Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2019/2020
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Docente Cheli Federico
Cfu 10.00 Tipo insegnamento Monodisciplinare

Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento

Obiettivi dell'insegnamento

This course provides the basic knowledge relating to the dynamic behavior of vehicles and their passive/active control, as well as the problems

associated with them (performances, comfort, handling, safety, etc.).


This course examines the analytical and numerical tools needed to model a road – rail  vehicle  in order to analyze the dynamic behavior

in different driving conditions.


Some road and rail vehicle models of different complexity  are described, with varying levels of the complexity, taking into account the presence of passive -  active control and based also on current regulations for approval.


Some of the topics of the course will be presented thanks to experimental test benches and visit to laboratories.



Risultati di apprendimento attesi

Dd 1; knowledge and understanding


After passing the exam the student:


• knows the methods and principles for modeling a real vehicle with a mathematical model that uses a concentrated, distributed, multibody approach

• understands and knows how to operate a ground vehicle on a large scale and linearizing the equations of motion

• knows and understands the stability and safety conditions of a vehicle

• knows and understands how the individual parts of the vehicle work: chassis, suspensions, tires, etc. and their effect on the dynamics of the vehicle itself.


Dd 2; ability to apply knowledge and understanding


After passing the exam the student

• is able to perform simple modeling with "N" degrees of freedom of the vehicle for comfort, performance and handling analysis

• is able to write a Matlab® or Simulink® code to simulate the vehicle's dynamic behavior (referred to in the previous point)

• is able to use some commercial multibody codes (ADAMS®, VI GRADE®, CAR MAKER®) to simulate the behavior of the vehicle

exploiting the capacities relative to the previous points,

• is able to calculate the motion of the vehicle and the forces transmitted to the environment

• is able to design the vehicle from the point of view of its dynamic behaviour

• is able to organize and communicate the results of laboratory tests and simulations activities.


Dd 3,4,5 (Making judments, Communications, Learning skills)

After passing the exam the student:

• is able to carry out optimisations of vehicle dynamic behaviour taking into account the characteristics and performance of the individual subsystems looking the vehicle as a complex system

• is able to communicate the results of the modeling and the analysis in a technical report

• gains the capability to work in team for a project.

Argomenti trattati

General notions. 

The dynamic behavior on the straight line and cornering of the vehicle. Concepts of "performance", "handling", “stability”, "ride comfort"

and “safety”.


Analysis of vehicle dynamics with Multi-Body techniques. 

Definition of space kinematics. Equations of motion in matrix form for nonlinear systems: the minimal set and the Lagrange multipliers methods.

Steady state and transient conditions, linearization; perturbed motion analysis.


The characteristics of the wheel-runway.

Tire-road: slips and slip angles, references to the main theories: "stretched string model", "brush model", "Magic Formula".

Wheel-rail: creepages, references to the main contact theories.


Vehicle dynamics and control

  1. Longitudinal dynamics, acceleration and braking motion, aerodynamic forces (notes).
  2. Ride comfort. The irregularity of the runway: random vibrations, track and road irregularity. Human response to vibration, and effects on health. Vehicle models for vertical dynamics, comfort indices (regulations), chassis deformability effects.
  3. Analysis of lateral dynamics. The equations of motion in a straight line and in cornering conditions with simplified models and complex 3D model: definition of steady state and transient conditions; linearization and stability analysis; sensitivity analysis. Behavior simulation on the straight line and cornering of the complete vehicle.


Modeling of road vehicles

Dynamics of the car on the straight line and cornering with simplified and complex models; steady state and transient definition; linearization and stability analysis; vehicle over and under steering concepts, handling diagrams. Simulation of the behavior on the straight and cornering of the complete vehicle (MB models). Safety and regulations.


Modeling of railway vehicles

The dynamics of the wheelset in the straight line. Safety and stability analysis.


Active control in vehicles.

Application examples. Controlled suspension, ABS, VDC, 4WS, 4WD, ADAS systems.


Knowledge in the field of dynamics and stability of mechanical systems is needed with particular reference to linear and non-linear differential calculus. Basic information on computer science (use of Matlab and commercial programs) is required.

Knowledge of the algebra of matrices is necessary.

Modalità di valutazione

Organization of the course and verification method


The course is divided into a series of lectures and numerical - informatic applications, related to the topics covered during the lessons aimed at consolidating the knowledge and methods learned in class.

Students, divided into different teams, will have to develop simulation programs (computer labs) on the various issues faced during the course.

Students must write for each exercise a short draft in free form that shows the model used and the obtained results. 

Seminars of company experts will be organized. 

There are some experimental lab tests on a real instrumented vehicle (mobile lab) an ABS / VDC indoor test rig, autonomous vehicle, formula student and moto student applications. Some experimental results are discussed and compared with those obtained by the simulation results obtained by the students. 

The exam consists of a final mandatory oral test on the different topics discussed in the course in a discursive form and developing equations related to the different problems faced and the different vehicles analyzed. 

Depending on specific organizational needs, it will be asked to answer questions in writing. The attendance of the numerical practices and of the experimental laboratories are compulsory: students must submit the collection of the simulations at the time of the final test (written reports) and the results will be discussed and examined.

Exam purpose is to assess:

• the knowledge and understanding of the students about the modelling approaches and tools for the dynamical simulations of a ground vehicles

• the capability of selecting, organising and communicating the resutls of the performed computer and physical laboratory activeties, in a clear, accurate and concise manner,

• the capability of judgment concerning design choices also from the capability of team working and ability to gain knowledge from industrial experts experience shared during the seminars

Risorsa bibliografica obbligatoriaF.Cheli, G.Diana, Advanced Dynamics of Mechanical Systems, Editore: Springer, Anno edizione: 2015
Risorsa bibliografica obbligatoriaLesson/esercise notes BEEP on line
Risorsa bibliografica facoltativaV.K. Garg, R.V. Dukkipati, Dynamics of Railway Vehicle System, Editore: Academic Press
Risorsa bibliografica facoltativaJ.Y.Wong, Theory of Ground Vehicle, Editore: Wiley & Sons
Risorsa bibliografica facoltativaM.Guggiani, THe Science of Vehicle Dynamics, Editore: Springer
Risorsa bibliografica facoltativaHans Pacejka, Tire and Vehicle Dynamics, Editore: Butterworth-Heinmann

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Informatico
Laboratorio Sperimentale
Laboratorio Di Progetto
Totale 111:09 138:51

Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese
schedaincarico v. 1.6.5 / 1.6.5
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