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McMaster University

Mini Baja Team

2008 Baja SAE Montreal Competition

Vehicle # 53

Technical Design Report


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#53

McMaster University Mini Baja Technical Design Report

Matt GreenMcMaster University

Copyright 2007 SAE International

ABSTRACT

The Society of Automotive Engineers sponsors anannual engineering design competition that challengesstudents from various colleges and universities todesign, construct, and race an off-road Mini Baja vehiclewith enough speed and agility to be capable of enduringvarious terrains. This year, the McMaster University MiniBaja Team has chosen to participate in the 2008 SAEBaja Montreal competition, hosted by Ecole deTechnologie Superieure in Montreal, Quebec, Canada.This competition requires each team to build a Mini Bajavehicle that fulfills both static and dynamic requirementsas outlined by SAE. Additionally, each team must submitan analysis of their unique design in the form of atechnical report.

INTRODUCTION

In 2007 the McMaster University Mini Baja Teamcompeted for its first time in over two decades. With noprevious information to pull from the newly formed team

started from scratch designing early 2006. In order tomake-up for the inexperience and hope to competeseveral trade-offs were made. The team focused onpurchasing prefabricated parts, purchasing the majorityof its suspension parts. The teams primary focus wasplaced on completed the endurance race, of which it wasable to succeed and place 33

rdin the endurance race at

the 2007 SAE Baja Midwest competition.

This year the McMaster Mini Baja Team will becompeting for only its second time. The rules of thecompetition state that no component of the Baja car canbe greater then two years, provided that at least one

major modification is made. This is going to allow us tofocus on one major modification while reusing a largeportion of our existing components. It was decided thatthe rear suspension redesign would be the primaryfocus. However this required the modification of our rearframe, which allowed us to improve upon several factorssuch as accessibility, performance, and appearance. Theteam has also focused on producing a more wellrounded vehicle using all of the experience that wasgained the year before.

VEHICLE DESIGN

As stated above the primary focus of this years design isthe redesign of the rear suspension. This resulted inmodifications to the rear portion of the frame as well asrearranging the drive train of the vehicle. Several othersystems have been improved upon as well and arereviewed first such as the pedal assembly and steeringgeometry. All the systems and components have beendesigned to comply with the rules and guidelines set outin the 2008 Baja SAE Competition Rules.

Figure 1: 2008 McMaster Mini Baja Model

BRAKING SYSTEM - The objective of the brakingsystem is to safely stop the vehicle. It is required tostatically and dynamically lock all four tires on both hard

and loose surfaces. Although the previous designworked effectively it was decided that modification of ouprevious pedal assembly was necessary in order toimprove the braking adjustability and simplify our pedaassembly and mount. Upon further investigation into theways in which the brake bias can be modified, the onechoice that fits the application of off-road use and allowsfor easy adjustment with little time and work is the brakebalance bar assembly. The operation of the balance barelies on the premise of the ability to change the ratio towhich the master cylinders are depressed depending onthe required application. It is effectively an adjustablelever via a threaded rod that moves the clevis that attach


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to the master cylinders. The rotation about a sphericalbearing that separates the two master cylinders (frontand rear) allows for this pivot. Turning the threaded rodallows for adjustment of where the two cylinders are withrespect to the central axis, to achieve a different ratio ofcompression when the brake pedal is depressed. Whenthe balance bar is centered, it pushes on both cylindersequally, and when adjusted to maximize the differencebetween the two cylinders, it pushes approximately twiceas hard on one cylinder as compared to the other.

Instead of buying a commercially available balance bar, itwas decided that for this application fabricating a customone to fit into our application would be more suitable andallow for ease of installment and maximize functionality.The ability to easily adjust our brake bias would allow fora broader application use of the vehicle, where it may bedesirable to have one set of tires lock-up before theothers. This addition to the pedal assembly will replacethe current set-up, which involves one master cylinderthat is at a fixed ratio with respect to the pedal ratio, andthe other which is adjustable via the track it is mountedto on the pedal. This took time to tune so that all tireslocked up at the same time. The balance bar will ease

the tuning transition from one surface to another, andmake for a more stable and user-friendly brake systemand pedal assembly.

DRIVE TRAIN With a common engine amongst allcompeting teams, a lot of emphasis had to be placed onthe design of the drive train. The objective of the drivetrain is to transfer power from the engine to the wheels.In order to satisfy all of the requirements the drive trainhad to optimize several desired characteristics to ensureadequate power was provided during all of themaneuvers and most importantly an enjoyable and trillingride. Items considered included towing capacity,acceleration, top speed, and durability. If possible, adesign that would allow a forward, neutral and reversegear was also desired.

Overview of Previous Design In keeping with the goalsof this years design the majority of the design of the drivetrain remained the same as the previous vehicle. All ofthe components from the previous year are beingreused. However, the arrangement is being modified inorder to improve the overall design. The engineperformance and setup remains the same with therequirement that it is governed to 3800rpm. Theperformance of the previous design was very goodmeeting all expectations. The same Comet 770 was

used as this CVT (continuously variable transmission)was very effective at maintaining power when climbinghills and towing, while offering competitive acceleration.Other advantages of the CVT also include its use as aclutch allowing the engine to power up to a sufficienttorque level. The Volkswagen transaxle was reused as itoffered excellent durability as well as offered a forward,neutral, and reverse gear. The availability of a reversegear proved very useful in tight quarters. Also since therear suspension is reusing the same wheel hub andbearing carriers it made sense to reuse the same driveshafts mated to the transaxle with the custom mate plateconstructed in the previous year. The durability gained

from using shafts and gears after the CVT is stilbelieved to outweigh the benefits such as adjustabilityand lower weight of a chain and gear system.

Shortfalls of Previous Design Due to the configurationof the previous years suspension, which utilizedindependent A-arms, the transaxle had to be mountedvertically. The CVT was then places horizontally asplacing it vertically would have severely raised the centeof gravity of the car and made refueling difficult. It couldnot be placed on an angle, such as 45 degrees backtowards the firewall as the base plate for the enginewould have caused interference. This arrangemenpresented two challenges. First, the guard for the CVTwas from Polaris and needed to be modified because theshock interfered with the cover. A section needed to beremoved and patched with a metal plate. Secondly, andone of the main reasons for this years modifications, isthat having the transaxle in the vertical orientation madeit very difficult to access because the engine andsuspension were in the way and had to removed firstThis means that the drive trains ease of serviceabilitywould be very low. All these factors became the basis fo

redesigning the layout of the vehicles drive train.

Modifications The layout of last years vehicle has thetransaxle vertical with the CVT running horizontal fromthe engine. As preciously discussed this caused severaproblems. This year it was decided to rearrange the drivetrain and place the transaxle horizontal and run the CVTin the vertical. The first advantage from having thetransaxle horizontal is it allowed the engine, which is thesingle heaviest item besides the driver, to be lowered twoinches resulting in a lower center of gravity. This lowercenter of gravity will increase stability during corneringlowering the chances of a roll over. With the CVT running

in the vertical it also removes the problem of lowaccessibility due to the close proximity to the suspensionand drive shafts. Maintenance can be done easily on theentire drive train now by removing the bolts, CVT guarddriven pulleys, and CV shafts. The transaxle can easilybe rotated out and the engine and shocks can be lefcompletely in place. The main goal of the framemodifications was to triangulate the rear members of theframe. This was previously not possible due to theplacement of the CVT guard. These modificationscombined with the changes in the rear portion of theframe and rear suspension resulted in greatly improvedaccessibility. For further details please refer to thesesections; REAR SUSPENSION, FRAME.

Shifter Re-Design The objective of the shifter is tocreate a reliable Forward-Neutral-Reverse shifter that wilnot damage the shifter cable and will remain in theoperators intended gear. The shifter needs to give aminimum of 2 travel on the shifter cable. The motion othe shifter cable must be linear to reduce damage andunnecessary stresses on the cable. In order to satisfy thecustomer requirements it must be easy to switch gearswill not accidentally shift gears, and will not break undepredicted usage. The primary alternative was to fabricatea linear shifter that would have 3 locking positions usinga spring to maintain the shifter in gear. The secondary


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alternative was to recreate the old shifter design using alarger gauge of shifter cable. The previous years designfailed to stay in the desired gear during the extremeimpact when landing a jump. It required the driver tooften hold the shifter during landing. This resulted inadded stress on the push pull cable, which resulted in itseventual failure after the competition. It also addeddistraction for the driver by having to move one hand tothe shifter occasionally. The design chosen was topurchase a Push/Pull Toggle Clamp from McMaster-

Carr, which provides a linear cable motion and hasexactly 2 of travel. The shifter is self-locking on eitherside of the travel meaning it will not come out of gearaccidentally like the previous years design. The strengthof the push pull cable was also increased to try andmake it more durable as well as to provide a smoother,stiffer shift.

ELECTRONICS The electrical system consists of thebattery, speedometer, reverse light, and reverse alarm. Itmust be designed to be safe, durable, and easy to use.

Battery The objective is to have a battery that will

power all the electrical systems in the car. The batterymust be able to power the reverse light and alarm as wellas the brake light. The batteries must be sealed and notleak in the event of a vehicle roll over. Two possibilitieswere examined. First is what was used last year, two 6volt 10 amp hour alkaline batteries. Secondly is a sealedlead acid 12-volt, 4-amp hour battery. The sealed leadacid battery was chosen over the traditional alkalinebattery that was used in last years design are; first thatthe new battery has the ability to be recharged; second isthat one 12 volt battery replaces two 6 volt batteries inseries. Both batteries will not spill if they are inverted,and both meet the amperage requirements of the car.

Current drawn by all electrical devices was measured,and was found to be 0.25 amps. Therefore the battery iscapable of providing constant power for 16 hours. Thismore than exceeds the maximum duration of any SAEcompetition as well as recreational use as it can becharged once daily. The battery will be mounted directlyto the frame in front of the engine just behind the firewall.It will be placed in a standard outdoor electrical box thatconsists of a sealed plastic box in order to protect it fromthe mud and water the car is exposed to.

Speedometer The objective of the speedometer is tohave a system in place that can display speed and ridetime. The system must be able to handle the rough

conditions that exist on the Mini Baja track such aswater, mud, sand, rocks, and generally rough terrain.The speedometer must be able to record speeds of up to50 km/h. Several alternatives were examined. First wasa traditional car speedometer. These setups would beable to withstand the harsh terrain but were too large,expensive and bulky for use in such a small vehicle.Second was a bicycle speedometer, which was cheapand capable of recording both speed and runtime.However they are not designed to handle the toughoperating conditions that will be encountered. The finalalternative is an ATV style computer speedometer. Thischoice incorporated all the good features of each of the

previous alternatives, it was cheap and capable odisplaying all the information required, and it wascapable of handling the operating conditions. The unitselected was a Trail Tech endurance model ATVcomputer. The unit comes complete will all the cablesand sensors necessary to install the computer. Lasyears car did not have a speedometer and a simplestopwatch was used as a ride timer. The improvementsare that the driver is now capable of monitoring speed aswell as ride time easily. The system will be mounted in

the cockpit right in front of the steering wheel. It is alocation where it will be safe from damage in the event oa rollover, and where it can be clearly seen by the driver.

Reverse Light and Alarm The objective of the reverselight and alarm is to inform nearby vehicles andpedestrians of the intent to backup. Each vehicle withreverse must have a backup light marked with a SAE Ron the lens or exceed the SAE standard. The alarm musalso be rated per SAE standard J1741. The alarm ismounted and activated the same as the previous designwith a mechanical lever depressing an electrical switchthat activates the alarm and light.

FRAME In keeping with the goals for this years designapproximately half of the frame is reused from theprevious year. The main changes in the construction othe frame include triangulating the rear supports with thefront of the car and changing the suspension and enginemounts to accommodate the new design. The frame hasbeen designed to carefully meet all requirements outlinedin the 2008 Baja SAE Competition Rules.

Materials Overview The existing steel members aremade up of two schedules of one inch, 1018 class steetubing. This was chosen for ease of manufacturing and

cost. The new sections of the frame are also constructedwith this material, as it will allow for easy fabrication andjoining of the new sections. The two schedules arerequired to ensure a proper and safe roll cage made outof the thicker tube whereas other frame members can bethinner to reduce weight.

Frame Modifications The majority of the framemodifications are behind the firewall. The only framemodification in the front and cockpit of the car is theremovable of two redundant support beams since therear of the car is now triangulated making themunnecessary. The removable of these members makesfor a better appearance by simplifying the front as well as

improving visibility for the driver. Another advantage oftriangulated the back bracing of the car is for greatlyimproved accessibility to the drive train and engine. Itwas designed in order to minimize intruding member byplaced the suspension supports around the outer edgeThis is greatly improved over last years design that hadthe problem of having to remove the suspension to get athe drive train and engine. The new design is also muchlighter. The addition engine members were removedThe rear suspension mounts are also much light. This isfurther outlined under REAR SUSPENSION.


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Figure 2: Frame Modifications: Rear

BODY DESIGN The objective of the body is to providethe vehicle with a strong but good-looking finish. Thisyear the body will be constructed of fiberglass and plasticin order to give the vehicle a new look that will beappealing to us and able to withstand the abuse of anoff-road vehicle as these materials dont rust and requireminimal maintenance. The plastic and fiberglassconstruction was chosen over aluminum sheetingbecause it will reduce noise as it will not produce soundwhen the body panels are attached to the car. Theprevious design utilized a sheet metal body panel that

produced excessive noise due to the vibrations of thecar. Fiberglas also has the property of absorbing energyvery well, which will help to protect the operator. The newfiberglass and plastic design will help to provide thedriver with a safer vehicle, increase the attractiveness ofthe car and decrease the noise produced by the vehiclebody panels.

STEERING The objective of the steering system is toprovide a reliable method for controlling the direction ofthe vehicle that is capable of withstanding the high stressplaced on it. There are no direct requirements for thetype of steering method used or how sharp you must be

able to turn. However there is a safety specification thatrequires all tie rods to be protected from a frontal impact.The majority of the steering components and setup fromthe previous is remaining the same. Previously an eleveninch, eye-to-eye, rack and pinion was used. This workedvery well, providing the necessary range and was verydurable as it was a purchased component designed forsand rails. The car was able to compete all maneuversduring competition. However the goal of the steeringmodifications is to correct the Ackerman geometry. Thiswill allow for tighter, more aggressive turning.

Ackerman Geometry The Ackerman concept is to haveall four wheels of a vehicle rolling around a commonpoint during a turn. This requires that the inside tire beturning at a tighter radius then the outside tire as shownin Figure 3: Ackerman Concept. This geometry transfersthe weight to the inside front tire causing the inside reatire to have lower contact force. This then allows for thekart to turn into a corner instead of trying to push straighahead.

Figure 3: Ackerman Concept

Steering Correction The previous steeringconfiguration had an improper Ackerman geometry. Thefront wheels were turning more parallel to each othethen having the inside more tightly turned. On losesurfaces this could be overcome by sliding the cornehowever on stickier surfaces such as grass and concreteif was harder to steer. This also would eventually result inincreased tire wear. To correct this effect the pivot poinbetween the steering upright on the wheel and the tie rodhad to be adjusted. Since we used the standard uprigh

and spindle from a 2003 Polaris Predator ATV it waseasiest to make an attachment for the steering uprightthat which would have the new pivot point. The correcpoint the pivot point needs to be was found by running astring from the center of the upright to the middle of therear drive shaft. Where the bracket intersected the planecreated by the string is where the new pivot point for thetie rod connection was made. This will now allow for amore aggressive steering and corning abilities resulted ina more responsive ride.

FRONT SUSPENSION The objective of the frontsuspension is to provide adequate shock absorption to

ensure comfort to the driver while maintaining a positivedownward force to keep the front wheels in contact withground. Without this proper contact force it would hindersteering giving the driver less control over the vehicleThe front suspension is maintained the same as theprevious years. It was found that the front suspensionpreformed to all expectations and therefore the focusshould maintain on the rear suspension redesignPrefabricated aluminum A-arms and uprights were usedfrom the 2003 Polaris Predator ATV. As this being onlythe teams second year of competition we thought thiswas the most reliable and cost effective design. Thesuspension is configured to offer eight inches of travel


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At full rebound there is a positive camber angle of 2degrees and 5 degrees regular camber at full jounce.This setup offered a comfortable ride to the driver andgood handling around corners and sloped ground. Theonly change to the front suspension is that new shockswere selected. As discussed in the REAR SUSPENSIONsection this was to accommodate the new design.However it was also decided that the front shocks alsobe replaced with the RYDEFX Air 2.0 in order to bettercontrol the rates over different stages giving us a more

desirable ride height while having a high top rate toprevent bottoming out. The shocks will be furtherexplained under REAR SUSPENSION, Shocks.

REAR SUSPENSION As previously mentioned thefocus for this years McMaster team was to redesign therear suspension. By modifying the rear suspension wealso incorporated the desired changes in drive train andframe. The objective of the rear suspension is to providea smooth ride as well as absorb the impact protecting theentire vehicle. The rear suspension in particles takes thebulk of the force as it has the most weight. Each rearwheel takes twice as much weight as each front wheel.

The rear axle is also the powered axle. Thereforemaintaining contact surface contact while moving overrough terrain is extremely important.

Design Change The previous rear suspension featuredunequal, independent A-arms. This design worked wellfor our first year of competition. However it is believedthat a three-link suspension system can improve overthis in several areas. First the large A-arms andmounting brackets were quite heavy. The new rear endwith have a lower weight moving the center of gravitytowards the front of the car offering better handlingcharacteristics. The three-link system will also offer a lot

of spatial freedom for the rear drive train with themodified frame. A primary concern with the previousdesign was the A-arms brackets and shock placementmaking the drive train difficult to access. The newsuspension will also offer a greater range travel. Thevertical wheel travel will be increased from the previouseight inches to ten inches. This will offer a smoothermore forgiving ride. Finally the incorporation of a swaybar into the rear suspension will help to reduce body roll.

Design Criteria

1. The existing CV shafts and transaxle will be used.2. The three links have to join to the existing wheel hub.

3. The existing coil-strut has a travel of five inches.

Design Analysis In order to satisfy the threeconstraints, it is important to consider the optimaldistance between the transaxle and the hub, becausedeviating from the optimal distance greatly reduces therange of bending available in the CV shaft. This is turncauses a reduction in the maximum attainable verticaltravel range of the wheel.

Figure 4: CV Shaft Angles

From the above figure one can see that when the shaft isat its maximum lengths it has a much larger bendingrange than at the minimum lengths. Because of this, therear links of the suspension are set to be 12.5 incheslong. Also if the coils are mounted in the center of the toprear link, 10 inches of wheel travel can be obtained while

maintaining the CV shaft length and angle constraints, incomparison to last years 8. The coil position informationis used in conjunction with the critical impact calculationsto determine the best spring rate for our suspension.

The results that optimize the design could be provided byan equivalent spring constant of 185 lbs/in (if the coil wasmounted at the hub). Therefore, the coil for this designwould need a spring rate of 370 lbs/in, as its positionhalfway up the rear link would reduce its effectiveconstant at the wheel to half. Due to financiaconsiderations, a commercially available coil is neededso a spring rate of 375 lbs/in and 12 inches long (lengthto fit the mounting constraints) was chosen.

From there, the best relative position and spacingbetween the two links to get the best camber angle wasiterated. Because the spring stiffness and the mass ofthe car are known, the springs compression at rideheight of the coils can be determined. The ideal camberangle at ride height is zero degrees, as this is theequilibrium position when driving forward. The desiredturn position of the wheel is when the outer rear wheeeffectively takes 2 times its usual weight during a turn(taken from the inner rear wheel). Small changes incamber angle at positions other than ride height arenegligible because of the soft tire. Some justification for

this is given towards the end of the report when furtherplans in designing the sway bar are discussed.

Relative rear link mounting positions were variedhorizontally (the offset) and vertically between the twolinks (distance apart). Using AutoDesk Inventoriterations are presented below in Table 1. The goal othese iterations is to maximize tire to road surfacecontact, which occurs when the tire is exactlyperpendicular to the road. This goal is satisfied at: zerodegree camber angle at ride height, 2.99 degreescamber when suspension is compressed so that the tireis 1.3 inches above ride height, and finally to minimize


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camber angle at both topped and bottomed out wheelpositions. Rows were not completed in some cases ifthere was one or more unacceptable camber angles, orif was already evident that a previous setup was better.

Offset Distance Apart Ride Height Bottomed Out Topped Out Desired Turn

0.250 3.50 0.36 out 10.20 4.65

0.500 3.50 2.5 in 4.42

0.375 3.50 1.1 in 11.50 3.23 2.96

0.375 3.00 0.00 14.00 5.75 2.50

0.375 2.50 1.12 2.40

0.500 2.50 0.35 in 17.8 (too high)

Relative Position (inches) Camber angle (degrees)

Table 1: Camber Angles at Wheel Positions

It was determined from these iterations that the best rideheight would be with a 3/8 inch offset with 3 inchspacing. Spacing was limited to 3.5 inches or less aslarger spacing would result in a reduced available wheeltravel. Also, because it became evident that at a spacingof 2.5 inches the camber angle at the bottomed outposition were unacceptable, smaller spacing values werenot looked into, as these would only cause larger camberangles at that position.

Once this was done, all that remained was fitting this

geometry and the trailing arm onto the frame. The trailingarm, as opposed to commonly being on the outer edgeof the frame, was brought inwards so that the change intoe angle of the tire would be reduced over the verticalwheel travel, but without compromising the advantagesof the 3-link design. In addition, the top rear link wasangle back as opposed to being straight across from thehub to the nearest point of the frame so that it could bemounted vertically to the frame (when looking at the carfrom the side).

Figure 5: Vehicle Model: Rear Suspension View

Shocks As discussed above a new spring rate isrequired to meet the need design of the rear suspension.In order to meet the requirement the new RYDEFX Air2.0 shocks were selected. These cutting edge air shockswill allow for several factors to be improved. The shockshave three available stages that can be set at differentspring constants. These shocks will also be used for thefront suspension in order to maximize performance. Thefirst stage of the shocks is set quite soft allowing for thedesigned ride height and an even ride over smallinconsistencies in the surface. The second and longeststage has a higher spring constant and is effective whenthe shock comes under load such as a jump or turn.

Finally the last stage of the shock is set quite high inorder to prevent bottoming out. The main advantage othese shocks is there large amount adjustability allowingfor the suspension to be fine-tuned to various drivingconditions and any future modification to the vehicle.

Figure 6: Rear Suspension Assembly

Stress Analysis Various stress calculations wereconducted on the need rear suspension elements. Thisis to ensure that the new design will be able to withstandthe loads placed on it during operation.

Trailing Arm The trailing arm needs to be designed tohandle the forces from a maximum of 50 km/h forwardimpact onto the rear tire which will impose a tensile forceon the trailing arm. The calculations for by be made byassuming that the trailing arm will experience 1/3 of thefull kinetic energy from a forward motion crash.

To determine if the available tubes (sizes 1 x (0.083 or0.120) thickness) are safe, the energy absorbed per univolume needs to be determined then percent elongationcan be found to see if this elongation is within theallowable range. An acceptable limit is assumed to beless 10% where too much change in suspension

geometry would occur.

From this, the equivalent force can be approximated andused for the purchase of commercially availablecomponents again by linear interpolation. Thecalculations for the above can be viewed in. Thecalculations concluded that the design is acceptableusing 1018 mild steel tubes 1 in diameter by 0.120 walthickness with a 6% elongation assuming that 1/3 of theenergy from impact is absorbed by one trailing arm.


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If 100% of the energy is to be transferred into the trailingarm, the maximum speed to survive an impact is30km/h.

( ) ( )

hkmv

vmhkmm

/30

2

1/50

2

1

3

1

max

2

max

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The use of a 1/8 thick by 5 long 1018 steel gusset willbe used to secure both tubes together on the trailingarm. To determine if the gusset design on the trailingarm is appropriate given the equivalent forces and theavailable weld electrode E7010, the trailing arm neededto be simplified from slightly angled welds on the gussetto a problem of torsion stress on a parallel weldedmember.

Rear Links Calculations were done to determine theeffects of horizontal impact on the rear links of thesuspension in cases if the car catches a rear wheel on astationary object (such as a tree stump) at a velocity of50 km/h. This is in a sense a continuation of the stressanalysis discussed in the previous section on the trailingarm, as the same impact load on the tire is used. Thecalculations conclude that with a factor of safety of 3,either type of tubing that we currently have available ismore than sufficient to withstand the load of impact.For the upper rear link, a 1-inch outer diameter ispreferred. However, analysis done by hand according tobending beam theory showed that any tube of 1 in outerdiameter, regardless of wall thickness would fail. Thus anew geometry with a 1 inch outer diameter and inchinner diameter and a large bracket would be exported toan FEA analysis in AutoDesk Inventor, developed byAnsys. This new design would prove too elaborate to

analysis by hand. FEA results showed that the lowestfactor of safety is 1.18 and proves that it would not fail.

Thread Engagement The minimum threadengagement length was calculated using the followingformula:

Engagement length =( )

( )pD

At

664952.05.0

2

)

The values for the variables in the equations above are

found for a given commercially available thread size suchthat minimum engagement length can be found. Fromthis calculation, the minimum engagement length of thethreads for the threaded rod ends is 0.3213 inches.

SWAY BAR The rear sway bar is intended to maintainthe rear wheels at equal heights throughout all drivingconditions. In maintaining the rear wheels at equivalentheights, the bar will reduce body lean by increasing thevehicles total roll stiffness. Increasing the rearsuspensions roll stiffness will consequently help to keepthe inside rear wheel from lifting off the groundthroughout a corner for greater traction. The other

primary goal is to limit the amount of under-steer byincreasing the total vehicle roll stiffness hence loweringthe rear wheel to run at a higher slip angle than the fronwheel. The customer requires better handling in turns toimprove overall lap times. Fine tuning the rearsuspension by changing geometries is the besalternative to a rear sway bar to increase total rolstiffness and help prevent under-steer. The caveat tosuch a solution is that the trial and error of creatingseveral different suspensions can be a lengthy process.

Sway Bar Comparison In order to accurately examinethe advantages of the sway bar incorporated into the rearsuspension two sets of body roll calculations wereconducted.

Body Roll Calculation without sway bar - The body rollangle will be the angle of the car reached when it isabout to roll over (on a turn at 0.8 gs). In this case, it isassumed that the inner tire is not taking any weight (it isabout to roll, therefore the inner wheel is about to lift offthe ground), and so the outer tire will take twice theweight as it would in the ride height position.

Because the rear wheels take twice as much weight asthe front wheels, the outer rear wheel will take two thirdsof the total weight of the car when it is about to roll.(2/3*781 lbs = 521 lbs). At this point, the outer wheel willrise 5.5 inches above topped-out position (kspring = 375lbs/in), while the inner wheel (feeling no weight from thecar) will be at topped out position. The centre-to-centredistance of the two rear wheels is 46 inches, so usingsimple trigonometry, a 5.5 inch difference in heightbetween the two wheels translates to 6.8 degrees ofbody roll (tan

-15.5/46). At a 5.5 inch compression, the

camber angle of the rear wheel will be about 3 degrees.The camber angle of the outer wheel on such a turnshould be equal to the body roll so that the outer wheelsits flat on the ground to provide maximum surfacecontact and maximum traction. Therefore, the body rollangle at 6.8 degrees and the camber of 3 degreeswithout a sway bar is a poor combination.

Figure 7: Turn Body Roll without Sway Bar


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Body Roll Calculation with sway bar The desiredspecifications for the sway bar are achieved throughiteration. A smaller body roll requires a smaller rise in theouter rear wheel during a turn, which is iterated to be 4inches (as opposed to 5.5 inches without sway bar). Toachieve this smaller compression, the equivalent springcoefficient has to be increased to 521 lbs/in. Theequivalent spring setup will be such that the suspensionof the outer wheel will be in parallel with the sway barand suspension of the inner wheel. Solving for the

required spring coefficient of the sway bar gives 250lbs/in, and under a 4-inch compression of the outer rearwheel, the inner rear wheel will compress 1.6 inches.This gives a height difference between the two wheels of2.4 inches, and a body roll angle of 2.99 degrees. Whenthe outer wheel is compressed 4 inches, the resultingcamber angle is 2.5 degrees, so the difference betweenthe body roll angle and the camber is half a degree.Reiterating to find a smaller angle difference is notnecessary, because with the tools that we have to buildthis rear suspension, we will not be able to machine thedesign at any higher level of precision anyway. Addingthe sway bar can reduce the body roll angle by half on a

turn of 0.8 gs, and can substantially reduce thedifference between the body roll angle and the camber,providing more traction between the outer rear wheel andthe ground on sharp turns.

Figure 8: Turn Body Roll with Sway Bar

Figure 9: Spring Diagram for Rear Suspension

Sway Bar Construction The rear sway bar assemblyconsists of a diameter 4140 steel rod 31 in lengthwith a keyway machined on either side. The primaryfunction of the 31 rod is to twist when the wheels moverelative to each other. The arms of the sway bar areconstructed from 1 square steel tubing, which isattached to the steel rod by a welded insert with akeyway. The end links consist of two rod endsconnected by a 6 long female threaded link. The bottomrod ends connect the sway bar to the rear suspension by

mounts. The required diameter rod was calculatedusing a max angle of twist of 9, and 150ft.lbs or torque.

Figure 10: Sway Bar Assembly

CONCLUSION

When undertaking any design project there are severafactors to be considered that are common to alengineering projects. A project must have a propescope with clearly defined goals. The goal of this yearsteam was the redesign of the rear suspension. This in

turn allowed for improvements of the drive train andframe. The drive train became much more accessiblewith was the biggest problem with the vehicle in theprevious year. Second the frame could be triangulatedThis not only improved its strength but also itsappearance. The car has a much more clean andsymmetry look. The team was also able to improve uponalmost every other system in the car. Theseimprovements were made possible from the experienceand lessons learned during the pervious year ofcompetition. It is hoped that this years vehicle is able tooutperform the previous years vehicle in every way. Themore responsive suspension and aggressive steering wil

make for a more competitive vehicle. It is also hoped thathe performance and reliability of several other systemshas been improved such as the new pedal assemblyFinally the McMaster Mini Baja Team hopes that theheightened appearance of this years car, along with itsimproved performance will make it a more noticeablecompetitor at this years competition.


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ACKNOWLEDGMENTS

The team would like to recognize the continuing supportof Dr. Tim Nye, the McMaster Engineering Society, andthe McMaster Engineering Faculty, allowing us tocontinue on for a second consecutive year ofcompetition.

REFERENCES

1. Rai, Singiresu, Mechanical Vibrations, FourthEdition

2. Budynas, Nisbet, Shigleys Mechanical EngineeringDesign, Eight Edition.

3. Ackerman Steering Geometry.http://en.wikipedia.org/wiki/Ackermann_steering_geometry.

CONTACT

Matt GreenMechanical Engineering & Coop, Level 4 of 5McMaster [email protected]

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