This year, the University of Rochester Yellowjackets is producing a vehicle to demonstrate the ability to perform in adverse off road situations. After several years of design iterations, the Yellowjackets will continue to build upon proven design concepts. The Baja SAE competitions will test the car’s robust designs and efficiency to evaluate its ability to meet the demands of off-road driving while still being a marketable product. To meet these demands, designs are focused heavily on optimizing fabrication, cost, and overall performance. In addition, certain components of the vehicle were modified to cater specifically to the comfort of the driver. Each major section of the vehicle looks to embody one or more of these design elements, resulting in a marketable off road vehicle.
The former design of the chassis has been reused with iterations to decrease weight, while being reconceptualized in order to interface to an improved drivetrain and suspension. The drivetrain design has been simplified to economize weight and streamline fabrication. Meanwhile the design of the suspension has undergone various weight decreases and changes to improve overall handling and maneuverability.
The drivetrain consists of the specified Briggs & Stratton 1450 series engine, a CVTech-IBC Continuously Variable Transmission (CVT), and a gear reduction. Constant velocity (CV) axles transmit power from the gearbox to the rear wheels. The CVT continuously shifts between 3:1 at engagement to a 0.43:1 ratio when fully shifted. The gearbox reduction ratio of 12.93:1 allows the drivetrain ratio to vary from a low ratio of 38.79:1 to a maximum ratio 5.56:1 with the CVT shifted fully. The previous year’s gearbox had a reduction of 10:1, which was too shallow, and created an unreasonable top speed of 57.8 MPH. The top speed of this year’s vehicle design at an engine speed of 3800 RPM is 44.7 MPH. Considering the engine power and drag coefficient of the car, the vehicle may achieve this top speed on a downhill, making this design much more reasonable. The increased torque output provided by the new gearbox increases acceleration through the the engine’s range of operation and at all speeds.
The new design improves other key properties of the drivetrain. Instead of using a chain and sprocket combined with a planetary, the reduction is achieved with two pairs of spur gears. The gears are cut from 8620, and the shafts are 4340 for high strength, durability, and shock resistance. These gears provide the greatest energy efficiency for the reduction with the least maintenance. Even though the spur gears will create some noise, they are simple to assemble and provide greater durability than helical cut gears. Splines mate the gears to their respective shafts for a very tough and accurate coupling. Snap rings align the gears on the shafts, and align the shafts in the case. The case is a two-piece design machined from 6061-T6 aluminum. The approximately symmetrical design of each half reduces material and manufacturing costs. Three bearings pressed into each half support their respective shafts. The double sealed, single row ball bearings handle radial loads on the shafts from torque and thrust loads from the CVT or driveshafts. Gear oil provides lubrication, while shaft seals and a Buna-N O-ring gasket to seal the mating faces minimize case leakage. Stress and fatigue were calculated according to ASME standards [Shigley Reference].
Last year’s vehicle, car #20, exhibited improved handling characteristics over it’s predecessor but was not able to perform well in tight spaces or demanding terrain. This year’s goal concerning vehicle dynamics was to address these problems, while maintaining stability and handling. The static ride height was raised from 8.5 inches to 14 inches to better overcome large obstacles. Wheel travel increased in the front and rear to 10.1 inches and 7.9 inches respectively. To capitalize on this travel Fox Float Rs, with adjustable rebound damping (see Shock section), were added to allow rebound to be tuned to various terrains.
Another design concern dealt with car #20’s tendency to understeer. To improve this, front wheel load increased statically and dynamically. Statically by shifting the front-rear weight distribution from 45-55 to 50-50 and dynamically by raising the CG and tilting the roll axis. The static ride height is increased by 5.5 inches thereby raising the CG. However every attempt has been made to keep the CG as low as possible to reduce the likelihood in rolling over[unnecessary?]. This resulted in an unmanned and manned(180 lbs) CG height of 21 and 26.35 inches, respectively, above the contact patch. Also the forward tilt of the roll axis was increased by lowering the front roll center and raising the rear roll center (see front and rear geometry sections). This allows the driver to induce oversteer more easily, especially in tight turns. Determine changes and increases in wheel loading..
The first problem encountered in tight spaces was simply the footprint of last years car. The car was long and with the rear track 2 inches wider than the front the inside rear wheel which often got hung up on obstacles during tight maneuvering. In response to this, the length behind the firewall was shortened by 5 inches and the rear track was adjusted so that outside of the rear tires were 1 ½ inches inside the centerline of the front tire. To achieve this without adversely affecting suspension dynamics, the rear of the car was narrowed by 4 inches and 22x7 tires with 4+1 wheels will be used at the rear instead of the 22x8 tires with 3+2 wheels of the previous year. With these changes, the rear track was narrowed to 40 inches but the scrub increased by less than .05 inches. Higher steering ratio plays a large part in tight maneuvering. Compared to the former vehicle’s 2½ revolutions, the steering wheel now only requires 1 revolution; made possible by moving the tie rod mount closer to the king pin axis. (see steering section for more detail)
To increase lateral steering forces, we took advantage of the rounded, bias ply tires (see Tire section) used by ATV’s and our car to induce camber thrust by increasing camber change with steering via increasing castor and decreasing the king pin inclination and by increasing camber change with travel to 1.75 degrees per inch of travel front (equal to body roll), 2.75 degrees per inch of travel rear. (see front geometry)
The team has a lot of experience and success using simple double wishbone front suspension with air shocks. Simple A-arms incorporating a single bend were used to maintain ease of manufacture. This year the top A-arm was widened by 8 inches at the frame mounting points. This increases their strength to frontal impacts by a factor of ? The arms are constructed from 1” OD, .049 wall thickness 4130 steel tubing. Finite element analysis with NASTRAN/PATRAN was used to verify the structural integrity of the design. Details? To build the A-arms A jig made of welded 1” square tubing was used. Jigs are used to constrain parts to the proper dimensions while they are welded and cool. The use of a jig allowed A-arms to be made consistently to the same dimensions without the warping. Jigs will provide quality control during mass production, because only properly fabricated tubes will fit into them. Nesscary?
The upper and lower inboard mount points were offset by 0.2” to induce a kingpin inclination of 1.8° from vertical, and a scrub radius of 1.65 inches. The mechanical trail, which is measured from the side view swing arm geometry (svsa), is approximately 1.35”, 3 degrees and ½” less than last year. This increases camber change with steering and thus camber thrust and reduces steering kickback. It is undesirable to have both mechanical trail and scrub radius at or near zero because this makes the front wheels very unstable and eliminates steering force-feedback. Since a positive camber produces camber thrust and is useful for stability in turns insert formula on camber thrust here .the front suspension has limited camber change with vertical wheel travel to reduce steering and handling instabilities and the force response the driver experiences.
Info about changing frame mount points and affect on roll centers
The trailing link style suspension used last year yielded excellent durability and performance. The ease of adjustment to camber and toe the links provided was also very popular with drivers. In response to this a similar setup is used this year but with a smaller, lighter trailing arm. Variable mounting tabs have been added for further adjustability (see diagram). These mounting points allow the camber change in bounce to quickly and easily be set to zero, matched to body roll, or twice body roll depending on the demands of terrain and preference of the driver. Additionally, if greater oversteer is desired, the higher mounting points can be used, raising the rear roll center and increasing scrub.
The suspension links include one toe link (also called a steering linkage or bump steer link) which can be modified to create bump steer. Bump steer is a toe change with vertical wheel travel. Default position is set to 0 degrees per inch of toe change, but can be modified for different handling characteristics, i.e. tighter turns in the land maneuverability event. The rear suspension steering characteristics are purely passive because body roll induces vertical travel of the rear tires. The front tie rods are exactly the same lengths as the rear suspension links, but the difference in lengths required for the rear suspension can be edited with the attached rod ends.
Shocks: Fox Float R air shocks are used for both the front and rear suspension. The front and rear shocks are respectively 16.9” and 18.5” long fully extended and have 4.3” and 5.3” of travel. The shocks are lightweight at only 2.1-2.25 lbs each and provide weight savings over heavier coil-over shocks utilizing steel springs. The shocks feature infinitely adjustable spring, and velocity sensitive damping rates, and adjustable rebound damping so that they can be easily tuned to meet the specific needs of the driver and terrain. Additionally, in testing and actual racing, the performance of the Float shocks did not deteriorate noticeably due the heating of the air inside. It was decided that the Float R shocks were optimal for a Baja SAE car, and so Fox EVOL shocks would not enhance the performance of the vehicle enough compared to the extra expense. The FLOAT R shocks cost $580 per pair, while the EVOL shocks roughly $1200 per pair. That is a significant difference. In fact the choice of shocks is one of the largest factors that keeps the prototype cost low and makes the vehicle so appealing to consumers. The shocks were placed so that they did not interfere with removal of the CVT or CVT cover, which was a problem in past designs.
Front Uprights/Hubs-Custom uprights had to be machined in order to fit the new suspension geometry. Aluminum billet was machined to the proper dimensions and a custom machined, tapered spindle was press fit into the center. For purposes of mass production, the uprights would be cast and then finished using light machining. The hubs used were from a Honda TRX 250 because that model is a similar size and power to our vehicle. Using hubs from a more powerful ATV would add unnecessary weight since hubs generally increase in size with vehicle power. Delrin bump stops are bolted to the steering links of front uprights to prevent the wheels from turning too much. They are simple rectangles that interfere with the wheels at large angles. Understeer occurs at extreme wheel angles, and the bump stops prevent the wheels from reaching these angles. They also prevent the destruction of the front steering assembly when the wheels encounter hard obstacles like trees and boulders. A hard impact can snap tie rods and ball joints by forcing them too far back, but the stops prevent this.
Rear Uprights/Hubs- CV shafts, hubs, and bearings from a Polaris Sportsman 500 were used as they had nearly the same operating dimensions as the rear of this years car and thus could be used with very limited modification. The rear uprights were machined from billet aluminum, which due to their simple design, does not need to be cast. The stress analysis for the front and rear uprights can be seen in Figure.
Tires-ITP Quadcross XC 22x7-10” tires will be used for the front and rear of the car. These tires have been developed and proven to provide excellent performance and durability in all terrain types, from hard-pack and rock to loam and mud, and been used widely on top finishers in cross-country ATV racing. The tires are manufactured with 6-bias-ply construction for higher durability and puncture resistance. An additional reason for switching from the Maxxis Rzr2 we have traditionally used is the tire construction and its effects on handling. ITP uses bias ply construction which offer increased camber thrust, a characteristic our suspesion design this year capatalizes on, over the radial construction of Maxxis. We chose front tires for the rear, because rear ATV rear tires are too wide and with limited horsepower would both decrease acceleration and make oversteer difficult to induce. Although front tires are primarily responsible for handling and traction, the rectangular tread pattern used on the Quadcross tires can be effectively used for driving wheels.
Wheels- ITP T-9 Pro Series Baja wheels were chosen for the front and rear which at are some of the lightest and strongest ATV style wheels on the market today. Based on the obstacles that the car may encounter, it is important that the wheels we choose are strong so that they will not dent, as damage to the wheels may cause the tires to leak air. Additionally with limited horsepower it is especially important keep rotating mass as light as possible to maximize acceleration, deceleration, and top-speed.
The main goals for this year for the braking system were to improve the master cylinder to pedal connection and improve the assembly mounting for the rear caliper. All the equations used for the design of the braking system are taken from The Physics of Braking Systems by James Walker Jr., a Professional Engineer that specializes in chassis, and brakes. As described by Article 11.2 the braking system must be split up into two independent hydraulic circuits. In order to fulfill this requirement, the front brakes are governed of one circuit and the rear brakes are governed by a separate circuit. Each front wheel requires its own independent caliper to stop the rotation of the wheel; and for the rear wheels only a singular caliper is need because the drive train utilizes a spooled rear axle which allows for a single caliper to effectively stop both of the tires. By utilizing an inboard braking system for the rear tires the cost of the production decreases by only having to use a single caliper and rotor for the rear brakes as opposed by two. This also decreases the upsprung mass on each tire which effectively improves the quality of the ride by readily moving in response to road bumps, which are often encountered in an off-road terrain. Dynamic Weight Shift- The braking forces from the calipers must be able to generate a torque on the brake rotors that can overcome the torque imparted on the tires by the ground friction. The friction between the tire and the ground is dependent on the weight placed on each tire. However, it is not enough to simply measure the weight under each tire as it is standing still because during deceleration, weight is transferred from the rear axle to the front. The equation for weight transfer is WT=(a/g)x(hcg/WB)* Vt where “a” is the maximum deceleration of the vehicle, “g” is the acceleration of gravity, hcg is the height of the cg, WB is the wheel base, and Vt is the weight of the vehicle. The maximum acceleration was assumed to be 1 g and the height of the cg was determined by the methods outlined in Race Car Vehicle Dynamics Once the normal forces at maximum acceleration were known, the system used to generate the necessary stopping force could be developed. To make the decision process simpler, the diameter of the rotors was fixed from the beginning. A 7’’ rotor was chosen because larger sizes would not fit with their affixed calipers inside the wheel rim. A larger 8’’ rotor was chosen for the rear because it is responsible for stopping both rear wheels. A 0.75’’ bore master cylinder was chosen for the front and rear because they are standard sizes for 400-500lb vehicles according to the Wildwood representative. Once the master cylinders and rotors sizes were chosen, a compromise had to be found between pedal size and caliper piston area. By taking measurements of the average force a driver can press on the brake pedal without an excessive amount of effort it was determined to be that on average force is 50 lbf that can easily be generated by an average driver. A spread sheet was made that listed variations of pedal length, and available piston sizes for the caliper. A pedal that creates a mechanical advantage between 4-5:1 was found to be satisfactory due to the confined space of the location for the brake pedal. Now only other factor that can be used to determine the mechanical advantage for the braking pedal was the size of the piston for the brake calipers. After calculating the braking force that different caliper size would generate it was determined that a calipers with piston area of 1.22 in2 be used for the front tires and a fixed caliper with piston area of around 2.8 in2 be used for the rear.
Out board braking is used in the front because the left and right A-Arms are independent. Each front wheel has 1.25’’ bore caliper. The front calipers are floating style because the two pistons needed for fixed calipers would take up too much room inside the limited space of the rim. Also, floating calipers will self-align, which is helpful in maintaining good contact between the rotor and brake pads. Rotors from Streamline Performance Braking are used because of it light weight characteristics. Rear Brakes- A Wilwood caliper with piston area of 2.80 in2 was used because of its mounting points that would allow for the caliper to be mounted flush with the gearbox. This allows for the location of the bleed nipple to be upright making the servicing of the brakes much easier compared to design of prior vehicles. Master Cylinders- Wilwood’s Integral Reservoir Master Cylinders were chosen because of the compact space due to having a built in fluid reservoir. This minimizes the weight of the car by not having to mount external reservoirs for the fluid.
Bias Bar- The design for the bias bar allows for an easily adjustable braking bias. By turning a knob at an end of the bias bar a mechanism utilizing a spherical bearing alters the ratio of force being applied to each master cylinder. Ideally both sets of wheels should lock up at the same time and bias adjustments allow this to be controlled. By having a brake bias adjustment, data can be taken using a pressure gage to adjust the braking bias to the optimal setting of the vehicle. From prior vehicles it is determined to be that a 60:40 brake bias (front to rear) is optimal.
Brake Lines- The selection of the brake lines was based on price and reliability. Wherever the brake line is not required to move, hard lines were used because of their much lower cost. Stainless steel braided lines are used are used in the front suspension throughout the A-arm because it is constantly moving up and down as the suspension travels.
Steering- Steering is achieved using an 14’’ rack and pinion connected to rod ends threaded into tie rods. The total mechanical advantage for the steering system is determined to be around 5:1. The rod ends then turn the wheels by pushing on mount points attached to the front uprights. The rack and pinion was chosen for its low cost ($98) and weight (≈2lb).The tie rods have both left and right hand threads to allow for quick adjustments to toe as well as jam nuts to keep them from moving during operation. The design of the steering tie rods is the exact same as the rear suspension links. This is very useful because limiting variability makes mass production easier. (but different lengths)
The steering column is design to have a telescoping adjustability of 5” allowing for a quick change in length for different driver preference. The telescoping mechanism works by having two shafts that fit within each other. The smaller shaft is then fitted into the larger one and a seat post clamp is used to grip on to both of the shaft thereby coupling them together. In the case that the seat post clamp fails or slips during the operation of the vehicle, a binding bolt is used that couples both inner shaft and outer shaft of the steering column to maintain control of the vehicle’s steering. To accommodate drivers with longer legs the angle of the steering wheel is adjustable, allowing the wheel to be moved above their knees. This is accomplished by bolting the flanged bearing into different locations along a vertical square tube, drilled with holes at different heights. The bearing has enough range of motion to accommodate the change in angle that accompanies the shift in height. A universal joint is necessary at the base of the rack and pinion to accommodate the changing angle of the steering shaft.
Need to talk about ackerman, steering angles and overal ratio:
Additionally, the lock to lock steering often needed in maneuvering in tight spaces required almost 2 ½ revolutions of the steering wheel which was difficult and tiring for the driver to execute. This year it was reduced to just over 1 revolution by moving the tie rod mount closer to the king pin axis .(see steering section for more detail)
The caster angle and king pin inclination were chosen to give some camber change while steering. The caster angle was chosen to be (need values from Nick°) and the king pin inclination was chosen to be (need values from Nick°) as well. These numbers were chosen so that the mechanical trail created will keep the steering stable at high speeds, but will not make steering too difficult at low speeds.
Frame and Body
This year, the redesign of the frame focused on facilitating fabrication. The geometry of the RHO and FBM have been modified to eliminate complex multi-planar bends in the tube. Elements of the rear system FAB and the SIM’s have been altered to connect to one joint (point S as defined per rule B184.108.40.206 ) on the RRH to eliminate unwanted tube members in addition to easing the installation of the firewall.
Another aspect of the redesign looked to improve driver comfort. One concern of last year’s design was it’s narrow space within the cockpit near the area of the driver’s shins and knees. In response to this, the major width between the SIM members was changed from 24 inches to 27 inches to increase leg room within the chassis and allow for easier entry and exit. [include figures in appendix]
The material used for constructing the frame was 1.25”x.065” 4130 Seamless Steel tubing. This tubing still satisfies the requirements put in place by Article B8.3.12 [reference this] which states that the primary roll cage members must be “a steel shape with bending stiffness and bending strength exceeding that of circular steel tubing with an outside diameter of 1”, a wall thickness of 0.120” and a carbon content of .18%”. Bending stiffness is calculated as EI, where E is the elastic modulus and I is the second moment of the area for the structural cross section. The elastic modulus is the same value for all steels but the second moment is found by the equation:
Bending strength is given as SyIC Sy is the yield strength of the material, and C is the major radius of the tubing. Calculated values show that the 1.25” x .065” 4130 tubing satisfies these requirements. [calculate actual variables and tabulate in appendix?] Use of thinner 4130 tubing over the thicker 1080 tubing allows overall weight of the frame to decrease while still maintaining the same structural integrity.
Finite Element Analysis
Two [finite element analyses] were conducted on the car design using PATRAN/NASTRAN software. The first tested a frontal impact with a stationary object. The second was a rollover impact analysis with force applied between the RHO and FBM. The factor of safety for each analysis was found using a yield stress of 63,100psi [reference] for 4130 seamless steel.
The load application for the front impact study was determined using data from a KEVA technical report. KEVA, an automotive engineering and consulting firm, conducted collision testing on a midsize four door sedan traveling at 35 mph. Upon collision, the stopping time was 0.11 seconds [reference] which can be translated to 14.5G’s of acceleration. This value was chosen for the frontal load since it acts as the true worst case scenario for our vehicle. Thus the resulting data would fully ensure driver safety during a frontal impact. A force equivalent to the combined weight of the driver and car was applied in the direction of impact. The force of the impact was calculated using the weight of the 95th percentile male driver between the ages of 30-39; 280 lbs[reference below]. The car was constrained in all six axial directions for this analysis. Figure 1 shows the finite element analysis results showing high stress areas in red or black. For the given collision, the roll cage factor of safety was found to be 1.40.
An initial load of 2G’s was applied between the top bend of the RHO and FBM for this analysis. The force was applied inward and downward providing a worst case scenario. The margin of safety accounts for the unlikely event in which the top bend hits the ground at a perpendicular direction. This is an unlikely scenario because when the car rolls, the frame does not come into full contact with the ground but is impacted at an angle with only a portion of the full load being applied. Figure 2 shows the resulting analysis from which a 1.14 factor of safety was calculated.
2013 Baja SAE Series Competition Rules
U.S. Census Bureau, Statistical Abstract of the United States: 2012 (131st Edition) Washington, DC, 2011;
Varat, Michael S., and Stein E. Husher. Crash Pulse Modeling for Vehicle Safety Research. Tech. KEVA Engineering. Web. 09 Sep. 2012.
Online Materials Information Resource http://www.matweb.com. 2011