Vehicle #49
GVSU Laker Racing Technical Design Report Jeff Blair, Karl Hiedemann, Cody Holstege, Mike Mulder, Michael Olson, Dan Schwarz, Andrew Tallman The 2008 Grand Valley State University Baja SAE Race Team
William Waldron, Ph.D. Faculty Advisor Copyright © 2008 SAE International
ABSTRACT
FRAME
An off-road racing vehicle, powered by the Briggs and Stratton Intek Model 20 engine, was successfully designed and manufactured to compete in the 2008 Montreal competition. The GVSU Baja team made improvements on the vehicle designed to compete in the 2007 race. Major design changes were made to improve driver ergonomics, and improve the performance of the vehicle. Additionally, the top speed of the vehicle was increased from 30 miles per hour to nearly 40 miles per hour, and the mass of components was decreased. The driver compartment, front suspension, and rear suspension were completely redesigned for the 2008 vehicle. Design changes were also made to the drivetrain, steering, and braking systems.
Frame Testing The 2006 frame was subjected to two static loading cases in order to study the stresses in critical members under typical driving and rollover conditions. Figure 1 shows the mounting locations for strain rosettes. As part of the test, specific frame members were removed and the test was resumed in order to study the significance of specific members on the frame rigidity. For the rollover test, the frame members removed were the top diagonal brace and the vertical roll cage support. For the drop test loads, the two members removed were the pedal mount tube and the dashboard mount tube. Roll Cage Support
INTRODUCTION Grand Valley State University Laker Racing Team is entering the Baja SAE competition for the fifth year. The team consists of seven engineering students ranging from sophomore to senior standing. Six of the team members will be participating for the first time this year. The 2008 vehicle design is based on testing conducted on previous vehicles, race results, and lessons learned by the previous teams.
Top Cross Brace
Top Roll Cage
Front Roll Cage
Pedal Brace
Front Upper Shock Mount
Speedometer Brace
Front and Rear Upper A-arms
Spindle
Front Lower A-arm Front Lower Shock Mount Lower Roll Cage Support
VEHICLE DESIGN
Side Impact Member Bottom Roll Cage
Extensive testing of the 2006 vehicle was performed. Strain of critical frame members and suspension components were measured under several vehicle loading conditions. Temperature at various locations on the secondary reduction box was measured as a function of time when the vehicle was running at full throttle, under load. The kingpin was analyzed as part of the vehicle strain testing, and using a tensile testing machine.
Figure 1: Mounting Locations of the 15 Strain Rosettes and the Three Members that were Removed During Testing
Frame Loading The first test simulated a rollover. For this test a downward load was applied to the top of the roll cage. The second test simulated a drop from 24 inches, landing on the front two wheels. The load was applied statically, therefore an equivalent load was calculated which accounted for inertia, the spring and damper forces, and the spring rate of the tire. A free body diagram was used to derive the state equations for the
any single member was 5. This was in the top roll cage after the vertical roll cage support had been removed. Sigma 1 Stress (psi)
dynamic loading, shown in Figure 2. Using Scilab mathematical software, the equations were numerically integrated using Runge-Kutta. Table 1 shows the values of the constants used for the simulation. The force due to the spring and damper acting on the frame was plotted against time and is shown in Figure 3. A maximum force of 1,100 pounds was found to be acting on the vehicle frame at each shock mount. Therefore, a static load of 2,200 pounds was applied to the front end.
Side Impact Member
8000 7000 6000 5000 4000 3000 2000 1000 0
Top Roll Cage Bottom Roll Cage
All Members Intact
Top Brace Upper Roll Removed Cage Support Removed
Front Roll Cage Lower Roll Cage Support
Testing Condition
Figure 4: Principal Stress (Sigma 1) Results from Rollover Test
All Members Intact
Top Brace Removed
Upper Roll Cage Support Removed
Figure 2: Spring Damper System and Corresponding Free Body Diagram (FBD) used to Determine Frame Loading Table 1: Constant values used for numerical integration of the vehicle loading state equations
Value 700 30.0 114 5.70 1140 13.1
Units pounds pounds lbf/in lbf·s/in lbf/in ft/s
Force (lbf)
Variable Mc Mw Ks Kd Kw V1
Sigma 2 Stress (psi)
0
Bottom Roll Cage Front Roll Cage
-4000 -6000 -8000
Lower Roll Cage Support
-10000 -12000 -14000 Te sting Condition
Figure 5: Principal Stress (Sigma 2) Results from Rollover Test
Figures 6 and 7 show the stresses measured in the three members during the drop test. The stresses experienced by the three members are all below the 60,000 psi yield strength of the steel members. When the pedal brace was removed, the side impact member to which the upper shock mounted experienced over 35,000 psi of tensile stress due to bending. This is equal to 58% of the yield strength and therefore is likely to cause fatigue failure under repeated loading. Although the cross tube between the side impact members showed little deflection before it was removed during testing, this member is essential to reducing the bending stress that the side impact members are subjected to during shock compression. 40000 35000 Principle Stress (psi)
Time (sec)
Figures 4 and 5 show the results of the rollover test for the six members experiencing the greatest stress. The results of the rollover test showed that the side impact member experienced the greatest amount of tensile stress. Removal of the top diagonal brace did not significantly increase or decrease stress in any of the members. Therefore, this member was eliminated. Removal of the vertical roll cage support member caused stress in the bottom roll cage member to be decreased significantly and the stress in the side impact members to increase. The lowest safety factor seen by
Top Roll Cage
-2000
Figure 3: Force as a Function of Time Acting on Car at Each Front Shock Mount due to a Drop of 24 inches
Results
Side Impact Member
30000 Original Frame
25000 20000
Pedal Brace Removed
15000 10000
Dash Brace Removed
5000 0 Front Lower Shock Mount
Front Upper Shock Mount
Lower Roll Cage Support
Figure 6: Principal Stress (Sigma 1) Results from Drop Test
Front Lower Front Upper Shock Shock Mount Mount
landing impact forces into the shock, rather than a shear force through the a-arms.
Lower Roll Cage Support
Principle Stress (psi)
0 -2000 -4000 -6000 -8000 -10000 -12000 -14000
Original Frame Pedal Brace Removed Dash Brace Removed
-16000
Figure 7: Principal Stress (Sigma 2) Results from Drop Test
Material Selection Figure 8: Frame Assembly
Roll Cage According to SAE rules, elements of the roll cage must, at minimum, be circular steel tubing with an outside diameter of 1 inch and a wall thickness of 0.120 inch and a carbon content of at least 0.18 or steel with at least equal bending stiffness and bending strength to 1018 steel having a circular cross section with a 1 inch outside diameter and a wall thickness of 0.120 inch [1]. Seamless Drawn-Over-Mandrel 4130 alloy steel tube with an outside diameter of 1.25 inches and a wall thickness of 0.065 inches was selected for the roll cage construction. This combination of material and tubing dimensions exceeds the minimum frame member requirements. Additional Frame Members According to SAE rules, the additional required members must be steel and only have a minimum thickness of 0.035 inch and a minimum outside diameter 1.0 inch [1]. These members include the Lateral Diagonal Bracing, Lower Frame Side, Side Impact Members, Fore/Aft Bracing, and Front Lateral Cross-member. Seamless Drawn-Over-Mandrel 4130 alloy steel tube with an outside diameter of 1.25 inches and a wall thickness of 0.035 inches was selected for all frame members forward of the fire wall, excluding the roll cage elements. The rear of the frame was constructed using 1.5 inch outer diameter tubing with a wall thickness of 0.035 inches.
Figure 9: Schematic of Suspension Compression
Cockpit Design For 2008, the frame was redesigned from the firewall forward, with heavy emphasis placed on improving driver ergonomics. The 2007 frame was very short, and narrow in the area of the driver’s feet. This, in addition to poor pedal placement, resulted in a very cramped driver compartment, especially for taller drivers. The 2008 vehicle was designed with a 3 inch longer wheelbase, and the front of the frame was increased an additional 3 inches. The front of the frame was also widened 5 inches. The foot area of the frame was widened more at the side impact members then at the lower frame sides, to accommodate an unequal arm length suspension, and give the driver additional foot room. Figure 10 shows a comparison between the 2007 and 2008 cockpit.
Frame Design Objectives The primary objective was to design a roll cage with the lowest mass possible that satisfied the safety requirements. Figure 8 shows the frame assembly. The results from the testing aided in the frame design. All unnecessary members were eliminated. The lower side members were used as mounting points for the lower A-arm. The lower side members were inclined 8˚ to improve the ride and control of the vehicle on severe off-road terrain. Figure 9 shows the direction of compression upon bump impact. The incline directs
2007 2008 Figure 10: 2007 and 2008 Foot Area Comparison
Pedal Placement To additionally improve the driver ergonomics, careful attention was paid to the packaging of the pedal assemblies. A lower pivot was chosen for the pedals, to leave more room above the driver’s feet. The location allowed the driver’s feet to rest in front of the steering rack mount, a position which is comfortable for both tall and short drivers. A model of the foot area with pedal assemblies is shown in Figure 11.
Figure 12 : Upper and Lower A-Arm
suspension compression. Under cornering conditions, the vehicle undergoes body roll, causing the outer suspension to compress. The increase in negative camber angle is designed to hold the wheels nearly perpendicular to the track surface, resulting in increased traction. The caster angle was set to 8˚ as a result of sloping the frame members to which the a-arms are mounted.
Figure 11: Driver Foot Area
Master cylinders with remote mounted reservoirs were mounted low, and between the driver’s feet to make maximum use of the space available. Additionally, this arrangement allowed the use of existing frame members as mounting points, thus eliminating the need for additional members. Manufacture Welded joints were used instead of bends for all members, excluding the rear roll hoop. All tubes were notched on a mill using a hole saw in order to ensure a gapless fit. TIG welding was chosen as the joining process for all frame elements based on the relatively higher power density when compared to MIG welding. This resulted in a reduced Heat Affected Zone (HAZ). FRONT SUSPENSION Geometry The front suspension of the vehicle was completely redesigned for 2008. A double a-arm setup was chosen for the system. Double a-arm style suspension allows for precise control of the camber angle, caster angle, and toe angle. The upper and lower a-arms are shown in Figure 12. The camber angle is controlled by the lengths of the a-arms. A neutral camber angle was chosen for the vehicle at ride height. Camber adjustments can be made using an adjustable upper ball joint. The suspension was designed with unequal length, non parallel arms. This geometry causes the camber angle to become more negative as the suspension compresses. Figure 13 shows a plot of camber as a function of
Figure 13: Camber Change as a Function of Suspension Compression
The front suspension was designed with a maximum compression of 10 inches, with a vehicle ground clearance of 12 inches. This ensures that the suspension will reach maximum travel before the front of the frame will hit the ground. The purpose of this is to decrease the shock experienced by the driver, and prevent unnecessary damage to the frame. In addition, the suspension was designed with 2 inches of extension travel. When cornering, weight is transferred from the inner wheel to the outer wheel. The extension of the suspension is intended to maintain contact between the inner wheel and the ground under these conditions. A-Arm Design and Fabrication The upper a-arm tubing is 4130 chromoly steel with an outside diameter of 1 inch and a wall thickness of 0.095 inches. The lower a-arm tubing is made of 4130 chromoly steel with an outer diameter of 0.625 inches. A fixture was fabricated for the upper and lower a-arms to ensure dimensional accuracy and repeatability. The shock was mounted using tabs which extend up from the lower a-arm. The a-arms were bolted to the frame through steel tabs using socket head shoulder bolts. Shoulder bolts were used in place of standard bolts to
reduce bushing wear and achieve a precision running fit. The suspension redesign achieved a mass reduction of 39% from 2007. A-Arm Testing Physical testing was performed on the upper and lower a-arms. The suspension was attached to a fixture simulating the vehicle frame, and a load was applied to the spindle. The load applied was 1400 pounds, to simulate the impact load of the full weight of the vehicle landing on one wheel. The test setup can be seen in Figure 14.
Shock Fully Compressed
Strain Rosette on Kingpin
Figure 15: On Vehicle Testing of the Front Kingpin Under a Simulated Drop Load.
Figure 14: A-arm Test Setup
Kingpin The strain was measured at the expected locations of maximum stress, including the tubes and near the welds. The results are shown in Table 2. It was determined from the results that the measured stresses were well below the allowable limits for the material.
Fixture
Figure 16: Tensile Testing of the Left Kingpin from the 2006 Vehicle
Table 2: Stress results from a-arm testing Location
Principal Stress (psi, σ1)
Principal Stress (psi, σ2)
Lower Tube Near Shock Attachment Lower Arm Tube Lower Shock Attachment Crossmember
9756
-3692
-1827
1694
3192
-
Kingpin Design and Fabrication 2006 Kingpin Testing In 2006, the right kingpin failed during the endurance race after 2 hours. A post race analysis was performed on the left kingpin. The analysis included on-vehicle strain measurement under loading, shown in Figure 15, and tensile machine testing, shown in Figure 16. FEA was also performed and compared to the physical testing data. Figure 17 shows the von Mises stress results. The maximum stress was 80,000 psi where the axle is welded to the upright tube. This is also where the right kingpin failed in the race.
Figure 17: von Mises Stress for the 2006 Kingpin
Design of Kingpin The kingpin was designed using the results of the testing as a guide. Failure of the 2006 kingpin at the HAZ resulted in the decision to machine the kingpin out of aluminum. The design incorporated the steering arm, tapered ball joint stud holes, and a large boss to accommodate pressing in the steel front axle. FEA was performed on the new design using the load conditions from the testing and analysis of the previous kingpin. Figure 18 shows the von Mises stress results for the new kingpin design. The maximum stress was 19000 psi at the point of contact between the boss and the front axle.
rods. As the suspension compresses, the ball joint follows a curved path. The system was designed to minimize bump steer. This was accomplished by choosing the tie rod to rack attachment point to be the centerpoint of the arc traced by the ball joint as it moves through its path. Neutral toe should be maintained throughout the compression of the suspension.
REAR SUSPENSION
Figure 18: von Mises Stress for the Kingpin
The front axle was manufactured on a CNC lathe. External threads were cut at the end of the axle for the 3/4-10 locknuts that secure the hub. STEERING Steering System Design The steering system consists of a steering wheel, rack and pinion, tie rods, ball joint rod ends, and a steering arm attached to the kingpin.
Kingpin Rotation (degrees)
g
Steering arm length is critical as it scales the linear motion of the rack to the rotational motion of the kingpin. A kinematics analysis of the kingpin rotation relative to the rack displacement was produced using Pro Engineer The results are shown in Figure 19. At full displacement of the rack, the kingpin was rotated approximately 45°.
A semi-trailing arm suspension was selected for the vehicle. The decision was based on the compromise between economical advantages of a rigid axle and the performance advantages of a double a-arm suspension. A rigid axle swing arm suspension is relatively simple to construct and inexpensive to manufacture. However, it is possible to design an independent suspension that is superior to a solid axle suspension with respect to controlling dynamic tire to ground contact [2]. This wheel to ground contact is important because it determines the tractive capability of the vehicle. The rear suspension geometry was redesigned for the 2008 vehicle to reduce the axial plunge and high operating angles experienced by the drive shafts throughout the suspension travel. The purpose of reducing the axial plunge and operating angles was to accommodate half-shafts with constant velocity joints instead of the single-cardan u-joints used in the previous design. A comparison between the 2007 and 2008 rear suspension is shown in Figure 20.
60 40 20 0 -20
2007 2008 Figure 20: Comparison between 2007 and 2008 Rear Suspension
-40 -60 -2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Linear Rack Displacement (inches)
Figure 19: Kingpin rotation versus rack displacement
Critical aspects of the steering system include toe angle, caster angle, and bump steer. A neutral toe angle was chosen, and can be adjusted by varying the lengths of the tie rods slightly. Another part of the system that provides straight line stability is caster angle. The suspension system has a caster angle of 8˚. Caster causes the wheel to trail behind the axis of steering. This causes the front wheels to self center. Bump steer is the change in toe angle during suspension compression. This is caused by variations in pivot alignment of the steering linkage, and is determined by the placement of the steering rack and lengths of the tie
The maximum axial plunge of the half shafts was reduced from 3.13 inches to 0.6 inches as shown in Figure 21. This goal was accomplished by moving the frame attachment point of the control arm up by 7.5 inches. The maximum operating angle of the half shafts was reduced from 38.5° to 27.6° to accommodate the 30° maximum operating angle of the constant velocity joints. This goal was accomplished by increasing the track width.
Axial Plunge vs. Hub Hieght 3.5
Axial Plunge (inches)
3.0 2.5 2.0
2007 Geometry
1.5
2008 Geometry
1.0 0.5
to reach steady state. The recorded temperatures can be seen in Figure 23. The bearings nearest to the engine and CVT reached approximately 53 ˚C at steady state. The highest temperatures were located on the input shaft to the reduction system due to the heat generated by the CVT driven pulley. Radiant heat from the engine block also contributed to the high operating temperature of the input shaft and bearings. The low horsepower rating due to roller bushing fatigue makes it undesirable to use chains for the first stage in the reduction casing. The use of a 17 tooth or larger driving sprockets would result in a system much too large for a compact race vehicle.
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
0.0 60
Hub Hieght (inches) 50
DRIVETRAIN Post Race Evaluation The 2006 drivetrain consisted of a continuously variable transmission followed by a two stage chain reduction. The sprocket reduction design was considered a failure after a post race inspection revealed that the lubrication had burned off the first stage chain, resulting in a chain temperature high enough to cause severe oxidation of the links after approximately 20 hours of operation. The failure can be seen in Figure 22. The 12 tooth sprocket on the input shaft of the chain reduction operated at 2363 ft/min (3737 rpm) when the vehicle was at top speed. At this velocity, the chain fatigue is limited by the roller bushings. The 12 tooth sprocket was calculated to have a horsepower rating of 2.12 hp operating at 3737 rpm, far below the 10 hp transferred through the system. The chordal variation of the input sprocket was relatively high at 3.4%, due to the small number of sprocket teeth.
Temperature (Celsius)
Figure 21: Axial plunge of 2007 and 2008 Driveshafts 40
Bearing A Bearing B Bearing C Bearing D Bearing E Bearing F
30
20
10
0 0
300
600
900
1200
1500
1800
2100
time (s)
Figure 23: Temperature as a Function of Time for Bearings A-F Approaching Steady State
Transmission A continuously variable transmission was chosen as the primary gear reduction for the vehicle. The CVT will allow the engine to operate nearly constantly at the engine speed corresponding to peak torque. The reduction ratio of the pulleys will vary infinitely to maintain this engine speed. Based on experience from the 2007 vehicle, it was determined that the top speed of the vehicle was too low. For 2008, a Comet 780 CVT was chosen, to increase the top speed over the Comet 770 used in 2007. This change increased the high gear ratio from 0.76 to 0.69, which, along with an increase in rear tire diameter from 21 to 23 inches, will result in an increase of top speed of nearly 21%. Gearbox Design
Figure 22: Photo of Failed 2006 Design
The failure was primarily attributed to the operating temperature of the reduction system. To obtain the steady state operating temperature of the system, a thermocouple was mounted near each of the six bearings in the casing. The drivetrain was operated at full throttle and LabView was used to measure the bearing temperatures until the readings were observed
A two-stage helical gear reduction system was designed and fabricated for the vehicle. Helical gears were selected due to the high pitch line velocity, relatively high operating temperature, and goal to produce a more compact and lightweight system. Because the design is meant for occasional weekend use, all fatigue calculations for gears, bearings, and shafts are for 960 hours of operation. This is calculated for 12 hours of operation per weekend, 10 weekends per year, for a total of 8 years.
Gear design The custom helical gear train design process included gear selection, shaft sizing, casing design, and selection of rotary shaft seals and tapered roller bearings. The gears were made out of 4140 steel alloy. The gear teeth were sized using ANSI / AGMA 2001-95 and 2101-95 with regards to bending and pitting failure. The calculations and factors used for this process, including gear dimensions, are shown in table format in the appendix. The helical gears were designed with a ˚ diametrical pitch of 12 and 30 helix angle. The safety factors for bending and pitting fatigue were calculated at both the high and lowest and are shown in Figures 24 and 25, respectively.
concentrations in the webbing design, and to determine the maximum stress and deflections of each gear. The analysis done on the gears is shown in Figures XIII through XVII of the appendix. The maximum stress and deflection for each gear is shown in Table 3. The helical gears were custom manufactured for this project.
8.00 7.11
6.90
7.00 6.00
5.32 4.96
5.00 4.00 3.00 2.00
2.05
1.85
1.48
1.39
1.00 0.00 P1
G1
P2
CVT 3.95:1
G2
CVT 0.95:1
Figure 24: Safety Factors (Sf) for Gear Teeth Bending Fatigue 7.00 6.39
6.00 5.52 4.95
5.00 4.49
4.00
3.00
2.00
Figure 26: Gear Train as Analyzed (note: shaft 1 is located 45˚ out of plane relative to shafts 2 and 3)
1.84
1.67
1.31
1.26
1.00
Bearing selection
0.00 P1
G1
CVT 3.95:1
P2
G2
CVT 0.95:1
Figure 25: Safety Factors (Sf2) for Gear Teeth Pitting Fatigue
The gear train consists of two reduction sets, each having a 28 tooth pinion and a 83 tooth gear. The face widths of the first and second gear sets are 0.625 and 1.25 inches, respectively. The gears on shaft 2, shown in Figure 26, both have a left hand helix angle, to reduce the resultant thrust load on the bearings.
The schematic used to determine the bearing reaction forces is shown in Figure 27. The reaction forces are shown in Table X of the appendix. The forces acting on the gear teeth were determined during the gear analysis. The forces acting on the CVT driven pulley were determined and are shown in Figure 27.
Table 3: Summary of Gear FEA Results
P1 G1 P2 G2
Max Gear Body Stress (psi) 12,300 44,550 20,420 57,120
Max Deflection (in) 0.00070 0.00259 0.00041 0.00338
In an effort to reduce mass, the profiles of the gears were webbed. FEA was used to identify the stress
Figure 27: FBD of Forces Acting on Comet 770® CVT Driven Pulley ®
Timken tapered roller bearings were selected for use due to the thrust load developed by the helical gear teeth. The calculated C90 and catalog C90 values for the bearings used in the gearbox are shown in Table 5.
Table 5: Bearing C90 Calculations
Bearing Shaft 1 Shaft 2 Shaft 3
A B C D E F
Calculated C90 (lbf) 840 1779 727 1687 1557 507
Catalog C90 (lbf) 1570 1760 2730
Shaft design Shear and bending moment diagrams were developed to determine the maximum bending moment on each shaft. The shafts are stepped to transfer the thrust loads from the gears to the bearings. The safety factors for shaft fatigue were calculated using GE Goodman criterion. The shafts were custom machined and ground from the same 4140 material as the helical gears. The bending moment diagrams for Shaft 1 in both perpendicular planes is shown in Figures I through XII in the appendix. The largest resultant bending moment between both planes was used to determine the safety factors against fatigue, these values are shown in Table 6. To contain oil inside the gearbox casing, the input shaft and output ® shafts are stepped and ground to fit SKF joint radial oil seals.
Figure 28: Solid Model of Drivetrain (left) and Cutaway View of Gearbox (right)
FEA was used to determine the rib structure around the bearing bosses based on the bearing forces from Table 7. The results of the FEA are shown in Figure 29. The design was developed with a safety factor large enough to allow for the design to be cast, although the prototype was machined. Exterior ribs were used to brace the bearing bosses and to increase the heat dissipation efficiency of the casing. The casing design includes an oil fill plug near the input shaft, and a magnetic oil drain plug near gear 2. A groove for a 3/32 inch o-ring was machined into the flange of the casing to ensure a good seal for the oil bath. Both plugs are positioned to allow for changing the gear oil without removing the casing from the vehicle. A Hall Effect sensor, water tight plug, and magnetic encoder were installed to measure the output shaft speed for use with a speedometer.
Table 6: Safety Factors Against Shaft Fatigue using GE Gerber Criterion
Shaft 1 Shaft 2 Shaft 3
Cycles 7 5 x 10 7 2 x 10 6 6 x 10
Sf 1.05 2.16 1.82
Casing design The solid models of the drivetrain and gearbox casing are shown in Figure 28. The casing was machined at GVSU on a CNC milling center. The casing was machined from 6013 aluminum alloy. The yield strength of 6013-T651 alloy is 55 ksi, compared with the 37 ksi yield strength of 6061-T6 alloy. The machinability of 6013 is 70% which is much greater than the 30% machinability of 6061 alloy. Machinability was a concern because almost 80 hours of toolpaths were run to prototype the casing design. A 2˚ draft angle was included in the gearbox design to allow this component to be cast if mass produced. Heat dissipation was a major consideration when designing the gearbox casing. The high thermal conductivity of aluminum provides an advantage over steel. Shaft 1 was oriented at a 45˚ angle with respect to the shafts 2 and 3. This allowed for the casing to be mounted as close to the vehicle bottom as possible, but still provide clearance for the 9.85 inch diameter CVT driven pulley and safety cover. Bosses were included around the input shaft to allow for mounting the CVT cover directly to the gearbox.
Figure 29: Plot Showing Minimum Safety Factor of 5.5 for Gearbox Casing
Axle When using a semi-trailing arm suspension, the drive axle must pivot and telescope with the motion of the suspension arm. The 2008 vehicle was upgraded from an axle utilizing U-joints, to an axle assembly with constant velocity joints. The 2007 axle assembly was necessary due to the high operating angle and required length change of the driveshafts. The increased width and higher attachment points of the 2008 rear suspension allowed the use of CV joints. CV joints are desirable due to the elimination of variation in angular velocity between the input and output shafts. Rear Hubs The rear hubs were CNC machined from 6061 aluminum, as seen in Figure 30. Based on hub keyway failure problems on the 2005 Mini Baja vehicle, an internal ball spline was machined into the hubs to increase the contact area between the hub and axle. Part of the 2005 failure issues were attributed to the fact that rear braking torque was transferred through the
keyway. The solution to this problem was to mount the rotors to the rear hubs. Braking Brake rotors were CNC machined on a milling center from 6061 aluminum for use with Wilwood Dynalite Single Floater calipers and ceramic brake pads, as seen in Figure 30. The rotors were slotted to provide a scraping surface to aid in even pad wear, a problem that can arise in off-road racing due to mud and debris collecting on rotors. A hole pattern was machined into the rotors. The holes allow for the displacement of gasses generated during heavy braking, thus eliminating brake chatter.
Tachometer A circuit was designed to read and display the rpm of the engine. The speed of the engine is measured by counting the time between sparkplug firings. The sparkplug discharge is sensed by placing 3 turns of 24 AWG wire around the sparkplug wire. This forms a very low turns ratio. The upper oscilloscope trace shows the input signal to the circuitry. The lower trace shows the output after being filtered and squared up with a comparator. The transformer sensing method allows the circuitry to be isolated from the 10kV sparkplug voltage and also prevents the addition of more rotational inertia to the engine shaft. The output of the circuit was compared with the output of a laser tachometer, and the error was less than 2% between the two measuring techniques.
CONCLUSION
Figure 30: Hub and Rotor Assembly
The brake pedal utilizes a lower pivot, which rotates a shaft with an attached lever to actuate the master cylinders. Testing conducted on the pedal assembly indicated over 650 pounds could be applied to the master cylinder input, using only ankle flexion. In addition to the foot braking system, a hand actuated cutting brake was added. This brake will allow the driver to apply only the rear brakes, which could be used to slide around tight turns. This is accomplished by using a secondary master cylinder in series with the primary foot actuated cylinder. ELECTRONIICS There are two main electronic components included on the vehicle, a tachometer and a speedometer. The tachometer and speedometer were constructed from custom printed circuit boards. The only difference between the two modules is the code loaded onto the microcontroller. Speedometer A digital speedometer display was built using a custom designed circuit board and 8x2 character LCD display. An encoder wheel was built to fit inside of the reduction case, and hold small neodymium magnets. The magnets were sensed by a 3-terminal hall-effect sensor. This sensing method was chosen for its robust characteristics and ability to be integrated into the transmission design. The magnetic sensing method is impervious to oil, dust, and debris between the magnet and sensor. The encoder holds two magnets which generate digital pulses to an Atmega 8 microcontroller. The speedometer can measure down to 2 mph.
A racing vehicle feasible for mass production was designed and prototyped for entrance into the 2008 Montreal competition. Further testing will be conducted to verify the design and craftsmanship prior to the competition date.
ACKNOWLEDGMENTS The GVSU Laker Racer team would like to thank Bob Bero for his commitment to the team and its efforts. The team would also like to thank Dr. William Waldron, and the School of Engineering faculty for their administrative, financial, and technical support of the 2007 vehicle project. Finally, the team would like to thank Shape Corp., the Grand Valley State University Student Life Organization, and The Grand Valley State School of Engineering for their financial support.
REFERENCES 1. SAE International. SAE Collegiate Design Series: Mini Baja. 2008. 2. D. A. Crolla, G. R. Firth, and D. N. L. Horton. The University of Leeds. Independent vs. Axle Suspension for On/Off Road Vehicles. 921662 SAE Technical Paper Series. September 1992. 3. Wan, Mark. Suspension Geometry. AutoZine Technical School. 1994. 4. Milliken, William, and Milliken, Douglas. Chassis Design. Society of Automotive Engineers, 2002.
APPENDIX
W (lbf) Cycles
639 5.E+07
640 2.E+07
1897 2.E+07
1901 6.E+06
Table I: Gear dimensions used in fatigue safety factor calculations
CVT 3.95:1 (High Torque)
N (teeth) Φn Ψ pn pt px F (in) base ψ Φt N Virtual Pn Pt dn dt rt rb
P1 G1 28 83 20 20 30 30 0.262 0.262 0.302 0.302 0.524 0.524 0.625 0.625 28.024 28.024 22.796 22.796 43.109 127.787 12 12 10.392 10.392 2.33 6.92 2.694 7.987 1.35 3.99 1.24 3.68 0.083
P2 G2 28 83 20 20 30 30 0.262 0.262 0.302 0.302 0.524 0.524 1.25 1.25 28.024 28.024 22.796 22.796 43.109 127.787 12 12 10.392 10.392 2.33 6.92 2.694 7.987 1.35 3.99 1.24 3.68 0.083
0.104
0.104
Addendum Dedendum O.D.
2.861
8.153 2.861 5.340
8.153
Table III: Helical gear tooth forces and cycle calculations at 10 hp, 960 hours of operation, and CVT input 95:1 (high speed)
n (rpm) T (lbf · in) V (ft / min) W t (lbf) Wr (lbf) Wa (lbf) W Cycles
P1 3737 168.65 2,636 125 53 72 154 2.E+08
G1 1258 500.99 2,630 125 53 72 154 7.E+07
P2 1258 500.99 887 372 156 215 457 7.E+07
Formatted: Body, Centered
G2 424 1486.44 887 372 156 215 457 2.E+07
Table IV: 4140 gear material properties regarding fatigue
P1 Steel Grade Hb St (psi) Sc (psi) J I Yn (See Cycles) Zn (See Cycles)
1 1
G1
P2 2 311 48,122 142,839 0.5 0.2020 1.1 1.1 1.05 1.05
G2
1.15 1.07
5.340 C.D.
Table V: K factors for gear tooth fatigue calculations with CVT input 3.95:1 (high torque)
0.710
Ko Kv Ks Km Kb Kt Kr Ktotal
0.710 Z term 1 1.751 1.751 Z term 2 2.069 2.069
P1 1.25 1.11 1.00 1.09 1.00 1.00 1.00 1.51
G1 1.25 1.11 1.00 1.07 1.00 1.00 1.00 1.49
P2 1.25 1.07 1.00 1.11 1.00 1.00 1.00 1.48
G2 1.25 1.07 1.00 1.09 1.00 1.00 1.00 1.45
Z term 3 0.392 0.392
Table VI: K factors for gear tooth fatigue calculations with CVT input 0.95:1
Z total
Table II: Helical gear tooth forces and cycle calculations at 10 hp, 960 hours of operation, and CVT input 3.95:1 (high torque)
n (rpm) T (lb · in) V (ft / min) W t (lbf) Wr (lbf) Wa (lbf)
P1 899 701 634 520 219 300
G1 303 2,080 634 521 219 301
P2 303 2,080 214 1544 649 891
G2 102 6,178 213 1547 650 893
Ko Kv Ks Km Kb Kt Kr Ktotal
P1 1.25 1.21 1.00 1.09 1.00 1.00 1.00 1.64
G1 1.25 1.21 1.00 1.07 1.00 1.00 1.00 1.62
P2 1.25 1.13 1.00 1.11 1.00 1.00 1.00 1.57
G2 1.25 1.13 1.00 1.09 1.00 1.00 1.00 1.54
Formatted: Body, Centered
Table VII: Gear tooth stresses with CVT input 3.95:1
σb (bending) σc (contact)
P1 26,079 110,421
G1 25,806 110,421
P2 38,088 133,444
G2 37,324 133,444
Figure I: Shear Diagram, Shaft 1, YZ plane Table VIII: Gear tooth stress with CVT input 0.95:1
σb (bending) σc (contact)
P1 6,833 56,522
G1 6,769 56,522
P2 9,711 67,381
G2 9,505 67,381
Table IX: V-belt force calculations on shaft 1 with CVT3.95:1
Hd (hp) n (rpm) Driver pulley pitch diameter (in) V (ft/min) Center distance (in) Driver pulley contact angle (rad) Μ exp[(f(ø)] Fc (lbf) ∆F (lbf) F1 F2 (lbf)
10 3550 1.7075 1,586.9 9.02 2.2384 0.5123 3.148 8.81 207.9 313.5 105.6
Figure II: Shear Diagram, Shaft 1, XZ plane
Figure III: Bending Moment Diagram, Shaft 1, YZ plane
Table X: Bearing reaction forces
Bearing
Shaft 1
Shaft 2
Shaft 3
Radial (lbf) Thrust (lbf) Radial (lbf) Thrust (lbf) n (rpm) Radial (lbf) Thrust (lbf) Radial (lbf) Thrust (lbf) n (rpm) Radial (lbf) Thrust (lbf) Radial (lbf) Thrust (lbf) n (rpm)
A B
C D
E F
CVT 3.95:1 (Max Torque) 667
CVT 0.95:1 (Max Speed) 161
824 300 900 876
199 72 3737 211
1038 591 303 1679
250 142 1258 405
831 891 102
200 215 424
Figure IV: Bending Moment Diagram, Shaft 1, XZ plane
Figure V: Shear Diagram, Shaft 2, YZ plane
Figure XII: Bending Moment Diagram, Shaft 3, XZ plane Figure VI: Shear Diagram, Shaft 2, XZ plane Table X: Gearbox shaft fatigue calculations at 960 hours of operation with CVT 3.95:1
Figure VII: Bending Moment Diagram, Shaft 2, YZ plane
Local Shaft Diameter (in) Cycles Ma (in · lbf) Tm (in · lbf) Se’ (ksi) Ka Kb Kc Ke Kf (material) Se Kf (notch) Kfs n
Shaft 1 0.8750 5.E+07 1,391 701
0.907
51.276 1.43 1.18 1.05
Shaft 2 1.0000 7.E+07 1,303 2,080 78.624 0.872 0.892 1 0.814 1 50.031 1 1 2.16
Shaft 3 1.1875 2.E+07 2,287 6,179
0.873
49.208 1 1 1.82
Figure VIII: Bending Moment Diagram, Shaft 2, XZ plane
State equations used in Scilab analysis: ⋅
(1)
x1 = v1 ⋅
(2)
(5)
− Kd K − Ks − Ks (3) v1 + d v2 + x1 + x2 v1 = Mc Mc Mc Mc ⋅ − Kd K − Ks − Kw − Ks v2 + d v12 + x2 + x1 (4) v2 = Mw Mw Mw Mc
(6)
x2 = v2 ⋅
Figure IX: Shear Diagram, Shaft 3, YZ plane
Figure X: Shear Diagram, Shaft 3, XZ plane
Figure XIII: von Mises stress on P1 (psi)
Figure XI: Bending Moment Diagram, Shaft 3, YZ plane
(7)
Principle Stress (psi)
Figure XVII: Displacement plot of gearbox under largest loads (CVT 3.95:1)
1000 0 -1000 0
5
10
15
-2000 -3000 -4000 Wheel Travel (inches)
Figure XIV: von Mises stress on G1 (psi)
Principle Stress 1 (psi)
Principle Stress 2 (psi)
Principle Stress (psi)
Figure XVIII: Plot of experimentally determined principle stresses in rear lower A-arm for wheel deflections of 4, 8, and 12 inches
12000 10000 8000 6000 4000 2000 0 -2000 -4000
4
8
12
Wheel Travel (inches)
Figure XV: von Mises stress on P2 (psi)
Principle Stress 1 (psi)
Principle Stress 2 (psi)
Figure XIX: Plot of experimentally determined principle stresses in front upper shock for wheel deflections of 4, 8, and 12 inches
Principle Stress (psi)
10000 8000 6000 4000 2000 0 4
-2000
8
12
-4000 Wheel Travel (inches) Principle Stress 1 (psi)
Principle Stress 2 (psi)
Figure XX: Plot of experimentally determined principle stresses in front lower A-arm for wheel deflections of 4, 8, and 12 inches
2000 Principle Stress (psi)
Figure XVI: von Mises stress on G2 (psi)
1000 0 -1000
0
2
4
6
8
10
12
14
-2000 -3000 -4000 Wheel Travel (inches) Principle Stress 1 (psi)
Principle Stress 2 (psi)
Figure XXI: Plot of experimentally determined principle stresses in lower roll cage support for wheel deflections of 4, 8, and 12 inches
