0.04
Frequency
The mirror is required to have a minimum resonant frequency of greater than or equal to 200 Hz. With a puck size
of 5 mm diameter and with the given flexures, the minimum frequency, as can be seen below, is 771 Hz.
Horizon Pointing
When the mirror is in it’s horizon pointing orientation there are slight deflections on the mirror itself. These were
modeled using FEA and the results are shown below.
Shock Loading
The mirror assembly also had to survive a shock loading of 20 G’s. This was modeled using FEA in Solidworks.
The results are shown below, in which the yield point is never reached for any component of the assembly with a 20
G shock. Thus, it was confirmed that the assembly will be able to meet the requirement.
Buckling
A brief buckling analysis was performed to determine the most likely mode of failure that the flexure would experience.
A 1 N force was applied to the flexure, and buckling occurred for a load factor of 710. This enormously exceeds the
weight of the mirror that would be applied to the flexure, so buckling is not a problem for this design.
Surface Error
Error
Self-weight Deflection
Temperature Effects
Tolerance Error
Surface Error
Total
Weight (nm)
6.96
5.04
1.001
2.8
Occurances
1
1
3/6
1
15.4 nm
With Self-Weight Deflection of 6.96 nm at the center the total surface error then comes out to be 8.57.
Overconstraint
The system was carefully designed to avoid overconstraint of the mirror. There are three contact points on the
outer edge face of the mirror. They contact points each provide a constraint in 2 directions, for a total of 6 DoF
being constrained. This takes into account all DoF without overconstraint.
Temperature Effect
Because the flexures are made of Aluminum while the mirror is a glass, there is a fairly significant difference in the
expansion between the two materials. However, the dimension which would cause the greatest error, expansion in
the radial direction, is addressed as the flexures can bend outward to account for the expansion. The main error
therefore is if there was a non-uniformity in the mount height of the mirror to each of the flexures, however, a tight
tolerance is described in the assembly portion to address this problem. The total RMS error from the thermal load
at maximum temperature is 5.04 nm.
Assembly Plan
The design is fairly straightforward so assembly is easy for the design. To start the flexures need to be mounted to
the base steel plate using ¼ 20 screws. The top of the flexures need to form a plane which is parallel to the plane of
the base plate to a degree of 0.002 mm. To achieve this shims must be used at the bottom of each of the flexures to
assure that they are all sitting at equal height. Once this tolerance has been achieved the mirror can be mounted.
This is done by placing the mirror on a secure surface to hold it in place. Next, the base plate and flexures must be
oriented and held above the mirror. A 1 inch diameter RTV epoxy, at .25 mm thick, should then be placed in the
center of each of the flexure faces, and then the flexures should be carefully pulled back and oriented such that the
mirror is in its correct final position when the epoxy adheres to the mirror outer face.
Appendix
Bill of Materials
Description
¼ 20” Hex Head Screws
Steel Plate
Aluminum Block
ULE Mirror
RTV Epoxy
Price
N/A
N/A
N/A
N/A
$9.00
Quantity
6
1
3
1
1
Saguaro Results
Saguaro was used to help determine the performance of the mirror with different size diameter pucks of RTV
adhesive. The results were analyzed to determine which diameter provided the best support for the mirror while
meeting the requirements. It was determined that a 5 mm diameter puck of RTV would be the best choice. The
results are shown below.
Puck diameter: 3 mm
Puck diameter: 5mm
Horizon Pointing
Thermal Effect
Drawing