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## Subject: VEHICLE CHASSIS DESIGN (A.A. 2024/2025)

### master degree course in AUTOMOTIVE ENGINEERING

Course year 2 9 Unit Progettazione del Telaio Mechanical Engineering (lesson) TAF: Compulsory subjects, characteristic of the class SSD: ING-IND/14 CFU: 9 Teachers: Sara MANTOVANI written final vote Italiano

### Overview

The course aims at giving an introductory overview of an automotive chassis design considering the type approvals and the virtual delivery targets. In addition, the course provides the fundamentals of analytical structural calculations by means of an algebraic manipulator and of numerical simulations by finite element models.

The course requires a good knowledge of solid and applied mechanics, of the beam theory and of the machine design. A good comprehension of the dimensioning procedures of classical machine components is required.

### Course contents

Basics of the theory of spacial beams.
and application of Castigliano's theorem for solving determinerà and redundant problems.
Thin-section beams bore to torsion: warping investigation and Vlasov effect.
The Maxima algebraic manipulator and its applications to structural calculus:
- evaluation of the deformation and stress states in simplified beam structures;
- definition and implementation of the Gaussian quadrature method.
(2 CFU)

History and nomenclature of the main car chassis architectures.
Virtual delivery for linear missions: global and local stiffnesses
Virtual delivery for non-linear missions: type approval criteria and customer rating
Basics of calculation of joints adopted in an automotive chassis: welding, glued joints and threaded connections. Introduction of kinematic models for the imposition of constraint relations and load distribution, e.g. servo link, RBE2, RBE3.
(2 CFU)

Thin plate theory.
Composite materials: theory, first dimensioning formulas, numerical modelling and experimental tests for automotive components for weight containment. Analisys of the main manufacturing processes.
Finite element method applied to the structural analysis of thin-walled components.
Extension of plate theory to lamination theory for composite materials.
(1.5 CFU)

Introduction to structural calculation using finite elements: 2-node, 3-node triangular, 4-node isoparametric and hexahedral elements.
Determination of shape functions and of the stiffness matrix for the aforementioned finite elements. Determination of strain and stress field for the above-mentioned elements.
Assembly and constraint of the global stiffness matrix of a discretized system.
Peculiar phenomena of modelling: mesh convergence, singularity ratio, shear locking and hourglass.
(2 CFU)

Dynamic analysis of structures: mass matrix definition, modal analysis and frequency response.
Theoretical outline of the buckling phenomenon.
Implementation of a finite element model of a formula SAE monocoque for the purposes of the virtual delivery based on global stiffnesses, modal analysis and frequency response.
Design parameters, dimensioning and numerical verification of a front crash absorber adopted in a formula SAE vehicle.
(1.5 CFU)

The splitting of the hours and credits among the different topics is indicative and may be subject to modest variations.

### Teaching methods

The adopted teaching methods include: - classroom lessons; - practical experimentations, that students will perform in pairs at the DIEF lab. The course will be delivered in Italian. Students are warmly encouraged to attend the class, although the attendance is not mandatory.

### Assessment methods

The exam consists of a written test and an optional oral exam. The written test is subdivided in two parts: 1) practical computer test focused on the solution of numerical methods problems (duration: 60 minutes), during which the student is asked to: a) complete two loadcases applied to a finite element model (MSC.Marc / Mentat 2021 or earlier versions), indicating some results expressly requested and commenting on the modelling choices used; b) compile a sheet of symbolic algebra (maxima CAS) for the solution of structural and numerical problems existing during the lessons, indicating some required results, and commenting on the calculation choices undertaken. 2) The second part of the written test will verify the knowledge of theoretical aspects and/or the attitude to solve small exercises of simple resolution presented during the course. To do so, three questions have been submitted to the student (duration: 60 minutes) The final grade of the written exam will span the range from the insufficiency to the full 30/30 mark. The commission reserves the right to evaluate the test as insufficient in the presence of errors, even isolated ones, which are considered particularly serious. Oral exam (optional): those who have passed the written test with a positive result (≥18) will be able to access the oral exam. At the oral test, the written grade will be totally questioned on the extent here, the outcome may be improved, remain unchanged or may take on a negative connotation. Three questions of increasing difficulty will be required aimed at ascertaining the knowledge gained on all the numerical and theoretical topics covered in the course. (Approximate duration 2 hours) The teacher evaluates the candidate’s operational capabilities with respect to the proposed tasks, his knowledge of the modelling and solution techniques employed, and finally his to discuss the topics and the contents of the course. The final grade will reflect any preparation gaps that emerged from the interview, or lack thereof. The tests could be carried out face to face or remotely depending on the evolution of the COVID19 situation. The tests will take place under the supervision of the teacher and his collaborators. The consultation of any type of material is not allowed for both the written and the oral tests.

### Learning outcomes

The Expected results using the Dublin descriptors
(1) Knowledge and understanding
Know and understand the main structural simulation methodologies applied to automotive chassis, their strengths, the limits and, approximations connected to them.

(2) Ability to apply knowledge and understanding
Ability to apply structural simulation methodologies thanks to the knowledge and understanding of the problem itself, of the nomenclature, of the simplifying strategies to be adopted and of how to setup the numerical and / or analytical structural analysis in the most appropriate way for a good number of specific loadcases.

(3) Autonomy of judgment
Development of a high level of judgment on the results obtained, thanks to the constant and in-depth critical analysis of the numerical results, based on the comparison with analytical models and on the correct physical-mechanical interpretation of the problem.

(4) Learning skills
The course provides the basis for further study on topics of analytical mechanical design and assisted by the computer for the virtual resolution of car chassis, as well as to be able to follow in the future, with a good degree of autonomy, the evolution of the methodologies object of this course.

In concomitanza dell’inizio di ogni lezione, sul portale Microsoft Teams relativo all’insegnamento in oggetto saranno rese disponibili (nel rispetto dei diritti d’autore):
i. le slide in formato pdf utilizzate per le lezioni frontali e le esercitazioni di laboratorio
ii. raccolte di esercizi svolti da impiegarsi per l’approfondimento e lo studio

- Megson, T.H.G., Aircraft structures for engineering students, 2012
- Lorenzo Morello, Lorenzo Rosti Rossini, Giuseppe Pia, Andrea Tonoli, The Automotive Body, Volume I–Components, 2011, Springer Ed.
- Giancarlo Genta, Lorenzo Morello, The Automotive Chassis: Volume 1: Components Design, 2008
- Giancarlo Genta, Lorenzo Morello, The Automotive Chassis: Volume 2: System Design, 2016
- Michael Costin, David Phipps, Racing and sports car chassis design, 1967
- Luigi Piano, La sicurezza passiva degli autoveicoli. Criteri di Progettazione e sperimentazione, 2009 Hoepli Editore.
- Vince Adams, Abram Askenazi, Building better Products with Finite Element Analysis. 1999, OnWord Press.
- Cook, R. D. (2007). Concepts and applications of finite element analysis. John wiley & sons.
- Irons, B., & Shrive, N. (1983). Finite element primer. JOHN WILEY & SONS, INC., 605 THIRD AVE., NEW YORK, NY 10158, USA, 1983, 150.