Design Project Formula SAE Drivetrain

Submitted to Neal Birchfield

MME 213: Computational Methods for EngineeringMiami University

byMarissa Shaffer

James EliasBob MuellerKalene Kelly

May 15, 2014

In order to begin thinking about a design that will transfer torque from the differential to the wheel of the car, it is important to understand the overall drivetrain of a FSAE car. The basic components include a differential, axles, and hubs as shown in the Figure 1 below:

Figure 1: This figure shows the various components of a FSAE drivetrain (Honeychuck)

The drivetrain of the FSAE car is responsible for transferring the torque produced by the engine to the wheels in order to make the car go.The torque that is produced by the engine is transferred to the differential. The purpose of the differential is to transfer the available power to the slowest spinning axel. This allows the car to gain better traction. The differential is purely a mechanical design which responds extremely quickly to slippage with minimal energy loss. From the axles, the power is then transferred to the wheel (Schwartz). This report will discuss potential design options for the drivetrain along with some ideas for optimizing the performance, strength and angle of torque projection. Additionally, one of the most important goals for the final design is to make sure that the drivetrain system transfers the torque from the engine to the wheels with minimal energy loss.

Drivetrain mechanical failure background

While designing the drivetrain, it is extremely important for the system to be as light as possible in order to maximize the power to weight ratio along with maximizing the strength of the material to prevent failure. By increasing the stiffness of the shaft, the angle of torsion will decrease, which will increase the direct flow of power to the wheel with minimal energy loss. By making the system more rigid, the shear stress experienced by the driveshaft will increase, however the performance of the car will increase. Minimizing the impulse thats being delivered from the transmission to the differential will reduce shear stress within the differential thus reducing the shear stress within the driveshaft. This can be done by adding a damping pad along a linear shaft. Typically this dampening pad will be located between the transmission and differential if the shaft is horizontal with the two systems. Failure within the driveshaft joint is directly related with the angle of projection. As the angle increases you increase shear stress which subjects it to failure. Failure typically occurs within the sleeve of the ball joints, which is the thinnest part of the design (Common Driveline Issues). Figure 2 shows a Universal Joint

that has cracked due to large amounts of internal shear stress. Most designs include a sleeve socket for the joint to fit in. The purpose of the sleeve is to allow the drive shaft axial displacement to change as the wheel vertically changes. Failure could also occur if the joint slips out of the sleeve, however this rarely happens unless a collision occurs.

Figure 2: Figure 2 shows a U-joint that has failed due to high shear stress (Cracked Axle Ear)

Suggested Designs

After research was conducted, it was found that the most important aspect of a drivetrain design is finding an efficient way to transfer the torque from the engine to the tires of the car. It is also imperative to limit the shear stress in the drivetrain, especially in the joints that are extremely susceptible to the effects of high shear stress. In order to reduce the stresses experienced by the joint and to protect the performance of the joint, different designs are presented in order to achieve the desired output. Therefore, all of the proposed design ideas will include a dampening unit to reduce shear stress that will be located behind the differential and transmission. The differential will ensure that both axles are always rotating at the same speed relative to one another. The dampening unit will reduce the impulse which will reduce the shear forces felt by the differential and along with the remaining system.

Ball Bearing Joint

A joint that allows the drivetrain to transfer torque from the engine to the wheels while still allowing the wheels a certain degree of vertical movement . An optimal design of a CV joint is lightweight and simple.

The first joint design proposed is a ball bearing type CV joint. This joint consists of an outer socket and an inner joint connected by a series of ball bearings. The ball bearings allow for the inner socket to be able to translate slightly in all directions as well sliding in the sleeve along the horizontal direction to allow for this motion. Figure 3 shows a ball bearing joint.

Figure 3: Figure 3 shows a ball bearing type CV joint (2 J’s Automotive)

CV Tripod-type joint

A second possible solution to the problem we face is a tripod-type CV joint. This joint acts much like the ball bearing CV joint, but instead of ball bearings transferring the torsional force between the outer socket and inner joint, there are 3 bigger bearings located at 120 degrees from each other. This design is more practical and durable than the ball-bearing type CV joint, however it gives a less angle of projection. Figure 4 describes a cut out view of a tripod joint.

Figure 4: Figure 4 describes a Tripod type CV joint (Nasioc Forums)

This design includes the common sleeve where the tripod bearings are able to adjust along the axial alignment depending on the position of the wheel. The purpose for this design is to include the projection of angle in all directions. The components within this consist of the spider, the spherical roller, retainer, needle roller and the rings. This is commonly used for front wheel drive cars where you're applying torque while the wheel’s direction is not aligned with the direction of the car.

Figure 5: Figure 5 shows the internal pieces of three types of Tripod joints (CV Joint Blog)

U-Joint

This design may be the most optimal design for the driveline. Since the wheels of the car are only moving in the vertical direction while staying aligned with the car, there is no rotational movement about the vertical axis. The join consists of a sleeve for displacement change just like the previous joints however this joint is more durable and simple. Failure does typically occur at the thinnest point of this joint which we can reduce the change by upsizing the joint, and by decreasing the impulse through the system.

Figure 6: This is a U-joint typical of FSAE drivetrains (CV Joint Blog)

Decision Matrix

The criteria below will be put into a selection matrix along with the three re-designs in order to help choose a design that will be the best for the project. Each section will be weighted from least importance to most importance to help aid in the search of a best design. Without choosing exact number rankings for the criteria, the performance will most likely be weighted the highest along with strength/durability. Another important aspect to consider is the mass. Next should come cost and the least important thing to consider should most likely be the appearance of the design. Reasoning for the ranking can be determined by the definitions provided.

Mass - the mass of the car should be as light as possible. Looking at the equation for the conservation of energy, kinetic energy depends on the weight of the object in motion. The lower the mass, the more acceleration there will be with a given amount of force coming from the engine.

Strength of the material used/ Durability - the material used needs to be strong and capable of withstanding the shear stress that will be experienced during the race. The material should also be long lasting and able to withstand multiple races. With a weak material, the drive train could fall apart and cause a rippleffect of destruction.

Cost - in any real-life scenario, the least amount of money spent is best. A design team may be on a certain budget, or has the goal of spending as little of their companies' money as possible.

Aesthetics - the physical appearance may not hold as important in the selection matrix, but it does hold some level of importance. The first impression of a design is judged by what a person can see. It is possible to have a great performing design that is aesthetically not pleasing. This may ruin the credibility of your design to others.

Performance - the way a design performs will really say it all. A design may appear to be well designed, but you don't know how great it is until it is put to the test. The performance of the car will determine how it stands out against the rest of the cars in the race.

Analysis Plan

The main point of failure the design needs to focus on solving is reducing the impulse torsional forces felt by the components of the drivetrain. Sudden braking, acceleration, and collision all send impulse torsional forces through our drivetrain that can damage components and affect the performance of the race car. Because the causes of torsional forces cannot be avoided in racing, the final design must include a plan to reduce their effects on the drivetrain to avoid component failure. One way this can be done is installing a dampening unit along the drivetrain to absorb some of the shear impulses and reduce their effects on the drivetrain components. Another failure can be avoided is choosing a material for the driveshaft that can absorb some of this impulse while still being strong and rigid enough to efficiently transfer the

torque from the engine to the wheels. The CV joint used can be upsized to increase their overall strength by using more material. Also, the joint strength is a function of its bending angle, therefore if the angle of projection can be reduced, the shear forces felt within our CV joint can be reduced. All of these things will reduce the efficiency of the torque transfer to the wheels and add weight to the car, but this is a necessary tradeoff to ensure that the final design does not fail during operation.

Proposed Designs:

Design 1

This design involves a hollow spline shaft made from heat treated precipitate strengthened aluminum. This shaft will connect a steel U-joint and a steel tripod joint to a hub interface plate that will match the bolt pattern to the wheel and differential. Starting at the differential of the driveline, a 1/4’’ aluminum interface that is part of the U-joint is bolted to the inboard spline shaft. The length of the U-joint will be 50.8 mm. The other end of this U-joint is splined and the teeth of this joint are then intermeshed with the teeth of the hollow aluminum spline shaft. Figure 7 shows how the spline shafts included in the design will be able to transfer torque through the components. This specific aluminum grade has a relatively low shear modulus compared to steel, which means it cannot absorb more shear without plastically deforming (MatWeb); however, the weight difference is great. The shaft design was able to be hollow and maintain the required allowable shear stress which is still less than the maximum allowable shear stress given from the material. The twist that occurs in the shaft is very minimal therefore the power will be transferred quickly, improving the performance. The right side drive shaft length is 393.7 mm with a radius of 50.8 mm and a thickness of 10.3 mm. We included a factor of safety of 2 to the thickness. These values were calculated from the equations in Appendix B. The left side drive shaft’s radius and thickness is the same as the right shaft, however the length will be 292.1 mm. The outer end of this aluminum shaft is splined as well and is connected with a steel tripod joint. This tripod joint will allow for vertical movement while also allowing for the horizontal movement of +/- .25 inches as required. The length of this tripod joint will be 76.2 mm. The outgoing shaft of this tripod joint will be splined and connect to the hub interface, which is made from 1/4’’ thick aluminum. The other end of the tripod joint will be splined and fit into the hollow aluminum splined shaft. The purpose of this hub interface is to connect the Tripod joint to the hub by utilizing the given bolt pattern .The hub interface will be directly bolted to the hub and splined to the tripod joint in order to transfer the required torque to the wheels. The purpose for the tripod joint is to utilize its additional function of the sleeve.

Figure 7: This figure shows how two spline shafts can be interconnected by the meshing of the teeth of each shaft. This is how torque can be transferred along the driveline. (Automotive

Engines)

Design 2

Design 2 also requires the use of the aluminum spline shaft with the radius and thickness matching the shaft in design 1, but with a different length. This design uses two steel U-joints and aluminum hub interfaces. Figure 8 shows a system of two U-joints and the sleeve design between the shaft and one U joint. Design 2 will allow telescopic motion on one end of the hollow shaft and fixed on the other. Starting at the differential, a 1/4’’ thick aluminum interface that will match the bolt design will be connected to a U-joint. This U-joint will have a length of 50.8 mm a radius of 25.4 mm and will be made of steel since most failures occur at the joint. From this U-joint, the aluminum shaft will be tightly splined to the other U-joint, allowing no movement. After calculating the applied shear stress on the drive shaft from the maximum torque from the wheels, the shaft’s material is going to be aluminum which has a reduced weight compared to steel. The right side drive shaft length will be 419.1 mm with a radius of 25.4 mm and a thickness of 10.3 mm. The left side drive shaft length will be 317.5 mm with the same radius and thickness.The thickness was developed from the shear stress and moment of inertia equations which can be found in Appendix B. Since this shaft is longer than the design 1 drive shaft, it will be able to absorb more shear stress since the angle of twist increased slightly; however, there will be a delay of transferring power which will dampen the acceleration. The outer end of this aluminum shaft will be splined as well and interconnected with a two inch long steel U-joint. This U joints splined shaft that will be connected to the drive shaft will hold a looser fit than the other side in order to allow a change of length as the wheel changes position. The U- joints will be experiencing a lot of shear stress, therefore the material they are fabricated out of must be strong and durable to prevent failure. The second U-joint is in turn connected to a 1/4’’ aluminum hub interface which is bolted to the hub, as described in Design 1.This horizontal movement is provided by the splines that connect each component of the driveline. The interlocking teeth will allow each part to move horizontally as needed, as long as they remain well lubricated and within its own range.

Figure 8: This figure shows a system of two U-joints connected by a spline shaft (Supplier & Distributor)

Design 3

The final design is composed of two steel tripod joint connected to the differential by an aluminum interface. Tripod joints allow for both horizontal and vertical motion, which will meet the constraints of the driveline. Connected to the tripod joint is a long splined aluminum shaft that is hollow. The right drive shaft length is 368.3 mm and the left side’s length is 266.7 mm. The thickness will be 10.3 mm and the radius is 25.4mm. The hollow shaft is extremely lightweight and takes less rotational energy to make it spin, maximizing the torque transfer through the shaft. The hollow shaft is then connected to another steel tripod joint. The outboard shaft of this joint is connected to an aluminum hub interface, which can be bolted onto the hub to complete the driveline.

The Selection Matrix

Taking the criteria described above, a weight for each category was added to ensure the optimal design was chosen. Aspects of the design that improved the functionality, such as weight, strength and performance were weighed very heavily. Other features such as cost and aesthetics were not important to the overall performance of the driveline and received a low weight rating. Each design received a score for each category of ranking, three being the best and one being the lowest possible score. Additionally, each of these categories carried a weight of importance, with all of the weights summing to 1. The scores of each design received for each category was then multiplied by that categories weight, and then all the scores for a given design were summed to give a final score. The most optimal design from the three proposals will be the one with the highest score. Table 1 below shows the decision matrix as well as the scores received by each design. When analyzing the data it is inferred that design 2 is the optimal design based off of the listed criteria.

Criteria (weight)

Design Mass (.2) Cost (.08) Aesthetics (.02)Strength/Durability

(.3)Performance

(.4) Overall Score1 2 2 2 2 3 2.42 3 3 1 3 2 2.563 1 1 3 1 1 1.04

Table 1: The table above shows the scores received by each design for every category considered as well as the Overall Score each design achieved.

Analysis Scoring of DesignsAll values and calculations for the analysis of the selection criteria can be found in Appendix C.

Mass:For each design the total mass was calculated by finding the mass of each part included

in the design. The mass of the U-joints and tripod joints were found through research (Supplier and Distributor). The mass of each shaft along with the interfaces was found by multiplying the density of the material with the volume. Once the mass of each individual piece was found, all the parts were added together. The total mass for design one is 5.28kg, design two is 4.99kg and design three is 5.57kg.

Cost:The cost of each design was determined through research. The U-joints and tripod joints

cost were found (Supplier and Distributor) and then the cost for an aluminum hollow rod with the desired diameter and thickness was found (MetalsDepot) with a length of the sum of all the shafts. A proportion was then used to find the cost of the shaft for each design. The total cost for design one is $145.84, design two is $99.24 and design three is $192.45.

Aesthetics:Aesthetics is best defined as how visually appealing the design is to someone. Tripod

joints are more contained than U-joints and therefore were deemed to be more aesthetically pleasing. Because of this, design 3 scored highest in aesthetics because it contained two tripod joints. Design 2 scored the lowest in this category because it was made up of two “ugly” looking U-joints.

Strength/Durability:In order to rate the strength/durability the shear stress on the shafts and joints was

calculated using τallowable equation found in appendix B. Since the only difference between the shafts is the length the shear stresses on all the shafts were the same. This shear stress value was compared to the maximum shear stress value to make sure that it did not exceed it. The allowable shear stress in the U-joints was much greater than the allowable shear stress of the tripod joint therefore the design with two U-joints got the highest rating.

Performance:Performance was evaluated based off of two criteria, the angle of twist that the shaft and

joints would be subjected to as well as the ease of horizontal movement of the driveline, as required in the constraints. It was found that U-joints have less of an angle of twist when subjected to torque, increasing the performance of the driveline. However, tripod joints allowed for horizontal movement more easily. A greater emphasis was placed on the angle of twist, because maximum torque transfer is the overall goal of the design. For these reasons, design 1 was ranked the highest due to its low angle of twist as well as its allowance of horizontal motion. Design 3 was ranked lowest because although it allowed for easy horizontal movement, its high angle of twist would greatly decrease the maximum torque transfer for this design.

Summary of Decision Matrix

It was found that the design composed of a hollow aluminum shaft, two aluminum interfaces, and two U-joints was the optimal design for this application based off of the criteria of mass, cost, aesthetics, strength, and performance. The low mass of this design along with its high durability and strength outweighed its visual flaws as well as its lacking in performance. Due to this designs light weight, it will take less kinetic and rotational energy to move and rotate, which increases the amount of energy it can transfer to the wheels of the car. The high durability of this design means that the driveline can withstand high amounts of shear stress without plastically deforming or breaking.

In the future, the design chosen has to be more fully analyzed. The calculations performed during this phase were mostly based off of gross estimations and simplifications that will not be adequate enough to base the final design off of. A three dimensional drawing will be created for all parts of this design using a drafting software. From this model, full analysis can be run to seen what areas will concentrate the most stress during operation and what parts, if any, need to be altered to handle the stresses the part will experience.

Final Design

The final design that was chosen consists of 2 U-joints, an aluminum outboard hub interface, an aluminum inboard hub interface, and a hollow, splined aluminum drive shaft. The splining used was 2 mm deep and 6 degrees apart for a total of 30 splines. The U-Joints are constructed from 1018 cold rolled steel and consists of two splined brackets connected by a solid steel cross piece. One bracket has a splined section that is 25.00 mm long that is splined to the hub interface on the outboard and inboard sides. The other U-Joint bracket has a splined section that is 35.00 mm long, and this connects inside of the hollow aluminum shaft. Starting from the left side of the drivetrain, there is a 6.35 mm thick outboard hub interface that is bolted to the wheel hub using 5/16 24 3/4’’ bolts (Home Depot). The hub interface is then connected to a U-joint by a splined extrusion of 25.4 mm. The splined extrusion of the hub interface is assembled with the splined extrusion of the U-joint. The splining allows for the hub and the joint to easily fit together and maintain a connection to transfer torque. This connection is essential to the durability and performance of the car. Connected to the same U-joint is another splined extrusion that is assembled to a 368.30 mm splined hollow aluminum shaft constructed from

6061-T6 Aluminum. The right end of the aluminum shaft is is splined to another U-joint. the other end of the U-joint is splined to a 6.35 mm inboard hub interface with 25.4 mm splined extrusion. The inboard hub interface is connected to the wheel hub using the 5/16 24 3/4’’ bolts. Detailed engineering drawings of all parts of the driveline can be found in appendix E. The left side of the driveline is made up of the same components, except a 266.7 mm aluminum shaft connects the two U-Joints.This systems of two U-joints allow for the torque to be efficiently transferred from the engine to the wheels with minimal energy loss as well as allowing for the vertical mobility required by the restraints of the cars suspension. The splining of the shafts allow for horizontal translation within the system by the overlap of the splining. The final length of the right side was 532.8 mm and the left side was 430.6 mm. It was calculated that the left driveline weighed 2.4786 kg and the right driveline weighed 2.8276 kg. It was decided that all parts would meet a 1.4 factor of safety to ensure that no components of the driveline would fail during operation.

Finite Element Analysis

After the design was finalized, the next step was to run finite element analysis through Abaqus. Each piece was analyzed separately and different constraints, boundary conditions and loads were applied.

U-Joint

For the U-Joint analysis from figure 9 and figure 10, a plane was created to divide the holes into two sections in order to apply a static general type surface traction. The pressure on each side that created a couple force is equal to (½)*Force. Applying the torque equation from Appendix B and additionally adding the factor of safety of 1.4, the applied force was calculated to be 1556.8 N. The below figures show the maximum shear stress that is occurring on both U-Joints with a maximum deflection multiplied by 7000. The maximum shear stress for figure 9 was 1.73*104 Pa and 1.252*104 Pa in figure 10.

Figure 9: U-joint Figure 10: Extended U-joint

Cross Joint

The cross joint from figure 11 was simulated in Abaqus similar to the U joints from figure 9 and figure 10. A plane was created in order to create two independent sections on the applied surface area. The pressure on each side created a couple force that is equal to (½)*Force. Applying the torque equation from Appendix B and additionally adding the factor of safety of 1.4, the applied force was calculated to be 1556.8 N. Figure 11 is showing the maximum shear stress along with a maximum deflection multiplied by 7000. The actual deflection experienced by this part was almost negligible, but it was present. The maximum shear stress that is occurring is 4.19*104 Pa, which is well under the maximum shear strength of the material according to Appendix A.

Figure 11: Cross joint. This piece connects the U-joint and extended U-joint

Hub Interfaces

For the hub interfaces a reference point was put in the center of the part and the inner splining was constrained to the reference point. The back of the interface was fixed and a moment of 62.27N/m was applied at the reference point. The moment was found by applying a factor of safety of 1.4 to the given maximum torque of 44.48 N/m. The figures below show the maximum shear stress in the interfaces, figure 12 is 2.698*10-2 Pa and figure 13 is 2.003*10-2 Pa. According to appendix A these values are well below the maximum shear strength of the material.

Figure 12: Outboard Interface Figure 13: Inboard Interface

ShaftsFor the shafts analysis a plane was added 35 mm in and a partition was made. The

partition was added in order to apply a moment on the specific region of the contact area. Again a reference point was put at the center of the part and the inner splining was constrained to the reference point and the moment of 62.27 N/m was applied. The other end of the shaft was fixed. The figures below show the maximum shear stress in the interfaces, figure 14 is 5.628*10-3 Pa and figure 15 is 6.996*10-3 Pa. According to Appendix A these values are well below the maximum shear strength of the material.

Figure 14: Left side shaft Figure 15: Right side shaft

Fatigue Analysis

One concern with the final design is the use of aluminum for the shaft material. Although this type of aluminum is extremely strong and lightweight, it is also susceptible to the effects of fatigue. Figure 16 shows a graph of the fatigue stress experienced by an aluminum alloy. Although this is not the exact alloy used in the final design, it accurately shows how aluminum alloys are vulnerable to the effects of fatigue. After about 105 cycles, the maximum stress the alloy can handle drops by nearly half, which would leave the shaft open to failure. The shaft is

subject to the most impulse torques and by far is loaded and unloaded the most during the course of a race. Using Abaqus, a fatigue analysis was run and the hollow shaft was loaded and unloaded many times. Figure 17 shows the results of the Abaqus analysis.

Figure 16: This figure shows a fatigue analysis of an Aluminum Alloy

Figure 17: This figure shows the deformation that occurs in the shaft after 36034 loading cycles

From these results, it can be concluded that the aluminum shaft will be able to be subjected to the loading and unloading required by the race without having its maximum shear stress lowering by a significant amount. Although this shaft will not be able to be used for years to come, it is strong enough to resist the effects of fatigue for these races.

Appendix AMaterial Properties

For the design, it was necessary to choose materials that would perform the best as well as be strong and durable enough to withstand the shear stress involved in multiple uses. Two materials were chosen to be implemented in the designs, a mild, low carbon steel and a precipitate strengthened aluminum alloy. The relevant material properties for each alloy can be found in the table below. (matweb)

Material 1018 Steel Aluminum 6061-T6

Shear Modulus 205 GPa 26.9 GPa

Possions Ratio .29 .33

Density 7.86109x10^-6 kg/mm^3 2.82336x10^-6 kg/mm^3

Shear Strength 237.5 MPa 207 MPa

Appendix B

Stress Analysis

Each equation was used in hand calculations in order to determine allowable shear stress, the twisting which occurred in each part, the polar moment of inertia which was developed due to the spinning of the material about each axis. Additional variables were derived due to specific constraints.

τ applied=TcJ

Jcylinder=π2

∆ r4φ=∑

i=1

∞ T i Li

Gi J i

I x=π (R4−r4)

64E=1

2m v2+ 1

2I ω2 F . S .=material strength

designload

Appendix C

Data and Calculations

See the attached spreadsheet appendix for information about calculations and the final calculated results for each design.

Appendix DBill of Materials

See the attached spreadsheet appendix for information regarding the materials purchased and the manufacturing time and cost. The manufacturing estimates and costs were obtained by an interview with Dave Kohler from Ultimate Machining Company.(Americas Metal Superstore, Home Depot, Manufacturing Estimates)

Appendix E

Engineering Drawings

Left Driveline Assembly Drawing

Left Driveline Hollow Splined Shaft

Right Driveline Assembly Drawing

Right Driveline Hollow Spline Shaft

U-Joint:Each U-Joint is made up of a cross piece as well as two splined brackets. One of the

brackets has an extended splined shaft component, this bracket goes into the aluminum shaft. The bracket with the shorted splined component attaches to the inboard or outboard interface.

Cross Piece

U- Joint Splined Bracket with Extended Spline

U-Joint Splined Bracket

Inboard Hub Interface

Outboard Hub Interface

Standard Parts

References

"Americas Metal Superstore." Metals Depot. Metals Depot, n.d. Web. 30 Apr. 2014. <https://www.metalsdepot.com/>.

"Area Moment of Inertia." The Engineering Toolbox. N.p., n.d. Web. 29 Apr. 2014.

"Automotive Engine Myths and Opinions." Home Built Airplanes. N.p., 22 Mar. 2012. Web. 29

Apr. 2014.

Bradford, Kip. "Carbon Fiber Driveshaft." Pb Works. N.p., 2009. Web. 29 Apr. 2014.

<http://engin1000.pbworks.com/w/page/18942689/Carbon%20Fiber%20Drive%20Shaft>.

"Common Drive Line Issues." Machine Service Inc. Machine Service Inc, 2009. Web. 14 May

2014.

<http://www.machineservice.com/technical-101/drive-shaft-failure-guides/>

Honeychuck, Michael. "Team FASE Powertrain." N.p., 13 Dec. 2010. Web. 21 Apr. 2014.

Kohler, Dave. "Manufacturing Estimates for a Driveline." Telephone interview. 13 May 2014.

Lionnet, Graham N. "Drive Line Design and Implementation for REV Formula SAE Electric

Vehicle." University of Western Australia, 28 Oct. 2013. Web. 29 Apr. 2014.

"Material Property Data." MatWeb. N.p., n.d. Web. 29 Apr. 2014. <http://www.matweb.com/>.

"Metals Depot - America's Metal Superstore!" Metals Depot®. ELCO INC, 2012. Web. 14 May

2014. <http://www.metalsdepot.com/hrsteel2.html>

"Metals Depot - America's Metal Superstore!" Metals Depot®. ELCO INC, 2012. Web. 14 May

2014.<http://www.metalsdepot.com/alum2.html>

"Military Standard Universal Joints." Apex Fasteners. Apex, n.d. Web. 29 Apr. 2014.

<http://apexfasteners.com/fasteners/images/UJCatalogue19.pdf>.

"Results For "5/16 24 3/4'' Bolts" (12 Products)." Search Results For 5/16 24 3/4'' Bolts at The

Home Depot. Home Depot, 2000. Web. 14 May 2014.

Schwartz, Paul. "Formula SAE Powertrain Phase 4: Performance Validation and Path Forward."

Formula SAE Powertrain. University of Delaware, 10 Dec. 2010. Web. 29 Apr. 2014.

<http://sites.udel.edu/meeg401/files/2011/08/FSAE_PowerTrain_Phase_4_NN.pdf>.

"SUPPLIER & DISTRIBUTOR OF UNIVERSAL JOINTS & DRIVESHAFT PRODUCTS."

The Rowland Company. Rowland Company, 2014. Web. 29 Apr. 2014.

Zhu, Y. "Torsion." NC State Archive. NC State, n.d. Web. 29 Apr. 2014.