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CENTRO: Center of Gravity System
Mid-Semester Report
Submitted to:
Professor Richard L. Roberts
&
Professor Peter S. Rourke
On:
June 11, 2010
By:
Ryan Michienzi
Ruben Medeiros
Andrew Maynard
WENTWORTH INSTITUTE OF TECHNOLOGY
Senior Capstone Design Project
Mech 690
Ryan Michienzi (508) 642-5952
60 Norton St. Attleboro, MA 02703
Ruben Medeiros (774) 451-3320
938 Jefferson St. Fall River, MA 02721
Andrew Maynard (781) 789-7370
93 Evans St. Weymouth, MA 02191
1
ABSTRACT
The design team has taken on the task of developing a 2-dimensional center of gravity
(COG) system for WIT’s SAE F1 Hybrid Race Car. This is a crucial aspect in designing a race
car. Most race cars try to achieve an equilibrium weight distribution. A 2-dimensional COG
system can help determine the optimal placement of the engine, driver seat and counter weights
if necessary. The team has taken it a step further and has been developing a 3-D COG system.
The physical parameters of the system are reaching the production stage with the software almost
fully functional. In the coming weeks the team plans to have the system fully operational leaving
only minor alterations left to be addressed.
2
TABLE OF CONTENTS
Abstract ......................................................................................................................................................................... 1
Executive summary ........................................................................................................................................................ 3
Introduction ............................................................................................................................................................... 3
Discussion of Design .................................................................................................................................................. 3
Discussion of Results ................................................................................................................................................. 4
Conclusion ................................................................................................................................................................. 4
Introduction ................................................................................................................................................................... 5
Design Data .................................................................................................................................................................... 6
Sample Calculations ....................................................................................................................................................... 7
Calculations for load cell ............................................................................................................................................ 7
LabView Formulas ...................................................................................................................................................... 8
2-D COG ................................................................................................................................................. 8
COGH ..................................................................................................................................................... 8
Results ........................................................................................................................................................................... 9
Alternative Designs .................................................................................................................................................... 9
Final Design .............................................................................................................................................................. 11
Graphs & Diagrams ...................................................................................................................................................... 12
Work Plan ................................................................................................................................................................ 12
Design Matrixes ....................................................................................................................................................... 13
Load Cell .................................................................................................................................................................. 14
Centro Program ........................................................................................................................................................... 16
Discussion of Results ................................................................................................................................................... 19
Conclusion ................................................................................................................................................................... 19
Bibliography ................................................................................................................................................................. 19
3
EXECUTIVE SUMMARY
INTRODUCTION
The Centro design team has been working on a center of gravity (COG) system for
Wentworth Institute of Technology’s, student developed F1 Hybrid race car. The system will be
capable of calculating the three dimensional center of gravity of the car in order to position
components on the vehicle, such as the motor and driver seat, while maintaining the optimum
center of gravity. This is a crucial aspect of the cars design because most race cars are designed
to have a balanced weight distribution. The Centro COG system will facilitate this process and
help verify future designs of the vehicle.
DISCUSSION OF DESIGN
The main function of the Centro system, will be to transmit the normal loads exerted by
the chassis, to a DAQ where it will be processed using LabView. That calculates the 2-D center
of gravity along the X and Z plane (the horizontal plane parallel to the ground). The design team
however will attempt to also develop the ability to calculate the vertical center of gravity along
the y-axis. This will allow the true 3-D center of gravity, or centroid, to be easily determined.
Three major design alternatives were considered for the system. These design
alternatives included using strain gauges attached to the frame of the vehicle, tire pressure
sensors, and separate chucks for each wheel containing a strain gauge for each. Four strain
gauges were provided to the group by Professor Dow. A group of students analyzed and tested
the strain gauges with the intent of being used in a center of gravity system for the F1 hybrid car.
All of these concepts include attaching the gauges or sensors to a DAQ and processing the data
in a LabView program the team has developed.
4
DISCUSSION OF RESULTS
The three major designs were evaluated using a design matrix. Each alternative design
was ranked on a scale of one to ten according to five parameters, also ranked from one to ten.
Once the final design was chosen, analysis of the optimum design began. This design has been
optimized for the most efficient system given the materials and time available. Fabrication of the
hardware has begun and the majority of the LabView program has been completed.
The design consisting of a set of chucks (one per wheel) was selected as the final design
to pursue in this project. Three sub designs have been developed and have been evaluated. The
final chuck design that was chosen allows for some optimization of the set up, which should
allow users to make new load cells to withstand large loads in the future. The design matrixes
used in the decision process can be found in the Graphs & Diagrams, Design Matrixes of this
report.
CONCLUSION
A prototype of the physical hardware has been completed; the team is currently in the
process of producing the final four chucks based off its design. In the coming weeks full testing
of the system is expected with the results becoming available shortly after. The LabView
program is nearly completed with only minor modifications needing to be made as the design of
the software is finalized. In its current state it is fully functional and needs only to be set up to a
DAQ to become operational.
5
INTRODUCTION
The Centro is a system designed to calculate the center of gravity of the F1 Hybrid vehicle that is
used by the SAE student chapter at Wentworth. The main function of the hardware will be to
transmit the normal loads exerted by the chassis, to a DAQ where it will be processed using
LabView. The SAE group will be using the system to layout the components for the F1 Hybrid
vehicle, such as the motor and driver seat positioning. This requires calculating the 2-D center of
gravity along the X and Z axis (according to practiced coordinate system). The design team is
attempting to also develop the capability to calculate the center of gravity height along the y axis.
This will allow the SAE group to calculate the true 3-D center of gravity.
It has been determined that load cells that have previously been tested by another group
of students, will be utilized in the design. These load cells, which consist of a strain gauge
attached to an aluminum beam, are housed in separate chucks for each wheel. The strain gauges
are tied into a data acquisition system which inputs the measured values to a LabView program
which manipulates the data and generates the coordinates of the center of gravity of the vehicle
as well as the total weight of the car.
The system is designed to efficiently calculate the center of gravity and weight, while
being easy to operate by the user. The use of chucks, make the Centro system easy to store.
6
DESIGN DATA
Table 1: The table above contains information regarding the load cells used in the Centro
design.
Table 2: This table includes parameters that were calculated by the Centro project team. The
values are assuming a 75 kg load on the beam which is being used as the maximum allowable
load.
7
SAMPLE CALCULATIONS
CALCULATIONS FOR LOAD CELL
In order to verify the team’s FEA setup the following calculation was performed to find
the deflection of the beam. A load of 75 kg was used. Equations from: Fundamentals of
Engineering Supplied-Reference Book, (Clemson, SC: National Council of Examiners
for Engineering & Surveying, 2008) 38
𝐹 = 75 𝑘𝑔 9.81𝑚
𝑠
𝐹 = 735.75 𝑁 0.225𝑙𝑏𝑓
𝑁
𝑭 = 𝟏𝟔𝟓.𝟓𝟒 𝒍𝒃𝒇
𝐼 =𝑏3
12=
2 𝑖𝑛 (0.25 𝑖𝑛 )3
12
𝑰 = 𝟎.𝟎𝟎𝟐𝟔 𝒊𝒏𝟒
𝛿 =𝐹𝐿3
48𝐸𝐼=
165.54 𝑙𝑏𝑓 (4.5 𝑖𝑛 )3
48 10×106 𝑝𝑠𝑖 (0.0026 𝑖𝑛4)
𝜹 = 𝟎.𝟎𝟏𝟐𝟎𝟕 𝒊𝒏
To find the maximum stress the strain gage could withstand, the following calculations were
completed using the strain gauge’s maximum strain which was 30,000 με.
𝜎 = 휀𝐸 = 30,000 × 10−6 휀 10 × 106 𝑝𝑠𝑖 𝝈𝒔𝒈 𝒎𝒂𝒙 = 𝟑𝟎𝟎,𝟎𝟎𝟎 𝒑𝒔𝒊
8
LABVIEW FORMULAS
Diagram 1: This diagram shows the Track Width and Wheel base measurements
Diagram 2: This diagrams shows the method for determining COGH
2-D COG
𝐶𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝐺𝑟𝑎𝑣𝑖𝑡𝑦𝑊𝑒𝑒𝑙 𝐵𝑎𝑠𝑒 = 𝑅𝑒𝑎𝑟 𝑊𝑒𝑖𝑔𝑡
𝑇𝑜𝑡𝑎𝑙 𝑊𝑒𝑖𝑔𝑡 𝑊𝑒𝑒𝑙 𝐵𝑎𝑠𝑒
𝐶𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝐺𝑟𝑎𝑣𝑖𝑡𝑦𝑇𝑟𝑎𝑐𝑘 𝑊𝑖𝑑𝑡 = 𝑅𝑖𝑔𝑡 𝑆𝑖𝑑𝑒 𝑊𝑒𝑖𝑔𝑡
𝑇𝑜𝑡𝑎𝑙 𝑊𝑒𝑖𝑔𝑡 𝑇𝑟𝑎𝑐𝑘 𝑊𝑖𝑑𝑡
COGH
𝐶𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝐺𝑟𝑎𝑣𝑖𝑡𝑦𝐻𝑒𝑖𝑔𝑡 = 𝑊𝑒𝑒𝑙 𝐵𝑎𝑠𝑒 ∗ ∆𝐹𝑟𝑜𝑛𝑡 𝑊𝑒𝑖𝑔𝑡
𝑇𝑜𝑡𝑎𝑙 𝑊𝑒𝑖𝑔𝑡 ∗ tan𝜃 + 𝑡𝑖𝑟𝑒 𝑟𝑎𝑑𝑖𝑢𝑠
tan𝜃 =𝐻𝑒𝑖𝑔𝑡
𝑊𝑒𝑒𝑙 𝐵𝑎𝑠𝑒
9
RESULTS
ALTERNATIVE DESIGNS
During the preliminary analysis of alternative designs for the Centro system, the means
of determining the center of gravity of the vehicle was chosen. Each of these designs were
ranked on a scale of one to ten according to five parameters, also ranked from one to ten. The
most heavily weighed factor was effectiveness (10). This was followed by feasibility (9) which
was how realistic it was to incorporate the design into the project. Implementation (9) was
weighed the same as feasibility and was how well we could reasonably produce the design. Cost
(5) and available parts (4) were also considered. This design matrix is shown in Figure 1 in the
Graphs & Diagrams, Design Matrixes section of this report.
There were three main design concepts. All three designs require a LabView program in
order to operate. The first consisted of implanting a pressure sensor in the actual tires of the F1
car. The relationship between the tire air pressure and the load on the corresponding wheel
would have been determined and the tire air pressure would be used to calculate the center of
gravity. This design’s main benefit would be that the system could be programmed to record
live data while the vehicle is in motion which allows the user to see how the load varies as the
car moves through turns and straights. This concept is shown in the illustration below. This
design did not get a high ranking in the design matrix. This is because implementation of this
idea would be difficult, the sensors needed would be fairly expensive and a prototype may be
difficult to test.
10
The second design alternative was using pre-existing load cells tested by another group of
students and given to the Centro design team by Prof. Dow to complete the project. In this
design, the strain gauges would have been attached to the vehicle between the A arms and the
frame. The strain readings for each wheel would then be translated into a load and the center of
gravity would be calculated. Below is a visual representation of this design. This design also
did not get the highest ranking in the teams design matrix because it would be very difficult to
calculate the strain because there are many pieces connecting the wheels to the frame. Very little
data could be found on the actual F-1 car as it was bought from an outside source with no
documentation. This would also make it difficult to determine which type of steel the frame is
made of.
11
FINAL DESIGN
The design that was chosen by the team also used the load cells given to the team by
Prof. Dow. This design consisted of four wooden “chucks,” one per wheel, which houses the
load cell beam in a way such that bending of the beam is not restricted. It also provides stability
to the system by preventing the car from moving while being weighed. The LabView program
calculates and displays the center of gravity of the vehicle for the user. A detailed description
along with diagrams can be found in the Centro Program section of this report. The final design
is shown in the images below.
12
GRAPHS & DIAGRAMS
WORK PLAN
The above table and timeline shows the Centro team’s work plan.
13
DESIGN MATRIXES
Figure 1: Above is the design matrix for the means of obtaining load data for calculating the
center of gravity
Figure 1-a: Above is the design matrix for the sub-designs of the chuck
14
LOAD CELL
Figure 2: The dimensions of the load cell beam are shown above. This includes dimensions that were chosen for
the distance between the supports on each end and the tire contact area on the beam.
Figure 3: The Finite Element Analysis stress plot is shown above, with a load of 75kg applied.
15
Figure 4: This diagram illustrates the deflection of the load cell beam with a 75kg load applied, it was
obtained using MDesign.
16
CENTRO PROGRAM
The program that is being developed for the Centro COG system is deep into its
development. The program currently includes four main tabs. There is COG, COGH, Vehicle
selection, and Calibration. The calibration tab has not been developed as the physical COG
system has not currently completed. Once it is completed that area of the program can be
developed using the system as a guide for calibration. Aside from the four tabs there is a save
values button which will write the current values to a file, as well as an LED display which gives
a 2-D representation of the COG location.
The tab above is the COG tab and will be the most commonly used in the program since
the main concern of the SAE team is the 2-D center of gravity. On this tab the exact 2-D COG
coordinates are displayed, along with the total weight and the weight at any given wheel. It also
has a warning light to alert the user when the car is not in proper position, for 2-D COG values.
Basically when the light is activated all values on this tab are invalid.
17
This tab will be utilized for the 3rd
dimension for COG which is referred to as COGH.
This tab has a brief note for how to use this tab as well as a diagram. To use this tab you must
capture the weights obtained in the 2-D test using the capture weights button, next you elevate
the rear axle until it is roughly 20+ inches from the ground. Once it is elevated one must measure
the elevation from the floor and input it in the height of elevation box. Once this is done the LED
display will light up giving the user a visual representation of the COGH. Next to the Led display
there is a numerical output which will give the exact COGH value in inches.
18
The final tab that has been developed is the Vehicle Selection tab. This is where the
wheel base and track width can be put in or selected. There is a brief diagram so if the user is not
familiar with the terms or measurements needed. On the left of the tab there is a present vehicle
list that will have a minimum of two options. The F1 Hybrid and manual input, it is set up to
default to the F1 Hybrid and will automatically use its dimension for calculations. However if a
different vehicle is in use when the preset is put on manual input the two input boxes on the right
will activate. This way the user can put in a dimension if there are any changes to the vehicle or
any changes in the dimensions for any other reason.
19
DISCUSSION OF RESULTS
The final design was chosen by the team and was analyzed in order to come to a refined
design from which a prototype was produced. The majority of problems occurred while
designing the chucks. The chucks had to be designed so that the vehicle’s wheels would stay on
the load cell beam and be positioned so that all the weight was applied to the center, suspended
part of the beam. The beam also needed to be allowed to deflect in the middle between the
supports, as well as at the ends in order to obtain accurate readings from the strain gauge. The
distance between the end supports of the beam was also a critical aspect of the design. The
maximum deflection without yielding was calculated for the beam. Using this deflection it was
determined that the strain gauge could withstand the maximum strain expected. This is shown in
the Sample Calculations section. This meant that the beam’s yield strength was the limiting
factor for the design. In order to optimize the load capacity while keeping a stress well below
the yield strength of the beam, a nominal distance between the beams was selected. This
distance was calculated to be 4.5 in.
SolidWorks Simulation was used to determine stress and corresponding deflections when
loads were applied to the load cell. Calculations were also performed to verify the setup. These
calculations can be seen in Sample Calculations.
The final design has been developed and a prototype is complete. The remaining
hardware is being developed and testing of the system should begin in the coming weeks with
results to follow shortly aft
CONCLUSION
The development and implementation of the Centro project is moving along as planned
with only minor setbacks. Testing of the prototype is in its initial stages and is expected to go
smoothly with results being completed in the next two weeks. This will leave the team time to
finalize any loose ends and fabricate all four chucks, completing the project.
BIBLIOGRAPHY
20
Milliken, William, and Milliken, Douglas. Race Car Vehicle Dynamics. Warrendale, PA
: SAE, 1995. Print.
Formula Hybrid. Thayer School of Engineering at Dartmouth. Web. 26 May. 2010.
‹http://www.formula-hybrid.org/›.
Center of Gravity Height. Longacre Racing Products, Inc. Web. 24 May. 2010.
‹ http://www.longacreracing.com/articles/art.asp?ARTID=22/›.
Fundamentals of Engineering Supplied-Reference Book. Clemson, SC: National Council
of Examiners for Engineering & Surveying, 2008.
