Driveshaft Senior Design Report

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Composite Driveshaft: Efficiency, Safety, and Economics

MEEN 4263/4264

Chad Keys Wesley Kinkler Alex Santiago

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Table of Contents

I. Introduction 3

a. Purpose 3

b. Objectives 4

II. Design 4

III. Fabrication 13

a. Mandrels 15

i. Mandrel 1 15

ii. Mandrel 2 15

iii. Mandrel 3 19

b. Process 20

c. Yokes 22

i. Selection Criteria 22

ii. Modification of Yokes 22

iii. Attaching Yokes 24

iv. Balancing 25

IV. Testing 27

V. Results 29

VI. Conclusions 30

VII. Lessons Learned 30

VIII. Appendices 32

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I. Introduction

A driveshaft is the connection between the transmission and the rear axle of the

car. As shown in Figure 1, power generated by the engine is transferred to the

transmission via a clutch assembly. The transmission is linked to the driveshaft by a

yoke and universal joint, or u-joint, assembly. The driveshaft transmits the power to the

rear end through another yoke and u-joint assembly. The power is then transferred by the

rig and pinion or rear differential to the rear wheels.

Figure 1: Vehicle Drive Train [1]

The entire driveline of the car is composed of several components, each with

rotating mass. The rule of thumb is that 17-22% of the power generated by the engine is

lost to rotating mass of the drive train. The power is lost because it takes more energy to

spin heavier parts. This energy loss can be reduced by decreasing the amount of rotating

mass. Light weight flywheels and transmission gears, aluminum and carbon-fiber drive

shafts, riffle-drilled axels, and aluminum hubs are all examples of replacement or

modified parts used to reduce the amount of rotating mass.

a. Purpose

To reduce to the amount of rotating mass in the drive train of a locally owned

1968 Mustang, a light weight driveshaft will be constructed. In racing, every hundredth-

of-a-second counts. The race car, pitted in an unending battle against the clock, is

modified to squeeze every bit of horsepower out of it. The drag car is full of racing

equipment, but currently has a steel driveshaft. The new drive shaft should take less

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energy to spin therefore more of the energy produced by the engine can be transferred to

the wheels.

In addition to increasing the efficiency, the composite shaft will be safer than a

steel driveshaft. When a steel shaft fails, it projects shrapnel in all directions. There is

also a possibility that the shaft may dig into the ground and catapult the vehicle into the

air. When a composite shaft fails, it breaks into small fiber fragments posing no danger.

b. Objectives

The objective of this study is to design a composite driveshaft, build it, and test

the performance of the car with the new driveshaft in place.

II. Design

A driveshaft is a hollow tube which transmits torque from the transmission to the

differential. The shaft has a yoke at each end which connects to the transmission and the

rear differential by the means of u-joints. A slip yoke, with internal gear teeth, slides into

the transmission and allows the shaft to travel in the axial direction of the shaft when the

rear axel moves up or down. This slip yoke allows transmittance of torque while

preventing the shaft from experiencing tensile or compressive loads. The u-joints allow

the transmittance of torque without applying bending stresses to the shaft.

Knowing that the primary driver for the design of the shaft will be the torque

loading, the maximum torque experienced by the shaft needs to be found. The initial

dynamometer results for the test vehicle to be used show that in 4th gear, which is a 1:1

ratio, the car produced 550 ft-lbs of torque. First gear, which is 3.02:1, will produce a

torque of 1661 ft-lbs. With a safety factor of 2, the torque value is 3322 ft-lbs. By

rounding this up to 3500 ft-lbs, there is an even number to work with that will take care

of the shock loading experienced by the shaft.

A rudimentary winding pattern is set up in the Laminate Design Software, a DOS-

based program conceived by Dr. Peel and Dr. Folkman. This program gives the

mechanical properties of a composite material when given the mechanical properties of

the reinforcement, filament, or tow, in this case, and the resin epoxy in this case. The

properties for the composite can then be used to find properties for the driveshaft.

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The maximum value of shearing stress (τ) occurs on the outside surface of the

shaft. Using the equation for torsional strength, Equation 1, the max shear stress can be

found. The Qcr and the Zi in Equation 1 require values from Laminate Design Software.

The software is discussed later in the text. The output for the program can be found

Appendix IV. Lay-up 3 has the final properties for the driveshaft. Equation 2 can be

manipulated to get the polar moment of inertia. The polar moment of inertia can then be

used to get the inner diameter of the shaft using Equation 3. This gives a starting point

for the dimensions of the driveshaft.

Equation 1: Torsional Strength - Max Shear

22222

421222112

43

222

22

2

12)(

925.0

2

2

rDAlAAAZ

Zk

lDkrQ

trQ

i

icr

crcr

cr

−=

=

=

=

ππ

πτ

Equation 2: Shear Stress

JroΤ

=τ

τ = 398000 psi

T = 3,500 ft-lbs = 42,000 in-lbs

ro = 1.49 in

J = 1.896 in4

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Equation 3: Polar Moment of Inertia

)(32

44io ddJ −=

π

J = 1.896 in4

do = 2.980 in

di = 2.778 in

Using Equations 1, 2, and 3 the polar moment of inertia is found to be 1.896 in4, the inner

diameter is found to be 2.778 in, and a required thickness is 0.101 in. These dimensions

can be used to find a mandrel for fabricating the shaft and for designing the winding lay-

up in Laminate Design Software.

The driveshaft rotates at a maximum of 7000 RPM. The design of the shaft

should include a critical frequency well above the cars operating conditions. If the

driveshaft were to turn at its natural frequency, it could vibrate severely and possibly

disintegrate. The fundamental flexural frequency of a shaft with on free end can be found

using Equation 4. If the shaft is operated at this frequency or a multiple of it, energy will

build up in the shaft causing it to come apart. The shaft will operate at a maximum of

7000 RPM which is 117 Hz. According to Equation 4, the calculated fundamental

flexural resonance frequency of the shaft was calculated to be 216 Hz or 13,000 RPM.

The shaft will be safely operated under the maximum RPM.

The fundamental flexural resonance frequency can be changed for a composite

shaft. By adding the 15° wrap, the fundamental flexural resonance frequency is raised.

The reverse holds true for removing layers. By moving the 15° layers around in the

laminate design we can lower the fundamental flexural resonance frequency. Several

tests were done on the computer in order to get the desired safety margin which was

deemed to be 1.8.

The frequency equation requires the Young’s modulus in the axial direction of the

shaft and the density of the composite material. The density is given by the Laminate

Design Software output. The equivalent Young’s modulus in the axial and transverse

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tAQ 11

11 = tAQ 12

12 =

direction, along with the equivalent shear modulus, equivalent orthogonal stiffness,

Poisson’s ratio, relationship for Poisson’s ratio can be found in Equations 5 through 10.

The calculated values are found in Table 1.

Equation 4: Fundamental Flexural Frequency

ρπ

222xo

HZE

lr

f =

Equation 5: Equivalent Modulus of Elasticity (E1) in the Axial Direction

112112111 )1( QQEE x ≈−== υυ

Equation 6: Modulus of Elasticity (E2) in the Transverse Direction

222112222 )1( QQEE y ≈−== υυ

Equation 7: Equivalent Shear Modulus

tA

G 6612 =

Equation 8: Equivalent Orthotropic Stiffness

Equation 9: Poisson’s Ratio

22

1212 A

A=υ

tAQ 22

22 =

8

Equation 10: Relationship for Poisson’s Ratio

2

21

1

12

EEυυ

=

This hollow shaft can be designed in such a way as to minimize the amount of

energy wasted turning itself. The moment of inertia is the rotational inertia of the shaft.

A larger shaft will have a larger moment of inertia. By making the diameter larger the

moment of inertia increases. Although this will make the shaft stronger it will make it

harder to turn. It will also be harder to stop since the inertia is higher. For a hollow

shaft the moment of inertia (I) can be calculated using Equation 11.

Equation 11: Moment of Inertia

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44io dd

I−

= π

As you can see the moment of inertia is a function of the shaft diameter and thickness.

Reducing the thickness of the shaft will reduce the moment of inertia which contributes

to making the shaft easier to turn. Less torque is being used for turning the shaft so more

is transferred. A simple way to see this is to take a weight on a string and spin it. The

closer to the weight you hold the string the faster the weight will spin with less effort. By

gripping the string farther away from the weight the slower it seems to go. But it has

more velocity therefore more inertia. The moment of inertia for the steel and composite

driveshafts can be found in Table 2.

The mass moment of inertia (Im) is one measure of the distribution of the mass of

an object relative to a given axis. For a hollow shaft the mass moment of inertia can be

calculated using Equation 12. Again, by lowering the mass moment of inertia we will

reduce the amount of torque it takes to spin the shaft. Reducing the mass of the shaft and

making it smaller in diameter will accomplish this task. This can also be done by making

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the total outside diameter as small as possible and by making the shaft thinner.

Calculated values for the mass moment of inertia can be found in Table 2.

Equation 12: Mass Moment of Inertia

2)(* 22

iom

rrmI +=

Table 2: Comparison of Polar and Mass Moment of Inertia

Driveshaft I Im

Steel 0.599 in4 36.837 lbm in4

Composite 0.390 in4 6.829 lbm in4

% Difference 34.89% 81.46%

Another important factor is the angular twist the shaft will experience. Equation

13 gives that angular twist of a shaft. Too much angular twist will cause a lag in the

torque transfer. Energy will be used up in twisting the shaft instead of going through the

shaft. A small amount is desirable to absorb shock from loading the shaft. The angular

twist is listed in Table 2.

Equation 13: Angular Twist

JGTL

=θ

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Table 1: Carbon Fiber Driveshaft Propertied Calculated Values

ρ 0.083 lb/in3

E1 9.65*106 psi

E2 6.15*106 psi

G12 4.05*106 psi

Q11 9.05*106 psi

Q22 6.15*106 psi

υ12 0.619

A11 9.46*105 lb/in

A12 3.73*105 lb/in

A22 6.03*105 lb/in

A66 3.97*105 lb/in

D22 718.5 lb-in

I 0.390 in4

Im 6.829 lbm-in2

J 4.463 in4

θ 6.66°

The same basic calculations were done for a drive shaft made from 6061-T6

aluminum in order to have a base to go from. It will be attempted to create a composite

shaft which is stronger than a standard aluminum driveshaft. The lay-up for the

composite driveshaft can be altered until appropriate strengths are reached. The values

for the aluminum driveshaft are shown in Table 3.

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Table 3: Aluminum Driveshaft Calculation Values

Length 50 in

OD 3 in.

thickness 0.125 in

I 1.169 in4

Volume 56.45 in3

ρ 0.0975 lb/in3

mass 5.504 lbm

Im 11.395 lbm-in2

J 2.337 in4

θ 6.48°

We chose to use a 2.75 in OD mandrel to wrap our driveshaft on. The available

yokes were 2.980 ID. The difference between the OD of the mandrel and the ID of the

yokes gives an adequate thickness for the driveshaft. The required thickness needed is

calculated using a Laminate Design Software package. This program uses the properties

of the fiber and resin to be used and calculates the thickness needed to carry the load.

The output for the Laminate Design Software can be found in Appendix III. The angle of

the force that was to be applied and lay-up of the composite part all had to be entered.

Several different angles for the layers were tried until a satisfactory result for the shaft

was reached. Table 1 gives the calculated values for the composite driveshaft.

To ensure that the driveshaft would hold up not only to the loading conditions set

by the test vehicle, but also the elevated torque given by the factor of safety, a finite

element analysis of the final shaft was performed. Material properties for the laminate

were taken from the Laminate Design Software and entered into NENastran v8.2. A

simple shaft was drawn without the yokes. The yokes were not included in the analysis

because they are proven, off-the-shelf racing equipment. In the NENastran Modeler, one

end of the shaft was fixed to prevent any translation or rotation. The opposite end of the

shaft was attached to a rigid plate of known dimensions. The plate is used to apply a

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couple, which generates a torque on the shaft. This gives an accurate representation of

the shaft. A couple generating 3500 ft-lbs of torque is applied.

The model is analyzed to get the stress on the shaft. The NENastran output in

Figure 2 shows a uniform stress of about 50-60 ksi for the whole shaft. The most

important finding given by Figure 2 is that the shaft has no separation which would

indicate a failure. A dynamic analysis was also performed on the shaft. The dynamic

analysis will give the critical frequency, or first natural frequency, which will be mode 1.

To do a dynamic analysis, the loads are removed and the ends are fixed. NENastran uses

the material properties to find the first few modes of the shaft. These modes are all

critical frequencies that, if operated at, can destroy the shaft. The dynamic analysis

shows that the first natural frequency is 329 Hz. This converts to 19740 RPM, which is

well above the operating speed of 7000 RPM. The modeled frequency is different from

that value generated earlier because the wind patterns have changed and the formula used

to get the initial value involved a shaft with a free end. Numerical values for the

NENastran stress analysis and dynamic analysis can be found in Appendix IV.

Figure 2: NENastran Stress Analysis Output

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Figure 3: NENastran Dynamic Analysis Output

III. Fabrication

There are several things to consider when picking a fabrication method. Time is a

major consideration. There is little time for fabrication, so the fabrication process has to

be quick. The fiber has to be laid at specific angles to give the shaft certain

characteristics. The weave patterns have to be tight and compact. Resin has to be

applied evenly. The shaft has to be wound in a way such that the yokes can be easily

attached. The easiest fabrication method for creating a hollow tube is filament winding.

Filament winding is an automated process in which a filamentary yarn in the form of tow

is wetted by resin and uniformly and regularly wound about a rotating mandrel. The

filament winder can be programmed to create specific and tightly wound patterns.

To create a composite part on the winder, a winding pattern is needed, along with a

mandrel, mold release, fiber, resin and hardener, a way to apply even pressure to the part and a

curing procedure. The wind patterns were determined by using Laminate Design software

created by Dr. Larry Peel. After entering mechanical properties for the resin and tow, different

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wind angles and layers were tried in the Laminate Design software until the driveshaft had the

desired characteristics. Table 4 gives the wind angle and its purpose.

The tow, resin and hardener, and adhesive are the most critical elements of the shaft.

Each structural component must be carefully selected so that the shaft has good mechanical

properties. The tow which was used in the Laminate Design Software calculations was chosen

because it is strong, light weight, and aerospace quality carbon fiber. Fiber used by the

aerospace, although expensive, is rigorously quality controlled. It was decided that this fiber

would be uniform, therefore giving the driveshaft uniform properties.

The resin and hardener were chosen for several reasons. First, the resin is tough. The

resin also has a high viscosity. High viscosity is desired because, with the wet winding process,

is easier to control the amount of resin being applied to the tow. Wet winding will be

discussed further in the process section. Another reason for choosing this resin is its

elongation at break. At 6% elongation at break, it is known that the resin will not be too brittle

and that the wound shaft will have some flex for absorbing the shock between shifting gears.

Finally this resin was chosen because of its high pot life. After mixing the resin and hardener,

there is a little over two hours before it begins to gel. This is enough time to wind the entire

shaft before the resin sets up.

The adhesive was chosen for a few reasons. Foremost, the adhesive also met the

criteria for high tensile lap shear strength at room and elevated temperatures. At room

temperature the adhesive has a lap shear strength of 4,200 psi. At 250 F the lap shear strength

is 2,300 psi. Also, the adhesive is aerospace grade, ensuring high quality.

Table 4: Wind Angles

Wind Angle Purpose

90° Serves as a base layer for friction and for compaction

Gives little to no structural support

45° Provides structural strength for torque loading

15° Used to increase the axial modulus there for increasing

the fundamental flexural resonance frequency

a. Mandrels

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The mandrel for the driveshaft project has gone through several derivations. Mandrels

made of cardboard tubing and solid shafts were considered. These ideas were never fabricated

because it would be hard to remove the mandrel from the wound tube. The resin would cause

the cardboard mandrel to stick to the shaft making it impossible to remove. A solid shaft of

steel or aluminum would be heavy, and expensive to create.

i. Mandrel 1

It was first decided to create a mandrel made of steel muffler tubing which was split

with a plasma cutter into four parts along its length. The idea was to wind the shaft, let it cure,

then dismantle the mandrel and remove the tube. Two pieces machined out of steel were

created and attached to the muffler tubing which allows the mandrel to be spun in the filament

winder. One end is chucked into the winder the other end has a live center which spins on a

center point. This mandrel did not work because the mandrel pieces could not be bolted to the

machined ends in a way that they were square. This was due to the fact that the muffler tubing

is cold rolled which means it is pre-stressed. Once the tubing was split into four pieces, each

piece bowed.

ii. Mandrel 2

A second mandrel was created using muffler tubing which was split into two pieces.

This mandrel was square when bolted into place. To keep the tension of the fiber from pulling

the gap in the mandrel closed, three round, wooden pucks were evenly spaced through the

center of the mandrel.

The second mandrel was used to create a practice drive shaft. The pucks were evenly

spaced through the center of the mandrel. Shrink wrap tape, which shrinks and applies

pressure when heated, is wrapped around the mandrel over the areas where the pucks are. The

tape applies pressure and keeps the pucks in an upright position as shown in Figure 4. Once

the pucks were set in place, a few dry runs were made with no resin. One pass of each fiber

angle was wound.

Figure 4: Wooden Puck in Mandrel

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Once the winding began, it became obvious that there was not enough turn around

room. When winding a composite part, there are four defined areas on the part. The entire part

consists of the head, the turn around, the useable shaft, and the tail. The winding layout is

shown in Figure 5. The wind angle is the angle the fiber makes with the center line of the

mandrel. The 45 degree and 15 degree wind angles did not have enough friction to stick to the

mandrel in the turn around areas. The fiber began to slip and bunch up, causing misalignment

in the pattern.

Figure 5: Winding Layout

This created a new problem. To keep the fiber from slipping, the turnaround area

needed to be lengthened. The mandrel at its current length just fits in the curing oven, making

Wooden Puck

Shrink Wrap Tape

Head

Turn Around

Tail Useable Shaft

Turn Around

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it impossible to lengthen the mandrel. To alleviate this problem, two pieces of pipe, about one

foot long each, were threaded into the ends of the machined pieces as shown in Figure 6.

Adding the extensions made more turn around area. These threaded pieces can be removed

once the shaft is wound and the resin sets up. When the extensions are removed the mandrel

can easily be placed in the oven to finish curing.

The wind patterns were tested again with the extended turn around room. The

extensions and the change in diameter kept the fiber from slipping, and allowed for full

uniform coverage by the fiber. The test patterns were removed, and resin and hardener were

mixed and poured into the resin bath to start a practice shaft. The resin bath applies resin to the

fiber before it is wound about the mandrel. The resin bath can be seen in Figure 7. A practice

shaft was wound using the setup shown in Table 6.

A practice shaft was wound for a few reasons. The practice shaft allowed testing of the

wind patterns with the resin and the fiber together. Curing temperature and time could be

observed. Dismantling the shaft can be attempted, and the shaft can be inspected for proper

resin wet out, roundness, and overall strength.

Table 6: Practice Shaft Wind Pattern Setup

Wind Angle Number of Passes

90° 2

±45° 1

±15° 1

90° 2

The practice shaft was set up. Peel ply was wrapped around the whole shaft. One layer

of each pattern was wound to test the lay up and turnaround. Wet winding was used in order to

simulate the actual winding as closely as we could. Excess IM6 12K tow was used for the test

pieces. This saved the more expensive IM-7 fiber for actual runs. The winding procedure

went flawlessly. After the shaft was finished being wound, we placed 2 layers of perforated

shrink tape onto the shaft and heated it up. This provided compaction of the fiber. The turn

around fiber was cut from the end of the shaft and the extension removed. 2 layers of breather

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cloth were then wrapped onto the shaft as well as a layer of vacuum bagging. This was to

protect the oven from excess resin. The shaft was cured in the oven at 200°F for 15 hours.

Figure 6: Mandrel Extensions

Figure 7: Resin Bath

Mandrel Extensions

Resin Reservoir

Resin Coated Drum

Carbon Fiber Tow

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The shaft was removed from the oven and the vacuum bagging and breather cloth was

removed. The vacuum bagging material, breather cloth, and shrink tape came off very easily.

Now the mandrel had to be removed from the shaft.

This was a very difficult process. First, the material that wrapped over the end caps had

to be cut back in order to expose the bolts holding it to the mandrel. Once this was

accomplished we began removing the bolts. Resin had seeped into the threads of some of the

bolts causing them to stick. The head of one bolt was twisted off trying to get it out. This bolt

was machined out. Once the caps were removed the shaft did not collapse as expected. The

gap were the mandrel had been split had filled in with resin. A tubing cutter was used to cut

the shaft into sections and then it was split in half with a band saw. A 2 foot piece was spared

and slid off the shaft. The ridge left inside the shaft was 0.125 inches deep. This created a

stress riser that severely reduced the integrity of the shaft. It was obvious that this mandrel was

not going to work.

iii. Mandrel 3

Improving upon the mistakes on the previous mandrels, a new, one piece, mandrel was

made from aluminum tubing. The tubing maintained a 2.75 inch OD and was readily

available. A 16 gauge 2.75 OD tube was purchased. The tubing is normally made for turbo

charger inlet ducting. A test piece was cut from the tube to be used for testing. The test piece

was wet sanded with 2000 grit sandpaper. A silicone mold release compound was applied to

the test shaft. 90° test patterns were wound onto the piece and cured at 250°F for 15 hours.

We used a higher curing temperature in order to expand the aluminum mandrel while

compacting the fiber. After curing was complete, we then placed the test mandrel in the deep

freeze that was 20°־F in order to shrink the aluminum tube. The test mandrel was removed

from the freezer. The tube was impacted onto a block of wood while holding the fiber. The

mandrel came out with no difficulty. This test was successful.

The third mandrel was fitted to the end caps. The end caps were then bolted to the

mandrel. Figure 8 shows the final mandrel.

Figure 8: Final Mandrel

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b. Process

The final mandrel was assembled and then checked to be square. Then the shaft had to

be polished. Wet sanding was done first using 2000 grit sandpaper and then 4000 grit

sandpaper to finalize the polish. The mandrel was now ready for winding the shaft. Teflon

coated tape was applied to the mandrel over the areas were we did not want the resin or fiber to

stick. A coat of silicone mold release compound was applied to the mandrel. We then began

wind our patterns. The driveshaft lay-up can be seen in Table 7. We left out 2 90° and 1 ± 45°

pattern in order to save some space since it was believed that we would have excess thickness

of resin. After completion, 2 layers of perforated shrink wrap tape were applied. The

extensions were removed from the mandrel. Breather cloth and vacuum bagging were applied

next. Again we cured the shaft in the oven at 250°F for 15 hours. After curing was complete,

the shaft was removed from the oven. The breather cloth had bonded to the excess resin

making its removal very difficult. The OD of the shaft was measured and found to be too

small. The OD was measured at 2.905 inches, 45 thousands less than the goal of 2.950 inches.

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Table 7: Driveshaft Lay-up

Wind Angle Number of Passes

+90° 1

±45° 3

±15° 4

±45° 3

±90° 1

±45° 3

+90° 1

More layers had to be wrapped. The mandrel extensions were replaced and the whole

mandrel was put back into the filament winder. The shaft was wet sanded with 150 grit

sandpaper in order to remove the high spots and rough up the shaft. This had to be done in

order to ensure that new layers of resin and fiber would bond. After sanding was complete, 3

layers of ± 45° and 1 layer of 90° were added onto the shaft. The whole wrapping and curing

process was done again. This time peel ply was wound onto the shaft to keep the breather

cloth from sticking to the resin. After completion the shaft was 2.958 inches in OD.

The mandrel and shaft were placed into the freezer again. After 2 hours, the shaft was

taken from the freezer and the end caps were removed as before. Once they were out of the

way, the shaft slid off of the mandrel with no problem. The shaft had been completed with no

flaws. The inside of the tube was perfectly smooth. There were no stress raisers present along

the length of the lube.

Once the mandrel was removed, the shaft was measured from end to end, and the center

was marked. The dimensions for the tube length were taken from the center to ensure that only

the useable part of the shaft was used and not the turnaround. Using a band saw, the shaft was

rough cut slightly larger than needed. The carbon fiber tube was cut to length and the ends

were squared off using a mill.

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c. Yokes

There were many different ideas for the yokes. Complicated designs were created, and

it was originally planned to mill the yokes out of a solid block of aluminum. These ideas were

not carried through for several reasons. First, a solid block of aluminum is expensive. Also,

the amount of time required entering the complicated design into a CNC machine and the time

required to mill the part would have greatly increased the production cost. It was decided to go

with a more standard yoke.

i. Selection Criteria

The yokes for this project had to meet a few criteria before being selected. First, the

yokes had to be readily available due to the lack of time for this project. Secondly, the yokes

had to be compatible with the existing equipment in the car, like the slip yoke. Thirdly, the

yokes also had to be light weight. Finally, the yoke had to have enough internal surface are for

gluing the shaft to the yoke.

It was decided to use standard, off-the-shelf, 3 inch yokes from Quartermaster USA.

Quartermaster USA has been building driveline pieces for cars for several years. These

particular yokes are designed for their 3 in. driveshaft. Typical construction for these drive

shafts is an interference fit between the yoke and the driveshaft. Aircraft quality rivets are then

placed in the yokes and shaft to hold them together.

ii. Modification of Yokes

The Quartermaster yokes needed to be modified to meet our criteria for the composite

driveshaft. Figure 9 shows the unmodified yokes. More surface area was needed on the ID of

the yokes. This surface area is the interface between the shaft and the yokes. More area was

needed for the adhesive in order to obtain the required safety factor. A piece of 6061 T6

aluminum had to be machined and interference fit to the existing yoke to increase the surface

area. A view of the modified yokes is displayed in Figure 10.

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Figure 9: Unmodified Yokes

A solid block of 6061-T6 aluminum was obtained from Santhuff Machine and

Engineering in Sinton, Texas. It had a 3in OD. Them inside and outside of the yoke had .002

in of the surface machined off. This took off the anodizing. The solid block of billet

aluminum was machined to 2.984 in. 2 inches deep from each end and then cut in half. The

pieces were then bored out to a 2 in. ID. The 6 inch piece was then placed in a bath of liquid

nitrogen. This cooled it enough to reduce the diameter to allow it to be pressed into the yoke.

The reduced area of the piece was pressed into the yoke and allowed to warm up. The sleeve

and the yokes were welded together using a 4043 Aluminum welding rod with a TIG welding

machine. The yoke was then bored out to and ID of 2.980 in. A small thin piece of the sleeve

was still in the original yoke. It was removed with a pair of pliers. The yokes were now ready

for installation.

Figure 10: Modified Yokes

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iii. Attaching Yokes

Now that the area of the adhesive surface had been increased and the shaft wound, they

two parts were ready to be assembled together. The parts can not just be glued together.

Several things had to happen before we could join them.

First a jig had to be made for the complete shaft. A piece of 2 x 3 x 0.125 in tubing 60

in. long was obtained. This would serve as the base for the jig. Two 3/8in holes were drilled

on the center of the tubing 51.5 inched apart. An end mill was used to ensure the holes were

square. The length was chosen since the completed shaft is to be 51.5 in. long center to center

on the yokes. Two, 6 inch long solid steel cylinder were made with an OD of 1.08 inches.

These fit right into the hole in the yokes intended for the u-joints. The cylinder were drilled

and tapped for a 3/8 in. bolt. The cylinders were bolted to the tubing in order to complete the

jig. After they were bolted on, they were checked for squareness and found to be satisfactory.

The jig was now complete.

The EA 9394 requires a specified amount of clearance for the adhesive properties to be

maximized. A clearance of 0.015 to 0.025 in. is required between the bonding surfaces. The

drive shaft OD was 2.958 in. and the yoke ID was 2.980 in. The clearance was 0.011 in. The

shaft had to be sanded down to 2.950 to 2.940 in. OD. 150 grit sandpaper was used to wet

sand the ends of the shaft to 2.950in. The rougher grit sandpaper was used to keep the surface

rough for the adhesive. The inside of the yokes were also sanded to create a rough surface for

improved bonding. The final clearance was checked to be 0.015in. Now the yokes and the

shaft were ready to be bonded together.

The yokes were test fit to the shaft on the jig to assure that the completed shaft would

be the required dimensions. Figure 11 shows the test fitting of the shaft on the jig. The EA

9394 was mixed in the proper ratios and applied to the inside of the yokes and outside of the

shaft. The yokes were slid onto the shaft. A turning motion was used to ensure that an even

layer of glue was in between the shaft and yokes. The completed shaft was then placed onto

the jig. The jig was placed in the oven at 150°F for 1 hour to cure the glue. After curing was

complete, the jig was removed from the oven and allowed to cool for a few minutes. The

cylinders were unbolted and removed from the jig and then they were slid out of the yokes.

Attaching the yokes to the shaft was now complete.

25

Figure 11: Assembly Jig Test Fit

iv. Balancing

The completed driveshaft was taken to Kelton’s Truck Center to be balanced. The first

step of the process was to install the correct size u-joints in the yokes. Since the yokes on the

shaft were aluminum we had to use specially coated u-joints to prevent galvanic corrosion

between the steel u-joints and the aluminum yokes. The transmission end of the driveshaft

took a 1310 u-joint while the axle end took a crossover joint for a 1310 to 1330 connection.

Greasable u-joints were selected to be used in the experiment, even though the original steel

driveshaft used sealed u-joints. The u-joints were installed using a press. Care was taken to

prevent the caps of the joints from galling the aluminum yokes by being pressed in at an angle.

After installing the u-joint on the transmission end of the driveshaft it was now possible to

install the slip yoke. The same process of using the press was used to do this. The position of

the zerk fitting in the yokes was noted to make sure it would be accessible after the joint was

installed. The u-joint on the axle end had to be removed after installation since it was realized

too late that a square u-joint instead of a crossover joint is required for the balancing machine.

With the shaft completely assembled it was now positioned in the balancing machine.

The assembled mandrel is fitted into the balancing apparatus as shown in Figure 12. The

machine was activated and began to take readings on the vibrations produced by the driveshaft.

It was found to be out of balance by about ten grams on one side. Instead of the standard

procedure of adding weight at 180° of the indicated point, weight was removed at that point.

26

This method was chosen to keep the weight down on the driveshaft. After removing about ten

grams of material the machine was restarted and the readings showed the driveshaft to be

within a reasonable margin of vibration. This completed the balancing procedure for the

driveshaft. On a side note the u-joint and slip yoke installed on the driveshaft weigh

approximately as much as the shaft itself.

Figure 12: Assembled Shaft on Balancing Machine

27

IV. Testing

Now that the driveshaft was completed it was ready to be tested. The test vehicle that

the shaft was designed for is a 1968 Ford Mustang with a 383 cubic inch stroker motor. The

transmission is a Jerico 4-speed manual transmission and the rear axle is a Ford nine inch. The

car produces around 400 horsepower on motor alone and 590 with the nitrous oxide. The car

and the driveshafts were taken to Chassis Dyno Service in Clarkwood. The dynamometer at

this site is a Dynotech chassis dynamometer. The car has to be backed onto a pair of drums, as

shown in Figure 13, and then the rear axle is strapped down as well as the front of the car to

prevent it form shifting while making pulls. The first three pulls performed were using the

steel driveshaft. Figure 14 shows the dynamometer output. After a sufficient baseline was

established the car was pulled off the dynamometer and the carbon fiber driveshaft was

installed. The car was then backed onto the dynamometer again and strapped back down.

Figure 15 shows the three pulls for the composite shaft. Three pulls with the carbon fiber

driveshaft were taken and the values were averaged. After the first three pulls the car began to

overheat because the cooling fan was too far from the front of the car. This problem was easily

remedied.

Figure 13: Car on Chassis Dynamometer

28

Figure 14: Test Results from Steel Driveshaft

Figure 15: Test Results from Composite Driveshaft

29

V. Results

After completing the tests on the chassis dynamometer the results were organized into

graphs to be compared. Figure 16 shows a comparison of the horsepower generated by the

steel shaft and the composite shaft. Figure 17 shows a comparison of the torque generated by

the steel and the composite shaft.

Figure 16: Comparison of Horsepower

393394395396397398399400401402

Run 1 Run 2 Run 3

Steel

Carbon Fiber

Figure 17: Comparison of Torque

355360365370375380385390395

Run 1 Run 2 Run 3

SteelCarbon Fiber

30

VI. Lessons Learned

In retrospective, now having completed the driveshaft, there are many situations that

could have been avoided. The largest challenge in the fabrication of the driveshaft was the

design of a suitable mandrel. First we learned that cold-rolled steel will deform if cut in pieces

regardless of cutting technique. This is due to the internal stresses remaining in the part from

the shaping process.

The next mandrel was cut in half instead of quarters to eliminate a majority of the

bowing. In this respect it succeeded. Once a test shaft was cured in the oven the problem

arose. Resin had seeped in the split and cured. This made removal of the shaft from the

mandrel next to impossible. Also in addition to this the resin that seeped into the mandrel and

cured left a ridge along the length of the tube. This created a stress riser and lowered the

overall strength of the shaft.

The final design used an aluminum tube that was left whole and polished to ease

removal. Another problem with the mandrel was a lack of room for turn around. This

prompted the design and fabrication of extensions for the mandrel. There were also many

smaller setbacks that were easily remedied. During the winding of the first test shaft resin

seeped into the bolt heads and made removal difficult. The final wound shaft also proved to be

too small in diameter. This resulted from more compaction than expected. To correct this

problem more layers were added to increase the outer radius of the shaft to provide adequate

bonding area for the adhesive. Peel ply was also placed between the layer of breather cloth and

the shaft itself to prevent the breather cloth from bonding to the shaft, which occurred on a test

run.

Removal of the cured shaft was a problem on the test shaft but was extremely easy on

the final shaft. One lesson learned that was not seen coming was the cost of overnight shipping

when the material is hazardous material. These are the main issues encountered during the

fabrication of the driveshaft.

VII. Conclusions

As evident from the graphs the results were not as expected. First, the tests were

unable to be completed with the nitrous oxide due to a glitch in the system. This was realized

on the third run with the steel driveshaft. There was a power increase but not what is to be

31

expected with the jetting of the nitrous system. The power gains were minimal since the

system only purged whatever pressure was remaining in the lines but did not complete the path

to the bottle to allow the full capability of the system. Due to this problem disregard the third

run for the steel driveshaft and use the lower baseline of engine alone. Now, with an

established baseline the comparisons can be made. The scale is relatively small so the

differences between the two values in reality aren’t all that large. This then leads to the fact

that the power gain with the composite driveshaft was negligible. This can be attributed to the

fact that even though the weight of the driveshaft was cut in half, the percentage of the rotating

mass of the driveline that is due to the driveshaft is roughly 4-6%. This fact is verified by the

results of the testing. To verify this hypothesis APCT, a company which manufactures carbon

fiber drive shafts for late model cars, was contacted. One of the suggestions made by the

company was that the chassis dynamometer was not sensitive enough to pick up the gains in

power produced by the shaft. Since the chassis dynamometer is sensitive to one tenth of a

horsepower, it is safe to say that if there were any gains present they were so small it would

hardly warrant the investment in a carbon fiber driveshaft. It might be useful to spend

resources in lightening other components of the drive train that are responsible for a higher

percentage of the rotating mass.

A person wishing to improve the performance of a vehicle should stick to an aluminum

driveshaft. The carbon fiber shaft, while lighter, will not justify the cost in this case study. An

aluminum driveshaft will cost about $300 while a purchased composite driveshaft will cost

about $800.

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VI. Appendices

Appendix I. Material Properties

i. Tow 33

ii. Resin and Hardener 35

iii. Adhesive 37

iv. Aluminum 41

II. Drawings

i. Mandrel End Caps 44

ii. Unmodified Yokes 46

iii. Modified Yokes 47

III. Winding Procedure 49

IV. Composite Shaft Properties

i. Laminate Design Software Output

1. Lay-up 1 51

2. Lay-up 2 54

3. Lay-up 3 57

ii. NENastran Output

1. Stress 60

2. Dynamic Analysis 63

V. Receipts

i. Tow 65

ii. Resin and Hardener 66

iii. Adhesive 67

iv. Aluminum Tubing 68

VI. Bibliography 69

33

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Data sheets for over 40,000 metals, plastics, ceramics, and composites.

HOME • SEARCH • FAQ • TOOLS • FORUM • SERVICES • HELP • SITE MAP • LOGIN

Searches: Sequential | Material Type | Property | Composition | Trade Name | Manufacturer

Aluminum 6061-T6; 6061-T651

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Subcategory: 6000 Series Aluminum Alloy; Aluminum Alloy; Metal; Nonferrous Metal

Close Analogs:

Composition Notes: Aluminum content reported is calculated as remainder. Composition information provided by the Aluminum Association and is not for design.

Key Words: UNS A96061; ISO AlMg1SiCu; Aluminium 6061-T6, AD-33 (Russia); AA6061-T6; 6061T6, UNS A96061; ISO AlMg1SiCu; Aluminium 6061-T651, AD-33 (Russia); AA6061-T651

Component Wt. %

Al 95.8 - 98.6

Cr 0.04 - 0.35

Cu 0.15 - 0.4

Fe Max 0.7

Component Wt. %

Mg 0.8 - 1.2

Mn Max 0.15

Other, each Max 0.05

Other, total Max 0.15

Component Wt. %

Si 0.4 - 0.8

Ti Max 0.15

Zn Max 0.25

Material Notes: Information provided by Alcoa, Starmet and the references. General 6061 characteristics and uses: Excellent joining characteristics, good acceptance of applied coatings. Combines relatively high strength, good workability, and high resistance to corrosion; widely available. The T8 and t9 tempers offer better chipping characteristics over the T6 temper.

Applications: Aircraft fittings, camera lens mounts, couplings, marines fittings and hardware, electrical fittings and connectors, decorative or misc. hardware, hinge pins, magneto parts, brake pistons, hydraulic pistons, appliance fittings, valves and valve parts; bike frames.

Data points with the AA note have been provided by the Aluminum Association, Inc. and are NOT FOR DESIGN.

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Physical Properties Metric English Comments

Density 2.7 g/cc 0.0975 lb/in³ AA; Typical

Hardness, Brinell 95 95 AA; Typical; 500 g load; 10 mm ball

Hardness, Knoop 120 120 Converted from Brinell Hardness Value

Hardness, Rockwell A 40 40 Converted from Brinell Hardness Value

Hardness, Rockwell B 60 60 Converted from Brinell Hardness Value

Hardness, Vickers 107 107 Converted from Brinell Hardness Value

Ultimate Tensile Strength 310 MPa 45000 psi AA; Typical

Tensile Yield Strength 276 MPa 40000 psi AA; Typical

Elongation at Break 12 % 12 % AA; Typical; 1/16 in. (1.6 mm) Thickness

Elongation at Break 17 % 17 % AA; Typical; 1/2 in. (12.7 mm) Diameter

Modulus of Elasticity 68.9 GPa 10000 ksi AA; Typical; Average of tension and compression.

Notched Tensile Strength 324 MPa 47000 psi 2.5 cm width x 0.16 cm thick side-notched specimen,

Ultimate Bearing Strength 607 MPa 88000 psi Edge distance/pin diameter = 2.0

Bearing Yield Strength 386 MPa 56000 psi Edge distance/pin diameter = 2.0

Poisson's Ratio 0.33 0.33 Estimated from trends in similar Al alloys.

Fatigue Strength 96.5 MPa 14000 psi AA; 500,000,000 cycles completely reversed stress;

Fracture Toughness 29 MPa-m½ 26.4 ksi-in½ KIC; TL orientation.

Machinability 50 % 50 % 0-100 Scale of Aluminum Alloys

Shear Modulus 26 GPa 3770 ksi Estimated from similar Al alloys.

Shear Strength 207 MPa 30000 psi AA; Typical

Electrical Resistivity 3.99e-006 ohm-cm 3.99e-006 ohm-cm AA; Typical at 68°F

CTE, linear 68°F 23.6 µm/m-°C 13.1 µin/in-°F AA; Typical; Average over 68-212°F range.

35

CTE, linear 68°F 23.6 µm/m-°C 13.1 µin/in-°F AA; Typical; Average over 68-212°F range.

CTE, linear 250°C 25.2 µm/m-°C 14 µin/in-°F Estimated from trends in similar Al alloys. 20-300°C.

Heat Capacity 0.896 J/g-°C 0.214 BTU/lb-°F

Thermal Conductivity 167 W/m-K 1160 BTU-in/hr-ft²-°F AA; Typical at 77°F

Melting Point 582 - 652 °C 1080 - 1205 °F AA; Typical range based on typical composition for wrought products 1/4 inch thickness or greater; Eutectic

melting can be completely eliminated by homogenization.

Solidus 582 °C 1080 °F AA; Typical

Liquidus 652 °C 1205 °F AA; Typical

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References for this datasheet.

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Carbon Fiber Driveshaft Winding Procedure

Setup:

1. Don proper personal protective equipment. a. Gloves b. Safety glasses c. Lab coat

2. Turn on filament winder 3. Have a good understanding and follow all safety procedures for the filament winder

and the oven. 4. Preheat the oven to the temperature designated by the resin and any possible post

curing process. 5. Always use a low speed while winding and keep one person near the panic button, 6. Place the “muffler tubing” mandrel in the filament winder. 7. Polish the mandrel with 2000 grit then 4000 grit paper. 8. Clean mandrel with acetone. 9. Apply vacuum bagging tape to the far left and right ends of the mandrel so the

vacuum bagging can be applied after winding 10. Apply good amount of silicone mold release to mandrel. 11. Use calipers to take several diameter measurements and get an average diameter. 12. Take several measurements of the tow as it is laid down over the curved surface. 13. Start up FiberGraphix on the designated computer.

a. Create the mandrel. b. Define the part length and turn-around distance. c. Define the winding angles. d. Test the pattern on the computer. e. Write the instruction to a disk. f. Transfer the pattern to the computer connected to the filament winder.

Winding:

14. Load the winding pattern into the winder. 15. Reset the winder computer. 16. Test the pattern on the winder without fiber. After a few passes, stop. 17. Test the pattern with fiber for a few passes. 18. Once the pattern has been tested, remove the fiber from the mandrel and run it

through the resin bath. 19. Tape the fiber to the start position. 20. Mix the resin and hardener in parts as indicated on the products’ packaging.

42

21. Fill the bath with enough resin-hardener mix to adequately cote the surface of the bath drum.

22. Start the winding, monitoring the amount of resin to the part. 23. After the first layer is wound, start winding second layer and continue until all

layers have been wound. 24. Wrap the shaft in two layers of shrink wrap tape. 25. Wrap shaft in breather cloth. 26. Vacuum bag the part.

Curing:

27. Carefully remove the part from the winder. 28. Remove the mandrel extensions and place it diagonally in the oven. 29. Allow curing for the amount of time designated by the curing process.

Retrieving finished part: 30. Once the part has cured, remove it from the oven. 31. Remove the shrink wrap, breather cloth, and vacuum bagging from the outside of

the part. 32. Remove the screws from the chucked and live center ends of the mandrel, and

remove the ends. 33. Put the shaft in the freezer and allow temperature to equalize. 34. Pull the mandrel from the center of the shaft.

Finishing the driveshaft:

35. Cut the shaft to length (50”), making sure to utilize the middle section of the shaft. Do not use the turnaround area of the shaft because it will have different properties than the mid section.

36. Square off the ends of the shaft with an end mill. 37. With course grit sand paper, rough up the inside of the yokes. 38. Using a finer grit sand paper, slightly rough up only the outer portion of the shaft

that will be inserted into the yokes. 39. Apply a generous amount of adhesive to the inner surface of the yoke and the outer

surface of the shaft that will be inserted into the yokes. 40. Twist the yokes onto the shaft and place in jig. 41. Allow adhesive to cure for one hour at 150 F before attaching to vehicle. 42. Burn rubber.

43

Lay-up 1 UNIAXIAL MATERIAL EDITING MENU

OPTIONS: Enter the Desired Values and Press Enter EDIT F2 - Exit edit mode F5 - Toggle Q's/E's F3 - Exit program F6 - Write material data to disk F4 - Toggle Display Units CURRENT DEFAULT MATERIAL drive shaft avg prop = E1= 0.8357E+07 Psi Youngs's Modulus Perpendicular to Fibers = E2= 0.6328E+07 Psi Poisson's Ratio (-e2/e1) = v12= 0.3916 Shearing Modulus = G12= 0.3440E+07 Psi Tensile Strength in the Fiber Direction = X= 0.0000 Psi Compr. Strength in the Fiber Direction = Xc= 0.0000 Psi Tensile Strength Perpendicular to Fibers = Y= 0.0000 Psi Compr. Strength Perpendicular to Fibers = Yc= 0.0000 Psi Shearing Strength = S= 0.0000 Psi Interaction Term for Failure Criteria = F12s= 0.0000 Thermal Expansion Coeff. in Fiber Dir. = A1= 0.0000 1/°F Thermal Expansion Coeff. Perp. to Fibers = A2= 0.0000 1/°F Hygro-Expansion Coeff. in Fiber Dir. = B1= 0.0000 Hygro-Expansion Coeff. Perp. to Fibers = B2= 0.0000 Cost per single layer of material = Cost= 0.00 $/sq. ft. Density of material = rho= 0.5300E-01 lb/cu. in. UNIAXIAL MATERIAL SELECTION MENU OPTIONS: Select the Default Material using the Arrow Keys F1 - Proceed to next page F5 - Toggle Q's/E's F3 - Terminate the Program F6 - Edit Material Property Data F4 - Toggle Display Units Key Default Material ID = 3 CURRENT DEFAULT MATERIAL Material AS/3501 Gr./Epoxy ID Description E1= 0.2001E+08 Psi 1 T300/5208 Gr./Epoxy E2= 0.1300E+07 Psi 2 B(4)/5505 Boron/Epox v12= 0.3000 3 AS/3501 Gr./Epoxy G12= 0.1030E+07 Psi 4 Scotchply 1002 Gl/Ep X= 0.2099E+06 Psi 5 Kevlar 49/epoxy Xc= 0.2099E+06 Psi 6 2024-T3 Aluminum Y= 7498. Psi 7 6061 Aluminum Sheet Yc= 0.2988E+05 Psi 8 steel sheet S= 0.1349E+05 Psi 9 Titanium F12s=-0.4992 10 IM7/8551-7a GR/epoxy A1= 0.9000E-06 1/°F 11 Epoxy Resin A2= 0.1000E-04 1/°F 12 Boeing IM gr/epoxy B1= 0.0000 13 E-glass/Epoxy (typ.) B2= 0.0000 14 Alm 7075-T6,reduced Cost= 0.00 $/sq. ft. 15 E glass/polyester rho= 0.0000 lb/cu. in. LAMINATE SEQUENCE SELECTION MENU OPTIONS: Key in Laminate Data Defaults in Effect F1 - Compute Modulus/Compliance Values Name = F2 - Back up to the Previous Menu Material ID = 3

44

F3 - Terminate the Program AS/3501 Gr./Epoxy Unsymmetric Laminate Ply Ply Single Ply Single Ply English Units Group Angle Number Thickness Material Cost Total Laminate Thickness ID (degrees) of Plies (Inches) ID $/sq. Ft. 0.8400E-01 1 90.0 1 0.7000E-02 3 0.00 2 45.0 2 0.7000E-02 3 0.00 Please Note: 3 -45.0 2 0.7000E-02 3 0.00 1-The first row with a 4 15.0 2 0.7000E-02 3 0.00 blank ply angle will 5 -15.0 2 0.7000E-02 3 0.00 terminate ply input. 6 45.0 1 0.7000E-02 3 0.00 2-For Symmetric and 7 -45.0 1 0.7000E-02 3 0.00 Antisymmetric Laminates 8 90.0 1 0.7000E-02 3 0.00 enter only the plies in half of the laminate. 3-For a zero modulus core enter a zero for the material ID. 4-Ply ID number 1 is on the bottom of the laminate. COMPUTED LAMINATE MODULUS AND COMPLIANCE OPTIONS: Key offset angle = 0.0 F1 - Compute Strains/Resultants F2 - Back up to the Previous Menu F3 - Terminate the Program F4 - Display Compliance Values F5 - Generate MSC/NASTRAN PSHELL cards F6 - Generate MSC/NASTRAN PCOMP cards Inplane Modulus (Pounds/Inch) A11 = 0.7942E+06 A12 = 0.2355E+06 A16 = 0.1528E-11 A22 = 0.6014E+06 A26 = -0.7425E-12 A66 = 0.2890E+06 Flexural Modulus (Pound-Inches) D11 = 251.4 D12 = 127.6 D16 = 14.46 D22 = 590.9 D26 = 24.28 D66 = 159.1 Coupling Modulus (Pounds) B11 = 2205. B12 = -607.5 B16 = -1965. B22 = -989.8 B26 = -1263. B66 = -607.5 COMPUTATION OF STRAINS OR RESULTANTS Options: Key in Strains or Resultants F1 - Display Stress Space Failure Analysis F2 - Back up to the Previous Menu F3 - Terminate Program F4 - Toggle Calculation of Strains/Resultants Stress Resultant in the x direction Inplane Strain in the x direction Nx = 0.0000 (Pounds/Inch) ex = -0.1151E-03 Stress Resultant in the y direction Inplane Strain in the y direction Ny = 0.0000 (Pounds/Inch) ey = 0.1280E-03

45

Shearing Stress Resultant Inplane Shearing Strain Nxy= 1536. (Pounds/Inch) exy= 0.5654E-02 Moment Resultant in the x direction Curvature in the x direction Mx = 0.0000 (Inch-Pounds/Inch) Kx = 0.4346E-01 (1/Inch) Moment Resultant in the y direction Curvature in the y direction My = 0.0000 (Inch-Pounds/Inch) Ky = 0.2105E-02 (1/Inch) Shearing Moment Resultant Curvature in the shear direction Mxy= 0.0000 (Inch-Pounds/Inch) Kxy= 0.1692E-01 (1/Inch) Equilibrium Temperature Change (from cure temp.) ¦T = 0.0000 Equilibrium Moisture Concentration ¦C = 0.0000 FAILURE ANALYSIS MENU OPTIONS: The Maximum Stress or Strain Index is White F2 - Back up to the Previous Menu F3 - Terminate the Program F4 - Toggle Stress/Strain Data Load Ply Ply Fiber Transverse Shearing Stress Load Reversal Group Angle Stress Stress Stress Space Failure Failure ID (degrees) (PSI) (PSI) (PSI) Index Factor Factor 1 90.0 243. -0.232E+04 -0.515E+04 -0.616E-01 3.20 -1.84 2 45.0 0.382E+05 -0.344E+04 0.144E+04 -0.205 4.19 -1.72 3 -45.0 -0.599E+05 0.195E+04 -847. 0.334 2.07 -3.47 4 15.0 0.260E+05 -0.119E+04 0.517E+04 0.596E-01 2.72 -2.06 5 -15.0 -0.195E+05 0.177E+04 0.543E+04 0.372 1.85 -2.76 6 45.0 0.715E+05 -0.182E+04 -793. -0.616E-02 2.96 -1.93 7 -45.0 -0.462E+05 0.406E+04 0.109E+04 0.594 1.47 -3.62 8 90.0 0.482E+04 0.212E+04 -0.650E+04 0.461 1.62 -2.47

46

Lay-up 2 UNIAXIAL MATERIAL SELECTION MENU OPTIONS: Select the Default Material using the Arrow Keys F1 - Proceed to next page F5 - Toggle Q's/E's F3 - Terminate the Program F6 - Edit Material Property Data F4 - Toggle Display Units Key Default Material ID = 10 CURRENT DEFAULT MATERIAL Material IM7/8551-7a GR/epoxy ID Description E1= 0.2103E+08 Psi 1 T300/5208 Gr./Epoxy E2= 0.1280E+07 Psi 2 B(4)/5505 Boron/Epox v12= 0.3600 3 AS/3501 Gr./Epoxy G12= 0.7100E+06 Psi 4 Scotchply 1002 Gl/Ep X= 0.2100E+06 Psi 5 Kevlar 49/epoxy Xc= 0.1140E+06 Psi 6 2024-T3 Aluminum Y= 7700. Psi 7 6061 Aluminum Sheet Yc= 0.3142E+05 Psi 8 steel sheet S= 0.1720E+05 Psi 9 Titanium F12s=-0.5000 10 IM7/8551-7a GR/epoxy A1= 0.0000 1/°F 11 Epoxy Resin A2= 0.4400E-08 1/°F 12 Boeing IM gr/epoxy B1= 0.0000 13 E-glass/Epoxy (typ.) B2= 0.0000 14 Alm 7075-T6,reduced Cost= 0.00 $/sq. ft. 15 E glass/polyester rho= 0.8300E-01 lb/cu. in. LAMINATE SEQUENCE SELECTION MENU OPTIONS: Key in Laminate Data Defaults in Effect F1 - Compute Modulus/Compliance Values Name = driveshaft2 F2 - Back up to the Previous Menu Material ID = 10 F3 - Terminate the Program IM7/8551-7a GR/epoxy Unsymmetric Laminate Ply Ply Single Ply Single Ply English Units Group Angle Number Thickness Material Cost Total Laminate Thickness ID (degrees) of Plies (Inches) ID $/sq. Ft. 0.9100E-01 1 90.0 2 0.3500E-02 10 0.00 2 45.0 4 0.3500E-02 10 0.00 Please Note: 3 -45.0 4 0.3500E-02 10 0.00 1-The first row with a 4 15.0 4 0.3500E-02 10 0.00 blank ply angle will 5 -15.0 4 0.3500E-02 10 0.00 terminate ply input. 6 45.0 3 0.3500E-02 10 0.00 2-For Symmetric and 7 -45.0 3 0.3500E-02 10 0.00 Antisymmetric Laminates 8 90.0 2 0.3500E-02 10 0.00 enter only the plies in half of the laminate. 3-For a zero modulus core enter a zero for the material ID. 4-Ply ID number 1 is on the bottom of the laminate. COMPUTED LAMINATE MODULUS AND COMPLIANCE OPTIONS: Key offset angle = 0.0 F1 - Compute Strains/Resultants

47

F2 - Back up to the Previous Menu F3 - Terminate the Program F4 - Display Compliance Values F5 - Generate MSC/NASTRAN PSHELL cards F6 - Generate MSC/NASTRAN PCOMP cards driveshaft2 Inplane Modulus (Pounds/Inch) A11 = 0.8631E+06 A12 = 0.3043E+06 A16 = -0.8892E-11 A22 = 0.6591E+06 A26 = -0.3887E-11 A66 = 0.3267E+06 Flexural Modulus (Pound-Inches) D11 = 308.0 D12 = 199.6 D16 = 10.88 D22 = 763.3 D26 = 16.44 D66 = 215.0 Coupling Modulus (Pounds) B11 = 1189. B12 = -344.0 B16 = -2409. B22 = -500.8 B26 = -1615. B66 = -344.0 COMPUTATION OF STRAINS OR RESULTANTS Options: Key in Strains or Resultants F1 - Display Stress Space Failure Analysis F2 - Back up to the Previous Menu F3 - Terminate Program F4 - Toggle Calculation of Strains/Resultants Stress Resultant in the x direction Inplane Strain in the x direction Nx = 0.0000 (Pounds/Inch) ex = -0.5934E-04 Stress Resultant in the y direction Inplane Strain in the y direction Ny = 0.0000 (Pounds/Inch) ey = 0.6217E-04 Shearing Stress Resultant Inplane Shearing Strain Nxy= 1536. (Pounds/Inch) exy= 0.4997E-02 Moment Resultant in the x direction Curvature in the x direction Mx = 0.0000 (Inch-Pounds/Inch) Kx = 0.3901E-01 (1/Inch) Moment Resultant in the y direction Curvature in the y direction My = 0.0000 (Inch-Pounds/Inch) Ky = 0.2609E-03 (1/Inch) Shearing Moment Resultant Curvature in the shear direction Mxy= 0.0000 (Inch-Pounds/Inch) Kxy= 0.5803E-02 (1/Inch) Equilibrium Temperature Change (from cure temp.) ¦T = 0.0000 Equilibrium Moisture Concentration ¦C = 0.0000 FAILURE ANALYSIS MENU OPTIONS: The Maximum Stress or Strain Index is White F2 - Back up to the Previous Menu F3 - Terminate the Program F4 - Toggle Stress/Strain Data Load Ply Ply Fiber Transverse Shearing Stress Load Reversal Group Angle Stress Stress Stress Space Failure Failure

48

ID (degrees) (PSI) (PSI) (PSI) Index Factor Factor 1 90.0 297. -0.217E+04 -0.337E+04 -0.155 6.37 -2.70 2 45.0 0.365E+05 -0.307E+04 953. -0.303 4.60 -1.50 3 -45.0 -0.582E+05 0.142E+04 -568. 0.558 1.53 -3.54 4 15.0 0.220E+05 -0.105E+04 0.315E+04 -0.124 5.49 -2.68 5 -15.0 -0.192E+05 0.131E+04 0.321E+04 0.273 2.62 -5.65 6 45.0 0.629E+05 -0.133E+04 -540. -0.174 3.30 -1.46 7 -45.0 -0.396E+05 0.329E+04 828. 0.648 1.40 -4.28 8 90.0 0.228E+04 0.207E+04 -0.372E+04 0.257 2.74 -5.82

49

Lay-up 3 UNIAXIAL MATERIAL SELECTION MENU OPTIONS: Select the Default Material using the Arrow Keys F1 - Proceed to next page F5 - Toggle Q's/E's F3 - Terminate the Program F6 - Edit Material Property Data F4 - Toggle Display Units Key Default Material ID = 10 CURRENT DEFAULT MATERIAL Material IM7/8551-7a GR/epoxy ID Description E1= 0.2103E+08 Psi 1 T300/5208 Gr./Epoxy E2= 0.1280E+07 Psi 2 B(4)/5505 Boron/Epox v12= 0.3600 3 AS/3501 Gr./Epoxy G12= 0.7100E+06 Psi 4 Scotchply 1002 Gl/Ep X= 0.2100E+06 Psi 5 Kevlar 49/epoxy Xc= 0.1140E+06 Psi 6 2024-T3 Aluminum Y= 7700. Psi 7 6061 Aluminum Sheet Yc= 0.3142E+05 Psi 8 steel sheet S= 0.1720E+05 Psi 9 Titanium F12s=-0.5000 10 IM7/8551-7a GR/epoxy A1= 0.0000 1/°F 11 Epoxy Resin A2= 0.4400E-08 1/°F 12 Boeing IM gr/epoxy B1= 0.0000 13 E-glass/Epoxy (typ.) B2= 0.0000 14 Alm 7075-T6,reduced Cost= 0.00 $/sq. ft. 15 E glass/polyester rho= 0.8300E-01 lb/cu. in. LAMINATE DEFAULTS SELECTION MENU OPTIONS: Key Laminate Name and/or Default Ply Thickness F1 - Proceed to the Ply Sequence Menu F2 - Back up to the Previous Menu F3 - Terminate the Program F4 - Toggle Laminate Symmetry F5 - Toggle Units Laminate Symmetry to be used: Symmetric Antisymmetric Unsymmetric Units Used to Display Results: Meters/Pascals Inches/Psi Laminate Description = driveshaft3 Default Single Ply Thickness = 0.3500E-02 Inches Number of Laminate Ply Groups = 10 LAMINATE SEQUENCE SELECTION MENU OPTIONS: Key in Laminate Data Defaults in Effect F1 - Compute Modulus/Compliance Values Name = driveshaft F2 - Back up to the Previous Menu Material ID = 10 F3 - Terminate the Program IM7/8551-7a GR/epoxy

50

Unsymmetric Laminate Ply Ply Single Ply Single Ply English Units Group Angle Number Thickness Material Cost Total Laminate Thickness ID (degrees) of Plies (Inches) ID $/sq. Ft. 0.9800E-01 1 90.0 1 0.3500E-02 10 0.00 2 45.0 3 0.3500E-02 10 0.00 Please Note: 3 -45.0 3 0.3500E-02 10 0.00 1-The first row with a 4 15.0 4 0.3500E-02 10 0.00 blank ply angle will 5 -15.0 4 0.3500E-02 10 0.00 terminate ply input. 6 45.0 3 0.3500E-02 10 0.00 2-For Symmetric and 7 -45.0 3 0.3500E-02 10 0.00 Antisymmetric Laminates 8 45.0 3 0.3500E-02 10 0.00 enter only the plies in 9 -45.0 3 0.3500E-02 10 0.00 half of the laminate. 10 90.0 1 0.3500E-02 10 0.00 3-For a zero modulus core enter a zero for the material ID. 4-Ply ID number 1 is on the bottom of the laminate. COMPUTED LAMINATE MODULUS AND COMPLIANCE OPTIONS: Key offset angle = 0.0 F1 - Compute Strains/Resultants F2 - Back up to the Previous Menu F3 - Terminate the Program F4 - Display Compliance Values F5 - Generate MSC/NASTRAN PSHELL cards F6 - Generate MSC/NASTRAN PCOMP cards driveshaft3 Inplane Modulus (Pounds/Inch) A11 = 0.9460E+06 A12 = 0.3731E+06 A16 = -0.1616E-11 A22 = 0.6026E+06 A26 = 0.3389E-11 A66 = 0.3972E+06 Flexural Modulus (Pound-Inches) D11 = 492.0 D12 = 313.0 D16 = 3.219 D22 = 718.5 D26 = -13.46 D66 = 332.3 Coupling Modulus (Pounds) B11 = -3566. B12 = 1032. B16 = -2531. B22 = 1502. B26 = -1737. B66 = 1032. COMPUTATION OF STRAINS OR RESULTANTS Options: Key in Strains or Resultants F1 - Display Stress Space Failure Analysis F2 - Back up to the Previous Menu F3 - Terminate Program F4 - Toggle Calculation of Strains/Resultants Stress Resultant in the x direction Inplane Strain in the x direction Nx = 0.0000 (Pounds/Inch) ex = 0.1022E-03

51

Stress Resultant in the y direction Inplane Strain in the y direction Ny = 0.0000 (Pounds/Inch) ey = -0.1376E-03 Shearing Stress Resultant Inplane Shearing Strain Nxy= 1536. (Pounds/Inch) exy= 0.4040E-02 Moment Resultant in the x direction Curvature in the x direction Mx = 0.0000 (Inch-Pounds/Inch) Kx = 0.2178E-01 (1/Inch) Moment Resultant in the y direction Curvature in the y direction My = 0.0000 (Inch-Pounds/Inch) Ky = 0.1780E-03 (1/Inch) Shearing Moment Resultant Curvature in the shear direction Mxy= 0.0000 (Inch-Pounds/Inch) Kxy= -0.1269E-01 (1/Inch) Equilibrium Temperature Change (from cure temp.) ¦T = 0.0000 Equilibrium Moisture Concentration ¦C = 0.0000 FAILURE ANALYSIS MENU OPTIONS: The Maximum Stress or Strain Index is White F2 - Back up to the Previous Menu F3 - Terminate the Program F4 - Toggle Stress/Strain Data Load Ply Ply Fiber Transverse Shearing Stress Load Reversal Group Angle Stress Stress Stress Space Failure Failure ID (degrees) (PSI) (PSI) (PSI) Index Factor Factor 1 90.0 -0.353E+04 -0.126E+04 -0.329E+04 -0.678E-01 6.36 -3.75 2 45.0 0.372E+05 -0.269E+04 447. -0.283 4.79 -1.61 3 -45.0 -0.533E+05 0.122E+04 -286. 0.485 1.69 -3.89 4 15.0 0.163E+05 -0.120E+04 0.267E+04 -0.134 6.73 -3.02 5 -15.0 -0.209E+05 686. 0.257E+04 0.200 3.24 -6.36 6 45.0 0.424E+05 -0.148E+04 -305. -0.205 4.75 -1.90 7 -45.0 -0.352E+05 0.191E+04 466. 0.423 1.95 -5.39 8 45.0 0.447E+05 -970. -627. -0.168 4.61 -2.04 9 -45.0 -0.274E+05 0.220E+04 788. 0.404 2.05 -6.20 10 90.0 -0.221E+04 0.140E+04 -0.244E+04 0.176 3.84 -8.75

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NE/NASTRAN Stress Output Output Set 1 MAX/MIN Set ID Value SHELL FIBER DISTANCE-1 Minimum 1 1602 -0.25 Maximum 1 3561 -0.052

SHELL NORMAL-X1 Minimum 1 3610 -

45140.4 Maximum 1 3813 45262.1 SHELL NORMAL-Y1 Minimum 1 3719 -19473 Maximum 1 3781 21395.2

SHELL SHEAR-XY1 Minimum 1 3467 -

27715.7 Maximum 1 1612 33649.3

SHELL-SHEAR ANGLE-1 Minimum 1 3739 -

89.4033 Maximum 1 3738 88.2893

SHELL MAJOR-PRINCIPAL-1 Minimum 1 3610

-4734.12

Maximum 1 3813 57114.7

SHELL MINOR-PRINCIPAL-1 Minimum 1 3610

-58744.3

Maximum 1 3813 4317.19 SHELL VON MISES-1 Minimum 1 3644 22.0713 Maximum 1 1612 59176.9 SHELL FIBER DISTANCE-2 Minimum 1 3561 0.052 Maximum 1 1602 0.25

SHELL NORMAL-X2 Minimum 1 3610 -

44950.3 Maximum 1 3813 45393.7

SHELL NORMAL-Y2 Minimum 1 3778 -

19847.8 Maximum 1 3672 21091.9

SHELL SHEAR-XY2 Minimum 1 3467 -

26868.5 Maximum 1 2518 39509.7

SHELL-SHEAR ANGLE-2 Minimum 1 3413 -

87.5079 Maximum 1 3474 89.4341

SHELL MAJOR-PRINCIPAL-2 Minimum 1 3610

-4736.27

Maximum 1 3813 57162.5

SHELL MINOR-PRINCIPAL-2 Minimum 1 3610

-58545.4

Maximum 1 3813 4407.83 SHELL VON MISES-2 Minimum 1 3433 16.0451 Maximum 1 2518 69258.6

53

Final MAX/MIN Set ID Value SHELL FIBER DISTANCE-1 Minimum 1 1602 -0.25 Maximum 1 3561 -0.052

SHELL NORMAL-X1 Minimum 1 3610 -

45140.4 Maximum 1 3813 45262.1 SHELL NORMAL-Y1 Minimum 1 3719 -19473 Maximum 1 3781 21395.2

SHELL SHEAR-XY1 Minimum 1 3467 -

27715.7 Maximum 1 1612 33649.3

SHELL-SHEAR ANGLE-1 Minimum 1 3739 -

89.4033 Maximum 1 3738 88.2893

SHELL MAJOR-PRINCIPAL-1 Minimum 1 3610

-4734.12

Maximum 1 3813 57114.7

SHELL MINOR-PRINCIPAL-1 Minimum 1 3610

-58744.3

Maximum 1 3813 4317.19 SHELL VON MISES-1 Minimum 1 3644 22.0713 Maximum 1 1612 59176.9 SHELL FIBER DISTANCE-2 Minimum 1 3561 0.052 Maximum 1 1602 0.25

SHELL NORMAL-X2 Minimum 1 3610 -

44950.3 Maximum 1 3813 45393.7

SHELL NORMAL-Y2 Minimum 1 3778 -

19847.8 Maximum 1 3672 21091.9

SHELL SHEAR-XY2 Minimum 1 3467 -

26868.5 Maximum 1 2518 39509.7

SHELL-SHEAR ANGLE-2 Minimum 1 3413 -

87.5079 Maximum 1 3474 89.4341

SHELL MAJOR-PRINCIPAL-2 Minimum 1 3610

-4736.27

Maximum 1 3813 57162.5

SHELL MINOR-PRINCIPAL-2 Minimum 1 3610

-58545.4

Maximum 1 3813 4407.83 SHELL VON MISES-2 Minimum 1 3433 16.0451 Maximum 1 2518 69258.6

54

55

NE/NASTRAN REAL EIGEN VALUES MODE EIGENVALUE RADIANS CYCLES NUMBER

1 4.27E+06 2.07E+03 3.29E+022 4.27E+06 2.07E+03 3.29E+023 2.86E+07 5.34E+03 8.50E+024 2.86E+07 5.34E+03 8.50E+025 6.95E+07 8.34E+03 1.33E+036 9.51E+07 9.75E+03 1.55E+037 9.51E+07 9.75E+03 1.55E+038 1.51E+08 1.23E+04 1.95E+039 1.51E+08 1.23E+04 1.95E+03

10 1.55E+08 1.25E+04 1.98E+03

56

57

58

59

60

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Bibliography

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Materials Park, Ohio: ASM International

[2] Figure 1 – Driveline http://auto.howstuffworks.com/transmission2.htm 4/08/2004

[3] Hicks, Tyler G. 1995. Standard Handbook of Engineering Calculations 3rd Ed. New

York: McGraw Hill

[4] Hyer, Michael W. 1998. Stress Analysis of Fiber Reinforced Composite Materials.

Boston, Massachusetts: McGraw-Hill

[5] Mischke, Charles R and Shigley, Joseph E. 1996. Standard Handbook of Machine

Design 2nd Ed. New York: McGraw-Hill

[6] Roark, Raymond J. 1965. Formulas for Stress and Strain. New York: McGraw-Hill

[7] Rosato, D.V. and Grove, C. S. Jr. 1964. Filament Winding: its development,

manufacture, applications, and design. New York: John Wiley and Sons, Inc.

[8] Schwartz, Mel M. 1996. Composite Materials, Volume II: Processing, Fabrication, and

Applications. New Jersey: Prentice-Hall

[9] Shoup, T. E. and M. F. Spotts. 1998. Design of Machine Elements 7th Ed. New

Jersey: Prentice-Hall