The Finite Element Method an Introduction to Kart

The Finite Element Method an Introduction to Kart Chassis Dynamics

Contents • Finite Element Method – What is it? – Formulation • Chassis Dynamics – Importance – Modeling – Data and Results – Beyond… 42 ℏ FEM and Chassis Dynamics

Who has ever heard of FEM? Who has ever used FEM?

Finite Element Method – What is it? • The Finite Element Method (FEM) is a numerical method of solving systems of partial differential equations (PDEs) • It reduces a PDE system to a system of algebraic equations that can be solved using traditional linear algebra techniques. Heat Conduction 42 ℏ Structural Mechanics E&M FEM and Chassis Dynamics

Finite Element Method - Formulation • There are several different formulations of FEM involving variational calculus and weighted residuals. • The variational formulation is based on our beloved Green’s Identity. 42 ℏ FEM and Chassis Dynamics

Finite Element Method - Formulation Partial Differential Equation Plus a set of boundary conditions Multiply by a test function v(x) and integrate over the domain Apply the Green’s Formula to derive the socalled weak formulation. 42 ℏ Require test functions to vanish on the boundary so that the boundary conditions disappear. FEM and Chassis Dynamics

Finite Element Method - Formulation Using the Lax-Milgram Theorem, principles of variational calculus, and principles of elliptical equations the problem can then be reduced to an algebraic system where xn are the displacements at the nodes. 42 ℏ FEM and Chassis Dynamics

Chassis Dynamics 42 ℏ FEM and Chassis Dynamics

Chassis Dynamics-Motivation Chassis Dynamics is a huge part of how a kart works. A greater understanding leads to better performance. 42 ℏ FEM and Chassis Dynamics

Chassis Dynamics - Modeling Used a program called Visual. FEA 42 ℏ FEM and Chassis Dynamics

Chassis Dynamics - Modeling • Simplifications – Doesn’t account for small miscellaneous pieces – Large masses centered at COM – Wheels are pinned at center – No steering geometry – No bent sections 42 ℏ FEM and Chassis Dynamics

Testing 1 2 3… • Reproduce Commonly known facts – Weight is transferred to the outside wheels in a turn – The rear track width effects handling – The drivers VCOM effects handling. • Static constant centripetal acceleration turns. (0 -1. 5 g) 42 ℏ FEM and Chassis Dynamics

42 ℏ FEM and Chassis Dynamics

42 ℏ FEM and Chassis Dynamics

42 ℏ FEM and Chassis Dynamics

42 ℏ FEM and Chassis Dynamics

42 ℏ FEM and Chassis Dynamics

Beyond… • Next Generation Models – – Improved frame geometry Steering geometry Inclusion of smaller objects Extension of larger objects • Tire Modeling and Measurements • Roll Cage Modeling Complete Functional Model 42 ℏ FEM and Chassis Dynamics

http: //physics. bgsu. edu/Quantum_Racing or on the links page of the Physics Department Website

Thank You! • A special thanks goes out to: – My advisors on this project Dr. Boughton Dr. Chou (Dept. of Mathematics and Statistics) Dr. Sun (Dept. of Mathematics and Statistics) – The Quantum Racing advisor Alex Hann – The Department of Physics and Astronomy