3. ▶ Industrias Lorenzo Eurostick; a widely used arcade joystick popularized in western arcades, the
battop design is one of the most iconic images of american arcades from the 1990s, commonly
described as being “built like a tank”
▶ Part list:
◦ Battop Joystick
◦ Dust Washer
◦ Spacer
◦ Hub
◦ Spring
◦ Z-stop
◦ Bracket
◦ Actuator
◦ E-clip
Product
16. ▶ Two different materials: ABS Plastic and Stainless Steel 304
▶ Material Properties:
◦ ABS Plastic
⚫Young’s Modulus: 2.25 GPa
⚫Poisson’s Ratio: 0.35
◦ Stainless Steel 304
⚫Young’s Modulus: 193 GPa
⚫Poisson’s Ratio: 0.29
FEA on Joystick (cont’d)
17. ▶ Two separate parts imported from SolidWorks
▶ Meshed using “tet” elements
FEA on Joystick (cont’d)
ABS Plastic Handle Stainless Steel 304 Shaft
18. FEA on Joystick (cont’d)
• The two parts were combined using the tie constraint
• Creates one rigid body
19. ▶ A distributed load of 222.411N (~50lbs) was applied on a section of the
handle
▶ Constrained at bottom
FEA on Joystick (cont’d)
20. ▶ Results
◦ Most of the stress is located in the ridges of the metal shaft
◦ The stress does not exceed 828 Pa, which is well below the yield stress of Stainless Steel 304
(~215MPa)
FEA on Joystick (cont’d)
22. ▶Geometry was meshed with “tet” elements
▶Material Properties:
◦ABS Plastic
⚫Young’s Modulus: 2.25 Gpa
⚫Poisson’s Ratio 0.35
FEA on Hub (cont’d)
23. ▶A distributed load of 222.411 N(~50 lbs) was applied to the inner part of
the hub where the spacer and battop joystick would sit
▶Constrained along the bottom and top of the Hub
FEA on Hub (cont’d)
24. ▶Results
◦The stress is localized within the space the load was placed and it can be seen that
the hub does deform a relatively large amount
◦The maximum stress is seen to be 3.77 MPa which is well below the Yield Stress of
ABS Plastic (42.5-44.8 Mpa)
FEA on Hub (cont’d)
28. ▶A distributed load of 222.411N (~50lbs) was applied on the inside.
▶Constrained around outside
edge.
FEA on Spacer (cont’d)
29. ▶Results
◦Most of the stress is located on the outside edge of the applied pressure.
◦The maximum stress felt in the spacer (438 x 10-3 MPa) is below the yield stress for
nylon (~45 MPa).
FEA on Spacer (cont’d)
30. ▶The three parts that were analyzed in Abaqus were found to be designed
with sufficient dimensions and materials. None of the parts yielded even
under an overestimated load of 222.411 N (~50lbs).
▶A possible improvement on this design would be to remove material in
certain areas to reduce cost.
◦A redesign and analysis of these parts would then be required in order to assure they
do not fail.
Conclusion
31. Garage Door and Spring Optimization with Stochastic
Analysis and Tolerances
Wallace Muhammad III
Illinois Institute of Technology
MMAE 445 Computer Aided Design Project I
Prof. Roberto Cammino
9/26/16
32. Background
The idea behind this project is to design a garage door opener that works by
compressing a spring with a button. There is a sensor attached to the spring
that aligns with a sensor attached to a sensor box aligned with a battery. The
opener needs to have a maximum length of 40mm including the length of
the button and the spring much have a solid compression length of 10mm to
activate the garage door with a force of 3N. The dimensions of the parts are
nominal values with a standard deviation of 5%. This information is used to
find tolerances, while stochastic analysis is used to assure the spring fits in
the opener and the two sensors align 99.9% of the time.
37. Tolerances and Stochastic Analysis Results
▶ Chosen Dimensions
- Mean Diameter – 10mm
-Total Displacement – 17mm
-Turns - 23
▶ Calculated values
Spring Constant (k) Turns (N) Shear Modulus (G) Elastic Modulus (E)
0.176 23 77519.340 2E+11
Coil Diameter (mm) Solid Length (mm) Free Length (mm) Box Length (mm)
0.847 19.326 36.326 29.326
Z Value Opener Width (mm)
(Sensor Box Space)
Sensor Box Standard
Deviation
Sensor Box Optimized
Width
2.999 (Table A-10) 8.526 0.426 8.720
Spring Standard
Deviation
Opener Length
Standard Deviation
1.816 1.466
Mean Standard
Deviation (Opener)
2.33
38. Discussion of Results
The first analysis was on
the on the length of the opener so
the spring could fit 99.9% of the
time. The total length of the opener
was calculated to be about 29mm.
With the standard deviation of the
spring and the length of the opener
being 5%, the length of the spring
has to be about 36.32mm as
calculated. The length of the spring
has to be greater than the length of
the opener to be able to fit snugly.
The Z value was calculated to be
about 3, which is for 99.9% success
rate from Table A-10 with these
values.
The spring also has to
compress to deflect enough to reach
the sensor, which is 10mm deflection.
The solid length of the of the spring
was calculated to be about 19mm
with the data from the materials, 23
turns, and an applied force of 3
newtons. The spring will first deflect
enough to fit into the opener, then it
will deflect 10mm to its solid length to
activate the sensor on the sensor box
99.9% of the time as calculated from
stochastic analysis with a Z value of
2.999.
39. Discussion of Results (Cont.)
Battery Used: CR11108 Lithium Cell
Height: 8.8mm
Diameter: 10.5mm
The standard deviation of the
length of the spring has to be
considered along with the standard
deviation of the length of the opener.
Two intersecting normal curves were
used to find the mean values of
standard deviation to calculate the
tolerance of 3 standard deviations.
This was also the case with finding
the right width of the sensor box, so
the sensor would align 99.9% of the
time. The width was calculated to
about 8.72mm.
45. Re-Designed Spring with 0.5% Standard Deviation
The spring is redesigned to fit
with a new standard deviation of 0.5%.
Also, with the new design is a material
chance to an oil-tempered steel wire, with
new dimensions to suite the material
change and to work with the previous
specifications, but with the new standard
deviation. New calculations were taken
place, changing the percent of standard
deviation and new equations were used
also for designing a spring. This changed
the dimensions of the spring for 5%
deviation from the previous spring design
using the AISI steel 1005 material. The new
dimensions calculated with the equations
and new material will be compared to the
0.5% deviation and the original design.
Additional Spring Equations Used
• 𝑆𝑠𝑦 = 0.45
𝐴
𝑑 𝑚
• 𝛼 =
𝑆 𝑠𝑦
𝑛 𝑠
• 𝛽 =
8 1+𝜖 𝐹 𝑚𝑎𝑥
𝜋𝑑2
• 𝐶 =
2𝛼−𝛽
4𝛽
+
2𝛼−𝛽
4𝛽
2
−
3𝛼
4𝛽
• 𝐷 = 𝐶𝑑
• 𝐾 𝐵 =
4𝐶+2
4𝐶−3
• 𝜏 𝑠 = 𝐾 𝐵
8 1+0.15 𝐹 𝑚𝑎𝑥 𝐷
𝜋 𝑑 3
• 𝑛 𝑠 =
𝑆 𝑠𝑦
𝜏 𝑠
47. Tolerances and Stochastic Analysis Results with New
Material, New Equations, and 5% Standard Deviation
Coil Diameter 0.25
Outer Diameter 1.636838659
Max force 3
Total Deflection 17.4
Material Oil-Tempered wire
Exponent, m 0.187
Area 1855
Shear Modulus 77.2
Elastic Modulus 196.5
Alpha 983.4424735
Beta 140.6369427
C 5.547354635
Mean Diameter 1.386838659
KB 1.260560266
Shear Stress 983.4424735
Turns 81.96671379
Total Turns 83.96671379
Solid Length 20.99167845
Free Length 38.39167845
Critical Length 7.294771345
Spring Length 38.39167845
Opener Length 30.99167845
Sensor Width 10.19167845
Box Width SD 0.509583922
Optimized SW 10.42363003
z 2.999613436
Mean SD 2.466984549
48. Tolerances and Stochastic Analysis Results with New
Material, New Equations, and 0.5% Standard Deviation
Coil Diameter 0.218
Outer Diameter 1.070010237
Max force 3
Total Deflection 10.8175
Material Oil-Tempered wire
Exponent, m 0.187
Area 1855
Shear Modulus 77.2
Elastic Modulus 196.5
Alpha 1008.956351
Beta 184.9551578
C 3.908303841
Mean Diameter 0.852010237
KB 1.39578206
Shear Stress 1008.956351
Turns 127.0645778
Total Turns 129.0645778
Solid Length 28.13607795
Free Length 38.95357795
Critical Length 4.481573849
Spring Length 38.95357795
Opener Length 38.13607795
Sensor Width 17.33607795
Box Width SD 0.08668039
Optimized SW 17.33997901
z 2.999246975
Mean SD 0.272568417
49. Comparison of Old Design and New Design with 5% Standard Deviation
With a new material of oil-tempered
steel wire and the application of the spring design
equations the diameter of the coil changes
significantly. It has been reduced from about
0.84mm to 0.25mm at a Z value of 2.999. The outer
diameter has also been reduced significantly from
about 10mm to 1.7mm. The free length and the
solid length did not change significantly, however,
to meet the specified length of the opener. The
free length of the original spring is about 36mm
while the free length of the new spring is about
38mm. The solid lengths are 19mm and 21mm. The
total displacement for both springs during
compression until the springs bottom out is about
17mm for compression during its snug fit and
during the 10mm required displacement to
activate the door opener.
Both boxes have a length of
about 30mm. The new spring also requires
much more turns, about 84 turns as
compared to 23 turns. The chosen
dimensions for the new design was also just
the coil diameter and the total displacement
of the spring during compression. The
reduction in diameter for the coil and the
outer diameter shows an improved design
as the same goal is achieved while reducing
material. Lastly the dimensions for the
sensor box are also very similar.
50. Comparison of 5% Standard Deviation with 0.5% Standard Deviation of New
Design
The most significant change with the
reduction of standard deviation is the total
deflection. 17.4mm being the spring with 5%
standard deviation while the spring requiring a
standard deviation of 0.5 has a total deflection of
about 10.8mm. This makes sense because with a
smaller standard deviation, the deflection should
not be too much greater than the minimal
deflection needed to activate the opener, 10mm.
The coil diameter, mean diameter and outer
diameter had been reduced slightly, which is good
to save material. The solid length and free lengths
were increased, increasing the number of turns
also. The remaining dimensions also increased to
accommodate these changes, such as the sensor
box and box length. Both springs had their
calculations with a Z value of 2.999, reflecting the
99.9 % success rate required.
What has also been significantly
changed was the difference between the free
spring length and the length of the box. For the
new standard deviation, the free spring length is
about 38.95mm, while the calculated box length
is 38.1mm for a Z value of 2.999. This is
compared to the free spring length of 38.39 and
the box length of 30.99 of the spring required to
meet a 5% standard deviation. The values are
much closer for the smaller deviation, which
makes sense and the length of the box is slightly
smaller than the free spring length in order to
ensure a snug fit. A loose spring will not allow
the sensor to activate the opener when
compressed to its solid length. This standard
deviation is more reasonable, as the pre-
compression of the spring during assembly of
the opener has been significantly reduced.
