OLD DOMINION UNIVERSITY
SAE Baja Final Report
Frame
Suspension
Drivetrain
Dan D’Amico
Peter Morabito
Kenneth Elliot
Curtis May
Michael Paliga
Patrick Mooney
Greg Schaffran
Brian Ross
Dylan Quinn
Faculty Advisor: Dr. Elmustafa
Table of Contents Section
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List of Figures…………………………………………………………………………………………………………………………………….…..ii Abstract…………………………………………………………………………………………………………………………………………….……iv Introduction………………………………………………………………………………………………………………………………….……….1 Background………………………………………………………………………………………………………………………………….….…….1 Methods ……………………………………………………..………………………………………………………………...……………….…….5 Results………………………………………………………………………………………………………………………………………..…………11 Discussion…………………………………………………………………………………………………………………………….……………….20 Conclusion ………………………………………………………………………………………………………………………………………..….26 Appendix A…………………………………………………………………………………………………………………….…………….........27 Appendix B…………………………………………………………………………………………………………………………………………...33 Appendix C……………………………………………………………………………………………………………………………………………34 Appendix D……………………………………………………………………………………………………………………………………………35 References…………………………………………………………………………………………………………………….......................36
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List of Figures Figure
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Figure 1. Camber Angle……………………………………………………………………………………………..………………………3 Figure 2. Caster Angle……………………………………………………………………………………………………………………….3 Figure 3. Toe Alignment………………………………………………………………………………………….…………………….…..4 Figure 4. Inclination of Suspension Axis …….………………………………………………………………………………….….4 Figure 5. SAE Axis Terminology ………………….…………………………………………………………………………….….……4 Figure 6. Revised Frame……………………………….……………………………………………………………………………………6 Figure 7. Briggs Stratton Engine ..……………….……………………………………………….………………………………..….7 Figure 8. CVT ……………………………………………….………………………………………………………………………..…….……7 Figure 9. Geartrain……………………………………….………………………………………………………………………….…...….9 Figure 10. Lewis and Barth Stresses…………………………………………………………………………………………….…..10 Figure 11. AGMA Stresses………………………………….………………..……………………………………………………...….10 Figure 12. Final Frame Model………………………………..…………………………………………………………………..….…11 Figure 13. Differential……………………………………….……………………….…………………………..…………………….….11 Figure 14. Side Impact Testing 3500lbs ……………………………………….…………..………………………………………12 Figure 15. Front Impact Testing 5000lbs………………………………………….………..………………………………….….13 Figure 16. Rollover Testing (Front) 5000lbs……………………………………….…………..…………………………………13 Figure 17. Rollover Testing (Top) 5000lbs…………………………………………….……..……………………………………14 Figure 18. Suspension Modeling in Optimum K…………………………………………………..……………………….…..14 Figure 19. FEA of Stress in Upper A- arm…………………………………………………..…………………………………..…15 Figure 20. FEA of displacement in Upper A-arm…………………………………………………..………………..…………15 Figure 21. FEA of stress in Lower A-arm…………………………………………………..…………………………………….…16 Figure 22. FEA of Displacement in Lower A- arm………………………………………………….……………………………16 Figure 23. FEA of Stress in Trailing Arm…………………………………………………………………….……………………….17 ii
Figure 24. FEA of Displacement in Trailing Arm………………………………………………………..……………………….17 Figure 25. Gearbox Model …………………………………………………………………………………………..……………………18 Figure 26. FEA of Stage 2 Pinion……………………………………………………………………………………….……………….19 Figure 27. FEA of Stage 2 Gear……………………………………………………………………………………………………………19 Figure 28. Maximum Stress and Safety factor in Gears………………………………………………………………….…..19 Figure 29. Design Comparison…………………………………………………………………………………………………………….20 Figure 30. Model of Upper A- arm………………………………………………………………………………………………………22 Figure 31. Model of Lower A- arm……………………………………………………………………………………………..……….22 Figure 32. Model of Trailing Arm………………………………………………………………………………………………………..22 Figure 33. Geartrain…………………………………………………………………………………………………………………….……..24 Figure 34. Model of Gearbox Mounts…………………………………………………………………………………………..……25 Figure 35. CVT………………………………………………………………………………………………………………………..………....25
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Abstract The Society of Automotive Engineers (SAE) Baja senior design project enables students to gain real world experience in the design, analysis, and manufacture of a vehicular product. Specifically, our team has been organized into frame, drivetrain, and suspension subgroups to allow a thorough and original design of all major components. The frame team has accomplished the creation of a new frame design that is concurrent with all SAE competition rules. Finite element analysis has been conducted on the frame to ensure the safety of the vehicle. Special consideration was given to weight and cost reduction which has been improved on from the previous years. The suspension team will focus primarily on the rear suspension. A reliable trailing arm design was created for rear suspension applications, while the front suspension consists of a standard double A- arm setup. The suspension has been analyzed with Optimum Kinematics and Solidworks software. The drivetrain team has designed a double reduction gearbox, with an emphasis on efficiency and weight reduction. The transmission will be a continuously varying transmission (CVT). Stress analysis has been conducted to ensure the reliability of the design. The purpose of this project is to design a SAE Baja vehicle from scratch so that this design can be utilized in the 2014 SAE Baja Competition.
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Introduction The SAE Baja senior design project is a semester long project intended to allow senior mechanical engineering students to design an off-road vehicle for competition. This project allows students to apply engineering theories and concepts that have been presented to them in previous courses. The purpose of this project is to further the design, manufacturing, teamwork and communication skills of the team members to prepare them for working in industry. The team has been divided into three subdivisions in order to design all the main aspects of the vehicle. The subgroups are: the drivetrain team, suspension team, and frame team. The drivetrain team will focus on designing a more efficient powertrain design. This will be achieved by replacing the existing chain driven system with a gearbox. A gearbox will greatly improve the vehicle’s reliability and efficiently as well as reduce the overall weight of the car. The gearbox will be paired with a CVT transmission to provide a range of gear ratios to improve the vehicle’s maximum torque and top speed. The suspension team will develop a more reliable and predicable suspension system. The front suspension will consist of a double A-arm set up, similar to previous years, to function with the new frame design. The rear suspension will consist of a four link trailing arm set up to allow for dynamic camber and the greatest possible suspension travel. This will be more reliable than last year’s design and should provide the same steering and suspension capabilities. The frame team will focus on producing a frame that is lighter than last year’s frame. This team has focused on shortening the frame so that less material is used and a smaller turning radius can be achieved. Additionally, this team has been working to provide the optimum suspension mounting points and rear end of the frame to accommodate the drivetrain and suspension team’s needs.
Background The first Mini Baja competition started in 1976 at the University of South Carolina with only 10 teams. Now more than 30 years later, the competition is formally known as Baja SAE and has expanded into 3 sub-regions: East, Midwest, and West. The Baja SAE competition has even grown into an international affair with competitions in Brazil, Korea, and South Africa. This year’s competition will be in Rochester, New York. The competition will include five dynamic events: Acceleration, Hill Climb, Maneuverability, Suspension & Traction, and Endurance. These events will put each vehicle through an intense test of performance and durability. The teams will also be judged on the vehicle’s styling and cost report. This competition is used to simulate real world engineering design projects and their related challenges, therefore, the purpose of the project is for each team to design, build, test,
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promote, and race an off-road vehicle that can survive the punishment dished out by each event, while keeping costs low and making it aesthetically pleasing. The SAE Baja has a large list of minimum requirements for frame design. These regulations must be met in order to ensure design integrity and driver safety. The purpose of the frame is to provide a protected space from which the driver can control the car. All of the frame requirements in the rule book have been set to ensure the driver will be as safe as possible in the event of an accident. The firewall is in place in case of a problem with the engine or drivetrain to protect the driver from fire or flying shrapnel. In the event of the car rolling over the roll cage is designed to withstand the weight of the car and keep the operator from being crushed. Sidebars provide support in case of a side impact and the nose section is designed to hold up in the event of a front end collision. The past Old Dominion University Mini Baja’s have mostly placed in the middle of the pack in terms of competition ranking. Last June the team took 55 th place out of 102 ranked teams. It is important to examine the previous Mini Baja to identify parts of the design that are not performing as well as they should. Potential areas of improvement can be identified by comparing Old Dominion’s 2012 car to other top performing schools. One of the main concerns is the overall weight of the vehicle. Last year the ODU car weighed 479 pounds compared to the 3rd place car from Cornell at 306 pounds [1]. The Old Dominion frame alone was at first said to be 330 pounds. However, when seeking further information the designer and builder of a previous frame said it only weighed 100 pounds. Table A.1 displays the event scores for the top four competitors and Old Dominion University from the SAE Wisconsin 2012 competition. The events where Old Dominion’s performances were much lower depended on high power to weight ratios. A lighter weight vehicle will improve the performances in acceleration, pulling, and endurance the most. The Baja SAE rulebook lays out many of the specifications that the designed vehicle must stay within in order to be considered eligible for competition. The maximum allowable width is 64in at the widest point of the car, wheels included [2]. With the suspension staying mostly unchanged, the car will fall well within the maximum allowable width. While there is no limit to the length, SAE suggests a maximum length of 108in [2]. The current design sits at 74.5in and is unlikely to change very much. The roll cage has been designed around the template driver that is supplied in the rule book. The first step in the design was to record all specification requirements to ensure that all were met. Barring any changes to the 2014 rule book, the designed Mini Baja will be fully eligible for the competition. The Baja’s suspension design has shown a marked progression through the years. The suspension has evolved from utilizing parallel double wishbone coil-over systems of unequal length on both the front and rear to unequal double wishbone systems on the front, and a trailing arm setup on the rear. The trailing arm rear suspension is advantageous in that it imbues greater platform stability and, as an added bonus, dynamic kinematic properties, such as toe and camber. Dynamically, criterion pertaining to toe, camber, castor, track width, 2
wheelbase, weight transfer, roll center, and suspension travel are crucial elements of a successful suspension design. According to the textbook Race Car Vehicle Dynamics, camber is defined as the angle between a tilted wheel plane and the vertical [3]. It is one of three terms used to describe a suspension’s alignment. The camber angle, γ, can have negative or positive orientations, where camber is considered positive if the top of the wheel leans outward, and negative if the top of the wheel leans inward. The figure below serves as a visual representation of positive and negative camber. If a vehicle’s wheels are properly cambered, a beneficial thrust force is produced. This thrust force, aptly named camber thrust, contributes a lateral force in the direction of the tire’s tilt. In other words, it ensures stability by pulling the bottom of the tire in the same direction the top is leaning. Figure 1 shows how the camber angle can change.
Figure 1
Figure 2
Castor, or the angle in side elevation of the kingpin axis with respect to the vertical plane, is another stability oriented kinematic property. Figure 2 above shows how the caster angle can change. The chief benefit of castor is that it is responsible for a steering centric restoring force, meaning that the amount of castor affects how the steering feels and the amount of effort required to turn the wheel. The figure to the right above depicts positive castor. Toe is the final parameter used to describe a vehicle’s alignment. From Bosch’s Automotive Handbook, toe specifies the degree to which non-parallel front wheels are closer together at the front than at the rear [4]. Tire wear is heavily dependent on toe distances. Figure 3 below shows what is meant by a toe-in alignment setup.
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Figure 4
Figure 3
The roll center has a significant impact on a suspension’s steering response; moreover, there is a direct correlation between roll center location and oversteer, understeer, or neutral steer suspension behavior depicted in Figure 4. In the book Tune To Win, author Carroll Smith defines the roll center as a point, in the transverse plane of the axles, about which the sprung mass of that end of the vehicle will roll under the influence of centrifugal force, where the sprung mass is the portion of the vehicle’s total mass that is supported by the suspension springs [4]. Furthermore, vehicles designed to understeer will require more steering input, whereas vehicles inclined to oversteer will require less steering input. Vehicles equipped with a tinge of oversteer are ideally suited for applications that demand maneuverability. The slight oversteer enables maximum agility while maintaining a forgiving nature, thus would be perfect for Baja applications. The right side figure above shows how varying the inclination of the roll axis affects steering behavior. Wheelbase is the longitudinal distance from the center of the front wheel hub to the center of the rear hub. Similarly, track width is the lateral length from wheel centerlines. The length of the wheelbase is of utmost importance when considering weight transfer and the vehicle’s center of gravity (CG). From a performance perspective, the center of gravity must remain as low as possible. Figure 5 below summarizes the SAE axes terminology and serves as a snapshot for many of the aforementioned dynamics and definitions.
Figure 5 4
Methods The first step in the design was selecting a suitable material. These are the minimum material specifications required by SAE. The metals were analyzed for their strength to weight ratio as well as their cost. The material chosen was 4130 chromoly steel. The initial steps in designing the frame was getting boundary dimensions from the SAE Baja rules. These minimum dimensions maintain a certain degree of safety for all drivers and ensure that the vehicle is rigid enough. The firewall was the first feature designed. It was angled to the maximum tilt of 20 degrees from vertical to decrease the air resistance and maximize available space for the engine and transmission as low on the frame as possible. The design was such to give a lateral breadth of 29 inches at 27 inches above the seat bottom as required in the SAE rulebook[2]. Diagonal bracing members were added no more than 5 inches from the end horizontal members of the firewall. Working forward, the front end was designed according to suspension mounting points predetermined by the suspension team. Members were drawn to accommodate the double A arms of the front suspension as well as a shock mounting point. Also in consideration was leaving space for the brake reservoirs. Consideration was also made for length for a driver's legs, leaving 44 inches between the seat bottom and the front most point on the car. The roll cage was designed by simply connecting the roll cage to the highest point on the front end. Consideration was made for minimum head clearance for driver safety. The horizontal portion of the roll cage was designed to maintain a 41 inch vertical clearance and a 12 inch forward clearance from the rear seat bottom. Upon uploading our initial design int and performing a finite element analysis we discovered that the design would not meet the minimum requirements given in the SAE regulations. After making this discovery a total of five members were added to the initial design in the weaker areas of the frame that had not shown satisfactory results. Two diagonal bars on each side, running from the side impact bar to the floor, and an additional horizontal bar across the firewall that meets the firewall perimeter hoop at the same point as the side impact bars. These members are seen in Figure 6 below and are indicated by the arrows. After making these changes to the design a finite element analysis was performed once again. The highest stress was 46.3 ksi and occurred during the front impact test. The results of the analysis for the improved design meet the SAE Mini Baja regulations.
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Figure 6
The suspension design has been broken down into two sections: front and rear. Mounting points of the suspension on the frame and hubs are used for suspension analysis. These points can be interpreted by suspension analysis software; a commonly used one is Optimum K (OptimumG, Denver, CO, USA). Optimum K allows a user to input the mounting points of a suspension and then place the designed set up through a series of tests that involve heave, pitch, roll, and steering. Solidworks (Solidworks corp, Waltham, Massachusetts) is a 3D modeling software that was used to model the frame. From this model the front suspension mounting points were calculated. These points were imported into the analysis software. Then, test points can be used to get desired results. The design for the rear suspension has been researched and a new geometry has been implemented. The rear trailing arm was redesigned such that dynamic toe was eliminated. The suspension design of the 2014 ODU Baja will remain largely unchanged with respect to the 2012 Baja car. Polaris RZR wheel hubs and parts from a Honda 400EX ATV will continue to be utilized. The design consisted of finding the optimum mounting points for the desired dynamics of the suspension. It involved a trial and error type analysis in order to find the optimum solution. The SAE BAJA 2013 rule book specifies that all teams shall use a Briggs & Stratton 1450 series engine which is shown in Figure 7 below. This engine produces a peak of 14.50 ft lbs of torque as shown in Figure A.1 and is rated at ~10 horsepower. The engine is tuned at competition by Briggs & Stratton technicians to insure that every team is running the specified engine without modifications at 3600 rpm. This is a single cylinder four stroke engine that is fed from a carburetor and manual choke. The only modification allowed to the engine at competition is a remote intake that must be specifically ordered from Briggs & Stratton and installed according to their instructions.
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Figure 7
The transmission we have chosen to pair with this engine is at Continuously Varying Transmission (CVT). This transmission is a variable diameter pulley system where the sheaves primary and secondary pulleys move in and out thus changing diameter and gear ratio. Figure 8 below demonstrates the extremes of the gear ratios that the CVT will travel through. CVT’s are ideal for the SAE Baja competition because the CVT adjusts to provide the best ratio depending on the speed of the input and output shafts thus providing max torque when needed and adjusting to the top speed ratio when needed. This type of CVT is adjustable with a system of springs and brass weights to allow tuning for specific events allowing for top speed or lower end torque bias.
Figure 8
One of the primary goals of the powertrain team is to develop a fixed ratio gearbox designed to complement the Briggs & Stratton engine and Gaged CVT system through maximizing drivetrain efficiency and reducing overall weight. The gearbox will be optimized to provide maximum vehicle performance throughout the range of events incorporated in the SAE Baja competition. The gearbox design process consists of three major areas:
Gear train and differential design Bearing and Shaft design Gearbox Housing and mounting design
Each of these areas of design requires vastly different design methods in order to produce a gearbox that will enhance the performance of the Baja vehicle.
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Gear train and differential design is crucial to the reliability of the gearbox and represents a large amount of the calculations in the project. A precise overall reduction ratio is required in order to achieve the acceptable performance out of the whole drivetrain system. The most challenging events in the competition for the powertrain team are the hill climb and endurance events, therefore the drivetrain will be designed specifically to excel in them. At the Rochester venue the hill is 36-37 degrees, the steepest of all the locations the Baja competition takes place at. The vehicle must produce enough torque with the chosen ratio to propel the vehicle up the incline from a stop with a margin of safety. Based on this, a conservative incline angle of 40 degrees was determined as well as an overestimated vehicle weight. Using the maximum reduction of the CVT as well as the average torque produced by the Briggs & Stratton engine calculations were completed to determine the minimum gearbox ratio needed to overcome the hill (Figure A. 2) In order to overcome the incline a minimum gearbox ratio of 7.7551:1 coupled with the initial CVT reduction is required. Based on this calculation it was decided that an 8.0:1 ratio would be chosen. In order to provide a margin of error the incline angle, vehicle weight, engine torque output and chosen reduction ratio were all conservatively estimated. Based on these values a total safety factor (Figure A.3) for the drive ratio of the vehicle as required on the hill climb competition was calculated to be 1.277. The final drive ratio of the car throughout the band of CVT manipulation is key to success at all of the events at the SAE Baja competition. The 8.0:1 gearbox ratio should provide good results in the hill climb and acceleration events, but it must also allow for a competitive top speed for the endurance race. The Briggs & Stratton engine is tuned at competition to have an RPM limit of 3600. Based on achieving this RPM, a theoretical top speed of 35.7 MPH was determined (Figure A .4). There are many constraints in gear train sizing and selection. The gear combinations must achieve many design characteristics:
Desired reduction ratio (8.0:1) Maintain compactness of the overall design Allow for housing of the selected differential inside the ring gear Maintain reliability under heavy use
Spur style gears will provide the most efficient transfer of power as well as the simplest bearing and support design due to the lack of lateral forces. Utilizing spur style gears will result in a noisier gear train however in a race vehicle application this is not all that significant. While helical gears can be designed to negate these lateral forces, spur gears are significantly cheaper than comparable helical gears. There is also a larger, more available selection of size and pitch combinations. The gear train will be split into two reductions in order to save space in the overall size of the gearbox. A single reduction box would require a very large spur gear to compliment the pinion gear in order to achieve the desired ratio.
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In order to aid in the selection of gears in the train a table of potential combinations was created (Table A.5). Included were available face widths, bore sizes and pitches. To ensure the chosen gear combinations would work well together, interference was calculated for each selection based on the following equation where K=1 for full teeth engagement and m=ratio.
Np = (2K/(1+2m)*sin20 deg)*(m+ sqrt(m^2 + (1+2m)*sin20 deg) Based on the results of the Interference table (Table A.5), the gears being used will have a modern pressure angle of 20 degrees and a pitch of 12. In order to achieve the 8.0:1 reduction ratio and overall size and strength the following gears have been chosen (Figure 9).
Stage 1 Reduction: (2.0:1) o Pitch = 12, Press Angle = 20° Pinion Gear: 20 Teeth - Dp = 1.6667 Spur Gear: 40 Teeth - Dp = 3.3333
Stage 2 Reduction: (4.0:1) o Pitch = 12, Press Angle = 20° Pinion Gear: 20 Teeth - Dp = 1.6667 Spur Gear: 80 Teeth - Dp = 6.6667
Figure 9
To determine the strength and reliability of the gear setup several calculation methods were employed to determine a safety factor for each of the gears: Lewis Bending Stress: Shown in Figure A.6X
- Wt is tangential force, F is face width, p is pitch and y is the Lewis Form Factor Barth Velocity Factor: Shown in Figure 10
-Kv is velocity factor, Wt is tangential force, P is pitch, F is face width & Y is Lewis factor 9
Lewis and Barth Stresses:
Figure 10 AGMA Stress and Strength: Shown in Figure 11
-Wt is tangential force, Kx are AGMA factors, P is pitch, F is face width and is J factor.
Figure 11 Finite Element Analysis was also performed on each gear modeled in Solidworks and the resultant Von Mises stresses were compared to the stresses calculated through AGMA, Lewis, and Barth methods. The differential, shown in figure 12, will be housed in the large output gear in the gearbox. The differential will allow for more maneuverability and better handling characteristics in the endurance competition by allowing a bias between the rear drive axles. The large gear will have to be machined to secure the differential.
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Figure 12
Results The frame design has been fully completed and fully complies with the SAE Mini Baja regulations. The overall design is narrower and has a shorter wheelbase than previous ODU cars. Also, the design is lighter than previous ODU designs while still providing the required level of structural integrity and driver-to-frame clearance mandated in the SAE Mini Baja regulations. This lighter design with a shorter wheelbase will improve handling ability and power to weight ratio of the car. The front end and rear end designs were created with careful consideration given to the mounting points of suspension and gearbox components requested by the suspension and gearbox teams. The final design satisfies all of these requested mounting locations and can be seen in Figure 13 below.
Figure 13
We selected 4130 'Chromoly' steel tubing with an outside diameter of 1.25 inches and wall thickness of 0.065 inches for the roll cage and firewall members. We selected 4130 'Chromoly' steel tubing with an outside diameter of 1 inch and wall thickness of 0.065 inches for the remainder of the frame members. We selected 4130 steel over other options such as 1020 11
steel or 1026 steel because 4130 has the highest strength to weight ratio and is within our budget. Also 4130 steel tubing is more readily available than other types. 4130 steel has a yield strength of 63.1 ksi and a density of 0.284 lb/in^3. The weight per foot for the primary tubing (Roll cage / Firewall) is 0.825 lb/ft. The weight per foot for the secondary tubing (All other members) is 0.651 lb/ft. The design requires approximately 23ft of the primary tubing and 70ft of the secondary tubing. The reduction in overall size of this years design and the use of the most weight efficient tubing material and cross section has resulted in an estimated overall frame weight of only 63.7 pounds. This represents a significant improvement from last years frame weight of over 70 pounds. These improvements over previous ODU designs should help to insure better performances at competition.
PATRAN analysis: The frame was analyzed under front impact, side impact, and two different rollover conditions. Analysis of the initial frame yielded stresses in the side impact condition of 74 ksi. This is well over the maximum yield stress of 63.1 ksi [1]. The frame failed in the vertical member of the firewall as well as midway through the side-bracing member on the side to which the force was applied. Because the vehicle must be maintained as safe, new members were added to direct the force away from the failure points.
Figure 14
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Loaded with a 3500 lb force applied on the side member. As seen in Figure 14, a horizontal brace was added to the firewall and support bracing was added between the top and bottom side members. Adding these additional members transferred the peak stress to the other side of the frame and reduced it to 23.9 ksi. This gives us a side impact safety factor of 2.64, which is well within safe limits.
Figure 15 For front impact, 5000 lbs was loaded on the vertical lift hook on the front end as shown in Figure 15. This load caused a stress of 46.3 ksi at the point where the side member meets the firewall. This is still under the maximum value of yield stress allowable in 4130 chromoly steel. The front impact safety factor is 1.36.
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Figure 16
Figure 17 Rollover testing, with a 5000 lb force applied at for rollover on the front with contact on the nose of the car, Figure 16, and the peak of the roll-cage and a 5000 lb force on the top of the roll cage, Figure 17. In either case, the maximum stress does not exceed 29.2 ksi. This gives a rollover safety factor of 2.16. The suspension was modeled in Optimum K, Figure 18, and was then put through a series of different simulations. The simulations were comprised of adjusting heave, roll, pitch and steering. Once the parameters are set, the simulation is played and various graphs are made displaying results on the dynamics of the suspension. These results were used in analyzing whether or not the suspension is capable to withstand the design requirements for competition.
Figure 18
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Figure 19 von Mises Stress of top front double a-arm with the two frame mounts fixed and a load of 800 pounds applied to the hub connector.
Figure 20 displacement of top front double a-arm with the two frame mounts fixed and a load of 800 pounds applied to the hub connector.
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Figure 21 von Mises Stress of bottom front double a-arm with the two frame mounts fixed and a load of 400 pounds applied to the hub connector. A 500 pound force was also added to simulate a shock applying a force to the cross member.
Figure 22 displacement of bottom front double a-arm with the two frame mounts fixed and a load of 400 pounds applied to the hub connector. A 500 pound force was also added to simulate a shock applying a force to the cross member.
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Figure 23 von Mises Stress of rear trailing arm. The frame mount being fixed and a load of 745 pounds applied to the center support in the negative z direction and a 350 pound force acting on the end in the positive z direction.
Figure 24 displacement of rear trailing arm. The frame mount being fixed and a load of 745 pounds applied to the center support in the negative z direction and a 350 pound force acting on the end in the positive z direction.
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In determining the basic overall reduction ratio of the Baja gearbox we based the selection heavily on overcoming the hill climb challenge while maintaining a competitive top speed. The conservative minimum gear ratio was calculated to be 7.775 as shown in Figure A.1. To achieve a larger factor of safety and for simplicity’s sake we decided to employ an 8.0:1 ratio. This provided us with a max torque at the wheels of 446.6 lb-ft from a standstill with the initial CVT ratio. The overall safety factor in torque to overcome the hill climb at competition is 1.277 based on Figure A.2. This is a reasonable factor of safety considering it is calculated at a standstill and on a full traction surface. In reality the loose dirt of the slope will allow for wheel spin or “slip” factor to avoid bogging the engine down and once in motion the momentum will help to keep the car travelling uphill. Considering this, the 1.277 factor is only meant to account for parasitic drivetrain loss through friction and rotating mass. The model of the gearbox is shown in figure 25. In order to keep Old Dominion’s Baja car competitive with other similarly funded schools in the endurance race a top speed of low to mid thirty mile per hour range is required based on past competition experience. Using the Gaged CVT system and the gearbox we have designed a theoretical top speed of 35.7 MPH has been calculated (Figure A.3). This is assuming achieving the maximum engine RPM of 3600 and negating the “ballooning” effect of the ATV tires being used. In reality we expect to see 33.5-34 MPH being achieved on the race course. Based on the overall size and 8.0:1 ratio requirements, the interference calculations in Figure A.4 and the stresses the gears must endure we determined the gear train to be:
Stage 1 Reduction: (2.0:1) o Pitch = 12, Press Angle = 20° Pinion Gear: 20 Teeth - Dp = 1.6667 Spur Gear: 40 Teeth - Dp = 3.3333
Stage 2 Reduction: (4.0:1) o Pitch = 12, Press Angle = 20° Pinion Gear: 20 Teeth - Dp = 1.6667 Spur Gear: 80 Teeth - Dp = 6.6667 Figure 25
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Figure 26
Figure 27
This should allow the ODU car to keep up with similarly funded teams on the faster sections of the course, as well as provide good low end power in the technical portions. The stresses calculated in Figure 26 and 27 lead us to determine a material based on material and safety factor. AISI 4130 Q&T at 1200 F allows adequate strength and availability to suite the requirements. The max stresses from each calculation method were compared to the yield stress of the material to determine the lowest safety factor. The AGMA stress method yielded the highest stress of 54 KSI and the lowest safety factor of 1.89. This is a reasonable safety factor as a worst case result.
Figure 28
After gear selection and calculation is complete a bearing and shaft system and housing will be developed. The shafts will rely on a shoulder coupled with snap rings to secure the gears in a lateral direction. A standard keyway will mate the gears to the shaft rotationally. The shafts will also contain shoulders to house bearings. The gearbox housing will be split horizontally into two sections along the centerline of the bearings allowing for access and support.
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Discussion The goal for the frame team is to reduce the size and weight of the frame without compromising structural integrity or performance of the vehicle. Size is a big factor in the weight difference between Old Dominion’s 2012 vehicle and the top competitors. Old Dominion’s frame was considerably larger than the other top competitors who favored a more compact vehicle. It can be seen in Figure 10 the length differences between the Old Dominion University, Oregon State, and Cornell vehicles. The driver of ODU’s Mini Baja has his legs almost fully extended and the steering column juts out a considerable distance. Both Cornell’s and Oregon State’s drivers have their knees bent and the steering column barely juts out from the front end.
Figure 29. Old Dominion mini Baja [9] (top left), Oregon State University mini Baja [10] (top right), Cornell University mini Baja [10] (bottom).
This large ODU Baja design was a result of concerns about the required driver clearances and exit time. These other teams have shown that all the required clearances and the exit test can be met while designing a smaller vehicle. The length and width of the car are the main focuses for reducing the frame size. Height will also be examined, but it is not believed to have as much room for reduction. Another possibility is the presence of redundant members built into previous frame designs. Identifying any members that are structurally unnecessary will help optimize the design. It is important that the power to weight ratio is improved so that the
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team can be more competitive in events such as acceleration, hill climb, maneuverability, and endurance. The results from the final frame design show that the overall frame weight will end up totaling 64 pounds. This weight was calculated using the mass properties function in SolidWorks. This weight is a slight reduction from the previous frame’s weight of around 70 pounds. Weight was reduced mainly by shortening the length of the car and finding members that did not increase the structural integrity of the vehicle. The next step was to determine whether the frame would be reliable in the event of a collision. A finite element analysis was run in PATRAN to determine how the frame would react to certain collision situations. It can be seen from the PATRAN models that the maximum stress was produced in the side impact testing. This stress of 46.3 ksi is less than the ultimate tensile strength of the 4130 steel, 63.1 ksi [5]. Therefore, the frame will remain structurally intact in the event of collision. The maximum deformation occurs in a front end collision with a deflection of 0.729 inches. This deformation represents the total deformation of the frame from the perspective of the nose section. All maximum deformations in other collision tests fall well below this and do not pose a threat to the driver. PATRAN testing has shown that the current frame design will hold up to required collision scenarios well and protect the driver effectively. There are quite a few limitations to how much the design can be improved and performance enhanced; some are within control and some outside of it. Money is a limitation that cannot be overcome by our team. The school is unlikely to drastically change the budget allotted to the Mini Baja team which leaves sponsors as the only other source of income. Without a dedicated marketing team and more impressive competition record it is unlikely that the income from sponsors will change much. This leaves the team without many of the advantages that better funded schools have, such as dedicated machine shops and the ability to manufacture parts from carbon fiber. These allow teams with such facilities and budgets to have large advantages over other teams. A limitation that can be controlled is the transfer of designs and information from one year’s design team to the next. This would be a great advantage in being able to perform necessary modifications to improve a design instead of starting a new one from scratch. However for this to have any effect the shop team actually needs to construct the vehicle that the design team drew plans for. There has been little communication between the shop team and the design team in previous years. This has led to design teams that have failed to meet the proper requirements and shop teams that have decided to design their own Mini Baja. This is less than optimal and results in little design information being passed on to the next year’s design team. It would be very beneficial for the faculty advisor to facilitate communication between the two teams and emphasize the passage of design information. The suspension team was tasked with improving the design and durability of the previous year’s rear trailing arm setup, while utilizing a standard double A-arm configuration in the front. Specifically, the suspension team’s prime directive is to eliminate the dynamic toe 21
feature of the rear trailing arm. Additional considerations pertaining to cost mitigation, and manufacturability were employed in order to minimize the amount of time and effort required for production. The 2012 Baja design team conducted extensive research into how the structural integrity of suspension components could be optimized. Building upon their conclusions, both A-arms and trailing arm utilize 4130 chromoly steel tube with one inch outside diameter, 0.065 wall thickness, and 69 kpsi yield strength. The fully modeled upper, lower A-arms and trailing arm can be found in Figure 30, Figure 31 , and Figure 32. The rear trailing arm has been designed such that it extends and mates to the toe-link receptacle on the rear wheel hub, thereby eliminating dynamic toe and maintaining manufacturability. To ensure a long lifespan and robust performance, all applicable suspension components were subjected stress analysis in SolidWorks. The assumptions pursuant to the stress analyses reflect what could occur in a worst case scenario. When subjected to an 800 lbf load near a heim join at the interface of the wheel hub, the upper A-arm incurs a maximum stress of 58 kpsi just after the frame connection points; 0.3 inch maximum displacement occurs at the heim joint, which concurs with the motion of the impact. The lower A-arm experiences a maximum stress of 68 kpsi at the same frame interface location and maximum displacement is 0.3 inch at the wheel hub interface. The maximum stress in the rear trailing arm is 45 kpsi and occurs at the midpoint of the arm. 0.3 inch is the arm’s maximum displacement.
Figure 30
Figure 31
Figure 32
The front and rear suspension setups have been finalized OptimumKinematics suspension analysis software. The results of the analysis are shown in Figure D.1, Figure D.2 Figure D.3, Figure D.4. Using Race Car Vehicle Dynamics as a reference, a minor aberration can be discerned in Figure D.2, which indicates steering is in need of further refinement. The center of gravity for the 2012 Baja car was calculated using rudimentary materials and the results are 22
included in Figure A.10. The center of gravity was found to lie approximately 10 inches above the axial center, and can be shortened by using lower mounting locations. Lastly, Fox Float Racing Shocks have been selected over re-using the Custom Works Shocks of previous years. The Float Racing Shock is an air shock that offers superior cost effectiveness. A pair of Fox Float Shocks cost $521.25 and the Custom Works Shocks cost approximately $859 per pair (Figure C.1). Figure A.8 and Figure A.9 serve as a verification of similar performance envelopes, so the compromise on behalf of cost will not severely impact performance. Qualitatively, compression and rebound force versus velocity curves are highly linear. Linear damping rates are acceptable, and one can see how the shock copes with the transition from minor to major undulations. The validity of the finite element analysis is heavily contingent upon the analyst’s assumptions. The stress and displacement analysis for each component of the suspension was taken with respect to the maximum load it could sustain while maintaining a factor of safety no less than one. The maximum load on the lower A-arm was 500 lbf and the load on the rear trailing arm maxed out at 745 lbf. An ideal loading on a single component would be 2g or 2-3 times the weight of the car and driver. In our analysis, loading amounted to about 1.5 times the weight of the car and driver due to considering the dynamic nature of the suspension. Our model is taken from the perspective of bottoming the shock out, where the maximum amount of the impact force can be transferred and dissipated. The Baja drivetrain will undergo significant upgrades this year, the largest of which is a new custom gearbox. The objective of this year’s gearbox design is to create a two-stage, double reduction gearbox. This type of gearbox will replace the belt drive system used in the previous car to save weight and improve efficiency. The new vehicle will not have an updated transmission as the Gaged CVT system worked well in the past. It will however have a differential incorporated into the gearbox design. These modifications will hopefully enhance the performance of Old Dominion’s Baja vehicle at competition. In order to achieve success and be competitive in all of the events at the competition, a more versatile gearbox design was chosen. After reviewing the types of events that the vehicle will likely encounter; a gearbox ratio of 8:1 was decided upon. A large reduction ratio was chosen to correspond with an emphasis toward acceleration rather than top speed. Also, the large ratio will be more adequate for completing the hill climb course. Spur gears will be used throughout the gearbox because they are more efficient and simpler to manufacture compared to helical gears. A two-stage compound gear train like the one in Figure 33 below, shows a design similar to the one that will be incorporated in the gearbox.
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Figure 33
In the quest for excellence, a decision was made to incorporate a more advanced design that involving a differential housed in the large output spur gear. The differential was added to the design mainly to increase the vehicles maneuverability to compensate for the large overall weight and length of the ODU car. Having an open differential allows for the wheels to rotate at different speeds when making turns leading to a smaller overall turning radius. This should allow the car to excel in the maneuverability challenge and improve high speed handling in the endurance race. The gear train design will be supported by 1 inch diameter AISI 1018 steel shafts. Ball bearings are held in place on the shafts by grooves and incorporated snap rings. Similarly, the gears are held in place laterally on the shafts by grooves and snap rings, but rely on a standard keyway to prevent rotation. The casing of the gearbox is machined out of 6061-T61 Aluminum and utilizes a hinge type mount on either end of the box in order to secure the gearbox to the sub frame assembly. In addition to the hinge mounts, tabs are also used to maintain adequate rigidity of the two sides of the case. The full case design is shown in figure 34 below.
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Figure 34
The transmission was chosen to be a Gaged GX-9 continuously variable transmission (CVT). This type of transmission will be able to transmit power at optimal efficiency while maximizing performance. It accomplishes this by being able to shift smoothly and continuously through an infinite number of gear ratios within a given range of 3.85:1 initial drive to 0.9:1 final drive. A picture of the Gaged GX-9 CVT without the belt is shown below in Figure 35. This system also removes the need for a clutch as the belt slips allowing the engine to spin freely when the secondary shaft is held.
Figure 35
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While the powertrain design of this year’s vehicle has some similarities to past cars, the gearbox design is very different than what has been run in the past. This year’s gearbox is radically different than last year’s design mainly due to chain drive issues that arose at competition in the past that were discovered and now corrected. A gear driven setup was chosen in order to calm to the complaints of the previous team about the added weight and noise of a chain drive. Difficulties in maneuverability in previous vehicles created a need to add a differential to the design. In doing so, the new car will be able to move more quickly in and out of turns. Both this year and last year’s teams have the same transmission Gaged CVT system which functions extremely well. Several limitations of this study are present and effect the possible conclusions that could be made. It is hard to say how effective the gearbox design actually is because the powertrain will not be physically tested at competition until next year. Although the project has limitations, its future implications create a meaningful assignment. Future teams will be able to analyze the performance and durability of past designs and make modifications and improvements to them. This type of project allows for ODU’s baja SAE vehicle to progress with each generation.
Conclusion The Baja design team set out to improve three sections of the current Mini Baja: the frame, drivetrain, and suspension. The team goals were to reduce the weight of the frame, improve the efficiency of the drivetrain, and increase the reliability of the rear suspension. The frame was based on the design of the previous year and underwent several revisions. The overall length, width, and height were reduced to save weight but still meet driver safety requirements. Members that did not aid in the structural integrity of the car were also removed. Once the final design had been finished and analyzed, the total frame weight came out to around 64 pounds. This was a decent improvement over the previous frame weighing around 70 pounds. Instead of the standard chain drive, this year the drivetrain designed a gearbox for the vehicle. All the appropriate gear ratio calculations were completed to meet the target speed and hill climb ability. The designed gearbox will be much more efficient over the previous chain drives. The gearbox should greatly improve the overall performance of the Old Dominion car at competition. During last year’s competition there was a failure in the rear suspension that severely limited performance. The rear suspension has been redesigned to avoid a similar failure that would severely hamper performance. The overall goals of the team were completed on time as can be seen in the current Gantt chart (Figure B.1).
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Appendix A
Figure A.1 Torque Curve
Minimum Ratio (X) to Overcome Incline Angle ENGINE TORQUE: 14 LB-FT CVT RATIO (INITIAL): 3.85:1 TIRE ROLLING DIAMETER: 1.0 FEET [VEHICLE WT]*[SIN(INCLINE ANGLE)] = REPELLING WEIGHT [650 LBS]*[SIN(40 DEGREES)] = 418 LBS REPELLING WT = (TIRE RADIUS)*(CVT RATIO)*(ENGINE TQ)*(X MIN) 418 LBS = (1.0 FT)*(3.85)*(14 LB-FT)*(X MIN) ----->XMIN= 7.7551 ENGINE TORQUE: 14 LB-FT CVT RATIO (INITIAL):Figure 3.85:1A.2 Minimum Reduction Ratio TIRE ROLLING DIAMETER: 1.0 FEET [VEHICLE WT]*[SIN(INCLINE ANGLE)] = REPELLING WEIGHT [650 LBS]*[SIN(40 DEGREES)] = 418 LBS REPELLING WT = (TIRE RADIUS)*(CVT RATIO)*(ENGINE TQ)*(X MIN) 418 LBS = (1.0 FT)*(3.85)*(14 LB-FT)*(X MIN) ----->XMIN= 7.7551
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Factor of Safety (Reduction Ratio) (Figure A.2X) VALUES: ESTIMATE / ACTUAL GEAR RATIO: (8.0 / 7.7551) = 1.0326 VEHICLE WEIGHT: (650 LBS / 600 LBS) = 1.0833 INCLINE ANGLE: (40 DEG / 37.5 DEG) = 1.0667 TORQUE: (15 LB-FT MAX / 14 LB-FT AVG) = 1.0714 TOTAL FS = (1.0326)*(1.0833)*(1.0667)*(1.0714) ----->TOTAL SAFETY FACTOR = 1.2772 VALUES: ESTIMATE / ACTUAL GEAR RATIO: (8.0 / 7.7551) = 1.0326 VEHICLE WEIGHT: (650 LBS / 600 LBS) = 1.0833 INCLINE ANGLE: (40 DEG / 37.5 = 1.0667 Figure A.2DEG) Reduction Ratio Verification TORQUE: (15 LB-FT MAX / 14 LB-FT AVG) = 1.0714 TOTAL FS = (1.0326)*(1.0833)*(1.0667)*(1.0714) ----->TOTAL SAFETY FACTOR = 1.2772
Top Speed Calculations (Figure A.3X) 3600 RPM Max ENGINE SPEED → 216,000 ROT/HOUR 0.9:1 FINAL CVT RATIO TIRE RADIUS = 1.0 FT TIRE ROLLOUT: (2π)*(1.0 FT) = 6.28319 FEET DISTANCE PER ROTENG = (6.28319 FT) / (0.9*8.0) = 0.872665 FT/ROTENG (216,000 ROT/HR)*(0.872665 FT/ROT) = 188,496 FT/HR (188,496 FT/HR)*[(1 MILE) / (5280 FT)] = 35.699 MPH ----->TOP SPEED @ 3600 RPM = 35.7 MPH
3600 RPM Max ENGINE SPEED → 216,000 ROT/HOUR 0.9:1 FINAL CVT RATIO TIRE RADIUS = 1.0 FT TIRE ROLLOUT: (2π)*(1.0 FT) = 6.28319 FEET Figure A.3FT) Top Speed Calculations DISTANCE PER ROTENG = (6.28319 / (0.9*8.0) = 0.872665 FT/ROTENG (216,000 ROT/HR)*(0.872665 FT/ROT) = 188,496 FT/HR (188,496 FT/HR)*[(1 MILE) / (5280 FT)] = 35.699 MPH ----->TOP SPEED @ 3600 RPM = 35.7 MPH
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Table A.5 Gear Specifications for Reduction Ratio.
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Figure A.8 Shock Compression Behavior.
Figure A.9 Shock Rebound Behavior
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Figure A.10 Baja Center of Gravity Calculations
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Rank School Overall (1000) Overall Dynamic (300) Overall Static (300) Cost (100) Design (200) Acceleration (60) Land Maneuverability (60) Mud Bog (60) Pulling (60) Suspension & Traction (60) Endurance Race (400)
1 Universite Laval
2 Oregon State University
3 Cornell University
4 EDTS
55 Old Dominion University
913.77
896.63
893.62
880.21
530.74
266.59
256.18
232.58
227.13
185.54
245.18
236.45
258.04
252.08
183.04
90.80
74.45
83.54
80.45
71.29
154.38
162.00
174.50
171.63
111.75
60.00
51.72
53.95
47.92
32.24
60.00
58.06
56.44
54.04
48.06
50.04
60.00
46.34
34.91
43.22
36.55
30.31
22.29
36.11
15.16
60.00
56.09
53.56
54.15
46.86
402.00 404.00 403.00 401.00 Table A.1 Score Breakdown of Top Four Schools Compared to Results for ODU Mini Baja Team [7].
162.16
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Appendix B
Figure B.1 Current Gantt Chart.
APPENDIX C: COST ANALYSIS Frame Tubing Material
Length
Price per Foot
Cost
1.25 OD x 0.065 T
23 feet
$6.55
$150.65
1.00 OD x 0.065 T
70 feet
$4.85
$339.15
TOTAL
$490.15
Gearbox Item
Quantity
Cost per Item
Total
Ball Bearings
6
$12.00
$72.00
6” Keyed Shaft
1
$17.00
$17.00
12” Partially Keyed Shaft
1
$40.00
$40.00
6061 Aluminum 4”x5”x12”
2
$210.00
$420.00
4041 Steel 1.5”x6”x 3ft
1
$400.00
$400.00
TOTAL
$949.00
Suspension Item
Quantity
Cost
Total
Shocks
2 pair
$521.25
$1042.50
1.00 OD x 0.065 T
20ft
$4.85
$97.00
Rear Hubs
2
$178.75
$375.50
Front Hubs
2
$140.00
$280.00
Wheels
4
$40.00
$160.00
Tires
4
$40.00
$160.00
TOTAL
$2115.00
APPENDIX D
Figure D.1 Castor vs. Roll
Figure D.3 Camber vs. Roll
Figure D.2 Wheel Angle vs. Steering Angle
Figure D.4 Camber vs. Heave
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References [1] Cornell Baja: The Cars. Cornell University. Available: http://baja.mae.cornell.edu/about.php [2] 2013 Collegiate Design Series: Baja SAE Series Rules, SAE International, Warrendale, PA, pp. 19-32. [3] Milliken, W. F., & Milliken, D. L., Race Car Vehicle Dynamics. Warrendale: Society of Automotive Engineers, Inc., 1995. [4] Smith, Carroll, Tune To Win. Rolling Hills Estates, CA: Carroll Smith Consulting Incorporated, 1978. Automotive Handbook, 2nd ed., Bosch, Stuttgart, GmbH, 1986, pp. 480-481. [5] 4130 Alloy Tube Round [Online]. Available: http://www.onlinemetals.com/merchant.cfm? id=250&step=2 [6] Aerospace Specifications: AISI 4130 Steel [Online]. Available: http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=m4130r [7] ASTM a513 alloys 1020 [Online]. Available: http://www.onlinemetals.com/alloycat.cfm?alloy=A513 [8] a513 Type 5 Steel Tube DOM [Online]. Available: http://www.onlinemetals.com/merchant.cfmid=283&step=2 [9] OnlineMetals Guide to Steel [Online]. Available: http://www.onlinemetals.com/steelguide.cfm
[10] Baja SAE Results. SAE International. Available: http://students.sae.org/competitions/bajasae/results/ [11] ODU Baja. ODU Baja Facebook Page. Available: http://www.facebook.com/ODUBaja/photos_stream [12] Baja SAE Oregon. Baja SAE Oregon 2012 Competition. Available: http://www.facebook.com/BajaSaeOregon/photos_stream
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