Flexure Design
Optomechanics 423
University of Arizona
Logan R. Graves
Design
The goal of this project was to design a flexure which would fit inside of a 4”x4”x1” container. This
flexure was to be crafted using a 3D printer, and thus the assumption was made that the flexure was
being crafted out of ABS plastic, a common 3D printer material. The job this flexure was envisioned
completing is securing an optical component which needs very fine lateral translation to a fixed stage. A
figure is shown below demonstrating the concept of the flexure. The design involves four through holes
for securing the device to a table. The optical component which needs fine lateral motion is attached to
the tapped hole in the top of the flexure. A screw is then threaded in through the bottom of the flexure,
and can be threaded to provide fine lateral motion of the optical component.
Calculations
To design this flexure preliminary hand calculations were made to determine the estimated stiffness and
behavior of the flexure. For a double bladed flexure there are simple equations which can be used to
calculate the stiffness of the material. From this the deflection based on an expected force can be
calculated.
Material Properties
Young’s Modulus
d
b
t
L
2 GPa
1.9 “
0.25 “
0.1”
0.45 “
𝐸 ∗ 𝑏 ∗ 𝑡 ∗ 𝑑2
𝑙𝑏𝑓
𝑁
𝑘𝜃 =
; 𝑘𝜃 = 2.9 ∗ 104
= 5.078 ∗ 106
2∗𝐿
𝑖𝑛
𝑚
𝑘𝑥 =
2∗𝐸∗𝑏∗𝑡
𝑙𝑏𝑓
𝑁
; 𝑘𝑥 = 3.2 ∗ 104
= 5.604 ∗ 106
𝐿
𝑖𝑛
𝑚
𝑡 3
𝑙𝑏𝑓
𝑁
𝑘𝑦 = 2 ∗ 𝐸 ∗ 𝑏 ∗ ( ) ; 𝑘𝑦 = 1591
= 2.78 ∗ 105
𝐿
𝑖𝑛
𝑚
Based on this data it is clear that the y spring constant is over and order of magnitude smaller than the
angular and x spring constants, which is ideal. We can expect a force of 10 N to be applied to the flexure
with the screw drive method. Thus, the expected deflection in the y direction is calculated as shown.
𝛿𝑦 =
𝐹
10𝑁
=
= 35.8 𝑚𝑖𝑐𝑟𝑜𝑛𝑠
𝑘𝑦 (2.78 ∗ 105 𝑁 )
𝑚
This is a very fine lateral motion and would be ideal for very fine lateral adjustment to optical
components using a fairly average force.
Thus, based on the calculations the design can be considered to be sufficient for the desired job. From
here a solidworks model was created and FEA was done to verify the design.
Solidworks Model
A model of the flexure was created using solidworks and the performance of the flexure was analyzed
using FEA. A fine mesh was used to model the flexure, as with too large of a mesh there was a nonlinear modeling of the corners of the flexure. It was found that as the mesh fineness increased the
stiffness in the y direction of the flexure increased, as the modeling became more accurate.
Range of Motion in Y Direction
Using FEA in solidworks the range of motion with three different forces applied to the flexure were
analyzed. The table below shows the maximum y travel of the flexure for each force applied. Further
the output for a 10 N force is shown below as well.
Force (N)
1
10
50
Figure 2.1, Displacement with 10 N applied
Travel (microns)
7.93
79.35
349.2
Stress and Strain
Next the stress and strain applied to the flexure was analyzed, again at 1, 10, and 50 N of applied force.
This was done to assure that no uncharacteristic behavior was occurring with the flexure or with the
FEA. Only the stress and strain for the maximum force, 50 N, is shown.
Figure 3.1, Stress with 50 N Applied
Figure 3.2, Strain with 50 N Applied
As can be seen with a maximum of 50 N applied there is no unreasonable stress or strain on flexure.
However, at this point it must be determined what the yield strength of the flexure is. Originally it was
expected that 10 N would be applied using a screw driven method. Therefore, it would be ideal to have
a yield strength at least double that force. To determine this a FEA was done using a yield of 60.2 MPa.
This corresponded to a maximum applied force of 44 N before exceeding the yield strength of the
flexure. This is shown below.
Figure 4.1, Yield Force
Frequency Analysis
A simple frequency analysis was run on the solidworks model to determine the first 4 modes for the
flexure. There are listed below along with the outputs from the FEA.
Table 5.1, Frequency Analysis
Mode
1
2
3
4
Frequency (Hz)
962
1156
2119
2599
Figure 5.1, Frequency 1
Figure 5.3, Frequency 3
Figure 5.2, Frequency 2
Figure 5.4, Frequency 4
The primary modes that are of interest are modes 1 and 2. These correspond to a y lateral force and a
shearing force in the x direction. Their frequency is relatively high however and should not be an issue
for the flexure.
Buckling Analysis
The most likely method of buckling for this flexure design would be a twist to the side. A buckling
analysis was done in solidworks, and is shown below. As can be seen there is a load factor of 35 before
buckling occurs, which seems perhaps excessively high for the model. However, the FEA was run
multiple times and that seems to be the load factor for buckling.
Detailed Drawings