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2011 Indianapolis University-Purdue University

Indianapolis Formula SAE Chain Drive Differential

Mounting Brackets Design Report

Jeff Hawkins

IUPUI FSAE 2011

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Abstract

This document describes the design and fabrication of the differential

mounting brackets for the Indianapolis University-Purdue University Indianapolis

Formula SAE design series competition car. The differential mounting brackets aredesigned around Quaife's Automatic Torque Biasing helical limited slip differential.

This design also includes mounting for a single inboard rear brake caliper. Dassault

Systems SolidWorks 3D CAD and simulation software was used to design and FEA

the differential mounting brackets. The differential mounting brackets were

designed, manufactured, and tested.

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1. Design Constraints

A set of design constraints must first be established in order to design the

differential mounting brackets. Quaifes Automatic Torque Biasing helical limited

slip differential was chosen to drive the rear wheels in IUPUIs Formula SAEcompetition car. The following sections outline these design constraints

1.1 Functional Requirements

y The differential mounting brackets are to locate the differential so the driven

sprocket face is parallel to the drive sprocket face.

y The differential mounting brackets are to allow the differential to spin freely.

y The differential mounting brackets are to be designed to accommodate

80mm nominal bearing diameter as well as a bearing fit tolerance.

y The differentia mounting brackets are to allow for ease of removal of thedifferential from the car.

y The right side differential mounting bracket is to incorporate an inboard

brake caliper mount.

1.2 Manufacturing

y The differential mounting brackets are to be manufactured on a CNC mill.

y CAD CAM software will be used to program the CNC mill.

1.3 Integration

y The differential is to be chain driven off of the engine.

y The differential is to be offset from the centerline of the car to account for

chain alignment.

y The left side differential mounting bracket is to be mounted to the chassis.

y The right side differential mounting bracket is to be mounted directly to the

engine via a bolt through the upper swing arm mount and through the engineblock casting.

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2. Design

2.1 Concept

Previously designed differential mounting brackets cannot be improvedupon since this is a first year Formula SAE competition car. A concept was chosenafter looking at previous differential mounting bracket designs from other

university's Formula SAE teams. A differential mounting bracket design was created

using this concept and the aforementioned design constraints.

The concept for the differential mounting bracket design was to incorporate

all the design constraints into a relatively simple and lightweight package. The right

side differential mounting bracket started out with a solid billet designed around

the aforementioned constraints. Pockets of material were machined into the solid to

decrease weight while ribs of material were left to stiffen the remaining material.

The left side differential mounting bracket was designed to take 90% of the forcefrom the chain tension. The right side mounting bracket was designed to take the

remaining force from the chain tension as well as all of the rear braking force.

The left side differential mounting bracket is to be mounted to one of the

chassis tubes. The square tube allows for a flat mounting surface. The top half of the

left mounting bracket will be mounted to the chassis using two bolts and will have

machined slots to accommodate for and aft translation. This translation will allow

for chain alignment. The swing arm top mounting point provides a practical way to

mount the top of the right side differential mounting bracket. A press fit dowel pinwill be used to mount the lower part of the right side differential mounting bracket

to the engine. A tolerance hole will need to be drilled into the engine to allow for the

dowel. The mounting constraints for the right side mounting bracket will not allowit to pivot laterally to accommodate for chain alignment, and will not allow for

longitudinal translation or rotation about its top mounting point.

Bearing caps were designed into the differential mounting brackets to allow

for easy disassembly of drivetrain components. This design also allows for quick

exchange of rear drive sprockets during testing. The mounting brackets were

machined with a transitional bearing fit tolerance to allow the bearing caps to be

removed. This bearing fit tolerance will not allow the bearings to spin in their seats

under load. This bearing fit tolerance also takes into account the extra material

added from anodizing.

2.2 Bearing Selection

Two of SKFs 62208-2RS1 sealed single row deep groove ball bearings are to

be used as differential carrier bearings. These bearings have a 80mm outside

diameter with a 40mm inside diameter and a width of 23mm. The limiting

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rotational velocity of these bearings is 5600 revolutions per minute. With a final

drive ratio of 48/12, an engine speed of 22,400 revolutions per minute can beachieved. This engine speed is well above our nominal engine operating speed.

These bearing have a dynamic and static load rating of 30.7 kilonewtons and 19

kilonewtons respectively. This works out to 6901 pounds-force and 4271 pounds-

force.

2.3 Material Selection

2024-T4 Aluminum was selected as the bulk material to be machined for the

car. This alloy was chosen for a number of reasons. 2024-T4 is a widely used

material and as such is highly available. This alloy is relatively strong compared to

its density, and its very cost effective for what it is being used for. 2024-T4 is also

very easy to machine. For the purpose of this design, a surface treatment was

chosen to surface harden the bearing seats. While aluminum has a passive layer as

one of its material properties, an anodized coating was chosen to add to this passivelayer as well as increase the surface hardness.

2.4 Manufacturing and Assembly

When designing a part, manufacturability should be a major consideration.

After several design iterations, both left and right side differential mounting

brackets were designed such that only three or four machining setup procedures

needed to be performed. A minimal design is always best, as it will cost less to

produce. Available tooling is another consideration, as well as setup and

manufacture time. The differential mounting brackets can be made in house on aCNC mill with readily available end mill sizes. Due to time constraints, only the

differential mounting bracket bearing caps will be made in house. The left and right

side differential mounting bracket upper halves will be outsourced.

Ease of assembly should also be taken into account when designing. All the

tooling required to assemble the differential mounting brackets are simple handtools.

2.5 Load Cases

Two load cases are to be taken into account when analyzing the differentialmounting bracket design. The primary load on the left side differential mountingbracket is due to the forces from the chain with some of this force being applied to

the right side differential mounting bracket. The primary load on the right sidedifferential mounting bracket is due to the braking forces from the inboard caliper.

The force due to the chain can be roughly calculated using the followingequation.

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T !War (1)

Where T is the torque, W is the mass of the vehicle, a is the longitudinal acceleration,and r is the tires loaded radius. A longitudinal acceleration of 1.5g will be assumed.

The weight of the car can also be assumed at 650 pounds-force and the tires loaded

radius is 10.25 inches. This results in a torque of approximately 833 foot-poundsforce. This torque is acting on the pitch diameter of the sprocket. In order to

calculate the associated force, the pitch diameter must be known. The pitchdiameter of the 48-tooth 520-pitch sprocket is 9.556 inches. The following equation

will allow us to calculate this force.

F !T

r (2)

Using this equation, a force of approximately 2100 pounds-force is found. Given that

this is the total force acting on the differential mounting brackets from the chain,

another calculation needs to be performed to calculate the force acting solely on the

left side differential mounting bracket. This force can be found by simply applying it as a static loading with a point load and two reactionary forces. The load at thereaction points is simply a percentage of the point load, where the load is being

applied to the distance between the reaction points. For the purpose of this analysis,a 2000 pound-force load will be used on the left side differential mounting bracket

with the remaining 100 pounds acting on the right side differential mounting

bracket.

The braking force on the right side differential mounting bracket can be

calculated in a similar way given equation 1 above. A longitudinal deceleration of

1.1g will be assumed. A 55% rear weight distribution is assumed. Given that the rear

of the car has a weight of 357.5 pounds-force and a tire loaded radius of 10.25inches, the resultant torque is approximately 336 foot-pounds force. This torque is

acting on the brake rotor at the radius where the brake pad contacts the brake rotor

surface. When using a 10-inch diameter brake rotor, this radius is 4.725 inches. This

resultant force acting on the right side differential mounting bracket is found to be

approximately 853 pounds-force.

2.6 Finite Element Analysis

The differential mounting brackets must be able to withstand the resultant

forces created by the chain tension and the brake caliper. These resultant forces arecalculated in the previous section entitled "Load Cases." Dassault Systems

SolidWorks Simulation was used to perform finite element analysis on the

differential mounting brackets.

In order to properly analyze the differential mounting brackets, features of

the part need to be fixed. These fixed features should be similar in nature to how the

actual part, once machined and assembled, will be affixed. The left side differential

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mounting bracket will be fixed to the rear chassis tube with bolts. To fix this feature

in SolidWorks Simulation, the entire top face is selected as a fixed feature. The right side differential mounting bracket will be fixed to the engine with a bolt through the

upper swing arm mount and a bolt through the aluminum casting of the engine. To

fix these features in SolidWorks Simulation, the upper mounting hole will be fixed

using the fixed hinge feature and the lower mounting face will be fixed as a fixedfeature.

Figure 1: SolidWorks Simulation Fixed Geometry

The next step in analyzing the differential mounting brackets is to apply theload cases. As stated previously, the primary load on the left side differential

mounting bracket is from the force of the chain tension. The load will be applied at the bearing surface, as such; a split face will be created to properly distribute the

load on only one half of the bearing face. The resultant force from the chain is not parallel to the ground, however. The correct angle is determined by the distancefrom the driven sprocket axis to the drive sprocket axis and a line tangent to both

pitch diameters of the sprockets. This angle is to be used when applying a split face.Once the split face is applied to the bearing surface, the force can be applied. As

previously calculated, this force is to be 2000 pounds-force.

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The primary load on the right side differential mounting bracket is from the

braking force from brake caliper. This load will be applied at the brake calipermount. Since the actual force is being applied above the differential mounting

bracket, a moment is being applied at the brake caliper mount. Split faces will be

applied to the brake caliper mounting holes. The angles at which the split faces are

applied are taken from the angle of the brake caliper mounting tabs. An easier wayto apply this load is to create another part to simulate the brake caliper. Since thepreviously calculated load is not going to be applied directly to the brake caliper

mount another part must be modeled. This will allow the force to be applied at a

distance from the brake caliper mount that coincides with the real part. As

previously calculated, this force is to be 853 pounds-force.

Occasionally it is necessary to analyze an entire assembly for accuracy of

results. Simplified models are also convenient when analyzing assemblies. A

pseudo-differential was used to impart the force on the assembly to analyze the

chain force. A simplified model of the brake caliper was used to impart the force on

the assembly from the braking force.

Figure 2: FEA Chain Force

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Figure 3: FEA Braking Force

Given that the yield strength of 2014-T4 Aluminum is 42,061 pounds persquare inch, both the right and left side differential mounting brackets are well

within a factor of safety limit of 1.8. The maximum stress seen due to the chain force

is 13,601.6 pounds per square inch giving a factor of safety of 3.09. The maximum

stress seen due to the braking force is 9,761.2 pounds per square inch giving a factor

of safety of 4.31.

2.7 Final Design

The final design does not differ much from the original design. Some features

ended up being either too complicated or too time consuming to actually machine. Aminimal design is easier to manufacture and is more cost efficient. Some features

were removed from the modeled parts before machining.

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Figure 4: Left Side Differential Mounting Bracket

Figure 5: Right Side Differential Mounting Bracket

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3. Manufacturing and Assembly

Once the design has been finalized, two-dimensional drawings were created.

The upper halves of the differential mounting brackets are to be outsourced to Don

Schumacher Racing, who has offered to machine these as a sponsor for the car. Thedifferential mounting bracket bearing caps are to be machined in house. The

drawings along with the solid model part file were given to the machine shop. Once

there, they will be entered into the CAD CAM software and the machining process

will be created. The Aluminum billets for the bearing caps will be set up in the CNC

mill and the CAD CAM software will tell the CNC mill how to machine the part. The

process will be the same for the upper halves of the differential mounting brackets,which were outsourced to Don Schumacher Racing.

After the parts have been machined in the CNC, final machining can be done.Final machining includes drilled and tapped holes, milling, and chamfering. 1/4-28

holes are to be drilled and tapped in the differential mounting bracket upper halvesfor the bearing caps to be bolted to. A size F drill bit will be used to drill all 1/4-inch

clearance holes, such as the bolt holes in the bearing caps. 3/8-inch clearance holes

are to be drilled into the brake caliper mount and a 5/16-inch hole is to be drilled

into to lower mount on the right side differential mounting bracket.

Next, after final machining, everything can be assembled. The bearing caps

are bolted to the upper halves and the upper halves are bolted to their respective

fixation points on the engine and chassis. After some indecision on how the right

side upper half of the differential mounting bracket was to be attached to the engine,

a spot face was machined and a through bolt was used to attach it. As for the left

side upper half of the differential mounting bracket, slots were machined into thetop to allow for some adjustability for and aft. This is to adjust for chain alignment.

The table below shows the hardware list associated with the assembly.

Table 1: Hardware List

Callout Qty

Bolt NAS1104-1 4

Bolt NAS1306-11 2

Bolt NAS1305-14 2

Dowel MS16555-653 1

K-Nut KFN542-6 2

K-Nut KFN542-5 2Washer AN960-416 4

Washer AN960-616 2

Washer AN960-516 2

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Figure 6: Left Side Differential Mounting Bracket

Figure 7: Right Side Differential Mounting Bracket

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4. Cost

As per the Formula SAE rules, a cost table has been created for the

manufacturing and assembly of the differential mounting brackets. Below is a table

that outlines the cost of each part. The actual cost report table for each part of theassembly will be provided in the appendices.

Table 2: Differential Mounting Bracket Cost

Part Material Material Cost Process Cost Q uantity Total Cost

Bearing Mount Cap Aluminum $1.34 $4.96 2 $12.60

Left Mounting Bracket Aluminum $2.12 $8.82 1 $10.94

Right Mounting Bracket Aluminum $5.44 $18.62 1 $24.06

Total $47.60

5. Testing

When finite element analysis was performed, the spot face was not modeled.

After testing, the bracket started to show a fracture starting at the sharp edge of the

spot face and propagating toward the opposite side. An alternative way to mount the right side mounting bracket could have saved the part from fracturing. In order

to get the bracket ready for further testing and ultimately competition, 1/8-inch

Aluminum gussets were welded to strengthen the affected area.

Figure 8: Spot Face Fracture

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Figure 9: Spot Face Fracture

7. Conclusion

The primary goal was to design, manufacture, and test the differential

mounting brackets. All of these goals have been met. The design and

implementation of the differential mounting brackets met all the functional

requirements. Improvements can be made to this design after further testing.

A concept was created with the design constraints in mind. The differential

mounting brackets located the differential so that the driven sprocket face and the

drive sprocket face were parallel to each other. The differential mounting brackets

allowed the differential to spin freely. The differential mounting brackets weredesigned to accommodate 80mm nominal bearing diameter as well as a bearing fit

tolerance. The differential mounting brackets allowed for ease of removal of the

differential from the car. The right side differential mounting bracket incorporated

an inboard brake caliper mount. Finite element analysis was completed with the use

of Dassault Systems SolidWorks Simulation. Both right and left side differentialmounting brackets were found to be within the stress requirement of a factor of

safety of 1.8.

Manufacturing was partly done in-house and outsourced. The left and right

side upper halves of the differential mounting brackets were outsourced to DonSchumacher Racing. The differential bearing caps were completed in-house using a

CNC mill and CAD CAM software.

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The differential mounting brackets were tested. The spot face was found to

be a point of high stress due to a sharp corner. Another way of mounting the right side differential mounting bracket could have been found with more assembly time.

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