William Bombardier    (MASc, BASc)

Motion Research Group
Systems Design Engineering

Office: E3-3168
Email: wbombard@engmail.uwaterloo.ca

Supervisor:
Prof. John McPhee

Thesis Title:

Symbolic Modelling and Simulation of Wheeled Vehicle Systems on Three-Dimensional Roads

Thesis Abstract:

In recent years, there has been a push by automotive manufacturers to improve the efficiency of the vehicle development process. This can be accomplished by creating a computationally efficient vehicle model that has the capability of predicting the vehicle behavior in many different situations at a fast pace. This thesis presents a procedure to automatically generate the simulation code of vehicle systems rolling over three-dimensional (3-D) roads given a description of the model as input.

The governing equations describing the vehicle can be formulated using either a numerical or symbolical formulation approach. A numerical approach will re-construct numerical matrices that describe the system at each time step. Whereas a symbolic approach will generate the governing equations that describe the system for all time. The latter method offers many advantages to obtaining the equations. They only have to be formulated once and can be simplified using symbolic simplification techniques, thus making the simulations more computationally efficient.

The road model is automatically generated in the formulation stage based on the single elevation function (3-D mathematical function) that is used to represent the road. Symbolic algorithms are adopted to construct and optimize the non-linear equations that are required to determine the contact point. A Newton-Raphson iterative scheme is constructed around the optimized non-linear equations, so that they can be solved at each time step. The road is represented in tabular form when it can not be defined by a single elevation function.

A simulation code structure was developed to incorporate the tire on a 3-D road in a symbolic computer implementation of vehicle systems. It was created so that the tire forces and moments that appear in the generalized force matrix can be evaluated during simulation and not during formulation. They are evaluated systematically by performing a number of procedure calls. A road model is first used to determine the contact point between the tire and the ground. Its location is used to calculate the tire intermediate variables, such as the camber angle, that are required by a tire model to evaluate the tire forces and moments.

The structured simulation code was implemented in the DynaFlexPro software package by creating a linear graph representation of the tire and the road. DynaFlexPro was used to analyze a vehicle system on six different road profiles performing different braking and cornering maneuvers. The analyzes were repeated in MSC.ADAMS for validation purposes and good agreement was achieved between the two software packages. The results confirmed that the symbolic computing approach presented in this thesis is more computationally efficient than the purely numerical approach. Thus, the simulation code structure increases the versatility of vehicle models by permitting them to be analyzed on 3-D trajectories while remaining computationally efficient.

Resume:

Portfolio:

  • Portfolio [pdf]

Areas of Study:

  • Vehicle Dynamics
  • Tire Modeling
  • Road Modeling
  • Engine Modeling and Control
  • Emission Reduction

Interests:

  • Hockey [HABS]
  • Curling
  • Soccer
  • Football
  • Swimming
  • Canoeing
  • Automobiles
  • Traveling

Publications and Presentations:

  • W. Bombardier, J. McPhee, C. Schmitke. Symbolic formulation of multibody dynamic equations for wheeled vehicle systems on 3D Roads. SAE World Congress. Detroit, Michigan, April 13th - July 15th, 2010. [Abstract]

  • W. Bombardier, J. McPhee. Symbolic modeling of wheeled vehicles on 3D roads. Multibody Dynamics 2009. Warsaw, Poland, June 29th - July 2nd, 2009. [Extended Abstract]

  • W. Bombardier, A. Fadel, X. Ding, I. Funkenhauser, B. Zuccato, M. Bowie, T. Tao, B. Huang. 2007 baja project - suspension report. University of Windsor Capstone Design Projects. August 3rd, 2007. [Report]

  • M. Barnett, W. Bombardier, M. Bowie, M. Burford, D. Chesnik, X. Ding, C. Drummond, A. Fadel, I. Funkenhauser, H. hiebert. B. Huang, C. jankowski, J. Juba, C. Kelly, J. Krzemien, K. Kbacki, D. Langlois, S. Masse, W. O'Moore, D. Pedro, M. Smith, E. Soulliere, Y. Tao, B. Zuccatto, B. Minaker. University of Windsor SAE Baja Design Repor. 2007 Baja SAE RITt. Rochester, NY, June 7th - 10th, 2007.

  • M. Zheng, U. Asad, R. Kumar, G. T. Reader, M. C. Mulenga, W. Bombardier, M. Wang, J. Tjong, An investigation of EGR treatment on the emission and operating characteristics of modern diesel engines. 2007 SAE World Congress. Detroit, MI, April 16th - 19th, 2007. SAE Paper Number: 2007-01-1083.

  • R. Kumar, M. Zheng, G. T. Reader, M. C. Mulenga, W. Bombardier, S. Jin-Ko, M. Wang. A study on the energy and emission efficacy of multi-pulse fuel injection on low-temperature combustion. Combustion Institute / Canadian Section. Spring Technical Meeting. Waterloo, Ontario, Canada, May 14th - 17th, 2006.

  • Poster presentation, M. C. Mulenga, M. Wang, D. S-K Ting, R. Kumar, Y. Tan, W. Bombardier, R. S-J Ko. Compatibility of biodiesels with modern common-rail diesel engine. 2006 Auto21 HQP Conference. Barie, ON, May 15th - 17th, 2006.

Other Information:

Travels:

  • Thanksgiving 2009: Northern Michigan
    • Traverse City
    • Sleeping Bear Dunes National Lakeshore Park
    • Old Mission State Park

  • Summer 2009: Euro Trip
    • Germany (Hamburg, Baltic Sea, Black Forest, Heidelberg, Bamberg, and Bielefeld)
    • Netherlands (Amsterdam)
    • France (Alsace region)
    • Poland (Warsaw and Krakow)

  • Christmas 2008: California
    • Thousand Oaks
    • Santa Barbara
    • Santa Monica
    • Hollywood
    • San Diego

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