Mechanical Engineering

Course Program – Vehicle System Dynamics Part I – Fundamentals of Vehicle Dynamics Introduction to ground vehicle dynamics. Kinematics of the rigid body and fundamental formulations. Dynamic equilibrium equations of the rigid body and Lagrangian formulation. Simplified vehicle models: from the full Newton–Euler system to the bicycle model. Degrees of freedom of the vehicle system and conditions for dynamic equilibrium. Concept of screw axis and its application to vehicle systems. Linearization of the equations of motion and modal analysis. Modal and forced response of the suspension system and associated screw axes. Dynamic definition of roll and pitch screw axes. Part II – Tire Theory Introduction to tire dynamics and future application scenarios. Modeling of the deformable tire: longitudinal slip in straight motion; pure and combined lateral slip; rolling resistance and elastic deformation; self-aligning moment and its influence on vehicle stability. Definition and analysis of the grip factor and the adhesion/sliding regions. Wheel alignment angles (camber, toe-in, toe-out) and their effect on vehicle dynamics. Synthesis of input–output relationships for tire models. Part III – Decoupled Motion Analysis of the Vehicle Sub-model decoupling and separate motion analysis. Planar motion (yaw–sway): equations of motion, dynamic response, and stability. Steady-state analysis: understeer and oversteer behavior. Suspension system: kinematic and dynamic principles. Roll motion: definition of the roll axis and response to lateral excitations. Pitch–heave motion: dynamic modeling, load transfer, and anti-dive characteristics. Longitudinal (headway) motion: traction models, aerodynamic resistances, and tire–road adhesion. Complete assembly of the vehicle’s equations of motion. Part IV – Vehicle Control Elements General architecture of vehicle control systems. Review of control theory and variational formulations. Euler–Lagrange equations applied to dynamic control. Introduction to the LQR (Linear Quadratic Regulator) approach for optimal control. Comparison between optimal control and heuristic tuning techniques. Application examples: vehicle stabilization and cruise control. Part V – Virtual Laboratory and Software Tools Introduction to MATLAB/Simulink/Simscape for vehicle dynamics modeling. Development of numerical models of the vehicle and tire subsystems. Simulation of dynamic scenarios: acceleration, braking, stability, and anti-dive effects. Analysis and validation of simulation results. Final workshop: Modeling Longitudinal Vehicle Dynamics with Simscape. Complementary Activities Practical workshop on modeling and simulation using MATLAB/Simulink/Simscape. Optional educational visit to the Vallelunga Racetrack, focused on vehicle control systems and telemetry applications.

To successfully attend the course, students are expected to have: a solid background in rational mechanics and rigid body dynamics; knowledge of mechanical vibrations and multi-degree-of-freedom dynamic models; fundamental skills in mathematics and linear algebra (differential calculus, linear systems, ordinary differential equations); basic understanding of automatic control (dynamic systems theory, stability, state-space models); preliminary experience with MATLAB/Simulink programming. These prerequisites are usually fulfilled within a Bachelor’s degree in Mechanical, Aerospace, or Automation Engineering (or equivalent).

Testi di riferimento • Nicola Roveri: dispense del corso • Antonio Carcaterra, “Notes on Vehicle System Dynamics”, 2018 • Massimo Guiggiani, "Dinamica del Veicolo", Città Studi, 2007 • Giancarlo Genta, "Meccanica dell'Autoveicolo", Levrotto & Bella, 2000 • Hans B. Pacejka, “Tyre and Vehicle Dynamics”, Butterworth-Heinemann, 2002 • Reza N. Jazar, Vehicle Dynamics: Theory and Applications, Springer • M. Abe, Vehicle Handling Dynamics, Theory and Application, Butterworth-Heinemann, 2011.

Frontal teaching, course attendance is recommended and is in class.

The assessment is divided into two complementary parts: Written test (1–2 hours) Includes 2–4 questions/exercises on course topics. Typical questions may cover planar vehicle dynamics, tire theory (brush model, longitudinal/lateral slip, grip factor), steering kinematics and dynamics, pitch/roll dynamics, cornering stability, or suspension geometry design. The use of a computer is allowed only for numerical computations in MATLAB, with prior authorization and under strict supervision. Simulation report and oral presentation Development of a virtual experiment in MATLAB/Simulink/Simscape, documented in a written report (minimum 5 pages) and accompanied by the developed code. Critical analysis of results and discussion of design implications. Delivery of a 15-minute video presentation, where the student illustrates the results in a format similar to a thesis defense (voice-over slides or recorded discussion). Final grading The final grade combines both parts: the written test evaluates theoretical mastery and problem-solving skills; the report and presentation assess practical competences, critical thinking, and communication skills.

Testi di riferimento • Nicola Roveri: dispense del corso • Antonio Carcaterra, “Notes on Vehicle System Dynamics”, 2018 • Massimo Guiggiani, "Dinamica del Veicolo", Città Studi, 2007 • Giancarlo Genta, "Meccanica dell'Autoveicolo", Levrotto & Bella, 2000 • Hans B. Pacejka, “Tyre and Vehicle Dynamics”, Butterworth-Heinemann, 2002 • Reza N. Jazar, Vehicle Dynamics: Theory and Applications, Springer • M. Abe, Vehicle Handling Dynamics, Theory and Application, Butterworth-Heinemann, 2011.

The course is mainly delivered through frontal lectures, with explanations provided by the professor supported by multimedia presentations and blackboard derivations. Lectures combine theoretical and application-oriented content, complemented by numerical examples and references to real-world cases. In addition, the course includes: guided exercises using MATLAB/Simulink/Simscape, aimed at introducing students to vehicle dynamics modeling and simulation; a dedicated hands-on workshop on software tools; possible seminars or technical visits (e.g., Vallelunga racetrack) as complementary learning activities. Attendance is not compulsory but recommended in order to facilitate learning and effective understanding of the course contents.

Course Program – Vehicle System Dynamics Part I – Fundamentals of Vehicle Dynamics Introduction to ground vehicle dynamics. Kinematics of the rigid body and fundamental formulations. Dynamic equilibrium equations of the rigid body and Lagrangian formulation. Simplified vehicle models: from the full Newton–Euler system to the bicycle model. Degrees of freedom of the vehicle system and conditions for dynamic equilibrium. Concept of screw axis and its application to vehicle systems. Linearization of the equations of motion and modal analysis. Modal and forced response of the suspension system and associated screw axes. Dynamic definition of roll and pitch screw axes. Part II – Tire Theory Introduction to tire dynamics and future application scenarios. Modeling of the deformable tire: longitudinal slip in straight motion; pure and combined lateral slip; rolling resistance and elastic deformation; self-aligning moment and its influence on vehicle stability. Definition and analysis of the grip factor and the adhesion/sliding regions. Wheel alignment angles (camber, toe-in, toe-out) and their effect on vehicle dynamics. Synthesis of input–output relationships for tire models. Part III – Decoupled Motion Analysis of the Vehicle Sub-model decoupling and separate motion analysis. Planar motion (yaw–sway): equations of motion, dynamic response, and stability. Steady-state analysis: understeer and oversteer behavior. Suspension system: kinematic and dynamic principles. Roll motion: definition of the roll axis and response to lateral excitations. Pitch–heave motion: dynamic modeling, load transfer, and anti-dive characteristics. Longitudinal (headway) motion: traction models, aerodynamic resistances, and tire–road adhesion. Complete assembly of the vehicle’s equations of motion. Part IV – Vehicle Control Elements General architecture of vehicle control systems. Review of control theory and variational formulations. Euler–Lagrange equations applied to dynamic control. Introduction to the LQR (Linear Quadratic Regulator) approach for optimal control. Comparison between optimal control and heuristic tuning techniques. Application examples: vehicle stabilization and cruise control. Part V – Virtual Laboratory and Software Tools Introduction to MATLAB/Simulink/Simscape for vehicle dynamics modeling. Development of numerical models of the vehicle and tire subsystems. Simulation of dynamic scenarios: acceleration, braking, stability, and anti-dive effects. Analysis and validation of simulation results. Final workshop: Modeling Longitudinal Vehicle Dynamics with Simscape. Complementary Activities Practical workshop on modeling and simulation using MATLAB/Simulink/Simscape. Optional educational visit to the Vallelunga Racetrack, focused on vehicle control systems and telemetry applications.

To successfully attend the course, students are expected to have: a solid background in rational mechanics and rigid body dynamics; knowledge of mechanical vibrations and multi-degree-of-freedom dynamic models; fundamental skills in mathematics and linear algebra (differential calculus, linear systems, ordinary differential equations); basic understanding of automatic control (dynamic systems theory, stability, state-space models); preliminary experience with MATLAB/Simulink programming. These prerequisites are usually fulfilled within a Bachelor’s degree in Mechanical, Aerospace, or Automation Engineering (or equivalent).

Testi di riferimento • Nicola Roveri: dispense del corso • Antonio Carcaterra, “Notes on Vehicle System Dynamics”, 2018 • Massimo Guiggiani, "Dinamica del Veicolo", Città Studi, 2007 • Giancarlo Genta, "Meccanica dell'Autoveicolo", Levrotto & Bella, 2000 • Hans B. Pacejka, “Tyre and Vehicle Dynamics”, Butterworth-Heinemann, 2002 • Reza N. Jazar, Vehicle Dynamics: Theory and Applications, Springer • M. Abe, Vehicle Handling Dynamics, Theory and Application, Butterworth-Heinemann, 2011.

Frontal teaching, course attendance is recommended and is in class.

The assessment is divided into two complementary parts: Written test (1–2 hours) Includes 2–4 questions/exercises on course topics. Typical questions may cover planar vehicle dynamics, tire theory (brush model, longitudinal/lateral slip, grip factor), steering kinematics and dynamics, pitch/roll dynamics, cornering stability, or suspension geometry design. The use of a computer is allowed only for numerical computations in MATLAB, with prior authorization and under strict supervision. Simulation report and oral presentation Development of a virtual experiment in MATLAB/Simulink/Simscape, documented in a written report (minimum 5 pages) and accompanied by the developed code. Critical analysis of results and discussion of design implications. Delivery of a 15-minute video presentation, where the student illustrates the results in a format similar to a thesis defense (voice-over slides or recorded discussion). Final grading The final grade combines both parts: the written test evaluates theoretical mastery and problem-solving skills; the report and presentation assess practical competences, critical thinking, and communication skills.

Testi di riferimento • Nicola Roveri: dispense del corso • Antonio Carcaterra, “Notes on Vehicle System Dynamics”, 2018 • Massimo Guiggiani, "Dinamica del Veicolo", Città Studi, 2007 • Giancarlo Genta, "Meccanica dell'Autoveicolo", Levrotto & Bella, 2000 • Hans B. Pacejka, “Tyre and Vehicle Dynamics”, Butterworth-Heinemann, 2002 • Reza N. Jazar, Vehicle Dynamics: Theory and Applications, Springer • M. Abe, Vehicle Handling Dynamics, Theory and Application, Butterworth-Heinemann, 2011.

The course is mainly delivered through frontal lectures, with explanations provided by the professor supported by multimedia presentations and blackboard derivations. Lectures combine theoretical and application-oriented content, complemented by numerical examples and references to real-world cases. In addition, the course includes: guided exercises using MATLAB/Simulink/Simscape, aimed at introducing students to vehicle dynamics modeling and simulation; a dedicated hands-on workshop on software tools; possible seminars or technical visits (e.g., Vallelunga racetrack) as complementary learning activities. Attendance is not compulsory but recommended in order to facilitate learning and effective understanding of the course contents.