Engineering 12: Physical Systems Analysis
Two Models of Vehicle Suspension Systems over Speed Bumps
March 17, 2004
Analysis By Mark Piper '06 and David Luong '06
Lab Instructor: Professor Bruce Maxwell
INTRODUCTION
The goal of our analysis was to predict the response of a vehicle when driven across speed bumps of different shapes at a variety of velocities. We developed two separate systems to approximate the suspension of an automobile. Model A consisted of a single car mass with a spring and a damper to simulate shock absorbers. Model B accounted for the presence of a tire by including an additional tire mass, spring, and damper. Both models are shown below.
Both models were fabricated as Simulink simulations. Using this, three theoretical
bump sizes were investigated: impulse (1cm x 5cm), standard (40cm x 10cm),
and Whittier (200cm x 15cm). These were run through our models at each
of 5mph, 10mph, and 20mph. The Model A responses to these inputs were also
calculated using both a second and a fourth order Runge-Kutta solver. Experimental
data was gathered of the profile of a real speed bump nearby Swarthmore
College. We compared the theoretical Simulink response to this bump with
the experimental response of real vehicles (gathered with camera data-capture
techniques).
Below are the two simulink models used to conduct our analysis.
Both were constructed using the respective differential equations of the
Models A and B.
A more descriptive and in-depth introduction and task section can be found here at Professor Maxwell's E12 lab protocol webpage.
ANALYSIS
All explored case results can be accessed with the links in the left panel. Please click and refer to them while reading the Discussion and Conclusions sections.
Simulink and m-files used in analysis
DISCUSSION AND CONCLUSIONS
Graphical representation of car and/or tire responses at different speed bumps are contained within the links in the left panel.
Comparing Models A and B in Modelling Vehicle Suspension System
Models A and B both provide a reasonable method for examining the dynamics of a vehicle suspension system over a speed bump. However, Model B is more descriptive of the real system, since Model A fails to take into account the tire's existence.
In Model A, the car reacts directly to the changes in x, meaning that the passenger feels the full changes in the ground, in this case the speed bump.
The additional features of Model B allow for the tire to absorb some of the changes in the ground, thereby reducing the changes felt by the vehicle and its passengers. As shown in the graphical results for the model, the vehicle experiences less vertical displacement than Model A because the tire absorbs some of that displacement.
Notice that the response due to the speed bump in Model B is an underdamped oscillatory one. The vehicle and passenger bounce up and down for a short time before returning to equilibrium at zero displacement. In Model A, this behavior does not exist as strongly, and it stems from the fact that the model includes only one spring connecting the vehicle and the road.
Going Over the Same Bump at Different Speeds
In both Models A and B, the faster a vehicle travels over a speed bump, the less displacement of the car. The reason behind this is the short duration the vehicle is actually on the bump which does not allow sufficient time for the vehicle to respond to the change in the road.
At lower speeds, there is sufficient time for the vehicles to respond to the full effects of the bump. But a Model B vehicle responds much more to the road change at low speeds. The damper and spring exert an initial upward force to create a greater vertical displacement than a Model A vehicle. All bumps exhibit this behavior.
Going Over Different Bumps
Looking at Model B for the three different bumps, the vehicle responds more to the bump as the bump size and height increases. This observation is drawn from the fact that the lag time between the tire and the vehicle is increasingly reduced for bumps with larger profiles.
Continuous Speed Bumps
Though seemingly much more complicated, a road made of a continuous stream of bumps actually causes a response that is similar to a single bump. Both arrive at a sort of “steady state” as time goes on, with the qualitative difference that with a stream of bumps, the steady state is an undamped periodic oscillation. The visual representation (Impulse, Standard, Whittier) of this finding is that the car almost skips over the bumps after awhile.
Why Pneumatic Tires?
Our data provides convincing support for the widespread use of pneumatic tires as opposed to more solid alternatives. This becomes most salient in the Model B response to impulse bumps with a height of 5 cm and a width of 1 cm. The bump takes almost no time to run over, but has a substantial height for which the suspension must compensate accordingly. However, the graphs demonstrate that even at a relatively low speed of 5 mph that the tire barely moves up 1 mm. This leaves 4.9 cm to be accounted for by the car to successfully bypass the bump. The explanation is that the tire itself must deform those 4.9 cm. These sorts of feats are accomplished through use of a pneumatic tire. A solid tire trying to overcome this obstacle would either break or be stopped in its tracks by a 5 cm tall wall.
The "Nastiness" of Speed Bumps
The "nastiness" of a speed bump, from the passenger's perspective, is the vertical accerlation experienced. As passengers, we like to experience gradual motion that we can foresee. Quicker accelerations give passengers sudden unanticipated movements, which can be discomforting and cause car sickness. The link corresponding to the "Nastiness" of Whittier Bump examines two speeds (1 mph and 3 mph) of a vehicle going over the bump for both Models A and B. As shown, the slower the vehicle moves of the bump, the lower the vertical acceration, and thus the less nasty the bump.
Smoothness of Traversing Bump
For a discussion of the smoothness of a ride over a bump, refer to the link, "Smoother Ride Over Small Bump."
Extending the Analysis to Real Results: Car and Truck
The Model B Simulink response to the measured Whittier bump profile decently resembles the video data-capture response of the car shown here. 10 mph graphs for both cases which allows for direct comparison, where we find that the response magnitude maximizes at the time of ~.5s. At all speeds, the shape of a slightly underdamped oscillatory response prevails (though quite fuzzy in the capture data) with an initial peak mirroring the shape of the bump. The general trend is in decreasing magnitude of the response with higher velocities, which agrees with the intuitive argument that less time exposed to the bump should result in less displacement change. When comparing the car and the truck, the truck seems to respond slightly less strongly, though the difference isn’t as obvious as one might expect.