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UNIVERSITY OF DELAWARE FSAE CHASSIS: PHASE IV REPORT

Date: 12/10/10

Table of Contents

Completed Frame .................................................................................................................... 2

Steel Frame Manufacturing...................................................................................................... 3

Frame Analysis and Validation: ................................................................................................ 4

Alternative Frame Analysis: Modal Analysis ............................................................................. 8

Fuel Tank................................................................................................................................11

Current Status and Path Forward ............................................................................................13

Budget ...................................................................................................................................13

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Completed Frame

The follow images show the manufactured chassis with the suspension, steering wheel, pedal

box, engine, fuel tank, and differential all mocked up. It is evident from these images that the vehicle

systems all integrate into the chassis purposefully.

The images following (Fig 5 and Fig 6) illustrate the front end suspension packaging. Note the

positioning of the upper shock mount. The upper shock mount has to bear the majority of the load that

the suspension carries. The chassis design has a triangular truss structure supporting this mount for the

sole purpose of supporting this load.

Figure 1) Front Isometric View of Frame Figure 2) Rear Isometric View of Frame

Figure 3) Rear Suspension Box Figure 4) Radiator View

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Steel Frame Manufacturing

The first step to manufacturing the frame was to

create the jig. A wooden spine type jig (Fig. 9) was chosen

because though it is not the most precise jig, it is the

cheapest and quickest to manufacture. After the jig was

complete, the next step was to complete all of the

sections of the car that were parallel to the front

bulkhead (Roll Hoops, Suspension Boxes, etc.). The roll

hoops were constructed using a tubing bender with a

4.5” radius dye and full scale drawings. These full scale

drawings were critical to ensure the tightest dimensional

accuracy possible while bending the tubes. Every bend

could be checked by laying the roll hoop on the drawing.

Once these parallel sections were complete, the tubes

connecting them were manufactured. The best way that was found to do this was with flat templates

(Fig 10) generated from SolidWorks. Each

complicated member was extracted from the

model, cut, and bent flat in SolidWorks. A 1:1

drawing of the tube was printed and wrapped

around the respective steel tube. The tube

was ground using a vertical belt sander and

filed to fit the template. These templates

usually got the tubes very close to perfect and

the tubes only usually needed a little custom

shaping with a file.

Figure 7) Front Suspension Detail Figure 8) Driver Compartment Detail

Figure 9) Frame in Wooden Spine Jig

Figure 10) Unwrapped Tubing Profile

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Frame Analysis and Validation:

SolidWorks finite element analysis package was utilized to design and optimize the chassis.

Many different chassis designs were analyzed using the same flexure and torsion tests in order to

minimize the amount of frame members used while still maintaining proper stiffness. The torsion

analysis (Fig 11 and Fig 12) was performed by fixing the rear suspension box and applying a couple to the

front suspension box. The flexure analysis (Fig 13 and 14) was performed by fixing the front of the rear

suspension box and the front of the front suspension box and applying distributed load along the bar at

the base of the main roll hoop.

Figure11) FEA Displacement due to Torsion

Figure12) FEA Stress due to Torsion

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Figure 13) FEA Displacement due to Flexure

Figure 14) FEA Stress due to Flexure

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Table 1) Metrics of Previous Car, Goal Value, and Actual Value

Metric 2008 UD FSAE Car Goal Value Actual Value

Manufacturability n/a 225 Hrs 450 Hrs

Torsional Rigidity 1500 ft-lb/deg 1800 ft-lb/deg -

Flexural Rigidity 4300 lbs/in 4500 lbs/in 6200 lbs/in

Weight 80 lbs 80 lbs 78 lbs

Vertical CoG 12 in 12 in 13.25 in

Manufacturability:

Manufacturability was measured as the amount of total hours it took the team to manufacture

the chassis and fuel tank. The goal value was set with the intention of building a torsional testing rig

before the end of the semester. Unfortunately the frame required more time than anticipated so the

actual value was twice the goal value of 225 hrs.

Torsional Rigidity:

Torsional rigidity has not yet been tested due to

insufficient time to manufacture the rigging to do so. The

test will be by fixing the rear suspension box to one of the

rigid steel support beams on the Spencer Lab loading dock.

The front suspension box will be supported longitudinally

with a roller support from the student shop to prevent the

cantilevering effects of fixing the rear of the frame. A truss

structure will then be assembled using extra square steel

tubing that will be bolted to the suspension pick up points as

shown in figure 15. A lever arm will then be loaded with

weight to create a couple at the front suspension box and the

corresponding angular displacement will be measured with a

digital level.

Figure 15) Torsion Test Rig

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Flexural Rigidity

To determine the

flexural rigidity, the

chassis was supported

under the front and rear

suspension boxes (Fig 16).

A reference mark was

placed on a horizontal

member in the center of

the chassis. The distance

between the reference

mark and the floor was

recorded to determine the

position when the frame

was unloaded. This

technique will calibrate

out any flexing of the

chassis from its own

weight. The center of the frame was loaded with test weights directly over the reference mark. Once the

frame settled, the distance between the reference mark and the floor was measured again. The change

in height due to the loading was determined. With this figure and the total amount of test weight, the

flexural rigidity in the longitudinal direction was calculated. As can be seen from table 1, the flexure

stiffness was 6200 lbs/in, and well exceeds the goal value of 6200 lbs/in.

Weight

The weight of the chassis was found by using digital scales. This metric was modified from the

initial design phases in order to incorporate the weight of the impact attenuator plate. The weight of

the chassis has decreased slightly from the 2008 frame with an increase in both stiffness and driver

cockpit size.

Vertical Center of Gravity

Figure16) Flexure Testing Method

RA R

B

A B C

δ

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x

y

The vertical center of gravity was measured as the height of the center of gravity from the

lowest member on the chassis. The value was determined by first weighing the frame front and

balancing the moments to find the line that the CoG is located on (Fig 17). Next the frame was lifted at

prescribed angle and weighed at the front end (Fig 17). The moments were balanced in this

configuration to find another line that the center of gravity was located on. With the locations of these

lines the height of the center of gravity was calculated.

The center of gravity of the current design is higher than the 2008 frame. This is due to the

addition of structural members around the driver’s section. These additional members, however, added

considerable rigidity to the frame.

Alternative Frame Analysis: Modal Analysis

One of the primary customer wants defined for the chassis is a high stiffness to weight ratio.

This figure is very useful for designing the chassis, and dictates a design that both maximizes stiffness

and reduces weight. High stiffness improves the responsiveness of the vehicle and allows for more

driver feedback, and lighter weight improves handling and overall performance. Thus, a high stiffness to

weight ratio indicates that the frame will perform well.

The conventional method for evaluating the stiffness to weight ratio is to both measure the

weight of the bare frame, and calculate the stiffness, either in flexure or torsion. The ratio of these two

numbers will then give the stiffness to weight ratio. A second method, recommended with the advice of

engineering panel member Dr. Ed Gargiulo, also exists to determine the stiffness to weight ratio using

analysis of the response of the frame under vibration. When perturbed, any solid body will vibrate at a

certain frequency, known as its natural frequency. The natural frequency is defined as follows:

Figure 17) Center of Gravity Diagram

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√

where is the natural frequency, k is the stiffness of the frame, and m is the mass of the frame.

Conveniently, the term under the radical is stiffness over weight. This indicates that the natural

frequency is a function of the square root of the stiffness to weight ratio. Thus, a higher natural

frequency indicates a higher stiffness to weight ratio. Additionally, many bodies may contain multiple

natural frequencies, called resonant frequencies, at multiples of the natural frequency, known as

harmonics, depending on the vibration type, or “mode”. When a body vibrates at a resonant frequency,

it will oscillate at larger amplitude than other frequencies, even those that may be larger than the

natural frequency. The body will oscillate with more and more amplitude in an attempt to dissipate the

energy stored within it. Since any real object has a certain amount of damping, the amount of amplitude

is limited. However, It may be large enough to still cause damage to the part.

In the context of the chassis, each member has its own set of resonant frequencies. If the

member is allowed to oscillate at one of its resonant frequencies, it may displace itself enough to cause

a failure in one of the welds holding the frame together. The primary source of vibrations in the chassis

is from the engine. The engine uses a single-cylinder configuration, which is inherently unbalanced. As a

result, large vibratory forces are transferred from the engine into the chassis. In fact, in the two previous

chassis designs for the FSAE team, the frame suffered weld joint failures near the engine. This indicates

that the frequencies produced from the engine vibrations corresponded to some of the resonant

frequencies of the chassis. In these chassis, special care was not taken to dampen any of these

vibrations, resulting in structural damage. This leads to two conclusions: the chassis should be analyzed

to find its resonant frequencies, and, should those frequencies correspond to common frequencies

created by the engine, that the engine should be damped to help reduce the chance of structural failure.

Similar to the static finite element analysis performed, the chassis can be analyzed with

Solidworks, using a technique called modal frequency analysis. This method will convert the frame to a

mesh, and simulate vibrations through the chassis using several different frequencies. The frequencies

that create the largest displacements are recorded, and the mode of vibration corresponding to each is

also recorded. The results supply each resonant frequency, and the “mode shape” for each

corresponding frequency. The usefulness of these frequencies and mode shapes is twofold: they can be

used to determine if the vibrations of the engine may cause damage to the chassis, and the mode

shapes can be used to see which frequencies are of relevance to the design of the chassis. Additionally,

this method can be used to compare two frame designs side by side. Since higher natural frequencies

correspond to a higher stiffness to weight ratio, a new frame design can be compared to previous

iterations to see if the stiffness to weight ratio has been improved.

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The modal frequency analysis was performed on both the current frame design and the 2008

frame design created by sponsor / former team member Mike Bauman. The list of natural frequencies is

given in Table 2.

Table 2: First 12 Harmonic Natural Frequencies of 2008 and 2010 Chassis

Frame 2008 Frame 2010

Harmonic Frequency (Hz) Harmonic Frequency (Hz)

1 0.001 1 1.23E-05

2 0.0008 2 0.0001

3 0.0006 3 0.0002

4 0.0001 4 0.0002

5 0.0002 5 0.0002

6 0.0005 6 0.0004

7 59.5 7 63.3

Figure 18) 7th Order Mode Shape

Figure 19) 8th Order Mode Shape

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8 63.6 8 66.4

9 82.2 9 88.6

10 94.8 10 104.7

11 105.8 11 124.3

12 115.6 12 128.3

From the above results, in both frames the first six harmonics are approximately zero. This

outcome is reached because the motion of the frame is completely unconstrained, allowing for six

degrees of freedom and thus six rigid body movements. For harmonics 7 through 12, the frequencies are

large enough to be appreciable. As a comparison tool, the 2010 design has larger natural frequency

values at each harmonic, meaning that for the same vibration, the 2010 design has a higher stiffness to

weight ratio than the 2008 design.

In the context of improving the performance of the 2010 frame design, the most pertinent

mode shapes correspond to the seventh and eighth order harmonics. The seventh order mode shape

corresponds to a twisting motion along the long axis of the chassis (Fig 18). A longitudinal flexure is

characterized by the eighth order harmonic (Fig 19). These two mode shapes are important, as two of

the key performance metrics for the frame are torsional and flexural rigidity. Thus, calculation of the

natural frequencies for these mode shapes can be used to judge the rigidity figures for each type of

loading. While the analytical results can be used as a ballpark figure, the results should be empirically

obtained using a physical test of the chassis.

Fuel Tank

The 2011 Formula SAE rules heavily govern the design of the fuel tank and components of the

fuel system. Due to the rules, a rigid tank, which can be seen in figure 20, must be used for safety of the

driver. Due to this rule, 5052 16 gauge sheet aluminum was choses. This thickness was chosen due to

the light weight, while maintaining a rigid tank. 5052 aluminum was chosen for its high workability and

ease of welding. Also, 5052 is use extensively in chemical storage tanks in industry. All of the sides of

the fuel tank were cut and bent out of one piece of sheet aluminum to minimize the amount of welding

needed. As seen in figure 21, the bottom of the tank is made out of four pieces of aluminum. The

trapezoidal pieces are made out of the 16 gauge sheet aluminum and were cut and welding to allow fuel

to drain towards the center of the bottom of the tank. The square section of the bottom of the tank was

made from a 3/8 inch aluminum plate to allow the fuel pump to properly seal to the gas tank. This

square section of the bottom of the tank was machined using a vertical mill to cut out the larger center

hole for the fuel pump to be inserted in and the six bolts used to secure the pump to the tank. These six

fasteners were welded to the tank to ensure a water tight seal. A in-tank fuel pump, figure 22, was

selected over a out of tank fuel pump for the lower cost, amperage use, and operating temperature as

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well as a high volume flow. To install the fuel pump, the fuel pump is inserted with the supplied o ring

into the gas tank. Then the supplied aluminum plate is place over the fuel pump and six 0.25 nuts are

used to secure the pump to the gas tank.

By FSAE rules, the filler neck must be at least five inches tall, 1.5 inches in diameter and angled

no more than 45 degrees from the vertical. Due to these constraints, a 1.5 inch inner diameter

aluminum tube was chose with a wall thickness of an 1/8th of an inch. The filler neck was angled at 30

degrees from the vertical for ease of filling and to maintain proper clearance from other vital parts of

the car. The filler neck incorporates a welded screw type gas cap attached to the end per FSAE rules.

Attached to the cap is a check valve that allows no spillage during hard cornering or acceleration. Per

FSAE rules, the gas tank must be equipped with a sight tube. This a clear plastic tube that has to be

more in three inches in length to allow the person filling the tank to know how much fuel is in the tank.

Two 90 degree aluminum elbows were welded four inches apart to the filler neck approximately one

inch from the gas cap. Clear plastic tubing connects the two elbows and the is secured using pipe

connectors. To mount the gas tank, three aluminum mounting flanges were welded to the underside

the gas tank and drilled to except a 0.25 inch bolt. Three steel flanges were welded to the frame to

secure the tank to the steel space frame utilizing the 0.25 inch bolts.

The volume of the fuel tank was decided based on multiple factors. The previous fuel tanks

have been 2.5 gallons in volume. The UD FSAE team has yet to run out of fuel after a hour of driving and

due to the fact that the longest event is the 45 minute endurance event, there is no need to enlarge the

volume of the tank. Also, due to the fact that the motor has not been properly tuned and may use more

fuel than currently set up, the gas tank volume was chosen not to change. Due to the addition of the in

tank fuel pump, the overall volume of the tank was enlarged by the volume of the fuel pump to 2.65

gallons.

Figure 20) Fuel Tank Model

Figure 31) Bottom View of Real Fuel Tank

Figure 22) Yamaha in-tank Fuel Pump

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Current Status and Path Forward

During the 3.5 month duration of senior design, all of the frame members have been cut and full

welded into the frame. Mounting tabs for all of the car components need to be finish welded. More

importantly the engine needs to be mounted correctly as to be in line with the rear sprocket as well as

clear the shifting lever. The fuel tank needs to have a hole drilled in it, have the filler neck welded to it

and have the mounting tabs welded to the bottom of it for it to be complete.

After these tasks are taken care of the next step will be to design and layup bodywork. The plan

is to use the materials donated by CCM to create a female mold and the actual bodywork itself.

Concepts will be generated during Christmas break so the manufacturing process can begin early in

winter session.

Budget

Item Purpose Cost

Engine Dampers Engine Mounts $21.70

Steel Tubing Frame $583.14

Wood Frame Jig $59.42

Full Scale Drawings Frame Manufacturing $16.50

Protractor Frame Manufacturing $5.99

Welding Jigs Frame Manufacturing $82.44

Fuel Pump Fuel System $77.80

O Ring Fuel System $23.38

Aluminum Bolts Fuel Tank $11.87

Aluminum Plate Fuel Tank $36.00

Composite Inserts Monocoque Manufacturing $29.11

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Hole Saws Notching Tubing $25.05

Total: $972.40