Technical analysis was essential to the design of each subsystem. By analyzing the critical components, design changes could be made to ensure that the parts and subsystems will perform as intended. This page details the significant analyses used in early stages of the design process.
Front Upright Structural Analysis
The front upright must withstand significant loads as the front suspension absorbs obstacles and jumps. It has been common practice among the Stevens Baja team to approximate the worst-case scenario of the suspension system to be subjected to a load of twice the vehicle weight on one wheel. This simulates the vehicle landing from a jump on only one wheel. For this analysis, a vertical load of 1250 pounds was added to the front hub. The upper ball joint was fixed to approximate the shock being bottomed out. The lower ball joint was able to react only in the direction of the lower control arm as it is a two-force member. The analysis showed acceptable stress results, but a slightly higher factor of safety was desired due to reliability concerns when welding. The redesign for lower stress can be seen in the Updated Designs tab.
Boundary conditions for front upright analysis
Front upright analysis results without supports (yield strength for 4130 steel is 66 ksi)
Steering Mount Structural Analysis
The steering mount required analysis efforts to ensure that it will not fail when quick changes in direction apply significant forces to the steering system. For this analysis, the holes in the steering mount were fixed, and both ball joints were given rotational freedom. An 860-pound force was added to the front hub to cause a torque around the steering axis. This torque was equivalent to a 400-pound force at the edge of the tire. This loading condition was used for the 2019-2020 Stevens vehicle which saw no steering mount failures. By analyzing both concepts, the lower stress in the sheet metal design made it simple to select that design. While the stress is slightly above the yield stress of 4130 steel of 66 ksi, the weld fillet around the steering mount will reduce the maximum stress.
Steering mount analysis boundary conditions
Square tube design von Mises stress results
Sheet metal design von Mises stress results
Rear Trailing Arm Technical Analysis
The majority of the stress in the rear suspension is focused on the rear trailing arm, which connects the wheel and shock to the frame. Similar to the front upright analysis, a 1200-pound vertical force was applied to the wheel hub. The lateral link mounts were able to react in the direction of the lateral links, which are two-force members. The rear shock mount was given a fixed constraint, and the heim joint was given a revolute joint. The maximum stress location was a spike where the shock mount met the trailing arm. Since the rest of the trailing arm had acceptable stress, this stress concentration was not of much concern because a weld fillet will be added to the area.
Boundary conditions for rear trailing arm analysis
Rear trailing arm analysis results (yield strength for A500 steel is 50 ksi)
Steering Tie Rod Analysis
The steering tie rod analysis was done to ensure that it would not buckle under the loads of the steering system. The applied load of 1100 pounds was equivalent to the torque used for the steering mount analysis. The load direction was based on the joints as it is a two-force member. A revolute joint was applied to the steering rack mounting holes, and the bottom face of the mounting tab was given a roller/slider constraint to fully constrain the model.
Stress results with boundary conditions shown
Detailed view of maximum stress location
Steering Rack Mount Analysis
Like the tie rod, the steering rack was analyzed to ensure it will anchor the steering system in place. A transverse force of 400 pounds was added to the mounting holes based on the steering mount analysis. The mount was fixed at the locations that it will be welded to the frame. It showed a relatively low factor of safety of about 1.07, but this is not a concern. With the several joints in the steering system, there is notable slack that can absorb the stronger forces to reduce the stress on the steering rack mount.
Steering rack mount stress results with boundary conditions shown
Ackermann Steering Angle Analysis
The idea behind Ackermann steering is that when turning around a corner, the inner tire must rotate more than the outer tire for them to rotate about the same center point. With the goal of pro-Ackermann steering, the inner tire should turn even more than what is required by the Ackermann model. This produces oversteer, which is especially useful in loose terrain. Several variables in the steering system dictate the Ackermann performance of the steering system including the rack offset from the wheel axis, the steering mount angle, the steering mount radius, and the wheel base of the vehicle. Due to the 4WD configuration, the steering rack is limited to being offset in front of the front differential. This also limits the steering mount angle because it will run into the brake rotor if increased too much. This limits the steering system's ability to achieve full Ackermann steering shown by the chart below. The system was able to achieve about 30% Ackermann, which means that the inner tire turns more than the outer tire, but the difference between the turning angles is only 30% of what the Ackermann model suggests. This will produce light understeer, but it will be predictable for the driver. Several other Baja teams have been successful with similar Ackermann percentages, so while we did not reach our goal, we do not think it will greatly hinder the vehicle's performance.
Ackermann equations
Steering mount radius and angle
Ackermann steering analysis results
Front Suspension Dynamic Analysis
The front suspension has a wide range of motion when combining the steering input with the vertical travel. Being able to dynamically model the front suspension helps determine if any interferences exist throughout the motion of the front suspension. It was found that the steering tie rod interfered with the upper control arm when the steering was at full lock, which required a redesign to remove the interference.
Initial Design
Updated Design
Suspension travel with no steering input
Suspension travel with steering at full lock to the left
Inboard Rotor Analysis
When deciding between inboard and outboard brakes for the rear suspension, the rear brake rotor mounting design was analyzed. Since we use floating calipers, one brake pad pushes on the rotor as springs are compressed in the caliper to allow the other brake pad to engage. The time between the first and second pad engaging causes an axial force on the rotor. Since #6-32 screws were the largest screws that could be used on the differential's output shaft, calculations were used to determine if the bolts would break under the load of the caliper. For reference, the force required to compress the springs in the brake caliper is about 40 pounds. Two failure modes were analyzed:
Bolts breaking in tension
The threads on the bolt stripping the threads in the differential because the bolt is made of a stronger material
Both failure modes had required forces much larger than the force required to compress the springs in the caliper, so this design was feasible in terms of attaching the rotor to the differential's output shaft.
Calculation for required force to break bolt in tension
Calculation for required force to shear threads tapped in differential