# Trophy Truck Suspension Design

# Team Members

Ramvineeth Nitta

Will Rice

Brian Schlotterbeck

# Project Description

This project examines the design of long-travel suspension systems. Long-travel suspension systems are mostly used for off-road racing and off-road recreation applications. Specifically this project will focus on the suspension system of a trophy truck which is used in races like the BAJA 1000. These suspension systems require specialized components in order to battle the rigors of high speed, off road travel. A properly working off road suspension system could be the difference between winning a race or ending up in a multiple roll crash resulting in broken bones and internal bleeding.

# System Description

Long-travel suspension systems are very similar to typical suspension systems found on passenger vehicles. However, long-travel suspension systems are customized to perform well in an off-road environment. The main components include shock absorber(s), coil springs, and linkages to connect the suspension system to the frame of the vehicle. Typically these shocks contain multiple bypass champers and remote reservoirs for the damping fluid; the coil springs, or sets of coil springs, can be progressively wound to provide a change in spring rate depending on the activity of the spring; the linkages are generally a (modified) double wish bone setup for independent suspension while if using a solid axle setup are usually found in the form of a four-bar like mechanism. These suspension systems can have upwards of 28 inches of travel and must be designed and tuned to withstand speeds of 130 mph or greater across perilous terrain for extended periods of time.

# Dymola Model

The outcomes of homework 3 are a Dymola model, and an animation of the trophy truck suspension. Building the Trophy Truck suspension model required segmenting the vehicle into several distinct parts that perform different functions. The systems that make up the Trophy Truck suspension are the rigid frame, multiple a-arms, multiple hubs, multiple coilovers, and wheels visualizers. The “outside” system that is utilized to model certain scenarios is the effect of gravity.

# Uncertainty Analysis

ModelCenter was used to run a sensitivity analysis, specifically a Design of Experiments, to determine the significance that each uncertain variable had on the outputs of our Dymola model, maximum displacement and maximum acceleration. Nine uncertain variables were identified in the Dymola model. High and low values, representing the 95th percentile and the 5th percentile respectively, were chosen for each uncertain variable. Using these values and the DOE tool in ModelCenter, a Central Composite method was used to complete the sensitivity analysis. Below are the results. The first figure is the result for the maximum displacement output. The second figure is the result for the maximum acceleration output.

The uncertain variables which were most significant were identified using the sensitivity analysis results. The next step was to to elicit CDFs for each of the significant uncertain variables. This exercise was done in Excel. Once the CDFs were elicited, the Excel plug-in in ModelCenter was used to link the CDFs to the Dymola model inside ModelCenter. Below is a picture of the Analysis Window in ModelCenter which shows the CDF spreadsheets linked to the Dymola model.

Once the CDF spreadsheets were linked to the Dymola model, the remaining uncertain variables were given simple triangular distributions. Now that all nine uncertain variables were described by a probability distribution function, a Monte Carlo analysis could be done to test 1000 different combinations of the uncertain variables. This analysis produces a PDF for the outputs of our model. This PDF tells us the mean, minimum, and maximum values of the outputs along with much more statistical analysis. From this we can get a better understanding of what the probability of a certain outcome will be for our model which is based on the uncertainty included in each uncertain variable. The figures below show the Monte Carlo results for the maximum displacement and the maximum acceleration.

# Optimization

__Design Space Exploration__

In order to better understand the design space, a space-filling DOE was performed. The goal of this exercise was to narrow down the design space that would be considered for optimization. The DOE consisted of the nine decision variables as inputs and the design variables along with the utility as the outputs.

The data produced by the DOE was extracted from Model Center and used to create a surface plot. The x and y axes represent the two design variables and the z axis represents the utility. This plot reveals two important things about the model. The first thing it reveals is that the behavior model and the utility function are valid. This is true because in our model the lower the value of the design variable, the higher the utility should be, and this is the case. The second thing that it reveals is an idea of how many local maxima exist in the design space. This information will allow us to better choose an optimization algorithm in later tasks.

From the figure above, it can be observed that the global maximum is located where the values for chassis displacement and maximum acceleration are low. This validates our behavior model as well as our utility function because low values for chassis displacement and maximum acceleration should correlate with a high utility.

__Deterministic Optimization__

The starting values for the first iteration of this
optimization were taken from the result obtained from Task 3. This allows us to reach an optimum quicker
since we will already be in the neighborhood rather than taking a shot in the
dark to start. Once the DOT optimization tool was chosen, it was important to
make sure to select “maximize” in the options in order to meet our goal of
maximizing utility. Also note that there are three script inputs into the
Demand tile: cost and two conversion scripts.
We have already discussed the cost script. The two conversion scripts take outputs of
the Dymola suspension model and put it in terms that the demand spreadsheet can
use properly. This means the
displacement is converted from meters to centimeters and acceleration is converted from m/s^2
to g-force. The Model Center model and the optimization results are shown below.

Deterministic Model with Optimizer

Results of Deterministic Optimization

Optimization Considering Uncertainty

For Task 5, uncertainty was introduced into the Model Center model by including the CDFs elicited in HW4 and adding a Latin Hypercube Sampling component (LHS). Below is a screen shot of the Model Center model with all of the components which include the Dymola model, the CDFs, the LHS, the optimizer, the cost function, the two scripts which convert the design variables to the correct units, and the Demand/utility model.

Model Center model with uncertainty included

The LHS is a probabilistic analysis tool which produces a
mean value of the utility which is also called the expected utility. The LHS is in a nested loop in which the
results from the probabilistic analysis are optimized. This maximum expected utility will be
different than what was determined to be the maximum utility in Task 4 because
uncertainty is now considered.

The optimization was run multiple times with an increasing number of samples. The first run only used 5 samples in the LHS. Once the optimization finished, the number of LHS samples was increased to 10 samples and the optimization was restarted using where the previous run ended as the starting point. The same steps were repeated for optimizations where the LHS completed 20 samples as well as 50 samples. Comparing the results of the successive optimizations showed that using 50 samples did not produce a maximum expected utility that was significantly different than the optimization that used 20 samples. Therefore, no further optimizations were completed. The results for the 20 sample run are below.

Optimization including uncertainty results for LHS with 20 samles

# Homework Assignments

Homework 2

Homework 3

Drop Test Animation - Under Damped with Medium Spring

Drop Test Animation - Over Damped with Medium Spring

Drop Test Animation - Medium Damping with Medium Spring

Drop Test Animation - Additional

Homework 4 (ModelCenter and Updated Dymola Files)

Homework 5 (Files)