Chassis
Introduction
Purpose and Goals
The chassis is the backbone of the Mini-Baja; it must support all the car’s
subassemblies as well as protect the driver. The chassis design is crucial to the success of
the project because if the chassis fails, that puts the Baja and the driver at tremendous
risk. The goal of the 2008 Mini Baja frame will be to protect the driver, offer sturdy
mounting for all subsystems, maintain all SAE rules and regulations, and still be
lightweight.
Background
Chassis design in the SAE Mini Baja competition is critical for a winning car.
These cars are all powered by 10 horsepower Briggs and Stratton engines. To extract
maximum acceleration from this engine a lightweight chassis is necessary. At the same
time the chassis must undergo the rigors of off-road racing. To analyze a structure that
will undergo such loads, finite element analysis (FEA) is often a viable solution. FEA
breaks the structure into smaller elements and analyzes each element as a body and can
calculate the stress, deflection and other reactions of any structure. A Transient FEA will
be the main simulation done to optimize the weight and strength of the 2008 Mini Baja
Chassis.
From here forward a few assumptions have been made to aid design and analysis.
The total weight of the Mini Baja car, without a driver, is estimated to be 400 lbs, with
the lightest car weighing 318lbs. [] This is the average weight of the most competitive
school’s cars from 2007. The driver will be referenced as a 6 foot 3 inch tall male
weighing 250lbs, as per the SAE rules. []
Design Objectives
To build a chassis to meet all of the previously mentioned goals the frame must:
•
Endure the maximum dynamic load according to SAE Technical paper 2006-013626[] with a factor of safety of 1.5
•
Keep a driver alive during a 7.9g front impact
19
•
Keep a driver alive during a 7.9g side impact
•
Keep a driver alive during a 7.9g Roll over situation
•
Abide by all SAE rules and Regulations
•
Weigh less than 80lbs
•
Have mounting structures for all subsystems that will withstand the loads
produced by those subsystems.
SAE Rules and Regulations
All SAE rules and regulations can be found in Appendix A. The Frame rules are
specifically in “SECTION 3 ROLL CAGE, SYSTEMS & DRIVER’S EQUIPMENT.”[]
Some highlights of that section are:
•
“The driver’s helmet to be 15.24 cm (6 in) away from the straightedge applied to
any two points on the cockpit of the car, excluding the driver’s seat and the rear
driver safety supports.”[]
•
“The driver’s torso, knees, shoulders, elbows, hands, and arms must have a
minimum of 7.62 cm (3 in) of clearance from the envelope created by the
structure of the car.”[]
•
Fit a 95% Male driver, while maintaining all constraints above.
•
The LBD, LFS, SIM, FAB, and FLC must be at minimum 0.035 wall thickness
tubing with a minimum outside diameter (O.D.) of 1 inch.
•
The RRH, RHO, FBM, and LC must be “(A) Circular steel tubing with an outside
diameter of 2.5 cm (1 inch) and a wall thickness of 3.05 mm (.120 inch) and a
carbon content of at least 0.18%”, or “(B) Steel members with at least equal
bending stiffness and bending strength to 1018 steel having a circular cross
section with a 2.5 cm (1 inch) outer diameter and a wall thickness of 3.05 mm
(.120 inch).”[]
Figure 2 below displays the location of each frame member referred to above.
20
Figure 2: Frame Members
Maximum Dynamic Load
The loading conditions used to analyze the Chassis are just as important as the
analysis itself. The more accurate the load the smaller the factor of safety can be used.
The 2008 Mini Baja Chassis team purchased SAE technical paper 2006-01-3626[],
Structural Considerations of a Baja SAE Frame. In this paper Auburn University
students used load cells to measure the amount of force translated into a Mini Baja Frame
during two loading conditions. These load cells, shown in Figure 3, gave a load data on a
time scale shown in Figure 3 for a “single wheel vertical impact” in Figure 4.
Figure 3: Left - Load Cell [], Right - Vertical Impact Graph []
21
Figure 4: Vertical Impact Demonstration []
This data can be directly used on the frame during a transient FEA analysis. Because the
material that will be used for analysis, chromoly steel, is a well-known material and the
loads and stresses that are being used for the shock force analysis are from actual test
cases a factor of safety of 1.5 is used for the analysis of the frame. (See Appendix B for
factor of safety justification)
7.9G Impact
Using data from “The Motor Insurance Repair Research Centre” [] the estimated
maximum g-force that the Mini Baja car will see is 7.9g’s. The Motor Insurance Repair
Research Centre did rear impact tests for vehicles of different masses. To estimate the
maximum g-force on the Mini Baja car the g-force of the closest in weight car will be
used. The mass and g-force of each car used in the impact test is shown in Table 1. []
Table 1: Left - Impact Acceleration [], Right - Vehicle Mass []
22
The mass of the Mini Baja car is 20.2 slugs, therefore the g-force that will be used for
analysis is 7.9g’s(the car with the closest mass(OW3718)). These values are highlighted
in Table 2 below.
Delta V MPH pulse(ms) g-force Mass of Car(slugg)
6.337986158
92
3
81.54090154
6.835083112
68
4.4
99.3565607
8.077825496
84
4.4
134.6452702
8.264236854
80
4.9
99.01395187
8.947745165
72
5.7
92.2988188
9.258430761
129
3.3
102.3029966
10.31476179
130
3.6
102.3029966
10.62544738
65
7.9
69.20698366
10.62544738
103
4.9
94.83412414
10.6875845
89
5.5
96.27308123
10.6875845
74
6.6
91.75064467
10.6875845
116
4.1
99.3565607
11.24681858
65
7.9
123.3391788
11.43322993
82
6.4
119.9130905
11.43322993
93
5.6
98.60282127
12.05460112
93
5.6
100.1103001
Table 2: Vehicle Mass and Acceleration []
Frame Weight
To calculate the maximum frame weight, the estimated values of each subsystem were
added up and subtracted from an estimated total vehicle weight of 400lbs. This resulted
in a frame weight of 80lbs as shown in Table 3.
Co m pon ent W ei gh t(lb)
Tir es
50
Suspe nsi on
50
Stee ri ng
15
Engin e
60
Transm i ssio n
60
Re ar Housi ng
40
Bo dy Panel s
10
Ski d Plate
10
Ele ctro ni cs
5
Br akes
20
Total
320
Tar ge t
400
Fram e w e ight
80
Table 3: Estimated Vehicle Weight
Design and Analysis
Material Selection
To build the Mini Baja frame steel must be used according to the rules. There are
many different types of steel available to the public. The frame of the Mini Baja will be
23
made from tubular sections. Tubular sections offer superior loading capabilities per
pound when compared to solid sections or square sections.
The material selection criteria are very similar, so the suspension material
selection chart will be used to choice a material for the chassis. According to that
material selection chart (Table 16 on page 69) 4130 steel is the preferred material for use
in the Mini Baja frame.
Roll Cage Tubing
According to Roll Cage Material Specifications 31.5 in the SAE Rules [Appendix
A] the roll cage must “(A) Circular steel tubing with an outside diameter of 2.5 cm (1
inch) and a wall thickness of 3.05 mm (.120 inch) and a carbon content of at least
0.18%”, or “(B) Steel members with at least equal bending stiffness and bending strength
to 1018 steel having a circular cross section with a 2.5 cm (1 inch) outer diameter and a
wall thickness of 3.05 mm (.120 inch).”[] From the material selection chart 4130 alloy
steel was chosen as the material to be used for the entire frame. There is a note in the
rules about the use of alloy steel: “NOTE: The use of alloy steel does not allow the wall
thickness to be thinner than 1.57 mm (.062 inch).” To allow the use of this alloy steel an
equivalency calculation must be made to that of 1018 steel.
This calculation is
demonstrated below in Equation 1.
“E = The modulus of elasticity” []
“I = The second moment of area for the cross section about the axis giving the lowest
value” []
“Sy = The yield strength of material in units of force per unit area” []
“c = The distance from the neutral axis to the extreme fiber” []
ID = Inside Diameter
Bstiff = Bending Stiffness
Bstrength = Bending Strength
For 1018 Steel:
E =29700ksi
 π 
 π 
4
4
4
4
4
 × ( c − ID ) = 
 × (1 − 0.75 ) = 0.03355583in
I =
 64 
 64 
Sy =53.7ksi
24
c =1inch
(
)
Bstiff = EI = 29700 × 103 × 0.03355583 = 996608.14
Bstrength =
(
)
SyI
53.7 × 103 × 0.03355583
=
= 1801.948057
c
1
Equation 1: Bending Stiffness and Strength
In Table 4 below the bending stiffness and strength were calculated for available sections
of 4130 steel tubing. The available sections were found using a popular metal vendor. []
OD(in) ID(in)
Moment of Inertia(in^4) bending stiffness(lb*in^2) bending strength(lb*in)
1
0.75
0.03355583
996608.14
2117.372856
1.125
0.959
0.037109744
1102159.40
2081.444313
1.25
1.134
0.038667283
1148418.30
1951.924434
1.25
1.12
0.042602298
1265288.25
2150.564008
1.25
1.084
0.052064518
1546316.18
2628.216858
1.25
1.06
0.057870556
1718755.52
2921.305677
1.25
1.01
0.068761719
2042223.06
3471.091583
1.5
1.37
0.075582124
2244789.09
3179.488024
1.5
1.31
0.103942577
3087094.54
4372.517738
1.5
1.26
0.124781421
3706008.21
5249.138454
1.625
1.509
0.08775855
2606428.95
3407.732022
1.625
1.459
0.119852623
3559622.91
4653.969554
1.625
1.435
0.134130926
3983688.51
5208.407041
1.625
1.385
0.161660136
4801306.03
6277.387421
1.5
1.43
0.043240292
1284236.66
1818.974939
1.5
1.402
0.058850911
1747872.06
2475.661658
1.5
1.37
0.075582124
2244789.09
3179.488024
Weight(lb/ft)
1.171028662
0.92596649
0.740207886
0.824671841
1.037046923
1.174775953
1.451807877
0.998653243
1.429056463
1.77300431
0.9730753
1.370288222
1.556196717
1.933602526
0.548978237
0.761224839
0.998653243
Table 4: Bending Stiffness and Strength of Available Tubing
The lightest section is in bold. This is the 1.25 O.D. tubing with a 0.065 thickness wall.
This is the lightest usable tubing that is still within all of the SAE restrictions.
The other members of the roll cage(frame) will use at a minimum 1.00 inch O.D.
tubing with a 0.035 wall thickness as per the minimum requirements in section 31.2.1[].
Design
The design of the chassis has to incorporate two major things, driver comfort and
safety and subsystem mounting. The driver safety for the design section is simply
satisfying all of the SAE frame rules.
Driver Comfort and safety
To verify that a driver of 6 foot 3 inch, 250lbs would fit comfortably into the
frame, a model of that person was drawn. The driver was then placed in the frame in the
25
driving position as in Figure 5. While this driver was in the frame measurements were
made to make certain all of the SAE safety rules were satisfied.
Figure 5: 95% Male in Mini Baja Frame
Subsystem Mounting
To mount the subsystems that subsystem was first placed in space in relation to
the frame with mounting tabs at the mounting location. Finally piping was routed to the
mounting tabs of that subsystem. This two step process is demonstrated with the
engine/gearbox assembly in Figure 6.
Figure 6: Two step subassembly mounting process step 1 on the left and step 2 on the right
Initial Design
Using the rules, subsystem dimensions, and a 95% male as the driving factors a
frame was designed using the minimum frame tubing specified in the Roll Cage tubing
26
section above. The total weight of the initial frame design is 49.875lbs. This frame is
displayed below in the left of Figure 7 without subsystems, and the right of Figure 7 with
subsystems.
Figure 7: Initial Frame without subsystems (left) and with subsystems (right)
Analysis
Shock Load
As stated before, a transient FEA analysis is preformed on the frame using the
force vs. time chart shown previously in Figure 3 on page 21. This force is broken up into
X and Y values because the shock is not mounted vertically. The maximum and
minimum angle of the shock (theta) in relation to the frame is 20.71 and 23.07 degrees
respectively. The calculation of the X and Y forces are shown in Equation 2, and the
resulting forces are listed in Table 5. This force will be applied to the front and rear
shock mount points individually.
27
Figure 8: Shock angle in relation to the frame
FX = F sin(θ )
FY = F cos(θ )
Equation 2: Calculation of X and Y components of the Shock Force
Total Force
X Force
Y Force
TIME(s)Load(lb)TIME(s)Load(lb)
TIME(s)Load(lb)
0.05
112.5
0.05 44.0836875
0.05 105.230475
0.075
112.5 0.075 44.0836875 0.075 105.230475
0.1
400
0.1
156.742
0.1
374.1528
0.125
1280 0.125
501.5744 0.125 1197.28896
0.15
800
0.15
313.484
0.15
748.3056
0.175
1460 0.175
572.1083 0.175 1365.65772
0.2
390
0.2 152.82345
0.2 364.79898
0.225
-450 0.225 -176.33475 0.225 -420.9219
0.25
150
0.25
58.77825
0.25
140.3073
Table 5: Shock Force X and Y Components
For the FEA analysis the mass of the driver and engine/transmission are also
modeled in the FEA program. To satisfy the SAE rules section 20.2 vehicle
configurations the driver is assumed to weigh 250lb. [] The engine and transmission was
weighed and found to be approximately 100lbs. The density of the frame tubing
(0.284lb/in^3) is also modeled with acceleration due to gravity taken into account.
28
The order of frame tubing used is listed below in Table 6. These are all readily
available sections according to our online retailer. [] They are listed in order of increasing
weight pre foot. If a section of tube needs to be larger to reduce stress the next size up
from Table 6 is used. This will insure that the lowest weight frame is created.
Cross Section
THICKNESS Wieght/FT Reference Number
1
0.035
0.359
1
1
0.049
0.5042
2
1
0.058
0.5912
3
1.125
0.058
0.6579
4
1.25
0.058
0.748
5
OD
Table 6: Frame tubing sections and reference numbers
Front Shock Load
The Initial frame was analyzed using the shock force at the front shock mount as
shown in Figure 9.
Figure 9: Front Shock Force
The results are shown in Table 7, with the graph of maximum von-mises stress shown in
Figure 10.
29
Initial CASE Initial Test with Minimum Tubing Thicknesses
MAX Stress =
42066.66667
Time
Maximum Von Misses Stress
Location
Location Reference # FAIL?
0
2337 Cross Bar
1 PASS
0.05
4614 SIM Triangle Support
2 PASS
0.075
4809 Cross Bar
1 PASS
0.1
9635 Cross Bar
1 PASS
0.125
28694 SIM Triangle Support
2 PASS
0.15
44062 SIM Triangle Support
2 FAIL
0.175
54093 Cross Bar
1 FAIL
0.2
52720 Cross Bar
1 FAIL
0.225
49861 SIM at RRH
3 FAIL
0.25
38674 SIM at RRH
3 PASS
Table 7: Maximum Von-Mises Stress for Front Shock Force
Figure 10: Time vs. Stress for Front Shock Force
To change the stress at the times that the frame fails the tubing sections were modified or
braces were added. The first time optimized was at 0.15s. At time = 0.150sec the
maximum von mises stress was 44062psi and is located at the SIM Triangle Support as
shown in the left of Figure 11. To decrease the stress value in the SIM the SIM tubing
size was moved up to tubing cross-section 2 from cross-section 1. This reduced the
maximum stress to 35400psi as shown in the right of Figure 11.
30
Figure 11: Left - Initial Von-Mises Stress at time 0.15sec, Right - Stress after increased SIM size
At time = 0.175sec the maximum von mises stress was 54093psi and is located at the
cross bar that connects the left and right front shock mounts as shown in the left of Figure
12. To decrease the stress value in the cross bar the tubing section was moved up to
cross-section 2 from cross-section 1. This reduced the maximum von mises stress to
42321psi as shown in the left of Figure 12. This is still above the maximum stress of
42066psi, so to further reduce the stress the cross bar section was increased to crosssection 3, which reduced the maximum von mises stress to 38372psi as shown in Figure
13.
Figure 12: Left - Initial Von-mises Stress at time 0.175sec, Right - first revision at time 0.175 sec
31
Figure 13: Final revision at time 0.175
At time = 0.200sec the maximum von mises stress was 52720psi at Cross Bar as shown
in the left of Figure 14. Due to previous changes in the Cross bar and SIM section size
the maximum von mises stress was reduced to 42852psi and moved to the SIM at the
RRH as shown in Figure 14. This is still above the maximum 42066psi, so a small
support of cross-section 1 tubing was added between the RRH and SIM. This reduced
the maximum von mises stress to 39818psi as shown in Figure 15.
Figure 14: Left - Initial Von-mises stress at time 0.200sec, Right - first revision at time 0.200sec
32
Figure 15: Final revision at time 0.200sec
At time = 0.225sec the maximum von mises stress was 49861psi and is located at the
SIM and RRH as shown in the left of Figure 16. Due to previous changes in the frame’s
tubing sections the maximum stress reduced to 40656psi as shown in the right of Figure
16.
Figure 16: Left - Initial Von-mises stress at time 0.225 sec, Right - Final revision at time 0.225sec
The changes to the frame to withstand the front shock load resulted in a gain of 8.381 lbs
giving a total weight of 58.256lbs. The new stress vs. time graph is shown below in
Figure 17 and the data in Table 8.
33
Second Test with Changes at Maximum Values
MAX Stress =
42066.66667
Maximum Von Misses Stress
Location
Location Reference # FAIL?
0
2184 Cross Bar
1 PASS
0.05
3744 SIM Triangle Support
2 PASS
0.075
3912 SIM Triangle Support
2 PASS
0.1
7094 Cross Bar
1 PASS
0.125
25744 Cross Bar
1 PASS
0.15
35217 SIM Triangle Support
2 PASS
0.175
38275 Cross Bar
1 PASS
0.2
39818 Bottom Spot
4 PASS
0.225
40656 Bottom Spot
4 PASS
0.25
33462 Front Triangle
5 PASS
Time
Table 8: Maximum Von-mises stress, time, and location after front shock force optimization
Figure 17: Time vs. stress of Frame after front shock force optimization
Rear Shock Load
The frame was analyzed using the shock force at the rear shock mount as shown in Figure
18.
34
Figure 18: Rear Shock Force
The results are shown in Table 9, with the graph of maximum von-mises stress shown in
Figure 19.
CASE 1 Initial Test with Minimum Tubing Thicknesses
Time Maximum Von Misses Stress
Location
0
10402 FAB at RRH
0.05
18831 FAB at RRH
0.075
12685 FAB at RRH
0.1
37894 FAB at RRH
0.125
143664 FAB at RRH
0.15
149620 FAB at RRH
0.175
120479 FAB at RRH
0.2
97511 FAB at RRH
0.225
67675 FAB at RRH
0.25
61185 Middle of FAB
MAX Stress =
42066.66667
Location Reference # FAIL?
1 PASS
1 PASS
1 PASS
1 PASS
1 FAIL
1 FAIL
1 FAIL
1 FAIL
1 FAIL
2 FAIL
Table 9: Initial Von-mises stress of rear shock load
Figure 19: Time vs. Stress Graph of Initial rear shock load
35
The maximum von mises stress at 0.125sec is 143664psi, and is located on the FAB at
the RRH as shown in the left of Figure 20. The FAB is in need of a bracing bar to
transmit the force from the shock. A bracing bar of cross-section 1 was added at shock
point to the RRH, this lowered stress to 69736psi and moved maximum stress point to the
FAB at the shock point. This is shown in the right of Figure 20. The tubing section of
the FAB was increased until the maximum stress went down to 38282psi with crosssection 4. This is shown in Figure 21.
Figure 20: Left - Initial Von-mises stress at time 0.125sec, Right - first revision at time 0.125sec
36
Figure 21: Final revision at time 0.125sec
At time = 0.150sec the maximum von mises stress was 149620psi and was located at the
RRH on the FAB as shown in the left of Figure 22. Due to previous changes in the
frame’s tubing sections the maximum stress reduced to 39854psi as shown in the right of
Figure 22.
Figure 22: Left - Initial Von-mises stress at time 0.150sec, Right - Final revision at time 0.150sec
At time = 0.175sec the maximum von mises stress was 120479psi and was located at the
RRH on the FAB as shown in the left of Figure 23. Due to previous changes in the
37
frame’s tubing sections the maximum stress reduced to 52332psi as shown in the right of
Figure 23. The FAB tubing was increased to cross-section 5 to reduce the stress to 41165
as shown in Figure 24.
Figure 23: Left - Initial Von-mises stress at time 0.175sec, Right – first revision at time 0.175sec
Figure 24: Final revision at time 0.175sec
At times 0.200, 0.225, 0.250sec the maximum stresses were reduced to 27442, 21503,
and 30276psi respectively due to previous changes. These results are displayed in Figure
25 and Figure 26 respectively.
38
Figure 25: Left - Final Revisions at time 0.200sec, Right - Final revision at time 0.225sec
Figure 26: Final revision at time 0.250sec
The changes to the frame to withstand the rear shock load resulted in a gain of 6.158 lbs
giving a total weight of 64.414lbs. The new stress vs. time graph is shown below in
Figure 27 and the data in Table 10.
39
CASE 2 Second Test with Changes at Maximum Values
MAX Stress =
42066.66667
Time Maximum Von Misses Stress
Location
Location Reference # FAIL?
0
2614 Shock mount on FAB
3 PASS
0.05
4458 Shock mount on FAB
3 PASS
0.075
4175 Shock mount on FAB
3 PASS
0.1
10392 Shock mount on FAB
3 PASS
0.125
35606 Shock mount on FAB
3 PASS
0.15
37495 Shock mount on FAB
3 PASS
0.175
41165 Shock mount on FAB
3 PASS
0.2
27442 Shock mount on FAB
3 PASS
0.225
21503 FAB at LC
4 PASS
0.25
30276 FAB at LC
4 PASS
Table 10: Maximum Von-mises stress after rear shock optimization
Figure 27: Time vs. Stress after rear shock load optimization
SubsystemSupport
The frame is analyzed at the mounting points of the suspension. The suspension
sub system translates the greatest reaction forces of all the mounted systems. The
reaction forces gathered from the suspension sub team’s FEA will be applied at the
mounting points. Table 11 summarizes those reaction forces and Figure 29 and Figure 30
displays the stress results. The rear suspension forces are added together and applied at
the same time because both the upper and lower arms are connected to the same mount as
shown in Figure 28. The forces and moments were applied dynamically to the frame.
40
A-Arm
Front Upper
Front Lower
Rear Upper
Rear Lower
Rear Total
Mounting Area
Front
Rear
Front
Rear
Single Mount
Front
Rear
Front
Rear
X
-568
-48
-116.715
-116.715
-616
-48.5895
-48.5895
-48.5895
-664.5895
Reaction Forces(lb)
Y
0
0
903.95
903.95
0
338.515
338.515
338.515
1242.465
Z
0
0
78.38
78.38
0
32.115
32.115
32.115
110.495
Reaction Moments(lb*in)
MY
0
0
0
0
1560
0
0
0
1560
Table 11: Suspension Reaction Forces
Figure 28: Rear Suspension Mount
Figure 29: (Left) Front Upper A-arm Stress, (Right) Front Lower A-arm Stress with support
41
Figure 30: (Left) Initial Rear Suspension Stress, (Right) Final Rear Suspension Stress
The stress values were initially above the max allowable 42,067psi for the front
lower analysis, so a bar of cross-section 1 was added as shown in right of Figure 29. The
rear suspension section was changed from section 1 to section 2 to stay below the
allowable stress.
Impact Loading
To calculate the forces used to analyze the 7.9g impact and newton’s second law
is used. The force calculation is shown below in Equation 3.
f = ma
m = 20.2slugs
ft
ft
= 254.38
sec
sec
f = ( 20.2 ) × ( 254.38) = 5138.476lb
a = 7.9 × 32.2
Equation 3: Newton’s Second law for Impact Force
The 5113.038lb force will be used in a transient FEA. The force will be ramped over a
pulse of 0.065sec. [] The impact analysis is done to verify that no frame member will fail
during the impact and the driver will therefore remain safe. The ultimate tensile strength
of the chromoly steel being used is 92,700psi. As long as the stress remains below this
value the frame will be considered safe enough. The displacement of the pipes will be
also be monitored to verify that the driver will not be harmed by any protruding bars
during the impact. SAE rules [] state that the driver’s arms etc must be at minimum three
inches from all structural members of the frame. Therefore any displacement values over
three inches will be deemed harmful to the driver.
42
Front & Side Impact
Only one modification was made to the frame during Front and Side impact
analysis. During the side impact force the part of the LFS that meets the RRH needed
extra bracing of 1 inch O.D. and 0.035 wall thickness to keep the stress below the
ultimate tensile of 92,700psi. The front and side impacted are summarized below in
Table 12.
Front Impact
Side Impact
Side Impact after Gussett Revision
Maximum Vonmises Stress (psi) Time (sec) Maximum Displacement (in) Setup Figure
90717
0.00345
0.041166
Figure 28
105770
0.069
0.505313
Figure 29
79985
0.069
0.510962
Figure 30
Table 12: Side and Front Impact Summary
Figure 31: Left - Front Impact Force, Right – Front Impact Stress
Figure 32: Left - Side Impact Force, Right - Side Impact Stress
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Stress Figure
Figure 28
Figure 29
Figure 30
Figure 33: Left - Supporting Member added to LFS at RRH, Right - Revised Side Impact Stress
Roll Over
The force used for the roll over analysis is dependent on the height of the drop.
The purpose of the roll over analysis is simply to rate the frame for a certain drop height.
The starting point will be a ten for drop. The force used to anlyze the frame at that height
is gathered using data from “The Motor Insurance Repair Research Centre.” [] A impact
velocity can be calculated using Equation 4. That impact velocity is then used to
interpolate a impact acceleration and pulse using data from “The Motor Insurance Repair
Research Centre.” []
PE = Potential Energy
KE =Kinetic Energy
h =drop height
v =impact velocity
PE = KE
PE = mgh
1
KE = mv 2
2
1 2
mv = mgh
2
Equation 4: Impact Velocity
For a ten foot drop the impact velocity is calculated to be 25.4 ft/s and impact
acceleration and pulse is interpolated as 6.8g’s and 70 miliseconds respectively. Using
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Equation 3 the impact force is calculated as 4423lb. The resulting stress is shown in
Figure 34.
Figure 34: (Left) Roll Over Force, (Right) Roll Over Stress for Ten Foot Drop
The stress values for the ten foot drop is 102,840psi which is above the UTS of
92,700psi. The frame is next analyzed at a eight foot drop. For a eight foot drop the
impact velocity is calculated to be 22.7 ft/s and impact acceleration and pulse is
interpolated as 6.3g’s and 72.5 miliseconds respectively. Using Equation 3 the impact
force is calculated as 4120lb. The resulting stress is shown in Figure 35.
Figure 35: Eight Foot Drop Stress
The stress value for the eight foot drop is 80,054psi which is below the UTS of
92,700psi. So our frame will be rated for a maximum roll over drop of eight feet. During
the Mini Baja race the car should not have to undergo a roll over drop over five feet. []
Design for Manufacturing
During initial design, design for manufacturing was considered. The Florida Tech
Machine shop has all of the necessary tools to cut, bend, cope, and weld chromoly tubing.
The shop only has a limited size of dies for the tube bender. Therefore tubing bend
45
radius is limited by the tubing outside diameter as per Table 13. The initial frame design
contained these constraints. There are no necessary revisions to the frame due to
manufacturing.
Tubing O.D. Bend Radius
0.5
2.5
1
3
1.25
3.5
Table 13: Available Bend Radii
Fabrication Process
To build the chassis chromoly tubing was purchased in eight foot sections then,
cut, bent, coped and welded in the appropriate spot on the car.
To cut and bend the tubing a chop saw and tube bender were provided in the
Florida Tech Machine shop. The tubes were then coped to fit a mating tube using a tube
notcher as shown in Figure 36 below.
Figure 36: Left to Right - Tube Bender, Chop Saw, and Tube Notcher
Detailed Drawings
Detail Drawings for the frame can be found in Appendix H.
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Budget
Description
Price
TUBING
Chromoly tubing (1.25x0.065)
Chromoly tubing (1.00x0.035)
Chromoly tubing (0.50x0.035)
Chromoly tubing (1.00x0.058)
Chromoly tubing (1.00x0.049)
Chromoly square tubing (0.50x0.035)
$197.40 48ft $197.40 onlinemetals.com
$91.68 32ft $91.68 onlinemetals.com
$26.95 8ft
$26.95 onlinemetals.com
$9.99 2ft
$9.99 onlinemetals.com
$43.60 10ft $43.60 onlinemetals.com
$1.61 2ft
$1.61 onlinemetals.com
TABS
Front suspension -11 Guage Radious tabs -PN2514
Rear suspension - Alloy Steel Sheet 4130 ANNEALED 0.1 thickness (12''x12'' Section)
Transmission/Engine -11 Guage Radious tabs -PN2514
Body Panels -Alloy Steel Sheet 4130 ANNEALED 0.05 thickness (12''x12'' Section)
Various -Alloy Steel Sheet 4130 ANNEALED 0.05 thickness (12''x12'' Section)
TOTAL
$2.00
$20.85
$2.00
$9.29
$9.29
QT Total
Vendor
20 $40.00 Tabzon Chassis Components
2 $41.70 onlinemetals.com
5 $10.00 onlinemetals.com
1
$9.29 onlinemetals.com
1
$9.29 onlinemetals.com
$481.51
Table 14: Chassis Budget
Manufacturing and assembly of the frame will be done by the students using
Florida Tech resources (welder, welding rod, coping tool, and mill). The school does not
require payment for these resources; therefore they are not listed above in the budget.
The complete budget with manufacturing, assembly and retail part cost can be found in
Appendix I.
Design Changes
During the spring 2008 Spring semester minimal design changes were done to the
chassis. Due to changes in the transmission type the rear end of the car had to be
redesigned. The dame FEA analysis was performed on the chassis to verify the changes
did not modify the results. The old and new rear end is shown Figure 37.
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Figure 37: Chassis Rear End Before (left) and after (right) transmission reselection
Scheduling
Plan for Completion
As of now the car is in racing condition, and has passed initial testing. Further
testing will be done to prove the chassis has satisfied all nondestructive design
constraints.
Gantt Chart
The Gantt Chart for the chassis section can be found in Appendix D.
Conclusions
After shock load, and impact analysis on the frame it is ready to endure a Mini
Baja race and fulfill all of its goals. Weighing in at a manufactured total of 80lbs (extra
weight added due to welding) the frame will help the overall performance of the car
during competition. The chassis is completed and has gone through initial testing. This
includes low and high speed testing over rough terrain and small (1 foot) jumps. There
are plans for high speed extremely rough terrain and larger (4 foot) jumps testing. As of
now the chassis is ready for the SAE competitions. The final frame is displayed in Figure
38.
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Figure 38: Final Frame after Complete Analysis
49