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McMaster University Mini Baja Team
2008 Baja SAE Montreal Competition Vehicle # 53
Technical Design Report
#53
McMaster University Mini Baja Technical Design Report
Matt Green
McMaster University
Copyright © 2007 SAE International
ABSTRACT
The Society of Automotive Engineers sponsors an annual engineering design competition that challenges students from various colleges and universities to design, construct, and race an off-road Mini Baja vehicle with enough speed and agility to be capable of enduring various terrains. This year, the McMaster University Mini Baja Team has chosen to participate in the 2008 SAE Baja Montreal competition, hosted by Ecole de Technologie Superieure in Montreal, Quebec, Canada. This competition requires each team to build a Mini Baja vehicle that fulfills both static and dynamic requirements as outlined by SAE. Additionally, each team must submit an analysis of their unique design in the form of a technical report.
VEHICLE DESIGN
As stated above the primary focus of this years design is the redesign of the rear suspension. This resulted in modifications to the rear portion of the frame as well as rearranging the drive train of the vehicle. Several other systems have been improved upon as well and are reviewed first such as the pedal assembly and steering geometry. All the systems and components have been designed to comply with the rules and guidelines set out in the 2008 Baja SAE Competition Rules.
INTRODUCTION
In 2007 the McMaster University Mini Baja Team competed for it’s first time in over two decades. With no previous information to pull from the newly formed team started from scratch designing early 2006. In order to make-up for the inexperience and hope to compete several trade-offs were made. The team focused on purchasing prefabricated parts, purchasing the majority of its suspension parts. The team’s primary focus was placed on completed the endurance race, of which it was rd able to succeed and place 33 in the endurance race at the 2007 SAE Baja Midwest competition. Figure 1: 2008 McMaster Mini Baja Model This year the McMaster Mini Baja Team will be competing for only it’s second time. The rules of the competition state that no component of the Baja car can be greater then two years, provided that at least one major modification is made. This is going to allow us to focus on one major modification while reusing a large portion of our existing components. It was decided that the rear suspension redesign would be the primary focus. However this required the modification of our rear frame, which allowed us to improve upon several factors such as accessibility, performance, and appearance. The team has also focused on producing a more well rounded vehicle using all of the experience that was gained the year before. BRAKING SYSTEM - The objective of the braking system is to safely stop the vehicle. It is required to statically and dynamically lock all four tires on both hard and loose surfaces. Although the previous design worked effectively it was decided that modification of our previous pedal assembly was necessary in order to improve the braking adjustability and simplify our pedal assembly and mount. Upon further investigation into the ways in which the brake bias can be modified, the one choice that fits the application of off-road use and allows for easy adjustment with little time and work is the brake balance bar assembly. The operation of the balance bar relies on the premise of the ability to change the ratio to which the master cylinders are depressed depending on the required application. It is effectively an adjustable lever via a threaded rod that moves the clevis’ that attach
to the master cylinders. The rotation about a spherical bearing that separates the two master cylinders (front and rear) allows for this pivot. Turning the threaded rod allows for adjustment of where the two cylinders are with respect to the central axis, to achieve a different ratio of compression when the brake pedal is depressed. When the balance bar is centered, it pushes on both cylinders equally, and when adjusted to maximize the difference between the two cylinders, it pushes approximately twice as hard on one cylinder as compared to the other. Instead of buying a commercially available balance bar, it was decided that for this application fabricating a custom one to fit into our application would be more suitable and allow for ease of installment and maximize functionality. The ability to easily adjust our brake bias would allow for a broader application use of the vehicle, where it may be desirable to have one set of tires lock-up before the others. This addition to the pedal assembly will replace the current set-up, which involves one master cylinder that is at a fixed ratio with respect to the pedal ratio, and the other which is adjustable via the track it is mounted to on the pedal. This took time to tune so that all tires locked up at the same time. The balance bar will ease the tuning transition from one surface to another, and make for a more stable and user-friendly brake system and pedal assembly. DRIVE TRAIN – With a common engine amongst all competing teams, a lot of emphasis had to be placed on the design of the drive train. The objective of the drive train is to transfer power from the engine to the wheels. In order to satisfy all of the requirements the drive train had to optimize several desired characteristics to ensure adequate power was provided during all of the maneuvers and most importantly an enjoyable and trilling ride. Items considered included towing capacity, acceleration, top speed, and durability. If possible, a design that would allow a forward, neutral and reverse gear was also desired. Overview of Previous Design – In keeping with the goals of this years design the majority of the design of the drive train remained the same as the previous vehicle. All of the components from the previous year are being reused. However, the arrangement is being modified in order to improve the overall design. The engine performance and setup remains the same with the requirement that it is governed to 3800rpm. The performance of the previous design was very good meeting all expectations. The same Comet 770 was used as this CVT (continuously variable transmission) was very effective at maintaining power when climbing hills and towing, while offering competitive acceleration. Other advantages of the CVT also include its use as a clutch allowing the engine to power up to a sufficient torque level. The Volkswagen transaxle was reused as it offered excellent durability as well as offered a forward, neutral, and reverse gear. The availability of a reverse gear proved very useful in tight quarters. Also since the rear suspension is reusing the same wheel hub and bearing carriers it made sense to reuse the same drive shafts mated to the transaxle with the custom mate plate constructed in the previous year. The durability gained
from using shafts and gears after the CVT is still believed to outweigh the benefits such as adjustability and lower weight of a chain and gear system. Shortfalls of Previous Design – Due to the configuration of the previous year’s suspension, which utilized independent A-arms, the transaxle had to be mounted vertically. The CVT was then places horizontally as placing it vertically would have severely raised the center of gravity of the car and made refueling difficult. It could not be placed on an angle, such as 45 degrees back towards the firewall as the base plate for the engine would have caused interference. This arrangement presented two challenges. First, the guard for the CVT was from Polaris and needed to be modified because the shock interfered with the cover. A section needed to be removed and patched with a metal plate. Secondly, and one of the main reasons for this years modifications, is that having the transaxle in the vertical orientation made it very difficult to access because the engine and suspension were in the way and had to removed first. This means that the drive train’s ease of serviceability would be very low. All these factors became the basis for redesigning the layout of the vehicle’s drive train. Modifications – The layout of last year’s vehicle has the transaxle vertical with the CVT running horizontal from the engine. As preciously discussed this caused several problems. This year it was decided to rearrange the drive train and place the transaxle horizontal and run the CVT in the vertical. The first advantage from having the transaxle horizontal is it allowed the engine, which is the single heaviest item besides the driver, to be lowered two inches resulting in a lower center of gravity. This lower center of gravity will increase stability during cornering, lowering the chances of a roll over. With the CVT running in the vertical it also removes the problem of low accessibility due to the close proximity to the suspension and drive shafts. Maintenance can be done easily on the entire drive train now by removing the bolts, CVT guard, driven pulleys, and CV shafts. The transaxle can easily be rotated out and the engine and shocks can be left completely in place. The main goal of the frame modifications was to triangulate the rear members of the frame. This was previously not possible due to the placement of the CVT guard. These modifications combined with the changes in the rear portion of the frame and rear suspension resulted in greatly improved accessibility. For further details please refer to these sections; REAR SUSPENSION, FRAME. Shifter Re-Design – The objective of the shifter is to create a reliable Forward-Neutral-Reverse shifter that will not damage the shifter cable and will remain in the operator’s intended gear. The shifter needs to give a minimum of 2” travel on the shifter cable. The motion of the shifter cable must be linear to reduce damage and unnecessary stresses on the cable. In order to satisfy the customer requirements it must be easy to switch gears, will not accidentally shift gears, and will not break under predicted usage. The primary alternative was to fabricate a linear shifter that would have 3 locking positions using a spring to maintain the shifter in gear. The secondary
alternative was to recreate the old shifter design using a larger gauge of shifter cable. The previous years design failed to stay in the desired gear during the extreme impact when landing a jump. It required the driver to often hold the shifter during landing. This resulted in added stress on the push pull cable, which resulted in its eventual failure after the competition. It also added distraction for the driver by having to move one hand to the shifter occasionally. The design chosen was to purchase a Push/Pull Toggle Clamp from McMasterCarr, which provides a linear cable motion and has exactly 2” of travel. The shifter is self-locking on either side of the travel meaning it will not come out of gear accidentally like the previous years design. The strength of the push pull cable was also increased to try and make it more durable as well as to provide a smoother, stiffer shift. ELECTRONICS – The electrical system consists of the battery, speedometer, reverse light, and reverse alarm. It must 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 battery must be able to power the reverse light and alarm as well as the brake light. The batteries must be sealed and not leak in the event of a vehicle roll over. Two possibilities were examined. First is what was used last year, two 6 volt 10 amp hour alkaline batteries. Secondly is a sealed lead acid 12-volt, 4-amp hour battery. The sealed lead acid battery was chosen over the traditional alkaline battery that was used in last years design are; first that the new battery has the ability to be recharged; second is that one 12 volt battery replaces two 6 volt batteries in series. 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 is capable of providing constant power for 16 hours. This more than exceeds the maximum duration of any SAE competition as well as recreational use as it can be charged once daily. The battery will be mounted directly to the frame in front of the engine just behind the firewall. It will be placed in a standard outdoor electrical box that consists of a sealed plastic box in order to protect it from the mud and water the car is exposed to. Speedometer – The objective of the speedometer is to have a system in place that can display speed and ride time. The system must be able to handle the rough conditions that exist on the Mini Baja track such as water, mud, sand, rocks, and generally rough terrain. The speedometer must be able to record speeds of up to 50 km/h. Several alternatives were examined. First was a traditional car speedometer. These setups would be able 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 cheap and capable of recording both speed and runtime. However they are not designed to handle the tough operating conditions that will be encountered. The final alternative is an ATV style computer speedometer. This choice incorporated all the good features of each of the
previous alternatives, it was cheap and capable of displaying all the information required, and it was capable of handling the operating conditions. The unit selected was a Trail Tech endurance model ATV computer. The unit comes complete will all the cables and sensors necessary to install the computer. Last years car did not have a speedometer and a simple stopwatch was used as a ride timer. The improvements are that the driver is now capable of monitoring speed as well as ride time easily. The system will be mounted in the cockpit right in front of the steering wheel. It is a location where it will be safe from damage in the event of a rollover, and where it can be clearly seen by the driver. Reverse Light and Alarm – The objective of the reverse light and alarm is to inform nearby vehicles and pedestrians of the intent to backup. Each vehicle with reverse must have a backup light marked with a SAE ‘R’ on the lens or exceed the SAE standard. The alarm must also be rated per SAE standard J1741. The alarm is mounted and activated the same as the previous design with a mechanical lever depressing an electrical switch that activates the alarm and light. FRAME – In keeping with the goals for this years design approximately half of the frame is reused from the previous year. The main changes in the construction of the frame include triangulating the rear supports with the front of the car and changing the suspension and engine mounts to accommodate the new design. The frame has been designed to carefully meet all requirements outlined in the 2008 Baja SAE Competition Rules. Materials Overview – The existing steel members are made up of two schedules of one inch, 1018 class steel tubing. This was chosen for ease of manufacturing and cost. The new sections of the frame are also constructed with this material, as it will allow for easy fabrication and joining of the new sections. The two schedules are required to ensure a proper and safe roll cage made out of the thicker tube whereas other frame members can be thinner to reduce weight. Frame Modifications – The majority of the frame modifications are behind the firewall. The only frame modification in the front and cockpit of the car is the removable of two redundant support beams since the rear of the car is now triangulated making them unnecessary. The removable of these members makes for a better appearance by simplifying the front as well as improving visibility for the driver. Another advantage of triangulated the back bracing of the car is for greatly improved accessibility to the drive train and engine. It was designed in order to minimize intruding member by placed the suspension supports around the outer edge. This is greatly improved over last year’s design that had the problem of having to remove the suspension to get at the drive train and engine. The new design is also much lighter. The addition engine members were removed. The rear suspension mounts are also much light. This is further outlined under REAR SUSPENSION.
Ackerman Geometry – The Ackerman concept is to have all four wheels of a vehicle rolling around a common point during a turn. This requires that the inside tire be turning at a tighter radius then the outside tire as shown in Figure 3: Ackerman Concept. This geometry transfers the weight to the inside front tire causing the inside rear tire to have lower contact force. This then allows for the kart to turn into a corner instead of trying to push straight ahead.
Figure 2: Frame Modifications: Rear Figure 3: Ackerman Concept BODY DESIGN – The objective of the body is to provide the vehicle with a strong but good-looking finish. This year the body will be constructed of fiberglass and plastic in order to give the vehicle a new look that will be appealing to us and able to withstand the abuse of an off-road vehicle as these materials don’t rust and require minimal maintenance. The plastic and fiberglass construction was chosen over aluminum sheeting because it will reduce noise as it will not produce sound when the body panels are attached to the car. The previous design utilized a sheet metal body panel that produced excessive noise due to the vibrations of the car. Fiberglas also has the property of absorbing energy very well, which will help to protect the operator. The new fiberglass and plastic design will help to provide the driver with a safer vehicle, increase the attractiveness of the car and decrease the noise produced by the vehicle body panels. STEERING – The objective of the steering system is to provide a reliable method for controlling the direction of the vehicle that is capable of withstanding the high stress placed on it. There are no direct requirements for the type of steering method used or how sharp you must be able to turn. However there is a safety specification that requires all tie rods to be protected from a frontal impact. The majority of the steering components and setup from the previous is remaining the same. Previously an eleven inch, eye-to-eye, rack and pinion was used. This worked very well, providing the necessary range and was very durable as it was a purchased component designed for sand rails. The car was able to compete all maneuvers during competition. However the goal of the steering modifications is to correct the Ackerman geometry. This will allow for tighter, more aggressive turning. Steering Correction – The previous steering configuration had an improper Ackerman geometry. The front wheels were turning more parallel to each other then having the inside more tightly turned. On lose surfaces this could be overcome by sliding the corner however on stickier surfaces such as grass and concrete if was harder to steer. This also would eventually result in increased tire wear. To correct this effect the pivot point between the steering upright on the wheel and the tie rod had to be adjusted. Since we used the standard upright and spindle from a 2003 Polaris Predator ATV it was easiest to make an attachment for the steering upright that which would have the new pivot point. The correct point the pivot point needs to be was found by running a string from the center of the upright to the middle of the rear drive shaft. Where the bracket intersected the plane created by the string is where the new pivot point for the tie rod connection was made. This will now allow for a more aggressive steering and corning abilities resulted in a more responsive ride. FRONT SUSPENSION – The objective of the front suspension is to provide adequate shock absorption to ensure comfort to the driver while maintaining a positive downward force to keep the front wheels in contact with ground. Without this proper contact force it would hinder steering giving the driver less control over the vehicle. The front suspension is maintained the same as the previous years. It was found that the front suspension preformed to all expectations and therefore the focus should maintain on the rear suspension redesign. Prefabricated aluminum A-arms and uprights were used from the 2003 Polaris Predator ATV. As this being only the teams second year of competition we thought this was the most reliable and cost effective design. The suspension is configured to offer eight inches of travel.
At full rebound there is a positive camber angle of 2 degrees and 5 degrees regular camber at full jounce. This setup offered a comfortable ride to the driver and good handling around corners and sloped ground. The only change to the front suspension is that new shocks were selected. As discussed in the REAR SUSPENSION section this was to accommodate the new design. However it was also decided that the front shocks also be replaced with the RYDEFX Air 2.0 in order to better control the rates over different stages giving us a more desirable ride height while having a high top rate to prevent bottoming out. The shocks will be further explained under REAR SUSPENSION, Shocks. REAR SUSPENSION – As previously mentioned the focus for this years McMaster team was to redesign the rear suspension. By modifying the rear suspension we also incorporated the desired changes in drive train and frame. The objective of the rear suspension is to provide a smooth ride as well as absorb the impact protecting the entire vehicle. The rear suspension in particles takes the bulk of the force as it has the most weight. Each rear wheel takes twice as much weight as each front wheel. The rear axle is also the powered axle. Therefore maintaining contact surface contact while moving over rough terrain is extremely important. Design Change – The previous rear suspension featured unequal, independent A-arms. This design worked well for our first year of competition. However it is believed that a three-link suspension system can improve over this in several areas. First the large A-arms and mounting brackets were quite heavy. The new rear end with have a lower weight moving the center of gravity towards the front of the car offering better handling characteristics. The three-link system will also offer a lot of spatial freedom for the rear drive train with the modified frame. A primary concern with the previous design was the A-arm’s brackets and shock placement making the drive train difficult to access. The new suspension will also offer a greater range travel. The vertical wheel travel will be increased from the previous eight inches to ten inches. This will offer a smoother more forgiving ride. Finally the incorporation of a sway bar 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 three constraints, it is important to consider the optimal distance between the transaxle and the hub, because deviating from the optimal distance greatly reduces the range of bending available in the CV shaft. This is turn causes a reduction in the maximum attainable vertical travel range of the wheel. Figure 4: CV Shaft Angles From the above figure one can see that when the shaft is at its maximum lengths it has a much larger bending range than at the minimum lengths. Because of this, the rear links of the suspension are set to be 12.5 inches long. Also if the coils are mounted in the center of the top rear link, 10 inches of wheel travel can be obtained while maintaining the CV shaft length and angle constraints, in comparison to last years 8”. The coil position information is used in conjunction with the critical impact calculations to determine the best spring rate for our suspension. The results that optimize the design could be provided by an equivalent spring constant of 185 lbs/in (if the coil was mounted at the hub). Therefore, the coil for this design would need a spring rate of 370 lbs/in, as its position halfway up the rear link would reduce its effective constant at the wheel to half. Due to financial considerations, a commercially available coil is needed, so a spring rate of 375 lbs/in and 12 inches long (length to fit the mounting constraints) was chosen. From there, the best relative position and spacing between the two links to get the best camber angle was iterated. Because the spring stiffness and the mass of the car are known, the spring’s compression at ride height of the coils can be determined. The ideal camber angle at ride height is zero degrees, as this is the equilibrium position when driving forward. The “desired turn position” of the wheel is when the outer rear wheel effectively takes 2 times its usual weight during a turn (taken from the inner rear wheel). Small changes in camber angle at positions other than ride height are negligible because of the soft tire. Some justification for this is given towards the end of the report when further plans in designing the sway bar are discussed. Relative rear link mounting positions were varied horizontally (the “offset”) and vertically between the two links (distance “apart”). Using AutoDesk Inventor, iterations are presented below in Table 1. The goal of these iterations is to maximize tire to road surface contact, which occurs when the tire is exactly perpendicular to the road. This goal is satisfied at: zero degree camber angle at ride height, 2.99 degrees camber when suspension is compressed so that the tire is 1.3 inches above ride height, and finally to minimize
camber angle at both topped and bottomed out wheel positions. Rows were not completed in some cases if there was one or more unacceptable camber angles, or if was already evident that a previous setup was better.
Relative Position (inches) Offset Distance Apart 0.250 3.50 0.500 3.50 0.375 3.50 0.375 3.00 0.375 2.50 0.500 2.50 Ride Height 0.36 out 2.5 in 1.1 in 0.00 1.12 0.35 in Camber angle (degrees) Bottomed Out Topped Out 10.20 4.65 11.50 14.00 17.8 (too high) 3.23 5.75 Desired Turn 4.42 2.96 2.50 2.40
Finally the last stage of the shock is set quite high in order to prevent bottoming out. The main advantage of these shocks is there large amount adjustability allowing for the suspension to be fine-tuned to various driving conditions and any future modification to the vehicle.
Table 1: Camber Angles at Wheel Positions It was determined from these iterations that the best ride height would be with a 3/8 inch offset with 3 inch spacing. Spacing was limited to 3.5 inches or less as larger spacing would result in a reduced available wheel travel. Also, because it became evident that at a spacing of 2.5 inches the camber angle at the bottomed out position were unacceptable, smaller spacing values were not looked into, as these would only cause larger camber angles at that position. Once this was done, all that remained was fitting this geometry and the trailing arm onto the frame. The trailing arm, as opposed to commonly being on the outer edge of the frame, was brought inwards so that the change in toe angle of the tire would be reduced over the vertical wheel travel, but without compromising the advantages of the 3-link design. In addition, the top rear link was angle back as opposed to being straight across from the hub to the nearest point of the frame so that it could be mounted vertically to the frame (when looking at the car from the side).
Figure 6: Rear Suspension Assembly Stress Analysis – Various stress calculations were conducted on the need rear suspension elements. This is to ensure that the new design will be able to withstand the loads placed on it during operation. Trailing Arm – The trailing arm needs to be designed to handle the forces from a maximum of 50 km/h forward impact onto the rear tire which will impose a tensile force on the trailing arm. The calculations for by be made by assuming that the trailing arm will experience 1/3 of the full kinetic energy from a forward motion crash. To determine if the available tubes (sizes 1” x (0.083” or 0.120”) thickness) are safe, the energy absorbed per unit volume needs to be determined then percent elongation can be found to see if this elongation is within the allowable range. An acceptable limit is assumed to be less 10% where too much change in suspension geometry would occur. From this, the equivalent force can be approximated and used for the purchase of commercially available components again by linear interpolation. The calculations for the above can be viewed in. The calculations concluded that the design is acceptable using 1018 mild steel tubes 1” in diameter by 0.120” wall thickness with a 6% elongation assuming that 1/3 of the energy from impact is absorbed by one trailing arm.
Figure 5: Vehicle Model: Rear Suspension View Shocks – As discussed above a new spring rate is required to meet the need design of the rear suspension. In order to meet the requirement the new RYDEFX Air 2.0 shocks were selected. These cutting edge air shocks will allow for several factors to be improved. The shocks have three available stages that can be set at different spring constants. These shocks will also be used for the front suspension in order to maximize performance. The first stage of the shocks is set quite soft allowing for the designed ride height and an even ride over small inconsistencies in the surface. The second and longest stage has a higher spring constant and is effective when the shock comes under load such as a jump or turn.
If 100% of the energy is to be transferred into the trailing arm, the maximum speed to survive an impact is 30km/h.
1 1 1 2 2 ⋅ m(50km / h ) = m(v max ) 3 2 2 v max = 30km / h
The use of a 1/8” thick by 5” long 1018 steel gusset will be used to secure both tubes together on the trailing arm. To determine if the gusset design on the trailing arm is appropriate given the equivalent forces and the available weld electrode E7010, the trailing arm needed to be simplified from slightly angled welds on the gusset to a problem of torsion stress on a parallel welded member. Rear Links – Calculations were done to determine the effects of horizontal impact on the rear links of the suspension in cases if the car catches a rear wheel on a stationary object (such as a tree stump) at a velocity of 50 km/h. This is in a sense a continuation of the stress analysis discussed in the previous section on the trailing arm, as the same impact load on the tire is used. The calculations conclude that with a factor of safety of 3, either type of tubing that we currently have available is more than sufficient to withstand the load of impact. For the upper rear link, a 1-inch outer diameter is preferred. However, analysis done by hand according to bending beam theory showed that any tube of 1 in outer diameter, regardless of wall thickness would fail. Thus a new geometry with a 1 ¼ inch outer diameter and ¾ inch inner diameter and a large bracket would be exported to an FEA analysis in AutoDesk Inventor, developed by Ansys. This new design would prove too elaborate to analysis by hand. FEA results showed that the lowest factor of safety is 1.18 and proves that it would not fail.
primary goal is to limit the amount of under-steer by increasing the total vehicle roll stiffness hence lowering the rear wheel to run at a higher slip angle than the front wheel. The customer requires better handling in turns to improve overall lap times. Fine tuning the rear suspension by changing geometries is the best alternative to a rear sway bar to increase total roll stiffness and help prevent under-steer. The caveat to such a solution is that the trial and error of creating several different suspensions can be a lengthy process. Sway Bar Comparison – In order to accurately examine the advantages of the sway bar incorporated into the rear suspension two sets of body roll calculations were conducted. Body Roll Calculation without sway bar - The body roll angle will be the angle of the car reached when it is about to roll over (on a turn at 0.8 g’s). In this case, it is assumed that the inner tire is not taking any weight (it is about to roll, therefore the inner wheel is about to lift off the ground), and so the outer tire will take twice the weight as it would in the ride height position. Because the rear wheels take twice as much weight as the front wheels, the outer rear wheel will take two thirds of the total weight of the car when it is about to roll. (2/3*781 lbs = 521 lbs). At this point, the outer wheel will rise 5.5 inches above topped-out position (kspring = 375 lbs/in), while the inner wheel (feeling no weight from the car) will be at topped out position. The centre-to-centre distance of the two rear wheels is 46 inches, so using simple trigonometry, a 5.5 inch difference in height between the two wheels translates to 6.8 degrees of -1 body roll (tan 5.5/46). 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 turn should be equal to the body roll so that the outer wheel sits flat on the ground to provide maximum surface contact and maximum traction. Therefore, the body roll angle at 6.8 degrees and the camber of 3 degrees without a sway bar is a poor combination.
Thread Engagement – The minimum thread engagement length was calculated using the following formula: Engagement length =
(2 At )
0.5π (D − 0.664952 p )
)
The values for the variables in the equations above are found for a given commercially available thread size such that minimum engagement length can be found. From this calculation, the minimum engagement length of the threads for the threaded rod ends is 0.3213 inches. SWAY BAR – The rear sway bar is intended to maintain the rear wheels at equal heights throughout all driving conditions. In maintaining the rear wheels at equivalent heights, the bar will reduce body lean by increasing the vehicle’s total roll stiffness. Increasing the rear suspension’s roll stiffness will consequently help to keep the inside rear wheel from lifting off the ground throughout a corner for greater traction. The other
Figure 7: Turn Body Roll without Sway Bar
Body Roll Calculation with sway bar – The desired specifications for the sway bar are achieved through iteration. A smaller body roll requires a smaller rise in the outer rear wheel during a turn, which is iterated to be 4 inches (as opposed to 5.5 inches without sway bar). To achieve this smaller compression, the equivalent spring coefficient has to be increased to 521 lbs/in. The equivalent spring setup will be such that the suspension of the outer wheel will be in parallel with the sway bar and suspension of the inner wheel. Solving for the required spring coefficient of the sway bar gives 250 lbs/in, and under a 4-inch compression of the outer rear wheel, the inner rear wheel will compress 1.6 inches. This gives a height difference between the two wheels of 2.4 inches, and a body roll angle of 2.99 degrees. When the outer wheel is compressed 4 inches, the resulting camber angle is 2.5 degrees, so the difference between the body roll angle and the camber is half a degree. Reiterating to find a smaller angle difference is not necessary, because with the tools that we have to build this rear suspension, we will not be able to machine the design at any higher level of precision anyway. Adding the sway bar can reduce the body roll angle by half on a turn of 0.8 g’s, and can substantially reduce the difference between the body roll angle and the camber, providing more traction between the outer rear wheel and the ground on sharp turns.
Sway Bar Construction – The rear sway bar assembly consists of a ¾” diameter 4140 steel rod 31” in length with a keyway machined on either side. The primary function of the 31” rod is to twist when the wheels move relative to each other. The arms of the sway bar are constructed from 1” square steel tubing, which is attached to the steel rod by a ¾” welded insert with a keyway. The end links consist of two ¼” rod ends connected by a 6” long female threaded link. The bottom rod ends connect the sway bar to the rear suspension by mounts. The required ¾” diameter rod was calculated using 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 several factors to be considered that are common to all engineering projects. A project must have a proper scope with clearly defined goals. The goal of this year’s team was the redesign of the rear suspension. This in turn allowed for improvements of the drive train and frame. The drive train became much more accessible with was the biggest problem with the vehicle in the previous year. Second the frame could be triangulated. This not only improved its strength but also it’s appearance. The car has a much more clean and symmetry look. The team was also able to improve upon almost every other system in the car. These improvements were made possible from the experience and lessons learned during the pervious year of competition. It is hoped that this year’s vehicle is able to outperform the previous year’s vehicle in every way. The more responsive suspension and aggressive steering will make for a more competitive vehicle. It is also hoped that the performance and reliability of several other systems has been improved such as the new pedal assembly. Finally the McMaster Mini Baja Team hopes that the heightened appearance of this year’s car, along with its improved performance will make it a more noticeable competitor at this year’s competition.
Figure 8: Turn Body Roll with Sway Bar
Figure 9: Spring Diagram for Rear Suspension
ACKNOWLEDGMENTS
The team would like to recognize the continuing support of Dr. Tim Nye, the McMaster Engineering Society, and the McMaster Engineering Faculty, allowing us to continue on for a second consecutive year of competition.
CONTACT
Matt Green Mechanical Engineering & Coop, Level 4 of 5 McMaster University [email protected]
REFERENCES
1. Rai, Singiresu, “Mechanical Vibrations, Fourth Edition” 2. Budynas, Nisbet, “Shigley’s Mechanical Engineering Design, Eight Edition.” 3. Ackerman Steering Geometry. http://en.wikipedia.org/wiki/Ackermann_steering_geo metry.
2008 Baja SAE Montreal Competition Vehicle # 53
Technical Design Report
#53
McMaster University Mini Baja Technical Design Report
Matt Green
McMaster University
Copyright © 2007 SAE International
ABSTRACT
The Society of Automotive Engineers sponsors an annual engineering design competition that challenges students from various colleges and universities to design, construct, and race an off-road Mini Baja vehicle with enough speed and agility to be capable of enduring various terrains. This year, the McMaster University Mini Baja Team has chosen to participate in the 2008 SAE Baja Montreal competition, hosted by Ecole de Technologie Superieure in Montreal, Quebec, Canada. This competition requires each team to build a Mini Baja vehicle that fulfills both static and dynamic requirements as outlined by SAE. Additionally, each team must submit an analysis of their unique design in the form of a technical report.
VEHICLE DESIGN
As stated above the primary focus of this years design is the redesign of the rear suspension. This resulted in modifications to the rear portion of the frame as well as rearranging the drive train of the vehicle. Several other systems have been improved upon as well and are reviewed first such as the pedal assembly and steering geometry. All the systems and components have been designed to comply with the rules and guidelines set out in the 2008 Baja SAE Competition Rules.
INTRODUCTION
In 2007 the McMaster University Mini Baja Team competed for it’s first time in over two decades. With no previous information to pull from the newly formed team started from scratch designing early 2006. In order to make-up for the inexperience and hope to compete several trade-offs were made. The team focused on purchasing prefabricated parts, purchasing the majority of its suspension parts. The team’s primary focus was placed on completed the endurance race, of which it was rd able to succeed and place 33 in the endurance race at the 2007 SAE Baja Midwest competition. Figure 1: 2008 McMaster Mini Baja Model This year the McMaster Mini Baja Team will be competing for only it’s second time. The rules of the competition state that no component of the Baja car can be greater then two years, provided that at least one major modification is made. This is going to allow us to focus on one major modification while reusing a large portion of our existing components. It was decided that the rear suspension redesign would be the primary focus. However this required the modification of our rear frame, which allowed us to improve upon several factors such as accessibility, performance, and appearance. The team has also focused on producing a more well rounded vehicle using all of the experience that was gained the year before. BRAKING SYSTEM - The objective of the braking system is to safely stop the vehicle. It is required to statically and dynamically lock all four tires on both hard and loose surfaces. Although the previous design worked effectively it was decided that modification of our previous pedal assembly was necessary in order to improve the braking adjustability and simplify our pedal assembly and mount. Upon further investigation into the ways in which the brake bias can be modified, the one choice that fits the application of off-road use and allows for easy adjustment with little time and work is the brake balance bar assembly. The operation of the balance bar relies on the premise of the ability to change the ratio to which the master cylinders are depressed depending on the required application. It is effectively an adjustable lever via a threaded rod that moves the clevis’ that attach
to the master cylinders. The rotation about a spherical bearing that separates the two master cylinders (front and rear) allows for this pivot. Turning the threaded rod allows for adjustment of where the two cylinders are with respect to the central axis, to achieve a different ratio of compression when the brake pedal is depressed. When the balance bar is centered, it pushes on both cylinders equally, and when adjusted to maximize the difference between the two cylinders, it pushes approximately twice as hard on one cylinder as compared to the other. Instead of buying a commercially available balance bar, it was decided that for this application fabricating a custom one to fit into our application would be more suitable and allow for ease of installment and maximize functionality. The ability to easily adjust our brake bias would allow for a broader application use of the vehicle, where it may be desirable to have one set of tires lock-up before the others. This addition to the pedal assembly will replace the current set-up, which involves one master cylinder that is at a fixed ratio with respect to the pedal ratio, and the other which is adjustable via the track it is mounted to on the pedal. This took time to tune so that all tires locked up at the same time. The balance bar will ease the tuning transition from one surface to another, and make for a more stable and user-friendly brake system and pedal assembly. DRIVE TRAIN – With a common engine amongst all competing teams, a lot of emphasis had to be placed on the design of the drive train. The objective of the drive train is to transfer power from the engine to the wheels. In order to satisfy all of the requirements the drive train had to optimize several desired characteristics to ensure adequate power was provided during all of the maneuvers and most importantly an enjoyable and trilling ride. Items considered included towing capacity, acceleration, top speed, and durability. If possible, a design that would allow a forward, neutral and reverse gear was also desired. Overview of Previous Design – In keeping with the goals of this years design the majority of the design of the drive train remained the same as the previous vehicle. All of the components from the previous year are being reused. However, the arrangement is being modified in order to improve the overall design. The engine performance and setup remains the same with the requirement that it is governed to 3800rpm. The performance of the previous design was very good meeting all expectations. The same Comet 770 was used as this CVT (continuously variable transmission) was very effective at maintaining power when climbing hills and towing, while offering competitive acceleration. Other advantages of the CVT also include its use as a clutch allowing the engine to power up to a sufficient torque level. The Volkswagen transaxle was reused as it offered excellent durability as well as offered a forward, neutral, and reverse gear. The availability of a reverse gear proved very useful in tight quarters. Also since the rear suspension is reusing the same wheel hub and bearing carriers it made sense to reuse the same drive shafts mated to the transaxle with the custom mate plate constructed in the previous year. The durability gained
from using shafts and gears after the CVT is still believed to outweigh the benefits such as adjustability and lower weight of a chain and gear system. Shortfalls of Previous Design – Due to the configuration of the previous year’s suspension, which utilized independent A-arms, the transaxle had to be mounted vertically. The CVT was then places horizontally as placing it vertically would have severely raised the center of gravity of the car and made refueling difficult. It could not be placed on an angle, such as 45 degrees back towards the firewall as the base plate for the engine would have caused interference. This arrangement presented two challenges. First, the guard for the CVT was from Polaris and needed to be modified because the shock interfered with the cover. A section needed to be removed and patched with a metal plate. Secondly, and one of the main reasons for this years modifications, is that having the transaxle in the vertical orientation made it very difficult to access because the engine and suspension were in the way and had to removed first. This means that the drive train’s ease of serviceability would be very low. All these factors became the basis for redesigning the layout of the vehicle’s drive train. Modifications – The layout of last year’s vehicle has the transaxle vertical with the CVT running horizontal from the engine. As preciously discussed this caused several problems. This year it was decided to rearrange the drive train and place the transaxle horizontal and run the CVT in the vertical. The first advantage from having the transaxle horizontal is it allowed the engine, which is the single heaviest item besides the driver, to be lowered two inches resulting in a lower center of gravity. This lower center of gravity will increase stability during cornering, lowering the chances of a roll over. With the CVT running in the vertical it also removes the problem of low accessibility due to the close proximity to the suspension and drive shafts. Maintenance can be done easily on the entire drive train now by removing the bolts, CVT guard, driven pulleys, and CV shafts. The transaxle can easily be rotated out and the engine and shocks can be left completely in place. The main goal of the frame modifications was to triangulate the rear members of the frame. This was previously not possible due to the placement of the CVT guard. These modifications combined with the changes in the rear portion of the frame and rear suspension resulted in greatly improved accessibility. For further details please refer to these sections; REAR SUSPENSION, FRAME. Shifter Re-Design – The objective of the shifter is to create a reliable Forward-Neutral-Reverse shifter that will not damage the shifter cable and will remain in the operator’s intended gear. The shifter needs to give a minimum of 2” travel on the shifter cable. The motion of the shifter cable must be linear to reduce damage and unnecessary stresses on the cable. In order to satisfy the customer requirements it must be easy to switch gears, will not accidentally shift gears, and will not break under predicted usage. The primary alternative was to fabricate a linear shifter that would have 3 locking positions using a spring to maintain the shifter in gear. The secondary
alternative was to recreate the old shifter design using a larger gauge of shifter cable. The previous years design failed to stay in the desired gear during the extreme impact when landing a jump. It required the driver to often hold the shifter during landing. This resulted in added stress on the push pull cable, which resulted in its eventual failure after the competition. It also added distraction for the driver by having to move one hand to the shifter occasionally. The design chosen was to purchase a Push/Pull Toggle Clamp from McMasterCarr, which provides a linear cable motion and has exactly 2” of travel. The shifter is self-locking on either side of the travel meaning it will not come out of gear accidentally like the previous years design. The strength of the push pull cable was also increased to try and make it more durable as well as to provide a smoother, stiffer shift. ELECTRONICS – The electrical system consists of the battery, speedometer, reverse light, and reverse alarm. It must 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 battery must be able to power the reverse light and alarm as well as the brake light. The batteries must be sealed and not leak in the event of a vehicle roll over. Two possibilities were examined. First is what was used last year, two 6 volt 10 amp hour alkaline batteries. Secondly is a sealed lead acid 12-volt, 4-amp hour battery. The sealed lead acid battery was chosen over the traditional alkaline battery that was used in last years design are; first that the new battery has the ability to be recharged; second is that one 12 volt battery replaces two 6 volt batteries in series. 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 is capable of providing constant power for 16 hours. This more than exceeds the maximum duration of any SAE competition as well as recreational use as it can be charged once daily. The battery will be mounted directly to the frame in front of the engine just behind the firewall. It will be placed in a standard outdoor electrical box that consists of a sealed plastic box in order to protect it from the mud and water the car is exposed to. Speedometer – The objective of the speedometer is to have a system in place that can display speed and ride time. The system must be able to handle the rough conditions that exist on the Mini Baja track such as water, mud, sand, rocks, and generally rough terrain. The speedometer must be able to record speeds of up to 50 km/h. Several alternatives were examined. First was a traditional car speedometer. These setups would be able 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 cheap and capable of recording both speed and runtime. However they are not designed to handle the tough operating conditions that will be encountered. The final alternative is an ATV style computer speedometer. This choice incorporated all the good features of each of the
previous alternatives, it was cheap and capable of displaying all the information required, and it was capable of handling the operating conditions. The unit selected was a Trail Tech endurance model ATV computer. The unit comes complete will all the cables and sensors necessary to install the computer. Last years car did not have a speedometer and a simple stopwatch was used as a ride timer. The improvements are that the driver is now capable of monitoring speed as well as ride time easily. The system will be mounted in the cockpit right in front of the steering wheel. It is a location where it will be safe from damage in the event of a rollover, and where it can be clearly seen by the driver. Reverse Light and Alarm – The objective of the reverse light and alarm is to inform nearby vehicles and pedestrians of the intent to backup. Each vehicle with reverse must have a backup light marked with a SAE ‘R’ on the lens or exceed the SAE standard. The alarm must also be rated per SAE standard J1741. The alarm is mounted and activated the same as the previous design with a mechanical lever depressing an electrical switch that activates the alarm and light. FRAME – In keeping with the goals for this years design approximately half of the frame is reused from the previous year. The main changes in the construction of the frame include triangulating the rear supports with the front of the car and changing the suspension and engine mounts to accommodate the new design. The frame has been designed to carefully meet all requirements outlined in the 2008 Baja SAE Competition Rules. Materials Overview – The existing steel members are made up of two schedules of one inch, 1018 class steel tubing. This was chosen for ease of manufacturing and cost. The new sections of the frame are also constructed with this material, as it will allow for easy fabrication and joining of the new sections. The two schedules are required to ensure a proper and safe roll cage made out of the thicker tube whereas other frame members can be thinner to reduce weight. Frame Modifications – The majority of the frame modifications are behind the firewall. The only frame modification in the front and cockpit of the car is the removable of two redundant support beams since the rear of the car is now triangulated making them unnecessary. The removable of these members makes for a better appearance by simplifying the front as well as improving visibility for the driver. Another advantage of triangulated the back bracing of the car is for greatly improved accessibility to the drive train and engine. It was designed in order to minimize intruding member by placed the suspension supports around the outer edge. This is greatly improved over last year’s design that had the problem of having to remove the suspension to get at the drive train and engine. The new design is also much lighter. The addition engine members were removed. The rear suspension mounts are also much light. This is further outlined under REAR SUSPENSION.
Ackerman Geometry – The Ackerman concept is to have all four wheels of a vehicle rolling around a common point during a turn. This requires that the inside tire be turning at a tighter radius then the outside tire as shown in Figure 3: Ackerman Concept. This geometry transfers the weight to the inside front tire causing the inside rear tire to have lower contact force. This then allows for the kart to turn into a corner instead of trying to push straight ahead.
Figure 2: Frame Modifications: Rear Figure 3: Ackerman Concept BODY DESIGN – The objective of the body is to provide the vehicle with a strong but good-looking finish. This year the body will be constructed of fiberglass and plastic in order to give the vehicle a new look that will be appealing to us and able to withstand the abuse of an off-road vehicle as these materials don’t rust and require minimal maintenance. The plastic and fiberglass construction was chosen over aluminum sheeting because it will reduce noise as it will not produce sound when the body panels are attached to the car. The previous design utilized a sheet metal body panel that produced excessive noise due to the vibrations of the car. Fiberglas also has the property of absorbing energy very well, which will help to protect the operator. The new fiberglass and plastic design will help to provide the driver with a safer vehicle, increase the attractiveness of the car and decrease the noise produced by the vehicle body panels. STEERING – The objective of the steering system is to provide a reliable method for controlling the direction of the vehicle that is capable of withstanding the high stress placed on it. There are no direct requirements for the type of steering method used or how sharp you must be able to turn. However there is a safety specification that requires all tie rods to be protected from a frontal impact. The majority of the steering components and setup from the previous is remaining the same. Previously an eleven inch, eye-to-eye, rack and pinion was used. This worked very well, providing the necessary range and was very durable as it was a purchased component designed for sand rails. The car was able to compete all maneuvers during competition. However the goal of the steering modifications is to correct the Ackerman geometry. This will allow for tighter, more aggressive turning. Steering Correction – The previous steering configuration had an improper Ackerman geometry. The front wheels were turning more parallel to each other then having the inside more tightly turned. On lose surfaces this could be overcome by sliding the corner however on stickier surfaces such as grass and concrete if was harder to steer. This also would eventually result in increased tire wear. To correct this effect the pivot point between the steering upright on the wheel and the tie rod had to be adjusted. Since we used the standard upright and spindle from a 2003 Polaris Predator ATV it was easiest to make an attachment for the steering upright that which would have the new pivot point. The correct point the pivot point needs to be was found by running a string from the center of the upright to the middle of the rear drive shaft. Where the bracket intersected the plane created by the string is where the new pivot point for the tie rod connection was made. This will now allow for a more aggressive steering and corning abilities resulted in a more responsive ride. FRONT SUSPENSION – The objective of the front suspension is to provide adequate shock absorption to ensure comfort to the driver while maintaining a positive downward force to keep the front wheels in contact with ground. Without this proper contact force it would hinder steering giving the driver less control over the vehicle. The front suspension is maintained the same as the previous years. It was found that the front suspension preformed to all expectations and therefore the focus should maintain on the rear suspension redesign. Prefabricated aluminum A-arms and uprights were used from the 2003 Polaris Predator ATV. As this being only the teams second year of competition we thought this was the most reliable and cost effective design. The suspension is configured to offer eight inches of travel.
At full rebound there is a positive camber angle of 2 degrees and 5 degrees regular camber at full jounce. This setup offered a comfortable ride to the driver and good handling around corners and sloped ground. The only change to the front suspension is that new shocks were selected. As discussed in the REAR SUSPENSION section this was to accommodate the new design. However it was also decided that the front shocks also be replaced with the RYDEFX Air 2.0 in order to better control the rates over different stages giving us a more desirable ride height while having a high top rate to prevent bottoming out. The shocks will be further explained under REAR SUSPENSION, Shocks. REAR SUSPENSION – As previously mentioned the focus for this years McMaster team was to redesign the rear suspension. By modifying the rear suspension we also incorporated the desired changes in drive train and frame. The objective of the rear suspension is to provide a smooth ride as well as absorb the impact protecting the entire vehicle. The rear suspension in particles takes the bulk of the force as it has the most weight. Each rear wheel takes twice as much weight as each front wheel. The rear axle is also the powered axle. Therefore maintaining contact surface contact while moving over rough terrain is extremely important. Design Change – The previous rear suspension featured unequal, independent A-arms. This design worked well for our first year of competition. However it is believed that a three-link suspension system can improve over this in several areas. First the large A-arms and mounting brackets were quite heavy. The new rear end with have a lower weight moving the center of gravity towards the front of the car offering better handling characteristics. The three-link system will also offer a lot of spatial freedom for the rear drive train with the modified frame. A primary concern with the previous design was the A-arm’s brackets and shock placement making the drive train difficult to access. The new suspension will also offer a greater range travel. The vertical wheel travel will be increased from the previous eight inches to ten inches. This will offer a smoother more forgiving ride. Finally the incorporation of a sway bar 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 three constraints, it is important to consider the optimal distance between the transaxle and the hub, because deviating from the optimal distance greatly reduces the range of bending available in the CV shaft. This is turn causes a reduction in the maximum attainable vertical travel range of the wheel. Figure 4: CV Shaft Angles From the above figure one can see that when the shaft is at its maximum lengths it has a much larger bending range than at the minimum lengths. Because of this, the rear links of the suspension are set to be 12.5 inches long. Also if the coils are mounted in the center of the top rear link, 10 inches of wheel travel can be obtained while maintaining the CV shaft length and angle constraints, in comparison to last years 8”. The coil position information is used in conjunction with the critical impact calculations to determine the best spring rate for our suspension. The results that optimize the design could be provided by an equivalent spring constant of 185 lbs/in (if the coil was mounted at the hub). Therefore, the coil for this design would need a spring rate of 370 lbs/in, as its position halfway up the rear link would reduce its effective constant at the wheel to half. Due to financial considerations, a commercially available coil is needed, so a spring rate of 375 lbs/in and 12 inches long (length to fit the mounting constraints) was chosen. From there, the best relative position and spacing between the two links to get the best camber angle was iterated. Because the spring stiffness and the mass of the car are known, the spring’s compression at ride height of the coils can be determined. The ideal camber angle at ride height is zero degrees, as this is the equilibrium position when driving forward. The “desired turn position” of the wheel is when the outer rear wheel effectively takes 2 times its usual weight during a turn (taken from the inner rear wheel). Small changes in camber angle at positions other than ride height are negligible because of the soft tire. Some justification for this is given towards the end of the report when further plans in designing the sway bar are discussed. Relative rear link mounting positions were varied horizontally (the “offset”) and vertically between the two links (distance “apart”). Using AutoDesk Inventor, iterations are presented below in Table 1. The goal of these iterations is to maximize tire to road surface contact, which occurs when the tire is exactly perpendicular to the road. This goal is satisfied at: zero degree camber angle at ride height, 2.99 degrees camber when suspension is compressed so that the tire is 1.3 inches above ride height, and finally to minimize
camber angle at both topped and bottomed out wheel positions. Rows were not completed in some cases if there was one or more unacceptable camber angles, or if was already evident that a previous setup was better.
Relative Position (inches) Offset Distance Apart 0.250 3.50 0.500 3.50 0.375 3.50 0.375 3.00 0.375 2.50 0.500 2.50 Ride Height 0.36 out 2.5 in 1.1 in 0.00 1.12 0.35 in Camber angle (degrees) Bottomed Out Topped Out 10.20 4.65 11.50 14.00 17.8 (too high) 3.23 5.75 Desired Turn 4.42 2.96 2.50 2.40
Finally the last stage of the shock is set quite high in order to prevent bottoming out. The main advantage of these shocks is there large amount adjustability allowing for the suspension to be fine-tuned to various driving conditions and any future modification to the vehicle.
Table 1: Camber Angles at Wheel Positions It was determined from these iterations that the best ride height would be with a 3/8 inch offset with 3 inch spacing. Spacing was limited to 3.5 inches or less as larger spacing would result in a reduced available wheel travel. Also, because it became evident that at a spacing of 2.5 inches the camber angle at the bottomed out position were unacceptable, smaller spacing values were not looked into, as these would only cause larger camber angles at that position. Once this was done, all that remained was fitting this geometry and the trailing arm onto the frame. The trailing arm, as opposed to commonly being on the outer edge of the frame, was brought inwards so that the change in toe angle of the tire would be reduced over the vertical wheel travel, but without compromising the advantages of the 3-link design. In addition, the top rear link was angle back as opposed to being straight across from the hub to the nearest point of the frame so that it could be mounted vertically to the frame (when looking at the car from the side).
Figure 6: Rear Suspension Assembly Stress Analysis – Various stress calculations were conducted on the need rear suspension elements. This is to ensure that the new design will be able to withstand the loads placed on it during operation. Trailing Arm – The trailing arm needs to be designed to handle the forces from a maximum of 50 km/h forward impact onto the rear tire which will impose a tensile force on the trailing arm. The calculations for by be made by assuming that the trailing arm will experience 1/3 of the full kinetic energy from a forward motion crash. To determine if the available tubes (sizes 1” x (0.083” or 0.120”) thickness) are safe, the energy absorbed per unit volume needs to be determined then percent elongation can be found to see if this elongation is within the allowable range. An acceptable limit is assumed to be less 10% where too much change in suspension geometry would occur. From this, the equivalent force can be approximated and used for the purchase of commercially available components again by linear interpolation. The calculations for the above can be viewed in. The calculations concluded that the design is acceptable using 1018 mild steel tubes 1” in diameter by 0.120” wall thickness with a 6% elongation assuming that 1/3 of the energy from impact is absorbed by one trailing arm.
Figure 5: Vehicle Model: Rear Suspension View Shocks – As discussed above a new spring rate is required to meet the need design of the rear suspension. In order to meet the requirement the new RYDEFX Air 2.0 shocks were selected. These cutting edge air shocks will allow for several factors to be improved. The shocks have three available stages that can be set at different spring constants. These shocks will also be used for the front suspension in order to maximize performance. The first stage of the shocks is set quite soft allowing for the designed ride height and an even ride over small inconsistencies in the surface. The second and longest stage has a higher spring constant and is effective when the shock comes under load such as a jump or turn.
If 100% of the energy is to be transferred into the trailing arm, the maximum speed to survive an impact is 30km/h.
1 1 1 2 2 ⋅ m(50km / h ) = m(v max ) 3 2 2 v max = 30km / h
The use of a 1/8” thick by 5” long 1018 steel gusset will be used to secure both tubes together on the trailing arm. To determine if the gusset design on the trailing arm is appropriate given the equivalent forces and the available weld electrode E7010, the trailing arm needed to be simplified from slightly angled welds on the gusset to a problem of torsion stress on a parallel welded member. Rear Links – Calculations were done to determine the effects of horizontal impact on the rear links of the suspension in cases if the car catches a rear wheel on a stationary object (such as a tree stump) at a velocity of 50 km/h. This is in a sense a continuation of the stress analysis discussed in the previous section on the trailing arm, as the same impact load on the tire is used. The calculations conclude that with a factor of safety of 3, either type of tubing that we currently have available is more than sufficient to withstand the load of impact. For the upper rear link, a 1-inch outer diameter is preferred. However, analysis done by hand according to bending beam theory showed that any tube of 1 in outer diameter, regardless of wall thickness would fail. Thus a new geometry with a 1 ¼ inch outer diameter and ¾ inch inner diameter and a large bracket would be exported to an FEA analysis in AutoDesk Inventor, developed by Ansys. This new design would prove too elaborate to analysis by hand. FEA results showed that the lowest factor of safety is 1.18 and proves that it would not fail.
primary goal is to limit the amount of under-steer by increasing the total vehicle roll stiffness hence lowering the rear wheel to run at a higher slip angle than the front wheel. The customer requires better handling in turns to improve overall lap times. Fine tuning the rear suspension by changing geometries is the best alternative to a rear sway bar to increase total roll stiffness and help prevent under-steer. The caveat to such a solution is that the trial and error of creating several different suspensions can be a lengthy process. Sway Bar Comparison – In order to accurately examine the advantages of the sway bar incorporated into the rear suspension two sets of body roll calculations were conducted. Body Roll Calculation without sway bar - The body roll angle will be the angle of the car reached when it is about to roll over (on a turn at 0.8 g’s). In this case, it is assumed that the inner tire is not taking any weight (it is about to roll, therefore the inner wheel is about to lift off the ground), and so the outer tire will take twice the weight as it would in the ride height position. Because the rear wheels take twice as much weight as the front wheels, the outer rear wheel will take two thirds of the total weight of the car when it is about to roll. (2/3*781 lbs = 521 lbs). At this point, the outer wheel will rise 5.5 inches above topped-out position (kspring = 375 lbs/in), while the inner wheel (feeling no weight from the car) will be at topped out position. The centre-to-centre distance of the two rear wheels is 46 inches, so using simple trigonometry, a 5.5 inch difference in height between the two wheels translates to 6.8 degrees of -1 body roll (tan 5.5/46). 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 turn should be equal to the body roll so that the outer wheel sits flat on the ground to provide maximum surface contact and maximum traction. Therefore, the body roll angle at 6.8 degrees and the camber of 3 degrees without a sway bar is a poor combination.
Thread Engagement – The minimum thread engagement length was calculated using the following formula: Engagement length =
(2 At )
0.5π (D − 0.664952 p )
)
The values for the variables in the equations above are found for a given commercially available thread size such that minimum engagement length can be found. From this calculation, the minimum engagement length of the threads for the threaded rod ends is 0.3213 inches. SWAY BAR – The rear sway bar is intended to maintain the rear wheels at equal heights throughout all driving conditions. In maintaining the rear wheels at equivalent heights, the bar will reduce body lean by increasing the vehicle’s total roll stiffness. Increasing the rear suspension’s roll stiffness will consequently help to keep the inside rear wheel from lifting off the ground throughout a corner for greater traction. The other
Figure 7: Turn Body Roll without Sway Bar
Body Roll Calculation with sway bar – The desired specifications for the sway bar are achieved through iteration. A smaller body roll requires a smaller rise in the outer rear wheel during a turn, which is iterated to be 4 inches (as opposed to 5.5 inches without sway bar). To achieve this smaller compression, the equivalent spring coefficient has to be increased to 521 lbs/in. The equivalent spring setup will be such that the suspension of the outer wheel will be in parallel with the sway bar and suspension of the inner wheel. Solving for the required spring coefficient of the sway bar gives 250 lbs/in, and under a 4-inch compression of the outer rear wheel, the inner rear wheel will compress 1.6 inches. This gives a height difference between the two wheels of 2.4 inches, and a body roll angle of 2.99 degrees. When the outer wheel is compressed 4 inches, the resulting camber angle is 2.5 degrees, so the difference between the body roll angle and the camber is half a degree. Reiterating to find a smaller angle difference is not necessary, because with the tools that we have to build this rear suspension, we will not be able to machine the design at any higher level of precision anyway. Adding the sway bar can reduce the body roll angle by half on a turn of 0.8 g’s, and can substantially reduce the difference between the body roll angle and the camber, providing more traction between the outer rear wheel and the ground on sharp turns.
Sway Bar Construction – The rear sway bar assembly consists of a ¾” diameter 4140 steel rod 31” in length with a keyway machined on either side. The primary function of the 31” rod is to twist when the wheels move relative to each other. The arms of the sway bar are constructed from 1” square steel tubing, which is attached to the steel rod by a ¾” welded insert with a keyway. The end links consist of two ¼” rod ends connected by a 6” long female threaded link. The bottom rod ends connect the sway bar to the rear suspension by mounts. The required ¾” diameter rod was calculated using 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 several factors to be considered that are common to all engineering projects. A project must have a proper scope with clearly defined goals. The goal of this year’s team was the redesign of the rear suspension. This in turn allowed for improvements of the drive train and frame. The drive train became much more accessible with was the biggest problem with the vehicle in the previous year. Second the frame could be triangulated. This not only improved its strength but also it’s appearance. The car has a much more clean and symmetry look. The team was also able to improve upon almost every other system in the car. These improvements were made possible from the experience and lessons learned during the pervious year of competition. It is hoped that this year’s vehicle is able to outperform the previous year’s vehicle in every way. The more responsive suspension and aggressive steering will make for a more competitive vehicle. It is also hoped that the performance and reliability of several other systems has been improved such as the new pedal assembly. Finally the McMaster Mini Baja Team hopes that the heightened appearance of this year’s car, along with its improved performance will make it a more noticeable competitor at this year’s competition.
Figure 8: Turn Body Roll with Sway Bar
Figure 9: Spring Diagram for Rear Suspension
ACKNOWLEDGMENTS
The team would like to recognize the continuing support of Dr. Tim Nye, the McMaster Engineering Society, and the McMaster Engineering Faculty, allowing us to continue on for a second consecutive year of competition.
CONTACT
Matt Green Mechanical Engineering & Coop, Level 4 of 5 McMaster University [email protected]
REFERENCES
1. Rai, Singiresu, “Mechanical Vibrations, Fourth Edition” 2. Budynas, Nisbet, “Shigley’s Mechanical Engineering Design, Eight Edition.” 3. Ackerman Steering Geometry. http://en.wikipedia.org/wiki/Ackermann_steering_geo metry.
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