Session: 07-08-03: Multibody Dynamic Systems and Applications III

Paper Number: 147175

147175 - A Symbolic-Numerical Approach to Kinematics and Compliance Analysis of Suspension Mechanisms 

The kinematics and compliance (K&C) characteristics of suspension mechanisms influence the performance and handling of a vehicle and are therefore crucial for the design process. To predict such characteristics, the geometry and flexibility of suspension components must be represented in a multibody dynamic model. This is typically addressed by generating K&C maps as look-up tables. These maps are computed offline and must be generated again whenever a single suspension parameter is changed, which makes both run-time changes in the simulation and design optimization tasks inefficient.

To overcome this limitation, the authors use computer algebra systems (CAS) to analytically formulate suspension K&C characteristics. CAS ease the process of developing and manipulating expressions of complex systems at a level that can not be reached by hand. By leveraging symbolic simplification, CAS can significantly reduce the computational cost of the numerical solution of the equations. Among these, MAPLE^® is unquestionably one of the most successful kernels. However, it does not provide any specific package to address the analysis of lean elastic structures. For this reason, the authors developed the TRUSSME library, which is used to symbolically describe and solve compliant structures either in the MAPLE^® or MATLAB^®/SIMULINK^® environments. TRUSSME is used for iso- and hyper-static structure deformation analysis through the direct stiffness method (DSM). This method is based on the assemblage of the stiffness matrices of the individual elements into a global stiffness matrix, which is then used to solve the system of equations that relates the displacements and rotations of the elements’ nodes to the internal and external forces and moments. Boundary conditions are enforced by appropriately modifying the global stiffness matrix as well as the force and displacement vectors. As a consequence, the DSM is a general method that can be used to analyze a wide variety of structural elements, including trusses, beams, frames, and plates, which can be combined into structures via rigid or compliant supports and joints. Fully symbolic or mixed symbolic-numeric solutions can be obtained, depending on the symbolic complexity of the problem. By taking advantage of symbolic computation, the library is used to generate a generic code for suspensions with the same topology. This provides a high level of generalization and potentially include chassis deformation and relative displacement of suspension hard points’ contributions in the simulation.

A racing car’s double wishbone suspension mechanism is considered as a demonstration. The K&C characteristics are analyzed and validated through the commercial finite element analysis (FEA) software ANSYS^®. The results show that the proposed technique is able to accurately predict the K&C characteristics of the suspension mechanism. Specifically, the estimated static deformations are in agreement with the FEA. Moreover, the dynamic analysis demonstrates the capability of the symbolic code to predict the suspension behavior up to the sixth mode of vibration while reducing the computational cost and enabling real-time simulation. The results give us a better understanding of the modeling techniques, which further advances the knowledge on the suspension mechanisms’ modeling and validity range of both the state-of-the-art approach and the proposed methodology. In essence, the methodology presented here provides a framework for generating symbolic code, facilitating efficient and accurate simulation not only of suspension mechanisms but also of any mechanisms where compliance plays a significant role.

Presenting Author: Matteo Larcher University of Trento

Presenting Author Biography: Matteo Larcher received a master’s degree in mechatronics engineering at the University of Trento, where he is currently working on vehicle dynamic models for real-time applications as part of his PhD research activity. His research interests are multi-body modeling of mechanical systems and hardware-in-the-loop simulations.

Authors:

Matteo Larcher University of Trento
Davide Stocco University of Trento
Matteo Tomasi University of Trento
Francesco Biral University of Trento