A Vehicle Dynamics Design and Simulation Tool for Capstone Projects

A vehicle dynamics simulation tool developed by students and for use by student design teams is presented in this work. The project is the result of work done by students participating in an exchange program between international partner universities. Students in the exchange program complete a Senior Capstone Design project and additionally write a Diploma Thesis as part of earning degrees from both universities. The simulation tool is meant for use in the early stages of the design of four-wheeled vehicle projects such as the SAE Mini-Baja challenge or the SAE Formula competition. The simulation tool uses MATLAB and Simulink and simulates a14degrees-of-freedom (DOF) system. The model can accommodate different suspension linkages and allows anti-roll bars in the simulation and includes is capable of simulating Ackermann, parallel steering and reverse Ackermann steering. Non-linear tire modeling simulates turning forces from different types of tires on various surfaces. Results of low speed cornering simulation are verified by a physical test with a passenger vehicle at low velocities. The results of the high velocity cornering analysis are cross-referenced with findings in vehicle dynamics literature. Simulations provide turning radius estimation and the determination of the under-steer and over-steer behavior of the vehicle. Suspension impact forces and suspension travel in cases of impact from a user specified height are included. The design and simulation tool is opensource allowing future teams access to the software for future updates or revisions. A tutorial is included that provides teams with instructions on the software usage, facilitating the decisionmaking process earlier in the capstone design schedule than would otherwise be possible. Background At the Milwaukee School of Engineering (MSOE) Mechanical Engineering students are required to complete either a two-term or three-term Senior Design sequence. Most students opt to complete the three-course sequence that begins in September and ends in May. The first term finds students developing a proposal for their group‟s design goals for the year. In the second term analysis, design and initial building or testing is accomplished. The third term in spring is devoted to building the project and perhaps bringing a device to a competition such as the SAE Mini-Baja, or SAE Aero competition, among others. Foreign Exchange Program and the Diploma Thesis MSOE has maintained an exchange program with the Lübeck University of Applied Sciences, or Fachhochschule Lübeck (FHL), for the past fifteen years beginning in the respective universities‟ electrical engineering departments. The mechanical engineering exchange program has been in operation for seven years. Approximately twelve mechanical engineering students from MSOE spend their entire third year studying in Lübeck, Germany alongside approximately twelve of their FHL exchange program counterparts. Then both MSOE and FHL students spend their fourth year in the USA. Completion of the program results in earning degrees from both universities. P ge 22121.2 For program participants, the MSOE degree requires completion of the three-term senior design sequence. In addition, the FHL degree requires the completion of a Diploma Thesis. The Diploma Thesis is expected to be a rigorous formal technical report. Students are advised that a Diploma Thesis is a “statement that justifies earning a diploma”. In that sense, students are expected to define an engineering problem to solve, systematically develop the best solution to the problem, then implement and test the solution. Senior design projects and thesis works may be done in parallel. However, the senior design projects are normally thought of as team efforts, while the thesis works must be produced by each student individually. Consequently, most program participants make efforts to use portions or all of their contributions to the team effort as work that will ultimately form their thesis. Of course, this may not be entirely possible as group goals may at times conflict with personal thesis goals. This conflict of goals is a fair representation what is often found in professional engineering circumstances and is a good experience for undergraduate students. Vehicle Dynamics and Vehicle Design As is the case with many undergraduate capstone programs, some projects, such as the SAE Mini-Baja vehicle design competition, are repeated year after year. But the incoming senior students may have little or no experience with any of the previous years‟ vehicles or with the previous students. Information is relayed in the form of technical reports, or by a faculty advisor who might also provide new goals each year for design or performance improvements. Vehicle dynamics is a complicated topic, especially for undergraduates. At Milwaukee School of Engineering, students may elect to take a course in introductory vehicle dynamics, but it is limited in scope to an introductory level. Thus students have a difficult time calculating, e.g., a turning radius at various speeds due to the many factors involved such as tire dynamics, suspension effects, and tire-to-road interface functions. Consequently, it is often the case that students may be aware that, for instance, the previous year‟s vehicle had poor handling characteristics in a certain competition event. Based on this information they proceed to make alterations to the vehicle to improve, say, the steering capabilities. This may be accomplished by shortening the wheelbase or redesigning the steering linkages. However, it is not always clear what effect their changes will have until the vehicle is built and tested. One goal of the tool in this work is to offer students a better chance at predicting the new performance levels by conducting and comparing simulations resulting from several design change schemes. Vehicle dynamics software packages are available on the market. At MSOE as is true on many campuses, students have access to one or several vehicle dynamics software programs that possess the capability to simulate vehicle dynamics under various operating conditions. These software packages allow students to vary vehicle design parameters and then simulate the dynamics ultimately facilitating a design decision. Unfortunately from a pedagogical standpoint, much of the software is a „black box‟ and students gain only limited experience in the underlying equations of motion necessary to effect simulations. Also, the software usually has good graphics capabilities and students tend to spend a great deal of time producing interesting graphical presentations, but at the expense of developing the equations of motion. P ge 22121.3 Now on the other hand, given the time constraints placed on undergraduates in their final year coupled with the task of actually building a vehicle, it may be a bit unrealistic to expect them to also develop multi-degree-of-freedom equations and write a numerical solver routine that accounts for the linear and nonlinear components of a vehicle. Consequently, analyses completed by students are usually limited to single-degree-of-freedom analyses such as the bounce and jounce of a quarter-car model that remains in contact with the ground. It is not the intention to suggest that „black box‟ simulations are necessarily inappropriate tools for learning. The purpose of this paper is to show an alternative approach used at MSOE that is meant to strike a balance between working from basic principles and using existing modeling software. Student Projects As mentioned earlier in this paper, MSOE and FHL students participating in the exchange program must write a Diploma Thesis to earn the FHL degree. Two of these students chose to write theses on vehicle dynamics and to also develop MATLAB® and Simulink ® based solvers to simulate vehicle dynamics. Part of the motivation for the development of these two theses was to provide an early design tool for future vehicle design teams. The solvers may be thought of as more like „gray boxes‟ in the sense that students need to read and understand the code as written, including examining the equations of motion and their multi-degree of freedom couplings. In addition, nonlinear functions such as tire lateral forces may be altered within the solver routines to make design decisions for vehicle components. Much of the detail provided in this work is the result of those two theses. [1, 2] Dynamics Modeling The modeling in the design tool is quite comprehensive and only a few of the modeling and simulation methods and results are provided in this paper. The modeling and solvers were designed to simulate the behavior of a vehicle under various inputs by both the road and the driver. Using these simulations, the influence of different design parameters on the vehicle behavior may be evaluated. The vehicle is modeled as a 14-DOF system consisting of three translational movements of the vehicle in its three local axes and the three rotations around these axes. Additionally, each wheel is able to move in the vertical direction and can rotate around its axis. Forces and model parameters, such as time-varying tire loads are also calculated and simulated. Aerodynamic forces are not taken into account in this design tool. One reason for this is that student competition vehicles‟ speeds are limited and the aerodynamic forces are assumed to be small [3]. Additionally, the aerodynamic forces vary greatly for possible shapes of the vehicle [3]. Of course, it is conceivable to add aerodynamics to the models, a fact that may influence future Diploma Thesis works! Page 22121.4 Students designing a specific vehicle will be concerned with many aspects of vehicle dynamics and performance goals. Handling is one significant aspect to consider. Handling performance is related the turning radius of the vehicle. Additionally, the brake-loose behavior of the tires is a parameter of interest. In this des