University of Toronto
The MIE301: Kinematics and Dynamics of Machines course at the University of Toronto teaches third year Mechanical Engineering students the principles of kinematics and dynamics as they apply to machine design problems. An optional project in the fall 2007 semester was offered in conjunction with the PACE program (Partners for the Advancement of Collaborative Engineering Education), in which U of T students were teamed with groups of students from the University of British Columbia, Canada. The project requirements were set by General Motors of Canada, who are primary sponsors of the PACE initiative. The goal of the project was to collaboratively design a front suspension system for a cross-over class SUV in order to sustain a pothole impact at 40 km/h.
The University of Toronto team was responsible for modeling the dynamics of the suspension system, and determining the optimum damping characteristics of the strut to minimize the loads transmitted to the vehicle body. As an added constraint to the problem, the force-deflection relationships for the strut and tire were prescribed by tabulated, non-linear curves.
In order to analyze the problem, a variety of methods were first considered. As the suspension system could be modeled as a two degree of freedom system, the first approach was to attempt a derivation of the equations of motion that described the system through the use of Lagrange's equations. The non-linearity of the strut spring and the tire made this option unattractive to the group, as these made it impossible to reach a closed form solution to the problem. Another challenge posed in modeling the system in this way was the intermittent contact between the tire and the ground. As a result, it was decided that a more suitable approach would be to model the system in ADAMS/View.
The group constructed a "test rig" model specifically for the suspension problem. Through the use of ADAMS/View's powerful Function Builder, the group was able to develop a model that incorporated the non-linearity of the strut and tire stiffness, as well as the intermittent contact between the tire and ground.
ADAMS/View's design study and optimization tools enabled the group to perform a series of experiments with the ultimate goal of minimizing the forces acting through the strut. One design change suggested by the UBC side of the team was to incorporate differing "bump" and "rebound" damping rates for the strut. The regular spring/damper entity in ADAMS, however, was not capable of taking into account differing damping rates on retraction or extension. With the help of the ADAMS help documentation and interrogation of the ADM files that ADAMS generates when performing simulations, the group was able to define a SFORCE entity in ADAMS/View that mimicked this "bi-directional damping" effect by employing the MAX function in the ADAMS/View function builder. The ability to model this non-linear damping force demonstrated to the group the true power of ADAMS and its potential for future design projects.
Submitted by: Mark Morreale, 3rd-year student at UT
(Group partner: Ricardo Faerron)